78034499 bp-frac-manual

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Table of Contents. 1-11-11. 1-1.... 2-1. 2-4..... 3-1... 3-10.. 3-24273-40

.... 4-1.... 4-7....5-1

5-2. 5-36.... 6.. 6-.. 6-36-306-49. 6-526-70

..

.... 7-47-19. 7-267-29.... 8-1.... 8-4. 8-14. 8-258-46

. 8-55

1.1 History of Hydraulic Fracturing .................................................................................1.2 Amoco Hydraulic Fracturing Course Outline ...........................................................1.3 Nomenclature ...........................................................................................................41.4 References ...............................................................................................................1-172.1 The Continuity Equation ...........................................................................................2.2 Model Differences and the Elasticity Equation .........................................................2.3 References ................................................................................................................. 2-83.1 Reservoir Response To Fracture Stimulation ..........................................................3.2 Steady-State Reservoir Response ...........................................................................3.3 Transient Reservoir Response ................................................................................3.4 Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material) ........... 3-3.5 Bilinear Flow - Gas Reservoirs .................................................................................3.6 References ..............................................................................................................3-494.1 Elastic Properties of the Formation ...........................................................................4.2 Fracture Toughness ................................................................................................4.3 Hardness .................................................................................................................4-104.4 References ...............................................................................................................4-115.1 Fracture Height/Fracture Height Growth - 3-D Modeling/Design .............................5.2 Fluid Loss .................................................................................................................. 5-205.3 Fluid Viscosity .........................................................................................................75.4 Treatment Pumping ..................................................................................................5.5 References ...............................................................................................................5-436.1 Fluid Selection ........................................................................................................-16.2 Fluid Classification ...................................................................................................16.3 Fluid Selection Criteria ............................................................................................6.4 Description of Fracturing-Fluid Types .....................................................................6.5 Rheological Testing Of Fracturing Fluids ................................................................6.6 Service Company Trade Names ..............................................................................6.7 Fluid Scheduling ......................................................................................................6.8 References ..............................................................................................................6-807.1 Introduction ................................................................................................................. 7-17.2 Proppant Properties .................................................................................................7.3 Conductivity/Permeability .......................................................................................7.4 Proppant Transport ...................................................................................................7.5 Non-Darcy Flow ........................................................................................................7.6 References ...............................................................................................................7-328.1 Introduction To Fracturing Pressure Analysis .........................................................8.2 Fracture Closure Stress ...........................................................................................8.3 Bottomhole Treating Pressure .................................................................................8.4 Pressure Decline Analysis .......................................................................................8.5 Pressure History Matching .......................................................................................8.6 Proppant/Fluid Schedule From Pressure Decline ....................................................

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Table of Contents

..8-

..

...9-3..9-20....0-29

.

.11-2.11-4.11-6...11-811-10.11-1311-14.. P-1.. P-2..1-1

..1-3..1-3..1-4...1-5...1-6...1-81-11..

...2-1

...2-4

....3-1

...3-1

...3-2

...3-3

8.7 Nomenclature ...........................................................................................................688.8 References ................................................................................................................8-709.1 Introduction ..................................................................................................................9-19.2 General Economic Criteria ........................................................................................9.3 Elements Of Fracturing Treatment Costs .................................................................9.4 References. ...............................................................................................................9-2110.1 Fracturing Tests ........................................................................................................10-310.2 Introduction To TerraFrac ........................................................................................110.3 References ...............................................................................................................10-4911.1 Introduction ................................................................................................................11-111.2 Stimulation Design and Planning ..............................................................................11.3 Water Quality Control ...............................................................................................11.4 Proppant Quality Control ..........................................................................................11.5 Fracture Treatment Setup ........................................................................................11.6 Fracture Treatment Execution ..................................................................................11.7 Post-Frac Cleanup ...................................................................................................11.8 Frac Treatment Reporting Requirements .................................................................FRAC School Problem No. 1 .............................................................................................FRAC School Problem No. 1 .............................................................................................9.9 History of Hydraulic Fracturing..................................................................................

Chapter 1 IntroductionDevelopments in Hydraulic Fracturing .....................................................................

Fracture Orientation: ............................................................................................Fracturing Fluid: ...................................................................................................Proppants: .............................................................................................................Fracture Treatment: ..............................................................................................

Early Fracture Design ................................................................................................9.10 Amoco Hydraulic Fracturing Course Outline.............................................................9.11 Nomenclature ............................................................................................................1-149.12 References...................................................................................................................1-179.13 The Continuity Equation............................................................................................

Chapter 2 Fracturing Models9.14 Model Differences and the Elasticity Equation .........................................................9.15 References.....................................................................................................................2-89.16 Reservoir Response To Fracture Stimulation ...........................................................

Fracture Length .........................................................................................................

Chapter 3 Reservoir AnalysisReservoir Permeability ..............................................................................................Fracture Flow Capacity .............................................................................................

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.. 3-8

... 3-1010-143-153-22.. 3-24-27-273-27-27-273-273-283-28. 3-293-30. 3-30. 3-31-33

. 3-33. 3-33-353-353-36-37

3-373-40

3-40. 3-40. 3-403-413-41. 3-42-43

. 3-43. 3-44-46. 3-47. 3-47.... 4-1

Fracture Orientation ..............................................................................................9.17 Steady-State Reservoir Response ...........................................................................

Effective Wellbore Radius, r'w ................................................................................... 3-A Direct Way Of Finding FOI ................................................................................... 3Optimizing Fractures for Secondary Recovery .........................................................Acid Fracturing ..........................................................................................................

9.18 Transient Reservoir Response .................................................................................9.19 Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)............. 3

Flow Periods For A Vertically Fractured Well .......................................................... 3Fracture Linear Flow ...........................................................................................Bilinear Flow ....................................................................................................... 3Formation Linear Flow ........................................................................................ 3Pseudo-Radial Flow .............................................................................................

Bilinear Flow Equations ...........................................................................................Constant Formation Face Rate ............................................................................Constant Formation Face Pressure .....................................................................

Bilinear Flow Graphs ................................................................................................Constant Formation Face Rate ............................................................................Constant Formation Face Pressure ......................................................................

End of Bilinear Flow ................................................................................................. 3Constant Formation Face Rate ............................................................................Constant Formation Face Pressure ......................................................................

Analysis of Bilinear Flow Data ................................................................................ 3Liquid-Constant Rate ...........................................................................................Liquid-Constant Pressure ....................................................................................

Effect of Flow Restrictions ....................................................................................... 3Effect of Wellbore Storage .......................................................................................

9.20 Bilinear Flow - Gas Reservoirs ..................................................................................Bilinear Flow Equations ............................................................................................

Constant Formation Face Rate ............................................................................Constant Formation Face Pressure ......................................................................

Bilinear Flow Graphs ................................................................................................Constant Formation Face Rate ............................................................................Constant Formation Face Pressure .....................................................................

End of Bilinear Flow ................................................................................................. 3Constant Formation Face Rate ............................................................................Constant Formation Face Pressure .....................................................................Analysis of Bilinear Flow Data ........................................................................... 3Gas-Constant Rate ..............................................................................................Gas-Constant Pressure ........................................................................................

9.21 References ............................................................................................................... 3-499.22 Elastic Properties of the Formation ..........................................................................

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.4-4..4-4.... 4...5-1..5-1

..5-2

.5-3

.5-65-10.5-125-125-125-15.5-17.5-18

5-20..5-.5-275-29..5-325-335-34..5-36..5-36..5-365-375-38.5-40.5..5-40..........6-1

Chapter 4 Formation Mechanical PropertiesEffect Of Modulus On Fracturing ...............................................................................Typical Modulus Values ...........................................................................................

9.23 Fracture Toughness ..................................................................................................-79.24 Hardness ...................................................................................................................4-109.25 References .................................................................................................................4-119.26 Fracture Height/Fracture Height Growth - 3-D Modeling/Design .............................

Factors Controlling Fracture Height ..........................................................................

Chapter 5 Design of Pseudo 3-D Hydraulic Fracturing TreatmentsFactors Controlling Fracture Height ..........................................................................Effect Of Closure Stress Profile On Fracture Height Growth ....................................Effect Of Bed Thickness On Fracture Height Growth ................................................Effect Of Other Factors On Fracture Height Growth .................................................Picking Fracture Height .............................................................................................(Estimating the In-situ Stress Profile) ........................................................................Factors Which Dominate In-situ Stress Differences ..................................................3-D Fracture Modeling/3-D Fracture Design .............................................................Measuring Fracture Height ........................................................................................Fluid Loss Height ......................................................................................................

9.27 Fluid Loss ...................................................................................................................5-20Fluid Loss Coefficient, Ct ..........................................................................................Spurt Loss .................................................................................................................24

9.28 Fluid Viscosity .........................................................................................................-27Viscosity Determination and Rheological Models .....................................................5Fluid Entry Conditions and Temperature Considerations ..........................................Reservoir Temperatures ...........................................................................................Effect of Proppant on Viscosity .................................................................................Summary For Fluid Viscosity ....................................................................................

9.29 Treatment Pumping ..................................................................................................Fracture Radius ........................................................................................................Pump Rate ................................................................................................................

Fluid Volume: ......................................................................................................Transport and Viscosity: ......................................................................................Summary for Pump Rate: .....................................................................................

Depth ........................................................................................................................-40Friction Pressure ......................................................................................................

9.30 References .................................................................................................................5-439.31 Fluid Selection ........................................................................................................6-19.32 Fluid Classification ...................................................................................................6-1

Water-Base Fracturing Fluid Systems ......................................................................

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.. 6-2.. 6-36-5-6. 6-7.. 6-9-11-14

6-186-236-306-306-326-38-406-416-466-486-49.. 6-52. 6-7-70

6-716-7.

.. 7-1.. 7-1... 7-1

.... 7-3

.. 7-3

.... 7-

... 7-4

... 7-. 7-5... 7-97-11-11

7-1. 7-16

Chapter 6 Fluid Selection and SchedulingHydrocarbon-Base Fracturing Fluid Systems ...........................................................

9.33 Fluid Selection Criteria .............................................................................................Safety and Environmental Compatibility ..............................................................Compatibility with Formation, Formation Fluids, and Chemical Additives ......... 6Simple Preparation and Quality Control ..............................................................Low Pumping Pressure ........................................................................................Appropriate Viscosity .......................................................................................... 6Low Fluid Loss .................................................................................................... 6Good Flow Back and Cleanup .............................................................................Economics ...........................................................................................................

9.34 Description of Fracturing-Fluid Types .....................................................................Water-Base Polymer Solutions .............................................................................Fast-Crosslinking Water-Base Gels ....................................................................Delayed Crosslinked Fluids .................................................................................Polymer Emulsion Fluid ...................................................................................... 6Foamed Frac Fluids .............................................................................................Gelled Hydrocarbons ...........................................................................................Gelled Methanol ..................................................................................................

9.35 Rheological Testing Of Fracturing Fluids ................................................................9.36 Service Company Trade Names .............................................................................9.37 Fluid Scheduling ......................................................................................................0

Fluid Scheduling Given the Fluid Rheology ............................................................ 6Fluid Scheduling Using Constrained Rheology .......................................................Warning: ....................................................................................................................3

9.38 References ............................................................................................................... 6-809.39 Introduction ................................................................................................................. 7-1

Why Do We Need Proppants? ...................................................................................Types of Proppants Available ....................................................................................Calculating the Stress on Proppant ..........................................................................

Chapter 7 ProppantsWhat Causes A Proppant To Be Substandard? ........................................................Overview of Chap. 7 ..................................................................................................

9.40 Proppant Properties .................................................................................................4Sphericity and Roundness ........................................................................................Hardness ..................................................................................................................4Size Distribution ........................................................................................................Crush Resistance ......................................................................................................Bulk and Grain Density ............................................................................................Acid Solubility .......................................................................................................... 7Turbidity ...................................................................................................................3Resin-Coated Proppant ............................................................................................

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..7-16.7-167-19-19

7-197-20-20-20-20-23..7-2.7-29....8-1.

..8-2

.....8-4...8-4...8-7...8-9.8-10..8-14-14.8-20.8-22.8-23..8-25.8-26.8-27.8-30.8-32-358-36.8-388-38

..8-42

..8-468-48-49

Precured Resin-Coated Proppant ........................................................................Curable Resin-Coated Proppant ...........................................................................

9.41 Conductivity/Permeability ........................................................................................Laboratory Methods of Measuring Fracture Conductivity .........................................7

Radial Flow Cell ...................................................................................................Cylindrical Pack ....................................................................................................Cylindrical Cell With Platens ...............................................................................7Cooke-Type Cell (API Cell) .................................................................................7

Long-Term Conductivity: Baseline Data ..................................................................7Long-Term Conductivity: Damage Caused By Frac Fluids and Additives ...............7

9.42 Proppant Transport ...................................................................................................69.43 Non-Darcy Flow .......................................................................................................9.44 References .................................................................................................................7-329.45 Introduction To Fracturing Pressure Analysis .........................................................

History .........................................................................................................................8-1

Chapter 8 Fracture Treating Pressure AnalysisSimilarity to Pressure Transient Analysis ..................................................................

9.46 Fracture Closure Stress ...........................................................................................Microfrac Tests .........................................................................................................Pump-In/Decline Test ...............................................................................................Pump-In/Flowback Test ...........................................................................................Step-Rate Injection Test ............................................................................................

9.47 Bottomhole Treating Pressure .................................................................................Nolte-Smith Log-Log Interpretation .........................................................................8Critical Pressure .......................................................................................................BHTP Measuring Techniques ..................................................................................BHTP Measuring Devices ........................................................................................

9.48 Pressure Decline Analysis .......................................................................................Fracture Stiffness ......................................................................................................Fluid Loss Rate .........................................................................................................∆P* - Pressure Decline Analysis ..............................................................................Type Curve Analysis ................................................................................................'G' Function Plot for∆P* ...........................................................................................8Fluid Efficiency .........................................................................................................Example/Guidelines .................................................................................................

Example - Pressure Decline Analysis: ..................................................................Pitfalls .........................................................................................................................8-39Post-propped-Frac Pressure Decline Analysis ........................................................

9.49 Pressure History Matching ......................................................................................Simple History Matching ..........................................................................................Simple History Matching Procedure & Example .......................................................8

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8-508-528-52. 8-558-568-56-588-598-628-648-6-65.. 8-668-668-67. 8-.

... 9-3

... 9-4

. 9-7

.. 9-8. 99-119-12-14-17. 9-209-20.

. 110-

10-310-510-50-60-7

Complex Geology Effects ..........................................................................................Problem Definition ....................................................................................................Pressure Decline Analysis Variables .........................................................................

9.50 Proppant/Fluid Schedule From Pressure Decline .....................................................Advantages of an Efficiency Derived Schedule ........................................................Disadvantages of an Efficiency Derived Schedule ....................................................Determining Fracture Fluid Efficiency ..................................................................... 8Pad Volume ..............................................................................................................Proppant Addition Schedule .....................................................................................Effect of Treatment Volume .....................................................................................Example .....................................................................................................................5Find Actual Job “Expected” Efficiency ..................................................................... 8Treatment Pad Percentage ......................................................................................Proppant Addition Schedule .....................................................................................Time/Temperature History .......................................................................................

9.51 Nomenclature ...........................................................................................................689.52 References ................................................................................................................ 8-709.53 Introduction ................................................................................................................. 9-1

Chapter 9 Economic Optimization of Hydraulic Fracture Treatments9.54 General Economic Criteria .......................................................................................

The Present Worth Concept ......................................................................................Profitability Index ......................................................................................................Discounted Return on Investment (includes Fracture Discounted Return

on Investment) ........................................................................................................Payout .......................................................................................................................-10Return on Investment .................................................................................................Incremental Economics ..............................................................................................Present Worth Vs. the Profitability Index ................................................................. 9Yet-to-Spend (Point Forward Evaluation) Vs. Full-Cycle Economics ...................... 9

9.55 Elements Of Fracturing Treatment Costs .................................................................Stimulation Service Company Costs .........................................................................

9.56 References. ............................................................................................................... 9-21

Chapter 10 Special Topics9.57 Fracturing Tests ........................................................................................................0-3

Introduction ................................................................................................................3Core Tests to Determine Mechanical Rock Properties and Fluid

Loss Coefficient ......................................................................................................Prefrac Logging Program ...........................................................................................Borehole Geometry Log ............................................................................................Long Spaced Digital Sonic Log (LSDS) .................................................................. 1Downhole Television and Borehole Televiewer ...................................................... 1

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.10-7..10-80-1010-110-120-1210-13.10-13.10-130-170-180-180-18

10-210-210-2

10-240-260-280-290-290-310-320-320-360-41

.

......1

......3.......4...4.......8.......9

....11

Cement Bond Log .....................................................................................................Temperature Logs .....................................................................................................Perforating and Permeability Determination ............................................................1Bottomhole Treating Pressure Measurement ..........................................................Procedure for Measurement of Static Pressure Tubing/Annulus .............................1Procedure for Recording Downhole with Surface Readout .....................................1Procedure for Downhole Pressure Measurement .....................................................Pressure Measurement Devices ...............................................................................Closure Stress Tests .................................................................................................Minifracs .................................................................................................................1Postfrac Logging Program ........................................................................................1

Temperature Decay Profiles ................................................................................1Postfrac Temperature Log Interpretation .................................................................1Postfrac Gamma Ray Logs ......................................................................................Fracture Azimuth Determination ..............................................................................1Tiltmeters .................................................................................................................12Borehole Geophones ...............................................................................................Oriented Core Analysis ...........................................................................................1Borehole Geometry .................................................................................................1

9.58 Introduction To TerraFrac ........................................................................................1General Description of the TerraFrac Simulator ......................................................1Input To Terrafrac ....................................................................................................1Terrafrac Simulation Runs .......................................................................................1

Confined Fracture Growth .................................................................................1Unconfined Fracture Growth .............................................................................1

Summary ..................................................................................................................19.59 References ...............................................................................................................10-499.60 Perforating .......................................................................................................................1

Hole Diameter ...........................................................................................................

Chapter 11 Fracture Stimulation GuidelinesandQuality Control

Chapter 12Number of Perforations .............................................................................................Perforation Phasing ..................................................................................................Perforating for Deviated/Horizontal Well Fracturing ..................................................Over-Pressured Perforating ......................................................................................Other Considerations ................................................................................................

9.61 WELLBORE CONFIGURATION 10Fracturing Down Casing ...........................................................................................

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...11...12...12....14

....16....17...18....18

...21

....23...24..30..33..34

......36

.....36.....41.....42....43...45

..46

....46

.....47

....47

....49....50

.....51....54

.

...

..P

...P

PP-1P-

Fracturing Down Tubing with a Packer ......................................................................Fracturing Down Open-Ended Tubing .......................................................................Methods of Obtaining Fracturing BHP .......................................................................Considerations for Frac-Pack Completions ...............................................................

9.62 PRE-TREATMENT PLANNING 16Data Collection Requirements ...................................................................................Preliminary Treatment Design ...................................................................................Frac “Brief” Procedure ...............................................................................................Service Co./Operator Interaction ...............................................................................

9.63 FRACTURING FLUID QC 20Base Mixing Fluid ......................................................................................................Transport and Storage of Fluid ..................................................................................Quality Controlling Water-Based Gels .......................................................................Quality Controlling Oil-Based Gels ............................................................................Quality Controlling Foam Fracturing Fluids ...............................................................Additional Fluid Quality Control Measures ................................................................

9.64 PROPPANT QC 36Closure Stress and Proppant Strength ......................................................................Proppant Particle Size ...............................................................................................Proppant Grain Shape ...............................................................................................Proppant Fines ..........................................................................................................

Interpretation ........................................................................................................Additional Proppant Quality Control Measures .........................................................

9.65 TREATMENT EXECUTION 46Lines of Authority and Communication ......................................................................Safety Meeting ...........................................................................................................Pressure Testing ........................................................................................................Treating Problems ......................................................................................................Flushing the Treatment ..............................................................................................When to Flowback .....................................................................................................

9.66 POST-FRAC LOGGING 51Temperature Logs .....................................................................................................Gamma-Ray Logs ......................................................................................................

9.67 FRAC School Problem No. 1 P-19.68 FRAC School Problem No. 2 P-2

Abstract .......................................................................................................................P-2Purpose .....................................................................................................................P-2Description .................................................................................................................-2Procedure: .................................................................................................................-9

9.69 Workshop Problem 3 P-10Abstract ......................................................................................................................-10Description .................................................................................................................0Objective ....................................................................................................................10

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. P-1

P-. P-P-15P-15

P-P-23P-2. P-2

. P-30P-34

P-43-43

P-48

Procedure: .................................................................................................................19.70 Workshop Problem 4 P-15

Abstract .....................................................................................................................15Purpose .....................................................................................................................15Geologic Setting ........................................................................................................Description ................................................................................................................

9.71 Workshop Problem No. 5 P-23Abstract .....................................................................................................................23Description ................................................................................................................Objective: ..................................................................................................................3Procedure: .................................................................................................................9

9.72 Water Injection Well Problem 6 P-30Pressure Falloff Test .................................................................................................“Mini-Frac” Pressure Data ........................................................................................

9.73 Tight Gas Problem 7 P-399.74 Oil Well Problem 8 P-43

Other Pertinent Information ......................................................................................Pressure Build-Up Data from Offset Well ................................................................ PResults from Minifrac Treatment ..............................................................................

9.75 Bili near FLow Problem 9 P-49P-49P-49P-49

Hydraulic Fracturing Theory Manual x June 1997

Chapter

maryo) inof allents

rves anised sig-

esti-n, asuring,e pro-ppli-r of

wells.

Introduction1
1.1 History of Hydraulic Fracturing
Hydraulic fracturing has made a significant contribution to the oil and gas industry as a primeans of increasing well production. Since fracturing was introduced by Stanolind (Amoc1947, over one million fracture treatments have been performed and currently about 40%wells drilled are stimulated using hydraulic fracture treatments. Fracture stimulation treatmnot only increase production rates, but are also credited for adding to the United States reseadditional seven billion barrels of oil and over 600 trillion scf of gas which would have otherwnot been economical to develop. In addition, hydraulic fracturing has accelerated recovery annificantly increased the present worth of U.S. reserves.

As we move towards the next century, we are challenged with applying this technology domcally in an attempt to offset large domestic trade deficits and declining production. In additioour industry’s focus moves internationally, methods of accelerating recovery, such as fractmust be explored. Fig. 1.1 presents a world cross section of producing oil wells, their averagduction and the total production of each country. This logarithmic plot shows that fracturing acations will continue to be important throughout North America, driven by the large numbewells available and the corresponding low producing rates presently experienced by these

Fig. 1.1 - Producing Wells and Average Production

1000000

100000

10000

1000

100

10Saudi Arabia U. K. Nigeria Mexico China Canada U. S.

10

8

6

4

2

0

No. Wells/Av. Production-bbl/d Total Daily Production-bbl

PRODUCING WELLS & AVERAGE PRODUCTIONLikelihood of Fracturing

Country

# Oil Wells Total ProductionWell Rate

Excerpted DOE/FE-0139

Hydraulic Fracturing Theory Manual1-1February 1993

Introduction1

con-y ofexper-per-n ingel

bilityed toin

ntiallyhoma

. The, andoline,

pplica-3,000yond

ensoco.

The idea of hydraulically fracturing a formation to enhance the production of oil and gas wasceived by Floyd Farris1 of Stanolind Oil and Gas Corporation (Amoco) after an extensive studthe pressures encountered while squeezing cement, oil and water into formations. The firstimental treatment intentionally performed to hydraulically fracture a well for stimulation wasformed by Stanolind in the Hugoton gas field in Grant County, Kansas, in 1947 as showFig. 1.2. A total of 1,000 gallons of napalm thickened gasoline was injected, followed by abreaker, to stimulate a gas producing limestone formation at 2,400 ft. However, the deliveraof the well was not changed appreciably. The hydraulic fracturing process was first introducthe industry in a paper written by J. B. Clark2 of Stanolind in 1948 and patented and licensed1949. These patents resulted in royalty income to Amoco in the 17 years following and essefunded the construction of the Amoco Production Research (APR) complex in Tulsa, Okla(i.e., APR is the house that fracturing built).

Halliburton Oil Well Cementing Company was given an exclusive license on the new processfirst two commercial fracturing treatments were performed in Stephens County, OklahomaArcher County, Texas, on March 17, 1949, using lease crude oil or a blend of crude and gasand approximately 100 to 150 pounds of sand. Both wells were successful and thereafter ation of the fracturing process grew rapidly, peaking, as shown in Fig. 1.3, at an average of +wells per month by the mid-1950s and increasing the supply of oil in the United States far beour early projections.3

The first one-half million pound fracturing job in the free world was performed in StephCounty, Oklahoma, in October 1968, by Pan American Petroleum Corporation, now Am

Fig. 1.2 - Hugoton Gas Field in Grant County, Kansas, 1947.

Hydraulic Fracturing Theory Manual 1-2 February 1993

History of Hydraulic Fracturing

udingin the

he firstabout

lons ofn gal-ndus-uringd; sandppants

and

of theory was

boretures,

ed by6were

Today, fracture treatments are performed regularly in all petroleum producing countries, inclthe Soviet Union. It is estimated that at least 30% of the recoverable oil and gas reservesUnited States can be attributed to the application of hydraulic fracturing.

Significant technical advancements have been made during the four plus decades since tcommercial treatments. After the first few jobs, the average fracture treatment consisted of750 gallons of fluid and 400 pounds of sand. Today, treatments average about 43,000 galfluid and 68,000 pounds of propping agent with the largest treatments exceeding one milliolons of fluid and three million pounds of proppant. This reflects advancements made by the itry in both theory and practice which have resulted in a better understanding of the fractprocess. As this process evolved; cleaner and more suitable fluid systems were developequality increased and higher concentrations were pumped; higher strength synthetic prowere developed for deep-well fracturing; pumping and monitoring equipment were improvedcomputerized; and fracture design and evaluation techniques grew in sophistication.

Developments in Hydraulic Fracturing

Fracture Orientation:

The original, shallow fracture treatments were thought to be horizontal, even though somedeep wells that had been squeeze cemented showed cement in vertical fractures. The thethat the overburden was lifted and the fracture was inserted in a horizontal plane. Clarket al.4

reported on a method of forming a vertical fracture in 1953 by plastering the walls of the wellto where it became a thick wall cylinder. Pressures were then applied to obtain vertical frac

otherwise it was theorized horizontal fractures were obtained. Huittet al.5-7 extended the theoriesin the late 1950s that the best fracture systems were horizontal and they could be obtainnotching the formation. Hubbert and Willis8 with Shell Oil Company presented a paper in 195reporting on the work they had done in a gelatin model. This work indicated that all fractures

Fig. 1.3 - Average Number of Fracturing Treatments per Month United States.

5000

4000

3000

2000

1000

1949 1955 1960 1965 1970 1975 1980 1985

YEARS

AVE

RA

GE

NU

MB

ER

OF

JO

BS

PE

R M

ON

TH


Introduction1

dus-izon-er 0.8hor-tahl

xcep-

frac-n 1952,portionwere

er vis-ainedand due

weressiumof the

chlo-, suchAque-turing

fluids

vertical, creating quite a controversy. In spite of this, it was not until the mid-1960s that the intry accepted the theory that practically all fractures were vertical and that only a few were hortal. Prior to this time, theories were advanced that all fractures with a treating gradient of ovor 0.9 psi per foot of depth were vertical. All those with treating gradients less than this wereizontal. Work initiated by Cochran, Heck and Waters and reported on by Anderson and S9

proved, without a doubt, that the majority of fractures were in fact vertical and it was a rare etion when a horizontal fracture was obtained.

Fracturing Fluid:

Hydraulic fracturing fluids have varied considerably over time as shown in Fig. 1.4. The firstture treatments were performed with gelled lease crude, later, gelled kerosene was used. Irefined and lease crude oils began to gain momentum, and by the latter part of 1952, a largeof all fracturing treatments were performed with refined and lease crude oils. These fluidsinexpensive and safer, permitting greater volumes to be pumped at a lower cost. Their lowcosities exhibited less friction than the original viscous gel, thus injection rates could be obtat lower treating pressures. Higher injection rates, though, were necessary to transport the sto the lower viscosity and high rates of leakoff for these fluids.

In 1953, with the advent of water as a fracturing fluid, a number of different gelling systemsdeveloped. Surfactants were added to minimize emulsions with the formation fluid and potachloride was added to minimize the effect on clays and other water sensitive constituentsformation. Later, other clay stabilizing agents were developed that enhanced the potassiumride and permitted the use of water in a greater number of formations. Other new innovationsas foams and addition of alcohol, have enhanced the use of water in a number of formations.ous fluids such as acid, water and brines are now used as the base fluid in over 70% of all fractreatments employing a propping agent. In the early 1970s, a major innovation in fracturing

Fig. 1.4 - Trend of Fracturing Base Fluids.

AQUEOUS BASE FLUID

OIL BASE FLUID

100

90

80

70

60

50

40

30

20

10

19891985198119771973196919651961195719531949

PE

RC

EN

T O

F T

RE

ATM

EN

T

YEAR



. Lessg cost.. Thisresult-

ilizerst thesel stabi-effect

s thegellingrove-f the

mov-earingnsureelop-

havereenedts, con-s soonhed onry largee mosts prop-Indian

d sands,

throughhenintro-

ity.

partialer the

ding with

was to use crosslinking agents to enhance the viscosity of gelled water base fracturing fluidspounds of gelling agent were required to reach the desired pumping viscosity, thus reducinIn many cases, however, too high a viscosity was obtained and pumping problems resultedsystem was soon perfected by reducing the concentration of gelling agents and crosslinker,ing in an economically satisfactory fracturing fluid system.

During the mid 1970s, fracture stimulations were designed for deeper formations. Gel stabwere developed to maintain the properties of the fluid system at the higher temperatures agreater depths. The first of these temperature stabilizers was 5% methanol. Later chemicalizers were developed that could be used alone, or with the methanol. There was a synergisticobtained when the chemical and the methanol were used together as stabilizers.

Recently, a new innovation was introduced which gives even greater temperature stability. Agelled fluid reaches the bottom of the hole and the temperature is increasing, a secondaryagent reacts giving a more uniform viscosity than previous surface crosslinked fluids. Impments in crosslinkers involve a delayed effect, thus permitting the fluid to reach the bottom ohole in high temperature wells prior to crosslinking. This system gives adequate viscosity foring the propping agent through the surface equipment and into the tubing, reducing the sheffect caused by tubulars, and supplying a good fluid in the hydraulically created fracture to eadequate proppant transport. These are only a few of the highlights of fracturing fluid devments. Many other developments have enhanced the performance of fracturing fluids.

Proppants:

To keep the artificially created hydraulic fractures open, proppants of many different kindsbeen used. The first fracturing treatment used a northern type sand for proppant; however, scriver sand was also employed on many early treatments. In fact, on some of these treatmenstruction sand sieved through a window screen was employed as the propping agent. It warealized, however, that a high quality sand was desirable and specifications were establisthe type of sand to be used. There have been a number of trends in the size of sand, from vedown to small. From the very beginning a 20 to 40 U.S. standard mesh sand has been thpopular and at the present time approximately 85% of the sand used is of this size. Numerouping agents have been evaluated throughout the years, including plastic pellets, steel shot,glass beads, aluminum pellets, high strength glass beads, rounded nut shells, resin coatesintered bauxite and fused zirconium.

Fig. 1.5 shows that the amount of sand used per fracture treatment has steadily increasedtime. As shown, the concentration of sand (lb/fluid gal) remained low until the mid-1960s wthe use of viscous fluids, such as complexed water base gel and viscous refined oil wereduced. At that time, large size propping agents were advocated to improve well deliverabil

Proppant design techniques at low sand concentration changed from the monolayer ormonolayer concept to pumping sand at multiple grain diameters and high concentrations. Ovlast decade, there has been another sharp increase in sand concentrations used corresponimproved hydraulic fracturing fluids and advanced pumping equipment.10 It is not infrequent to


Introduction1

meansions of

s, theto over

00 hhpwas

Rates

see proppant concentrations averaging 10 to 12 lbm/gal used throughout the treatment. Thisthat low concentrations are used at the start of the job and rapidly increased to concentrat15 lbm/gal or more.

Corresponding to increased fluid viscosity, higher pump rates and deeper well applicationhydraulic horsepower (hhp) used in treatments has increased from an average of about 751500 hhp as shown in Fig. 1.6.

Fracture Treatment:

There are cases where as much as 15,000 hhp has been available on jobs with over 10,0actually being utilized. Contrast this to some of the early jobs where only 10 to 15 hhprequired. The initial jobs were performed at rates of two to three barrels per minute (bpm).

Fig. 1.5 - Trend of Average Fracture Treatments in the United States.

a

Fig. 1.6 - Evolution of Fracturing Techniques.

100

90

80

60

50

40

30

20

10

00

10

20

30

40

50

60

70 70

80

90

100

Fluid/treatmentP

ound

s S

ands

(T

hous

and)

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4San

d C

once

ntra

tion

1949 1953 1957 1961 1965 1969 1973 1977 1981 1985 1989Years

SandConcentration

Sand/treatment

Gal

lons

of F

luid

(T

hous

ands

)

HHP/JOB

30

25

20

15

10

5

01949 1953 1957 1961 1965 1969 1973 1977 1981 1985 1989

YEARS

3000

2500

2000

1500

1000

500

0

HY

DR

AU

LIC

HO

RS

EP

OW

ER

INJECTIONRATE

RAT

E, b

bl/m

in



y, jobsugo-etimesure andto over

ring75 to

thesecompa-t waspmentarge,

d bytreat-Northorthlionproxi-

t fewfrac-

increased rapidly until the early 1960s where rates around 20 bpm became popular. Todaare performed at a low rate of about 5 bpm, to a high rate of over 100 bpm. At one time in the Hton gas field, pumping rates of over 300 bpm were employed. Surface treating pressures somare less than 100 psi, yet others may approach 20,000 psi. Today, as treatment size, presspump rate increase, treatment costs have also increased, ranging from less than $10,000$1,000,000. The first two commercial treatments cost between $900 and $1,000.

Conventional cement and acid pumping equipment were utilized initially to execute fractutreatments. One to three units equipped with a jet mixer and one pressure pump delivering125 hhp were adequate for the small volumes injected at the low rates. Amazingly, many oftreatments gave phenomenal production increases. As the treating volumes increased, acnied with demand for greater injection rates, purpose built pumping and blending equipmendeveloped to perform these specialized functions. Today, the development of fracturing equicontinues, including intensifiers, high pressure manifolds, and computer control systems. Lmassive hydraulic fracturing (MHF) treatments as illustrated in Fig. 1.7, were developeAmoco in the Hydraulic Fracturing Department, Amoco Production Research in Tulsa. Thements were developed to convert non-commercial, tight gas deposits found throughoutAmerica into viable, commercial properties. MHF treatments require several million dollars wof equipment, utilize in excess of one million gallons of fluid and have placed over 3.3 milpounds of sand, injected in one continuous operation pumped over 10 hours at rates of apmately 40 bpm.

Sand and fluid are mixed in a piece of fracturing equipment called a blender. For the firsyears, sand was added to the fracturing fluid by pouring it into a tank or jet mixer containing

Fig. 1.7 - Massive Hydraulic Fracture Treatment.


Introduction1

ddledevel-ning a

thees ofped to

ioningputer

is nec-ure ishere itcos-a com-usly,

alcula-atmente-halftil therams,

s-rough

turing fluid and connected to the pump suction. Later with less viscous fluid, a ribbon or patype batch blender was employed. Finally, the continuous proportioner and blender wasoped. Blending equipment has become very sophisticated to meet the need for proportiolarge number of dry and liquid additives, then properly blending them into the base fluid withspecified concentrations of sand or other propping agents. In order to handle large volumpropping agents required in large treatments, special storage facilities have been develofacilitate storing and moving the propping agents at the proper rate to the blender. Proportand mixing of the gelling agents has become a very sophisticated procedure utilizing comcontrol systems to step or ramp sand concentrations in the blender as shown in Fig. 1.8. Itessary to blend them in a uniform method to give the maximum yield viscosity. One procedto use a concentrated gelling agent prepared prior to the treatment, then taken to the field wis proportioned into the base fluid in a semi-continuous method. A very uniform high yield visity is obtained. With the advent of larger size treatments, it has become necessary to haveputer control center (Fig. 1.9) to coordinate all of the activities that are transpiring simultaneoeach of which is critical.

Early Fracture Design

The first treatments were designed by very complex application charts, nomographs and ctions to arrive at the treatment size to be pumped. The calculations generally predicted a tresize of 800 gallons, or multiples thereof, of fluid, and the sand at concentrations of around onto three-fourths lbm/gal. A hit and miss method of designing treatments was employed unmid-1960s when programs were developed for use on simple computers. The original progbased on work developed by Howard and Fast11 on fluid efficiency and the shape of a fracture sytem, were a great improvement. Since that time, many innovations have been introduced th

Fig. 1.8 - Schematic Diagram of Sand Fluid Proportioner.

FRACTURINGFLUID

METERINGPUMP

PROPORTIONINGCONTROL

SANDBULK OR SACK

SAND - FLUIDMIXTURE TOPUMP TRUCK

PRESSURIZER

AGITATOR



men-

ing abilizerariousgh theeasest anal-

o deter-

ouldal oth-

beenturingg pro-2.

earlyd gasgramsminifrac

mathematical modeling in both fixed height, two-dimensional and variable height, three-disional solutions.

Today, programs are capable of determining temperature profiles of the treating fluid durfracturing treatment. Such a profile can assist in designing the gel concentrations, gel staconcentrations, breaker concentrations and propping agent concentrations during the vstages of the treatment. Models have been developed to simulate the way fluids move throufracture and how the propping agent is distributed. From these simulations, production incrcan be determined. Following a fracturing treatment, reservoir models and pressure transienysis methods can then be used to history match the pressure and production performance tmine what type of treatment was actually achieved.

The history of fractured reservoir response analysis dates from the late 1960s. Tinsleyet al.12 didwork on an electrolytic model to determine the effect fracture lengths and flow capacity whave on the production increase obtained from wells with a different drainage radius. Severers developed mathematical models for similar projections. Nolte and Smith13 developed proce-dures to correlate between observations made during fracturing treatments and Britt14,15 and

Veatch16-18 presented methods to optimize the fracturing process. Several theories haveadvanced by this work which added considerably to the understanding of the hydraulic fracprocess. This technology added considerably to the understanding of the hydraulic fracturincess and is summarized in the SPE Monograph Volume 119

Marked advancements were achieved by Amoco and the industry during the 1970s and1980s. Much of what was learned during this period is now being applied to fracturing oil anformations. The most notable contribution was field test procedures and data collection prodeveloped to better estimate fracture design parameters. These include prefrac stress tests,

Fig. 1.9 - Computer Control Console.


Introduction1

turing.avior,ome-roach

cessbe inberryBruyoma;Texasn Col-north-

ation in. Theainsinuingle inionale end

calibration treatments and the measurement of bottomhole treating pressures during fracObservations from these tests indicate lateral fracture extension rate, vertical growth behfracturing fluid leakoff rate, and general characteristics associated with defining fracture getry. This information has led Amoco and the industry to a more precise and systematic appto fracture treatment design.

Well stimulation by hydraulic fracture treatment is an important production engineering proto Amoco Production Company. There are many fields in the United States that would notexistence today if it had not been for hydraulic fracturing. Some of these include the Spraytrend in west Texas; the Pine Island field in Louisiana; many wells in the Anadarko Basin, theRiver and Cardinal Fields in Canada, a large number of Morrow wells in northwestern Oklahthe entire San Juan basin of New Mexico; the Denver Julesburg basin of Colorado; the Eastand north Louisiana trend in the Cotton Valley; the tight gas sands of south Texas and westerorado; the tight gas sands of southwestern Wyoming and many of the producing areas of theeastern part of the United States. Recent economic developments and the constant fluctupetroleum prices have led to a near-halt in the development of tight gas fields until recentlyindustry has turned its attention more to low risk, high profit type projects. Still, fracturing remas important to many of these projects as to the earlier tight gas developments. With contadvancements in technology, hydraulic fracturing promises to continue playing a vital rounlocking otherwise unobtainable reserves and extending field life accordingly. For additinformation on current hydraulic fracturing technology, refer to the technical references at thof this chapter.


Amoco Hydraulic Fracturing Course Outline

uring, rocknd moste. Thisppli-ech-

n innduc-eak-ionsn is

sedppant

ctionerall

n andn.

gn ofonseior aremizingr por-

1.2 Amoco Hydraulic Fracturing Course Outline

The purpose of this course is twofold. The course will present the principles behind the fractprocess which will assist you in understanding the dependencies between fluid hydraulicsproperties, resulting fracture geometry and associated reservoir response. The second, aimportant purpose, is to provide a technical understanding to evaluate the results you achievunderstanding will allow you to improve field applications and develop new techniques for acation. Significant financial benefits are possible by diligently applying the current state of tnology, and overcoming arbitrary and poorly implemented procedures and attitudes.

A question often asked today is, “What can be changed to maximize profits?” As showFig. 1.10, the optimum treatment results from balancing different parameters, i.e., fracture cotivity, fracture length and reservoir permeability, to achieve the maximum profit. Generally sping, the desired fracture length for optimal production is bigger for lower permeability formatas shown in Fig. 1.11. Conversely, the desired fracture conductivity for optimal productiogreater for higher permeability reservoirs.

The optimum treatment will differ from field to field and from one area of a field to another baon reservoir characteristics and treatment cost. Recognize that the amount of fluid and prorequired to achieve a desired penetration will vary greatly from location to location as a funof lithology, wellbore stresses and fracture containment. Therefore, it is very important for ovfinancial optimization, that the optimization process be completed for each different situatiothat at least two or three different fluid and proppant systems be evaluated for each situatio

Fig. 1.12, illustrates a simplified schematic of the optimization process used in the desihydraulic fracture stimulations. The upper portion of Fig. 1.12 considers the reservoir respresulting from fracturing and the revenue produced. The detailed aspects of reservoir behavcovered in other courses, however, a general discussion of how these topics relate to optirevenue through fracture design is included in this manual in Chap. 3 and Chap. 9. The lowe

Fig. 1.10 - Critical Factors to Optimum Fracture Stimulation.


Introduction1

cturesequired.e pri-

e usedtion,imen-is-n of

is and

tion of Fig. 1.12, relates to creating the fracture (i.e., the cost aspect). Unlike reservoirs, fraare created by humans and therefore can be changed and made both longer and wider as rThe design and implementation of a propped hydraulic fracture stimulation treatment is thmary topic of this course.

The topics detailed in this course include how a fracture is created, what proppants should bto hold it open and how the fluid flow in a reservoir is altered. The effect of fracture penetrathe importance of fracture height development, the concepts of effective wellbore radius, dsionless fracture conductivity (FCD) and folds of increase (FOI) for steady-state conditions are dcussed. The effect of early time transient production and bilinear flow, and the applicatioeconomic analysis and revenue optimization are elements of coupled reservoir analys

Fig. 1.11 - Desired Fracture Half-lengths for Different Formation Permeabilities.

Fig. 1.12- Fracture Stimulation Design--The Total Concept for Optimization.

Frac. 1/2 Length1000’s Feet

4

3

2

1

0

MDMicroDarcies

In-Situ Gas Permeability

.0001 .001 .005 .01 .05 .1 1.0 10.0 100..1 1 5 10 50 100 1000 10,000 100,000

ExtremelyTight

VeryTight Tight

NearTight Conventional

ReservoirSimulator

HydrafracSimulator

Cum

. Pro

d.Tr

eatm

ent V

ol.

Years Length

Length

Fracture Length

Fracture Length

$ R

even

ue$

Cos

t

$ RevenueLess

$ Cost

Fracturing


Amoco Hydraulic Fracturing Course Outline

prac-ize ahichanual.on

hydraulic fracture treatment designs covered in this course.

The financial results obtained in fracturing can be significantly increased, over the standardtice of the industry, through a better understanding of the fracturing process, how to optimtreatment design, and the implementation of quality control in the field. The nomenclature wfollows on the next pages summarizes the most important and frequently used terms in the mThe SPE Monograph Volume 1219 provides a comprehensive review and list of referencesmany of the aspects covered in this course.


Introduction1

s hy-

in

in

n

be-

the

1.3 Nomenclature

BHCP Bottomhole closure pressure in psi. It is equal to fracture pressure; it is alsoσc.

BHTP Bottomhole treating pressure in psi. It is equal to surface treating pressure pludrostatic pressure minus friction pressure. It is also equal toBHCP plusPN.

bpm Barrels per minute.

C Fracturing fluid leakoff coefficient. It is also equal toCt in .

CI Part ofCt. It is the effects of the frac fluid viscosity and relative permeability.

CII Part ofCt. It is the effects of the reservoir fluid viscosity and compressibility.

CIII Part of Ct. It is the effects of the wall building properties of the frac fluid i.

Ct The total effects of the frac fluid leakoff coefficient in .

Ct It is the total compressibility factor of the reservoir and fluid in psi-1. It is used tocalculate part ofCIII .

E Modulus of Elasticity in psi.

FCD A dimensionless fracture capacity. It is related to the contrast in permeabilitytween the fracture and the formation.

FOI Folds of Increase. It is the ratio of the stabilized production after fracturing toproduction before fracturing. It is equal toQFRAC/QUNFRAC.

Rock porosity in decimal percent.

H Total or gross fracture height in feet.

hhp Hydraulic Horse Power in hp.

Hp Permeability Height. That portion of the frac height,H, to which frac fluids may belost.

k Reservoir permeability in millidarcies (md).

kf Fracture permeability in md.

kfw Fracture conductivity in md-ft.

ft/ minute

ft/ minute

ft/ minute

ft/ minute

ft/ minute

φ


Nomenclature

at a

ra-

In-

n psi,

essure

rop-fluid.

ual to

tive

K' A property of gelled frac fluids called consistency index and is shear stressstrain rate of 1 sec-1. Data supplied by service companies.

L Hydraulic fracture length from tip to tip. It is equal to 2 times the hydraulic fracdius,xf, in feet.

µ Viscosity in cp.

n' A property of gelled frac fluids called Power Law Exponent or Flow Behaviordex. Data supplied by service companies. Related toK'.

OB Overburden pressure in psi. Generally, it is one timesTVD in psi.

∆p The difference between the pressure in the fracture and reservoir pressure iused inCI andCII.

Pc Critical Pressure or Pressure Capacity. It is the net pressure above closure prwhere a fracture may become unconfined.

PFCF Proppant Fall Correction Factor. It is a term used to tell the computer that a ppant other than 20-40 mesh is being used, or that fall is through a crosslinked

PN Net Pressure. The pressure in the fracture above closure pressure. It is eqBHTP minusBHCP.

PPG Pounds of Proppant Per Gallon of liquid in lb/gal.

PPSG Pounds of Proppant Per Gallon of Slurry in lb/gal.

Q Pump rate in barrels per minute (bpm).

Same as FOI. A measure of the results of the fracture stimulation.

re Drainage radius in feet. Generally, it is one-half the distance to the next well.

rw Wellbore radius in feet.

r'w The stimulated wellbore radius effect due to the fracture in feet. It is the effecor pseudo-wellbore flow radius resulting from the fracture.

S.G. Specific Gravity relative to water.

SIBHP Shut In Bottomhole Pressure,PR, in psi.

SIBHT Shut In Bottomhole Temperature in F.

SPF Perforation density in Shots Per Foot.

QFRAC

QUNFRAC----------------------

°


Introduction1

the

t Time in minutes.

c Closure Stress. Equal toBHCP.

TVD True Vertical Depth in feet.

VFRAC Volume of fracture cavity in cubic feet.

VIN Volume of frac fluid pumped into the well in cubic feet.

VLOST Volume of frac fluid leaked from the crack into the formation in cubic feet.

w Fracture Width in feet (may also be in inches).

Average Fracture Width in feet (may also be in inches).

xf Fracture radius in feet (or fracture half-length). Measured from the center ofwellbore to the end of the proppant on one wing of the fracture.

σ

w


References

Sand

rop-

pre-iversity,

-23

ec-

”

”

uction

1.4 References

1. Farris, R. F.: U. S. Patent reissued Nov. 10, 1953, Re 23733.

2. Clark, J. B.: “A Hydraulic Process for Increasing the Productivity of Oil Wells,”Trans., AIME (1949)186, 1-8.

3. Maly, J. W. and Morton, T. E.: “Selection and Evaluation of Wells for Hydrafrac Treatment,”Oil & Gas J, (May3, 1951) No. 52, 126.

4. Clark, R. C.et al.: “Application of Hydraulic Fracturing to the Stimulation of Oil and Gas Production,”Drill. &Prod. Prac., API (1953) 113-22.

5. Huitt, J. L. and McGlothin, B. B. Jr.: “The Propping of Fractures in Formations Susceptible to Propping-Embedment,”Drill. & Prod. Prac., API (1958) 115.

6. Huitt, J. L., McGlothin, B. B. Jr., and McDonald, J. F.: “The Propping of Fractures in Formations in Which Pping Sand Crushes,”Drill. & Prod. Prac., API (1958) 115.

7. Huitt, J. L.: “Hydraulic Fracturing with Single Point Entry Technique,” JPT, (March 1960) XII, No. 3, 11.

8. Hubbert, M. K. and Willis, D. G.: “Mechanics of Hydraulic Fracturing,”Trans., AIME (1957)210, 153-66.

9. Anderson, T. O. and Stahl, E. J.: “A Study of Induced Fracturing Using an Instrumental Approach,”JPT (Feb.1967) 261-67;Trans., AIME, 240.

10. Coulter, G. R. and Wells, R. D.: “The Effect of Fluid pH on Clays and Resulting Formation Permeability,”sented at the Southwestern Petroleum Short Course, Dept. of Petroleum Engineering, Texas Tech UnLubbock, Texas, April 17-18, 1975.

11. Howard G. C. and Fast, C. R.: “Optimum Fluid Characteristics for Fracture Extension,”Drill. & Prod. Prac.,API (1957) 261-70.

12. Tinsley, J. M.et al.: “Vertical Fracture Height--Its Effect on Steady-State Production Increase,”JPT(May 1969)633-38;Trans., AIME, 246.

13. Nolte, K. G. and Smith, M. B.: “Interpretation of Fracturing Pressures,”JPT, (Sept. 1981), 1767-75.

14. Britt, L. K.: “Optimized Oil Well Fracturing, Phase I Report,” Amoco Production Company Report F84-P(May 25, 1984).

15. Britt, L. K.: “Optimized Oil Well Fracturing, Phase II Report,” Analysis of the Effects of Fracturing on the Sondary Recovery Process; Amoco Production Company Report F85-P-7 (Jan. 24, 1985).

16. Veatch, R. W. Jr.: “Overview of Current Hydraulic Fracturing Design and Treatment Technology--Part 1,JPT(April 1983) 677-87.

17. Veatch, R. W. Jr.: “Overview of Current Hydraulic Fracturing Design and Treatment Technology--Part 2,JPT(May 1983) 853-64.

18. Veatch, Ralph W. Jr.: “Economics of Fracturing Some Methods and Case Study Examples,” Amoco ProdCompany Report F89-P-58 (Aug. 3, 1989).


Introduction1n, TX
19. Gidley, J. L., Holditch, D. E., Nierode, D. E., and Veatch, R. W., Jr.:, Monograph Series, SPE, Richardso
(1989)12.


Chapter

draulicuitythatticityand

terion

to thejected

on bystant

Fracturing Models2
Fracture design models attempt to simulate the natural phenomena associated with the hyfracturing process. They account for the total volume of fluid injected in the ground (continequation) and estimate the fluid volume that leaks off in the formation and the fluid volumeremains within the fracture; they relate fracture width to the applied hydraulic pressure (elasequation); they account for pressure loss due to flow within the fracture (fluid flow equation);they predict fracture dimensions due to fluid pressure by satisfying a fracture propagation criat the fracture tip.
In many cases, the consideration of continuity and elasticity equations provides insight inbasic relationship between directly measured qualities of the fracturing process, such as involume and treating pressure.

2.1 The Continuity Equation

Thecontinuity (or volume balance) equation expresses the relationship:

Volume Pumped = Volume Lost + Volume in Fractureor

(2.1)

It states that the volume pumped into the fracture is equal to the volume lost to the formatifluid loss plus the volume remaining or stored in the fracture. The individual terms (for a conheight fracture, pumped at a constant rate) are defined as follows:

(2.2)

(2.3)

(2.4)

Substituting Eqs. (2.2) - (2.4) into Eq. (2.1) , and solving for the tip to tip length, L, gives

(2.5)

VIN VLOST VFRAC .+=

VIN Qt proportional to total cost( )=

VLOST 3CHp L t proportional to lost cost( )≅

VFRAC wHL (proportional to effectivecost)=

LQt

3CHp t wH+-------------------------------------=

Hydraulic Fracturing Theory Manual2-1July 1993

Fracturing Models2

dth

vari-rear-

time

time)

ation-imilar

whereQ = pump rate in cubic feet per minute (5.6 cu. ft. = 1bbl),t= pump time in minutes,C =

fluid loss coefficient in ft/ ,Hp = permeable fracture height in feet, = average fracture wiin feet, and H = total fracture height in feet.

Eq. (2.5) determines the length which will result for a fracture treatment in terms of the otherables and compares within 10-15% of computer fracture models. Also this equation can be

ranged to form a quadratic equation in terms of . Solving this equation gives the pumping(i.e.,VIN) to obtain a desired fracture length.

Inspection of Eq. (2.5) indicates that increasing any of the terms in the denominator (exceptwill decrease the fracture length. In particular, changing theheight, H, and/orfluid loss coeffi-cient, C, can have dramatic effects on fracture length. Fig. 2.1 shows an example of the relship between fracture height and length for a given treatment volume. Fig. 2.2 shows a srelationship between fluid loss coefficient and length.

Fig. 2.1 - Fracture Height vs. Fracture Length 300,000 Gallon Treatment Design.

min w

t

600

500

400

300

200

100

00 1000 2000 3000

Hei

ght -

Fee

t

Fracture Length - Feet

Hydraulic Fracturing Theory Manual 2-2 July 1993

The Continuity Equation

Fig. 2.2 - Fracture Length vs. Volume Pumped for Low (emulsion) and High (base gels) Fluid LossBehavior.

Low Fluid Loss

High Fluid Loss

PolymerEmulsion

Water & OilBase Gels

150 ft Fracture Height20 BPM

Length

Height2000

1500

1000

500

020 60 100 140 180 220 260

Volume (1000s Gallons)

Fra

ctur

e Le

ngth

(ft)


Fracturing Models2

men-

thel wasdel as

ne-d slitaxis

, andlastic-delwhich

ferentr vol-

rac-

tures

2.2 Model Differences and the Elasticity Equation

Thewidth term, , in Eq. (2.5) , has caused the industry many problems because two fundatally different model assumptionsare used forconstant heightdesigns which give significantlydifferent results. The two models are commonly termed the Perkins and Kern (PK)1 and the Khris-tianovic (K) model.2 The differences in the models result from their different applications oftheory of elasticity to hydraulic fracturing. It should be noted that the Perkins and Kern modelater extended by Nordgren,3 while the Khristianovic model was extended by Geertsma andKlerk.4 As a result, “PK” and “PKN” are used synonymously for the Perkins and Kern mode“K” and “GDK” are for the Kristianovic model.

A classical solution in the theory of elasticity predicts that, for an infinite, elastic slab, in plastrain (i.e., deformation restricted between parallel planes in the slab), with a pressurizethrough the slab, the slit will deform into the shape of an ellipse. The ellipse will have a majorequal to the slit half-length and a minor axis proportional to the pressure and slit lengthinversely proportional to the elastic modulus as seen in the upper portion of Fig. 2.3. This esolution was applied to hydraulic fracturing, but indifferent directionsas seen in the bottom portion of Fig. 2.3. As shown, the ellipse in the PK model is vertical while the ellipse in the K mois horizontal. As a result, a continuing debate has been waged during the last 30 years as tois correct. This debate is more than academic since the two models predict significantly diffluid volumes to achieve a desired fracture length. In this regard, the K model requires greateume per foot of length. Additionally, the K model implicitly assumes free slip between the ftured bed and bounding beds which is physically improbable at depth.

The prevailing thought within Amoco is that the PKN model ismost applicablefor fractures whichare long when compared to their height and that the GDK model is more applicable for frac

Fig. 2.3 - Two Very Different Models.

w

Fracture Pressure and Width

VOLIN = VOLLOST + VOLFRAC W H L

ELASTICITY

TWO MODELS

ELLIPSE

ELLIPSEELLIPSE

P=S+p

L/2L=D

W~D_E

p

“PERKINS & KERN” MODEL “KHRISTIANOVIC” MODEL


Model Differences and the Elasticity Equation

ional

e dif-of are and

; thusictss asngth,

cantlyAlso,th inl was

which are short compared to their height. In this latter scenario, a “penny frac” or a 3 Dimensmodel would be more appropriate.

Fig. 2.4 shows the resulting difference between the PKN and GDK models as a result of thferent application of the elasticity relation. Note that their relationships for viscosity (for flowNewtonian fluid), rate, and rock modulus are the same. However, the relationships for pressuwidth are very different as shown in Table 2.1.

For the general case with length greater than height, the PKN model will predict less widthfrom Eq. (2.5) , the PKN model will generally predict more length. Also, the PKN model predthat thenet pressure(fluid pressure in fracture minus formation closure pressure) increaselength,L, (or time,t,) increases, while the GDK model predicts net pressure decreases with leL, (or time, t,) as shown on Fig. 2.5.

Bottomhole pressure measurements indicate that, if height is relatively constant and signifismaller than fracture length, the pressure will increase as predicted by the PKN model.downhole televiewer pictures obtained by Amoco, which directly measured the fracture widan open hole completion, indicated that the pressure-width relationship of the PKN modemost applicable.

Table 2.1 - Comparison of Perkins and Kern and Khristianovic Models.

Elasticity Fluid Flow (Newtonian)

Perkins and Kern p ~ L1/4

Khristianovic p ~

P&K Model Khrist. Model

I. Elasticity

II. Friction From Fluid Flow(Newtonian)

III. Combining I & II

Fig. 2.4 - Comparison of Perkins and Kern and Khristianovic Models.

W H∼

W L∼1

L1 2/----------

WHE---p∼

Wπ4--W=

W~W~ L_P

p

WµQL

E--------( )

1/4∼ W

µQL2

EH-----------

1/4

∼

pE

3/4

H---------∼ µQL( )1/4

pE

3/4

L1/2

---------∼ µQL( )1/4


Fracturing Models2

rison ofs made

le 2.2.

oughton thel. It ismodelllbore.d with

The consequence of the different width assumptions in the models can be seen by a compaservice company designs based on exactly the same requested input. This comparison waby Amoco in 1980. The input variables supplied to the service companies are shown in Tab

Table 2.3 shows the dramatic variations in the results because of the different schools of thin each company at that time. As shown, the Halliburton and Dowell Programs were basedGDK model, while the Western, Smith and Amoco programs were based on the PKN modenoted that the BJ program set the leakoff height to 200 ft instead of 100 ft and the Westernassumed that the fracture width down the complete length was the maximum value at the weThe large differences in the output indicate the impact of modeling assumptions associate

Fig. 2.5 - “Perkins & Kern” (PKN) Model and “Khristianovic” (GDK) Model. 5

Table 2.2 - Input Values - Service Company Designs.

Input Variables Input Values

Propped Radius 2000 ft

Frac Height 200 ft

Leakoff Height 100 ft

Modulus 6x10 psi

Loss Coefficient 0.001 ft/min

Pump Rate 25 BPM

Viscosity 100 CP

Proppant Concentration 1 lb/ft

Frac gradient, depth, surface and reservoir temperatures, androck type also specified.

p L 1/4∼ p µQ( )1/4∼ p1

L1/2-------∼

log

L

log t (or VOL.)

log

p

log

p

log L log L(TIME )

“PKN”

“GDK”

PKN Model GDK Model


Model Differences and the Elasticity Equation

yourns.

comparing service company bids and highlight the importance of knowledgably designingown treatments. However, many oil companies still rely on the service companies for desig

Table 2.3 - Results - Service Company Designs.

Company Model TypeAverage

Width Inches Sand, M lbVolume,

M gal Pad, M gal

Amoco PKN 0.24 715 250 110

B-J PKN 0.39 800 630 125

Dowell GDK 0.51 1280 420 110

Halliburton GDK 0.69 1150 535 150

Smith PKN 0.29 657 166 36

Western PKN 0.40 1425 400 80


Fracturing Models2

ds,”

rac-

2.3 References

1. Perkins, T. K. Jr. and Kern, L. R.: “Widths of Hydraulic Fractures,”JPT(Sept. 1961) 937-49;Trans., AIME, 222.

2. Khristianovic, S. A. and Zheltov, Y. P.: “Formation of Vertical Fractures by Means of Highly Viscous FluiProc., Fourth World Pet. Cong., Rome (1955)II , 579.

3. Nordgren, R. P.: “Propagation of a Vertical Hydraulic Fracture,”SPEJ(Aug. 1972) 306-14;Trans., AIME, 253.

4. Geertsma, J. and de Klerk, F.: “A Rapid Method of Predicting Width and Extent of Hydraulically Induced Ftures,”JPT (Dec. 1969) 1571-81;Trans., AIME, 246.

5. Nolte, K. G. and Smith, M. B.: “Interpretation of Fracturing Pressures,”JPT (Sept. 1981) 1767-75.


Chapter

Ju

terrela-ervoir

apac-

to-

that

ctiv-

rvoirs.ction

3 Reservoir Analysis

3.1 Reservoir Response To Fracture Stimulation

To understand the reservoir response to fracture stimulations, one must understand the intionship between the important reservoir and fracture variables. These variables include respermeability, fracture conductivity, and fracture half length. The Dimensionless Fracture City, FCD, describes this interrelationship. This equation:

(3.1)

relates the fracture's ability to flow fluids to the wellbore to the reservoir's ability to flow fluidsthe fracture. If, for example,FCD is low (FCD ≤ 1.6) the fracture has finite conductivity and the reservoir fluids would rather flow towards the wellbore than the fracture. It further indicatesincreasing fracture length would not result in improved reservoir response. Conversely, ifFCD ishigh (FCD ≥ 500), the fracture has infinite conductivity. As a result, increasing fracture conduity would not improve reservoir response. For practical purposes, fractures havingFCD > 30 act asinfinite conductivity fractures. The parameters used to defineFCD are illustrated in Fig. 3.1.

Fracture Length

Fracture length or penetration generally has the greatest impact on low permeability reseThe following examples are from the Wattenberg Field, which is operated by Amoco Produ

Fig. 3.1 - Major Factors Affecting Performance.

FCD

kf w

k x f----------=

Fracture Length, x f, feetFormation Permeability, k, mdFracture Flow Capacity, k fw, md-ft

•••

xf

kkf

w

Hydraulic Fracturing Theory Manual3-1ly 1999

Reservoir Analysis3

0.005,-year

ndturedwell,re in

ursure con-rawn.

frac-st dis-

acitythelinescase,nefit

Company. This field is located north of Denver, Colorado, and has a permeability of aboutmd. Fig. 3.2 shows the effect of fracture half-length,xf, on cumulative gas production. As shownincreasing fracture half length results in significant incremental gas recovery over a 25period.

Reservoir Permeability

Reservoir permeability,k, and its effect on fractured well performance is illustrated in Fig. 3.3 aFig. 3.4. Shown in the figures is the pressure distribution map for only one quadrant of a fracwell. The pressure distribution map was obtained from a computer simulation after thelocated in the upper left corner, was produced for a period of time. The simulated fractuFig. 3.3 is located vertically on the left and has a high fracture flow capacity,kfw. The formationpermeability,k, in the computer simulator was very low at 0.005 md (5 micro darcies). Contoof the pressure profile in psi were made and because gas flows perpendicular to these presstour lines, “streamlines” which represent the path by which the gas travels to the well can be dSince the formation permeability is extremely low relative to the fracture flow capacity (kfw), theflow is nearly linear and the fracture acts as an infinite conductivity fracture. As a result, theture carries almost all the total gas flow to the well. The path of least resistance is the shortetance to the fracture.

Fig. 3.4 shows a pressure distribution map for a fractured well with the same fracture flow capas in Fig. 3.3, but this time the formation permeability is significantly higher at 100 md. Sinceformation permeability more nearly approximates the fracture flow capacity, equal pressurebecome circular and the flow is nearly radial as can be seen by converging flow lines. In thisthe fracture carries a relatively small fraction of the total gas flow which indicates that the be

Fig. 3.2 - Effect of Fracture Length Cumulative Gas Produced (25 Years).

ADDITIONAL RECOVERY BYINCREASING FRACTURE LENGTH

RADIAL FLOW

Time (years)

0 2 4 6 8 10 12 14 16 18 20 22 24

200

400

600

800

1000

1200

1400

1600

1800

2000

1500 ft

1000 ft

400 ft

Cum

mul

ativ

e G

as P

rodu

ctio

n -

MM

CF FRACTURE LENGTH


Reservoir Response To Fracture Stimulation

is pri-

rvoir

inturem thefrac-

eby the

archuidAPR.zirco-

realized from the fracture stimulation was minimal. In this case, the path of least resistancemarily via the reservoir.

Fracture Flow Capacity

The key difference in Fig. 3.3 and Fig. 3.4 is the ratio of the fracture flow capacity to the resepermeability,k.

Fracture flow capacity is defined as the product of the permeability in the fracture,kf, and the frac-ture width,w, with dimensions of md-ft. It is also referred to as fracture conductivity. ShownFig. 3.5 are three types of fracture flow capacity. An infinite flow capacity fracture is a fracthat acts similar to a large diameter pipeline where there is essentially no pressure drop frotip of the fracture to the wellbore. A finite flow capacity fracture has a pressure drop along theture that is proportional to the fracture flow capacity,kfw. Nearly all created fractures have finitcapacity. The reservoir response associated with variable conductivity fractures is governedarithmetic average flow capacity.

Estimates ofkfw are available from the service companies and Amoco's Production Rese(APR) Department. The STIM-LAB data in Fig. 3.6 shows the effect of proppant type on liqpermeability. The entire set of Stimlab data can be accessed in the Proppants Manual or fromFig. 3.6 shows that the manufactured proppants bauxite, intermediate density proppant andnia have high permeability up to very high closure stresses.

Fig. 3.3 - Pressure Distribution andApproximate Streamlines, Reservoir K =

0.005 md.

Fig. 3.4 - Pressure Distribution and Approxi-mate Streamlines, Reservoir K = 100 md.

PRESSU

400

psi

600

psi

1000

psi

1200

psi

800

psi

FRACTURE

Streamlines

PressureContour

Lines

1200

psi

Well

Flow is nearly linearFCD > 25 (Inifinite Conductivity)Fracture carries almost the total gasflow to the well

400

psi

800

psi

600

psi

1000

psi

FRACTURE

600

psi

800

psi

1000

psi

1200

psi

400

psi

Flow is nearly radialFCD << 25 (Finite Conductivity)Fracture carries almost no gasto the well

PressureContour

Lines

Streamlines

Well


Reservoir Analysis3

ttawa)er per-moreer (i.e.,lar sand

tee finerpacity

theseebris.

indi-e

rform.3. If

The resin coated sand has intermediate permeability values, and the sands (Brady and Ohave the lowest values at higher stresses. Fig. 3.6 indicates that the “Brady” sand has highmeability for closure pressure less than 5000 psi (i.e., nominally 6000 to 7000 ft) than thepure silica sand of the “Ottawa” type. This results because the Brady sand tends to be coarsmore toward 20 mesh) and more angular. At higher stresses the less pure and more anguhas less permeability (i.e., more crushing).

Fig. 3.7 shows laboratory values of conductivity,kfw for both Brady and Ottawa type sands. Nothat the Ottawa types are not available in the coarser sizes, while Brady is not available for thsizes. Notice that at 4000 psi, the 8/16 Brady sand has about 5 times more conductivity or cathan the commonly used 20/40 Ottawa (i.e., 15,000 vs 2800 md ft).

Post treatment evaluation experience indicates that in-situ capacity is dramatically less thanlaboratory values. This results from gel residues, fluid loss additives and potentially rock dIndicated values are about 1/3 - 1/10 of the lab values. In addition, Amoco's design programcates that propped widths of more than 1 lb/ft2 are difficult to achieve. It is noted that some serviccompanies claim they achieve 4 lb/ft2. Since the laboratory standard (i.e., Fig. 3.7 is 2 lb/ft2); a fur-ther reduction for width must be made. The best method to determine in-situ capacity is to pewell tests in the field and use the bilinear flow analysis techniques discussed in Section 3actualin-situ values are not available, the followingguideline for capacity should be used.

(3.2)

Fig. 3.5 - Fracture Flow Capacity.

(Fracture Perm. x Fracture Width)

INFINITE CAPACITY

FINITE CAPACITY

VARIABLE FINITE CAPACITY

kf

kf

kf1

kf2

expected kf w 0.3k f w lab data

lb/ft2

lab data---------------------------------lb/ft

2expected=



tionctor isctureries

till the

ughtivity

lts aren as

Most lab tests are run at 2 lb/ft2. However, your test data may be different. Proppant concentraat which the tests were run should be available, or the data should not be used. The 0.30 faa permeability reduction applied to the lab data to correct for inherent differences in in-situ fraconditions and idealized laboratory conditions. This is nothing but a “fudge-factor” and vawidely. This correction may be used for scoping studies, but pressure transient testing is spreferred technique to obtain the actual in-situ value ofkfw.

The importance of fracture conductivity and fracture length are illustrated in Fig. 3.8 throFig. 3.10. These figures show the results of simulations which combine variations of conducand length with reservoir permeabilities of 0.005, 0.08, and 5.0 md, respectively. The resushown as the ratio of flow rate after fracturing to that before stimulation. This ratio is know“Folds of Increase,” FOI.

Fig. 3.6 - Effect of Proppant Type on Flow Capacity.


Reservoir Analysis3

Fig. 3.7 - Laboratory Fracture Conductivity for Frac Sands.

Effe

ct o

f Pro

ppan

t Siz

eon

Flo

w C

apac

ity

Cla

ss E

“ot

taw

a” F

rac

San

d

Gal

esvi

lle S

ands

tone

Iront

on/G

ales

ville

San

dsto

neJo

rdan

San

dsto

neS

aint

Pet

er S

ands

tone

Spe

cific

Gra

vity

: 2.6

5 (2

2.1

lb/g

al)

Bul

k D

ensi

ty: 1

.65

g/cm

3 (1

02.7

lb/ft

3)

Pro

ppan

t Con

cent

ratio

n2.

0 lb

/ft2 N

ote:

No

allo

wan

ces

have

bee

n m

ade

for

embe

dmen

t or

any

form

of

pack

dam

age.

AP

I Mes

h S

ize

12/2

0

16/3

0

20/4

0

30/5

0

40/7

0

70/1

40

12JU

L83

RW

A

Clo

sure

Str

ess,

psi

in 1

000’

s2

46

810

12

10 8 6 4 3 2 1.0

0.8

0.6

0.4

0.3

0.2

2030406080100

Fracture Conductivity, klx Wf, darcy x foot, D x ft

10 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 1

“Otta

wa”

San

d

Effe

ct o

f Pro

ppan

t Siz

eon

Flo

w C

paci

ty

Cla

ss D

“br

ady”

Fra

c S

and

Hic

kory

San

dsto

ne12

/20

& 2

0/40

Bid

ahoc

hi F

orm

atio

n6/

12-1

2/20

Aeo

lian

dune

san

d

Spe

cific

Gra

vity

:2.

65 (

22.1

lb/g

al)

Bul

k D

ensi

ty: 1

.61

g/cm

(10

0.5

lb/ft

3A

PI M

esh

Siz

e6/

12

8/16

12/2

0

16/3

0

20/4

0

80 40 30 20 10 8 6 4 3 2 1.0

0.8

0.6

0.4

0.3

0.2

Not

e: N

o al

low

ance

s ha

ve b

een

mad

efo

r em

bedm

ent o

r an

y fo

rm o

fpa

ck d

amag

e.

14JU

L83

RW

A

60Fracture Conducitivty, klx Wf, darcy x foot, D x ft

0 9 8 7 6 5 4 3 2 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 21

Clo

sure

Str

ess,

psi

in 1

000’

s0

24

68

1012

14

“Bra

dy”

San

d

Fracture Conductivity, kl x Wf, darcy x foot, D x ft



city,sed

tys, theher.

al

Fig. 3.8 shows for a formation permeability equal to 0.005 md that as the fracture flow capakfw, is reduced from 1000 md-ft to 1.0 md-ft, the effect of improved flow rate due to increafracture length is diminished. However, the effect becomes significant whenkfw is increased from1 to 10 and 100 md-ft. Beyond akfw = 100 md-ft, the effect of increasing fracture flow capacihas diminishing returns. Fig. 3.9 and Fig. 3.10 show that as formation permeability increaseeffect of improved flow rate due to increasing the fracture length diminishes furt

Fig. 3.9 shows a similar graph where formation permeability,k, is increased to 0.05 md. Noticethat increasing the flow capacity,kfw, above 100 md-ft will still have an effect on improving flowrate. This was not the case whenk was 0.005 md. Also note that for fracture flow capacities equto 10 md-ft or lower, there is little rate improvement as the fracture length increases.

Fig. 3.8 - Formation Permeability Equal to0.005 md.

Fig. 3.9 - Formation Permeability Increasedto 0.05 md.

Fig. 3.10 - Formation Permeability Equal to 5.0 md.

0 200100 300 400 500 600 700 800

K=0.005 MDkfw = 1000 Md-ftkfw = 100 Md-ft

kfw = 10 Md-ft

kfw = 1 Md-ft

12

11

10

9

8

7

6

5

4

3

2

1

Qfr

ac/Q

unfr

ac

Fracture-Half Length

K=0.05 MD

Kfw=1000 Md-ft

Kfw=100 Md-ft

Kfw=10 Md-ft


12

11

10

9

8

7

6

5

4

3

2

1

Qfr

ac/Q

unfr

ac

0 100 200 300 400 500 600 700 800

Kfw=1 Md-ft

Kfw = 1000 Md-ft

Kfw = 100 Md-ftKfw = 10 Md-ft

0 100 200 300 400 500 600 700 800

12

11

10

9

8

7

6

5

4

3

2

1


Qfr

ac/Q

unfr

ac

K=5.0 MD


Reservoir Analysis3

e.

e-ut

tesort,d in

te and

smallere per-

longer.ellip-g. Theation.er onanda 300

or-age ort suf-d rate

t belosersincefer-

tten-

Fig. 3.10 shows a similar plot with formation permeability,k, of 5.0 md. This plot shows thatincreasing fracture length beyond 200 ft in a 5 md reservoir, has little productivity advantag

Fig. 3.10exposes the myththat fractures are only for low permeability wells. As reservoir permability increases, theQfrac/Qunfrac ratio decreases for a given fracture length and conductivity. Bsince for radial flow, the base rate is directly proportional to permeability, the base rate (Qunfrac) isincreasing. Would you invest in a frac for a 5 md well making 10 MMCFD? Fig. 3.10 indicathat a 100 ft, 1000 md-ft frac would make it a 25 MMCFD well. When the importance of shhigh conductivity fractures is better understood, many high permeability wells will be fracturethe future. In general, wells in high permeability reservoirs are the least expensive to stimulaoften provide the greatest incremental benefit.

Fracture Orientation

As a reservoir's permeability decreases, the drainage pattern becomes more elliptical (i.e.,aspect ratio) for an optimum fracture. This results because of two reasons: first, the drainagpendicular to the fracture face decreases, and second, the optimum fracture length isFig. 3.11 shows the effect of fracture orientation on reservoir drainage. This figure shows thetical patterns after 10 and 25 years for Wattenberg reservoir conditions on 320 acre spacinupper portion of Fig. 3.11, shows fractures placed properly with respect to the fracture orientAs shown, there is little interference and relatively complete drainage would occur. Howevthe lower portion of Fig. 3.11, for a azimuth, there is significant overlap of the patternssubstantial areas of the reservoir that will not be drained. Also note that the contours are forpsi drawdown at 10 and 25 years - very far from depletion.

If a similar contour map of the well configuration (unfavorably oriented) shown in the lower ption of Fig. 3.11, was made after 100 years of production, it might show as complete a coverdrainage as the well configuration in the upper portion of Fig. 3.11 has shown in 25 years. Ifices to say that fracture orientation can have a significant affect on both ultimate recovery anacceleration benefits derived from fracturing.

It is obvious that to generally benefit from knowing the orientation, well placement musselected in a manner that differs from normal practices. The required spacing is with wells cin the direction perpendicular to the fracs and farther apart in the direction of the fracs. Alsothe orientation is likely not to be near or , the optimum well placement will be quite difent than normal patterns of subsequent quartering sections. An SPE paper by M. B. Smith1 givesan excellent study of the effect of fracture azimuth, well spacing, and lost production for Waberg.

45°

0° 45°



Fig. 3.11 - Optimum Well Placement vs. Fracture Orientation.

DRAINAGE AREASINITIAL PRESSURE - 2800 PSI FORMATION PERMEABILITY = 0.004 md

DRAINAGE AREASINITIAL PRESSURE - 2800 PSI FORMATION PERMEABILITY = 0.004 md

2500 PSI

10 YEARS

2500 PSI

10 YEARS

25 YEARS

25 YEARS

5280

5280

5280

'52

80


Reservoir Analysis3

hes ae casero-

s per-

rs isuringently

f pro-

-y are

2

h

se thecturebore-

3.2 Steady-State Reservoir Response

The fracturing response for wells in moderate to high permeability reservoirs quickly reacpseudo steady-state condition which can be modeled by radial flow behavior. This is not thfor very low permeability formations which are in transient flow for a significant part of their pductive life. Transient flow will be addressed in Section 3.3.

The pseudo steady-state radial flow for fractures in moderate-to-high permeability reservoirmits modeling by the “effective wellbore” concept. This concept was introduced by Prats2 alongwith the term,FCD, discussed previously (page 3-1).

Effective Wellbore Radius,r'w

This powerful tool indicates that fracturing wells in moderate-to-high permeability reservoiequivalent to increasing the area of the wellbore, i.e., a giant “under-reaming” job. Thus fractin moderate-to-high permeability reservoirs is equivalent to enlarging the wellbore. Consequthe relative benefits of fracturing are the same for heavy or light oils.

Theoretically, for an infinite conductivity fracture, Prats found that

(3.3)

Taking the wellbore analog further and using the steady-state radial flow equation, the ratio oduction after and before fracturing is

(3.4)

whereFOI= folds of increase,qf = postfrac production rate,qo = prefrac production rate,re= exter-nal drainage radius,rw = actual wellbore radius, andr'w = effective wellbore radius. When evaluating the ratio of production in Eq. (3.4), the drawdown pressure, permeability and viscositassumed the same before and after fracturing.

Prats also gave the theoretical relationship betweenr'w and dimensionless flow capacity. Fig. 3.1gives this relationship in terms ofFCD. The figure shows that forFCD > 30, thatr'w = 0.5 xf; i.e.,the fracture acts as an infinitely conductive fracture and there is no benefit from increasingFCD.Fig. 3.12 also shows for smallFCD (i.e., less than 0.3) thatr'w is independent of the fracture lengtand depends only on conductivity.

Studying Fig. 3.12 will reveal where the producer should be spending his money to increaresults of a fracture stimulation. For example, if the reservoir permeability is 10 md, the frahas a conductivity of 1000 md-ft, the fracture half length is 500 ft, wells are 2000 ft apart, andhole diameter is 5.5 in:

r 'w 0.5( ) xf ; FCD large=

qf

qo----- FOI

ln re/rw( )ln re/r 'w( )------------------------= =


Steady-State Reservoir Response

From Fig. 3.12, for anFCD = 0.2,

Therefore,

TheFOI = (ln 1000/0.229(ID of 5.5 in CSG))/(ln 1000/24)

FOI = 7.6/3.73 = 2.04

Assuming that this FOI is not acceptable, will a bigger frac help?

From Fig. 3.12

Therefore,FOI = (ln 1000/0.229)/(ln 1000/24) is the same as before.

Notice that the cost of the fracture stimulation would have more than doubled by going fromxf =500 ft toxf = 1000 ft withNO increase inr'w or FOI.

Suppose, instead of a longer frac, the decision is made to improvekfw. If kfw = 2000 md-ft insteadof 1000 md-ft.

FCD 1000/10 500× .2= =

r 'w/xf .048=

r 'w .048xf .048 500× 24'= = =

xf 1000 ft=

FCD 1000/10 1000× .1= =

r 'w/xf .024 forFCD .1= =

r 'w .024 xf .024 1000× 24 ft .= = =

FOI 2.04=

FCD 2000/10 500× .4= =

r 'w/xf .09=

r 'w .09 xf .09 500× 45= = =

FOIln 1000/0.229( )

ln 1000/45( )--------------------------------------=

7.6/3.1 2.45= =


Reservoir Analysis3

Fig. 3.12 - Effective Wellbore Radius vs. F CD.



view6/30

t-

Notice by doubling conductivity, a productivity increase of 20% has been accomplished. A reof Fig. 3.7 indicates that conductivity could be doubled simply by changing from 20/40 to 1mesh sand.

In summary, forFCD less than 0.5, increasingxf is a total waste of time and investment. The invesment should be made on a higher conductivity proppant.

Another example, ifk = 0.02 md,kfw = 1000 md-ft,xf = 1000 ft,

The decision is made to improve fracture conductivity,kfw from 1000 to 2000.

Notice, greatly improving fracture conductivity,kfw, hadNO effect on increasingFOI.

However, ifxf is doubled to 2000 ft,

r e 2000 ft, rw 0.229 ft= =

FCD 1000/.02 1000× 50= =

r 'w/xf .5=

r 'w .5 xf .5 1000× 500 ft= = =

FOIln 2000/0.229( )ln 2000/500( )

--------------------------------------=

8.294/1.386=

FOI 5.98=

FCD 2000/.02 1000× 100= =

r 'w/xf .5=

FOIln 2000/0.229( )ln 2000/500( )

-------------------------------------- which is the same as before=

5.98=

FCD 1000/.02 2000× 25= =

r 'w/xf .48=

r 'w .48 xf .48 2000× 960 ft= = =


Reservoir Analysis3

is

ssed in

ines the

ation

,

ure

It is evident from the above, that ifFCD is greater than 25 to 30, improving fracture conductivitynot helpful. The investment should be made to achieve more fracture length to increaseFOI, if theincreased production offsets the increased cost of the treatment (i.e., economics, addreChap. 9). WhenFCD's are between 0.5 and 25,FOI will experience an increase ifxf or kfw isincreased. Therefore whenFCD's fall in the range of 0.5 to 25, economics must be used to determwhether improving conductivity or creating longer fractures, or some combination of both, imost cost effective (i.e., profitable).

A Direct Way Of Finding FOI

In using theFOI technique just shown,xf must be determined by trial and error for a design. This, once aFOI is selected, ar'w can be calculated that will be required to effect a given productincrease. However, since for finite conductivity fractures,xf affects bothr'w andFCD, the xf isrequired to yield the desiredFOI.

Fig. 3.13 shows a modified version of Fig. 3.12 which includes the conversion of

on the left vertical axis. On the right vertical axis are variousxf /re curves. The horizontal axis iskfw/kre. This parameter should be known for specific proppant size and concentration (i.e.kfw)since thek andre should be known. Also fromxf /re on Fig. 3.13,xf can then be determined fromthe knownre.

Fig. 3.14 shows the use of Fig. 3.13 for a case with a desiredFOI = 5 (denoted by “a”), 160 acrespacing (denoted by “b”), a horizontal line (denoted by “c”), the value ofkfw/kre = 1.1 (denotedby “d”), the intersection (denoted by “e”), and finally the indicatedxf /re of 0.75 (denoted by “f”)to achieve theFOI.

Fig. 3.13 can also be used in reverse; i.e., find theFOI for a given xf /re.

Another example, the objective is anFOI = 4, well spacing is 640 acres (re = 2640),k is 0.1 mdand the proppant selected will have akfw of 1320 md-ft at the proposed concentration and closstress. This giveskfw/kre = 5

FOIln 2000/0.229( )ln 2000/960( )

--------------------------------------=

8.294/.734=

FOI 11.3=

FOIln re/rw( )ln re/r 'w( )

-------------------------=



c-the

tors:andwellsctureeco-

acture

toeports

valid.

res-s than

ration.

Enter Fig. 3.13 from the left vertical axis withFOI. Find the intersection forFOI of 4 and the wellspacing of 640 acres. This determinesr'w/re. A horizontal line should be drawn from the intersetion of theFOI and the spacing line, completely across the graph. Then enter Fig. 3.13 frombottom withkfw/kre of 5. Draw a vertical line up to intersect ther'w /re line. A curved line shouldbe drawn to the right vertical axis from the intersection ofkfw/kre andr'w/re parallel to thexf /relines,xf/re is then determined to be 0.2.

Therefore,

Notice, that by varyingkfw on the horizontal axis,xf /re and thereforexf will change.

Studying this graph will also show quickly where to invest time, effort and money. When thexf /recurves become horizontal, increasingkfw will not result in an increase inFOI. Also, whenkfw/kreis very small, increasingxf has a minimal effect onFOI.

Optimizing Fractures for Secondary Recovery

When designing any fracture stimulation, engineers must consider two primary fac(1) designing the treatment to yield the highest productivity or injectivity per dollar cost,(2) designing the treatment to minimize any loss in reserves. For moderate permeabilityunder primary recovery, fracture length should be optimized to reservoir permeability and fraconductivity. For reservoirs under secondary recovery, the fracture length must not only benomically optimized as above, but other factors such as the impact of fracture length and frorientation upon recovery must be addressed.

Two research reports by L. K. Britt,3,4 have been published which provide significant insight inthe importance of length and fracture orientation on secondary recovery projects.These rdrew several conclusions that are pertinent to fracture stimulation design in waterfloods:

1. The older potentiometric reservoir response models, such as McGuire and Sikora are in

2. Prats' “effective wellbore radius” concept (Fig. 3.12), whereby the effect of a fracture uponervoir response is modeled as an increased wellbore radius, is valid if frac lengths are les25% of the interwell distance.

3. Short fractures cause no loss in reserves, and can contribute significantly to rate accele

What frac radius will be required to achieve this FOI?

xf /r e 0.2=

xf 0.2 r e( ) 0.2 2640 ft( )= =

xf 528 ft=


Reservoir Analysis3

Fig. 3.13 - Folds of Increase vs. Relative Conductivity.



Fig. 3.14 - Folds of Increase vs. Relative Conductivity.


Reservoir Analysis3

r mayucer)

1-50

data.

odelRuns

lboremodel

a frac-five-

tures

e basisthat

4. Fracture length (radius) greater than 25% of the distance between injector and producereduce reservoir recovery when the fracture orientation is unfavorable (injector or prodand improve recovery when the fracture orientation is favorable (injector to injector).

5. The economically optimum fracture stimulation for moderate permeability reservoirs (md) is short, with very high conductivity.

6. In-situ fracture proppant conductivity is on the order of 10-30% of published laboratory

To verify that Prats' results were correct using Amoco's reservoir simulators, the Coning mwas used to simulate primary recovery from a fractured moderate-permeability reservoir.were made comparing productivity by combining a radial model using Prats' effective welradius to simulate the effect of the fracture, and an areal gridded model using the Coningwith actual fracture parameters. The results were found to be nearly identical.

This comparison was further evaluated for secondary recovery by using a model to compareture simulated in a radial mode using Prats' effective wellbore radius to an areal model for aspot waterflood pattern with both injectors and producers stimulated with identical frac(Fig. 3.15).

Increasing the fracture length on the gridded model provides the “correct” answer used as thfor the evaluation. Increasing the effective wellbore radius in the radial model to compare to

Fig. 3.15 - Validation of the Effective Wellbore Radius Concept.

FRACTURE VS. EFF. WELL RADIUSFIVE SPOT PATTERN DEVELOPMENT

XFP/XFI EQUALS 1

PERCENT ERROR IN WATER/OILRATIO EVALUATED AT THEECONOMIC LIMIT OF 2 BDPD

0 0.2 0.4 0.6 0.8 1

100

80

60

40

20

0

FRACTURE HALF LENGTH/INTERWELL DISTANCE

PE

RC

EN

T E

RR

OR

(%

)



s 25%t.

abilityoveryta isline

recov-th ofif thethat-

wes mustry duemaxi-

oir, thefavor-

tab-ouldd, and

in the areal model introduces about 10% error when the fracture length for each well reacheof the interwell distance, implying that Prats' radial flow curves are in error beyond this poin

The effect of fracture length on recovery was also evaluated for a five-spot moderate permewaterflood pattern. Fig. 3.16 shows the results of increasing fracture length on recovery. Recis relatively unaffected for fracture lengths up to about 25% of the interwell distance. This dafor the most unfavorable fracture orientation, where the producing well fracture is directly inwith the injection well fracture.

It should be noted that even though recovery is about the same for short fractures, the rate ofery can be significantly different. For moderate permeability, and a maximum fracture leng25% of the interwell distance, 2 HCPV of water could be injected 20-30 years sooner thanwell were unfractured, significantly increasing the economic viability of the project. Note alsoresults of a study conducted by Connie Bargas5 indicate that unfavorable mobility recovery processes (i.e., CO2 floods) are even more sensitive to fracture length and orientation.

When fracture stimulation is used to work over wells to restore lost injectivity or productivity,must ensure that the two goals stated at the beginning of this section are met. That is, fracturebe designed to yield the maximum rate of return on investment, and must not reduce recoveto excessive length. In most cases, the economically optimum length will be less than themum to affect recovery.

To assure that secondary recovery is not affected by the placement of fractures in the reservdesign fracture radius should not exceed the maximums shown in Table 3.1 unless wells areably oriented.

In any situation where the potential to infill drill a field is high, some guidelines must be eslished for the tightest well spacing that might be drilled. The maximum design frac length shnot be allowed to exceed 25% of that interwell distance. Once a hydraulic fracture is create

Fig. 3.16 - Loss in Secondary Recovery vs. FRAC Radius.

0 10 20 30 40 50

50

40

30

20

10

0

FRAC RADIUS/INTERWELL DISTANCE, %

PE

RC

EN

T L

OS

S IN

RE

CO

VE

RY


Reservoir Analysis3

t frac
conductivity established either by proppant or by acidizing, we obviously cannot reduce thalength.
Table 3.1 - Maximum Design Fracture Radius.

Well Spacing Frac Half-Length

10 ac 165 ft

20 ac 233 ft

40 ac 330 ft

80 ac 466 ft

160 ac 660 ft



on-

Class Problem

Find: xf

Given: k = 1 md, 160 acre spacing, Depth = 6000 ft (normal grad.),re = 1320 ft

Find: xf for 20-40, 12-20, 6-12 Brady sand to obtain 5-fold increase in production over ndamaged or stimulated wellbore.

Solution: kre = 1 x 1320 = 1320 md-ftUse capacity guidelines (1 lb/ft) @ 6000 ft = 4000 psi

kfw - 20-40 500 md-ft [Fig. 3.7 and Eq. (3.2)]

12-20 ____________8-16 ____________

What is the optimum proppant size, and why?

Explain:

Mesh kfw' kfw/kr e re/r‘w xf/re xf

20-40 500

12-20

8-16


Reservoir Analysis3

an be

frac-

sandnot beppedy

uction

Acid Fracturing

Fracturing with acid in carbonates creates a highly-conductive, etched fracture. Fig. 3.13 cused for predicting performance of an acid fracturing treatment by assumingFCD = (i.e., infinite)or effectively greater than 30. The line shown on Fig. 3.17 represents an infinite conductivityture (FCD > 30), and is equivalent to the vertical line for a specifickfw/kre for a propped fracture(i.e., line “d” on Fig. 3.14). Equivalently for a givenxf /re or FOI a horizontal line can be drawndirectly across Fig. 3.17 to determine the relationship betweenFOI andxf /re.

Many carbonate wells are initially acidized and later fractured with proppant. This causes aproduction problem after the fracture treatment because any sand in an acid channel willtrapped and is eventually washed into the wellbore by production fluids. Therefore, if a profracture would give a largerFOI, it would be desirable to conduct this fracture initially, therebsaving the cost of an acid treatment, obtaining more production, and reducing sand prodproblems.

For 40 acre spacing, maximum acid xf = 150 ft, maximum kfw = 1300 md-ft forproppant, find if an acid frac or propped frac appears more optimum for k = 1 mdand k = 5 md.

∞



Fig. 3.17 - Use of FOI Curves for Acid Fractures.


Reservoir Analysis3

timedius)le for

seudoline,nt type

prove--te ift forpor-

ityside

3.3 Transient Reservoir Response

The fracturing response for low permeability reservoirs can exhibit a substantial period ofduring which steady-state conditions (i.e., a constant folds of increase or effective wellbore rado not hold. Steady-state conditions, as discussed in Section 3.2, first become applicabdimensionless time of about 3, as shown on Fig. 3.18 by the indication of the start of i.e., pradial flow (i.e., semilog straight line). For the period prior to the start of the semilog straightthe reservoir response must be analyzed using transient conditions such as an aerial extecurve, as shown in Fig. 3.18, or a reservoir simulator such as Amoco’s GAS3D.

Fig. 3.18 also shows thatfracture conductivityis even more important for transientflow thanpseudo steady-state flow. For the steady-state case of Prats (Fig. 3.12), there was little imment forFCD greater than 10; however, Fig. 3.18 shows that fortDf < 0.1, there is a dramatic reduction in qD (approximately proportional to the inverse of flow rate), or a dramatic increase in ra

is increased from 1.004 to 1.234. This approximate doubling of flow rate is very significanfractures in very low permeability reservoirs which can stay in transient flow for a substantialtion of their productive life.

The dimensionless time (tDf) on Fig. 3.18 is proportional tok/xf2. Therefore, low permeability res-

ervoirs which require large xf's tend to fall on the left side of Fig. 3.18, while higher permeabilreservoirs which require only short, but highly conductive fractures, tend to fall on the rightwhere the much simpler steady-state analyses are applicable.

aa

Fig. 3.18 - Production Decline Analysis.

Transient Flow Pseudo Radial Flow

η

Infinite Conductivity

Unstimulated

η defines the degreeof stimulation


Transient Reservoir Response

d thethe:luere,

ion oft onif the

low)eilin-esresult

lls,

thaton-ponseurse

frac-the

Fig. 3.18 also shows finite capacity fracture behavior (i.e.,η ≥ 1.045≤ 1.234). In finite capacityfractures, bilinear flow can occur. During bilinear flow, the pressure transient has not reachetip of the fracture; both linear flow from the reservoir to the fracture and linear flow downlength of the fracture are occurring. Thebilinear flow region, is very important for two reasons(1) unique fracture length cannot be foundfrom the production response, and (2) the actual vaof conductivity in-situ, kfw can be determined. The log-log curves, either constant rate or pressuhave a 1/4 slope for bilinear flow.

Fig. 3.19 shows a plot of pressure change vs. the fourth root of time for fractures with an FCD ofgreater than 1.6, equal to 1.6, and less than 1.6, respectively. In addition, the lower portFig. 3.19 shows the effect of damage on the fourth root of time behavior. The upper ploFig. 3.19 shows that a straight line should result on a pressure change vs. fourth root of timefracture is in bilinear flow. It also shows how the data deviates from the straight line (bilinear fis a qualitative indicator ofFCD. If, for example, the data deviates up from the bilinear flow linthis indicates thatFCD is greater than 1.6. Conversely, if the data deviates downward from the bear flow line theFCD < 1.6. The lower plot on Fig. 3.19 indicates that if the bilinear flow line donot go through the origin, the entrance to the fracture is damaged. This loss of production canfrom:

• inadequate perforations - reperforate and/or redesign perforations on subsequent we

• turbulent flow - increase proppant size/concentration,

• over displacement of proppant - do not overflush,

• kill fluid was dumped into the fracture - let fracture “clean up” before conducting test.

Fig. 3.20 shows an example of these plots and the indicated kfw.

The data in Fig. 3.20 deviates downward from the bilinear flow line qualitatively indicatingtheFCD is less than 1.6. SinceFCD is low, efforts should be made to either increase fracture cductivity, reduce fracture length, or both. A more complete presentation of the transient resof fractured wells is included in the Pressure Transient Analysis manual from the PTA cogiven by the Training Center. Because of the importance of bilinear flow in the analysis oftured reservoirs and the improvement of treatment design, the section on bilinear flow fromPTA course is included in this chapter for ease of reference.


Reservoir Analysis3

Fig. 3.19 - Bilinear Flow on Fourth Root of Time Plot.

Fig. 3.20 - Example of Bilinear Flow Analysis.

FCD > 1.6

END OFBILINEAR FLOW

SLOPE = mbf

∆p, p

si FCD < 1.6

t1/4, hours 1/4

BILINEAR

DAMAGE ORCHOKED FRACTURE

IDEAL

t1/4, hours 1/4

∆ps

00

∆p, p

si

Mbf = 134Kfw = 1168/RcD = 1320 mdft

BILINEAR FLOW ANALYSISNORTH COWDEN UNIT WELL - A

Downward DeviationFrom Bilinear FlowLine indicates FCD isless than 1.6

AMERADA BOMB


Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)

tical

dpan-the

re-e lin-

-the

dur-dur-, it

docu-

ions

nt

al-

3.4 Bilinear Flow - Liquid Reservoirs (Reproduction of PTA Course Material)

Flow Periods For A Vertically Fractured Well

Fig. 3.21 depicts the various flow periods which are associated with finite conductivity verfractures.

Fracture Linear Flow

The “Fracture Linear Flow”, (a) on Fig. 3.21, is the first flow period which occurs in a fracturesystem. Most of the fluid which enters the wellbore during this period of time is a result of exsion within the fracture, i.e., there is negligible fluid coming from the formation. Flow withinfracture during this time period is linear.

Equations which can be used to predict the following formation face pressure,pwf, during fracture

linear flow are presented by Cinco-Ley et al.,6 for the constant rate case. This reference also psents an equation which predicts the time when this flow period ends. Unfortunately, fracturear flow occurs at a time which is too early to be of practical use in well test analysis.

Bilinear Flow

The next flow period to occur is called “Bilinear Flow,” (b) on Fig. 3.21, because two types of linear flow simultaneously occur. One flow is linear incompressible flow within the fracture andother is linear compressible flow in the formation. Most of the fluid which enters the wellboreing this flow period comes from the formation. Fracture tip effects do not affect well behavioring bilinear flow; accordingly, unless a well test is run sufficiently long for bilinear flow to endwill not be possible to determine fracture length from the data.

Bilinear flow was first recognized by Cinco-Ley et al.6 Since its introduction into literature, theuse of bilinear flow analysis to characterize both formation and fracture properties has been

mented.7-11 The details of analyzing bilinear flow data will be detailed in subsequent discussbeginning on page 3-35.

Formation Linear Flow

The analysis of “Formation Linear Flow”, (c) on Fig. 3.21, is covered in the Pressure TransieAnalysis course manual.

Pseudo-Radial Flow

The analysis of “Pseudo-Radial Flow”, (d) on Fig. 3.21, is covered in the Pressure Transient Anysis course manual.


Reservoir Analysis3

Bilinear Flow Equations

Constant Formation Face Rate

Dimensionless Pressure:

(3.5)

Dimensionless Time:

(3.6)

Dimensionless Fracture Conductivity:

(3.7)

Fig. 3.21 - Flow Periods for a Vertically Fractured Well.

WELL

FRACTURE

FRACTUREWELL

(a) FRACTURE LINEAR FLOW (b) BILINEAR FLOW

(c) FORMATION LINEAR FLOW (d) PSEUDO-RADIAL FLOW

FRACTUREFRACTURE

WELL

PD

kh pi pwf–( )141.2qBµ

------------------------------- oil( ) PDkh∆m p( )1424Tq

----------------------- gas( )= =

tDxf0.0002637kt

φµctxf2

------------------------------=

FCD

kf w

kxf---------=



tests.differ-

Bilinear Flow Equation:

(3.8)

(3.9)

Bilinear Slope (graph ofpi-pwf vs. t1/4):

(3.10)

Constant Formation Face Pressure

Dimensionless Rate:

(3.11)


(3.12)

(3.13)

Bilinear Slope (graph 1/q of vs.t1/4):

(3.14)

Note: The equations presented in this section are written specifically for pressure drawdownThese equations can be modified for pressure buildup tests by replacing the pressure

PD

2.45 tDxf

1 4/

FCD1\/2

----------------------=

pi pwf–44.1qBµ

h kf w( )1/2 φµctk( )1/4------------------------------------------------------- t

1/4=

mbf494qT

h kf w( )1/2kφµct( )1/4

--------------------------------------------------=

qD141.2qBµ

kh pi pwf–( )------------------------------- (oil) qD

1424Tqkh∆m p( )----------------------- (gas)= =

1qD------

2.72 tDxf

1/4

FCD1/2

------------------------=

1q--- 48.9Bµ

pi pwf–( )h kf w( )1/2 φµctk( )1/4--------------------------------------------------------------------------- t

1/4oil( )= =

1q--- 494T

h kf w( )1/2kφµct( )1/4 ∆m p( )

--------------------------------------------------------------------- t1/4

(gas)= =

mbf48.9Bµ

pi pwf–( )h kf w( )1/2 φµctk( )1/4--------------------------------------------------------------------------- (oil)=

mbf494T

h kfw( )1/2kφµct( )1/4 ∆m p( )

------------------------------------------------------------------- (gas)=


Reservoir Analysis3

l-

ace is

nds,ard

d.

or. If

thisuring

ential , and the producing time,t, with appropriate values as shown in the folowing table:

Bilinear Flow Graphs


When the rate of a well is maintained constant, the pressure change at the formation fdescribed by Eq. (3.9). This equation indicates that a plot ofpi-pwf (pws-pwf) for buildup tests) vs.

t1/4 (∆t1/4 for buildup tests) will yield a straight line with slope,mbf, predicted by Eq. (3.10). Theplot of pressure change vs. fourth root of time is illustrated by Fig. 3.22. When bilinear flow ethe straight line will end and the plot will exhibit curvature which is concave upward or downwdepending upon the value of the dimensionless fracture conductivity,FCD. WhenFCD ≤ 1.6, thecurve will be concave downward; a value ofFCD > 1.6 will cause the curve to be concave upwar

WhenFCD > 1.6, bilinear flow ends because the fracture tip begins to affect wellbore behavia pressure transient test is not run sufficiently long for bilinear flow to end whenFCD> 1.6, it is notpossible to determine the length of the fracture. WhenFCD ≤ 1.6, bilinear flow in the reservoirchanges from predominately one-dimensional (linear) to a two-dimensional flow regime. Incase, it is not possible to uniquely determine fracture length even if bilinear flow does end dthe test.

Test Differential Time

Drawdown ∆p = pi-pwf t

Buildup ∆p = pws-pwf ∆t or ∆te

Fig. 3.22 - Bilinear Flow Graph for a Constant Rate Well.

∆p pi pwf–=

FCD > 1.6

END OFBILINEAR FLOW

SLOPE = mbf

t1/4, hours 1/4

∆p, p

si FCD < 1.6



rom

me as

the

ons as

f

rec-

A more diagnostic plot to recognize the occurrence of bilinear flow is the log-log plot. FEq. (3.9),

(3.15)

Eq. (3.15) indicates that a log-log plot ofpi-pwf vs. t will yield a straight line with a one-fourthslope; this is illustrated by Fig. 3.23.


When formation face pressure remains constant, the formation face rate will change with tidescribed by Eq. (3.13). According to Eq. (3.13), a plot of1/q vs. t1/4 should yield a straight linewith slope,mbf, defined by Eq. (3.14) this plot is depicted by Fig. 3.24. Following the end of

bilinear flow period, the curve for will be concave downward and the curve forFCD >2.8 will be concave upward. The straight line caused by bilinear flow ends for the same reasdescribed for the constant rate case.

Eq. (3.13) also indicates that a log-log plot of1/q vs. t should yield a straight line with a slope oone-fourth:

(3.16)

The plot illustrated by Fig. 3.25, is the primary diagnostic tool by which bilinear flow can beognized.

Fig. 3.23 - Log-log Plot Illustrating the Effect of Ideal Bilinear Flow for the Constant Rate Case.

pi pwf–( )log44.1qBµ

h kf w( )1/2 φµctk( )1/4-------------------------------------------------- 1

4--- t .log+log=

SLOPE = 1/4

t, hours

∆p, p

si

FCD 2.8≤

1q---

log48.9Bµ

pi pwf–( )h kf w( )1/2 φµctk( )1/4--------------------------------------------------------------------------- 1

4--- t .log+log=


Reservoir Analysis3

Fig. 3.24 - Bilinear Flow Graph for a Constant Pressure Well.

Fig. 3.25 - Log-log Plot Showing Effect of Ideal Bilinear Flow for the Constant Rate Case.

FCD > 2.8

END OFBILINEAR FLOW

SLOPE = mbf

t1/4, hours 1/4

Dp,

psi FCD < 2.81/q

SLOPE = 1/4

t, hours

Dp,

psi1/q



ip

ip

End of Bilinear Flow


The relationship between(tDxf)ebf andFCD is depicted graphically by Fig. 3.26. This relationshcan be approximated as:

(3.17)

(3.18)

(3.19)

For the case whereFCD ≥ 3, the dimensionless pressure at the end of bilinear flow is

(3.20)

Therefore,

(3.21)

and,

(3.22)


The relationship between (tDxf)ebf andFCD is presented graphically by Fig. 3.27. This relationshcan be approximated by the following equations:

(3.23)

2 < FCD < 5: See Fig. 3.27

(3.24)

For the case whereFCD ≥ 5,

FCD 3: tDxf( )ebf0.1

FCD2

----------≅≥

1.6 FCD 3: tDxf( )ebf 0.0205 FCD 1.5–( ) 1.53–≅< <

FCD 1.6: tDxf( )ebf4.55

FCD

-------------- 2.5– 4–

≅≤

pD( )ebf1.38FCD---------- .=

FCD1.38pD( )ebf

------------------=

FCD194.9qBµ

kh pi pwf–( )ebf

------------------------------------- .=

FCD 5: tDxf( )ebf≥ 6.94 102–×

FCD2

---------------------------=

0.5 FCD 2: tDxf( )ebf≤ ≤ 1.58 103–FCD

1.6×=


Reservoir Analysis3

(3.25)

Therefore,

(3.26)

and,

(3.27)

Fig. 3.26 - Dimensionless Time for the End of the Bilinear Flow Period vs. Dimensionless FractureConductivity, Constant Rate Case. 6

10-1 1 101 102

1

10-1

10-2

10-3

10-4

10-5

FCD

(tD

xf)

ebf

1qD( )ebf

------------------1.40FCD---------- .=

FCD 1.40 qD( )ebf=

FCD

197.7qebf Bµkh pi pwf–( )--------------------------------- .=



riatevs.

and

e

r

Analysis of Bilinear Flow Data

The conventional analysis of bilinear flow data requires two plots - a log-log plot of the approprate or pressure function vs.t, and a cartesian plot of the appropriate rate or pressure functiont1/4.

Liquid-Constant Rate

The following procedure can be used to analyze bilinear flow data for fracture conductivityfracture length when the production rate is constant:

1. Make a log-log plot of(pi-pwf) vs. equivalent producing time,tp.

2. Determine if any data fall on a straight line of quarter slope.

3. If any data form a quarter slope in Step 2, plotpi-pwf vs. t1/4 on cartesian paper and identify thdata which form the bilinear flow straight line.

4. Determine the slope,mbf, of the bilinear flow straight line.

5. Using the slope,mbf, from Step 4, compute the fracture conductivity,kfw, using Eq. (3.10):

(3.28)

It should be noted that this calculation can only be made ifk is known from a prefrac test.

6. If the bilinear flow straight line ends and the data riseabovethe straight line, determine thevalue of∆p, i.e.,∆pebf, at which the line ends. Then, from Eq. (3.24),FCD can be computed as

(3.24)

with FCD known, the fracture length can be computed using Eq. (3.7):

(3.29)

It should be noted that Eq. (3.24) assumesFCD ≥ 3. If enough data is available beyond bilineaflow, a type curve match should be attempted to verify that this is true.

k f w44.1qBµ

mbf h φµctk( )1/4--------------------------------------

2

.=

FCD194.9qBµ

kh pi pwf–( )ebf

------------------------------------- .=

xf

k f w

kFCD------------- .=


Reservoir Analysis3

e used

e

Liquid-Constant Pressure

When formation face pressure remains constant during a test, the following procedure can bto analyze the bilinear flow data for fracture conductivity and fracture length:

1. Make a log-log plot of1/q vs. t.


3. If any data in Step 2 form a quarter slope, plot1/qvs. t1/4 on cartesian paper and determine thslope,mbf, of the bilinear flow straight line.

4. Using the slope,mbf, from Step 3, compute the fracture conductivity,kfw, using Eq. (3.14)

Fig. 3.27 - Dimensionless Time to the End of Bilinear Flow for Constant Pressure Production. 9

FCD = 5

10-1

10-2

10-3

10-4

10-510-1 10-21 2.8 10

(tD

xf)e

bf

FCD



, a

ccursn bysian.

extra

e an

(3.30)

5. If the bilinear flow line ends and the data riseabovethe straight line, determine the value ofqwhere the line ends, i.e.,qebf. Then, from Eq. (3.27),FCD can be computed as

(3.27)

With FCD known, the fracture length can be computed using Eq. (3.24):

(3.29)

Eq. (3.27) assumesFCD ≥ 5 ;accordingly, if enough data are available beyond bilinear flowtype curve match should be attempted to verify that this is true.

Effect of Flow Restrictions

When a flow restriction exists in the formation adjacent to the fracture, or when a restriction oin the fracture near the wellbore, the ideal bilinear flow behavior discussed previously, showFig. 3.22 and Fig. 3.24 will be altered. Ideal bilinear flow results in a straight line on a carteplot of ∆p (constant rate) or1/q(constant pressure) vs.t; further, this line passes through the originBilinear flow still exists when a flow restriction is present; however, the restriction causes anpressure drop,∆ps, in the system. This additional pressure loss does not alter the slope,mbf, of thebilinear flow straight line; instead, rather than passing through the origin, the line will havintercept equal to∆ps for the constant rate case. This behavior is depicted by Fig. 3.28.

Fig. 3.28 - Effect of a Flow Restriction on Bilinear Flow, Constant Rate Case.

k f w48.9Bµ

mbf pi pwf–( )h φµcth( )1/4---------------------------------------------------------------

2

.=

FCD

197.7qebfBµkh pi pwf–( )------------------------------- .=

xf

k f w

k FCD--------------- .=


IDEAL

t1/4, hours 1/4

∆ps

00

∆p, p

si

{


Reservoir Analysis3

flowcase.

d on

ng

of the

A log-log plot of∆p (constant rate) or1/q (constant pressure) vs.t will exhibit a straight line withquarter slope for ideal bilinear flow. The slope of this line will be altered, however, when arestriction is present. This non-ideal behavior is depicted by Fig. 3.25 for the constant rate

Effect of Wellbore Storage

Wellbore storage will alter or completely mask the bilinear flow straight lines ideally expectethe cartesian and log-log plots of∆p or 1/q vs. t1/4 and∆p or 1/q vs. time, respectively. Fig. 3.30depicts the effect of storage on a plot of∆p vs. t1/4 for the constant rate case. The correspondi

effect of storage on the log-log plot is shown in Fig. 3.31. It has been reported by Cinco-Leyet al.,6

that the end of wellbore storage effects occurs approximately three log cycles after the endunit slope line.

Fig. 3.29 - Effect of a Flow Restriction on the Log-log Plot for the Constant Rate Case.


SLOPE = 1/4

t, hrs

∆p, p

si



Fig. 3.30 - Effect of Wellbore Storage on a Plot of ∆p vs. t 1/4 for the Constant Rate Case.

Fig. 3.31 - Effect of Wellbore Storage on the Log-log Plot for the Constant Rate Case.

∆p, p

si IDEAL BILINEARFLOW

EFFECT OFWELLBORE STORAGE

t, hrs

∆p, p

si

t, hrs

SLOPE = 1/4

UNIT SLOPE

= 3 LOG CYCLES


Reservoir Analysis3

3.5 Bilinear Flow - Gas Reservoirs

Bilinear Flow Equations


Dimensionless Pressure:

(3.31)

Dimensionless Time:

(3.6)

Dimensionless Fracture Conductivity:

(3.7)


(3.8)

(3.32)

Bilinear Slope (graph of∆m(p) vs. t1/4):

(3.33)


Dimensionless Rate:

(3.34)

PD

kh m pi( ) m pwf( )–[ ]1424qT

--------------------------------------------------=

tDxf0.0002637kt

φµctxf2

------------------------------=

FCD

kf w

kxf---------=

PD

2.45 tDxf

1 4/

FCD1\/2

----------------------=

m pi( ) m pwf( )–444.6qT

h kf w( )1/2 φµctk( )1/4-------------------------------------------------- t

1/4=

mbf444.6qT

h kf w( )1/2 φµctk( )1/4--------------------------------------------------=

qD1424qT

kh m pi( ) m pwf( )–[ ]--------------------------------------------------=


Bilinear Flow - Gas Reservoirs

downg the

face is

nds,ard

d .

or. If

thisuring


(3.12)

(3.35)

Bilinear Slope (graph of1/q vs. t1/4):

(3.36)

NOTE: The equations presented in this section are written specifically for pressure drawtests. These equations can be modified for pressure buildup tests by replacinpseudopressure differential,∆m(p), and the producing time,t, with appropriate values asshown in the following table:

Bilinear Flow Graphs


When the rate of a gas well is maintained constant, the pressure change at the formationdescribed by Eq. (3.32). This equation indicates that a plot ofm(pi)-m(pwf) vs. t1/4 for drawdowntests, orm(pws)-m(pwf) for buildup tests, will yield a straight line with slope,mbf, predicted byEq. (3.33). This plot described by Eq. (3.32) is illustrated by Fig. 3.24. When bilinear flow ethe straight line will end and the data will exhibit curvature which is concave upward or downwdepending upon the value of the dimensionless fracture conductivity,FCD. WhenFCD ≤ 1.6, thecurve will be concave downward, a value ofFCD > 1.6 will cause the curve to be concave upwar

WhenFCD > 1.6, bilinear flow ends because the fracture tip begins to affect wellbore behavia pressure transient test is not run sufficiently long for bilinear flow to end whenFCD > 1.6, it isnot possible to determine the length of the fracture. WhenFCD ≤ 1.6, bilinear flow in the reservoirchanges from predominately one-dimensional (linear) to a two-dimensional flow regime. Incase, it is not possible to uniquely determine fracture length even if bilinear flow does end dthe test.

A more diagnostic plot to recognize bilinear flow is the log-log plot. From Eq. (3.32)

Test Pseudopressure Differential Time

Drawdown ∆m(p) = m (pi)-m(pwf) t

Buildup ∆m(p) = m(pws)-mp(pwf) ∆t or ∆te

1qD------

2.72 tDxf

1/4

FCD1/2

------------------------=

1q---

493.6T

h kf w( )1/2 φµctk( )1/4m pi( ) m pwf( )–[ ]

---------------------------------------------------------------------------------------------- t1/4

=

mbf493.6T

h kf w( )1/2 φµctk( )1/4m pi( ) m pwf( )–[ ]

----------------------------------------------------------------------------------------------=


Reservoir Analysis3

me as

the

ed for

c tool

(3.37)

Eq. (3.37) indicates that a log-log plot ofm(pi)-m(pwf) vs. t will yield a straight line with a one-fourth slope; this is illustrated by Fig. 3.35.


When formation face pressure remains constant, the formation face rate will change with tidescribed by Eq. (3.35). According to Eq. (3.35), a plot of1/q vs. t1/4 should yield a straight linewith slope,mbf, defined by Eq. (3.36) this graph is depicted by Fig. 3.24. Following the end ofbilinear flow period, the curve forFCD ≤ 2.8 will be concave downward and the curve forFCD > 2.8will be concave upward. The straight line for bilinear flow ends for the same reasons presentthe constant rate case on page 3-41. Eq. (3.35) also indicates that a log-log plot of1/qvs. t shouldyield a straight line with a slope of one-fourth:

(3.38)

The log-log plot of pressure change vs. time, illustrated by Fig. 3.35, is the primary diagnostiby which bilinear flow can be recognized.


FCD > 1.6

END OFBILINEAR FLOW

SLOPE = mbf

t1/4, hours 1/4

∆p, p

si FCD < 1.6

m pi( ) m pwf( )–[ ]log444.6qT

h kf w( )1/2 φµctk( )1/4-------------------------------------------------- 1

4--- t .log+log=

1 of q( )log493.6T

h kf w( )1/2 φµctk( )1/4m pi( ) m pwf( )–

----------------------------------------------------------------------------------------- 14--- t .log+log=



lly

End of Bilinear Flow


The relationship between(tDxf)ebfandFCD for constant formation face rate is depicted graphicaby Fig. 3.37. This relationship can be approximated as:

(3.17)

Fig. 3.33 - Log-log Plot Showing Effect of Ideal Bilinear Flow for the Constant Gas Rate Well.


SLOPE = 1/4

t, hours

∆p, p

si

FCD > 1.6

END OFBILINEAR FLOW

SLOPE = mbf

t1/4, hours 1/4

∆p, p

si FCD < 1.6


Reservoir Analysis3

ph-

(3.19)

(3.20)

For the case where FCD ≥ 3, the dimensionless pressure at the end of bilinear flow is

(3.39)

Therefore,

(3.40)

and,

(3.41)


The relationship between(tDxf)ebfandFCD for constant formation face pressure is presented graically by Fig. 3.37. This relationship can be approximated by the following equations:

Fig. 3.35 - Log-log Plot Illustrating the Effect of Ideal Bilinear Flow for the Constant Pressure Case.

SLOPE = 1/4

t, hours

∆p, p

si

1.6 FCD 3: tDxf( )ebf 0.0205 FCD 1.5–( ) 1.53–≅< <

FCD 1.6: tDxf( )ebf4.55FCD---------- 2.5–

4–≅≤

pD( )ebf1.38FCD---------- .=

FCD1.38pD( )ebf

------------------=

FCD1965.1qT

kh m pi( ) m pwf( )–[ ]ebf

--------------------------------------------------------- .=



(3.23)

2 < FCD < 5: See Fig. 3.37

(3.24)

For the case where FCD ≥ 5,

(3.25)

Fig. 3.36 - Dimensionless Time for the End of the Bilinear Flow Period vs. Dimensionless FractureConductivity, Constant Formation Face Rate Case. 6

10-1 1 101 102

1

10-1

10-2

10-3

10-4

10-5

FCD

(tD

xf)

ebf

FCD 5: tDxf( )ebf6.94 10

2–×FCD

2---------------------------≅≥

1qD( )ebf

------------------1.40FCD---------- .=


Reservoir Analysis3

ion vs.

Therefore,

(3.26)

and

(3.42)

Analysis of Bilinear Flow Data

The conventional analysis of bilinear flow data requires two plots - a log-log plot of the appropriaterate or pressure function vs. t, and a cartesian plot of the appropriate rate or pressure functt1/4.

Fig. 3.37 - Dimensionless Time to the End of the Bilinear Flow for Constant Pressure Production. 9

FCD = 5

10-1

10-2

10-3

10-4

10-510-1 10-21 2.8 10

(tD

xf)e

bf

FCD

FCD 1.40 qD( )ebf=

FCD

1988Tqebf

kh m pi( ) m pwf( )–[ ]-------------------------------------------------- .=



and

-

r

e used

Gas-Constant Rate

The following procedure can be used to analyze bilinear flow data for fracture conductivityfracture length. When rate is constant:

1. Make a log-log plot of m(pi)-m(pwf) vs.t.

2. Determine if any data fall on a straight line of quarter-slope.

3. If any data in Step 2 form a quarter-slope, plotm(pi)-m(pwf) vs.t1/4 on cartesian paper and identify the data which form the bilinear flow straight line.

4. Determine the slope,mbf, of the bilinear flow straight line.


(3.43)

It should be noted that this calculation can only be made if k is known from a prefrac test.

6. If the bilinear flow straight line ends and the data riseabovethe straight line, determine thevalue of∆m(p), i.e.,[∆m(p)]ebf, at which the line ends. Then, from Eq. (3.42), FCD can be com-puted as

(3.42)


(3.29)

It should be noted that Eq. (3.43) assumesFCD ≥ 3. If enough data is available beyond bilineaflow, a type curve match should be attempted to verify that this is true.

Gas-Constant Pressure

When formation face pressure remains constant during a test, the following procedure can bto analyze the bilinear flow data for fracture conductivity and fracture length:

1. Make a log-log plot of1/q vs. t.


k f w444.6qT

mbf h φµctk( )1/4--------------------------------------

2

=

FCD1965.1qT

kh m pi( ) m pwf( )–[ ]ebf

--------------------------------------------------------- .=

xf

k f w

kFCD------------- .=


Reservoir Analysis3

e

e of

, a

3. If any data in Step 2 form a quarter-slope, plot1/qvs. t1/4 on cartesian paper and determine thslope,mbf, of the bilinear flow straight line.


(3.44)

5. If the bilinear flow line ends and the data rise above the straight line, determine the valuqwhere the line ends, i.e.,qebf. Then, from Eq. (3.43),FCD can be computed as

(3.42)


(3.29)

Eq. (3.29) assumesFCD ≥ 5; accordingly, if enough data are available beyond bilinear flowtype curve match should be attempted to verify that this is true.

k f w493.6T

mbf h φµctk( )1/4m pi( ) m pwi( )–[ ]

---------------------------------------------------------------------------------2

=

FCD

1988Tqebf

kh m pi( ) m pwf( )–[ ]-------------------------------------------------- .=

xf

k f w

kFCD------------- .=


References

per3-26

-23

ec-

Ad-

Dam-tion, San

0043,.

tured

ing at

nt Be-onfer-

3.6 References

1. Smith, M. B.: “Effect of Fracture Azimuth on Production With Application to the Wattenberg Gas Field,” paSPE 8298 presented at the 1979 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 2

2. Prats, M.: “Effect of Vertical Fractures on Reservoir Behavior - Incompressible Fluid Case,”SPEJ(June 1961)105-18;Trans., AIME, 222.

3. Britt, L. K.: “Optimized Oil Well Fracturing, Phase I Report,” Amoco Production Company Report F84-P(May 25, 1984).

4. Britt, L. K.: “Optimized Oil Well Fracturing, Phase II Report,” Analysis of the Effects of Fracturing on the Sondary Recovery Process; Amoco Production Company Report F85-P-7 (Jan. 24, 1985).

5. Bargas, C. L.: “The Effects of Vertical Fractures on the Areal Sweep Efficiency and Relative Injectivity ofverse Mobility Ratio Displacements,” Amoco Production Company Report F89-P-13 (Feb. 13, 1989).

6. Cinco-Ley, H. and Samaniego-V., F.: “Transient Pressure Analysis for Fractured Wells,”JPT(Sept. 1981) 1749-66.

7. Cinco-Ley, H. and Samaniego-V., F.: “Transient Pressure Analysis: Finite Conductivity Fracture Case vs.aged Fracture Case; paper SPE 10179, presented at the 1981 Annual Technical Conference and ExhibiAntonio, Oct. 5-7.

8. Cinco-Ley, H.: “Evaluation of Hydraulic Fracturing by Transient Pressure Analysis Methods,” paper SPE 1presented at the 1982 SPE Intl. Petroleum Exhibition and Technology Symposium, Beijing, March 19-22

9. Bennett, C. O., Reynolds, A. C., and Raghavan, R.: “Performance of Finite-Conductivity, Vertically FracWells in Single-Layer Reservoirs,”SPEFE (Aug. 1986) 399-412;Trans., AIME, 281.

10. Guppy, K. H., Cinco-Ley, H., and Ramey, H. J. Jr.: “Pressure Buildup Analysis of Fractured Wells ProducHigh Flow Rates,”JPT (Nov. 1982) 2656-66.

11 Rodiquez, F., Horne, R. N., and Cinco-Ley, H.: “Partially Penetrating Vertical Fractures: Pressure Transiehavior of Finite Conductivity Fracture,” paper SPE 13057, presented at the 1984 SPE Annual Technical Cence and Exhibition, Houston, Sept. 16-19.


Reservoir Analysis3


Chapter

For-ness.cture

oge-esti-ys bemptionated

lasticdas its

sily aa coreerizes

side aacture

e

re

Formation Mechanical Properties4
The following mechanical properties are of interest in fracturing: (1) Elastic Properties of themation (i.e., Modulus of Elasticity and Poisson’s Ratio), (2) Fracture Toughness, and (3) HardRock strength plays only a small role in the fracturing process and is not included in the fradesign calculations.
4.1 Elastic Properties of the Formation

As an engineering simplification, the formation is often assumed to be a linearly elastic homneous material. This simplification allows the use of solutions from the theory of elasticity tomate, for example, fracture widths and stresses in the formation. However, it should alwaremembered that the formation is neither homogeneous nor isotropic. Therefore, the assuof a linearly elastic isotropic formation may be grossly violated, especially in poorly consolidformations.

Based on this simplifying assumption, formation properties can be characterized by two econstants, the modulus of elasticity (or Young’s modulus),E, given in psi or units of pressure, anPoisson’s ratio (in honor of the great French mathematician), , a dimensionless numbername implies. The modulus characterizes how “stiff” the formation is and quantifies how eacore is deformed by an axial stress (tension or compression). Poisson’s ratio quantifies how“bulges” (expands or contracts laterally) by an axial compression or tension and it charact(together withE) the transmittal of horizontal pressure due to the overburden.

Fracture design is greatly affected by how much the formation opens for a given pressure infracture. Fracture width depends on both fracture dimensions and formation stiffness. Frwidth is inversely proportional to the formation plane strain modulus,E , given by

. (4.1)

Fig. 2.3 in Chap. 2 expressed this spring stiffness type relation as

(4.2)

where, for simplicity’s sake,E was used instead ofE . This is usually a good approximation sinca rough estimate for the Poisson’s ratio for most rocks is between 0.20 to 0.35. Therefore, E isexpected to be about 4 to 12% larger thanE. Note that the theoretically expected values for a

ν

′

E′ E1 ν2–( )

-------------------=

WDE----∼ p

′′

ν

Hydraulic Fracturing Theory Manual4-1March 1993


thou-

com-itions.e one

an besonicstaticy beodulioduli.

smallminus

, andBothlength

re.

iginalction).iginal

between 0 and 0.5 while moduli could have a much greater variability, from a few hundredsand psi to over 10 million psi.

Both of the elastic constants of a formation can be measured in the laboratory using a singlepression test. This test gives the modulus and the Poisson’s ratio under “quasi” static condThese static properties characterize rock behavior under “slowly” varying loading, such as thresulting from the hydraulic fracturing process. Different values for the elastic constants cinferred (using elasticity relations) from the travel times of the compressional and shearwaves (e.g. sonic logs) under dynamic conditions. The differences between dynamic andelastic constants are primarily of practical significance for the modulus. Dynamic moduli mamuch larger than static moduli and some correlation is usually needed to infer the static mneeded for fracturing design; in some cases the static moduli are 50 to 75% of the dynamic m

Fig. 4.1 shows the typical result of a compression test (in this case, Bedford limestone). Acore plug is jacketed and subjected to a confining pressure (usually equal to the overburdenreservoir pressure) in the triaxial cell; it is then loaded axially to produce plots of axial, lateralvolumetric strain vs. axial stress in excess of the confining pressure (Effective Axial Stress).the axial and lateral strains are quantities calculated from measuring the decrease of the coreand the increase of the core diameter using strain transducers that are mounted on the co

The axial strain represents the ratio of the core “shortening” (length decrease) over its orlength and is a dimensionless number which is plotted positive for a length decrease (contraThe lateral strain represents the ratio of the core “bulging” (diameter increase) over its or

Fig. 4.1 - Typical Stress-Strain Curve for Brittle Rocks.

ULTIMATEAXIALLOADS

CONFININGPRESSURE

YIELD

TANGENTMODULUS

SECANTMODULUS(DO NOT

USE)

12000

10000

8000

6000

4000

2000

0

EF

FE

CT

IVE

AX

IAL

ST

RE

SS

, PS

I

-2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0

*10-3STRAIN

AXIAL STRAIN

LATERAL STRAIN

VOLUMETRIC STRAIN

Hydraulic Fracturing Theory Manual 4-2 March 1993

Elastic Properties of the Formation

reasey the

lotted

od-rawnformeded forcom-

stressfining

ons arecondi-oint ofus of

m theine is

ateral.and

e. Thehave) are’s ratio

orma-

ssure.sub-tressweene thatzero.

diameter and is a dimensionless number which is plotted negative for core diameter inc(expansion). The volumetric strain, also shown on Fig. 4.1, is a calculated quantity given bfollowing algebraic sum

volumetric strain = axial strain + 2× lateral strain . (4.3)

It represents the ratio of the volume change over the original volume of the core, and is ppositive for contraction.

By definition, the initial slope of the axial strain curve is the modulus of elasticity or Young’s mulus,E, in psi. It is also called a “tangent” modulus because it is the slope of the dashed line dtangent to the stress-strain curve at the origin (Fig. 4.1). Since the compression test was perat a confining stress approximating the in-situ conditions, this is the value that should be usmodulus in a fracture design. By this, we mean that the formation in-situ is at a state of stressparable to the one near the origin of the plot; any loading due to fracturing would make thestate go up or down on the curves near the origin. However, modulus depends on the conpressure, and some judgement should be exercised when data for the specific in-situ conditinot available. Modulus data should be used with a good understanding of what the testingtions represent because some labs draw, for example, a straight line from the origin to the pfailure and report the slope of that line as modulus. This value is called, the “Secant” ModulElasticity and should not be used for fracture design calculations.

Poisson’s ratio, , represents the ratio of the lateral strain over the axial strain, both taken frolinear behavior of the core near the origin, (i.e., over the range that the modulus straight ldetermined).

Poisson’s Ratioν = - lateral strain / axial strain (4.4)

For the Bedford Limestone example in Fig. 4.2, at an effective axial stress of 4,000 psi the lstrain is -0.25 x 10-3 and the axial strain is 0.9 x 10-3. The Poisson’s ratio from Eq. (4.4) is 0.277Poisson’s Ratio quantifies the tendency of the material to “bulge” out for a given axial straintherefore how the material “pushes” laterally when it is subjected to an overburden pressurtheoretical range of Poisson’s ratio for uniform materials is between 0 and 0.5. Rocks whicha competent structure (i.e. rocks with porosity that does not change significantly with loadingexpected to have Poisson’s ratios in the same range. Good approximate values for Poissonfor fracture width calculations are 0.25 for sandstone formations and 0.33 for carbonate ftions.

However, Poisson’s ratio strongly affects how the closure stress is related to overburden preFor example, a formation with will develop almost no horizontal closure stress whenjected to overburden; in contrast, a formation with will develop a horizontal closure salmost equal to overburden, and will behave like a liquid! Real rocks fall somewhere betthose values, with the more ductile and plastic rocks having a higher Poisson’s ratio. Notrocks that have high porosity and low cementation (e.g. Valhall chalk) may have a close to

ν

ν 0≅ν 0.5≅

ν



ore is

lumemakes

ess) on. There-eteight

oduluseasingdu-

tions

This is because their porosity changes considerably with loading, and the bulging of the caccommodated by porosity reduction.

Effect Of Modulus On Fracturing

Though the predicted fracture width and penetration for a fixed fracture height and fluid voare relatively insensitive to modulus, the relation between fracturing pressure and modulusmodulus one of the more important variables considered in fracture design. Fig. 4.2 shows anexample of the dependence of net fracturing pressure (injection pressure minus closure strthe modulus of elasticity; generally speaking, as modulus increases, net pressure increasesfore, if a stimulation is designed with a value for“E” that is smaller than the actual value, the npressure during a job will be higher than predicted, possibly leading to unanticipated hgrowth.

Typical Modulus Values

Fig. 4.3 and Fig. 4.4 show typical ranges of values for modulus for sands and carbonates. Musually increases with confining pressure and decreases with increasing porosity and incrgrain size.If nothing else is known, these figures may be used to determine an estimate of molus. However, significant variations from either figure can exist due to mineralogical composiand depositional differences.

Fig. 4.2 - Example of the Effect of Modulus on Net Fracturing Pressure.

Example DataH = 100 ft Fluid Loss H = 100 ftC = .001 Spurt = 0Q = 20 bpmViscosity = 100 cp (n' = 1)Design Penetration (1/2 Length) = 500 ft

Req

uire

d (1

000

gal)

20

15

10

5

2 4 6 8

800

600

400

200

Net

Fra

ctur

ing

Pre

ssur

e (p

si)

Slu

rry

Vol

ume

Young’s Modulus (10 6 psi)


Elastic Properties of the Formation

rma-ld be

,000coretive to.

esti-sionaln,dulusations

ation.

Also, the modulus values in Fig. 4.3 and Fig. 4.4 are for small samples. Many carbonate fotions are naturally fractured; and in such a case, the modulus for the “bulk” in-situ rock woulower than a value for a small sample.

A similar chart for shales is not practical since Young’s Modulus for shales can vary from 500psi for a high porosity, clay rich, shale to 6-8 million psi for a quartz cemented siltstone. If nois available for shales, sonic logs have been used to predict the modulus of the shales relathe modulus of the pay formation where core is available and modulus has been measured

Table 4.1 lists typical modulus values for two “special” formation types.

Fig. 4.5 is a plot that allows the use of conventional Sonic Log data (compressional wave) tomate modulus. This “dynamic” modulus (i.e., estimated from correlation based on compreswave velocity in the formation) isgreater than the “static” modulus needed for fracture desigbut, if laboratory tests are not available, the dynamic modulus sets an upper bound for moand is preferable to Fig. 4.3 and Fig. 4.4. It can also be used to estimate the modulus in formwhere core is not available if lab data is available from other formations in the same well.

A better technique than conventional Sonic Logs is to calculate Young’s Modulus,“E,” fromLong Spaced Sonic Log data, using the compressional and shear wave velocities of the form

Fig. 4.3 - Modulus of Elasticity for Sand-stones.

Fig. 4.4 - Modulus of Elasticity for Carbon-ates.

Table 4.1 - Typical Modulus Values for Two “Special” Formation Types.

Formation PorosityModulus (106 psi)

Chalk (North Sea) 35 - 50% 0.5 to 1.5

Diatomaceous Earth 40 - 50% 0.4 to 1.0

Low Porosity (< 10%), Very Fine Grained

High Porosity (> 25%), Coarse Grained

Overburden-Pore Pressure (1000 psi)5 10

8

6

4

2

You

ng's

Mod

ulus

(mill

ion

psi)

5 10

10

8

6

4

2

Low Porosity, Dolomite

High Porosity

Overburden-Pore Pressure (1000 psi)

You

ng’s

Mod

ulus

(mill

ion

psi)



e

f this issignctually

Again, this dynamic modulus will be anupper bound for the static modulus used for fracturdesign.

The best solution is to obtain core samples and have tangent modulus measured in a lab. Iimpossible andE must be estimated, try to estimate on the high side. This will result in a dewith a narrower fracture width, higher net pressure and greater fracture height than should aoccur, providing a conservative “safe” approach to fracture design.

Fig. 4.5 - Young’s Modulus (E) vs. Acoustic Travel Time.

E x 106 - psi

Sand

DolomiteLime

2 4 6 8 10 12 14 16

100

80

60

40Aco

ustic

Tra

vel T

ime

(mic

rose

cond

s/ft)


Fracture Toughness

actureatchingena that

ability

to tol-ssivee threeuntilIt maylso on. for-

bora-in the

straincture

c frac-

e

00

bout 1

s of the

c ande for

s indi-

ider-

4.2 Fracture Toughness

Fracture toughness is one of the most elusive material properties that comes from linear frmechanics. It is discussed here because it is often used in numerical simulators as a mparameter of the treating pressure and because there are many near fracture tip phenomcould appear as “apparent” fracture toughness.

Without getting too deep into theory, the fracture toughness concept comes from Griffith’s1 workon the fracture of brittle solids. The fracture toughness of a material represents its naturalto resist the propagation of a fracture. To quote an article by Srawley and Brown,2 “In the simplestterms, the fracture toughness of a material determines how big a crack the material is ableerate without fracturing when loaded to a level approaching that at which it would fail by exceplastic deformation.” Fracture toughness can be quantified by lab experiments (such as thpoint loading of the Chevron notch) from which the loading vs. deformation curve is plottedfailure, and the energy spent to fracture the specimen can be calculated from this diagram.be noted that loading capacity of a specific specimen depends not only on crack size, but acrack shape, bulk of the specimen, crack orientation with respect to layering of material (e.gmation), temperature, rate of loading, etc. For this reason, it is very difficult to extrapolate latory results to the field, and an indirect assessment of “apparent” fracture toughness is donefield from treating pressure behavior using fracturing simulators, as described below.

The fracture toughness is quantified by either of two related parameters: (1) the criticalenergy release rate,G, expressed in energy per area of created fracture (not the area of the frafaces) in units of force/length; and (2) the critical stress intensity factor,Kc, expressed in units ofpressure times square root of length. The relation between the two parameters for hydraulituring problems (plane strain problems) is

G = Kc

2/E'. (4.5)

Typical laboratory range ofKc values are given by Thiercelin3 in Table 4.2. From Table 4.2 we se

that typical laboratoryKc’s are of the order of 900 to 2000 psi with a value of about 15

psi being a good rough estimate. A corresponding rough estimate of fracture energy is apsi-in. Note that some simulators requireKc and some require G as input.

Fracture toughness relates the pressure required to propagate a fracture with the dimensionfracture. Let us consider an example from the Wattenberg field,4 where fractures in the Muddy Jformation are highly confined by shale layers above and below the pay. Stress tests, minifrafracturing treatments in the example well show that a fracture height of 90 ft is representativthese type of calculations. Furthermore, net pressures,PN, on the order of 400 to 550 psi for mini-frac treatments and 2100 psi for the main fracture treatments are typical. These observationcate the magnitudes of the formation toughness (i.e., critical stress intensity factorKc), theconfining stress contrast∆σc between layers, and other rock mechanics considerations. Cons

in

in



f the

ressurectureFromck

en

t have

the lab

com-.

ing the lateral propagation of the fracture tip of this highly confined fracture gives estimates oMuddy J pay toughness, or, better, its “apparent” toughness.

The fracture tip is essentially a penny shaped fracture that is subjected to the net treating pPN. There is no stress contrast confining the fracture in the horizontal direction. Therefore, fratoughness is expected to be a dominant confining mechanism in the horizontal direction.fracturing mechanics,5 the stress intensity factor,K, in the opening mode of a penny shaped craunder uniform pressure is given by

(4.6)

whereR is the radius andPN the uniform net pressure. The fracture propagates whenK is equal tothe formation fracture toughness,Kc (which is a material property), and remains stationary whK < Kc.

The fracture tip geometry of the Wattenberg fractures is characterized byR= 45 ft = 540 in andPN

= 500 psi. This value of net pressure is estimated from the minifrac treatment which does no

the additional friction due to a proppant. With these values, Eq. (4.6) givesKc = 13110 psi . Thisestimate is approximately 10 times greater than the fracture toughness of rocks measured in

which have a typical toughness value of 1000 to 1500 psi . Note that this discrepancy is amon phenomenon and consequently the calculatedKc is called an “apparent” formation toughness

Table 4.2 Fracture Toughness and Properties as a Function of Confining Pressure.

LithologyPorosity

%

Young’s ModulusConfiningPressure KIc

MPaError 106

psi MPa psi MPa% Error

psi

Mesa VerdeSandstone-

5-10--

--

32,000 (3) 11%

--

4.8

0.13.820.7

020683102

2.12 (2)2.4 (2)3.6 (1)

11%17%

199322563384

Mesa VerdeMudstone

--

-45,000 (2)

9% -6.7

0.20.7

03102

2.12 (1)2.6 (1)

19932444

CardiumSandstone

13-

-25,500 (2)

-31%

-3.8

0.21.0

03147

0.98 (3)3.3 (2)

14% 6%

9213102

BereaSandstone--

23---

--

19,400 (2)20,500 (1)

--

2%

--

2.93.1

0. 5.010.020.0

074

914992997

1.11 (2)1.3 (2)1.3 (2)1.5 (3)

5% 8% 8%13%

1043122212221410

Note: the figures in parentheses show the number of samples tested.

± m ± in

K 2 PNRπ---= (penny crack)

in

in


Fracture Toughness

d couldionzone)tip duerauliced gelor allc frac-

Several near fracture tip hypotheses contribute to an increased net fracturing pressure ancontribute to an increasedKc. The most popular within the research community are (1) formatplasticity, (2) non-penetrated (“dry”) zone near the tip, and (3) process zone (microfracturearound the tip. Hypotheses (1) and (3) contribute to increased energy expenditure near theto plastic flow and intense microfracturing. Hypothesis (2) assumes a region where the hydpressure is not easily transmitted to the fracture tip due to asperities, gel plugging, increasviscosity due to dehydration, and great frictional losses within very narrow crack opening. Fthe above reasons, it is quite common to input increased fracture toughness in the hydraulituring simulators to match treating pressures and predict fracturing geometry.



caus-

pants seenmentacturets and

4.3 Hardness

Rock hardness is important to fracture conductivity. The proppant may imbed into soft rocks,ing the fracture conductivity to decrease and the propped fracture to lose its effectiveness.

For most rock types, this is not a problem if a nominal design guideline of one pound of propper square foot of fracture is achieved. For very soft formations (chalks are one example ain Fig. 4.6), this is not sufficient and special fracture designs are required. If proppant embedis suspected due to productivity declines or pressure transient tests showing a loss of frcapacity with time, special lab tests are available to test core samples with various amountypes of proppant.

Fig. 4.6 - Effect of Propped Fracture Thickness on Flow Rate.

TEMP = 200F2X2 DANIAN CHALK

Legend0.4" PROPPED FRAC

0.25" PROPPED FRAC

0.1" PROPPED FRAC

MATRIX FLOW

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

1000

100

10

1

0.1

GROSS CONFINING PRESSURE PSI

TO

TA

L C

OR

E P

ER

ME

AB

ILIT

Y M

D

10096-97


References

s Test-

gs of

Fieldeport

Rich-

4.4 References

1. Griffith, A. A.: “The Phenomena of Rupture and Flow in Solids,”Phil. Trans., Royal Soc. of London (1920) Ser.A, 221, 163-98.

2. Srawley, John E., and Brown, William F., Jr.: “Fracture Toughness Testing Methods”, Fracture Toughnesing and Its Applications Symposium, 1964 Annual Meeting of ASTM, Chicago, June 21-26.

3. Thiercelin, M.: “Fracture Toughness Under Confining Pressure Using the Modified Ring Test”, Proceedinthe 1987 US Symposium of Rock Mechanics, 149-56, June 29-July 1.

4. Moschovidis, Z.A., Broacha, E., and Gardner, D.: APR, “Tectonic Correction of Closure Stress Profiles andData Analysis for Fracture Design for Wattenberg Gas Field, Colorado;” Amoco Production Company RF91-P-59 (Nov. 1990).

5. Warpinski, N. R., and Smith, M. B.: “Rock Mechanics and Fracture Geometry,” Monograph Series, SPE,ardson, TX (1989)12, vi, 57-80.




Chapter

sily

at

nt. Aowthth,

n acreatedaterhave, but

or lim-

epth

Design of Pseudo 3-D Hydraulic Frac-turing Treatments

5
5.1 Fracture Height/Fracture Height Growth - 3-D Modeling/Design
As emphasized in Chap. 2 in the discussion of the basic fracture models,fracture heightandfrac-ture height growthare themajor variables governing treatment design or analysis. This is easeen in the simple relation derived from conservation of mass for a confined fracture

(5.1)

where fracture height,H, and fluid loss height,Hp, appear in the denominator and have a greeffect on fracture length.

H is the total or “gross” fracture height which, of course, changes with time during a treatmereasonable estimate of the “initial” fracture height, and of the variables governing height gris critical to an accurate solution for fracture length since, as seen in the relation above, lengL,and height,H, are inversely proportional. It is usually desirable to maintain frac height withireasonable distance above and below the pay zone, to minimize “useless” fracture area (and propped fracture area which will not contribute to production) or to avoid fracturing into wbearing layers. The fracture height obtained is largely controlled by formation properties. Wesome influence over the height obtained through controls on pump rate and fluid viscositymust recognize the limits to which we can control height development.

Factors Controlling Fracture Height

Numerous oil field techniques and wellbore arrangements have been proposed in the past fiting fracture height:

• Perforate a limited section and only frac where the perfs are

• Set a packer in the wellbore so that you do not frac up

• Perforate low in the wellbore, since everybody knows that you cannot frac below Total D(TD)

• Perforate high in the wellbore, so that you do not frac into water below.

• Everybody knows that fracs grow up!

LQ tp

3 C Hp tp w H+-----------------------------------------------=

Hydraulic Fracturing Theory Manual5-1December 1995

Design of Pseudo 3-D Hydraulic Fracturing Treatments5

ow out

n somer the

hows

Pumpvery

ulice dom-

• Pump at low rate so that the frac will stay in zone.

• Pump at high rate so that you get the job pumped before the fracture has a chance to grof the zone.

• Use of a 2D model, then height won’t change!

Though these approaches may sound silly, we have all probably tried to use these or others iform or fashion. Some of them have limited application and may exert some influence oveultimate frac height obtained, but overall, they have minimal impact on frac height. Fig. 5.1 sa schematic of a fracture which basically grows where it wants to.The only wellbore conditionthat can have a significant impact on frac height is the cement bond.A poor cement bond canallow annular communication with another zone, and thus bypass a potential confining bed.rate and fluid viscosity do affect frac height through their indirect control on pressure, but to asmall degree when compared to formation properties.

Vertical fracture growth and resulting fracture height is controlled by the interaction of hydrapressure inside the fracture with mechanical properties of the rocks and in-situ stresses. Thinant factors controlling frac height are listed below in order of decreasing importance.

Factors Controlling Fracture Height

• Closure stress differences between pay and bounding beds

• Thickness of bounding beds & Thickness of “pay”

• Fracture pressure from high modulus (naturally high/low closure stress, etc.)

Fig. 5.1 - A Frac Grows Where It Wants To!!

Pay Design

Water Actual

Fracture Height = ?

Not Perforated Height!

Hydraulic Fracturing Theory Manual 5-2 December 1995

Fracture Height/Fracture Height Growth - 3-D Modeling/Design

tresss-

open.bound-

stress.foratedt, the

bore.ma-ractureositywell-ure.

en then net

2 and 3,ure ineightnd theith infi-etweens differ-nd thereac-ntinue

willaddi-

• Modulus contrast between pay and bounding beds

• Interface or bedding plane slip - applicable at shallow depth?

• Ductility of bounding bed - may facilitate bedding plane slip, (small coal seams)

• Stress gradient due to fluid pressure - generally insignificant

• Fracture toughness or strength differences - probably not a barrier

Effect Of Closure Stress Profile On Fracture Height Growth

The most dominant controlling mechanism for frac height is vertical variations in closure sthrough strata of varying lithology and rock properties.1 Closure stress is the minimum, compresive, in-situ stress. Pressure in the fracture must exceed this before a hydraulic fracture canFig. 5.2 shows a simplistic, idealized case of three zones of different stress. In this case, theing beds (Zones 2 and 3) are assumed to be of infinite thickness and have the same closureThe stress in the bounding beds is greater than that in the pay zone (Zone 1). Zone 1 is perand a fracture is initiated. The fracture grows unrestricted to the height of Zone 1. At this poinrelationship shown in Fig. 5.2 goes to work (Point A).

As injection continues, the fracture begins elongating and extending laterally from the wellNet fracture pressure,Pn, (bottomhole treating pressure outside the perforations minus the fortion closure pressure, discussed in more detail in Chap. 8), begins to increase as the fextends. During this period, the fracture is essentially acting as a “pipeline” carrying high viscfluid from the wellbore to the fracture tip. As the pipeline grows longer, the pressure at theboremust increase to overcome the increased friction drop along the ever lengthening fract

As net pressure,Pn, increases, the ratio of net pressure to the closure stress differential betwepay zone and bounding beds begins to increase, moving one “up the curve” (Point B). Whepressure has increased to about 50% of the stress differential between Zone 1 and Zonesfracture height has increased to about 135% of the initial frac height (Zone 1). As net pressthe fracture increases, frac height continues to grow, until the frac height is twice the initial hat a net pressure equal to 70% of the stress differential (Point D). The thickness of Zone 1 aabsolute values of the stresses are independent of this relationship for a three zone system wnite bounding beds. Obviously, after net pressure reaches 70-80% of the stress differential bthe pay zone and bounding beds, small increases in net pressure (the net pressure to stresence ratio) can add much additional frac height. The fracture height cannot be contained, afracture grows uncontrollably out of zone.Note, however, that after this point is reached, fractulength growthdoes not stopthough it is slowed considerably. Thus, if no danger exists of the frture breaking into another (possibly undesirable) low stress zone - pumping may safely coin order to create a longer fracture. The “economics” of creating this additional fracture lengthbe affected though, with significantly greater treatment volumes now being needed to create



d con-

we canssure.r hand,ependsrowthn be

tional length. Similarly, sand is distributed over a greater and greater height, reducing the sancentration per unit area.

This means that if we are to contain a fracture within zone, wemust havesome idea of closurestress in the pay zone and bounding beds. If stress differences are only 700-800 psi, thenexpect the fracture to grow uncontrollably out of zone at about 500-600 psi net fracture preFracture treatments could be designed to stay within this net pressure limitation. On the otheit may be difficult to achieve the length desired at these net pressures (since net pressure don fracture length), and the treatment would have to be designed with this fracture height gin mind. Conversely, if the stress differential is on the order of 1500 psi, net pressure ca

Fig. 5.2 - Effect of Closure Stress Variations on Fracture Height.

Gamma Ray Closure Stress

Shale

Shale

Sand σc1

σc2

σc2

∆σc σc2 σc1–=

Zone 2

Zone 1

Zone 3

Hi

a b

A

B

CD

0 1 2 3 4 5

0.2

0.4

0.6

0.8

1.0

Ratio Frac Height:

Initial Frac HeightHH i----( )

Rat

io N

et P

ress

ure:

Str

ess

Diff

eren

ce

Pn

∆σ

c----

---

0

c

A B C D

dPressure

A

BC

D

Time



ne.

ta forprofileultipleever,forlosureaboutents abeen

allowed to rise to 1000-1100 psi before the fracture will begin to grow significantly out of zoThis would allow an ample pressure limitation for designing most fracture treatments.

Obviously, an in-situ fracture closure stress profile, as seen in Fig. 5.3, is the major input da3-D or Pseudo 3-D fracture treatment design. The example in Fig. 5.3 illustrates a stressgenerated by conducting multiple small volume, microfrac stress tests. Generally, such mstress data are not available and some form of log-stress correlation will be required. Howthis example illustrates another important item - namely “typical” (or “maximum”) valuesin-situ stress differences. Consider data from the sandstone at ft showing a fracture cpressure (closure stress) of psi. Then consider the stress of psi at a depth of7650 ft in the Mancos Tongue Shale. This stress difference of psi at this depth represstress difference of psi/ft - and this is about the maximum stress difference which hasrecorded, verified, and published. Thus,assuming some lithology differences exist, anoptimisticestimate for in-situ stress differences might be:

Max Stress Difference, = 0.2 psi/ft of depth.

Fig. 5.3 - Variations in Fracture Closure Stress in a Sand/Shale Sequence.

7500±6500± 8000±

1500±0.2±

∆σ

00.0

50.0

100.

0

150.

0

200.

0

0.3

0.2

0.1

0.0

0.1

ft7300

(2225m)

7400(2255m)

7500(2286m)

7600(2315m)

7700(2347m)

7800(2377m)

7900(2408m)

8000(2438m)

8100(2459m)

GAMMA (GAPI) POROSITY

COAL

SILT

SHALE

SAND

MA

NC

OS

TO

NG

UE

CO

ZZ

ET

TE

MA

NC

OS

TO

NG

UE

RO

LLIN

SP

ALU

DA

L

6000

7000

8000

9000

STRESS (psi)

m

2250

2300

2350

2400

2450

45 50 55 60 MPa

Estimated over-burden stress(1.05 psi/ft)



g withset of

re)heightes withally arowth

ed, andeously.logy)ne.

other

sure

antnces.

rtificial

ds arerow

g a 10haleat

as tri-itialtress

rgeThus,rd”

The effects of lithology on in-situ stress (fracture closure stresses or closure pressure) alonthe effect of closure stress variations on fracture geometry may also be seen in Fig. 5.4, afield data presented by Esso Canada.2 Fig. 5.4 compares two cases (within the same wellboshowing measured in-situ stresses along with pre and postfrac radioactivity logs for fracturegrowth. For Case 1, several stress tests (microfrac type stress tests) were conducted in zon(based on differing gamma ray readings) varying lithology. This stress data showed basic

psi/ft (e.g. normal) stress gradient - and the postfrac logs suggest massive height goutof-zone. Case 2 shows stress data collected from two zones, both of which were perforata propped fracture treatment was conducted attempting to stimulate the two zones simultanThe upper zone shows a significantly higher closure stress (associated with a different lithoand the postfrac logs indicate that the entire treatment entered the deeper, lower stress zo

Thus we see examples - in the same wellbore - of lithology changeswith andwithout associateddifferences in fracture closure pressure. A guideline for interpreting stress profiles where noinformation exists might be:

Theremustbe some change in lithology in order to expect some variations in closure pres- and thus some degree of fracture height confinement.However, do not try to quantifylithology logs. That is, relatively minor apparent lithology changes could signify significstress differences, OR a major lithology change might have no associated stress differe

As discussed in Chap. 4, the one exception to this would be for stress changes created by achanges in reservoir pressure (e.g. depletion).

Effect Of Bed Thickness On Fracture Height Growth

In addition to the stress difference in the beds, bed thickness is important. If the bounding benot infinitely thick, then we must consider their thickness to determine if the fracture might gcompletely through the bounding beds and into zones of lower stress. A 2 ft shale boundinft pay zone is obviously not going to stop a fracture from growing out of zone, nor will a 20 ft sbounding a 50 ft zone.A good rule for beds immediately bounding a zone to be fractured, is ththey should be at least as thick as the zone being stimulated to confine frac height;the “basis”for this “rule-of-thumb” is discussed under Picking Fracture Height on page 5-12.

Consider the “Pressure-Height Curve” as seen in Fig. 5.2b. At the point where the fracture hpled in height (e.g., H/Hi = 1 and the fracture has grown “upwards” a distance equal to one inheight and “downwards” one initial height), net pressure has reached % of the in-situ sdifference. Also at this point, pressure-height behavior is fairly “flat”, that is, relatively laamounts of height growth begin to occur for small increases in bottomhole treating pressure.even for “infinite” bounding beds, fracture height will begin to increase rapidly after an “upwaor “downward” growth about equal to one original formation thickness.

0.7±

80±



Case 1Apparent Lithology No Stress Difference

Case 2Large Stress Differences

No FRAC in High Stress Interval

Fig. 5.4 - Examples of Lithology Changes, With and Without Associated Stress Differ-ences.

CollarLocations

2675

2700

2725

2750

Increasing Gamma Activity

Gamma Ray

Post-Frac

Gamma RayBase

Par

ts

Dep

th (

met

ers)

0.7 psi/ftgradient

6000

7000

Closure Stress (psi)

Upp

erZ

one

Low

erZ

one

CollarLocations

2060

2060

2060

Dep

th (

met

ers)

Per

fsP

erfs

Base

GRPost-Frac GR

Increasing Gamma Activity Closure Stress (psi)

4000

5000



illus-ssede topatingeded to

o drop

The first important effect of bed thickness then is the thickness of bounding formations astrated by the four drawings in Fig. 5.5. This figure repeats the “three-layer” behavior discuabove until “point C” is reached - e.g. the fracture has approximately tripled in height and thof the fracture has just reached the top of the barrier formation. At that point in time, the trepressure inside the fracture, near the wellbore, is considerably greater than the pressure nepropagate a fracture into the shallower low stress zone. Thus treating pressure will begin t(sometimes fairly rapidly) as the fracture preferentially migrates into this new formation.

Fig. 5.5 - Fracture Height Growth Through Finite Bounding Beds.



n havend onsuchcture

ssureness ofral paye con-at 200n alsotic-

lso bes, if a

t treat-ill bequiredandturinges ofuired

This can, in extreme cases, even lead to the main fracture beginning to grow shorter and camajor (usually undesirable) effects on the ability to pump proppant, proppant placement, astimulation effectiveness. Some of the treatment pumping problems which can arise fromheight growth behavior are discussed in Chap. 8. Also, some of the fracture modeling/fradesign issues raised by such a fracture geometry are briefly discussed below.

Thesecondmajor importance of bed thickness is thickness of the pay zone itself. The net prewhich the stress and thickness of the bounding beds must counteract depends on the thickthe pay zone. Fig. 5.6 illustrates the net pressure required to create a 500 ft fracture for sevezone thicknesses. This figure shows that height growth would probably not be expected to bfined to a 20 ft zone at 2000 psi, but height confinement could be expected for a 200 ft zonepsi. While the actual net pressures tabulated in Fig. 5.6 are for a specific case, the figure cabe used, in a general,qualitative, sense to estimate the potential for height confinement for parular zones.

The actual net pressures tabulated in Fig. 5.6 are for a specific case. However, they might aviewed as “typical” values of net treating pressure for various gross zone thicknesses. Thuformation being considered for fracturing has a gross thickness on the order of 30 ft - then neing pressure will probably be psi, and stress differences on the order of 1600 psi wneeded to give reasonable height confinement. Assuming a formation depth of 6000 ft, the re“gradient” of stress difference would be 0.27 psi/ft - good height confinement is unlikelyextensive height growth would be expected. On the other hand, a typical net pressure for fraca zone with a gross thickness of 60 ft might be on the order of 800 psi - with stress differenc

psi needed for reasonable height confinement. For a formation depth of 8000 ft, the req

Fig. 5.6 - Net Pressure Required to Create a 500 ft (1/2 Length) Fracture.

1500±

900±



airly

stress.8 and

he payy nar-

p mayctures notlip ofwith

” of athese

gradient difference is “only” 0.1 psi/ft - and assuming some lithology differences exist - then fgood height confinement may be a reasonable possibility.

Effect Of Other Factors On Fracture Height Growth

• Modulus contrast between pay and bounding beds

• Interface or bedding plane slip - applicable at shallow depth?

• Ductility of bounding bed-may facilitate bedding plane slip, rare

• Stress gradient due to fluid pressure - generally insignificant

• Fracture toughness or strength differences-probably not a barrier

Probably the most important of the remaining variables which affects frac height (after theand pressure behavior), are modulus contrasts (Fig. 5.7), and bedding plane slip (Fig. 5Fig. 5.9).

Though not as strong a barrier as once thought, bounding beds with higher modulus than tzone can retard height growth by causing fracture width in the bounding formations to be verrow. However, as seen in Fig. 5.7, the maximum possibleL to H ratios are fairly small - that is theheight confining effect of modulus contrasts is actually quite minimal.

For shallow depths, overpressured formations, or highly jointed formations such as coals, slioccur along bedding planes at the top or bottom tip of the fracture, Fig. 5.8, blunting the fraand arresting height growth. This would be a very strong barrier; however, it probably doeoccur often in oil and gas well fracturing except possibly at the interfaces with coal seams. Sthis type would be required for the Geerstma de Klerk model to be applicable for fractureslengths greater than their height (L/H > 1).

Fig. 5.9 presents the results of a series of lab tests conducted to determine the “likelihoodhydraulic fracture stopping at an unbonded interface between two rock layers. As seen from

Fig. 5.7 - Effect of Modulus Contrast on Fracture Containment.



e pres-ffec-

cleargas

radient. Thisinside

200 ftre isessureThusbottomrather

rder ofnsig-h forry lowvery

results, for an effective vertical stress across the interface (e.g. overburden weight minus porsure) of only psi the fracture crossed the interface for almost all rock types. Since an etive vertical stress of this magnitude would correspond to a depth of only about 2000 ft - it isthat interface slip will not be an effective barrier to vertical frac height growth for most oil andwell situations.

Fracture closure pressure or closure stress generally increases with depth, with a typical gof psi/ft - e.g. for each 100 ft increase in depth, closure pressure will increase by 70 psiincrease in closure stress is generally greater than the increase (with depth) in fluid pressurethe fracture due to the hydrostatic gradient of the fluid. As an example, consider a fracturein height which is filled with a water based fluid. Closure stress at the bottom of the fractugreater by about 140 psi than closure stress at the top; at the same time the driving fluid prat the bottom is greater by psi (assuming a hydrostatic gradient of 0.43 psi/ft for water).net pressure (e.g. driving fluid pressure minus closure pressure) is about 54 psi less at theof the fracture than at the top. Thus the fracture would have some tendency to grow upwardthan downward.

However, for many (most?) fracturing cases net pressure may have a typical value on the o500 to 1000 psi - thus a difference (over the height) of psi in net pressure is relatively inificant. Stress gradients, then, only become significant in affecting fracture height growtcases where significant height already exists (e.g. several hundred feet), or for cases of venet pressure (e.g. typically associated with low modulus formations and/or the pumping oflow viscosity fluids).

Fig. 5.8 - Illustration of Fracture InterfaceSlip.

Fig. 5.9 Interface Slip vs. Stress.

1000±

0.7±

86±

50±



e prin-thatinto a

turendingere willeing

orma-uring)

stressting

Picking Fracture Height

(Estimating the In-situ Stress Profile)

Obviously, normal strata are not as simple as the idealized case described in Fig. 5.10, but thciples are still applicable. If the bounding beds are not infinitely thick, then we must ensurethey are of adequate thickness so the fracture does not grow completely through them andzone of lower stress. A 2 ft shale bounding a 10 ft pay zone is obviously not going to stop a fracfrom growing out of zone. As discussed on page 5-6, a good rule for beds immediately boua zone to be fractured is that they must be at least as thick as the zone being treated. Still, thbe some height growth into the bounding layers with the final magnitude of fracture height bpredominantly determined by the stress difference between the “pay” and the bounding ftions. Thus predicting or picking fracture height becomes an exercise in estimating (or measthe in-situ closure stress for various zones.

There are tools which may, under some conditions, possibly aid in determining the in-situ“profile.” However, in general, consideration of two dominant parameters will aid in construcreasonable estimates of in-situ stresses.

Factors Which Dominate In-situ Stress Differences

• Lithology Changes

• Pore Pressure

• Pore Pressure Variations

Fig. 5.10 - Illustration of Stress Gradient Effect on Frac Height Growth.

Generally Insignificant Except in Case of UnrestrainedVertical Growth Where Height Becomes Very Big



withoundaryologynge in

an-t anditude of

as beene payrovingult toe pres-or fac-o pore

tones

ndi-ange inir clo-

pressureclosuret con-nater pres-

miningsticityre

y “cal-lex andm the

One minimum consideration for height confinement is significant lithology changes as seena Gamma Ray log. Shales often have higher closure stresses than clean sands so thick bshales can confine fractures. Such confinement is not always the case, but the lack of lithchanges virtually ensures unrestricted height growth or radially shaped fractures. Thus a chalithology makes itpossiblefor stress differences to exist. However, one should not try to “qutify” a Gamma Ray log, e.g., if a lithology difference exists, then stress differences may exisfracturing pressure analysis (as discussed in Chap. 8) must be used to determine the magnthe stress differences.

As discussed, closure stress is related to reservoir pressure. Therefore, a reservoir that hdrawn down, as in a producing well, is likely to have a lower closure stress than normal in thzone, and consequently a higher stress differential between pay and the bounding beds, impchances for height confinement. On the other hand, height confinement could be more difficachieve in an injection well due to pressuring up of the pay zone. Thus pore pressure and porsure differences between zones (e.g. due to partial depletion from offset production) is a majtor to consider in estimating in-situ stresses. Fracture closure stress is generally related tpressure by3

(5.2)

whereOB = Overburden Pressure 1 psi/ft, p = pore pressure, = Poisson’s ratio, Sands = 25, and Carbonates = .33.

Inspection of Eq. (5.2) for a “typical” sandstone reservoir with a Poisson’s ratio, of 0.25 icates that for every psi change in reservoir pressure there is a corresponding 2/3 of a psi chclosure pressure. Thus a depletion of 1500 psi in a sandstone will typically cause a reservosure pressure to decrease by about 1000 psi. Since there should presumably be no porereduction in the surrounding impermeable shales, this 1000 psi decrease in the pay zonepressure would be added to any “naturally” existing stress differences and very good heighfinement can exist in depleted formations. Further inspection of Eq. (5.2) for a “typical” carboreservoir would show a 1/2 psi change in closure pressure for every psi change in reservoisure.

Special logs have been developed and marketed which may, sometimes be of value in deterthe in-situ stress profile (see Chap. 10). However, these logs are based on simple, elaassumptions and should be treated withextreme caution. For sand/shale sequence geology, theis often some “relative truth” in the logs and the actual stresses can frequently be successfullibrated” against the log derived stress values. Carbonate geology tends to be more compthe value of the logs is more questionable. In either case, however, the raw information frologs shouldnever be used. If test procedures are not planned in order to calibrate the logs -thenthe logs should not be run.

σcν

1 ν–------------

OB p–( ) p+=

≈ νν ν

ν



suredthings

f

notede fine0 psi.

ust be

zones inicht, but

An example of a stress/log calibration is shown in Fig. 5.11, showing a comparison of meastress vs. log stress from several sand/shale sequence formations. It is important to note twoon Fig. 5.11: (1) the correlation, which is reasonably strong, isnot 1:1, e.g. the absolute values olog stresses are probably never correct, and (2) this datais not intended for application, but merelyas an example of how one might proceed to calibrate such special logs. Finally, it should bethat while on a scale of “absolute stress,” the correlation appears very good. Examining thdetail shows that the actual stress sometimes differs from the “correlation” by 500 to 100Since the stress of interest is not theabsolute valuebut instead is thedifference- such a deviationrepresents as much as a 50 to 100% error. Thus any type of “general” stress correlation mtreated with care.

A measured/log stress correlation can be based on stresses actually measured in severalthe wellbore usingclosure stress testsas described in Chap. 8. This technique is the only one whprovides quantitative, in-situ data by which to determine the potential for height confinemen

Fig. 5.11 - Stress/Log-Stress Correlation.



s areme ofe war-roughed in

n,ectingthick-o better

ea-r esti-re is

essfulcome

of then fact,e there.

manyand the

ates,ntly

as a, thisres-ed for

ls alsoletionble ined in

ewedg.

requires perforating and testing multiple zones in the well. If a number of fracture stimulationto be performed in the field, and height confinement is questionable and critical to the outcothe stimulations, then such testing coupled with running sonic logs as described above may branted. Alternatively, a 3-D type fracture simulator may be used to infer the in-situ stresses thhistory matching actual bottomhole treating pressure (BHTP) data. This is also discussChap. 8.

In summary,fracture height is the most critical variable to successful fracture treatment desigand yet is one of the most difficult variables to measure. The three variables most strongly affthe ultimate frac height achieved during a treatment are: (1) closure stress differentials, (2)ness of the bounding beds, and (3) net fracture pressure. Several techniques exist by which tquantify frac height, involving everything from qualitative guesses to detailed quantitative msurement. Finally, there is no substitute for experience in an area for picking fracture height omating the in-situ closure stress profile, but whether an established field or a wildcat, theplenty of room for sound, engineering judgments.

3-D Fracture Modeling/3-D Fracture Design

Since fracture height and fracture height growth are the dominant variables affecting succpropped fracture treatment design, fracture models which can account for height growth bepowerful, even indispensable, tools for modern job design or analysis. This is true in spitecommon statement - “We never have the data required to really use such fracture models.” Ione must realize that, in reality, 2-D fracture models are much harder to accurately use sincis never, under any conditions, any way of accurately estimating fracture height in advance

However, we can make reasonable estimates for the in-situ stress distribution. Also, since incases the bottomhole pressure during a treatment is a strong function of the in-situ stressesstress profile, we can use pressure data along with 3-D models to verify or modify these estimfinally arriving at a reasonably accurate description of the formation(s). This is most efficiedone via a pressure history matching procedure as discussed in Chap. 8.

It is important to realize, however, that there are two “types” of 3-D fracture simulators.

Fully (or true) 3-D models calculate fracture width and fracture propagation at every pointfunction of the fluid pressure distribution everywhere inside the fracture. Among other thingsensures that the fully 2-dimensional flow field inside the fracture is used in calculating fluid psure and fracture width at each point. Models such as this are powerful tools and can be usanalyzing quite complex geologic settings and complicated fracture geometry. Such moderequire extensive computer resources and are not usable for any type of “routine” well compdesigns. TerraFrac is one commercial fracture simulator of this type and this model is availaAmoco. The TerraFrac model is discussed and some of its capabilities are briefly describSection 10.2 of this manual. Also, a few different fracture geometry cases are briefly revibelow along with some notes as to which “geometry types” require such “fully 3-D” modelin



h sev-

proxi-ertical

e netoint

.

n withe andmon

length, Per-ndi-as ifbove,o be

existes sev-

A more common, and usable, type of fracture simulator has been termed apseudo 3-Dmodel. Suchmodels are made more “usable” (in terms of time and required computer resources) througeral simplifying assumptions including:

1. The fracture length is at least equal to the fracture height, though through analytical apmations, such models can also give at least rough estimates of fracture geometry where vheight growth may be somewhat greater than fracture length.

2. Fracture height growth at any point along the length of the fracture is related only to thpressure at that point. Also, fracture width (and the vertical fracture width profile) at any palong the fracture length is assumed to be related only to the net pressure at that point

3. The greatest fracture penetration is occurring in the zone where the fracture initiates. Evethese simplifying assumptions, however, pseudo 3-D models have proven in field practicthrough comparison with fully 3-D models, capable of handling many realistic and comcases.

Schematically, a pseudo 3-D type fracture model proceeds as pictured in Fig. 5.12. Fracturepropagation is calculated using calculations and assumptions similar to the traditional, 2-Dkins & Kern (PKN) fracture geometry. Along the fracture length the fracture is broken into ividual segments or cells, and the vertical fracture height growth for each “cell” is calculatedthis cell represented a single Geertsma de Klerk (GDK) fracture geometry. As mentioned athe fracture width and width profile along with the height growth for each cell is assumed trelated solely to the net pressure in that particular fracture segment or cell.

While pseudo 3-D models are good, usable tools, it is important to realize that limitations doand to recognize when the use of more sophisticated models is necessary. Fig. 5.13 illustrat

Fig. 5.12 - Pseudo 3-D Fracture Modeling.

Geertsma deKlerkSolution

Perkins & KernSolution

Theoretical Basis ofPseudo 3-D Type FractureModels

Fracture Length is BrokenInto Segments and HeightGrowth and Width of EachSegment is CalculatedIndependently



mod-

ightvail-prove

a Rayrantsed in

eral possible fracture geometries and briefly comments on the applicability of “Pseudo 3-D”els to each case.

Measuring Fracture Height

Just as it is difficult to pick a fracture height or to estimate the stress profile controlling hegrowth, it is also difficult to measure fracture height after a job. However, several tools are aable and these should be employed whenever possible to allow post-job evaluation and to imfuture jobs. The primary techniques for measuring height include temperature and Gammlogs (GR log); when conditions allow, an open hole completion; and, when the situation warit, downhole televiewer logging. Procedures involved in running these logs are discussSection 10.1 of this manual.

Fig. 5.13 - Fracture Geometries.

Ideal “P3D” Geometry

StressProfile

Radial Frac

OK for “P3D” Modeling

OK for “P3D” Model

Requires “Full 3-D” Model



ctureraturewill

wingkepti-

ssable

g is” lineand

eingand”) can

re issis orwells.ve at

Temperature logs are, and will probably remain, the most widely used logs for measuring fraheight. However, one significant restriction of the log should always be considered. Tempelogs are very shallow investigative tools; and if the fracture deviates from the wellbore, itquickly become “invisible.” In general, a temperature log (or postfrac Gamma Ray log) shofracture height confined exactly to the perforated interval should be treated with extreme scism.

Fluid Loss Height

The prediction of fluid loss height, Hp, is important for the design of a fracture treatment. The loheight represents the net height in the fracture which will dominate the fluid lost to permezones.

One method of selecting Hp, is illustrated in Fig. 5.14, where an Spontaneous Potential (SP) loused. For this procedure, the net section to the left of a line 1/3 the distance from the “shaleto the maximum “sand” deflection. This procedure neglects potential (if any) loss to “shale”“dirty” sands. A Gamma Ray Log might be used in a similar manner, with fluid loss height bthe net section to the left of a line 1/3 the distance from the “shale” line and the maximum “sline. If adequate definition from a SP or GR log cannot be obtained, other cutoffs (porositybe used.

For a given field, the potentially arbitrary nature of this procedure is overcome if the proceduconsistently used for fluid loss coefficients determined from minifrac pressure-decline analycalibrated along with loss coefficients from the success or failure on past designs of offsetThis works because fluid loss height and fluid loss coefficient are multiplied together to arri

Fig. 5.14 - Selecting Fluid Loss Height.

Selecting Fluid Loss Height

“Shale” Line

Fluid LossOr

“Permeable” Line

Fluid Loss Height = Net section height toleft of “permeable” line

Neglect Shales, ?

Max.“Sand” Line



loss

are

a “fluid loss capacity” analogous to reservoir flow capacity(kh). Doubling fluid loss height andhalving fluid loss coefficient yields exactly the same results as the base values. The fluidheight is commonly and wrongly confused with net pay height. Fluid loss height willalways begreater than the pay height. In many reservoirs where the net pay cutoffs from porosity logswell established, one should ensure that all net pay is included as fluid loss height.



. Theof the

ig. 5.15ts and

treat-

ith the

,other.

nts are

an--

5.2 Fluid Loss

This section discusses the values for thefluid loss coefficientandspurt lossused in fracture designand/or analysis.

The amount of fluid lost to the formation during a treatment is a primary design considerationlost fluid is essentially wasted and represents a significant portion (i.e., generally 30 to 70%)total fluid and cost of treatment.

The rate of fluid loss is described by the expression

(5.3)

whereC is the fluid loss coefficient,A is the fracture wall area andt is the time since the areaAwas exposed to fluid. The loss coefficient depends on three separate effects as shown on Fand each of the three have the square root of time relationship given in Eq. (5.3). These effechow they are determined are discussed below.

The best estimate of fluid loss is obtained from the pressure decline analysis of a calibrationment (discussed in Chap. 8).

Fluid Loss Coefficient,Ct

The composite fluid-loss coefficient depends on three separate linear flow mechanisms wseparate coefficients,CI - fracturing fluid viscosity relative permeability effects,CII - reservoirfluid viscosity-compressibility effects, andCIII - wall building effects. In any fracturing treatmenteach of these mechanisms acts simultaneously to varying extents and complements theThese mechanisms act analogously to a series of electrical conductors and their coefficiecombined as shown in the following equation:

(5.4)

The fracturing fluid viscosity and relative permeability (i.e.,filtrate) effect can be obtained fromthe following equation:

(5.5)

Permeability,kf (md), to the fracturing fluid filtrate may be obtained by correcting pressure trsient test derived permeabilities (ko, kw or kG) by reducing the value by a factor of about 5. How

qlC A

t----------=

1Ct----- 1

CI------ 1

CII------- 1

CIII---------+ +=

CI 0.0469k f Φ ∆p

1000 µ f------------------------=


Fluid Loss

notis ton be

atu-rositye

hole

baseer.tion

ever, if the filtrate from the frac fluid is similar to the reservoir fluid, than this reduction isnecessary (i.e., water frac on a water injection well). The purpose of the reduction factoraccount for relative permeability effects. If relative permeability curves are available they caused to determinekf.

Effective porosity should be obtained by correcting the formation porosity for in-place fluid srations. If, for example, a water based fluid is being used to frac a reservoir, the effective pois reservoir porosity multiplied by(1-So-Sg). If a hydrocarbon based fluid is used; the effectivporosity is the reservoir porosity multiplied by(1-sw).

Pressure differential, (psi), across the fracture face is the difference between bottomtreating pressure (i.e., ) and reservoir pressure.

Since polymers are generally filtered from the base fluid by a low permeability matrix, theleakoff fluid viscosity, , is usually that of 2% KCl water containing a slight amount of polymA maximum value for might be 5 cp with a minimum value of 0.5 cp, depending on formatemperature.

Fig. 5.15 - Fluid Loss.

∆P Pf Pp : p– pore, f– filtrate, c– Cake–=

CII =

CI =

CIII =

∆Pkc φ

2µp------- (OIL)

(CARTER, SPE 1957)

∆Pk

2µf-------- (GAS)

k c ∆P

2µf f c------------- (POLYMER, SOLIDS)

fc FRACTION OF FLUID LOSS ON CAKE

Fra

ctur

e

Reservoir

CIICICIII

Invaded Zone(usually ~ 2-3 in.)

WallCake

Three Components of Fluid Loss:CI = Frac Fluid Effect

CII = Reservoir Fluid Effect

CIII = Wall Building Effect

∆p∆p BHCP PN PR–+=

µ fµ f



the

h as

lowh

ientssure

en-pres-s testr, i.e.,neg-

ther-r-t timetraightd loss

loss

TheCI effect is primarily governed by the viscosity of the filtrate of the fracturing fluid. Sinceviscosity is generally very small (i.e., < 1 cp), theCI term is generally large for current fracturingfluids and is not effective for fluid loss control. This is not the case for very viscous oils sucthose used during the 50s and 60s.

The reservoir fluid viscosity-compressibility (i.e.,formation fluid) effect can be obtained from thefollowing equation:

(5.6)

TheCII effect is primarily governed by the compressibility,ct and therefore is very important forliquid filled reservoirs such as oil wells or water injection wells. These generally have a veryct compared to gas reservoirs. However, theCII term has negligible control in gas reservoirs whichave a relatively highct (ct gas = 1/pr gas).

Permeability to the reservoir fluids(kHC) (millidarcies) should be measured by a pressure transtest. Viscosity and compressibility of the reservoir fluids should be determined as in a pretransient analysis (e.g., lab tests, tables, or calculations).

Thewall building effect for the fluid loss coefficient is determined from data obtained experimtally in a laboratory as shown in Fig. 5.16. A standard fluid loss test is conducted in a highsure-high temperature Baroid filter press containing core samples or filter paper. The fluid losis run with a pressure differential of 1000 psi as standard, although may be much large3000 psi. Additional work is required on the effect of which is currently assumed to beligible.

For very lowk rocks (< .1 md), the tests should be run using filter paper instead of cores. Owise, the data forCIII will be erroneous due p of the filtrate through the core during the early potion of the test which has a high loss rate. The fluid loss in cubic centimeters is measured aintervals of 1, 4, 9, 16, 25, and 36 minutes; and these fluid loss values are then plotted on scoordinate paper against the square root of time in minutes (Fig. 5.16). The experimental fluicoefficient is then calculated as follows:

(5.7)

wherem is the slope of the plotted data (cc/ ) andA is the cross sectional area (cm2) of the corewafer.

Normally, CIII is furnished by the fracturing service company. For critical treatments, fluidtests for the specific fluid and in-situ conditions should be requested.

CII 0.374 ∆pkHC ct ΦHC

1000 µHC--------------------------------=

∆p∆p

∆

CIII 0.0164m/A=

t


Fluid Loss

tag. At2t thefor-

veryd. Thef thehaseymer

akes

per-roatsal-

ures.y

n suchsilica

ures.

Fig. 5.17 shows a qualitative comparison ofCIII values for different fluids based on laboratory dafrom low permeability cores. These test data were run at 150 F and one polymer loadin250 F, it has been found that theCIII values for most frac fluids increased by a factor of 1.5 tobecause of the reduced viscosity of the filtrate through the wall (Fig. 5.15). Keep in mind thadata in Fig. 5.17 is approximate and the wall building ability of a fracturing fluid depends onmation temperature, and the fracturing fluid type and polymer loading under consideration.

The addition of 5% hydrocarbon to crosslinked water systems (Type III, on Fig. 5.17) can be aeffective loss control additive for permeabilities less than 1 md and is generally recommendeaddition of a hydrocarbon dispersion works primarily by reducing the relative permeability opolymer cake to water and by droplet plugging of pore throats. Adding the second (oil) preduces the relative permeability to water. Since the hydrocarbon works primarily in the polcake, this technique provides little benefit if most of the fluid loss isCI or CII controlled, as in highpermeability reservoirs. The effect of droplet plugging on a low permeability formation also mwall building fluid loss control important for emulsion and foam fluids.

Solid fluid loss additives are sometimes required for efficient fracturing in moderate to highmeability or naturally fractured reservoirs. These agents work by blocking the larger pore th(i.e., required to form wall building) and fractures. Fig. 5.18 shows the effect of silica flour (Hliburton's WAC-9) onCIII . Such agents are silica flour, 100 mesh sand and manufactured mixtThese additives must be used withextreme cautionif they are mixed with the proppant, since thecan plug the proppant,unless they are designed to dissolve in the produced fluid. Use of theseadditives with proppant laden fluid is not recommended unless absolutely required and thethat the total does not exceed 1% of the total proppant during the treatment. The addition offlour to the padat a loading of 15 lb/1000 gal has been used to seal off closed natural fract

WALL BUILDING FLUID LOSS TEST

Fig. 5.16 - Standard Fluid Loss Test.

°°



atural

lterment.spurt, thevery

5.1 is

ntsForle 5.1nal

Also, 100 mesh sand for the initial sand stage (1/4 to 1 lbm/gal) is effective for sealing open nfractures.

Spurt Loss

The total fluid lost when wall building dominates is a combination of the fluid lost before a ficake has begun to form (spurt loss) and the fluid lost through the filter cake during the treatThe point where the fluid loss curve intersects the ordinate on a fluid loss plot is known as theloss (see Fig. 5.16). For fluids that build effective wall cakes and low permeability formationsspurt loss is low. In this case, a value of zero (0) is used for spurt loss if the permeability islow (i.e., less than 0.05 md).

Generally, the service company supplies the spurt loss values for their various fluids. Tablean example from the Dowell “Fracturing Fluids” book showingCIII (i.e., Cw) and spurt for anon-wall building fluid for various high permeability rocks (i.e., relatively high spurt) and amouof silica flour. Spurt loss can be significant for moderate to high permeability formations.example, assume a 500 ft fracture radius, 50 ft fluid loss height, and 5 md permeability. Tabshows 20 gals/100 ft2 spurt loss even with 20 lb/1000 gal silica flour. This equates to an additio20,000 gal of fluid loss which must be included in the treatment design.

Fig. 5.17 - Wall Building for Various Fluid Systems.


Fluid Loss

Fig. 5.18 - Silica Flour for Moderate to High Permeability.

Table 5.1 - Spurt Loss Dependence on Permeability and Additives.

FLUID LOSS OF FLUIDS PREPAREDWITH J160 THICKENER

J160(lb/1,000 gal)

Temperature( F)

K(md)

J84(lb/1,000 gal)(Silica Flour)

Cw X 1000(ft/

Spurt(gal/100 ft 2)

202020

125125125

2.21.5

22.5

02050

30.09.96.0

0.07.9

59.0

3030

125125

1.04.8

2020

5.04.2

1.819.5

4040

125125

1.04.8

2020

5.04.2

1.819.5

6060

125125

2.93.1

2020

4.94.1

15.519.8

80808080

125125125125

3.73.95.1

25.0

20304050

3.31.83.13.0

5.95.99.3

44.0

Permeability0.1 - 150 md

0 20 30 40 50 60 70 80 90 1000.0001

0.0050.0040.003

0.002

0.001

0.00050.00040.0003

0.0002

WAC-9 Concentration -- lb/1000 gal water

CW

-- ft

/min

1/2

° min



FLUID LOSS PROBLEM

Find: The Combined Fluid Loss Coefficient

Given: Gas Reservoir: 170 F;

Pr = 2300 psi,

;

Sg = 0.50;

k = 0.1 md (buildup test)

;

BHTP = 4000 psi

Lab Data: @ 150 F

(For Water Filtrate: 0.45 cp @ 150 F

0.21 cp @ 250 F)

°

ΦHC 0.125=

µg 0.0174 cp=

CIII 0.001 ft\/ min= °

°

°

UFCIII: Calculate Total Fluid Loss Coefficient

Res Fluid Visc (cp) 0.017

Filtrate Visc (cp) 2.4

Formation Temp (deg F) 170.

Pressure Diff (psi) 1700.

C-III 0.001

Permeability (md) 0.100

Porosity (fraction) 0.125

Compressibility (lbs/gal) 200.0

((Clos Pres + 500 (psi) - Res Pres)

@ Test Temp (deg F) 150.

C-I = 0.004463

C-II = 0.026517

C-III = 0.001090 ft/min**.5 at 170. (deg F)

Harmonically Weighted Ct = 0.00085

PF3 Continue PF12 Exit

09:23:40 03/04/92

File : UFDEMOS FRC Well Name: CARTHAGE (COTTON VALLEY) FIELD

User ID: ZWXY01

U L T R A F R A C 2 . 0


Fluid Viscosity

fluidandrease.the

dmit-uffi-ficient

lized,eachea wither

nt Co.hearurfaceed byspeed

rateratee cup.eters.

er, ofendentasingired tolated by

nian,lected

5.3 Fluid Viscosity

For most fracture treatments, a significant portion of the cost is for chemicals to create awhich will maintain a relatively high viscosity throughout the treatment. As the treatment timeformation temperature increase, the relative cost for the required chemical additives also incFluid viscosity is required primarily to transport the proppant from the wellbore to the tip offracture. Fluid viscosity also affects the fracture width which is a consideration for proppant atance; however, sufficient width is normally created for proppant entry by a fluid which has scient viscosity for proppant transport and/or as a result of the fracture length created by a sufpad.

Viscosity Determination and Rheological Models

The viscosity values of fluids are determined by laboratory tests. The simplest, but ideaexperiment of fluid flow is fluid being sheared between plates moving parallel and relative toother. The shear stress on the fluid is the shear force exerted on the plates divided by their arthe units of pressure. Theshear rateor velocity gradient is the relative velocity divided by distancof separation and has the units of 1/time, usually in sec-1. The viscosity is defined as the sheastress/shear rate.

The rotating cup/bob viscometer has been popularized in the industry by the Fann Instrume(now under the ownership of NL Baroid). As shown in the idealized drawing, Fig. 5.19, the sstress is the force exerted on the walls (sensed by the torque on the bob) divided by the sarea, and the shear rate is the relative velocity of the stationary bob and the rotating cup dividthe gap distance. For the standard system, i.e., the R1-B1 Rotor-Bob Geometry, a rotatingof 100 RPM represents a shear rate of 170 sec-1, and a speed of 300 RPM represents a shearof 511 sec-1. Unfortunately, this device is not suited to some crosslinked polymer fluids, e.g. bocrosslinked gels, because of their viscoelastic nature. Borate gels can “crawl” up and out of thIn spite of this, most published data for borate gels are determined using cup and bob viscom

Viscosity is sufficient to characterize the stress-flow behavior, i.e., the rheological charactsome simple fluids such as water and refined oils. These simple fluids have shear rate indepviscosity. Most fracturing fluids, however, show shear-dependent viscosities, usually decrewith increasing shear rate, i.e., shear thinning, and thus more than one parameter is requcharacterize the rheology. Experimental shear stress and shear rate data are usually corresome approximating rheological model.

The rheological models commonly used in the industry for many types of fluids are the NewtoBingham Plastic, and Power Law Models, as shown in Fig. 5.20. These models are sebecause they yield straight lines on linear or log-log graphs of shear stress vs. shear rate.



Fluid Flow (Rheology)

Fig. 5.19 Fluid Testing.

Fig. 5.20 - Models for Fluid Flow.

I. Idealized

A

F, ν

ν(x)Fluiddx

τ = Shear Stress = F/A (Pressure)

= Shear Rate = νd-- d ν

dx----- 1

time---------( )=ϒ̇

II. Rotating Cup & Bob(e.g., Fan Viscometer:

Industry Standard)

TW

Turn Cup: WTorque on Bob: T

Ri

Ro

H

ϒ̇ νd--

w R o

Ro Ri–----------------≅=

τFA--

T /Ri

2πRi H------------- T

2πRi H-------------= = =

Rheological Models

I. Newtonian II. Bingham III. Power Law

τ µ

τ µϒ̇=

τYp

τ Yp µp+=

µp

log τ

n'

log1.0

K'

τ K'ϒ̇n=

Yp →0 n' →0

Newtonianµp µ=

NewtonianK' µ=

ϒ̇ ϒ̇ ϒ̇

ϒ̇


Fluid Viscosity

vis-

ieldparentzerory for

aighto-

elured,d

tory.when

t forflow,

le-upat frac

mplesity atple

ws ar anal-

ries.0.2

ntersy flows afterfrac-

A Newtonian type fluid has a linear relationship between the variables with a slope equal tocosity, i.e., water, brines, and oils.

A Bingham Plastic type fluid differs from a Newtonian fluid by a non-zero stress (i.e., Plastic YValue) at zero shear rate. The slope of the line is termed the Plastic Viscosity (not equal to apviscosity). The initial work on these fluids was done by Bingham on paints and printer's ink -flow (shear rate) on vertical surfaces (shear stress). This fluid model is used in the industdrilling muds and cements.

The Power Law fluid model is commonly used for representing frac fluids and predicts a strline on a log-log plot with the slope denoted asn' (generally < 1) and termed the Power Law Expnent or Flow Behavior Index(n' = 1, Newtonian;n' > 1 shear thickening;n' < 1, shear thinning).The stress at a shear rate of unity is denoted asK' and is termed the Consistency Index. This moddoes not predict a yield value (no flow with stress, e.g., can form a stationary lip when poremains as a glob on the table). TheK' andn' values of real fluids change with increasing time antemperature (generallyK' decreases and n tends toward unity) and depend on their flow hisMost service companies attempt to account for downhole flow conditioning in some mannertesting crosslinked fluids.

Although the power law is the primary model used for fracturing fluids, it does not accounother aspects of flow behavior exhibited by many fluid systems, such as nonhomogeneouse.g., slip or particle migration, or viscoelasticity. These factors can influence rheological scaand proppant transport and are presently the subject of research. All fracturing simulators trefluids as if they were homogeneous power-law fluids.

Fig. 5.21 defines and gives an example of apparent viscosity for a power law fluid. The exashows a realistic case for fracturing fluids. Different service companies have reported viscodifferent shear rates (i.e., 170 sec-1 or 511 sec-1). The rate in a fracture can be 40/sec. The examshows that the same fluid can be reported by one company to have 100 cp (at 170 sec-1), anotherto have 58 cp (at 511 sec-1) and the fluid may have 206 cp (at 40 sec-1) in the fracture.Therefore,in selecting fluids it is importantto know what shear rate the data represents. Table 5.2 shotypical rheological data set presented by service companies for use in fracture design and/oysis.

Fluid Entry Conditions and Temperature Considerations

The viscosity of some fracturing fluids, can be very sensitive to their flow and thermal histoFluids often encounter intense flow energies while being pumped downhole, ranging fromhp/ft3 to 8 hp/ft3. Delayed crosslinked gels are formulated to start crosslinking after the gel ethe fracture and starts to heat up to avoid degradation of the crosslinks during high energcondition. Foams and oil-base gels, on the other hand, may actually achieve better viscositiesubjected to high-energy flow conditions. Thus, the viscosity of the frac fluid as it enters theture is frac-fluid system dependent and is influenced by flow and thermal conditions.



eres-basetightgller

holeriationes lin-e cur-Moreted orprofiles

An entry temperature and corresponding wellboren' andK' values are required to calculate thentry viscosity of the frac fluid. As the fluid flows down the wellbore it acquires heat from theervoir and from conversion of flow energy to heat. As an estimate for fluid heat up for water-fluids and CO2 foams at typical fracturing flow rates, one can use 10°F temperature increases a7000 ft, 10,350 ft, 12,900 ft, 15,120 ft, and 16,780 ft. Thus, if pumping to 13,000 ft, one mexpect the fluid entry temperature to be about 30°F higher than surface temperature. If pumpinoil-base gels, the fluid heats up roughly 25°F at each of the above depths because of their smaheat capacities (e.g., 0.4 Btu/lbm -°F vs. 1.0 for water).

As the fracturing fluid flows down the fracture it continues to heat to reservoir static bottomtemperature (BHT). Some fracturing design programs assume a bilinear temperature vabased on the Perkins and Kern width model as shown in Fig. 5.22. The temperature increasearly from the entry temperature to the reservoir temperature during the first one-quarter of thrent fracture wing length and remains constant for the remaining three-fourths of the wing.advanced programs calculate the fluid-temperature profile down the fracture using calculaassumed heat-transfer coefficients and material heat capacities. The resulting temperatureare sensitive to fluid heat capacity and may vary significantly from Fig. 5.23.

• Example

Fig. 5.21 - Effect of Shear Rate on Power-Law Viscosity.

τ

τ1

µa

ϒ1

Power Law: Given: n' = .5

µa = 100 cp, =170 sec -1

Find: K', µa at 40 and 511 sec -1

K' = 100 x (170) .5/ 4.8 x 104 = 0.27µa (511) = (170/511).5 x 100 = 58 cpµa (40) = (170/40).5 x 100 = 206 cp

µa4.8 10

4K'×

ϒ̇ 1 n–( )--------------------------=

•

µa cp=

For Power Law Model

1/sec, sec1–

K' lb sec–n'

/ft2

=

Find: K', µa at 40 and 511 sec-1

K' = 100 x (170).5 / 4,8 x 104 =. .027

µa (511) =170511--------( )

0.5x = 58 cp

µa (40) = 17040--------( )

0.5x 100 = 206 cp

ϒ

ϒ =

•µa

τ1

ϒ̇----= Depends on ϒ̇( )•


Fluid Viscosity

d as

d orga-

As alluded to previously, the entry viscosity of the fluid depends on the type of fracturing fluiwell as on the fluid and thermal histories at the surface and down the wellbore.Not all fluids havemaximum viscosities at the entry temperature. Some gelled oil systems, and most all delaye

Table 5.2 - Typical Service Company Rheology Data (DS - 1984).

Fluid

Temp Time

n' K'

Viscosity (cp)

( F) (hr) 170 sec-1 511 sec -1

YF440YF440YF440YF440YF440

225225225225225

12468

0.6000.6570.7460.8080.848

0.0950.0520.0170.00650.0027

582426225116

60

375293167

9450

YF440YF440YF440YF440YF440YF440

260260260260260260

123456

0.6400.6970.7450.7860.8200.849

0.0360.0230.0140.00910.00570.0036

272230186145109079

183165141114

8967


260260260260260

12468

0.6000.6570.7460.8080.848

0.0560.0350.0160.00810.0047

342289205145103

221197157117

87


285285285285285

12468

0.6400.6970.7860.8490.888

0.0300.0180.00680.00290.0014

228178108

6539

152130

865433


260260260260260

12468

0.5800.6370.7260.7880.828

0.0910.0550.0230.0110.0058

502409270177115

317273199140

95


285285285285285

12468

0.6000.6570.7460.8080.848

0.0570.0330.0130.00560.0027

350274166100

59

225186127

8150

Fig. 5.22 - A Bilinear Temperature Variation Down the Fracture.

°



rature.5.23. Thethat

nif-

l to be

to sittem-ttom

nometallic crosslinked gels show viscosities to increase as the fluid heats to reservoir tempeAfter attaining reservoir temperature, an eventual decline in viscosity will be observed. Fig.shows typical viscosity trends for various fracturing fluids as a function of time at temperaturefirst point at 0 hours is the entry point and in this case it takes 1.3 hours to attain BHT. Notethese viscosity trends are at different BHT.

Reservoir Temperatures

Reservoir temperature is a very important variable since the viscosity of the fluid will vary sigicantly depending on the amount of time the fluid has been at reservoir temperature (TR onFig. 5.22). Therefore, it is best to get a measured BHT.Notice - It is not the maximum log tem-perature shown on the open hole logs. That value is much too low. The difference between 250°Fand 270°F can be significant.

Reservoir temperature should be determined by running a static temperature log in the welfractured. This log can be run with a cement bond log. The well must be atstaticconditions for thelog to yield the temperature that we are interested in. It is suggested that the well be allowedidle, with no downhole operations of any kind, for at least 1 week prior to running the staticperature log. After a number of such logs are run (5-10 wells) in a given field, the static bohole temperatures measured can be plotted against depth to mid pay to determine astatic temper-ature gradient. Static temperature is expressed asT static = (T gradient (°F/ft) * Depth (ft)) +

Fig. 5.23 - Typical Gel Viscosity Trends with Time at Temperature.


Fluid Viscosity

adient,

y at 4

sity.tod frac-

nryed by

Ambient surface temperature. Once sufficient data has been obtained to determine this grthe calculated static temperature can be used on future frac designs.

Note from Table 5.2 that for a YF400-5 fluid, a 25°F error in temperature (285°F vs. 260°F) resultsin only 2/3 the desired viscosity at 1 hr (228 cp vs. 342 cp) and only 1/2 the desired viscosithr (108 cp vs. 205 cp).

Get the most accurate BHT possible!

Effect of Proppant on Viscosity

When proppant is mixed into a fracturing fluid, the effect is an increase in apparent viscoRecent experiments indicate that bothK' and n' are changed when proppant is addeduncrosslinked fluids, but there is no consensus on the best correlations to use on crosslinketuring fluids. The proppant effect onK' for the slurry can be approximated by:

with Ck = (1 - Cv /Cm)-2.5

HereCv is the proppant volume fraction andCm is the maximum possible proppant volume fractioset to 0.6. This expression forK'slurry is supported by a limited amount of unpublished laboratodata. Fig. 5.23 shows the effect of proppant concentration on slurry viscosity as developAmoco and GRI, respectively.

Fig. 5.24 - Effect of Proppant on Slurry Viscosity

K 'slurry K ' fluid Ck( )n'×=

zlkb02.038

Sand Concentration, lb/gal

Slu

rry

/ Flu

id V

isco

sity

1000 2 4 8 12106

101

Pnet = E' [µQL]1/4Η

GRI

14

AMOCO



icientucey (i.e.,

w sub-com-s and

nsider-effectrolledreases.rates

he 170

ted byre toy ofwouldtion,to 10

ettlingencedctured vis-f vis-

s in ad be, thises notles areate isscosity

Summary For Fluid Viscosity

Fluid viscosity is critical for the successful execution of pressure controlled treatments. Suffviscosity is required for proppant transport, while excessive viscosity will proportionally redthe fracture penetration prior to the fluid pressure reaching the formation's pressure capacitinefficient fracture extension).

For proppant transport, crosslinked gels are preferred over noncrosslinked gels. Studies shostantial reduction (e.g., 78%) in proppant fall rates through crosslinked gels, under shear,pared to noncrosslinked gels with the same apparent viscosity. The fall rate through foamemulsions are also believed to be less than indicated by the apparent viscosity. Another coation is particle concentration which increases slurry viscosity and retards particle fall. Theof increased slurry viscosity due to proppant concentration is important for pressure contdesigns and requires the base fluid's viscosity to be reduced as proppant concentration incAlso, the apparent viscosity for non-Newtonian fluids depends on the shear rate with lowerproducing higher apparent viscosities. Generally, the shear rate in the fracture is lower than tsec-1 normally used to characterize fluids.

The above considerations can significantly reduce the viscosity requirement over that indicaa direct use of Stokes Law. An example, illustrated in Fig. 5.3, show that if proppant fall webe limited to 10 ft in four hours, a direct application of Stokes Law would require a viscosit1500 cp for 20-40 mesh sand. Assume that under fracturing conditions the crosslink effectretard fall only by 50% in contrast to the 78% for ambient and laboratory conditions. In addiassume the slurry dehydrates from a low proppant concentration as it enters the fracturelbm/gal, Fig. 5.3, at the end of the treatment. For these conditions, the effect of hindered swould be equivalent to a multiple of 3.2 in the time-averaged value of viscosity. If the referviscosity is at 170 sec-1, the shear rate in the fracture is 40 sec-1 and the fluid can be characterizeby the power law with n = 0.6, the apparent viscosity would be 1.8 times greater in the frathan for the reference. If, during the time in the fracture and at reservoir temperature, the fluicosity reduces by a factor of 10 with a log-viscosity vs. time relationship, the average value ocosity would be 4.3 times the final value. Combining these factors (2 x 3.2 x 1.8 x 4.3) resultmultiple of 50, as shown in Table 5.3, and for the fluid considered, sufficient viscosity woulachieved if it had a final viscosity of 1500/50 = 30 cp at the end of the treatment. Furthermoreestimate may be conservative since a reduction of the crosslink effect was used, the fluid doexperience reservoir temperature for a portion of the fracture length, and suspended partictransported in the center portion of the channel (for viscoelastic fluids), where the shear rlower and the apparent viscosity higher than the channel average. Consequently, the virequirements for proppant transport can be grossly overestimated and a reference value of100 to150 cp can provide significant transport.


Fluid Viscosity

es to
The next chapter, Chap. 6, gives more background for selecting specific fluids and additivachieve the desired viscosities throughout a treatment.
Table 5.3 - Why Low Viscosity Fluids Work.

Sufficient Viscosity (µ = 1500cp)

1) X-L FLUID (HARRINGTON-HANNAH

β = 0.22; USE 0.5

2) HINDERED SETTLING: 1 10 (ppg) 0.3

3)µ 40 =µ 17017040---------

0.4; (n' = 0.6) 1.8 OR 0.55

4) µ i = 10 x µ f (e.g. 500 50) 0.23

0.5 x 0.3 x 0.55 x 0.23 = 0.019

x 1500 = 28 cp (FINALµ )



rpreta-

nt tothelow,

refracoppedtween

reasesficantcrit-reduc-Some

5.4 Treatment Pumping

There are numerous parameters of some importance to hydraulic fracturing design and intetion. The remainder of this chapter is devoted to the most critical of these.

Fracture Radius

The term radius implies one wing of the fracture or the fracture’s half length and is equivalethe reservoir notationxf. However,xf is the apparent productive length and may be smaller thandesign value of hydraulic fracture length as shown in Fig. 5.25. If the production is in bilinear fthe productive length is increasing with time, or if the conductivity is very low, (i.e., FCD < 1), theproductive length may be much larger than the apparent productive length, xf.

Consequently, the design radius should be larger than the desired productive length,xf, because ofthe above discussion and for a safety margin. If the created fracture length is too small, amay be required, and there is some question if refracing can effectively increase the prlength. Ideally, a calibration for each field should be made to determine the relationship bedesign radius and productive length,xf.

Pump Rate

The consideration for pump rate has many facets and some fiction. Although pump rate incnet pressure in the fracture, and hence, the potential for height growth, normally the signieffect on height believed by some in the industry is more fiction than fact. If height growth isical, reducing rate toward the end of the treatment will accomplish the required necessarytion in net pressure and will facilitate the surface handling of the higher sand concentrations.of the considerations for rate are discussed below.

Fig. 5.25 - What is Fracture Length?

Fracture Length = ?

Pay

ProductiveLength

ProppedLength

HydraulicLength


Treatment Pumping

, i.e.,vol-

ssindi-effi-wereffi-, i.e.,iencyh after

in therease

if fric-

eration,

Fluid Volume:

As shown on Fig. 5.26, the pump rate affects all three volume terms of the continuity equationpump time, fluid loss time, and fracture volume (width). Increasing pump rate increases theume of fluid stored in the fracture (increasedp, w) and decreases the volume lost (less fluid lotime). As a result, pump rate affects fluid volume required for a given length. The examplescate that the balancing point is for fluid efficiency of about 0.6-0.7. For treatments with higherciencies, increasing rate will store more volume than is saved in fluid loss, while for loefficiencies the opposite occurs. Rate becomes most important for very low efficiency. Asciency goes to zero, the volume required for a given length is inversely proportional to ratedoubling rate reduces the required volume by one-half. The increase in volume for high efficis generally not a consideration because the extra stored fluid will increase the fracture lengtshut-in, i.e., free extension will occur until the tip screens out.

Increased pump rate will significantly increase friction-loss pressures in the tubulars (andperforations if inadequate number and size) and result in a small, but potentially critical, incin net fracture pressure, as shown in Fig. 5.27.

The increase in friction pressures also can dramatically increase horsepower requirementstion-loss is a significant portion of the total surface pressure.

For cases where horsepower and pressure capacities of tubulars are an important considthese considerations for rate become important.



Transport and Viscosity:

Pump Rate and Time

Fig. 5.26 - Effect of Rate on Volume.

Pump Rate and Time

SURFACE AND NET FRAC PRESSURES

SP - CLOSURE - HEAD + FRICTION + p

HHP - SP x Q HHPF ∼ Q2.75

Fig. 5.27 - Effect of Rate on Pressures.

VOLIN VOLLOST= VOLFRAC Qt→+ 8/3

π HpCL t WHL+=

=

VOLQ

-------- IN

µQL( )1/4ρ∼

=

FRAC

LOSTlog Q

log VOL

FOR FIXED LFLUID LOSS &VOLUME REQ’MENTS

1 ) Q2 1.5 Q1× LOST2→ 0.82 LOST1 FRAC2,× 1.11 FRAC1×= = =-18% +11%

CAN SHOW VOLIN ifVOLFRAC

VOLIN-------------------> eff 62%>=

2 ) Q2 2/3Q1 LOST2 1.22 LOST1; FRAC2× 0.90 FRAC1×= = =+22% -10%

3 ) eff 0 VOLIN 1/Q∼→

F Q1.75∼ µQL( )1/4∼

TURBULENT( )

1 )Q2 1.5 Q1× F2→ 2.0 F1;HHPF2× 3.0 HHPF1

;p2× 1.11 p1×= = = =+100% +200% +11%

2 )Q2 2/3Q1 F2→ 0.49 F1;HHPF2× 0.33 HHPF1

;p2× 0.90 p1×= = = =-51% -67% -10%

MAY BE CRITICALTO HEIGHT CONFINEMENT


Treatment Pumping

mount5.28.)

ments.sportallow

gnifi-ystemsnif-

Increasing pump rate will increase proppant transport distance (per fall distance) by an aapproximately proportional to the pump rate increase (as shown by the examples in Fig.(Note that transport distance is independent of height.)

The examples also indicate that increasing pump rate can reduce the fluid viscosity requireThese reduced requirements result from both the lower ultimate viscosity for proppant tranneeded and from the smaller residence times which reduce the initial viscosities required tofor time degradation. This can be very significant for large jobs in hot zones.

However, high pump rates down “small tubulars” (i.e., high friction pressures) may cause sicant fluid degradation for some fluid systems. These systems are nondelayed crosslinked swith metallic bonding (e.g., Titinate). Guidelines for these systems which will not result in sigicant degradation are:

Pump Rate and Time

PROPPANT TRANSPORT

& 1.5 > µ ENDURANCE

Fig. 5.28 - Effect of Rate on Transport and Viscosity Requirements.

Tubulars Maximum Rate (bpm)

2-3/8 7

2-7/8 12

3-1/2 15

4-1/2 28

5-1/2 40

7 65

HV2

V1

D

DH--

V1V2-----= V1 FLUID VELOCITY=

Q

HW------- Q

H µQ( )1/4------------------- Q

3/4

Hµ1/4----------- or ; V2∼ ∼ FALL RATE

1µ--∼= =

DH-- Q

3/4µ3/4

H----------------- (D indep. of H)∼

1 )Q2 1.5 Q1 D2→× 1.35 D1 same µ( ) ;× µ2 0.79 µ1× same D( )= = =+35% D -21% µ

2 )Q2 2/3Q1 D2→ .74 D1 µ2 1.28µ ,= = =-26% D +28%µ



at very

nker,rove

ifferent

e sur-lcula-

Gen-

For these degradable systems, pumping down the annulus can cause significant degradationlow rates due to the effect of the tool joints.

Degradation is not a consideration for fluids which rebuild their crosslink, i.e., borate crosslior fluids which benefit from shear, i.e., foams or emulsions. High pump rates can actually impthe quality of foams and polyemulsion fluids.

Summary for Pump Rate:

Pump rate has far reaching effects on many aspects of a fracture treatment, and these daspects (Fig. 5.29) should be weighed o arrive at the optimum rate for a given treatment.

Depth

The depth to mid point of perforations is used in the wellbore hydraulics equation to estimatface pressure. At the present time it is considered to be true vertical depth for hydrostatic cations.

Friction Pressure

The pressure loss associated with the flow of fracturing fluid and proppant through tubulars.erally the values to be entered are estimated for the fluid system in units of psi/100 ft.

Pump Rate and Time

Summary

I. VOLUME REQUIREMENTS REDUCE VOLUME:

a) EFF > 60 - 70%; DECREASE RATEb) EFF < 60 - 70%; INCREASE RATEc)

II. PROPPANT TRANSPORT INCREASING RATE WILL:

a) BETTER TRANSPORTb) REDUCE REQUIREMENTSc) REDUCE TIME ENDURANCE FOR FLUID

III. PRESSURES DECREASING RATE WILL:

a) LESS PRESSURE FOR TUBULARSb) LESS HHPc) REDUCE NET FRAC PRESS.

Fig. 5.29 - Considerations for Rate.

EFF 0; VOL 1/Q∼→

µ


Treatment Pumping

anies'mined,ed.

The following table shows an example of data obtained from various fracturing service compliterature, measured at 20 bpm. Once the type of frac fluid and tubular size has been deterthe base friction value from the service company for the required fluid system can be enter

Table 5.4 - Turbulent Friction Pressures at 20 bpm (psi/100 ft).

Fluid 2-3/8 2-7/8 3-1/2 4-1/2 5-1/2 2-3/8:4-1/2 2-3/8:5-1/2 2-7/8:5-1/2

DowellYF-400 80 40 14 4.5

HalliburtonVersagel 1500 120 55 27 9.0 4.0 47 13 25

WesternApollo 20-40 120 55 20 5.5 2.5 33 8 13

Polyemulsion 370 145 55 20.0 8.0 90 28 40

Water 460 165 60 15.0 5.5 100 20 35

K = The constant that can range from about 1/4 to 1/3.Normally, K = 1/3 for sandstones

OB = Overburden pressure - generally 1 psi per foot of depth

P = Reservoir pressure



Fig. 5.30 - Example Friction Pressure Data for”Base Friction.”

A B C D E F G H I

JK

L

M

N

Apollo Gel 20 30 40

1000

500

100

50

10

Fric

tion

Pre

ssur

e -

psi/1

000

ft

1 5 10 50 100

Injection Rate - BPM

A - 1 1/4 in, 2.4 lb tubingB - 2 3/8 in, 4.7 lb tubingC - 2 7/8 in, 6.5 lb tubingD - 2 3/8 in, 4 1/2 in, 9.5 annulusE - 3 1/2 in, 9.3 lb tubingF - 2 7/8 in, 5 1/2 in, 15.5 lb annulusG - 4 in, 11 lb tubing

H - 2 3/8 in x 5 1/2 in, 15.5 lb annulusI - 4 1/2 in, 9.5 lb casingJ - 5 1/2 in, 15.5 lb casingK - 2 7/8 in, 7 in, 23 lb annulusL - 2 3/8 in x 7 in, 23 lb annulusM - 7 in, 23 lb casingN - 7 5/8 in, 29.7 lb casing


References

drau-

esent-

inkedon, Las

5.5 References

1. Warpinski, N. R., Schmidt, R. A., and Northrop, D. A.: “In-Situ Stresses: The Predominant Influence on Hylic Fracture Containment,”JPT (March 1982), 653-64.

2. Kry, R. and Gronseth, M.: “In-Situ Stresses and Hydraulic Fracturing in the Deep Basin,” paper 82-3321 pred at the 1982 Petroleum Soc. of CIM Annual Meeting, Calgary, Alta., June 6-9.

3. Hubbert, M. K. and Willis, D. G.: “Mechanics of Hydraulic Fracturing,”Trans., AIME (1957)210, 153-66.

4. Harrington, L. J., Hannah, R. R., and Williams, D.: “Dynamic Experiments on Proppant Settling in CrosslFracturing Fluids,” paper SPE 8342 presented at the 1979 SPE Annual Technical Conference and ExhibitiVegas, Sept. 23-26.




Chapter

ydro-rouped

ive

rbon

al

Fluid Selection and Scheduling6
6.1 Fluid Selection
Fluid Classification

Service companies offer fracturing fluids which can be categorized as either water-base or hcarbon-base depending on the nature of their continuous phase. Fracturing fluids can be ginto the following classes:

Water-Base Fracturing Fluid Systems

• Slick Water:

Small amounts of polymer in water for turbulent friction pressure reduction

• Uncrosslinked Polymer Solutions:

Guar, HPG, CMHPG, CMHEC, HEC, xanthan, polyacrylamide, secondary gelling system

• Crosslinked Polymer Solutions (Gels):

Polymers crosslinked with titanium, zirconium, boron, aluminum, or antimony

1. batch mixed (an emulsion if hydrocarbon fluid-loss additive is used)

1. continuous mixed (1/2 vol% hydrocarbon emulsion up to 5 vol% if liquid fluid loss additis used)

1. energized with up to 50% N2 or CO2

• Polymer Emulsion:

Approximately 33% aqueous polymer solution as the external phase with 67% hydrocainternal phase

• Aqueous Foams:

N2, CO2, or 45%-CO2/25%-N2 in water, polymer solution, or gels with 65 - 85% gas internphase



t fric-

y acid

and

ys--GO

micaln pageker,

must

Hydrocarbon-Base Fracturing Fluid Systems

• Slick Hydrocarbon:

Diesel, kerosene, or crude with small amounts of synthetic polymer for reducing turbulention pressures

• Crosslinked Hydrocarbons:

Diesel, kerosene, or crude crosslinked with phosphate acid ester and aluminum, or fattand caustic

1. batch mixed

1. continuous mixed

1. energized with up to 50% N2 or CO2

• Hydrocarbon Foams:

N2 or CO2 in diesel, kerosene, or crude oil with 65% - 85% gas internal phase

• Gelled Methanol [with or without CO2 up to 75 vol% (single phase w/CO2)]:

Methanol in water-base polymer solutions- up to 25 vol% with guar, 60 vol% with HPG,100 vol% with dimethylacrylamide or hydroxypropylcellulose (can also be crosslinked).

Within any of the above classes of fracturing fluids, the engineer is confronted with a list of mterious sounding fluid system names (e.g. Saturn II, Water Frac, Versagel-HT, YF550-HT, YFIII, Polyemulsion, etc.), and associated with each, an equally cryptic list of trade-name checomponents and additives. As an example, the components for Versagel-HT (referenced o6.7) include WG-11, Cl-18, K-34, and HYG-3 with possible additives of GEL-STA, SP BreaWAC-12L, CLA-STA, SEM-7, EnWaR-288, BE-3, ABF, etc.

To select the “best” fluid system for a particular hydraulic fracturing treatment, the engineerconsider various criteria. The next section will discuss these criteria.


Fluid Selection Criteria

sub-y per-nsidererties

ction


Probably the first criteria that an engineer considers when selecting a fracturing fluid are of ajective nature including regional history and tradition, personal experience, service companformance, and service company advice. In addition to these criteria, the engineer should cospecific factors concerning the formation to be fractured, the fracture desired, and the propof the fracturing fluid. These criteria can be grouped into the following categories:

• Safety and Environmental Compatibility

• Compatibility with Formation, Formation Fluids, and Additives

• Simple Preparation and Quality Control

• Low Pumping Pressure

• Appropriate Viscosity (for desired geometry and proppant transport)

• Low Fluid Loss

• Good Flow Back and Cleanup (for high fracture conductivity)

• Economics

The following sections will discuss each of these. Table 6.1 gives qualitative ratings for selecriteria for various types of fracturing fluids.


Flu

id S

ele

ction

an

d S

che

du

ling

6Hyd

rau

lic Fra

cturin

g T

he

ory M

an

ua

l6-4

July 1

99

9

Table 6.1 - Qualitative Fluid Selection (courtesy of NSI).

luidoss Cost

Safetyand

Environ.

Prep.andQC

3 5 5 5

1 4 5 4

4 4 5 4

4 4 4 3

4 4 4 3

4 4 4 3

4 4 4 3

5(*) 2 2 2

5(*) 2 2 2

2 3 2 2

4 3 2 2

5(*) 3 2 3

4 2 1

Fluid System

PropPackKfW

LowPumpPres.

Viscosity

Breaking

Compatibility

FL

Prop-Transport Stable Life

Formation/Fluid

ReservoirPressure

Linear Gel HPG/Guar (<130 - 150°F) 4 5 3 3 3 5 3 3

Linear HEC Gel(<180°F) 5 5 3 3 3 4 3 3

Borate X-Link(<180°F) 4 3 4 3 5 5 3 3

Delay Borate X-Link(160 - 280°F) 4 4 4 4 5 5 3 3

Delay metallic X-Link(180 - 220°F) 2 4 5 4 5 2 3 3

Delay Metalic X-Link(220 - 280°F) 3 4 5 3 5 3 3 3

Delay Metalic X-Link(280 - 350°F) 3 4 4 2 4 4 3 3

Nitrogen Foam(<5000 ft) 5 1 4 4 ? 5 5 5

CO2 Foam(5000 - 1000 ft) 5 1 4 4 4 5 5 5

Lease Crude 4 3 2 3 3 5 5 4

Gelled Oil 2 4 4 4 4 3 5 4

Polymer Emulsion 4 2 4 4 5 4 4 4

Gelled Methanol 3 4 4 5 5 1 5 4

1 - BAD5 - Excellent(*) - Good loss control for permeability < 1md (+/-)


luidsto usecientsed)arbons

d fre-ial pre-) when

raying

f leaking

etha-endere. Oxi-urces.SD)

as cer-e sup-

Safety and Environmental Compatibility

Safety is a primary consideration in the selection of fracturing fluids. Hydrocarbon-base fhave the inherent risks associated with flammable or combustible materials. It is advisableone which has a flash point (the minimum temperature at which a liquid gives off a vapor suffito form an ignitable mixture with the air near the surface of the liquid or within the vessel uhigher than expected ambient temperatures. Flash points of some commonly used hydrocare shown in Table 6.2.

It is easy to see why diesel No. 2 is so popular. In Canada FRAC OIL and methanol are usequently, perhaps partly because of colder weather which makes their use more safe. Speccautions are used when pumping flammable liquids such as brass hammers (to avoid sparkstightening surface tubing, tarpaulins to cover surface hoses to protect personnel from sphydrocarbons, spark arrestors, and the prohibition of smoking.1 Foamed fluids, which can behydrocarbon or water-base, are even more dangerous because of the expansion energies ofoams.

There are varying degrees of toxicity associated with fracturing fluid components such as mnol, FRAC-OIL, biocides, surfactants and crosslinkers. Breathing apparatus is required for bloperators and anyone exposed to methanol vapors which can do irreversible brain damagdizers, such as ammonium and sodium persulfate should not be allowed to contact fuel soCorrosive acidic and basic additives should be handled with care. Material Safety Data (Msheets should be reviewed for all chemicals on location.

The recent emphasis on environmental awareness has limited the use of some additive suchtain extremely toxic biocides and crosslinkers (e.g. chromium-base). Service companies ar

Table 6.2 - Flash Points of Some Commonly Used Hydrocarbons.

Hydrocarbon Flash Point

Gasoline (60 Octane) - 45 F

Condensate < 32 F

Toluene 40 F

FRAC OIL (GOODFARE) 45 F

Methanol 52 F

FRAC OIL (KAYBOB) 83 F

FRAC OIL (EDSON) 85 F

Diesel No. 1 100 F

Diesel No. 2 125 F

40 API Crude Oil

°°°°°°°°°

°


Fluid Selection and Scheduling6moco

thesys-

ld be

l addi-KCl orandof theelling

oly-tial ofof thet for-h astests

usinguld be

g theocar-r wetse of

ged,ove-d cat-

. sandythey

suchwell

posedly knowledgeable about environmentally acceptable frac fluid systems. Consult your Aenvironmental representative if in doubt.

Compatibility with Formation, Formation Fluids, and Chemical Additives

A primary consideration in the selection of a fracturing fluid system is its compatibility withformation, the formation fluids, and the chemical additives specified for the particular fluidtem.

A fracturing fluid may damage a reservoir to various degrees. Ideally, core flow tests shoudone to evaluate the sensitivity of a particular rock to the fracturing fluid.

If a reservoir has swelling or migrating clays, the engineer should use adequate clay controtives when using water-base fluids or should use an oil-base system. Certain salts such asammonium chloride are effective to some extent in stabilizing swelling clays such as illitemontmorillonite by replacing exchangeable cations in the clays which can cause expansionstacked clay platelets when exposed to fresh water. Modified polyamines can reduce clay swand clay migration by adsorbing on clay particles and “locking” them into place. Cationic pmeric clay stabilizers adsorb on to clay particles even more strongly but they have the potenplugging pore throats (because of their relatively large size) and can change the wettabilityformation. Clay control additives, other than 1% KCl, are generally not recommended for tighmation gas plays for this reason. 1% KCl is adequate for clay control in fluids with pH as hig10. For higher permeability formations (where more conductive fractures are required) coreshould be performed to assess the effectiveness of the prescribed clay stabilizers.

Water in fracturing fluids can actually dissolve the cementing material in some formations cathe release of damaging fines and consolidation problems. Again, core flooding tests shoconducted to evaluate this possibility.

The ionic nature of the components in a fracturing fluid system have the potential of changinwettability of formations. Ionic surfactants have ionic water soluble ends and nonionic hydrbon or fluorocarbon tails which are oil soluble. Sandstone formations, which are usually wateand negatively charged, will adsorb cationic surfactants and will thus become oil wet becautheir oil-soluble tail. Limestone formations, which usually are water-wet and positively charwill adsorb anionic surfactants and become oil wet. Since water-wet formations promote mment of oil through the rock, anionic surfactants should be used in sandstone formations, anionic surfactants should be used in limestone formations. For heterogeneous formations, e.glimes, nonionic surfactants should be used. If surfactants do not improve fluid recoveryshould not be used unless they are required for foam or emulsion stabilization.

Another consideration is the introduction of anaerobic bacteria (i.e. sulfate reducing bacteriaas Desulfovibrio) into the formation which can produced hydrogen sulfide and can turn thesour. This is particularly a concern in wells less than 170°F. The fracturing fluid water should be



s, theation

e miti-ce ten-nd is

can

turingeck

ctants. APIecipita-

er-ation

ctants,break.

akers

ions areadsorbpatiblearbon-ld be

t andixingmen-

s, suchnate)l sta-layuce

treated with an environmentally acceptable biocide. Thus, even in continuous mix operationuse of biocides should be considered. In very hot wells, the possibility of bacterial contaminin the cooler regions of the wellbore exists.

When using water-base fluids, sometimes problems with water blocks occur. These can bgated by using fluorocarbon surfactants and/or methanol which have especially good surfasion lowering qualities. Water with reduced surface tension has lower capillary pressure amore easily displaced from pore throats through the rock matrix.

Fracturing fluid compatibility with the reservoir fluids is likewise important. Water-base fluidsform emulsions with crudes or induce scaling with insitu water, e.g. CO3

-- in sodium or potassiumcarbonate buffers can form CaCO3 scale by reacting with CA++ in the formation water. Oil-basefluids can induce sludging with crudes such as asphaltene or paraffin precipitation. The fracfluid system should be mixed with the reservoir fluids prior to specifying the treatment to chfor incompatibilities, preferably at reservoir temperature and pressure. Fluorocarbon surfashould be used in dry gas wells where there is no danger of forming oil-water emulsionsRP392 describes a procedure conducted at ambient pressure, that tests for emulsion and prtion potential.

The compatibility of the fracturing fluid with its additives should be checked at location by pforming pilot tests before pumping. Sometimes incompatible additives can be brought on locsuch as certain surfactants and biocides which can interfere with crosslinking. Some surfae.g. foams, may adsorb on silica surfaces, such as sand or silica flour and cause the foam toMethanol is incompatible with guar at concentrations higher than 20 wt%. Most enzyme brewill not work when used at pH higher than 8.5 or at temperatures greater than 120°F. Methanolshould not be used with breakers since it renders them useless unless very large concentratused. Resin-coated proppants can interact with fluid additives. Some resin coatings canbreaker and crosslinker, and can lower fluid pH. Some encapsulated breaker are not comwith resin coated sands if the oxidizer breaker is released before the resin cures. For hydrocbase fluids, the effect of additives on the value of the recovered fluid after flow back shouconsidered.

Simple Preparation and Quality Control

A fracturing fluid composition should be kept as simple as possible since every componenadditive adds to the burden of monitoring chemical quality, proper chemical addition, and m- not to mention adding to the total expense. However, referring to the Versagel-HT systemtioned on page 6.2, chemical additives are needed for a variety of good reasons. Viscosifieras HPG (WG-11), are polymers for thickening water; buffers, such as K-34 (sodium bicarboand HYG-3 (fumaric acid), are used to adjust the pH for hydration, crosslinking, and thermability; salt (KCl) or cationic polymers (e.g. CLA-STA) are used to prevent clay swelling and cmigration; a liquid hydrocarbon fluid loss agent (WAC-12L) or 3 - 5 vol% diesel are used to red


Fluid Selection and Scheduling6nhancepera-ntingcar-o pre-every

HPGe lateaverocar-n onsite

es tom-n vis-vortexng theave to

ixinge andhectiva-iumd to thent willas to

oppedproved

-time

al andut 1

thee

water loss to the formation; chemicals, such as SP Breaker (sodium persulfate), are used to epolymer degradation; GEL-STA (sodium thiosulfate) is used to enhance polymer high-temture stability; surfactants are used for better load recovery (EnWar-288), to aid in preveoil-water emulsions in the reservoir (LOSURF-251 nonemulsifier), and for emulsifying hydrobon in water (SEM-7); biocides are used to prevent biodegradation of the fracturing gel and tvent contamination of the well; etc. Service companies should be able to justify the use offluid component and additive which they specify.

The fluid system should be easy to mix, with the polymer readily dispersed and hydrated.was developed in part to give better dispersibility and hydrating properties than guar. In th1980’s, advances in fluid formulations, equipment control, and fluid property monitoring hmade continuous mixed fluid systems more popular. Continuous mixed water-base and hydbon-base gels and foams are attractive because of reduced costs resulting from reductions itime and fluid waste.

A sample of frac fluid should be mixed before the treatment using all onsite chemical additivtest for proper hydration, crosslinking, and additive incompatibilities. After noting the fluid’s teperature and pH, viscosities of uncrosslinked gels should be checked with the Model 35 Fancometer or equivalent. Qualitative checks on water-base gel crosslinking can be made usingclosure tests (e.g. 100 ml sample in a 250 ml beaker stirred at 450 rpm) and visually observicrosslink strength by pouring the gel from the cup. Today’s delayed crosslinked systems hbe heated somewhat to initiate crosslinking. Usually crosslinking begins between 90°F and 140°F.

Hydrocarbon gel viscosities can be checked using the Fann 35 or equivalent noting that mintensity can effect extent and degree of crosslinking. Hydrocarbon gels are difficult to preparrequire close quality control.1 The gellant and activator must be pilot mixed on location with tparticular hydrocarbon to determine the proper amounts of gellant and activator. Too little ator will yield no viscosity and too much will give gel degradation (activator is a base, e.g. sodaluminate, which can also serve as a breaker). The phosphate ester gellant must be addehydrocarbon before the activator. If the activator and gellant are added together, a precipitaresult. When the ester is uniformly distributed, the activator is added. Sometimes, the fluid hbe circulated at the highest rate possible for 20 minutes to form the gel. Gelation can be stby contaminants in the tanks such as residual surfactants, treating chemicals, or water. Imcontinuous mixed hydrocarbon gel systems are making preparation easier.

Gel quality control of continuous-mix jobs is possible if the service company has reliable realpH and viscometer instrumentation on their preblenders.

Onsite rheological testing of foamed systems is not possible. However, the foaming potentihalflife can be checked by putting the liquid with all its additives into a Waring blender aboinch above the impeller and mixing at maximum rate to entrain air. The time it takes for 1/2solvent to return to its original state (drain) is the halflife.1 Foams with foaming agents hav



oams

ssen-sys-

terials

tionrictionfric-cryla-theticl, ands aregive. 6.1give

mers.

atergh-ssuresformu-res-epowerulatedpoly-

waterr 2%l to

oamedmpera-vol%n

halflives of 3-4 minutes, stabilized foams have halflives of 20-30 minutes, and crosslinked fhave halflives over an hour.

For every type of fracturing fluid, proper additive metering and carrier vessel cleanliness are etial aspects of quality control. In the 1990’s, chemical addition is automated so that complextems, such as binary foams, can be successfully pumped. Quality control of fracturing mawill be discussed in more detail in Chap. 11 of this manual.

Low Pumping Pressure

Most fracturing fluids have the desirable property of being drag-reducing (giving lower fricpressure than the solvent alone) when pumped under turbulent conditions. Fig. 6.1 shows fpressures in 3-1/2 inch tubing (3.00 inch ID) for various solvents and the effect of Halliburtontion reducers. Water-base friction reducers are high-molecular weight polymers, e.g. polyamide, and oil-base friction reducers are hydrocarbon soluble polymers (e.g. certain syncationic polymers such as polyisodecylmethacrylate). The friction pressures of water, diese40oAPI oil are of similar magnitude. When friction reducers are added, the friction pressurelowered by a factor of two to four. Note that adding more friction reducer does not alwaysmore friction pressure reduction (e.g., FR-30 at < 15 BPM at 2 and 8 lb). Also shown in Figare friction pressures for 40 lb/1000 HPG solution and a gelled diesel fracturing fluid. Thesefriction pressure reductions similar to when using drag reducers. High molecular weight polyhave a critical concentration where the maximum in friction pressure reduction is achieved

Friction pressures for various types of fracturing fluids are shown in Fig. 6.2 compared with wfor flow in 3-1/2 inch tubing (3.00 inch ID). Polyemulsion (i.e., polymer emulsion) gives the hiest friction pressure, even greater than water. There is some variation in reported friction preby different service companies, the largest being for borate gels and foams. Today, speciallations of delayed borate crosslinked gels are available which significantly lower friction psures. Friction pressure can cause a significant increase in wellhead pressure and horsrequirement and is an important consideration in design. Water-base solutions and gels formwith high-molecular weight polymers, e.g., guar, guar derivatives, cellulose derivatives, andacrylamide derivatives, are all drag reducing.

For overpressured reservoirs (i.e. those with reservoir pressures greater than hydrostaticpressure at that depth), either water-base fluids with hydrostatic gradients of 0.438 psi/ft foKCl fluids or hydrocarbon-base fluids with gradients ranging from 0.343 psi/ft for methano0.379 psi/ft for 30°API crude can be flowed back with natural pressure.

For underpressured reservoirs, lower density hydrocarbon-base fluids, energized fluids, or ffluids can be used to assist flow back. Nitrogen foams at typical treatment pressures and tetures can have gradients less than 0.2 psi/ft. In addition, foams, by their composition of > 65gas, only require about 1/3 as much liquid load return. CO2 foams can have gradients greater tha



Fig. 6.1 - Friction Pressures for Friction Reducers.

Fig. 6.2 - Friction Pressures: Various Frac Fluids.

Water

Diesel (Western)40 deg API Oil (Western)2 lb FR-30 Slick Water (Halliburton)

8lb FR-30 Slick Water (Halliburton)1 gal FR-7A Slick Diesel (Halliburton)2 gal FR-7A Slick Diesel (Halliburton)

40 lb HPG soln. (WG-1dGelled Diesel 8/3 (Halliburton)

Down 3 1/2 in tubing (3 in ID)

Fric1 Data

WaterPolyemulsion w/40 lb WG-11 (Halliburton)40 lb HPG-Borate (BJ Services)40 lb HPG-Borate (D-S)40 lb HPG-Titanium (BJ Services)40 lb HPG-delayed TI (Halliburton)40 lb HPG soln. (WG-11)Gelled Diesel 8/3 (Hallibruton)70 Qual. D-S Stabil. Foam70 Qual. -40 lb HPG Foam (Hallib. correl.)

Down 3 1/2 in. tubing (3 in. ID)

Fric2 Data



ce as it

ssurese fluid.umping

ventientr (e.g.sity

ringre can.”

guousslickvonian

g fluidnsport

solu-e frac-

orted)bora-arilye sus-e as

0.2 psi/ft at typical treating pressures and temperatures. However, the solubility of CO2in fluids isgenerally high compared to nitrogen (see Fig. 6.32), and can give added flow back assistancomes out of solution.

When using less dense fluid, however, one must consider the higher surface treating prerequired since up to 0.25 psi/ft hydrostatic head pressure can be lost relative to a water-basHigher treating pressures can reduce the maximum allowable pump rates and/or increase phorsepower (cost).

Appropriate Viscosity

Fracturing fluids are formulated to give sufficient viscosity to create wide fractures to pre“pinch outs” and to give sufficient width to create a conductive proppant pack. Widths sufficto prevent pinch outs are approximately equal to 2.5 times the maximum proppant diameteabout 0.1 inch for 20-40 sand). Lower widths can conduct slurry if the fluid flow rate and viscoare high enough. Fracture width is generally not a strong function of viscosity (e.g. widthfor the PKN model with a Newtonian fluid). Excessive fluid viscosity can increase the fractupressure to the point where natural fractures open up giving additional fluid loss or the fractubreak through confining zones and grow height. These conditions can lead to “screen outs

Fluid viscosities should be sufficient for adequate proppant transport. This is a rather ambicriteria, however, since proppant has been pumped with very low viscosity fluids includingwater. Even nitrogen gas has been used successfully to pump 20/40-mesh sand in the Deshale when pumped at high rates. Generally speaking, however, larger quantities of fracturincan be pumped away at the higher viscosities. This may be a result of better proppant traand/or higher fracture pressures creating wider and higher fractures.

When using thin fluids to transport proppant, such as slick water or uncrosslinked polymertions at elevated temperatures, it is probable that a settled bank forms along the bottom of thture. Research by Biot and Medlin3and Medlin, Sexton, and Zumwalt4 indicates that the formationof an equilibrium bank (a settled bank of constant height above which all proppant is transpmay not apply to field scale fractures although equilibrium banks have been observed in latory-scale slot flow devices. They believe that for thin fluids, proppant transport results primfrom viscous drag where the suspension has nearly uniform proppant concentration. As thpension flows down the fracture, a relatively clear fluid layer forms at the top of the fracturproppant from the suspension falls to the settled bank. At any horizontal positionx

1, down the frac-

ture, the clear-fluid height above the slurry top is given by:

whereU is the average fracture fluid velocity andvt is the terminal settling velocity of a particle.

µ1 4/∝

Z1 vt /U( )o

x1

∫= dx (for constant settling rates)vt x1/U ;≅


Fluid Selection and Scheduling6rs.izedinde-

tem-in a 40s at 0ell

a sus-t,:

xplic-

ived

Medlin et al. set forth the criteria that whenvt /U is less than 0.1, suspension transport occuWhen0.1<vt /U<0.9, bed load transport occurs which is defined as the transport from a fluidlayer of sand. However this fluidized layer is not very thick (less than a few inches) and ispendent of fracture size. Whenvt /U > 0.9, proppant will not be picked up. Values ofvt depend onthe particle size and density and on the rheological nature of the fluid. For instance at roomperature under static conditions, 20/40-mesh sand can settle in water at a rate of 1.7 ft/sec;lb/1,000 gal HPG solution at 0.005 ft/sec; in a borate gel at 0.0007 ft/sec; and in titanium gelft/sec. Under fracturing conditions, effective settling velocities of flowing slurries are not wdefined at this time.

For viscosities greater than 50 cp at 170 1/s, we will assume that the proppant is flowing aspension with settling rate defined using some correlation relating the particle drag coefficienCD,to the generalized particle Reynolds number,N'Rep. These dimensionless groups are defined as

whereg is the acceleration of gravity,dp is the particle diameter (inches),ρp is the particle density(lbm/gal),ρ is the fluid density (lbm/gal),K' is the consistency index (lbf-sn'/ft

2), and vt is terminal

particle velocity (ft/sec).N'Rephas been written using an effective particle shear rate such as:5

The actual shear rate on a particle surface settling in a power-law fluid can not be calculated eitly, and thus has been defined differently by various authors. If the relation ofCD to N'Rep isgiven, thenvt can be solved. For instance, for laminar settling (Stokes Settling),

and if this is assumed to apply to Non-Newtonian fluids, then the following relation is derusing the expression forN'Rep:

in oil-field units:

CD

4 g dp

3 v2t

----------------ρp ρ–

ρ--------------- ; NRep

′ dpn′

vt2 n′– ρ

3n′ 1–

K′------------------------

0.695 dpn′

vt2 n′– ρ

K′-----------------------------------------= = =

(in Oil-Field Units)

γ̇ p 3 vt /dp 36 vt /dp (in oil-field units).= =

γ̇ p

CD24

NRep------------ , WhereNRep

dp vt ρµ

-----------------= = = Newtonian particle Reynolds no.,

vt

g dpn′ 1+ ρp ρ–( )

18 K′ (3)n′ 1–

---------------------------------------=

1/n′

dpn′ 1+ ρp ρ–( )

9.626 36( )n′K′

----------------------------------=

1/n′

, for N′Rep 2.0 .<



ons

-

rationoncen-smallan beusrop-

-

geis ofot yet

esignnd lown-base2500e sta-

ample

els. Itand

ter thanitaneter

es the

If the calculatedvt, does not give aN'Repless than 2., then the higher Reynolds number correlatican be used.5 For 2 < N'Rep< 500, CD = 18.5/N'Rep

0.6; and for500 < N'Rep< 200,000, CD = 0.44.Thus, this can involve a trial and error approach. Shah6 developed a method using empirically generated correlation constants which avoids trial and error.

Note that the above are relationships for single particle settling. As proppant concentincreases, the particles may clump and give accelerated settling. Above a certain proppant ctration, however, i.e. 4 lb/gal liquid, the separation between proppant particles becomesenough where hindered settling starts to reduce the settling velocity. Hindered settling ctreated by increasing theK' to reflect an increase in the effective viscosity of the continuomedium. Novotny7 performed static settling tests in simulated fractures using concentrated ppant slurries in polyacrylamide solution and found the hindered settling velocity,vh, to be relatedto proppant concentration as

whereppgis the lbm proppant/gal liquid, andρp is the proppant density in lbm proppant/gal proppant (e.g. 22.1 for sand). Thus, forppg = 8, andvt = 0.005 ft/sec, vh would be 0.0009 ft/sec. For afracture flow velocity,U, of 0.56 ft/sec, (40 BPM down a 50 ft high by 0.25 inch wide two-winfracture) this would givevh /U equal to 0.0016, which according to Medlin’s criteria would givsuspension flow. The clear fluid layer at the fracture top after 1000 ft would only be 1.6 ft. Thcourse is a rough estimate of settling. The settling properties of flowing suspensions are nwell established.

The viscosity is affected by temperature and time and should be accounted for in fracturing dsince this can affect fracture width and proppant transport as stated above. There are high atemperature versions of water-base crosslinked and uncrosslinked gels, of hydrocarbocrosslinked gels, and foams. Polyemulsion is usually restricted to temperatures less than°F.High temperature stabilizers, such as sodium thiosulfate or methanol, are used above 20°F toretard oxidative hydrolysis of water-base polymers. At pH less than 6., the sodium thiosulfatbilizer is not effective in some cases.

There can be a large variation of high temperature behavior for similar gel systems. For exin Fig. 6.3, various service company high temperature gels are compared at 265°F. All the gelswere tested by Amoco using the Amoco procedure for testing organometallic crosslinked gis apparent that high temperature stability is a function of pH and type of polymer, buffer,crosslinker. In some cases, service companies reported viscosities to be up to six times greathose measured in Amoco’s lab (e.g. those for the Saturn I, Apollo I, Gemini III DXL, and TXL gels). The discrepancy is the result of many factors including conditioning method, viscombob, viscometer procedure, and calculation method. At this time we feel our procedure giv

vh 1 ppgppg ρp+----------------------–=

5.5vt ,


Fluid Selection and Scheduling6om-

oly-er-itivent theoirsitivese hasls.

bilitywhenmul-he fluid(i.e.,lding

most realistic data. As of 1991, the API is still a couple of years away from approving a recmended practice for testing organometallic crosslinked gels.

Low Fluid Loss

Fracturing fluid systems offer varying degrees of fluid loss control. Water-base fluids with pmer give fluid loss control by building filter cake as the fluid leaks off in formations having pmeability less than 5-10 md. In higher permeability formations, a particulate fluid loss add(preferably a degradable product, 100 mesh sand, or silica flour) should be used to prevepolymer from flowing into the pores. This is especially true for naturally fractured reservwhere the natural fractures provide the bulk of the permeability. Particulate fluid loss addshould be used only in the pad to avoid damaging the fracture conductivity. The gel filter cakpermeability on the order of 1x10-6 md and thus can significantly lower fluid loss. Crosslinked gegive fluid loss control roughly the same as uncrosslinked gels at the same polymer loading

Fluids with internal phases can have additional fluid loss control when used in low permeareservoirs ( < 1.md). This is true when the internal phase is a hydrocarbon, such as is the casediesel fluid loss additive is used. Aromatic hydrocarbons with surfactants which yield microesions are also used but to a lesser extent. Generally speaking 3% diesel gives about 80% of tloss reduction possible with hydrocarbon fluid loss additives. Accordingly, polyemulsionpolymer emulsion), with 67% hydrocarbon internal phase, gives the lowest values of wall bui

Fig. 6.3 - Ti and Zr Continuous-Mix Gels at 265 F.

All Delayed CrosslinkedExcept Gemini II DXL Gel.Conditioned at 0.8 hp/ft3for 5 min to simulate40 BPM down 5 1/2" casingAll contain 10 lb stabilizerand no breaker.

40 lb Versagel HT, HPG-Ti, pH 8.32

40 lb Ultra Frac RXL, Guar-Zr Lactate, pH 7.9

40 lb Saturn II, HPG-Zr, 2 gal XLD, pH 9.0

40 lb Pur-Gel III, CMHPG-ZrNH4C1, pH 6.56

40 lb Titan XL, CMHPG-Zr AL acetate, pH 5.2

40 lb Gemini III DXL, CMHPG-Zr-Al, pH 6.-5.6

40 lb MY-T-Gel HT, Guar-Ti, pH 8.7-7.9

40 lb Saturn I, Guar-Zr, pH 9.5-9.0

40 lb Appollo I, Guar-Ti, pH 7.3-5.8

t6399-08 DATA

°



edrme-hroats-

most

arbon

bilityl-hat

gell

ed byibil-res-from

fluid loss coefficient, Cw. Typical values for polyemulsion are < for permeabil-ity < 25 md using guar or for permeability < 2 md using HEC. The dispershydrocarbon acts to reduce the permeability to water in the polymer filter cake by relative peability effects. At permeabilities greater than 5 - 10 md, the hydrocarbon can penetrate pore tand the use of particulate fluid loss additive is also advisable. Cw generally decreases with increasing polymer loading, except when using hydrocarbon fluid loss additive, in which case it is alindependent of polymer concentration. Fig. 6.4 and Fig. 6.5 show Cw as a function of fluid-lossadditive type and concentration, and polymer concentration.8

Foams with gas internal phases can give fluid loss control comparable to gels with hydrocwhen the liquid external phase of the foam is stabilized with polymer. FoamCw’s are also depen-dent on formation permeability. Fig. 6.6 shows D-S fluid loss coefficient values vs permeafor some of their foams at 150°F. Oil-base gels exhibit similar fluid loss behavior in that the voume of fluid leaked off is proportional to the square root of time. It is not clear at this time wkind of mechanism is responsible for this, i.e. “polymer” build up, pore throat plugging, orinvasion. Most oil-base fluids use some form of non-oil-soluble fluid loss additive.

At reservoir permeabilities less than 0.1 md, the total fluid loss coefficient,CT, starts to becomeinfluenced by leakoff resistance in the reservoir rock. Reservoir-leakoff resistance is influencthe fracturing fluid filtrate and the formation fluids, the porosity of the reservoir, the compressity of the formation fluids and the leakoff-driving pressure (the fracturing pressure minus theervoir pressure), as well as the reservoir permeability. Increasing the leakoff driving pressure

Fig. 6.4 - Wall-Building Coefficient vs. Fluid-Loss Additive Type and Concentration at 125 F.

< 0.0007 ft min< 0.0015 ft min

LegendPolymer-resin Mix

Silica Flour

Polymer-Silica-Clay MixDiesel (1-10 md)

0.01

0.001

0.00040 10 20 30 40 50

Fluid Loss Additive Concentration (lb or gal/Mgal)

Cw

(ft/

min

1/2 )

°



Fig. 6.5 - Wall-building Coefficient vs. Gelling Agent Concentration for Linear Gels at 125 FThrough 0.1- to 100-md Cores.

Fig. 6.6 - Fluid-Loss Coefficient for a 55-75 Quality Foam at 150 F.

Legend0 lb Silica Flour/Mgal

25 lb Silica Flour/Mgal



0.005

0.004

0.003

0.002

0.0010 30 40 50 60 70 80 90 100

Gelling Agent Concentration (lb/Mgal)

Cw (

ft/m

in1/

2 )

°

°



d,

ring

intoitivesulatecase

es-

a filterff into

filterilities

rivingsities

500 to 2000 psi can increase CT by a factor of 3. At a reservoir permeability less than 0.0001 mthe reservoir resistance dominates leakoff and the fluid leakoff properties, (Cw), no longer areimportant. Little added fluid-loss reduction is gained by using fluid loss additives. Most fractusimulators consider reservoir effects when calculating fluid loss.

For naturally fractured reservoirs, it is of primary importance not to allow polymer to leak offand plug the natural fractures which can be the primary source of permeability. Fluid loss addshould be considered which prevent polymer from entering the natural fractures (particagents) and which reduce the leakoff of the filtrate (hydrocarbon fluid loss additive). In theof naturally fractured reservoirs, Cw again will control fluid loss. Fig. 6.7 shows calculated CT as afunction of reservoir permeability for an East Texas Cotton Valley well with leakoff driving prsure and diesel concentration as parameters for cases with and without natural fractures.9 In thisfigure, particulate fluid loss additive is assumed necessary to seal natural fractures so thatcake can form. Experimental tests have shown silica flour to be necessary to stop leakosmaller natural fractures (i.e., 10 to 20 microns).8

The spurt loss of a fluid, which can be defined as the fluid loss/area before the formation of acake, can be significant in naturally fractured reservoirs as well as reservoirs with permeabgreater than 1. md. Spurt values increase strongly with reservoir permeability and leakoff-dpressure and are affected by factors which affect fluid flow in reservoirs such as filtrate visco(and thus temperature) and compressibility effects. Spurt values in excess of 1 gal/100 ft2 can be

Fig. 6.7 - Calculated Total Fluid Loss Coefficient vs. Permeability ETCV at 275 F and 5000 psiReservoir Pressure. Leakoff Driving Pressure as a Parameter; With and W/O 3% Diesel

Legend5000 psi, w/o diesel5000 psi, 3% diesel2000 psi, w/o diesel2000 psi, 3% diesel1000 psi, w/o diesel1000 psi, 3% diesel500 psi, w/o diesel500 psi, 3% dieselCW w/o dieselCW w/ 3% diesel

With Natural Fractures: 500 - 5000 psi (No diesel)

psi

psi

With Natural Fractures:500 - 5000 psi (3% diesel)

°


Fluid Selection and Scheduling6values6.11spurt

o be

ingopor-Lab-Cot

eableovedrockd off

emul-

expected for reservoirs with permeability greater than 10 md. Lab measurements show spurtare affected by fluid loss additive and polymer type, as well as permeability. Fig. 6.8 - Fig.show the effects of fluid loss additive type and concentration, and polymer concentration onvs. permeability values.8

The preceding discussion dealt with fluid loss behavior of static fluids. Fluid loss can alsaffected by fluid flow in the fracture. For uncrosslinked polymer solutions, Cw is independent ofshear rate up to 300 1/s, but Cw for crosslinked gels can increase with shear rate. Leakoff drivpressure can affect the functional form of fluid loss. Fluid loss can increase from being prtional to to proportional to t as the leakoff-driving pressure decreases from 1000 to 0 psi.oratory tests have shown that flowing proppant does not change the dynamically measuredw forproppant concentrations up to 5 ppg.10 Dynamic fluid loss is a new technical concern which is nconsidered in all fracturing simulators.

Good Flow Back and Cleanup

The objective of hydraulic fracturing is to create a conductive fracture which requires a permproppant pack and permeable fracture face. To achieve this, the fracturing fluid must be remfrom the formation. As discussed above, it is essential to prevent polymer from invading thematrix and natural fractures. Good fluid loss control can accomplish this. However, the leakefiltrate must be removed. Producing the well will help remove load water but in some cases

Fig. 6.8 - Spurt Loss vs. Permeability for Linear HPG Gels in Water at 125 F. °

t



Fig. 6.9 - Spurt Loss vs. Permeability and Additive for 40 lbm Complexed HPG Fluids at 125 F.

Fig. 6.10 - Spurt Loss vs. Permeability and Gel Concentration For Complexed HPG Fluids at 125 F.

°

°



ion,ce thearbon

frac-

eraturesffec-

eakers

uponorbinge aftern

iginalsomedi-uring

sions, scales, or water blocks will form. Methods described in the “Compatibility With FormatFormation Fluids, and Chemical Additives” section starting on page 6.6 can be used to reduseverity of these problems when using water-base fluids. If these are not effective, hydrocbase fluids or foams should be considered.

Gel breakers oxidize the polymer backbone enabling the polymer to be flowed back out of theture. Ammonium or sodium persulfate are commonly used at high temperatures > 150°F or lowertemperatures with an activator. Enzyme breakers such as hemicellulose are used at templess than 120°F and pH < 8.5. Western Company claims to have an enzyme breaker which is etive to pH 10. In 1991, service companies began offering encapsulated or crushable brdesigned to release the oxidizer after pumping has stopped.

Cellulose polymers or synthetic polymers (e.g. polyacrylamide) leave negligible residuebreaking! However, these broken polymers can damage the rock matrix, apparently by adson pore surfaces. Water-base fluids using guar or guar-derivatives, leave insoluble residubreaking, that can occupy from 1 - 3 vol% of the original fluid volume. This residue has beeshown to damage fracture conductivity. If the residue is dried, it loses more than 98% of its orvolume and, therefore, would no longer be a problem. However, most reservoirs are wet todegree, and this residue, which is not mobile,11 can permanently damage proppant packs. In adtion, the effective polymer concentration is increased considerably by leakoff after shutin d

Fig. 6.11 - Spurt Loss vs. Permeability and Additive for Gelled Diesel at 125 F. °



, (

l

5, thed. It

frac-zenyhu-k per-,ese wall,e res-sever,s

g con-ulfate)troyedenera-trationsmosts above

kingsulatedker pre-

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fracture closing. For instance, the pounds of polymer per gallon of proppant pack pore spaceCp)eff

is:

whereρp is the proppant density (lbm/gal proppant),p is the proppant pack porosity,Cp is thepolymer concentration before closure (at shutin) in lbm/gal, andCs is the pounds of proppant/gaof liquid in the fracture at shutin.

For example, if at shutinCs is 8 lbm proppant/gal liquid andCp is 0.04 lbm HPG/ gal liquid, forsand proppant with a density of 22.1 lbm/gal proppant and a proppant pack porosity of 0.3effective polymer concentration after fracture closure would be 0.205 lbm HPG/gal liquiwould concentrate over 5 times. In addition to this, there is polymer already deposited on theture wall before shutin which will contribute to the residue. Using a model based on the Koequation12 for permeability which accounts for polymer residue from leak off during and after stin, Fig. 6.12 and Fig. 6.13 can be derived which show the normalized impaired proppant pacmeability,k'/k, as a function ofCT andVrf for a position in the fracture with a width of 1/4 inchand a fracture age of 60 minutes.Vrf is defined as gal of residue/gal of fluid. Shown in these figurare two hypothetical extremes. The first is where all the residue concentrates at the fractur(effectively reduces the fracture width--the most optimistic case) and the second is where thidue is uniformly distributed--the most pessimistic case. Studies13 have shown that residue tendto concentrate near the wall, so, the optimistic values are probably more realistic. Howextreme permeability impairment can occur whenCs is less than 5 ppg at typical fracture widthand leakoff rates, as shown in Fig. 6.12 and Fig. 6.13.

The preceding impairment discussion assumes that all the polymer breaks. In reality, usinventional breaker loadings, this is probably not the case since solid breaker (e.g. sodium persdoes not concentrate with the residue (it leaks off) and enzyme breakers are frequently desby temperature, high pH, and chemical additives. This realization has spawned the new gtions of crushable and controlled release breakers which can be used at much higher concenthan before and which will accumulate with the polymer. Thus, it is now possible to achieve alcomplete polymer breaks. These new types of breakers are even being used at temperature275°F to maximize breaking, especially of high pH fluids. They also may be useful in breamethanol gels which are very stable and require high breaker loadings. Some kinds of encapbreakers are incompatible with resin coated sands and can release varying amounts of breamaturely, e.g., 5% during a 3 hr treatment.14

Encapsulated breakers are used very aggressively in the pad stage (e.g., 7 lb/1,000 gal)14 with theconcentration reduced somewhat during later proppant stages. Sometimes conventional bradded at the final stages of the treatment to enhance near wellbore cleanup. The benefit oflarge amounts (greater than 2 lb/1,000 gal) of conventional breaker is suspect. Tests have

Cp( )eff

ρp 1-φp( )Cp

Cs φp------------------------------- ,=

φ



Fig. 6.12 - Gel Residue Flow Impairment - Fluid Loss During & After Pumping; Residue UniformlyDistributed or All on Wall.

Fig. 6.13 - Gel Residue Flow Impairment - Fluid Loss During & After Pumping; Residue UniformlyDistributed or All on Wall.



o the

fluidslower

n thein the

he sur-

ir rel-costs.uld beensiveir costsf fluid

l frac-

lue ofbothdam-turing

anual

that a frac fluid with 2 lb/1,000 gal breaker can be broken prematurely before it gets down tfracture.

Fewer problems with fracture conductivity impairment result when using hydrocarbon-baseor foams, as long as they break properly. Hydrocarbon gels are broken with base additive. Attemperatures, e.g. < 120°F, breaking hydrocarbon gels can be a problem. Foams break wheliquid drains (half life), when the surfactant adsorbs onto the rock, and/or when the polymerliquid phase breaks. Flow back with foams has the added advantage of the nitrogen or CO2 expan-sion. Polymer emulsions break when the polymer in the continuous phase breaks and/or tfactant adsorbs onto the rock.

Economics

After narrowing the list of possible fracturing fluid systems, the engineer should compare theative costs. The costs of the base fluid and additives should be tallied along with disposalFor hydrocarbon-base fluids and polymer emulsion, the value of recovered hydrocarbon shosubtracted. In the past, hydrocarbon fluid and foam treatments were considerably more expbecause of the added safety, equipment, and implementation costs. However, presently theare becoming more comparable to water-base systems. Pumping cost is also a function otype through the effect on friction pressure and hydrostatic gradient. See Table 6.3 for typicaturing chemical and hydraulic horsepower prices (ca. 1992).

In addition to the cost of materials and pumping, one should consider the net present vapost-frac production. This is a function of the fracture geometry and conductivity which areaffected by the fluid system through the fluid rheology, proppant transport, leakoff, and gelage. Making this evaluation is best done using an integrated design package including a fracsimulator, production simulator, and economic optimization program. See Chap. 9 of this mfor information on economic optimization.



sys-etail

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Description of Fracturing-Fluid Types

In the preceding section, various types of fracturing fluids were discussed with regards to fluidtem selection criteria. In this next section, types of fracturing fluids will be described in more dand some flow-behavior data will be included.

Water-Base Polymer Solutions

Water-base polymer solutions are prepared primarily from naturally occurring water-solublemers or their chemical derivatives, although there is limited use of the more expensive synproducts.

The term “gelling agent” for water is synonymous with the term “water soluble polymer;” hoever, only the latter properly describes the material. The family of “natural” water soluble pmers consists of vegetable products, such as cellulose (although it is not water soluble, manderivations are), starch, alginates and natural gums. Also included in this list of natural gagents are animal products such as gelatin, glue and casein. Synthetic products fall into twocategories: modified natural products and completely synthetic products. The modified nproducts are starch, natural gum or cellulose molecules which are modified with various cheside chain substitutions. Some completely synthetic products are polyalcohols, polyacids,ethers, and polyamides, made from a variety of synthetic monomers. Natural and syntheticsoluble polymers are listed in Table 6.4.

The water soluble polymers most commonly used in fracturing fluids include guar gum andof its derivations, hydroxypropyl guar (HPG) and carboxymethyl hydroxypropyl guar (CMHPwhose chemical formuli are shown in Fig. 6.14 and Fig. 6.15.

Other types of water soluble polymers used for fracturing fluids include cellulose derivativesmost common of which are hydroxyethyl cellulose (HEC) and carboxymethyl cellu(CMHEC). HEC and CMHEC leave no residue when broken, but are more expensive thaguar-based polymers. HEC cannot be crosslinked, but CMHEC can. Polyacrylamides areused as friction reducers although recently some companies have started using various focrosslinked polyacrylamide. Although the large family of water soluble polymers has breduced to a relatively few that are commercially important, the interaction between these vpolymers, the ability to crosslink them and the possibilities of adding other materials to altephysical properties make the choice of fracturing fluid difficult at times. Table 6.5 lists the primtypes of water-soluble polymers used in fracturing today. Most service companies havguar-based polymers available as “polymer concentrates” for continuous mix application.

The rheology of uncrosslinked polymer solutions is easily measured. Resulting viscodecrease with shear rate and show power law behavior at shear rate greater than 10 1/s. Fshows HPG solution viscosity behavior as a function of shear rate at different temper



s at

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ro-cture.

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Fig. 6.17 and Fig. 6.18 show power law parameters for Halliburton’s HPG (WG-11) solutionvarious concentrations as a function of temperature.

Fast-Crosslinking Water-Base Gels

Water-base fracturing fluids were originally crosslinked using fast crosslinking chemical formtions of organo titanates and zirconates, boron, aluminum, and antimony. Of these, the titand zirconates are not often used anymore without some kind of crosslinking delayer sincflow energy conditions down the tubular goods irreversibly degrade covalentTi and Zrcrosslinks,15 as shown in Fig. 6.19. Boron, aluminum, and antimony form relatively weak hydgen bonds that can reform if broken by shear, and their gels can regain viscosity in the fraFig. 6.20 shows Halliburton data for their borate crosslinked Boragel at 225 F.

Guar, HPG, and CMHPG are the most commonly crosslinked fracturing polymers. CMHPGbe crosslinked by aluminum and/or organic-zirconates because of its dual crosslinked functio(see Fig. 6.21). Titanate and zirconate crosslinkers are used at temperatures above 180 Fof their high temperature stability. Refer to Table 6.6 for pH and temperature ranges for crosers. Notably, the use of boric acid and borax is limited to temperatures less than 225 F. Ssolubilizing naturally occurring borate ores, such as Colemanite or Ulexite can be used at hconcentrations, avoiding gel overcrosslinking at the surface but providing more boron at dowtemperatures giving adequate viscosities to 275 F. Recently, B.J. Services developorgano-complexed borate crosslinker (OCB) which they claim is effective to 300 F.16

Specialty fracturing fluids include residue-free crosslinked cellulosic derivatives, sucCMHEC. These residue-free crosslinked fracturing systems are useful in water injection wellulations, tertiary recovery projects, and conventional treatments where residue free fluidneeded.

In the mid 1980s, service companies introduced the use of polymer (gel) concentrates whichbe continuously mixed during the treatment, rather than batch mixed the day before. This proboth the service company and operating company with cost and time savings. However,monitoring of fluid streams and quality must be maintained during pumping. Typically, a polyconcentrate is prepared by mixing the polymer (e.g. guar, HPG, or CMHPG) in diesel at cotrations of up to 5 lbm/gal diesel. Suspension stabilizers are used to keep the polymer dispWhen added to the mix water, the polymer in the gel concentrate hydrates rapidly and crosdown the wellbore or in the fracture. This produces a gel with hydrocarbon (e.g. diesel) aspersed phase usually at a concentration near 0.5 vol%.

Delayed Crosslinked Fluids

In the mid 1980s, “delayed crosslinked” fracturing fluids became very popular. This type ofsystem has evolved due to evidence of significant viscosity degradation at high shear levshown in Fig. 6.19) with conventional titanate and zirconate crosslinked fracturing fluids.

°

°

°

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Fluid Selection and Scheduling6e flu-g toless

ations.

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basic idea behind delayed crosslinked frac fluids is to retard the crosslinking reaction until thids exit the very high shear regime occurring within the treating string, allowing crosslinkinoccur under relatively low shear conditions within the fracture. Crosslinking under this muchsevere shear regime results in a much higher in-situ viscosity with lower polymer concentr

There is some confusion as to whether delayed crosslinkers are time or temperature actCrosslinking is a chemical reaction; therefore, chemical reaction kinetics apply. This infers thcrosslinking rate (change in viscosity or molecular weight with time) is a function of concentraof reactants, and temperature, as well as some sort of an effective activation energy.

The ideal delayed crosslinked fluid would undergo minimal crosslinking within the treating stbut quickly become crosslinked as soon as it left the perforations and entered the formationis not likely to occur, unless there was a rapid and significant temperature change at the frentrance (physically improbable due to heat transfer and subsequent temperature equilibPractically, a sort of balancing act may be required. It is desirable to maximize in-situ fluid visity as near the wellbore as possible to maintain adequate proppant transport in order to minexcessive proppant banking that can cover the lower perforations, thereby increasing the pofor a near-wellbore screenout. This objective is weighed against the original objective of decrosslinked frac fluids--increased fracture viscosity by not crosslinking within the treating str

The practical solution may come by allowing a certain degree of “sacrificial” crosslinking to owithin the treating string such that the reaction is proceeding as the fluid enters the fraenhancing proppant transport early near the wellbore, and accepting loss of some “long tercosity” potential. In order to do this, variables such as treating string residence time and spflow energy, base fluid temperature, gel pH, polymer concentration, and heat-up rate withfracture need to be known or estimated. Service companies also have developed dual-crossystems (e.g. boron-delayedTi or aluminum-delayedZr) which provide viscosity at the wellboreas the boron and aluminum crosslinks reheal. Later in the fracture, as the gel heats up, theTi andZr crosslink under low shear and give good viscosity at high temperature.

Generally, full delay of crosslinking is desired throughout the pad volume with progressivelydelay as proppant is added and the fracture is cooled down. High temperature delayed crosfrac fluids are not designed to be used below 200 F. They may not break completely at loweperatures or their crosslinkers may not react rapidly enough with cooled formations to providequate near-wellbore proppant transport.

Fig. 6.22 shows Halliburton’s n' and K' data for their delayed crosslinked Versagel HT at 25Fig. 6.3 shows the viscosity behavior at 265 F of Versagel HT compared to other service comorganometallic delayed-crosslinked gels formulated with 40 lbm/1,000 gal of various polymedetermined by Amoco.

°

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Delayed crosslinked borate gel systems are also available. Delayed borate gel systems weroped to reduce the relatively high friction pressures of borate crosslinked gels (e.g., the BJgel in Fig. 6.2) and to provide high viscosities to 275 F. Crosslinking can be delayed by thof delayed pH-control additives or by using slowly solubilizing borate ores.

Polymer Emulsion Fluid

The polymer emulsion fluid is a very efficient (i.e., low fluid loss) and relative clean fluid capaof achieving deep fracture penetrations. The fluid is normally prepared by emulsifying 2/3 hycarbon as the internal phase in 1/3 aqueous polymer solution. Emulsifier concentration is no2-8 gals/1000 gals of total fluid. The upper temperature limit is usually set at 260 F (based onexperience). Sand carrying capability is a function of viscosity and pump rate. Polymer emuis an ideal pad fluid--both low viscosity and fluid loss. The main disadvantages are safety andhigh friction-pressure which can limit treating rates (see Fig. 6.2). As for foams discussed bthe viscosity is developed by a high volume fraction of internal phase (i.e., hydrocarbon). Tanalogous to the increase in slurry viscosity when high proppant concentrations (internal pare added. The effect of internal diesel oil phase is shown in Fig. 6.23.

When mixing proppant into polymer emulsion, the proppant effectively adds to the internal-pvolume fraction with a subsequent viscosity increase and, if in turbulent flow, an increase intion pressure. The latter is responsible for “friction-outs” where pumping must be stopped beof excessively high well-head treating pressures.17 To avoid this, polymer emulsions should bpumped using the “constant internal phase” philosophy where the emulsion quality is reducproppant is added to maintain a nearly constant viscosity. Table 6.7 shows how the emulsionity is varied as proppant concentration is increased to maintain constant internal phase vfraction and constant viscosity.17 There is little difference in the two approaches which implies thmaintaining constant internal phase is a convenient means of maintaining viscosity. Tooproppant can cause the emulsion to break, e.g. when the total internal phase approaches

Fig. 6.24 shows the shear thinning behavior of polymer emulsion as a function of temperatua 0.67 quality fluid17 and Fig. 6.25 shows the effect of increasing the polymer concentration inwater phase.18 Fig. 6.26 shows the effect of temperature and quality on viscosity at 511 1/sWestern Co. diesel oil /0.57 wt% guar emulsions.

Polymer emulsion viscosity is also dependent on mixing energy, where viscosity increaseincreasing energy input. Fig. 6.27 shows the effect of emulsion droplet size on emulsion viscViscosity doubles as droplet-size decreases by 50%. Thus, field mixing method can effect vity significantly.17

Foamed Frac Fluids

Foamed Fracturing Fluids consist of 55-85% by volume of gas dispersed in a suitable wateor hydrocarbon-base liquid.Advantagesof foams include: less liquid introduced into the forma

°

°


Fluid Selection and Scheduling6reignettling.itro--

r 1000tiallytil an

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tion, quicker fluid recovery due to gas expansion, less formation damage from invasion of foliquids or additives, and good proppant transport due to yield stresses retarding proppant sA typical composition of a foamed fracturing fluid is 70%, by total foam volume, of gaseous ngen, carbon dioxide, or 50%/20% CO2 /N2 (a binary foam) as microscopic bubbles in water containing 1-6 gallons of a surface tension reducing surfactant (foamer), 40 pounds of HPG pegallons of liquid, and a breaker, if appropriate. The viscosity of [foam increases exponenabove approximately 55 quality (percent dispersed gas volume to total foam volume) ununstable condition is attained around 95 quality.

Not only are rheological properties of foams very dependent upon foam quality, but theydepend upon the viscosity of the constituent fluids, bubble size, and size distribution (foamture). The smaller the bubble and the larger the fraction of these small bubbles, i.e., the fintexture, the higher the viscosity and stability of the foam at a given quality. Fig. 6.28 and Fig.show n', K', and viscosity data for nitrogen foams as a function of temperature and/or sheawith quality and HPG concentration as parameters.15 Fig. 6.30 shows the effect of shearing timon bubble size diameters.15 Fig. 6.2 shows some reported friction pressure data for foamsFig. 6.31 gives the friction pressure of Dowell Schlumberger’s stabilized foam in 2 7/8 inching.

Texture depends upon the conditions under which the foam was generated. High shear consuch that intimate liquid-gas contact can occur, enhances the generation of fine foam teIncreasing the viscosity of the aqueous phase via polymers also increases foam viscosity ability. This is thought to occur by retarding the rate at which bubbles coalesce, as well as increthe resistance to bubbles slipping past one another.

The foam composition, amount of energy input during the generation of the foam, as well asquality, may have a dramatic effect upon the resultant rheological properties. Typically, wipolymer, foams follow a Bingham plastic rheological model. With the addition of polymer, powlaw properties are introduced. Increasingly finer foam texture and higher polymer concentraresult in increased non-Newtonian flow behavior. (See Chap. 5 of this manual for a discussrheological models.)

There are questions to be answered about the feasibility of using foams for long-term, highperature, fracturing applications. There are limited data to verify that under typically low fracshear rates and for extended periods of time at high temperatures, foams retain sufficient visto ensure continued leakoff control, and sufficient proppant transport capabilities to maketruly competitive with conventional fracturing fluids. This is particularly a concern after pumphas stopped and flow near the wellbore almost ceases. It may be advisable to crosslink tstage of a foam job to give better wellbore stability.Disadvantagesof foam are higher treatingpressures (for nitrogen foams) due to reduced head, and low proppant concentrations becthe low fraction of water. This can be overcome by reducing the quality as higher sand conc



ppant

f

d testroughsen-

y also

Oiloton

ives,were

f caus-ityinum

re ther-

rough-r thin-tions.mplex.If

and

etimeses tot.

ls. This

t trans-

tions are required. As in the case of polymer emulsions, constant internal phase during proaddition maintains the foam viscosity approximately constant.19

Western Company has recently developed the use of binary foam composed of 50% CO2/20% N2

which they claim gives better well cleanup than pure CO2 foams. Fig. 6.32 shows the solubility oCO2 and N2 in water,20 andFig. 6.33 shows the viscosity of a 60 lbm CO2 foam vs. a 50 lbm binaryfoam.20

Foams are difficult to characterize because of their sensitivity to preparation techniques anconditions. There are no long-term foam data available where the foam was not circulated tha pump (and perhaps restabilized). STIM-LAB testing has also indicated that foam stability issitive to silica flour. Apparently, surfactant may adsorb onto the silica surface. The same mabe true to some extent when using sand proppant.

Gelled Hydrocarbons

Gelled hydrocarbons were the first fluids used in hydraulic fracturing. In 1947, Stanolindpumped four stages of gelled gasoline followed by a gasoline flush down a well in the HugField. Aqueous frac fluids were avoided until 1957, when it was found that clay control additsuch as KCl, were effective in water sensitive formations. The earliest gelled hydrocarbonsnapalm-type fluids of aluminum octoate, and later in the 1950s, fatty-acid soaps composed otic and tall oil fatty acids were successfully used.21 These gels usually provided adequate viscosto 150 F. In 1970, high-temperature gelled-hydrocarbon systems composed of alumcrosslinked orthophosphate esters were introduced, eventually leading to systems that amally stable to 350 F.

The reaction of the ester and base (e.g., sodium aluminate) forms an association complex thout the hydrocarbon which increases its viscosity (see Fig. 6.34). The resulting “gel” is sheaning (n' typically lower than 0.25) and is capable of rehealing after seeing high shear condiIn fact, in preparing these gels, high shear conditions are required to form the association coHydrocarbons such as kerosene, diesel, and FRAC-OILTM are often used to prepare these gels.the produced crude has high enough gravity, e.g., > 35 (0.85 g/cm3), it can also be gelled.21 Useof the produced crude is advantageous since it can reduce fluid incompatibility problems.

The primaryadvantagesof gelled hydrocarbons are low damage to water sensitive formationslow damage to proppant packs if the gel breaks properly. Thedisadvantagesinclude the fire haz-ards associated with pumping hydrocarbons, higher pumping pressures resulting from somhigher friction pressures and lower specific gravity (less head), more fluid loss, sensitivitipolar contaminates such as water, difficult quality control and mixing, and higher initial cos

The viscosity of hydrocarbon gels appears less sensitive to temperature than water-base geis true when measured at higher shear rates. However, the low-shear (< 100 sec-1) viscosity maybe reduced significantly as temperature increases, and low-shear viscosities control proppan

°

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port. Unlike water base fluids, the viscosity of hydrocarbon gels increases with pressure6%/1000 psi) giving an additional viscosity edge over published data which are generally obtat pressures less than 1000 psi. These trends are seen in Fig. 6.35.

Table 6.8 shows the results of a comparative evaluation of Halliburton’s continuousMY-T-OIL IV and batch mixed MY-T-OIL II using FRAC-OIL 200 and crude. Viscosities a158 F (70 C) are a function of gellant, activator, and breaker concentrations. Table 6.9 givefor Western Company’s MAXI-0-74 gel.

Gelled Methanol

In 1974, aqueous polymer solutions with up to 25% methanol in guar solutions and up to 60HPG solutions started being used in water-sensitive formations. The maximum amount of mnol is limited by precipitation of the polymer. Some polymers, such as hydroxypropylcelluloseviscosify 100% methanol. In 1987 crosslinked forms of methanol became available, e.g. thBJ Services. These methanol gels can be used with CO2, which is generally soluble in methanol aall concentrations, forming a single phase.

Methanol gels are suited for water sensitive formations because of lower water concentrMethanol reduces surface tension which aids load recovery and the removal of water blocks.gels also have low fluid loss, low friction pressure and, when used with CO2, give energized flow-back. Disadvantages include high cost, high flammability, toxic vapors, and large amounbreaker needed to break the polymer (methanol is a high temperature stabilizer). In water-seformations, gelled oils or diesel are generally preferred over gelled methanol.20

Rheological Testing Of Fracturing Fluids

A Fann Model 50C rotational (Couette) viscometer is generally used to test the rheologicalerties of fracturing fluids. The Fann Model 50C can test fluids at pressures up to 1000 psi antemperature of 400 F. Rotation of the “cup” imparts shear on the fluid and the resulting strmeasured as the torque transmitted to the bob. The apparent viscosity is simply the ratioshear stress and the associated shear rate. The addition of polymer to water results in a norelationship between the shear rate and shear stress, i.e., converts a Newtonian fluidnon-Newtonian fluid. These non-Newtonian fluids are usually described by “power-lawpseudo-plastic type rheological models, and usen' andK' parameters to mathematically describthe relationship between shear stress and shear rate. (Refer to Chap. 5 of this manual for asion of these models.) One of the major problems in testing crosslinked fracturing fluids refrom an effect occurring under shear conditions known as “normal forces,” [which tends tofluid samples up the stationary bob shaft resulting in measuring inaccuracies. It is possibleorganometallic crosslinked gels (i.e., titanium and zirconium gels) because they eventuallyment” into dispersions which stay in the test-gap. Borate gels, however, only partially fill thegap and resultant data are suspect. Tubular data are preferable for borate gels and foams.

° °

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Service Company Trade Names

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crosslinked fracturing-fluids rheology is affected by preparation technique, shear condiinstrument geometry, temperature, and time; meaningful, or even reproducible results are dto obtain.

To further complicate matters, there is no standardized laboratory test for measuring fracfluid viscosity. This implies that some of the data currently in the literature and used by seand production company personnel are not directly comparable, let alone physically represeof actual conditions of application. Currently, the API Committee on Well Completion Fluidsa subcommittee investigating the possibility of developing a standardized testing techniqucrosslinked frac fluids. Such an API recommended procedure is not expected before 1993not expected to be applicable to borate crosslinked gels.

Amoco has issued a recommended test procedure for determining the rheology of titanium aconium gels (report F90-P-73).22 This procedure conditions the fluid in a bench-top mixer to simulate downhole pumping in casing and tubing before pumping the gel to the Fann 50C. Sshear ramps are performed to check for slip flow, which can give anomalously low viscosit

Test procedures which subject the fluid to simulated field mixing and turbulent down-holeconditions before pumping into the Fann viscometer are preferred by Amoco, because of flowthermal-history sensitivities of some fluids. Halliburton conditions its fluids by circulating throa small loop using a Jabsco gear pump at a high flow rate for four minutes to simulate flow dshallow wells and for ten minutes for flow down a deep well. DS conditions its gels by flowthrough capillary tubing at nominal shear rates matched to field nominal shear rates (2.5 mat 675 sec-1 for the shallow well case and for five minutes at 1350 sec-1 for the deep well case).However, the DS technique does not simulate turbulence, because capillary flow occursReynolds numbers. It also does not match flowing energies. The Amoco method mentionedmatches volumetric flow energy and achieves turbulence using a specially designed benmixing device. The API will probably standardize testing using the DS capillary method of cotioning. However, test data run using any form of conditioning is preferable to the old Rmethod which uses no fluid conditioning.


Most service companies consider their fracturing products as proprietary, providing only liminformation regarding chemical components, concentrations, mixing techniques, testingniques, data reduction, etc. Service companies usually designate their different fracturing fludigital codes, Latin words, planetary bodies or other relevant titles. The fracturing fluids for aservice companies are quite similar. One of the most commonly used fracturing fluids forments are crosslinked HPG systems frequently containing 5% hydrocarbon. Table 6.10 giveical components for the titantium crosslinked HPG systems.

As an example of service company fluid system nomenclature, consider Halliburton’s Versystem. Versagel is the trade name of Halliburton's conventionally crosslinked HPG-titanate



e.g.,lymer,igiter perG oris theercent

ation(titan-tituentme of

Theselies

HPG.ar ando theirayed.is a

ls aremerals areG,

catedseen2 wt%of theidueameder-sys-liesature

turing fluid. Halliburton has devised a four-digit designation associated with a Versagel fluid,Versagel 1400. The first digit of the Versagel designation indicates the use of a base poeither WG-11 (HPG) or WG-12 (HPG with internal breaker). The second digit of the four-dVersagel designation is the polymer concentration of the base gel in 10's of pounds polym1,000 gallons water. The third digit indicates the use of delayed hydration polymer, either HPHEC. The HP guar is designated as WG-14, and HEC is designated WG-17. The last digitsecondary gelling agent polymer concentration in 10's of pounds per 1,000 gallons. Five phydrocarbon can be added to Versagel for leakoff control.

More frequently, the delayed crosslinked Versagel HT is used, especially if fluid shear degradis anticipated (as is almost always the case). CL-18 (delay organo-metallic) as well as CL-11ate) are used to modulate the extent of initial crosslinking. The percentages of either conswill vary depending upon mix water, pH, temperature, treating string, residence time, etc. SoHalliburton's HPG systems (as of 1989) are given in the cross reference (Table 6.11).

Dowell Schlumberger also has a coding system for some of its water-base crosslinked gels.gels are labeled as “YF” for “wide frac” and have a three integer suffix. The first integer impboth the polymer type and the crosslinker. If odd, it is a guar system, whereas if even, it isThis first integer is set to 1 or 2 if borate is the crosslinker (1 means a borate crosslinked gu2 a borate crosslinked HPG). Likewise, 3 and 4 refer to titanium systems and 5 and 6 refer tdelayed zirconium gels. For their borate gel, they add the letter “D” to denote whether it is delThe next two integers refer to the polymer concentration in lb/Mgal. For example, YF-140Ddelayed crosslinked borate guar gel at a concentration of 40 lb/Mgal.

In 1991 Western Company changed their water-base crosslinked fluid naming system. Genow referred to by a name that corresponds to the crosslinker type followed by a roman nudesignation for the polymer type. Titanium, aluminum, zirconium, and borate gel systemreferred to as APOLLO, GEMINI, SATURN, and VIKING respectively. Guar, HPG, CMHPand CMHEC are indicated by I, II, III, IV respectively.

Generally, service company fluid trade names give little information about the nature or indiapplication of the fracturing fluid. Looking at the fluid cross reference (Table 6.11), it can bethat there are some exceptions. The most simple system, water with friction reducer (< 0.1polyacrylamide) is given names such as Aqua Frac, Water Frac, and Slick Water. SomeCMHEC systems are given names like Kleen Gel or Krystal Frac XL which refer to the low res(essentially zero) of the CMHEC when it breaks. Some gelled oil systems are aptly nMY-T-OIL or YF-GO III. Halliburton’s new high temperature system (to 370 F) is called Thmagel (a high pH zirconium crosslinked CMHPG). Halliburton adds a suffix to some of itstems’ names referring to maximum intended temperature. Their “LT” designation impmaximum intended use of 125 F, i.e., low temperature. “HT” refers to intended high temperuse up to 300 F.

°

°°



imilariffer.hichperioruperior

The cross reference (Table 6.11) provides a method for getting a general idea of generically ssystems for different service companies. However, the exact chemical formulations may dSome service companies, especially the “big four” take pride in their special formulations, waccording to their own testing, can give superior performance. Sometimes, however, the “superformance” may be a result of the particular test method used to evaluate it, rather than a scomposition.



p atmust

ratingeffect

fluid0 cpppant

actingpicallye in

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timetom-cturell as

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jobsneer

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6.2 Fluid Scheduling

After a fluid type is selected, the engineer must decide what composition of the fluid to pumthe various stages of the fracturing treatment, i.e. the fluid schedule. The fluid compositionyield enough viscosity for adequate fracture width and proppant transport without geneexcessive viscosity resulting in breaking out of zone and excessive height growth. Also, theof fluid composition on fluid loss and fracture conductivity must be considered.

At this time, the viscosity guideline (discussed in Section 5.3 of this manual) will be used forscheduling. This guideline states that if a “neat” (proppant-free) fluid can maintain at least 5at 170 1/s shear rate during its lifetime in the fracture, then it is probable that adequate protransport will result. This statement is based on the assumption that the effective viscosityto reduce proppant settling is increased by the presence of proppant and by shear rates tylower than 170 1/s in the fracture. In addition, at times earlier than the total fluid exposure timthe fracture, viscosity is usually greater since the fluid has had less exposure to degrading teffects. Field experience has shown that fluids meeting this viscosity guideline can succestransport proppant. Whether this transport proceeds via perfect proppant transport, slow sor an equilibrium banking process is presently the subject of research.

Fracturing design simulators require a knowledge of the viscosity of a fluid element at a givenand position in the fracture. The fluid-element rheology is a function of exposure time at bothole temperature (BHT). However, the fluid-element exposure time is a function of the frageometry and leakoff which are in turn functions of the fluid rheology and composition (as wethe fracturing model used --PKN, GDK, etc.). Thus, the engineer does not know before thelation, what BHT exposure time each fluid stage is going to experience. Therefore, optimal suling of fluids with the “appropriate” viscosity is an iterative process. The following are tapproaches to fluid scheduling. The first uses a given fluid system with known rheology (n', andK' as functions of time at temperature) and the second constrains the rheology of the fluid elin the fracture to be between 200 cp and 50 cp. The first technique is more suited for smallerments (less than three hours), whereas the second method is useful for larger treatments.

Fluid Scheduling Given the Fluid Rheology

Fluid scheduling given the rheology of a particular fluid system is appropriate for smallerusing only one fluid stage. The following method of fluid scheduling will assume that the engiis designing for a particularfracture length and heightwith a desiredmaximum slurry proppantconcentration, given thepump rate. In this case, a fluid system is selected which gives viscositgreater than 50 cp at 170 1/s for the estimated pump time, and which will permit pumping aface pressures within wellhead pressure constraints. If the simulator does not have an estiroutine for the fluid volume (and therefore pump time), the engineer can make a rough estimdividing the desired fracture volume by the pump rate and the expected fluid efficiency. If the


Fluid Scheduling

tively

are,fromnduc-e fluidhosenient;

too(if

or aless

vis-iscouss less

lessthe

e uti-

cosi-s, the

s to

es-e frac-

times

01andpre-tures or

age fracture width and fluid efficiency are not known, values of 0.25 inches and 0.4 respeccan be assumed as starting values.

The values ofn' andK' at fracture entry temperature and at time at bottomhole temperatureentered into the simulator. Also, a value ofCw for the fluid system or a total fluid loss coefficientCT, representative of the particular fluid system in a particular reservoir (ideally obtainedminifrac testing) are input. The simulator is then run. If the desired fracture geometry and cotivity are not attained, the design engineer must examine the simulator results and adjust thsystem accordingly. For example if the job screens out prematurely, a new fluid could be cwhich gives more viscosity; a fluid-loss additive could be added to lower the fluid loss coefficor the maximum proppant concentration could be reduced. If the resulting conductivity issmall, the engineer could try a more viscous fluid which would give wider fracture widthsheight growth is not a problem); a cleaner fluid which gives less conductivity impairment;larger maximum slurry proppant concentration. If the calculated pump time is substantiallythan the viscous life of the fluid (the time at bottomhole temperature during which the fluidcosity at 170 1/s exceeds 50 cp), the engineer may try repeating the simulation with a less vfluid. This is particularly desirable when pumping water base gels where less polymer meanfluid expense and better ultimate conductivities at a given fracture proppant concentration.

This method of fluid scheduling is essentially a trial and error approach, involving more oriterations depending on the engineer’s familiarity with the particular fracturing simulator andformation. The next method is more suited for jobs where multiple fluid types or stages arlized.

Fluid Scheduling Using Constrained Rheology

For treatments where different fluid stages are utilized in order to maintain more uniform visties in the fracture (e.g. between 200 and 50 cp at 170 1/s) and to minimize polymer loadingfollowing method can be usedif the fracturing simulator can calculate fluid-element time at tem-perature vs. volume pumped. As in the previous fluid scheduling method, the engineer wishecreate a fracture having a particularlength and heightwith a desiredmaximum slurry proppantconcentrationusing a givenpump rate. The maximum pump rate is constrained by wellhead prsure limitations. In this case the engineer can enter the viscosities of the fluid as it enters thture and when it first reaches bottomhole temperature as 200 cp at 170 1/s. Ann' of 0.75 and aK'of 0.01508 lbf-sn' /ft2 corresponding to 200 cp can be assumed. The remaining viscosities atgreater than or equal to 1 hour can be set to 50 cp at 170 1/s withn' of 0.75 andK' of 0.003771. Atotal fluid loss coefficient,CT, representative of the type of formation being fractured (e.g. 0.0

for permeability less than 0.1 md, 0.0025 for permeabilities between 0.15.0 md, or 0.005 for permeabilities greater than 5 md) can be input. If the simulatordicts a screen out, the engineer can increase the viscosities at appropriate time-at-temperaperhaps use a lower fluid loss coefficient.

ft/ min ft/ minft/ min



lator,ure vs.recom-logicalt tem-ked offcurve.lymercissa.50 lbppantl and

stage.r addi-

em (hetivity,loss,

createch of

omen thentially(e.g.

y vseakerscosity

ferentmon

een

After the desired fracture length and fracture conductivity have been calculated by the simuthe engineer can schedule a fluid system. Fig. 6.36 shows the fluid-element time at temperatvolume pumped calculated by a simulator using an assumed constant viscosity, such asmended above (i.e. 200 cp initially and 50 cp thereafter). The engineer then uses the rheodata for the selected fluid system (e.g. the X-CEL gel system in Fig. 6.37) to mark the times aperature corresponding to when the particular fluid reaches 50 cp. These times are then maron the ordinate of Fig. 6.36 and extended horizontally to intersect the time-at-temperatureThe fluid volumes corresponding to the intersection points define the stages of various poloading for the fluid system. Fig. 6.36 shows the resulting gel schedule marked off on the absThe pad consists of 20,000 gal of a 50 lb crosslinked gel plus 60,000 gal of a stabilizedcrosslinked gel (X50S). The X50S gel continues for another 40,000 gal up to the 4 ppg prostage. Then 40,000 gal of crosslinked 50 lb gel followed by 30,000 gal of crosslinked 40 lb ge50,000 gal of crosslinked 30 lb gel complete the pumping of proppant through the 10 ppgThe middle sand stages on Fig. 6.36 have been reduced below the theoretical to account fotional slurry dehydration.

Using the specified gel schedule, the engineer inputs the rheology for the selected fluid systn'andK' as functions of time at temperature) plus theCw appropriate for each stage and reruns tsimulator. If the simulated results meet the engineer’s specifications of length and conducthen the design is completed. If not, the engineer must make appropriate rheology, fluidand/or maximum slurry proppant concentration modifications.

For a class problem, plot the data in Table 6.12 on the semilog graph paper in Fig. 6.38 toan exposure time plot similar to Fig. 6.37. Also, indicate the optimum time exposures for eathe fluid stages.

Warning:

The testing of crosslinked gels is very difficult, with highly varying results from test to test. Sservice company data result from gels that were conditioned to simulate the flow history dowtubular goods before testing on the viscometer. Viscosities of conditioned gels can be substadifferent from those of unconditioned gels. Also, if breakers are required for a fluid systemfor temperatures less than 250°F), they should be added to all proppant laden portions of the fluid.Breakers can significantly lower a fluid’s viscosity while pumping, and therefore, the viscosittime at temperature plots (e.g. Fig. 6.37) should be adjusted accordingly. Encapsulated brare now available which slow and/or delay the release of the breaker to avoid premature visbreaking and to allow high breaker concentrations for better gel breaking.

The uncertainty in some of the data can be overcome by comparing similar systems for difcompanies and using field experience. Fig. 6.39 - Fig. 6.41 provide guidelines for three comfluid systems. Theseguidelinesinclude the comparisons with various companies and have b


Fluid Scheduling

m-main-

owncon-

sys-uring-d

successfully appliedin the field. Guidelines include the use of viscosity stabilizers at higher teperatures and longer exposure times. The use of stabilizers allows higher viscosity to betained without using additional polymer.

Anotherguideline,which has been successfully applied, is for pad fluids. This guideline is shon Fig. 6.42 and was based on gel stability at high temperatures for an effective wall cake totrol fluid loss. However, this guideline may be too conservative for the high temperature fluidtems currently available. Also, recent data for fluids with 5% hydrocarbon (generally used dpad or first half of treatment with X-L gel and lowk) indicate that polymer loading may not significantly affect fluid loss. Thesereservationsconcerning Fig. 6.42 should be evaluated if fluischedules are developed which differ from the guideline.



n instern'sted

ents or

PROPPANT AND FLUID SCHEDULING PROBLEM

Using the prior guidelines for fluid scheduling and the example plot of simulator results showFig. 6.43 develop a complete fluid and proppant schedule assuming the fluid system is WeAPOLLO II/APOLLO II H system (Fig. 6.41). Assume the results in Fig. 6.43 are calculaassuming the minimum viscosity requirements discussed previously.

Since frac tanks are generally 500 BBLS (20,000 gals), fluids should be selected in 20,000 gallon incremanother increment which is convenient for the tank size actually used.


References

ids,”

t the

4469

ions,”

ference

Diesels Co-

ea-onfer-

Based(Feb.

Termand Ex-

per

rdson,

6.3 References

1. Ely, J. W.:Stimulation Treatment Handbook, An Engineer’s Guide to Quality Control, PennWell Publishing Co.,Tulsa, OK (1985).

2. RP 39, Recommended Practice for Standard Procedures for the Evaluation of Hydraulic Fracturing FluAPI, Dallas (1983).

3. Biot, M.A. and Medlin, W.L.: “Theory of Sand Transport in Thin Fluids,” paper SPE 14468 presented a1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 22-25.

4. Medlin, W.L., Sexton, J.H., and Zumwalt, G.L.: “Sand Transport Experiments in Thin Fluids,” paper SPE 1presented at the 1985 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 22-25.

5. Daneshy, Ali: “Proppant Transport,” Monograph Series, SPE, Richardson, TX (1989)12, vii, 210-22.

6. Shah, S. N.: “Proppant Settling Correlations for Non-Newtonian Fluids Under Static and Dynamic ConditSPEJ (April 1982) 164-70.

7. Novotny, E.J.: “Proppant Transport,” paper SPE 6813 presented at the 1977 SPE Annual Technical Conand Exhibition, Denver, Oct. 9-12.

8. Penny, G.S. and Conway, M.W.: “Fluid Leakoff,” Monograph Series, SPE, Richardson, TX (1989)12, vii,147-76.

9. Cameron, J.R.: “Fluid Loss Testing on East Texas Cotton Valley Sand Cores to Determine the Effects ofand Polymer Concentration; With Consideration on Design Values of Spurt Loss and the Overall Fluid-Losefficient,” Amoco Production Company Report F88-P-21 (July, 1987).

10. McGowan, J.M. and McDaniel, B.W.: “The Effects of Fluid Preconditioning and Test Cell Design on the Msurement of Dynamic Fluid Loss Data,” paper SPE 18212 presented at the 1988 SPE Annual Technical Cence and Exhibition, Houston, October 2-5.

11. Cooke, C.E., Jr.: “Effect of Fracturing Fluids on Fracture Conductivity,”JPT (Oct. 1975) 1273-82;Trans.,AIME, 259.

12. Cameron, J.R.: “Vol% Residue of HPG Vs. Guar in Borate Crosslinked Gels and Flow Impairment Modelson Vol% Residue and Fracturing Design Parameters,” Amoco Production Company Report F90-P-411990).

13. Penny, G.S.: “Evaluation of the Effects of Environmental Conditions and Fracturing Fluids on the Long-Conductivity of Proppants,” paper SPE 16900 presented at the 1987 SPE Annual Technical Conferencehibition, Dallas, Sept. 27-30.

14. Small, J.,et. al.: “Improving Fracture Conductivities with a Delayed Breaker System: A Case History,” paSPE 21497 presented at the 1991 SPE Gas Technology Symposium, Houston, Jan. 23-25.

15. Cameron, J.R. and Prud’homme, R.K.: “Fracturing-Fluid Flow Behavior,” Monograph Series, SPE, RichaTX (1989)12, vii, 177-209.


Fluid Selection and Scheduling6uctiv-onfer-

3 pre-

n Re-11-13.

onium

16. Brannon, H.D. and Ault, M.G.: “New Delayed Borate-Crosslinked Fluid Provides Improved Fracture condity in High-Temperature Applications,” paper SPE 22838 presented at the 1991 SPE Annual Technical Cence and Exhibition, Dallas, Oct. 6-9.

17. Roodhart, L.P. and Davies, D.R.: “Polymer Emulsion: The revival of a Fracturing Fluid,” paper SPE 1641sented at the 1987 SPE/DOE Low Permeability Reservoirs Symposium, Denver (May 18-19).

18. Sinclair, A.R., Terry, W.M., and Kiel, O.M.: “Polymer Emulsion Fracturing,”JPT (July 1974) 731-38.

19. Harris, P.C., Klebenow, D.E., and Kundert, D.P.: “Constant Internal Phase Design Improves Stimulatiosults,” paper SPE 17532 presented at the 1988 SPE Rocky Mountain Regional Meeting, Casper, WY, May

20. Western Binary Foam System, Technical Manual, 1990.

21. Ely, J.W.: “Fracturing Fluids and Additives,” Monograph Series, SPE, Richardson, TX (1989)12, vii, 131-146.

22. Cameron, J.R. and Gardner, D.C.: “Suggested Amoco Procedure for Testing Titanium and ZircCrosslinked Gels,” Amoco Production Company Report F90-P-73 (Oct. 1990).


References




References




References




References




References




References




References

Table 6.3 - Smith Energy Services Fracturing Services & Products.

EQUIPMENT

ZONE A ZONE B

MILEAGE

33000 All units excluding sand and chemical delivery fromthe nearest SES operating point, one way, per unit,per mile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.48 2.48

FRACTURING PRESSURE (psi)

Per HHP, four hours or less

330103301533020330253303033035330403304533050330553306033065

0 to 5,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5,001 to 6,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6,001 to 7,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7,001 to 8,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8,001 to 9,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9,001 to 10,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10,001 to 11,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . .11,001 to 12,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . .12,001 to 13,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . .13,001 to 14,000 . . . . . . . . . . . . . . . . . . . . . . . . . . . .14,001 to 14,500 . . . . . . . . . . . . . . . . . . . . . . . . . . . .Over 14,500. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.204.665.256.357.619.35

11.1812.6514.6515.5017.20

*P.O.R.

3.653.994.435.386.307.568.98

10.4912.1613.0214.70

*P.O.R.

FRACTURING PUMP EQUIPMENT

Based on hydraulic horsepower, ordered or used, whichever isgreater, calculations are carried to the nearest BPM obtained whilepumping the combined volume of fluid and solids. The average in-jection rate and average injection pressure to the nearest 100 psiand measured at the surface during fluid injection. Any abnormalfluctuations in pressure of short duration, such as high breakdownpressure are excluded. Minimum pressure used in this calculationwill be 800 psi. HHP ordered is defined as the HHP required to pro-vided the specific injection rate at specified injection pressures ascalculated from the formula below:

* Priced on Request

CHEMICAL ADDITIVES

HHPBPM average( ) psi average( )×

40.8--------------------------------------------------------------------=



ZONE A ZONE B

BACTERIA CONTROL

340003401034020340303403134033

BCS-1; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .BCS-2; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .BCS-3; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .BCS-4; (Dryocide), per pound. . . . . . . . . . . . . . . . . .BCS-5; sodium hypochlorite, per gallon . . . . . . . . . .BCS-7; (X-CIDE 600), per pound . . . . . . . . . . . . . . .

33.8355.3132.2316.506.48

52.80

33.8355.3132.2316.506.48

52.80

BREAKERS FOR GEL SYSTEMS

34040340503405134060349613406234070

3407434077

OXB-3; oil gel, per pound . . . . . . . . . . . . . . . . . . . . .WCB-1; water gel, per pound . . . . . . . . . . . . . . . . . .WCB-2; water gel, per pound . . . . . . . . . . . . . . . . . .WCB-LT; breaker aid, water gel, per gallon . . . . . . .WCB-LTA; breaker aid, water gel, per gallon . . . . . .WCB-ACT; breaker activator, water gel, per gallonWEB-2; water enzyme breaker, per half galloncontainer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .EWB-1; encapsulated breaker, per pound** . . . . . . .DWB-1; delayed breaker, per pound . . . . . . . . . . . .

4.133.082.75

18.9814.1955.79

113.3039.6014.85

4.133.082.75

18.9814.1955.79

113.3039.6014.85

**Dowell Schlumberger License Fee Applies

BUFFERS

3408034090341003411034120341303414034145

BW-1; per pound. . . . . . . . . . . . . . . . . . . . . . . . . . . .BW-3; per pound. . . . . . . . . . . . . . . . . . . . . . . . . . . .BW-4; per pound. . . . . . . . . . . . . . . . . . . . . . . . . . . .BW-5; per pound. . . . . . . . . . . . . . . . . . . . . . . . . . . .BW-6; per pound. . . . . . . . . . . . . . . . . . . . . . . . . . . .BW-9; per pound. . . . . . . . . . . . . . . . . . . . . . . . . . . .BW-10; ammonium chloride, per pound . . . . . . . . . .AA-11; caustic soda, per pound . . . . . . . . . . . . . . . .

1.90.43

2.401.952.681.121.18

*P.O.R.

1.90.43

2.401.952.681.121.18

*P.O.R.

* Priced on Request



References

CHEMICAL ADDITIVES

ZONE A ZONE B

CLAY CONTROL CHEMICALS

341503415534156341603417034175

CCC-3; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .CCC-4; CLAYLOKR, per gallon**. . . . . . . . . . . . . . . .CCC-5; clay control alternative, per gallon . . . . . . . .KCI; potassium chloride, per cwt . . . . . . . . . . . . . . . .LPA-1; per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . .BRN-1; brine water, per barrel. . . . . . . . . . . . . . . . . .

34.28*P.O.R.

24.7524.7526.90

*P.O.R.

34.28*P.O.R.

24.7524.7526.90

*P.O.R.

** Chevron License Fee Applies

CROSSLINKERS

341803418934190342003421034220342303424034245342503425134252

3425334254

CX-1; aqueous gel, per gallon . . . . . . . . . . . . . . . . . .CX-4; low temperature, low pH, per gallon . . . . . . . .CX-5; low pH, per gallon . . . . . . . . . . . . . . . . . . . . . .CX-6; cold water, per gallon . . . . . . . . . . . . . . . . . . .CX-12; brine water, per gallon. . . . . . . . . . . . . . . . . .CX-13; high pH, per gallon . . . . . . . . . . . . . . . . . . . .CX-14; high temp., per gallon . . . . . . . . . . . . . . . . . .CX-15; high temp., per gallon . . . . . . . . . . . . . . . . . .CX-16; aqueous gel, per gallon . . . . . . . . . . . . . . . . .CX-91; aqueous gel, per gallon . . . . . . . . . . . . . . . . .CDA-2; crosslink delay additive, per gallon . . . . . . . .CX-DB2; high temperature delayed borate crosslink-er, per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .DBX-1; delayed borate crosslinker, per gallon . . . . .RM-18; high pH boric acid, per pound. . . . . . . . . . . .

40.9945.0070.0631.7134.0016.1724.2332.3851.8130.9647.85

29.704.99

*P.O.R.

40.9945.0070.0631.7134.0016.1724.2332.3851.8130.9647.85

29.704.99

*P.O.R.

* Priced on Request



Flu

id S

ele

ction

an

d S

che

du

ling

6Hyd

rau

lic Fra

cturin

g T

he

ory M

an

ua

l6-56

July 1

99

9

NE B

.202.822.11.20

4.223.45

30.1530.15

36.0028.14

6.602.48.61

3.8518.15

12.97.60


CHEMICAL ADDITIVES

ZONE A ZO

DIVERTING AGENTS

342553426034270342803429034300

DA-1; rock salt, course, per pound . . . . . . . . . . . . . .DA-2; naphthalene, per pound . . . . . . . . . . . . . . . . .DA-3; benzoic acid flakes, per pound . . . . . . . . . . . .DA-4; rock salt, graded, per pound . . . . . . . . . . . . . .DA-5; wax beads, per pound. . . . . . . . . . . . . . . . . . .DA-6; paraformaldehyde flakes, per pound. . . . . . . .

.202.822.11.20

4.223.45

EMULSION PREVENTION SURFACTANTS

3431034320

EPS-4; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .EPS-9; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .

30.1530.15

EMULSIFIERS

3433034340

PEM-1; water external, per gallon . . . . . . . . . . . . . . .PEM-3; 5% hydrocarbon systems, per gallon . . . . . .

36.0028.14

FLUID LOSS ADDITIVES

343503436034370343803439034395

34396

OFL-1; (Adomite Mark II) per pound . . . . . . . . . . . . .WFL-1; (Adomite Aqua) per pound . . . . . . . . . . . . . .WFL-2; per pound . . . . . . . . . . . . . . . . . . . . . . . . . . .WFL-3; (Adomite Regain), per pound . . . . . . . . . . . .WFL-4; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .WFL-5; (Adomite Regain) diesel based slurry pergallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .WFL-6; cornstarch, per pound. . . . . . . . . . . . . . . . . .

6.602.48.61

3.8518.15

12.97.60

DEFOAMING AND FOAMING AGENTS

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l6-57

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9

63.06

31.50

21.05

NE B

23.288.25

26.2432.25

42.9015.2951.1551.00


3441034420

34430

AGD-2; defoamer, per gallon . . . . . . . . . . . . . . . . . .FAA-1; (Adofoam BF-1), foaming agent for fresh wa-ter and brines, per gallon. . . . . . . . . . . . . . . . . . . . . .FAA-2; foaming agent for fresh water, brine, and acid,per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63.06

31.50

21.05

* Priced on Request

CHEMICAL ADDITIVES

ZONE A ZO

FRICTION REDUCERS

34440344453445034451

OFR-1; oil friction reducer, per gallon . . . . . . . . . . . .WFR-1; water friction reducer, per pound . . . . . . . . .WFR-2; water/acid friction reducer, per gallon . . . . .WFR-3; water/acid friction reducer, per gallon . . . . .

23.288.25

26.2432.25

GELLING AGENTS - OIL

34460344703448034490

OGA-1; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .OGA-2; complexer, per gallon. . . . . . . . . . . . . . . . . .OGA-3; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .OGA-4; high temp., per gallon. . . . . . . . . . . . . . . . . .

42.9015.2951.1551.00

DIESEL FUEL

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9

P.O.R.P.O.R.

6.176.106.174.57

20.3527.5027.50

23.87

26.16

1.90


3449534496

DIE-1; number one diesel, per gallon . . . . . . . . . . . .DIE-2; number two diesel, per gallon . . . . . . . . . . . .

*P.O.R.*P.O.R.

**

GELLING AGENTS - WATER

3450034510345203453034550345603456534567

34568

WGA-2; HPG, per pound. . . . . . . . . . . . . . . . . . . . . .WGA-4; CMHEC, per pound . . . . . . . . . . . . . . . . . . .WGA-5; CMHPG, per pound. . . . . . . . . . . . . . . . . . .WGA-6; premium guar, per pound . . . . . . . . . . . . . .CMG-1; Continuous Mix Gel - Guar, per gallon . . . .CMG-2; Continuous Mix Gel - HPG, per gallon. . . . .CMG-3; Continuous Mix Gel - CMHPG, per gallon.CMG-4; Environmentally Safe Continuous Mix Gel -Guar, per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . .CMG-5; Environmentally Safe Continuous Mix Gel -HPG, per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.176.105.174.57

20.3527.5027.50

23.87

26.16

GEL STABILIZING AGENTS

34570 HTS-2; high temperature, per pound. . . . . . . . . . . . . 1.90

* Priced on Request

CHEMICAL ADDITIVES

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9

NE B

55.8352.2564.76

20.79

35.9721.7118.2226.4046.7028.1731.3732.31

.91125.00

.91125.00

5.50121.0011.00


ZONE A ZO

SURFACTANTS

34580345853459034591

34598

34600346103462034622346303464034650

FRS-1; fluid recovery surfactant, per gallon . . . . . . .FRS-2; fluid recovery surfactant, per gallon . . . . . . .FRS-3; fluid recovery surfactant, per gallon . . . . . . .FRS-4; fluid recovery surfactant, non-fluorocarbon,per gallon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .MCFRS;methanecoalfluidrecoverysurfactant,pergallonSAA-1; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .SAA-2; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .SAA-3; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .SAA-4; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .SAA-7; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .SAA-8; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .USS-N; per gallon . . . . . . . . . . . . . . . . . . . . . . . . . . .

55.8352.2564.76

20.79

35.9721.7118.2226.4046.7028.1731.3732.31

CHEMICAL DELIVERY

3466034665

For chemical delivery to location, per ton mile . . . . .Minimum delivery charge for all chemicals . . . . . . . .

.91125.00

CHEMICAL RETURN

3466634667

For chemical return from location, per ton mile . . . . .Minimum return charge . . . . . . . . . . . . . . . . . . . . . . .

.91125.00

CHEMICAL HANDLING CHARGE

Handling charge for chemicals furnished by customer

346703468034681

Dry chemicals, per cwt . . . . . . . . . . . . . . . . . . . . . . .Liquid chemicals, per 55 gallon drum . . . . . . . . . . . .Liquid chemicals, per 5 gallon container . . . . . . . . . .

5.50121.0011.00

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9

P.O.R.


CHEMICALS NOT INCLUDED IN PRICE LIST

34999 Chemicals not included in Smith Energy Services’price list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . *P.O.R. *

* Priced on Request

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Table 6.4 - Water Soluble Polymers.

NATURAL

ANIMAL ORIGIN BACTERIA ORIGIN VEGETABLE ORIGIN

GELATINGLUE

CASEINCHITIN

BIOPLOYMERSXANTHAN

CELLULOSESTARCH

SEED GUMSGUAR GUM*

LOCUST BEAN GUMQUINCE, FLAX & OKRA GUM

TAMARINDPLANT EXUDATES

GUM ARABICGUM GHATTIGUM KARAYA

GUM TRAGACANTHSEQWEED EXTRACTS

AGARALGIN

CARRAGEENANPLANT EXTRACTS

LARCH ARABINOGALACTANPECTIN

SYNTHETIC

MODIFIED NATURAL PRODUCTS SYNTHETIC PRODUCTS

CARBOXYMETHYCELLULOSE (CMC)* POLYVINYL ALCOHOL

ETHYCELLULOSE POLYVINYLPYRROLIDONE

HYDROXYETHYLCELLULOSE (HEC)* POLYVINYLMETHYL ETHER

CARBOXYMETHYL HYDROXYETHYLCELLULOSE (CMHEC)* POLYACRYLIC ACIDS & SALT

ETHYLHYDROXYETHYLCELLULOSE POLYACRYLAMIDES*

METHYLCELLULOSE ETHYLENE OXIDE POLYMERS

STARCH AMYLOSE

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Table 6.4 - Water Soluble Polymers.

STARCH AMYLODPECTIN

STARCH DEXTRINS

STARCH HYDROXYETHYL ETHERS

HYDROXYPROPYL GUAR (HPG)*

CARBOXYMETHYL HYDROXYPROPYLGUAR (CMHPG)*

HYDROXYETHY GUAR

* PRIMARY GELLING AGENTS FOR HYDRAULIC FRACTURING FLUIDS.

Fig. 6.14 - Where Guar Comes From.

NATURAL

ANIMAL ORIGIN BACTERIA ORIGIN VEGETABLE ORIGIN

y

Guar GumMolecule

A High Molecular Weight Carbohydrate Polymer(Polysaccharide)

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Fig. 6.15 - Principal Guar Derivatives.,

Fig. 6.14 - Where Guar Comes From.

DoublePurifiedSplits

SinglePurifiedSplits

GuarSeeds

GuarPods

Hydroxypropyl Guar (Generalized Structure)

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Carboxymethyl Hydroxypropyl Guar

Table 6.5 - Primary Gelling Agents for Fracturing.

Water Soluble Polymers

Guar GumHPGCMHPG

Cellulose DerivativesHECCMCCMHEC

Polyacrylamides

Fig. 6.15 - Principal Guar Derivatives.,

(Generalized Structure)

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.

Fig. 6.16 - HPG Solution: Effect of Shear Rate & Temperature.

Fig. 6.17 - Flow Behavior Index (n') vs. Temperature of Halliburton’s HPG Solution


Fig

.6.1

8-

Con

sist

ency

Inde

x (K

'a)

vs.

Tem

pera

ture

of H

allib

urto

n’s

HP

G s

olut

ion.


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July 1

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9

cetonate
Fig. 6.19 - Comparison of 40-lbm/1,000-gal Hpg Gels Crosslinked with Titanium Acetyl ASubjected to Various Turbulent Flow and Temperature Histories.



References



Fig. 6.20 - Viscosity of Halliburton’s Boragel (Borate Crosslinked Guar) as a Function of Time at225 F.°


References

Table 6.6 - Useful Crosslinkers for Guar and Guar Derivatives.

Crosslinking Guar

CrosslinkerpH Range of

FluidEffective Temperature

Region

Borate 8-10 60 F - 275 F maximum

Antimony 2-3.5 140 F maximum

Titanate 7-8 or higher 300 F +

Zirconium 7-8 or higher 350 F +

Aluminum 4-8 160 F maximum

Zirconium <1 (acids) <100 F

Fig. 6.21 - Generalized Crosslinking Scheme.

° °°

°°°

°°

Crosslinking Through COOH Groups(CMHPG)

Crosslinking Through cis OH Groups



Fig. 6.22 - Power Law Data for Halliburton’s Versagel HT Fluid 250 F.

Versagel HT - 250 deg F

MEOH GEL-STAABCD

WG-1140404040

5500

100

100

DB

CA

0 1 2 3 4 5 6

1.0

0.8

0.6

0.4

0.2

n'

Time (hr)

Consistency Index (K' a) vs. Time

Flow Behavior Index (n') vs. TimeVersagel HT Fluids

0 1 2 3 4 5 6

1.0

0.1

0.01

0.001

K'a

Time (hr)

A

C

B

D

°


References

Fig. 6.23 - Effect of Internal Phase on Polymer Emulsion Viscosity.


Table 6.7 - Comparison Of “Constant-Internal-Phase” Concept With “Constant-Viscosity-Concept”
For Two Polymer Emulsion Slurries With The Same Polymer Loading.

Proppant Loading(lb/gal)

Constant Viscosity Constant Internal Phase

Emulsion Quality(-)

Slurry Viscosity(mPa.s)

Emulsion Quality(-)


0 0.70 266 0.70 266

2 0.67 266 0.67 266

4 0.66 266 0.65 254

6 0.64 266 0.62 236

8 0.62 266 0.59 228

10 0.59 266 0.56 228

12 0.56 266 0.54 244

Proppant Loading(lb/gal)

Constant Viscosity Constant Internal Phase

Emulsion Quality(-)


Emulsion Quality(-)


0 0.67 197 0.67 197

2 0.63 197 0.64 205

4 0.61 197 0.61 197

6 0.59 197 0.58 191

8 0.56 197 0.55 191

10 0.52 197 0.52 197

12 0.48 197 0.50 200


References

Fig. 6.24 - Flow Curves of a 0.67 Quality Emulsion at Various Temperatures.

Fig. 6.25 - The Effect of Shear Rate onPolymer Emulsion Viscosity.

Fig. 6.26 - Viscosity vs. Temperature forWestern Super K-Frac (Polyemulsion).

= 176° F

1000

100

1070 90 110 130 150 170 190 210

Temperature ( °F)

(Vis

cosi

ty, c

p @

511

sec

-1)

708075

70

807560

50

5060



Fig. 6.27 - Plot of Viscosity of a 0.67 Quality Emulsion Vs. Mean Droplet Size.


References

Fig. 6.28 - Power-law Data for a Water/ N2 Foam Stabilized With 40 lbm Thickener/1,000 Gal Water.

Fig. 6.29 - Effect of HPG Concentration (lbm/1,000 gal) on the Viscosity of a 0.70-Quality Foam.



Fig. 6.30 - Effect of Shear History on the Texture of an Aqueous/N 2 Foam.

Fig. 6.31 - Friction Pressure for Dowell Schlumberger’s Stabilized Foam.

Foam Friction PressurePipe Data: 2 7/8 in. OD EUE tubing - 6.5 lb per ft

1000900800700

600

500

400

300

200

100908070

60

50

40

30

20

10

1000900800700

600

500

400

300

200

100908070

60

50

40

30

20

101 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100

Flow Rate - BPM

Fric

tion

Pre

ssur

e -

psi p

er 1

000

ft

Foam Quality

0.85

0.80

0.75

0.70

0.65

0.60

0.55


References

Fig. 6.32 - Comparison of the Solubility of Carbon Dioxide and Nitrogen in Water.

Fig. 6.33 - 70 Quality: CO 2 Foam Vs. Binary Foam.



Fig. 6.34 - Aluminum Orthophosphate Ester Hydrocarbon Gel.

Fig. 6.35 - Pressure Effect on a Partially Gelled Diesel at Ambient Temperature and at 180 F [databy J. R. Cameron, courtesy Amoco Production Co. Research, Tulsa, OK (1986)].

Association Complex ...

Reversible to shear but sensitive to polar contaminates

°


References

Hydrocarbon

f-secn'/ft 2

K'

l Final

Crude Oil 7 0.0223

Crude Oil 7 0.0488

Hydrocarbon

f-secn'/ft 2

K'

l Final

Crude Oil 0 0.433

Crude Oil 0 0.0751

Frac Oil 200 2 0.150

Frac oil 200 9 0.149

MO-55A and FMO-56 and FDK-34 is sodium“initial” values and final value

Table 6.8 - MY-T-OIL II & MY-T-OIL IV Comparative Evaluation

MY-T-OIL IV (Continuous-Mix System)

Temp CHours at

Temp

(cp)Viscosity@ 170 1/s n'

(1b

(L/m3)FDP-5445A

(L/m3)FDP-5445B

(Kg/m 3)K-34 Initial Final Initial Final Initia

6 6 0.4 70 24 263 51 0.093 0.407 0.57

6 6 0.35 70 19.6 329 76 0.098 0.33 0.70

MY-T-OIL II (Batch System)

Temp CHours at

Temp

(cp)Viscosity@ 170 1/s n'

(1b

(L/M3)MO-55A

L/m(L/M 3)MO-56

(Kg/m 3)K-34 Initial Final Initial Final Initia

13 4 3.5 71 2.5 302 215 0.13 0.11 0.55

12 3.6 3.4 70 2.2 91 60 0.19 0.20 0.12

7 2.4 2.0 71 2.2 102 81 0.25 0.12 0.10

8 2.7 3.0 70 2.2 155 81 0.19 0.13 0.28

DP-5445A are gellantsP-5445B are activators bicarbonate breakerare at 0 time at temperatures are at total hours at temperature

°

°


Table 6.9 - Power-Law Rheology as a Function of Temperature, Western Maxi-0-74 Gelled Oil
System.

Maxi-0-74 GelTemperature

F Time n' K'Viscosity170 sec-1

8 gal1

8 gal1

8 gal1

8 gal1

8 gal1

8 gal1

8 gal1

80120140160180200220

InitialInitialInitialInitialInitialInitialInitial

.28

.26

.25

.25

.26

.28

.36

.15

.15

.15

.14

.13

.094

.048

17816115314213911286

8 gal2

8 gal2

8 gal2

8 gal2

8 gal2

8 ga2

8 gal2

80120140160180200220

InitialInitialInitialInitialInitialInitialInitial

.28

.23

.20

.19

.22

.27

.30

.12

.13

.14

.14

.12

.08

.035

1421191101051059046

1. Gal/1000 of gellant in kerosene.2. Gal/1000 of gellant in No. 2 Diesel.

Table 6.10 - Typical Chemical Components of Organo-Metallic Crosslinked Frac Fluids.

POLYMER: 30-60 #/1000 gal, 0.4 m.s. HPG

BUFFERING AGENTS:Example:

Weak acid and/or saltFumeric acid/sodium bicarbonate or sodium carbonateSulfamic acid/sodium bicarbonate or sodium carbonateAcetic acid or anhydride/sodium acetatepH: 5-7 or 8-10 stability requirements

CROSSLINKER: Titanium chelates of acetyl acetonate (TiAA),triethanol amine (TiTE), lactic acid (TiLA),or TiTE/TiAA. TiTE + water (slower react.)

STABILIZER: Alcohol (5-10% MeOH, sod. thiosulfate (10-20 #/1000 gal)

BREAKER: Enzymatic, cellulose (<140 F), oxidative, persulfates(>140 F)

ADDITIVES: Surfactants: non-emuls., surface tension reduct.; Clay Control:KCl (1-2%), cationic polymers, polyamines.

°

°°


References

Co Western

Water and Fric er Frac

Gelled water ed Water

Gelled water wadditive

xi-Pad)stpad A)lable

Low residue ge6) J-20

No residue gell Gel) J-6

Crosslinked HP NG IING II DHTLLO II

URN II LTURN II

Crosslinked gu NG ING I DHTLLO I

Thin prepad witto control upwa

ilable

Oil prepad withdiverting agentwater encroach

Crosslinked HPhydrocarbon fo

LLO II HURN II H

Crosslinked HPstabilizers

rn Gel

Crosslinked CM LLO IV LPH

Table 6.11 - Competitive Cross Reference of Similar Additives.

mposition BJ ServicesDowell

Schlumberger NOWSCO LTD Halliburton Smith

Water Based Gel Systems

tion reducer Aqua Frac River Frac Friction Reducer Available Slick Water Wat

Gelled WaterAqua Frac

Water FracWF-100 (guar)WF-200 (HPG)

Gelled Water Water Frac Gelled WaterWGA-6WGA-7

Gell

ith a fluid loss Gelled water plusFLA

Redifrac Gelled water &Fluid Loss

Water Frac plusFLALogel 100 & FLA

Gelled WaterwithFL Additive

(Ma(Weavai

lled water (HPG) GW-8GW-32

WF200 LSR-1NB WG-11, 12,HYG-5,WG-20

WGA-2 WGA-8 J-12(J-1

ed water (HEC) GW-21 YFHC HEC Hygel 100,300 &500, LOGEL 100WG-17, WG-21

WGA-3 Plus(J-5

Crosslinked Gel Systems

G Terra Frac T(Titanate)

YF-400(Titanate)Delayed AvailableYF-200YF-200DYF-600-HT(Zirconium delayed)

Ultravis LPWVersagelVersagel LTVersagel HTHybor Gel

GWX-7GWX-9

VIKIVIKIAPOSATSAT

ar system additive Ultra FracTerra Frac

YF-100YF100D(Delayed)100 - BorateYF-300(Titanate)YF-500-HT(Zirconate Delayed)

Hy Vis MY-T-GELMY-T-GEL LTMY-T-GEL HTHybor GelKO GelThrifty Gel

GWX-7 LT,GWX-7 HTGWX-9

VIKIVIKIAPO

h buoyant diverting agentrd growth

Invertafrac Ava

a polymer coated sandto control downward andment

Divertafrac

G with 3-5%r fluid loss

Terra Frac-D Stratafrac II Service(Available with mostsystems)

Ultravis LPW+5% Diesel

Versagelplus Diesel

GDX-7 APOSAT

G with high temperature Terra FracRXL II

YF400YF600-HT

ThermoVis Versagel HT GWX-7HT Satu

HEC Krystal FracRXL

Krystal Frac XLKrystalFrac-D(5% Diesel)

HyClean Kleen Gel Available APO



Crosslinked CMture

100018 Gel

Crosslinked gu NG IING II DHTNG ING I DHT

CO2 compatibl URN II LT

Economical, losystem

LLO I

Controllable detem

URN IILLO II

Controllable detemperature sy

URN IILLO II

Gelled water - 100013 Gel

Crosslinked wa 100013 Gel

Oil without visc rac

Gelled Oil Friction

Crosslinked geperature

i-0-74 Gel

Crosslinked geatures

i-0-86 HT

Water external Exxon

er K-Frac

Continuous cro

Co Western

HEC for high tempera- Super KrystalFrac

Kleen Gel II WZ-

ar or HPG with Borate Ultra Frac YF-100 (guar)YF-200 (HPG)

HyVisBoragelHybor Gel

GWX-9Guar orHPG

VIKIVIKIVIKIVIKI

e fracturing fluid Krystal Frac(CMHEC)Super Terra Frac

YFLPH(HPG)

PurGel II, &IIIACIDGEL FracACIDGEL Frac IIVersage LTKleenGel,MY-T-GEL LTKlexenGel IIAlcogel IMY-T-Oil I, II, &IIILOGEL 100HYGEL 100 &300

GWX-4LTGWX-4HT

SAT

w residue cross-linked Terra Frac T(Low pH system)

YF-LPH Ultravis LPW Pur-Gel WGA-5GWX-5

APO

layed crosslink HPG sys- Terra Frac RXLII

YF-600-HT Ultravis H-T Versagel HT& CL-18Hybor Gel

GWX-7 SATAPO

layed crosslinked highstem

BJ-Titan RXLSpectraFrac G

YF600-HT (HPG)YF500-HT (Guar)

Thermo-Vis ThermagelPur-Gel III(CMHPG)

GWX-7HT SATAPO

Alcohol Water Systems

alcohol system Alcogel I & IIAlcogel IV

WZ-

ter-alcohol system Metho Frac(G-8)

AlcoholWaterfrac(J-160)

Ultravis LPW Alcogel II-X Available WZ-

Oil Systems

osifier Available Crude Frac Sandoil Available Oil F

Oil BasedUltra Frac

Petrogel Hycar 2000 Viso-O-FracV-O-Gel

Gelled Oil LowFrac

lled oil for medium tem- Allo Frac YF-GO III HLG-1HLG-5

My-T-Oil II PGO-1 Max

lled oil for higher temper- Allo Frac HT YF-GO IV My-T-Oil III PGO-1 MaxGel

emulsion developed by Polyemulsion Super SandFrac K-1

Polyemulsion SuperEmulsifrac

WEP-1 Sup

sslinked gelled oil YF-GO III My-T-Oil IV





References

Water and nitrogel

t-Foam, N2

Acid and nitrog t-Foam, N2

Hydrocarbon a o Foam

NOWFOAM fol ilable

Methanol and n ilable

Water and CO2 tFoam, CO2

Water and 50% ry Foam Sys-

Crosslinked ge ilable

Powdered guarhydration, desigcations.

J-4

Powdered guarhydrating, desigapplications. C

breaker)

Powered HydroDelayed hydratbatch mix applibreaker.

(J-18)

Powdered hydrfier. Rapid hydrtinuous mix appinternal breake

6) J-200)

Powdered hydrfier. Delayed HDesigned for usbatch mix appli

Chemically moin crosslinked fl

Powdered hydrdelayed hydratigel in high tem

Co Western

Foamed Systems

gen foam with or without Aquafoam FoamfracStabilizedFoam Soulution(SFS)

Foam Frac FoamfracAquaFoam

FoamFrac

Wes

en foam Etching foam Available Foamed Acid Available FAS-1 Wes

nd Nitrogen foam Available Available Foamed Hydro-carbonFrac

N10 Frac FoamedOil

Petr

lowed by a gelled fluid Combo Frac Ava

itrogen foam Foamed Alcohol AlcoFoam FoamedMethanol

Ava

foam Available Available Poly-CO2 C-O-TWO FracPur-Gel IIPur-Gel III

CDM-1GWX-4LTGWX-4HT

Wes

CO2/20% N2 Binatem

lled water foam Super foam Available GWX-4LTGWS-4HT

Ava

Water Base Polymers

gum polymer. Delayedned for batch mix appli- GW-27

J111, J424J877

G-308WB WG-19WG-22a

WG-23

WGA-6 J-2,

gum polymer. Rapidned for continuous mix

ontains internal breaker.

GW-5 J133

J457

WG-6 J-4(no

xypropylguar gum.ion polymer, designed forcations. No internal

GW-32 J347J362J456J876

LSR-1NB WG-11 WGA-2WGA-8

J-12J-20

oxyproplyguar viscosi-ating, designed for con-lications. Contains

r.

GW-8GW-30

(80% HPG)J348(Sea Water)

WG-12 (J-1(J-1

oxyethylcelluloseviscosi-ydration polymer.e as a secondary gel or

cation.

AG-21R J164 HECWG-17

WGA-3 J-6

dified HEC for useuid. No internal breaker.

WG-21

oxypropylguar foron used as a secondaryperature applications.

HYG-5






Powdered carbcosifier. Rapid both batch andtions.

)

Powdered carbcellulose viscoshydration. Can continuous app

Powdered xantfor viscosifyinghydrochloric acor mixed contin

A proprietary bfied low residuehydration mixtuapplications. N

Chemically moup to 80% meth

100313

Chemically mogelling 100% m

ilable

Chemically moCMHPG

499579

Liquid Viscosifi el

Liquid viscosifie el Lt temp)

HPG with KCl

Guar with KCl

HPG without K

Guar in diesel s

Guar and Ammslurry

HPG in diesel s L

Co Western

oxymethylcellulose vis-hydration, designed for continuous mix applica-

G25 (J-8

oxymethylhydroxy-ethyl-ifier. Designed for rapidbe used both batch andlications.

GW-28GW-29GW-34GW-36GW-44

J-365 WG-15 WGA-4 J-13

hate polymer Designed 15% or lower strengthids. Can be batch mixeduously.

AG-26 J360J312

AGA-1 J-15

lend of chemically modi-guar polymers. Delayed

re designed for batch mixo internal breakers.

J424 WG-19 WGA-6 J-4

dified natural polymer foranol.

GW-20GW-25GW-35

J-271 G-317 MGA-1 WZ-

dified natural polymer forethanol

GW-55 LSR-5 WG-20 MGA-1 Ava

dified natural polymer GW-44GW-36

G-313 WG-18 WGA-5 WZ-

er for acid AG-11 J429-J425 SGA-HT AGS-1AGA-1,AGA-2AGA-4,AGA-5

Acig

r for acid up to 15% AG-12 J425(15-28%)M33

DSGALiquid

SGA AGS-1AGA-1AGA-2AGA-4AGA-5

Acig(low

Continuous Mix Gel Concentrates

in aqueous slurry LGC-I

in aqueous slurry LGC-II

Cl in aqueous slurry LGC-III

lurry LFC-1 LSG LGC-IV CMG-1 J-4L

onium chloride in diesel LGC-IV M J-4L

lurry LFC-2LFC-2ALFC-2B

LSG LGC-V CMG-2 J-20





References

CMHPG in dies L

CMHEC in dies ilable

Liquid anionic preducer for wat

2028d Water)

Liquid cationic reducer for acid

Powdered aniofor acid, brines

-16)-2, Water)

Powdered catioacid, brines an

-6)

Liquid friction r 5AW

Selectively gradused in water, o

Combination ofand degradablepolymers. Non-tive used in wa

Seal M

100 mesh benzacid or foam fra

ilable

100 mesh sandacid

mesh

100 mesh oil soand acid

Seal

100 mesh salt mesh salt

Fluid loss addit aseal 2

Proprietary liqu aseal L

Fluid loss addit(Adomite Aqua

ilable

Fluid loss addit(Adomite Mark

mitek II

Fluid loss additdegradable fluibase fluid used

aseal WS

Co Western

el slurry LFC-3 LGC-VI CMG-3 J-22

el slurry LGC-VII Ava

Friction Reducers

olyacrylamide frictioner

FRA-12FRW-11

J313(Water Brine)

FRC-26LC WFR-2 FR-FR-(Har

polyacrylamide frictions, brines & fresh water.

FRA-10 J321 F-657 FR-28LC AGA-2,AGA-4AGA-5,AFR-1

nic friction reducer and fresh water.

J166(Water, Brine)

FR-20 (FR(FR

nic friction reducer ford fresh water.

J120(Acid)

FR-30 (FR

educer for hydro-carbonsFRO-18RequiresActivator

J257 F-100 FR-5FR-7RequiresActivator

OFR-1 FR-

Fluid Loss

ed fine mesh silica flouril and acid

FLC-8 J84J418

Silica Flour WAC-9 WFL-2 F-11

graded oil soluble resin low molecular weightdamaging fluid loss addi-ter and acid

FLC-1 J238 WAC-11D AFL-2 Frac

oic acid used in water,cturing treatments.

FLC-1 J227(Particulate)

Available Available Flakes-DA-3 Ava

used in water, oil and 100 meshsand

FLA100S100

100 meshsand

100 meshsand

100 meshsand

100sand

luble resin used water FLC-2 FLA10005 FL-30 OSR-100 AFL-3 Frac

100 meshsand

Available DA-4AFL-2

100

ive for water and oil WAC-10 AFL-4 Aqu

id fluid loss solution FLC-15FLC-17

J-451 WAC-12LFLD-1

WFL-4 Aqu

ive used in water and oil)

AdomiteAqua

J110 AdomiteAqua

AdomiteAqua

WFL-1 Ava

ive used in oil base fluids II)

AdomiteMark II

J126 AdomiteMark II

AdomiteMark II

OFL-1 AdoMar

ive. Powdered fullyd loss additive for water 120 - 350 F

B1 WLC-4 WFL-3 Aqu




°



Fluid Loss Add

Liquid fluid losswells with wate80-300 F (die

ilable

Solid fluid loss for use in water150-200 F.

Enzyme breaketives and cellul

, B-11L

Oxidizer breaketives and cellul

High temperatuguar, guar deri

Acid breaker foand cellulose d

Low temperatuborate systems

2

Low temperatu , B-23

Breaker for pho

Gel breaker anTreatment followfluids. Used fro

Oil breaker - Lo

Oil breaker - H

Oil breaker 4)

Breaker for pho iumrbonate,

Oil soluble resi -530

Graded rock sa tblock,

Co Western

°

°

itives - Acid AFL-1AFL-2AFL-3AFL-4WFR-2

additives for use in oilr based fluids fromsel or other hydrocarbon)

Available Available Available Available Available Ava

additive and gel breaker based fluids at

OPTIFLO C

Breakers

r for guar, guar deriva-ose derivatives

GBW-10 J134 Breaker F GWV-3GBW-30

WEB-2 B-11

r for guar, guar deriva-ose derivatives

GBW-5 J218 Breaker S SP Breaker WCB-1 B-5

re oxidizer breaker forvatives and cellulose

GBW-5 Breaker T HT Breaker B-9

r guar, guar derivativeserivatives

GBA-1 Breaker H MYF-5 P-4

re breaker activator for GBW-10 J318-J466 WCB-LT B-1

re oil breaker GBO-1 Breaker MOHL Breaker

OXB-3 B-20

sphate ester oil gels GBO-3 J318, YF 60 IIJ-295 YF60 IIIIIJ603 YF60 III

Breaker MO IIK34

OXB-3 B-15B-16B-25

d filter cake degrader.s water based fracturing

m 80-270 F.

Optikleen

w Temperature Y3, M3 Breaker VLT OXB-3 B-20

igh Temperature Breaker VH OXB-3 B-23

J318(YF-GO II)

Breaker3700

OXB-3 (B-1

sphate ester gels GBO-6 J295(YF-GO II, IVJ-603, J860, GO III

K-34 OXB-3 SodBicaB-25

Diverting Agents

n in aqueous solution FLC-11 J237 L-12 Matriseal-0 AFL-1 ASP

lt Rock SaltSalt-Trimix

J66 Rock Salt TBA-110 DA-4 WesS-6




°


References

Flake Benzoic tblock 3X

Nonaqueous so ilable

Polymer coatedwater contact

Oil soluble grad

Diverting agent

Water soluble d

Inorganic diverbuoyant

ospheres

Guar or hydrox Block WX

Hydroxyethylcecrosslinked

ilable

Crosslinked hy -1, Highion Gel

Crosslinked gusystem

ilable

Oil external emHCl-organic mi

Emulsifier for p laid 266

Emulsifier for pemulsion or CO

5), E-16

Co Western

Acid Benzoic AcidSuper FlakeRegular

J227A Benzoic Acid TLC-80 DA-3 Wes& 4

lution Matriseal - OWG Ava

sand which swells upon S41(Divertifrac)

ed napthalene Moth Balls J116 TLC-15 DA-2 S-3

used in acid FLC-18 (Concentrate)(Solution)

Matriseal 0MatrisealOSR-100TBA-350TLC-80TBA-100Matriseal OWGTLC-155

iverting agent FLC-18 J363, J175(Acid & Water),J187 (Fracturing)

TBA-110TLC-80

ting material which is J423(invertafrac)

Cen

Polymer Plugs

ypropylguar system ProtectozoneWL 300, 500

Temblok 80,90, 100

Gel

llulose system linear or ProtectozoneWC 500, 750

P5-Plug Temblok 75120

Ava

droxypropylguar system ProtectozoneWH 500, 700(not crosslinked)

Temblok 4050, 60

TDAFrict

ar or hydroxy-propylguar Temblok 4050, 60

Ava

Emulsifiers

ulsifier for HCl andxtures

E U74 (D.A.D. acid),U60 (Super SandFrac), U80

DL-22 AF-61 AAE-1 E-9

olyemulsion E-2, E-5 U78A (not for diesel) WS-50 SEM-5SEM-6SEM-7

PEM-1 Wel

olyemulsion and CO2

2 foams.FAW-16 U78E EF-10 SEM-5, ACO-1

SEM-7HC-2AQF-1AQF-2AQF-4

PEM-1FAA-2

(E-1

Clay Stabilizers






Cationic polym master 4

Cationic clay st lok SM*1 (Multi-useuct)2

*All Companies*SM Service M

Nonionic fluoroacid systems

Back 10

Cationic fluorosacid systems

1)

Nonionic nonem a Flow 40

Nonionic nonem a Flow

Anionic nonem ow,sol D

laid 215

Nonionic nonem 40, Aqua

Anionic nonem

Anionic nonemand dispersible

owsol D,1,xit 7652

Nonionic nonemacid

a Flow7 40

Co Western

er for stabilizing clays Claytrol5 L53 (W-Winterized)L42

CSA-6 Cla Sta IICla Sta 0Cla Sta FSCla Sta XP

CCC-3 Clay

abilizer Claytrol 3Claytrol 4Claylok SM

M38W ClayFix II CCC-4Claylok Sm

ClayWK-prodLT-2

’ have KClark of Chevron Research Company

Surfactants

surfactant for water and Inflow50 F-75N WS-70 SuperFlo II FRS-2FRS-3USS-N

Flo FS-2

urfactant for water and Inflo 45Inflo 100

TEA-380 EnWaR-288 FRS-1 (FS-

Nonemulsifiers

ulsifier W53 EPS-4, EPS-5EPS-9, SAA-2,SAA-8

AquNine

ulsifier for oil 3N, 1N SAA-5 Aqu

ulsifier for oil HD10-60HD10-70

SAA-3 F-FlParaWel

ulsifier F38 EPS-4, EPS5,EPS-9, SAA-2SAA-8

NineFlow

ulsifier J-10 SAA-3, SAA-7 LT-5

ulsifier for oil in water

W31(Freflow D)K224

Hyflo IVAnionic

Nonionic mixtureOil soluble

SAA-3 F-FlParaLT-3Core

ulsifier for water and NE-4NE-15NE-18S100S200S400S600

F40EZEPlo, W39

W5-6 One LOSURF-251259, 300, 357Pen-5, LOSURF0

EPS-4, EPS-5EPS-9SAA-2, SAA-8

AquLT-1Nine





References

Anionic nonem , AS-25, LT-31,ow,sol D

Cationic nonem LT-227, WK-1ow,sol D

Nonionic fluoroacid

(FS-F)

Nonionic surfacfor water and a

1

Anionic nonemacid

, LT-25

Nonionic fluoroacid

F) FS-2

Fines suspendAlso functions

1

Cationic fines s -3), MR-1

Anti-sludge age 2, LT-31

Strong base stic Soda,G-6)

Weak organic a er 1

Weak organic a er 2

Synergistic addtion times at ele

-25-26

Strong base iumonate,

er 4

Co Western

ulsifier NE-10NE-31NE-32S-500

F78, M38W22, W27,W39, M38W

DL-22 TRI-SFracflo IIMorFlo II

SAA-3SAA-7

LT-5LT-2F-FlPara

ulsifier for water and acid NE-1NE-7NE-2NE-6NE-9NE-11NE-12NE-13NE-20NE-21NE-22

F75N(nonionic)marketed asEzeflo F75

AI-170 Cationic NCompounds

SAA-4SAA-1EPS-1EPS-3EPS-6

I-5, LT-1F-FlPara

surfactant for water and Inflo50 Superflo USS-N FS-2

tant and nonemulsifiercid

D-4 F40 Pen-5Also foamingagent for acid

EPS-4, EPS-5EPS-9, SAA-8

LT-2

ulsifier for water and DL-26 Fracflow,3N

SAA-7 LT-5

surfactant for water and USS-N (FS-

Fines Suspender

ing agent for acid.as nonemulsifier

SS-100 HC-2 SSS-2 LT-2

uspendor F78 LPA-1 (CS

Anti-Sludge Agent

nt for acid W35 (W50)

DL-22DL-26

AS-5, AS-6AS-7, AS-8

SPS-1 AS-

pH Control

D-2 J465, M2, U28U28, J-221(2% caustic)

Caustic Soda Caustic Soda Caustic Soda Cau(G-5

cid CW-1 BW-6 Buff

cid Fumaric Acid HYG-3 BW-2 Buff

itive for extending inhibi-vated temperature

D-2 L6L36

Formic Acid MYF-2L Formic Acid WTIWTI

M3 Nowplix 6P K-35 SodiumCarbonate

SodCarbBuff






Buffers (proprie er 1er 2er 4

Strong base oniumroxide

Powdered wea iumrbonate

Sulfamic Acid

Proprietary cro

Proprietary cro -Saturn-Saturn

Proprietary cro 100470

Proprietary cro , T.I.C.,2

Proprietary cro , Powder),

Proprietary cro 4, CL-14W1

Proprietary cro ilable

Foaming Age mex, LT-30c Foam 1

Foaming Agen foam BF-1

Foaming Agen 0

Foaming agent mex

Foaming age 2 (FS-F)

Foamer for hy ro Foam 1

Foaming agesates

ro Foam 1

Co Western

tary) BF-1, BF-5BF-2BF-3BF-4

M47 BA-10, BA-20BA-30BA-40

BW-1, BW-5BW-7, BW-10

BuffBuffBuff

AmmoniumHydroxide 30%,50%

M11 AmmoniumHydroxide

AmmoniumHydroxide

AmmHyd

k base M-223 K-34 SodiumBicarbonate

SodBica

Sulfamic U43 BA-2 Sulfamic P-4

Crosslinkers

sslinking control agent XLW-3 CLM

sslinking control agent XLAXLD

sslinking agent (Sb) AKXL MYF-10 WZ-

sslinking agent (Ti) XLW-39 (J352) ATX-25 CL-11CL-18

CX-1, CS-91,CS-6

CL-9CL-1

sslinking agent (Borate) XLW-1, XLW-2 L10 (Powder) BXL-1W CL-22 CS-13(liquid)

(2-CCL-2

sslinking agent Zr XLW-52 J366, J367(Activator)J444 (Temp. Acti-vated)

2R-XL CL-24CL-15CL-21CL-23

CX-7, CX-14CX11A, CS-15CX-16

CL-1CL-1

sslinking agent AL XLW-6 CAX CL-19 CX-5 Ava

Foamers

nt FAW-12 F78 HC-2, AQF-1AQF-2, AQF-4

FAA-1FAA-2SNF-1SNF-4

FoaFra

t Adofoam F52, 1 5F-1 Howco Suds FAA-1, FAA-2SNF-4, SNF-7

Ado

t Pen-5 FAA-1, FAA-2SNF-4, SNF-1

LT-3

for water and brine FAW-16 F52.1(Water, Brine, Acid)

TRI-S FAA-1FAA-2

Foa

nt for water and acids FAW-9 F78 (Foamer andFines Suspender)

SF-2 AQF-1,SGA-1,Pen-5

FAA-2FS-

drocarbons FAO-25 OFA-2 SNF-1 Pet

nt for oil and conden- FAO-25 SF-3 OFA-2 SNF-1 Pet





References

Foaming ageanol

Foam 1

Foaming ageand methano

ilable

Scale Inhibito

Scale Inhibito

Scale Inhibito a Sol II

Scale Inhibito

Scale Inhibito , P-3

Co Western

nt for water and meth- FAW-20 SF-8 ACO-1 SNF-4 Frac

nt for 100% methanoll water mixtures

FAW-20 SF-8 ACO-1 SNF-4 Ava

Scale Inhibitors

r ScaleTrol 4 L47,L49

P-300 PhosphonateScale Inhib.

GSI-1 P-9

r ScaleTrol 6 L50 SST-245 PhosphonateScale Inhib.

GSI-1 P-8

r ScaleTrol 8 L45 PhosphonateLP-60Scale Inhib.

GSI-1 Ultr

r X-4 LP-55 GSI-1, GSI-2GSI-3

P-7

r X-6 L35 Similar toLP-55

GSI-2, GSI-1GSI-3

P-2






Liquid stabilizture

hanol

Powdered staatures

Master

Stabilizer

Defoamer for 111111L

Defoamer for 1

Liquid viscosi , G-6

Powdered vistional oil gels

7 (G-30)

Liquid viscosiester gels

ioilioil HT

Liquid activatgels

ioilivator

High Tempera ioil XHT

Bactericide c Cide 10,c Cide 2

Biocide c Cide 20

Bactericide cide

Biocide mall

Biocide c Cide 2,c Cide 20ocide

a. Especially for

Co Western

Gel Stabilizer

er for high tempera- Methanol K46 Methanol Methanol,LiquidGel-Sta

Methanol Met

bilizer for high temper- GS-1GS-2GS-3

J353 GS-1 Gel-Sta HTS-2HTS-2

Gel

J59

Defoamer

aqueous fluids D-37LAntiFoamer-1

D47,(Cold Water)

AFA-Z AGD-2 DF-AF-AF-

oil base fluids J291 RFP-1 DF-

Oil Gelling Additives

fier for soap type gels G-20 U27, U28& U34

VI-10 G-5

cosifier for conven- HYCAR-2000 MO-33,VO-15

G-1

fier for phosphate GO-23,24 J452 HLG-1HLG-5

MO-55,MO-65

OGA-1OGA-3OGA-4

MaxMax

or for phosphate ester GO-53 J453J602J601L

HLG-2 MO-56,MO-66, andMO-67

OGA-2 MaxAct

ture oil gelling agent MO-HT B Max

Biocides

X-Cide102 M123 (Solid)

X-cide102W

BCS-2BCS-3BCS-4

FraFra

X-Cide 207 BE-3 BCS-1 Fra

Adocide M155 Adocide Adocide Ado

Adomall M76 Adomall Adomall Ado

X-cide207

M-275 BE-4 FraFraDry

use in oil base slurry.





References

Fig. 6.36 - Simulator Results of Fluid-Element Time at Temperature vs. Volume Pumped.

Fig. 6.37 - Viscosity vs. Time-at-Temperature for Various Polymer Concentrations.

Fluid Time Range (Min.)

X30 0 - 12 (Use for Temp < Reserv.)

X30+

X40+

X50+

X60+

x40


Table 6.12 - Selecting Polymer Loading to Achieve Desired Viscosity.
Super Gel System Time, Hours K' n' Viscosity at 170 sec-1

X200

.25.00108.00017

.951.0

408

X30

0.25

5

.00812

.00355

.00376

.85

.951.0

1803818

X30SGS

0.25.5

.751.01.5

.02262

.00700

.00339

.00188

.00111

.00049

.75

.80

.85

.90

.93

.97

30012074543720

X40SGS

0.5

1.01.52.0

.05294

.01146

.00320

.00111

.00051

.65

.75

.85

.93

.97

420152713721

X50SGS

0.51

1.52

2.53

3.5

.06932

.02194

.00905

.00496

.00311

.00240

.00178

.00122

.65

.7

.75

.8

.85

.87

.90

.95

5502251208569595145

X60SGS

0.51

1.52

2.53

3.5

.08823

.03130

.01486

.00875

.00564

.00428

.00342

.00286

.65

.7

.75

.8

.85

.87

.89

.90

7003211971501251059382


References

Fig. 6.38 - Class Example of Selecting Optimum Fluid for Time at Temperature.



Fig. 6.39 - Dowell YF-400 Fluids (Sand Laden).

Fig. 6.40 - Halliburton Versagel Fluids (Sand Laden).


References

Fig. 6.41 - Western Company APOLLO II/APOLLO II H Fluids.

Fig. 6.42 - Guidelines for Pad Fluids.



Fig. 6.43 - Scheduling Example.


References

Stage M-Gal PPG Fluid Additives

1

2

3

4

5

6

7

8

9

10




Chapter

tech-ies toeveral

In addi-hnicalctorstration,ll per-ll be

Proppants and Fracture Conductivity7
7.1 Overview
The selection of a proppant for use in hydraulic fracturing is an economic decision requiringnical input. The purpose of this chapter is to provide the engineer with the technical capabilitmake good economic decisions with respect to fracture design. This chapter is broken into ssections.

First, the sources of the available fracture sands and commercial proppants are discussed.tion, the size and quality of these materials is reviewed to provide the engineer with the tecinformation required to make proppant decisions for fracture design. Next, the critical fawhich affect fracture conductivity are reviewed. Factors such as closure stress, size, concenstrength, shape, and gel residue effects can impact fracture conductivity and ultimately, weformance. Finally, the economic aspects of proppants and/or fracture conductivity wireviewed.



detri-easonerally

frac-caseservoir

would

uctivebelowpac-idealposed

radialrac-om-ers of

7.2 Introduction

Historically, fracture stimulations have been performed for two reasons; to overcome themental effects of wellbore damage and/or to stimulate the well’s performance. The former rhas been typically applied to wells in moderate to high permeability reservoirs and genresulted in the creation of short fractures. The latter generally resulted in the creation of longtures in wells in low permeability reservoirs. The success or failure of fracturing in eitherdepended on whether or not the created fracture had adequate flow capacity so that the refluids flowed to the fracture and then to the wellbore.1,2 If the flow capacity of the fracture waslarge by comparison to the reservoir flow capacity, tremendous performance improvementsbe realized.

The purpose of the proppant is to keep the walls of the fracture propped apart so that a condpath to the wellbore is retained after pumping has stopped and fluid pressure has droppedthat required to hold the fracture open. Ideally, the proppant will provide large enough flow caity to make negligible pressure losses in the fracture during fluid production. In practice, thismight not be achieved because the selection of a proppant involves many compromises imby economic and practical considerations.

The propped fracture must have a conductivity at least high enough to eliminate most of theflow path that exists in an unfractured well and to allow linear flow from the reservoir into the fture. This requires relatively unimpeded linear flow within the fracture to the wellbore. To accplish this, the proppant must enable the propped fracture to have a permeability several ordmagnitude larger than that of the reservoir rock.


Effect of Fracture Conductivity on Well Productivity

ine theadye anal-alue ofthere-

ues ofuring

drain-e ver-arly

nd oneasso-ft andngth,xam-00 ftf thein ativitysig-cturetivity

7.3 Effect of Fracture Conductivity on Well Productivity

Historically, steady state performance predictions have been used by the industry to determeffect of fracture conductivity on well productivity. However, there are limitations to the stestate analysis of fracturing which must be considered. One such limitation is that steady statyses exclude the economic benefits of unsteady state flow, rate acceleration, and the time vmoney. In addition, the effective wellbore radius concept is used in the steady state analysis,fore, the analysis is subject to the limitations of this concept. However, steady state techniqPrats provide a useful method of comparing the impact of fracture conductivity on the fractprocess.

Figure 7.1 is a plot of steady state folds of increase versus fracture half length for a 40 acreage area. This plot shows the productivity improvement associated with a 1000 md-ft fractursus an unstimulated well in a reservoir with permeabilities of 1 and 10 md. This figure cleindicates that there is no economic benefit associated with increasing fracture length beyohundred feet in a 10 md reservoir while in a 1 md reservoir there is some economic benefitciated with an increased fracture length. Figures 7.2 and 7.3 show similar plots for 2000 md-3000 md-ft fractures, respectively. Analysis of these figures indicates that, for any fracture leincreases in fracture conductivity result in increased productivity. In a 10 md reservoir, for eple, a productivity improvement of 2.2 could be realized by creating a fracture of half length 1and conductivity of 1000 md-ft. A 2.6-fold increase could be realized by creating a fracture osame length with a 2000 md-ft conductivity. Creation of a 3000 md-ft fracture would result2.7 fold production increase over an unstimulated well. Thus, increasing fracture conducfrom 1000 md-ft to 3000 md-ft would result in an additional 23% production increase withoutnificantly increasing the treatment cost. It is this concept that underlies the importance of fraconductivity to fracturing. Performance improvements can be realized by improving conducat little or not cost.

Fig. 7.1

Ste

ady

Sta

te F

olds

of I

ncre

ase



Fig. 7.2

Ste

ady

Sta

te F

olds

of I

ncre

ase

Fig. 7.3

Ste

ady

Sta

te F

olds

of I

ncre

ase


Commercial Proppants

s wastoday’sore thor-

a, Illi-

penedto bensoli-to sep-

foundul for

80sre sup-inne-

duneinally,oducele 7.1per-

d highhan the

pants

sand-ng themalln the

quartzrated,

7.4 Commercial Proppants

Historical Perspective

One of the first proppants used in the early days of hydraulic fracturing during the late 1940sand dredged from the Arkansas River. Initially, the sand was not cleaned and screened asstandards require, but as the need became evident, steps were taken to process the sand moughly. During the mid-1950s, sand from the Saint Peter sandstone formation near Ottawnois, entered the market.

As the need for a more economical and readily available fracturing sand grew, mines were onear Brady, Texas, in 1958, and production from the Hickory sandstone formation beganmarketed. This sand, as well as most other high-quality sand used today, is mined from codated sandstone formations. The mining process includes crushing, screening, and washingarate the sandstone matrix into its individual sand grains. A wide range of particle sizes isin the deposits. Typically, only 20 to 30% of such deposits is found to be in a size range usefhydraulic fracturing applications.

The explosive growth of the hydraulic fracturing industry from the mid-1970s to the early 19created shortages of fracturing sand. Supplies from the Saint Peter sandstone of Illinois weplemented by high-quality material from the Jordan, Ironton, and Galesville sandstones of Msota and Wisconsin. Similarly, sand from the Bidahochi formation in Arizona and aeoliansand of Colorado augmented proppant production from the Hickory sandstone in Texas. Fnew sand-processing plants were constructed in Minnesota and Wisconsin specifically to prfracturing sand and to replace plants designed to supply sand for other applications. Tabhighlights general information on available fracturing proppants. Figure 7.4 shows a plot ofmeability versus stress for various 20/40 mesh proppants. As shown, the intermediate anstrength proppants generally have greater retained permeabilities at higher stress levels tsands.

The subsequent sections will describe the physical properties of commercially available propwith the importance of these properties described in more detail in Section 7.5.

Commercial Fracturing Sand

Brady-Type Sand

This rounded quartz sand, also known as brown or Texas sand, is mined from the Hickorystone in central Texas near the town of Brady. The Hickory sandstone was deposited duriUpper Cambrian Age some 500 million years ago. The color of this sand results from samounts of iron oxide contamination in the crystal structure. Color variation has no bearing ostrength of this sand or on any other sand discussed here.

As mined, the sand is polycrystalline; i. e., each whole grain is composed of more than onecrystal bonded together, leaving cleavage planes in the whole grain. In terms of fines gene



Fig. 7.4 - Plot of all Proppants and Stress.



sibler. Pro-phys-

le 7.1.

Ari-sandactur-esh

. Thiss, 6/12sizes,he API

the API crush resistance test typically yields from <50 to as much as 85% of the API permisfines. The deposit yields acceptable fracturing sand in the 20/40 mesh size range and largeduction in sizes smaller than 20/40 mesh is not sized to meet API recommendations. Typicalical properties, fracture permeability, and pack-width data for this sand are presented in Tab

The Bidahochi formation sand is mined from shallow, lightly consolidated lenses in easternzona. It was deposited during the Pliocene or Tertiary Age some 6 million years ago. Thiscontains grains of chert, which is stronger than quartz, along with rose and smoky quartz. Fring sand from this formation is available in limited quantities in 12/20, 20/40, and 40/70 monly.

The aeolian dune sand is mined in central Colorado from shallow, lightly consolidated lensessand was deposited during the Holocene Age less that 1 million years ago. The large sizethrough 12/20 mesh, are as high in quality as those from the Hickory formation, but the small16/30 through 70/140 mesh, contain so much feldspar that they produce excessive fines in tcrush resistance test.

Table 7.1 Typical Physical Properties of Brady-Type Fracturing Sand*

API Mesh Size

API PropertyRecommended

Limits 6/12** 8/16 12/20 16/30 20/40

Particle diameter range, µm Standard 3350 to1700

2360 to1180

1700 to850

1180 to600

850 to425

Sieve analysis, wt% retained

Top sieveBetween primary sievesSecond and sixth sievesPan

0.1 maximum90.0 minimum

1.0 maximum

0.095.74.20.1

0.093.16.60.3

0.091.08.50.5

0.098.51.00.5

0.191.68.00.4

Total 100.0 100.0 100.0 100.0 100.0

Krumbein shape factor

RoundnessSphericity

0.6 minimum0.6 minimum

0.70.7

0.70.7

0.70.8

0.70.8

0.60.7

12/3 HCI/HF solubility,

30 minutes at 150° F, wt% 3.0 maximum 0.4 1.0 1.0 0.8 0.8

Silt and fine particle, FTU†

Crush resistance, % finesgenerated at closure stress, psi

Particle density, lbm/galBulk density, lbm/ft3

Clustering, wt%

250 maximumVariable with size

22.11 maximum105.0 maximum

1.0 maximum

2017.9200022.195.5<1.0

9513.4200022.198.0<1.0

12015.5300022.199.9<1.0

458.3

300022.1

101.10.0

11511.4400022.1

100.50.0

* All tests performed according to Reference 11 or 12. Sources include Saint Peter, Jordan, Galesville, and Ironton sandstones. Values shown areaverages of multiple production samples over a 4-year period.

** Available in limited quantities on special order only.† FTU = formazine turbidity units.



gener-fines

grainspact

sed andck-

districtblepale

ring thely in

Ottawa-Type Sand

This well-rounded, very pure quartz sand exceeds API recommendations. In terms of finesated, the API crush resistance test typically yields less than half of the maximum acceptableon this sand. The sand also is monocrystalline. Crushed particles are primarily large chippedrather than individual quartz crystals. Color variation is widespread in this sand, but has no imon its performance characteristics as a proppant. For the most part, the sand is well procesof high quality for fracturing applications. Typical physical properties, permeability, and pawidth data of this sand are presented in Table 7.2.

The Saint Peter sandstone, commonly known as Ottawa sand, was deposited in the Ottawaof Illinois during the Middle Ordovician Age some 460 million years ago. This sand is availain 20/40 mesh and smaller sizes only. Color variation runs from white through gray-white toyellow.

The Jordan sandstone was deposited in south central Minnesota and western Wisconsin duUpper Cambrian Age some 500 million years ago. Jordan fracturing sand is available on

Table 7.2 Typical Physical Properties of Ottawa-Type Fracturing Sand*

API Mesh Size


Limits 12/20** 16/30 20/40 30/50 40/70 70/140


1180 to600

850 to425

600 to300

425 to212

212 to160




1.0 maximum

0.093.26.60.2

0.097.92.10.0

0.091.58.00.5

0.093.1

6.50.4

0.191.8

7.60.6

0.190.09.10.8

Total 100.0 100.0 100.0 100.0 100.0 100.0


RoundnessSphericity


0.70.7

0.70.7

0.70.8

0.70.8

0.70.7

0.60.7


30 minutes at 150° F, wt% 3.0 maximum 1.5 1.0 1.0 0.9 1.2 2.5

Silt and fine particle, FTUCrush resistance, % fines

generated at closure stress, psiParticle density, lbm/galBulk density, lbm/ft3

Clustering, wt%

250 maximumVariable with size

22.11 maximum105.0 maximum1.0 maximum

685.4

300022.195.50.0

1101.6

300022.198.60.0

804.0

400022.1

102.70.0

603.3

400022.1

103.00.0

403.4

500022.1

102.70.0

1302.5

500022.1

103.00.0

* All tests performed according to Reference 11 or 12. Sources include Saint Peter, Jordan, Galesville, and Ironton sandstones. Values shown areaverages of multiple production samples over a 4-year period.

** Available in limited quantities on special order only.



w to

esternnd ismaller

vels,istics.ressllets,rmablesingleppants

prop-fail cat-provedintro-corun-nder

oday.

Underst such

a lessum.

s lower.

ted byues asmina

a kiln

12/20 mesh and smaller sizes. The color varies from white through gray-white to pale yellobrown.

The Galesville and Ironton sandstones were deposited in south central Minnesota and wWisconsin during the Upper Cambrian Age some 500 million years ago. Ironton fracturing saavailable in 12/20 mesh and smaller; the Galesville sand is available in 20/40 mesh and ssizes only. Its color varies from white to light tan.

Efforts to Improve on Fracturing Sand

Because of the well-recognized limitations of fracturing sand, especially at high stress leefforts have been made to find a different proppant with improved performance characterMany of the deficiencies of sand relate to its brittle failure from point loading under high stlevels. Likewise, much effort has concentrated on materials as iron shot, aluminum pequenched-glass beads, walnut hulls, plastic beads, and a vast array of high-strength and defoparticles were manufactured in the 1960s and evaluated as potential proppants. With theexception of glass beads, none survived until the early 1970s because each of these profailed to achieve the desired results in actual field applications.

With the drilling of deeper wells, the shortcomings of glass beads and quartzitic materials aspants became apparent. Such materials are weakened by hot formation brines and tend toastrophically under high closure stress. These factors accelerated the search for immaterials, and in the mid-1970s, a high-strength ceramic proppant, sintered bauxite, wasduced. The inertness and strength of sintered bauxite are caused by its major constituent,dum, a form of aluminum oxide. Although expensive, sintered bauxite retains permeability uvery high stress and severe reservoir conditions better than any other proppant available t

The expense of sintered bauxite motivated efforts to find less costly, but useful substitutes.development at the same time as sintered bauxite, curable resin-coated sand was the firproduct to find application.

Research and development on other ceramic proppants during the early 1980s producedexpensive proppant containing mullite, another form of aluminum oxide, in addition to corundIt has helped to bridge the cost-performance gap between sand and bauxite. Because of itcost and high performance, this material has enjoyed widespread use since its introduction

Improved Commercial Proppants

Sintered Bauxite

As previously described, sintered bauxite is an inert, high-strength ceramic proppant. PatenCooke et al., this high-density proppant is produced by the same manufacturing techniqrefractory ceramics and metal-working abrasive grits. The raw material is primarily high-alubauxite ore from South America. The ore is first ground to a particle size less than 15µm, shapedinto small ceramic pellets using water and a binder, and, after drying and screening, fired in



cess,per-

terialshard-

rtz is 7simplyce is

efore

brasionocesshe beststandard

to bind the edges of the individual particles that make up each pellet. After the sintering prothe color of the product varies from black to brown or gray. Typical physical properties, packmeability, and width data for this proppant are presented in Table 7.3.

Sintered bauxite draws its strength from the unique manufacturing process and from the mapresent in the bauxite ore. Corundum, the major component of sintered bauxite, is one of theest materials known to man. It measures 9 on Moh’s hardness scale. For comparison, quaand diamond is 10. When crushed, bauxite does not shatter as completely as the sands; itsplits into large pieces that are still capable of providing flow capacity. This crush resistancaused partially by sintered bauxite’s elastic properties, which allow slight deformation bfailure under high stresses.

The first sintered bauxite proppants were angular in shape, which could cause increased aand failure of pumping equipment, treating lines, wellhead equipment, and chokes. Primprovements have produced a material with roundness and sphericity values better than tfracturing sand and, thus, less abrasive than its predecessor. This proppant has become theagainst which all other proppants are measured.

Table 7.3 Typical Physical Properties of Sintered Bauxite - High-Strength,Sintered Ceramic Proppant 17*

API Mesh Size


Limits 12/20 16/20 20/40 40/70


1180 to600

850 to425

452 to212




1.0 maximum

0.096.33.70.0

0.095.34.70.0

0.094.0

6.00.0

0.095.4

4.60.0

Total 100.0 100.0 100.0 100.0


RoundnessSphericity


0.80.9

0.80.9

0.80.9

0.80.9


30 minutes at 150° F, wt% 7.5 maximum 2.0 2.0 2.0 2.0

Silt and fine particle, FTUCrush resistance, % fines generated

at 7500 psiat 10,000 psiat 12,500 psiat 15,000 psi


Clustering, wt%

250 maximumVariable with size and stress


80

5.410.616.822.5

30.88140.0<1.0

100

6.412.218.023.2

30.88140.0

0.0

100

2.64.36.8

10.730.88140.0

0.0

120

1.73.05.27.3

30.88140.0

0.0

* All tests performed according to Reference 11 or 12. Values shown are averages of multiple production samples over a 4-year period.



priateloserite, thisthat ofort and

mina,prop-

s mul-nt ofan-

, pack

Intermediate-Density Proppant

Even though this material is often called “intermediate-strength proppant,” a more approterm is “intermediate-density proppant (IDP).” The strength of this type of proppant is much cto that of sintered bauxite than to sand. While neither as strong nor as inert as sintered bauxmaterial has an advantage over sintered bauxite in that it has a lower density (approachingsand) than bauxite. The moderate density of these proppants makes them easier to transpplace in the fracture than the denser sintered bauxite.

The search for a more economical replacement of sintered bauxite revealed that high-aludomestic bauxitic ores could be used to produce a high-performance, sintered proppant witherties approaching those of sintered bauxite. In addition to corundum, this proppant containlite, a less-dense mixed form of aluminum oxide. The result is a dark brown to tan proppalower bulk density and lower specific gravity than bauxite. This new material is produced by mufacturing techniques similar to those used for sintered bauxite. Typical physical propertiespermeability, and width data for this proppant are presented in Table 7.4.

Table 7.4 Typical Physical Properties of High-Strength, Intermediate-Density,Sintered Ceramic Proppant 17*

API Mesh Size


Limits 12/20 16/20 20/40 40/70**


1180 to600

850 to425

452 to212




1.0 maximum

0.098.02.00.0

0.092.47.60.0

0.093.76.30.0

0.095.24.80.0

Total 100.0 100.0 100.0 100.0


RoundnessSphericity


0.80.8

0.80.8

0.80.9

0.70.9


30 minutes at 150° F, wt% 7.5 maximum 4.5 4.8 6.2 5.0

Silt and fine particle, FTUCrush resistance, % fines generated

at 7500 psiat 10,000 psiat 12,500 psiat 15,000 psi


Clustering, wt%

250 maximumVariable with size and stress


100

6.413.619.326.9

26.29113.0<1.0

100

10.319.427.433.9

25.95107.0<1.0

100

3.26.09.8

14.325.62106.0<1.0

120

1.42.74.67.4

26.12113.0<1.0

* All tests performed according to Reference 11 or 12. Values shown are averages of multiple production samples over a 4-year period.** Currently available in limited quantities on special order only.



thosells. Atacity.dnessonly

depthsay be

ensity,coatedroducerahamn 1982,

pre-ot as

sand.brittlenven-

nsandprop-e con-tensilethan itsresin-

as sin-in frac-me as

ghg pro-place.

While the durability and strength of intermediate-density proppant are somewhat less thanof sintered bauxite, performance is virtually equivalent in all but the deepest and hottest wehigh stress levels, the proppant breaks into large particles capable of providing good flow capThe proppant particles have good resistance to corrosion by hot formation brines; their rounand sphericity are better than those of the best fracturing sands, while their bulk density isslightly higher.

Despite higher cost, intermediate-density proppants may replace sand at intermediate wellbecause of their improved performance. Within the next few years a variety of sources mdeveloped to make this material widely available at lower costs.

Resin-Coated Proppants

The most commonly available resin-coated proppants are resin-coated sands. These low-dintermediate-strength proppants are available in two forms: curable and precured resin-Ottawa-type fracturing sands. Both are manufactured by a process similar to that used to pcoated sand for the foundry industry. Curable resin-coated sand was originally patented by Get al., for use in gravel-packing operations. Precured resin-coated sand became available iabout 7 years after the first curable product was used in fracturing operations.

The emergence of a high-quality, curable resin-coated sand, along with the availability of acured type, has led to a wide variety of fracturing applications. Although this proppant is nstrong nor as tough as the ceramic proppants, it is a significant improvement over uncoatedThe plastic coating distributes point loads over a wider area on the sand grain and retardsfailure. As such, the product is useful at higher stress levels (e. g., in deeper wells) than cotional fracturing sand.

The major application of thecurable resin-coated sandis as a tail-in material to retain the sand iproducing zones that will not retain ordinary fracturing sand. The curable coating bonds thegrains together after they are in place in the fracture. This in-situ consolidation often preventspant flowback, subsequent productivity loss, and damage to well equipment. Because of thsolidated nature of the proppant pack formed with resin-coated sand, compressive orstrength is often used as the critical physical property to describe resin-coated sand rathercrush resistance. Typical physical properties, pack permeabilities, and width data for curablecoated sand are presented in Table 7.5..

A curable resin coating can also be applied to proppants other than sand, and such materialstered bauxite, intermediate-density proppant, and zirconia have all been coated and usedturing treatments. The use of a curable resin coating in these applications is largely the sawith sand - to prevent proppant flowback.

The major application ofprecured resin-coated sandis to enhance the performance of sand at histress levels. This proppant is produced by heat curing the coating during the manufacturincess rather than allowing curing to occur after the resin-coated sand has been pumped into



ed finesation

and.erablyl.

The resin coating also encapsulates the sand grains, thus, preventing the migration of crushduring fluid production. It has also been shown to be resistant to destruction by hot formbrines and crude oils at temperatures up to 300°F [150°C].

At low stress levels, the performance of this material is not materially different from that of sAt higher stress levels, however, performance of the resin-coated sand is improved considover the original uncoated sand. Table 7.6 shows typical physical properties of this materia

Table 7.5 Typical Physical Properties of Curable Resin-Coated Sand - Low-Density,Intermediate-Strength Proppant 17*

API Mesh Size


Limits 12/20** 16/30 20/40


1180 to600

850 to425




1.0 maximum

0.095.54.30.2

0.098.02.00.0

0.094.45.60.0

Total 100.0 100.0 100.0


RoundnessSphericity


0.80.9

0.80.9

0.80.8

12/3 HCI/HF solubility, wt%

30 minutes at 150° F, wt% 7.5 maximum 0.5 0.6 0.5

Compressive strength, after100 hours at 195°F, psi

Tensile strength after 3minutes at 450°F, psi

Resin content, wt%Coating Continuity, count %Uncoated particles, wt%Particle density, lbm/galBulk density, lbm/ft3

Clustering, wt%

Variable with size

Variable with size3.6 to 4.4

98.0 minimum0.5 maximum


1400

180.03.7

99.50.2

21.396.0<1.0

2000

220.04.0

99.00.3

21.295.5<1.0

2800

270.03.8

98.50.2

21.396.0<1.0

* All tests performed according to Reference 11 or 12. Values shown are averages of multiple production samples over a 4-year period.** Currently available in limited quantities on special order only.


Table 7.6 Typical Physical Properties of Precured Resin-Coated Fracturing Sand -
Low-Density, Intermediate-Strength Proppant 17*

API Mesh Size


Limits 12/20** 16/30 20/40


1180 to600

850 to425




1.0 maximum

0.096.43.50.0

0.098.02.00.0

0.093.76.30.0

Total 100.0 100.0 100.0


RoundnessSphericity


0.80.9

0.80.9

0.80.9


30 minutes at 150° F, wt% 7.5 maximum 0.3 0.3 0.4

Silt and fine particle, FTUCrush resistance, %

fines generatedat 7500 psiat 10,000 psiat 12,500 psiat 15,000 psi

Resin content, wt%Coating Continuity, count %Uncoated particles, wt%Particle density, lbm/galBulk density, lbm/ft3

Clustering, wt%

250 maximum

Variable with size and stress

3.6 to 4.498.0 minimum0.5 maximum


40

-----11.2----------3.7

99.50.2

21.297.4<1.0

40

3.07.0

24.339.63.9

99.00.3

21.398.0<1.0

50

0.83.07.2

11.24.2

99.70.2

21.398.6<1.0

* All tests performed according to Reference 11 or 12. Values shown are averages of multiple production samples over a 4-yearperiod.

** Currently available in limited quantities on special order only.


Factors Affecting Fracture Conductivity

opedbora-dis-.

g of thereduceppantity fur-rtant.ctiv-a soft

seenerme-y less

bottom-ctionextent,

is theation:

-

ure isher (

nt will

seen, and

7.5 Factors Affecting Fracture Conductivity

This section discusses five factors that significantly affect the fracture flow capacity develwith proppants used in hydraulic fracturing. These factors can be readily evaluated in the latory, and their effect on fracture conductivity is relatively well established. Other factors to becussed later, have not been evaluated routinely; therefore, their effects are less well known

Closure Stress

The stress transmitted from the earth to the proppant during fracture closure causes crushinproppant, reducing particle size and increasing surface area of the proppant, both of whichpermeability of the propped fracture. In addition to crushing, the stress applied to the propack serves to compact the particle bed, to reduce its porosity, and to reduce its permeabilther. The last effect occurs even at relatively low stress levels when breakage is not impoCycling of stress, as would occur with periodic shut-ins of a well, also reduces fracture conduity irreversibly. Closure stress may also cause proppant particles to embed into the walls offormation, thus, decreasing fracture width and conductivity further.

An example of how closure stress affects permeability of different proppant materials can beby comparing the permeability data for sand to sintered bauxite. Figure 7.5 shows a plot of pability versus stress for 20/40 mesh Hickory sand and Bauxite. As shown, Bauxite is clearlaffected than sand within the stress levels tested.

The stress a proppant sees will depend on the overburden stress, the reservoir pressure, thehole flowing pressure, the ability of the vertical stress to be transmitted to the horizontal dire(related to Poisson’s ratio), tectonic stress (such as nearby mountain ranges) and to somethe fracture geometry (usually a small contribution). A prefrac well test called a “stress test”best method of estimating the stress on proppant. Or it can be estimated by the following equ

wherek = ratio of horizontal stress to vertical stress (k = (r/1-r)), OB= overburden stress (approximately 1 psi/ft of depth),Pr = reservoir pressure,Pf = fluid pressure in the fracture andPt = stressdue to tectonics (usually unknown and omitted).

A few observations can be made by studying this equation. First, as the reservoir pressdepleted, the stress on the proppant decreases. Second, as the well is drawn down furtPfbecomes smaller at the wellbore), the stress on the proppant will increase. Also, sincePf increasesas one moves down the fracture (away from the wellbore), the maximum stress that a proppasee is early in the life of a well near the wellbore, assumingPf does not change with time.

Proppant Particle Size

The permeability of a proppant is controlled largely by the proppant particle size, as can bein Figure 7.6. This figure shows a plot of permeability versus stress for 20/40, 16/30, 12/20

Stress k OB Pr–( ) Pr Pf– Pt+ +=



Fig. 7.5 - 20/40 Mesh Hickory versus Sintered Bauxite.



er con-mesh.crease

l parti-t size

mini-eptedthreemeterpants,rma-ppant

dur-ay betrans-

wallsquareters,ringntra-

n the

ture.20/40

, thisdivided

f prop-draulic

8/16 Hickory sand. As shown, the larger mesh proppants - e. g., 8/16 mesh - provide a greatductivity at lower stress levels than the more commonly used smaller sizes, such as 20/40As stress levels increase and particles are crushed, these differences in conductivity debecause particle size distribution, porosity, and surface areas become similar despite initiacle-size differences. At this point, other factors often play a more dominating role in proppanselection than conductivity considerations.

Consideration of proppant size is important in the design of fracturing treatments because amum fracture width is needed to allow the proppant to enter the fracture. The generally accvalues for this so-called admittance criterion require fracture widths in the range of two totimes the largest grain diameter. An admittance criterion based on twice the largest grain diarequires fracture widths of 0.187, 0.066, and 0.033 in. for 8/16, 20/40, and 40/70 mesh proprespectively. The largest of these values may be difficult to achieve in very deep wells with fotions having high bottomhole fracturing pressures and usually requires the use of smaller profor successful completion of the fracturing treatment.

Additionally, it should be thoroughly understood that proppant transport must be considereding the selection of the size of the propping agent. Even though a 12/20 mesh proppant mmuch more conductive than a 20/40 mesh proppant, the smaller proppant is much easier toport deeply into a fracture than the larger proppant.

Proppant Concentration

The term “proppant concentration” refers to the amount of proppant per unit area of fracture(measured on one side only). In customary units, it is expressed in pounds of proppant perfoot of one wall of the fracture. If proppant settles to the bottom of a vertical fracture as it enthe concentration will be determined by the width of the fracture at the time of entry (i. e., dupumping). If the proppant is suspended in the fracturing fluid until the fracture closes, concetion will be determined by both the width during pumping and the concentration of proppant ifluid.

Fracture conductivity increases with increasing concentration of proppant in the fracFigure 7.7 shows a plot of fracture conductivity versus proppant concentration developed forOttawa sand at an in-situ stress of 5000 psi.

Proppant Strength

The strength of proppants is of major concern in the design of propped fractures. Historicallystrength has been expressed in terms of the load required to crush a single grain of proppantby the diameter squared of its contact area at the point of crushing.

Another test, the API crush resistance test, was designed to determine the relative strength opants in packs and has been tested and adopted by API for testing sands to be used in hy



Fig. 7.6 - 20/40, 16/30, 12/20, 8/16 HIckory.



Fig. 7.7 - 20/40 Ottawa Showing Effect of Concentration on Conductivity.



k. Theroppant

ove for, pack-ght tosingle-ifficultritical

ich isr per-sandand, asovid-

fracturing. The API test uses an apparatus for imposing a sustained load on a proppant pacdegree of size reduction sustained by the proppant is taken as an inverse measure of pstrength.

The API crush resistance test is a more complex measure of strength than that described absingle particles. The values obtained are influenced by grain shape, particle-size distributioning arrangement, and other attributes of the particle pack. Although these factors are thoumake the test more representative of proppant performance under field conditions than theparticle test, sensitivity of the measurement to several pack attributes makes the test more dto reproduce, and small variations in results (e. g., 2 or 3%) are considered insignificant in ccomparisons.

Figure 7.8 shows the relationship of closure stress to flow capacity of various proppants, whdetermined primarily by proppant strength. This figure shows that Hickory sand has greatemeability at low stress compared to Ottawa sand. This effect results from the fact that Hickoryhas a larger sand distribution (20/30 mesh particles predominate) as compared to Jordan swell as the fact that Hickory sand is more angular. These attributes result in Hickory sand pring greater permeability than Jordan sand up to nearly 5000 psi stress.

Effect of Proppant Type on Flow Capacity

Closure Stress, psi in 1000's

Per

mea

bilit

y, k

o, d

arcy

0 2 8 10 14

1,000

400

200

1006040

20

16

600

1064

2

Intermediate DensitySintered Ceramic Proppant

ZirconiaSintered Bauxiye

Frac SandOttawa Type

Precured Resin-Coated Sand

Frac SandBrady Type

4 12

Sintered Bauxite

Fig. 7.8 - All Proppants (non-Ultrafrac).



rticles.to have

thesee com-parable

impor-

of car-vels, aack aserme-ome-0 psi

ppant-

Above 5000 psi [34.5 MPa] closure stress, some of the largest grains break into smaller paThus, at higher stresses, Ottawa sand, which had not broken as much as Brady sand, is seenthe higher proppant-pack permeability. While the conductivity measurements on whichresults are based are very sensitive to proppant-pack attributes and difficult to reproduce, thparison cited is from measurements made in the same laboratory and therefore are as comas current measurement techniques permit.

Proppant Grain Shape

Roundness and sphericity are proppant particle properties that affect performance. Theirtance depends somewhat on the stress level at which the proppant is to be used.

Because the surface stresses are more uniform, a well-rounded, spherical particle is capablerying higher loads without crushing than a less-rounded particle. Therefore, at high stress lehigh degree of roundness and sphericity contribute to higher proppant particle does not pwell as a well-rounded particle and, thus, has more porosity and correspondingly greater pability. An example of this phenomenon was described previously. Hickory sand, which is swhat more angular than Ottawa sand, has slightly better flow capacity below about 500[34.5 MPa] than Ottawa sand, although the more rounded Ottawa sand is superior in propack permeability at higher stress levels.



ctureed.

, andmbed-

may

tests ofodern

prop-ction.nt andof its

ion of aracturef resi-ower,0 showse fig-damage

buildymerenersn can

n flu-tremeTGilities

ted assabletem-

7.6 Other Factors Affecting Fracture Conductivity

This section discusses five additional factors which typically have an adverse effect on fraconductivity. The full effect of these factors on future treatment design is yet to be determin

Embedment

If proppant particles penetrate the walls of the fracture, the effective width of the fracturethereby the conductivity, is decreased. Not only is the width of the fracture decreased by ement, but fine particles are generated by failure of the formation rock. These fine particlesalso contribute to the loss of fracture conductivity.

An attempt to assess the severity of embedment has been made by ball-point penetrometerformation rock. These tests are not as important as was earlier thought because in most mfracture designs the proppant pack is many particles thick in the fracture. The intrusion of thepant into the fracture wall represents only a small fraction of the proppant-to-proppant interaHowever, in soft formations such as North Sea Chalks, proppant embedment can be significafracture designs are modified to increase fracture width and minimize the detrimental effectsoccurrence.

Fracturing-Fluid Residues

The pore space of proppants packed in a fracture is sometimes decreased by the depositresidue from water-based fracturing fluids. Such residue may cause a drastic decrease in fconductivity under certain conditions. The problem is most pronounced when the volume odue from the polymer is higher, when the concentration of proppant in the closed fracture is land when stress on the fracture is higher which causes lower porosity. Figures 7.9 and 7.1pictures of the residue from borate and zirconate crosslinked fluid systems, respectively. Theures show the proppant pack damage that occurs due to residue and also indicate that thisis minimized by using borate crosslinkers.

The most common residue is a product of the degradation of water-soluble polymers used toviscosity in fracturing fluids. Service companies have devoted much effort to reducing polresidues in fracturing fluids. Recent research has focused on developing more efficient thickwith more soluble degradation products. Some of the detrimental effects of residue depositiobe alleviated by minimizing polymer concentrations, using higher proppant concentrations iids that suspend the proppant, using foam or emulsion fluids, and avoiding conditions of exproppant crushing. STIMLAB has developed a program “PREDICTK” (available from EPFracture Applications Team) which tabulates available data comparing retained permeabafter breaking and cleanup of various generic fracturing-fluid types. The data are presenretention factors that can be applied to API-type short-term permeability data to obtain a uvalue of proppant-pack flow capacity. The retained permeability includes the effects of time,perature, and fluid residues.


Other Factors Affecting Fracture Conductivity

ading40

%.91 to

per-with

eanupcom-trend.

typeinly of

Inspection of this program reveals a direct comparison of the effects of increasing gellant lofor a titanate cross-linked hydroxypropyl guar gum (HPG) type fluid. Increasing gellant fromto 50 lbm/1000 gal [4793 to 5991 b/m3] decreases retained permeability by an additional 15Further reduction is encountered by a gellant increase from 50 to 60 lbm/1000 gal [597190 g/m3] of about 15%.

Another comparison of fluid effects, i. e., guar gum vs HPG, shows little difference in retainedmeability. Virtually no difference is seen between titanate cross-linked fluids and those linkedzirconates.

Fracture closure, fluid leakoff, and viscosity breaking processes have a dramatic effect on cland regained permeability of the proppant pack. Breaking times of 2, 10, and 24 hours arepared for a generic cross-linked fluid. Slow and fast breaks are compared for gelled oil. Theis the same: more rapid breaks tend to be more effective in terms of regained permeability

In a comparison of the damaging effects of different types of generic fracturing fluids, onestands out as being the least damaging: foam fracturing fluids. These fluids, composed ma

Fig. 7.9 - Borate Crosslinked Fluid System.



oten-

k per-vesti-have

ducingay beh the

a gas and minor amounts of gelled water, permit a proppant pack to regain 70 to 90% of its ptial flow capacity.

Fines Movement

The fine particles created by grain failure at higher stress levels lead to lower proppant-pacmeability. The particle-size distributions resulting from such crushed particles have been ingated by several authors and their effects on fracture conductivity reported. Fine particlesbeen shown to migrate through the propped fracture and to plug the pore throats, thereby refracture conductivity. The long-term decreased permeability of sand proppant reported mcaused at the least partially by movement of preexisting fines with continued flow througsand.

Non-Darcy Flow

For non-Darcy flow, the pressure drop in the fracture can be expressed by

Fig. 7.10 - Zirconate Crosslinked Fluid


Other Factors Affecting Fracture Conductivity

as aes

-rateanal-pres-flow

(7.1)

where

∆p = pressure,

∆Lf = length of proppant pack in direction of flow,

µ = viscosity,

v = velocity,

kf = permeability,

β = turbulence factor, and

ρ = fluid density.

The second term of the equation, with coefficientβ, expresses the increased pressure gradientresult of deviations from Darcy’s law. Values ofβ have been measured for a variety of sand sizat different values of stress.

Non-Darcy effects can substantially reduce the effective fracture conductivity in high-flowgas wells. This reduction in conductivity will decrease the well’s PI and can complicate theysis of pressure-transient tests. To analyze wells properly where non-Darcy flow affects thesure distribution in and around the fracture, a reservoir simulator that includes non-Darcymust be used by the analyst.

∆p ∆L f⁄ µv kf⁄ β( ) ρ( )v2+=



omicsthisnol-torsoppantviewedpro-ssis-

7.7 Economic Proppant Selection

Successful hydraulic fracturing requires the integration of technical proppant data with econto allow the development and implementation of an optimum fracture design. To facilitateoptimization effort, the Fracture Applications Team of the Exploration and Production Techogy Group (EPTG) has developed a fracture optimization tool, ULTRAFRAC. The critical facaffecting fracture conductivity, described in the previous section, such as closure stress, prsize, proppant concentration, strength, embedment, fracturing-fluid residues can each be reboth from a technical and economic perspective with ULTRAFRAC. For aid in the use of thisgram, please contact Larry K. Britt (8-422-3958) or Sandra Dougherty (8-422-3332) for atance.


Chapter

om-havior,ased onuring

por-ey and

re

erently

aterctice.

f thisr larger

esented

xten-re.”and amith

ss) vs.

Fracture Treating Pressure Analysis8
8.1 Introduction To Fracturing Pressure Analysis
Hydraulic fracturing, as with other drilling, completion, and reservoir behavior problems, is cplicated by the fact that processes cannot be directly observed. For describing reservoir bethis deficiency has been overcome by the development over the past 50 years of analyses bwellbore pressure and flow rate. But, only in the last few years has similar analyses for fractbeen introduced and successfully applied.

History

Shortly after the introduction of hydraulic fracturing and its acceptance by the industry, the imtance of fracturing pressure data was recognized, as evidenced by a quotation from GodbHodges1

“By obtaining the actual pressure on the formation during a fracture treatment, and if theinherent tectonic stresses are known, it should be possible to determine the type of fractucreated.”

Later, fracturing pressure and the relation between pressure and in-situ stresses were inhincluded in pioneering model development work of Khristianovic and Zheltov,2 Perkins and Kern,3

and Geertsma and de Klerk4 during the 1950s and 1960s. However, it was still several years lbefore the analysis of fracturing pressure data started to become an accepted industry pra

In 1978, Amoco Production Company initiated a coordinated program of field data collection5 andanalysis to improve the understanding of the mechanics of the fracturing process. Much ounderstanding had not changed since the early 1960s and was being severely tested by eveand more expensive treatments. A series of papers at the annual meeting of SPE in 1979 prresults from this program, including a paper by Nolte and Smith6 which first introduced a basis forthe interpretation of pressure behavior during a fracture treatment, and one by Nolte7 for interpret-ing pressure decline after the treatment.

The paper by Nolte and Smith presented a means for inferring periods of confined-height esion, uncontrolled height growth, and, more importantly, identification of a “critical pressuWhen a treatment reaches the critical pressure, fracture extension is reduced significantlypressure (screenout) condition or undesired fracture height growth can follow. Nolte and Sdemonstrated in the paper that a log-log plot of net fracturing pressure (above closure stre



essively sincecs and

nd thee thismeterscient,ringor use

to

m the-ls,-terdata

servoirinter-

rovidetinuitynt tothat,is dif-

. How-ile the

t. There dur-uringtreat-

treating time could be used to identify periods of unrestricted extension, confined height, excheight growth, and restricted penetration. This plot and technique has been used extensiveits introduction by both operators and service companies to determine fracture characteristigeometry, and as an evaluation tool for optimizing treatment designs.

Nolte7 also presented analyses permitting some of the parameters that quantify a fracture afracturing process to be estimated from the pressure decline following fracturing. At the timwork was presented, there was no direct or simple procedure for evaluating the basic paracontrolling a fracture treatment. Procedures were presented for quantifying fluid loss coeffifracture length and width, fluid efficiency, and time for the fracture to close from the fractupressure decline. The “minifrac” procedure was introduced for obtaining these parameters fin designing the actual fracture treatment.

The analysis procedures from these two papers6,7 have been used extensively by the industryevaluate fracture treatments related to tight gas massive hydraulic fracturing,8-10 waterfloodwells,11 moderate permeability oil wells,12 and geothermal formations.13 The work by Nolte andSmith was extended to include analysis for determining proppant and fluid schedules frofluid efficiency when little or no information is available,14 e.g., wildcat area. In addition, theoretical work has extended the analyses to cover the three popular 2-D fracture geometry mode15 tocover more complex geometries involving fracture height growth,16 and to consider such phenomena as pressure dependent fluid loss.17 In recent years, the service companies have built computreatment monitoring vehicles for use on-site in collecting and analyzing fracturing pressureusing the analysis techniques presented by Nolte and Smith.18

Similarity to Pressure Transient Analysis

Analysis of fracturing pressure response is analogous to pressure transient analysis in reengineering. In both cases the pressure response resulting from fluid flow in rock can bepreted using basic principles to provide insights into a complicated physical process and pthe basis for rational decision making. In both cases the same basic principles apply - conof flow (e.g., mass balance), fluid flow resistance (for fracturing, width squared is equivalepermeability in porous media), and system compressibility. Another important parallel isalthough the principles remain the same for all applications, each application in a new areaferent and requires additional data collection and the participation of experienced personnelever, an important difference is that pressure analysis of reservoirs is a mature discipline whapplication to fracturing is still in its infancy.

Fig. 8.1 shows the first recording of bottomhole pressure during and after a fracture treatmenanalogy to transient pressures in reservoirs can be seen in the figure with increasing pressuing injection and the pressure falloff or decline after shutdown. The figure also shows that dthe first half of the treatment, the pressure was increasing, while during the last half of the


Introduction To Fracturing Pressure Analysis

s periodheight,nt, the

et for-luidessureant atthe

yondservoired back

is and.

ment, the pressure remained essentially constant, e.g., a critical pressure was reached. Thimight be interpreted that the increasing pressure indicates extension at essentially constantwith subsequent increasing height during the constant pressure period. During the treatmerock was confining fluid at a pressure up to 1400 psi above the in-situ rock stress of the targmation. During the initial portion of the decline (41-44 hours), the fracture is closing due to floss with the rate of loss proportional to the rate of pressure decline. The increased rate of prdecline after 44 hours is due to the increasing stiffness of the fracture closing on the proppthe wellbore. This time is significant for two reasons -- the propped width can be inferred fromnet pressure, and the well could be backflowed with minimum proppant production. Be44 hours, the fracture is essentially closed on proppant and the pressure decline reflects reparameters as pressure declines back to initial conditions. At 56 hours, pressure has decayto initial reservoir pressure.

The following discussion presents the basis for and examples of fracturing pressure analysdesign. Also included are procedures for the successful field application of this technology

Fig. 8.1 - Example of Fracturing Related Pressures.

Bottomhole Treating Pressure (BHTP) (psi)

9000

8000

7000

6000

5000

(50MPc)

FractureTreatment Fracture

ClosingTransient ReservoirPress. Near Wellbore

Frac. Closeson Propat Well,

Pe∝ Propped

Width

Reservoir Press.

Pressure Decline

• Pressure FromBottomhole BombInferred Pressure

PeNet FracturePressure= Pbh-Dc

Closure Press, P c= Horiz. Rock Stress

38 40 42 44 46 48 50 56 58Clock Time (hrs)



” e.g.,stress)

of ancular totress,nimumure is

ressure

ure andor frac-initiallso beexten-otherure clo-n test,c frac-sed: (1)ssure),

small,al withperfo-rfo-

waterc) oflose

zed iny be anl

8.2 Fracture Closure Stress

Fracturing pressure analysis is based entirely on interpreting the “net fracturing pressure,treating pressure above the minimum in-situ stress (the fracture closure pressure or closureof the target formation. Thus an accurate knowledge of closure stress isessentialto the technology.The term “closure pressure” is defined as the fluid pressure required to initiate the openingexisting fracture. This pressure is equal to, and counteracts, the stress in the rock perpendithe fracture. Since the fracture preferentially opens perpendicular to the minimum in-situ ssince any other direction would require a higher pressure, closure pressure equals the miin-situ stress. In the analysis of bottomhole treating pressure while fracturing, closure pressanalogous to the flowing bottomhole pressure measured during well tests, e.g., it is a base pabove which pressure analysis is performed.

Closure pressure is equal to or less than the breakdown pressure required to initiate a fractless than the pressure required to extend an existing fracture (fracture extension pressureture parting pressure). An upper bound for closure pressure might be estimated from theshut-in pressure (ISIP) after a small volume acid or prepad injection. An upper bound can afound from the breakpoint on a step-rate injection test (fracture parting pressure or fracturesion pressure). However, for quantitative analysis, a more definitive value is needed. Whilemethods such as logs and core analysis, Chap. 10, exist to measure or estimate in-situ fractsure stress, the only definitive data for pressure analysis comes from some type of injectioe.g., we must hydraulically fracture the rock in order to measure the data needed for hydraulituring pressure analysis. For measuring closure stress, three basic types of tests are upump-in/decline tests, (2) step-rate injection tests (used to measure fracture extension preand (3) pump-in/flowback tests.

Microfrac Tests

Microfrac tests are a special type of pump-in/decline test used to measure closure stress in adiscrete zone. The test may be conducted in open-hole sections by isolating the test intervinflatable packers; however, for most commercial fracturing cases, testing is conducted byrating a short (1 to 2 ft) interval of casing, typically at 4 to 6 shots per foot with a 60 or 90 peration phasing.

These types of stress tests are discussed thoroughly by Warpinski19 and McLennan,20 and an idealtest might appear as seen in Fig. 8.2. Tests typically might consist of injecting 20 gallons ofat 5 gpm, the basic theory being that, after injecting a small volume (e.g., the term microfralow viscosity fluid at a low rate, the ISIP (instantaneous shut-in pressure) will be a very capproximation to the actual closure pressure. In fact, where a clear ISIP exists as idealiFig. 8.2, or seen for real data in Fig. 8.3, selecting closure pressure as equal to the ISIP maacceptable approximation. However, as emphasized by Warpinski,19 testsmustbe repeated severa

°


Fracture Closure Stress

reduceened.peat-

und for, pick-ces, are clo-

ressurer flowd hole

times in order to ensure that the value is repeatable. Generally, multiple repeat tests tend toany influence of rock strength since the fracture is no longer being extended but only reopThis will tend to make an ISIP more definitive and easier to pick, and, if the value is also reable, then a good value for closure stress has probably been found.

However, it should be realized that the instantaneous shut-in pressure is always an upper boclosure pressure since a fracture cannot shut instantly when pumping is stopped. Thereforeing an ISIP value and making use of this value must be done with care. Also in some instandefinitive ISIP is never realized and other analysis methods must be used to determine fractusure pressure.

The most common analysis procedure, and the procedure recommended here, is to plot pvs. the square root of shut-in time. A change in slope indicates a drastic change in the lineabehavior, and is taken to indicate the fracture closing. For example, Fig. 8.4 shows a case

Fig. 8.2 - Ideal Microfrac Stress Test.

Fig. 8.3 - Microfrac Stress Test with “Clear” ISIP.

First Cycle Second CycleInitial Breakdown (Pb 1) Secondary Breakdown

Pressure (Pb 2)Propagation PressurePropagation Pressure

Shut-in Pressure (Ps 1) Shut-in Pressure (Ps 1)

Time

Bot

tom

hole

Pre

ssur

e

ISIP

7500.000

6750.000

6000.000

5250.000

4500.000

3750.000

3000.0000.0000 2.500 5.000 7.500 10.000 12.500 15.000 17.500 20.000 22.500 25.000

Time (minutes)

Bot

tom

hole

Pre

ssur

e (p

sig)



learlyut-infigure.

-he twoor clo-ot plotlysis

microfrac stress test conducted in the Mesaverde formation of the Rocky Mountains - and cno definitive ISIP can be picked. However, plotting the pressure falloff vs. square root of shtime shows a definitive change in slope, and closure pressure is chosen as identified in theFor this Mesaverde well, closure stress was measured by Warpinski21 in several intervals, and thisdata was reanalyzed as discussed by Miller and Smith22 using the “reservoir type” analysis of plotting pressure vs. the square root of shut-in time. As seen in Fig. 8.5, agreement between tanalysis methods was nearly perfect. Thus, picking an ISIP value does give a good value fsure stress. However, in many cases an ISIP could not be identified, whereas the square rogave a definitive value and in virtually every case, the “reservoir type,” square root plot anayielded a more subjective, definitive analysis.

Fig. 8.4 - Bottomhole Pressure, Square Root Time and Elapsed Time Since Shut-In.



to mea-ll vol-cticalcom-

ever,might

t thepen awith a

a rateineinter-suretimetests

., KClt thecline

ussed

Pump-In/Decline Test

As discussed on page 8.4, microfrac tests are a special class of pump-in/decline tests usedsure stress in small, discrete formation intervals, and these “micro” tests typically use smaumes of water injected at rates measured in gallons per minute. However, often it is more prafor commercial fracturing applications to measure the closure stress over the entire intendedpletion interval. The basic test procedure is, of course, identical to a microfrac type test; howvolumes are now measured in barrels and injection rate in bpm. For example, a typical testinvolve injecting 50 barrels of water at 20 bpm. The important, indeed critical, point is thainjected volume and injection rate must be guaranteed to be sufficient to create and/or ohydraulic fracture. For this reason, it is often desirable to proceed the actual stress teststep-rate injection test as discussed on page 8.10.

For a pump-in/decline test, closure pressure is determined by injecting a volume of fluid atsufficient to create a fracture; then shutting in the well and allowing pressure to naturally declto below closure pressure (e.g., allow the fracture to close). For testing an entire completionval, this type of test is most useful in moderate to high permeability formations, where clooccurs reasonably quickly. For very low permeability zones, e.g., “tight” reservoirs, closuremay be so long that closure becomes difficult to identify. For these cases, pump-in/flowbackmay be preferable as discussed on page 8.9.

Testing is usually conducted with the base fluid being used to prepare the fracturing fluid, e.gwater, diesel, produced formation fluid, etc. The pump-in portion of the test is performed afracturing rate, and in most cases consists of 50 to 100 barrels of fluid. While a pump-in/detest over an entire completion interval may be procedurally similar to the microfrac tests disc

Fig. 8.5 - Comparison of ISIP vs. Root Time Analysis of “Microfrac” Stress Tests.

0.7 0.8 0.9 1 1.1

0.8

0.9

1

1.1

0.7

ISIP “Pick” (psi/foot)

Roo

t Tim

e A

naly

sis

(psi

/foot

)



er vol-n pres-ndatory

ysis isted on

trap-ay beg, thededradiallized

ma-and aay bef theanal-ly to, the

earlier, a simple ISIP cannot be used to approximate closure pressure. Because of the largumes and higher rates needed to ensure that the completion interval is fractured, the injectiosure can easily be several hundred psi above closure pressure; thus, special analysis is main order to identify fracture closure.

Since the test is, hopefully, being conducted in a porous, permeable formation, the first analto plot a Horner plot of the pressure decline as seen in Fig. 8.6. For this plot, pressure is plotthe “y” axis on a linear scale, and “Horner time,”[tp+ts]/t s, is plotted on the “x” axis on a logarith-mic scale. If a semilog straight line is starting to develop as seen in Fig. 8.6, and if this line exolates to a reasonable value for reservoir pressure, then radial or pseudoradial flow maffecting the pressure decline behavior. In order for this pseudoradial flow to start developinfracture mustalready be closed, thus pressure data falling on the semilog straight line is exclufrom the closure stress analysis. Next, the pressure falloff (prior to the point where pseudoflow may be starting to affect the decline) is plotted vs. the square root of shut-in time as ideain Fig. 8.7. Initially, pressure should decline on a straight line indicating linear flow in the fortion. The point where the fracture closes should cause a drastic change in the flow systemdistinct change in slope on the square root plot. Note, however, that the change in slope meither “up” or “down,” depending on the relationship of the fracture's variables and those oreservoir. This implies a theoretical possibility that no change in slope may occur. Thus thisysis method should be treated with caution. In particular, this type of problem is most likeoccur in low permeability formations where closure time is extended. In such situationspump-in/flowback test, discussed below, should be utilized.

Fig. 8.6 - Illustrative Horner Plot for Shut-InDecline Test.

Fig. 8.7 - Illustrative Root Time Analysis forClosure Stress.

Bot

tom

hole

Pre

ssur

e SHUT-IN DECLINEPUMP IN

POSSIBILITIES

ts (Shut-In Time)



uiterootcture

allyain-. Theid isin ther idealto 2. Oncerepeat-

es ofd there, thee anddrasticcture

ssure

stressases,

Pump-In/Flowback Test

For low permeability, “tight” formations, the time-to-close for a pump-in/decline test may be qlong, making identification of fracture closure (e.g., identifying two distinct slopes on a squareplot) difficult. For these cases, a pump-in/flowback test (PI/FB) may be used to accelerate fraclosure-- thus making closure pressure more identifiable.

For a PI/FB test, the injection is immediately followed by a flowback at a constant rate, typicthrough a flowback manifold similar to that shown in Fig. 8.8. The constant flowback rate is mtained with an adjustable choke or valve and should be metered with a low-rate flowmeterprimary purpose of the flowback is to flow back at a rate on the order of the rate at which fluleaking off to the formation. For this flowback rate, a characteristic reverse curvature occurspressure decline at closure pressure as shown by the middle curve in Fig. 8.9. The proper oflowback rate must be determined through trial and error, performing the first flowback at 1bpm and changing the rate until the “S-shaped” character of the pressure decline is achievedthe desired rate is achieved, at least one additional PI/FB test should be performed to ensureability.

The principle behind a pump-in/flowback test is illustrated in Fig. 8.10. During the early stagthe flowback pressure decline (“A”), the fracture and formation are dominating behavior anpressure decline is “normal.” When pressure declines equal closure pressure at the wellbofracture begins to close in the near well region. However, this closure is over a limited distancsince even a closed fracture possesses significant permeability, there will be no sudden,change in pressure decline behavior. Also, it should be noted that away from the well the frais still open; driving fluid to the wellbore and preventing any sudden increase in the rate of predecline.

With further pressure drawdown in the wellbore, the effective stress (e.g., fracture closureminus pore pressure in the fracture) acting over the closed portion of the fracture incre

Fig. 8.8 - Flowback Manifold for PI/FB Stress Tests.

Digital Readout

DisposalPit

Adjustable Chokeor Gate Valve

Digital Readout

2 inchFlowmeter

1 inchFlowmeter

FlowbackLine

Gate Valveor Lo-Torque

Valve

Wellhead



e andsimplys therts isat the

1. Foriden-

max-for ahoulde raterun aneriv-

e pre-pres-losuremined

pedlottedbpm.

decreasing the permeability of the closed fracture. This begins to reduce flow into the wellborthe rate of pressure decline starts to accelerate as the flowback is increasingly coming fromthe pressurized fluid in the well. The acceleration of the rate of pressure decline (“B”) createcharacteristic “reverse curvature” behavior (“C”), and the point where this acceleration staidentified as fracture closure pressure, e.g., the point where the fracture first begins to closewellbore.

An additional analysis procedure for PI/FB tests is a derivative plot such as seen in Fig. 8.1this plot the change in pressure with respect to time, dP/dt, is plotted vs. time. Since closure istified at the point where the rate of decline accelerates, closure would be identified with theimum point on the derivative plot. For the example in the figure, the derivative is constantfairly long period time, e.g., pressure is declining linearly with time. In such a case, closure sprobably be identified at the end of the constant derivative period, e.g., at the point where thof pressure decline begins to accelerate. For this case, it would probably be advisable toadditional case with a higher flowback rate to achieve a more identifiable maximum on the dative plot, and thus a more distinct value for closure pressure.

Step-Rate Injection Test

As mentioned previously, stress testing of a gross completion interval should generally bceded by a step-rate injection test (SRT). This test will yield a value for the fracture extensionsure which is a good upper bound for closure pressure, typically being 100 to 200 psi about cpressure. Also, by noting the rate where fracture extension begins, a minimum rate is deterfor subsequent injection/decline or PI/FB tests.

The SRT procedure is similar to that performed for reservoir flooding purposes. Fluid is pumat incrementally increasing rates and the final injection pressure recorded for each rate is pvs. rate as seen in Fig. 8.12. A typical test may include rates ranging from 0.25 bpm to 20

Fig. 8.9 - Illustrative PI/FB Stress Test Analysis (linear p vs. t plot).

Time

Bot

tom

hole

Pre

ssur

e



Fig. 8.10 - Pump-In/Flowback Test.

Pressure Holding Frac Openk = Infinite

Pressure = P ck = Finite

Flowback

Leakoff

Pressure < P cso frac is “stressed”k = very small



fracturee (typ-roperll IDain-

The resultant pressures at each rate are plotted vs. rate and the breakpoint is identified asextension pressure. For best results each rate should be maintained for a fixed period of timically 2 to 5 minutes). Also, because of the very low rates at the beginning of the test, the ppumping equipment is required (e.g., low rate acid injection pump), equipped with a smaflowmeter for accurate metering. Conventional fracture pumping units have a difficult time mtaining constant rates at less than 2 bpm.

Fig. 8.11 - Example PI/FB Test with Derivative.

a) Start Injection, 5 BPMb) Increase Injection to 7 BPM, Start 2 BPM Flowbackc) Stop Injection, Maintain Constant Flowback at 2 BPM



Fig. 8.12 - Illustrative Step-Rate Injection Test.

Table 8.1 - Summary of Analysis MethodsIn-Situ Stress Tests

Microfrac Test (measure stress in small, discrete interval)Pick ISIPPlot Pressure vs. Square Root of Time

Pump-In/Decline Test(stress in gross completion interval)Horner Plot (to identify any pseudoradial flow effects)Plot Pressure vs. Square Root of Shut-In Time(distinct change in slope identifies closure)

Pump-In/Flowback Test (stress in gross completion interval)Plot Pressure vs. Time

(reverse curvature identifies closure,looking for “broad” curvature down, NOT “wiggles”)

Superimpose plot of dP/dt vs. time(maximum on derivative plot identifies closure“or end of flat derivative”)

Step-Rate-Injection Test (measure extension pressure)Plot Pressure at End of Each Rate Step vs. Rate

(“break” indicates start of fracture extension andsets a good upper bound for closure pressure)



ment toted toystemhaviorture

ssure. Othera;

ovidedasingretationg pro-

nter-te andtifica-ctedased

w

d

5, and

8.3 Bottomhole Treating Pressure

Bottomhole pressure is the single parameter that can be measured during a fracturing treatinterpret the fracturing process. All other parameters controlling fracture growth can be relathis pressure. Pressure in the fracture is a function of formation parameters and the fluid sused to create the fracture. If the pertinent rock and fluid properties can be defined, the beof bottomhole treating pressure (BHTP) while fracturing can provide valuable insight into fracgrowth/geometry characteristics.

The equation used to define fracturing pressure is

where net pressure,pnet, is the total fluid pressure minus closure pressure, and the closure preis equal to, and counteracts, the horizontal rock stress perpendicular to the fracture planeparameters in the equation are rock modulus,E', which can be obtained from laboratory core datfracturing fluid viscosity,µ; injection rate,Q; and created fracture height and length,H andL. Thisrelation predicts that net pressure should increase with time as fracture length increases, prfracture height is near constant or restricted. However, variations from this prediction of increpressure have been observed in numerous cases. The following discussion presents interptechniques to interpret and analyze these pressure variations to aid in defining the fracturincess for different situations.

Nolte-Smith Log-Log Interpretation

A log-log plot of net fracturing pressure vs. treating time has proven to be a powerful tool for ipreting the fracturing process. From pressure behavior observations during fracturing, NolSmith6 presented four distinct pressure “modes,” as seen in Fig. 8.13, which permit the idention of periods of confined-height extension (Mode I), constant height growth (Mode II), restriextension (Mode III), and uncontrolled height growth (Mode IV). These interpretations are bon combining historical work performed by Perkins & Kern3 and Nordgren,23 showing that netpressure is proportional to time raised to an exponent as seen in Fig. 8.14.

For actual fluids used for fracturing, the exponent,e, can be bounded for cases of high and lofluid loss, and where the fluid’s non-Newtonian power law exponent,n, varies from 1 for a New-tonian fluid ton = 0.5 for a highly non-Newtonian fluid. For the Newtonian fluid with high fluiloss, the exponent,e, would equal 1/8. For a highly non-Newtonian fluid with low fluid loss,ewould be 1/4. This defines the boundaries for Mode I fracture extension, as seen in Fig. 8.1the following discussion centers on the four characteristic slopes shown in Fig. 8.16.

PnetE'H----- µQL[ ]1/4

=


Bottomhole Treating Pressure

s thatss istant.

f eachtion,height,d 3 inode II

Mode I - A log-log net pressure to pump time slope of 1/8 to 1/4, as discussed above, impliethe fracture is propagating with confined height, unrestricted extension, that fluid lolinear flow dominated, and that injection rate and fluid viscosity are reasonably consThese assumptions comply with the Perkins and Kern fracture growth model.

Fig. 8.16 shows the net treating pressure for three fracture treatments, the initial portion otreatment indicating confined height, unrestricted extension (Mode I). Beyond this porthough, the treating pressure deviates from the 1/8 to 1/4 slope, mentioned above - confinedunrestricted extension, linear flow fluid loss, and constant rate and viscosity. For cases 1 anthe figure, the slope is nearly flat, indicating near constant pressure which characterizes Mbehavior.

Fig. 8.13 - Nolte-Smith Plot Slope Interpretation.

Fig. 8.14 - Theoretical Basis for Fracturing Pressure Interpretation.



n' is Non-Newtonian Fluid Power Law Exponent

n' = 1 n' = 0.5e Newtonian Fluid Very Non-Ne wtonian Fluid

High Loss 1/2(2n'+2) 1/8 1/6Low Loss 1/(2n'+3) 1/5 1/4

Fig. 8.15 - Nolte-Smith Slope Limits for Mode I (Restricted Height, Unrestricted Extension).

Fig. 8.16 - Example Nolte-Smith Plots with Different Characteristic Slopes.

P te

≅

Nolte-Smith Plot

Slope: 1/8 to 1/4

Log Time

Log

Pne

t



s bal-

orede II

hichown inrowth

eases,anda low

indicat-sed

ten inarea,stressnd the

e reg-Mode

fis-pingmusted, the

e 3 ofressure

To analyze what may cause this flattening of the pressure - time slope, the continuity or masance equation can be examined;

whereqFracis the rate of fluid storage in fracture volume (e.g.,∆w + ∆H + ∆L). Pressure is propor-tional to fracture width, thus the equation can be rewritten as

whereK is a constant. For the Mode I behavior, injection rateQ is constant, height is constant (∆H= 0), andqLoss increases with time as fracture area increases. Also,∆P and∆L are increasing withtime. If ∆P goes to zero, thenql and/or∆H must increase to honor the equation. As a result, mfluid is lost to the formation or stored in additional height. This leads into a discussion of Mobehavior on a log-log net pressure vs. time plot.

Mode II - A flat pressure:time slope indicates stable height growth or increased fluid loss wnegates the predicted pressure increase. The potential for height increase is shFig. 8.17, where the fracture penetrates a section of higher stress at a constant grate. As additional height is generated, the cross-sectional area of the fracture incrthus reducing the flow velocity and frictional pressure drop down the fracturereducing the normal pressure increase. If height growth continues and reachesstress zone, as seen in the figure, the pressure:time slope may become negative,ing uncontrolled, rapid height growth (Mode IV). This type of behavior is discuslater on page 8.19. The other variable that can change besides∆H, without violating thecontinuity equation isqLoss (fluid loss). One mechanism for a higher fluid loss rawould be opening of natural fissures intersected by the main fracture as showFig. 8.18. The opening of natural fissures increases fracture volume and fluid lossand decreases the pressure in the fracture. When pressure declines below theholding the fissures closed, the fissures re-close. Pressure then increases slightly afissures reopen, etc. This opening-closing-opening of the fissures is like a pressurulator, producing a constant pressure profile. Due to the increased fluid loss rate,II will normally be followed by undesired behavior such as a screenout.

Looking back at the continuity equation, if something occurs to stop fracture extension (i.e.,∆L =0), then either∆P or ∆H must increase. As shown in Fig. 8.18, increased fluid loss to naturalsures may dehydrate the slurry to the point that a proppant bridge forms in the fracture. If pumcontinues, no additional fracture penetration will occur. If the fracture is contained, pressureincrease at a higher rate as seen in cases 1 and 2 on Fig. 8.16. If the fracture is not containrate of height growth will increase and pressure will decrease with time as shown by casFig. 8.16. In the case where the fracture is contained and the pressure increases, this rapid pincrease is characteristic of Mode III behavior on the log-log Nolte-Smith plot, Fig. 8.21.

Q qLoss qFrac+=

Q qLoss K ∆P ∆H ∆L+ +[ ] ,+=



-logpro-por-me

well-etion(dis-

nt fall-

aturend. Duepoint”the

Mode III - This behavior is characterized by a region of positive unit slope (i.e., 1:1 logslope), indicating a flow restriction in the fracture. This implies that the pressure isportional to time or, more importantly, that the incremental pressure change is protional to the incremental injected fluid volume. This 1:1 slope is similar to the saslope in Pressure Transient Analysis, indicating storage of fluid, in this case by sing or ballooning the fracture. Common causes of this behavior are pad deplwhere proppant reaches the fracture tip, slurry dehydration to natural fissurescussed above), excessive height growth increasing fluid loss area, and/or proppaout due to poor gel quality.

Fig. 8.19 shows how excessive height growth can cause slurry depletion resulting in a premscreenout. The fracture has grown through a shale section into a lower closure pressure sato the higher stress in the shale, the fracture width is less than in the sands forming a “pinchwhich will not allow sand to pass through, yet allows fluid to pass, dehydrating the slurry in

Fig. 8.17 - Height vs. Net Pressure for Multizone Geology.

Fig. 8.18 - Effect of Natural Fractures, Critical Pressure Causes Increased Fluid Loss.

P + S < σ : I P + S > σ : IIP V 1/1 Slope“Screenout”: III

Regulator



ure.

treat-high

ely be

tained,slope

tressficantore of

newngthatible

highly aease

target interval. As the slurry dehydrates it forms a plug which will eventually bridge in the fractThe approximate distance to the bridge can be calculated from:

whereQ = pump rate (bpm),E' = modulus (psi),H = frac height (ft), and∆p/∆t = rate of pressureincrease (psi/min). This information can be useful in postanalysis and the design of futurements. A near-wellbore bridge would likely be caused by natural fissures, height growth, or asand concentration slug; whereas a bridge some distance from the wellbore would more likdue to pad depletion, or sand fallout due to poor gel quality.

As noted previously on page 8.14, if fracture extension ceases and the fracture is not conthen rapid, unstable height growth will occur as pumping continues and the pressure:timewill become negative. This is Mode IV behavior as seen during case 3, Fig. 8.16.

Mode IV - A negative slope can be interpreted as rapid height growth into a lower closure szone. Referring back to the continuity equation, discussed on page 8.17, a signidecrease in pressure must be accompanied by a significant increase in one or mthe other variables. A significant increase in fluid loss is possible from openingfractures or fissures, but is not likely with decreasing pressure. An increase in leis not consistent with a decrease in pressure. The only change which is compwith a decrease in pressure is an increase in height.

The steepness of the negative slope would imply the rate of unstable growth. Arate of growth would exhibit a steep slope, while a low negative slope would implow rate of growth. If the fracture grows into a much lower stress zone, the decr

Fig. 8.19 - Example of Height Growth Directly Leading to Premature Screenout.

Log WidthTop

Top

Rmax xf max– 1.8QE'

H2∆p/∆t

----------------------= =



neg-

ck ofents

ion ofshown

. As anitialbeginscase,

turelete

n mind

re vs.h or athe

ntialcritical

in pressure will be rapid. If the fracture grows into a slightly lower stress zone theative slope will be shallower.

A negative slope observed from the beginning of the treatment indicates a laheight confinement. In this case the fracture will grow radially and future treatmshould be designed using a radial model.

While the observed pressure behavior on the net pressure vs. time plot is primarily a functfracture geometry, other parameters may interfere with interpretation. These parameters arein Fig. 8.20, clearly showing that an increase in rate or viscosity will increase net pressuresimple example of this, consider the plot in Fig. 8.21 for a gelled oil fracture treatment. The ideclining pressure indicates unconfined fracture height, and then after 9 minutes, pressureto increase. This might be interpreted as a change in fracture geometry but, for this simplethis is simply the time when gelled fluid is on the perforations. After 4 or 5 minutes, the fracis filled with this new, higher viscosity fluid, and pressure again begins to decline. Comprecords of treating parameters must be kept, and what was happening during a job borne iwhen interpreting net pressure behavior.

Critical Pressure

As mentioned in the previous discussion on page 8.17, Mode II behavior on the net pressutime plot is usually followed by some undesirable behavior such as excessive height growtscreenout. For this reason, the net pressure where the pressure:time slope flattens is termedcrit-ical pressure. For the case of height growth, critical pressure is roughly 70-80% of the differeclosure stress between the initial zone and bounding beds. When natural fissures exist,

Fig. 8.20 - Variables Affecting Fracture Pressure.

±

“P & K”Confined Height

Fracture

Unconfined Height“Penny” Shaped

Fracture

Elasticity

Fluid Friction

Combining

WHE--P∼ W

RE--P∼

W µQLE--( )1 4/∼ W µQ

RE--( )1 4/∼

PE1 4/

H--------- µQL( )1 4/∼ P

E3 4/

R--------- µQR( )1 4/∼



l to the

earlysure,o keepf it isy pos-

pressure is approximately the net stress component (above closure pressure) acting normaplane of the fissures, holding the fissures closed.

In fieldwide studies, critical pressure has been found to be reasonably constant. During thedevelopment of a field, strategic wells should be monitored to determine the critical preswhich can then be extrapolated to offset wells. Treatment designs can then be formulated tnet treating pressure below the critical pressure, possibly by reducing viscosity or rate. Iimpossible to stay below critical pressure by these means, unconventional-type designs masibly be developed to minimize height growth or screenout tendencies.

Summary of Nolte-Smith Slope Analysis

Fig. 8.21 - Viscosity Effect of Nolte-Smith Plot.

Small (1/8 to 1/4) Positive SlopeContinued height or restricted height growthUnrestricted extension

“Normal” C/ fluid loss

Flat Slope - Constant Net PressureCRITICAL PressureIncreased Height GrowthIncreased Fluid LossReduced Rate of Fracture Length Extension

Rapidly Increasing Pressure - 1:1 SlopeRestricted Fracture Extension, e.g., Screenout

Negative Slope - Declining Net PressureUnconfined Height Growth

Pump Time (minutes)

Net

Pre

ssur

e (p

si)

time



a veryssure(e.g.,latingunt fordownpecially

and in

. 8.22.ording.e mea-rationwhichonfigu-r, withhe lastoratedata isniques,sign ordetail

ter side.

andjectioneriod-andusly. Ife, the

runas the

ssion

BHTP Measuring Techniques

To perform a meaningful analysis of fracturing pressures requires direct measurement oraccurate calculation of bottomhole treating pressure (BHTP) during the injection and predecline. The primary objective is to record the fluid pressure at the entrance to the fracturejust outside the perforations). While several companies have developed software for calcuBHTP from surface pressure, to date no technique has been developed to accurately accoall variables affecting friction pressures. In some cases of shallow wells, where injection waslarge casing, these programs have given reasonable results. But, in deeper wells, and esthose where the fracture treatment was pumped down tubing, results have been erroneousmany cases have led to incorrect decision making during the treatment.

Three techniques which are recommended for measuring fracturing BHTP are seen in FigThe first configuration uses a tubing string with an open annulus and a surface pressure recThe treatment is pumped down the tubing or casing, with the other side static. Pressures arsured on the static side and corrected for hydrostatic pressure to obtain BHTP. This configuis applicable if the fracturing pressure is greater than the hydrostatic head on the static side,is usually the case except in severely underpressured or depleted reservoirs. The second cration involves running the pressure sensor inside a side-pocket mandrel, above a packepressure transmitted to the surface via an electric line fastened to the outside of the tubing. Ttechnique is running a downhole recording pressure gauge inside a tail pipe below a perfjoint and packer. With this technique real-time access to the data is not possible. The daccessed after the treatment, when the pressure recorder is retrieved. With the first two techon-site computers can be used to manipulate and analyze the data for fracture treatment deto make on-site judgmental decisions during the treatment. The following describes in morethe procedures for using these three BHP measurement techniques:

1. Open-Ended Tubing- Run tubing (no packer) to within 100 ft of the perforations. Circulaout any gas so as to leave a liquid filled static column, whether this is on the tubing or annulaGas in the static column will reduce the hydrostatic head from which BHTP is calculatedreduce the accuracy of the true BHTP due to gas compression and expansion during the inand shut-in periods. The density of the fluid used to circulate the hole should be measured pically, so the hydrostatic head of the static column will be accurately known. During testingthe actual fracture treatment, both tubing and annular pressure should be recorded continuoinjecting down the annulus, the tubing pressure will reflect bottomhole pressure and likewisannular pressure will reflect BHTP when injecting down tubing.

2. Surface Recorded BHP Gauge- A side pocket mandrel containing the pressure gauge isabove the packer. The wireline for the pressure gauge is strapped to the outside of the tubingstring is run in the hole, and a port from the mandrel to the inside of the tubing allows transmiof pressure to the gauge. This type system is commercially available.



owto toprfo-repares are

a slicktment,b or

Thishe prop-ave a300cussed

ent arec, etc.,For theonds ishavemay

3. BHTP Gauge Tail pipe Assembly- In this configuration, the pressure gauge is placed bela perforated joint and packer in a tail pipe assembly. The complete assembly from bottomwould consist of a joint of tubing with a “NO-GO” nipple at the bottom, a seating nipple, a perated sub, and a pup joint below the packer. The most reliable and least expensive way to pthe perforated sub would be to drill the holes in a machine shop. This would ensure all holeopen, large, and properly spaced. The BHTP gauge would be run into the seating nipple online, and the treatment pumped down the tubing and out the perforated sub. After the treathe bomb could be retrieved with a slick line by latching into a fishing neck on top of the bomby pulling the tubing string.

BHTP Measuring Devices

During prefrac testing, a BHTP gauge can be run on wireline to just below the perforations.procedure cannot be used on the main treatment, though, because of damage caused by tpant to the wireline. Many wireline companies can supply quartz pressure gauges which hpressure range of 0-12,000 psi, a resolution of 0.01 psi, and an operating temperature up to°F.This same type gauge can be run in the side pocket mandrel assembly in the previously disconfiguration #2.

Accurate pressure measurements during prefrac testing and the actual fracture treatmrequired for useful analysis and evaluation. For prefrac tests, i.e., closure pressure, minifrapressure resolution to nearest 2 psi and 10 second data acquisition is normally adequate.main treatment pressures recorded to the nearest 5 psi, one data point every 20 to 30 secsufficient. In-line pressure transducers normally supplied by the fracturing service companiesproven to be unreliable for this type work. Aside from the resolution of the transducers, they

Fig. 8.22 - Well Configurations for Recording Bottomhole Treating Pressure.

PtQt

PaQa

Qt - 0

Pt - BHP-Pnor

Qa - 0

Pa- BHP-Pn

WIRELINE

SIDE POCKETMANDRIL

PRESSURESENSOR

MANDRILPORT

PACKER

Q Q

PACKER

PERFORATEDSUB

(BLAST JOINT)

PRESSUREBOMBSEATINGNIPPLENO-GO NIPPLE

( ) (b) ( )

1 2 3



usually
not be accurately calibrated. Given adequate notice, however, service companies canobtain the precision-type transducers required.

Pressure Decline Analysis

nt, thisangeation

ownress-

ctoriencyry) to

-filledd from

P-V-Trection),

8.4 Pressure Decline Analysis

Prior sections presented an analysis of injection pressure behavior during a fracture treatmebehavior being a function of several variables, height, length, leakoff rate, etc., all of which chwith time. However, shortly after pumping stops, the fracture stops growing and a simpler situexists, e.g.,Q, ∆H, and∆L become zero in the continuity equation,

(8.1)

leaving the rate of pressure decline,∆pnet, proportional to the rate,qLoss. From pressure declineanalysis, values for fluid efficiency and fluid loss coefficient can be determined as will be shin this section. Note that while the equation above contains a term for changes in fluid compibility, Cp, this effect will not be included in this discussion. In general, this is not a major fafor pressure decline analysis. The analysis of the pressure decline for fluid loss and fluid efficis then combined with the Nolte-Smith analysis of treating pressures (for fracture geometgive a complete description of the fracturing process. Note -neither analysis can truly standalone, they are complementary and must be used together to describe the process.

The pressure-volume, P-V, relationship of a fracture can be thought of as analogous to a fluidelastic membrane (e.g., balloon) as depicted in Fig. 8.23. The fluid volume can be determinethe pressure in terms of the membrane's stiffness - fracture stiffness,S, being a function of fracturegeometry and the elastic modulus of the formation(s). If the balloon develops a leak and therelationship is known, then the rate of fluid,qLoss, can be determined from the rate of pressudecline. Since the fracture system is much simpler after shutdown (as opposed to during injee.g., only two variables changing with timeP andV, it is possible to solve for these variables.

Fig. 8.23 - Volume Relationship of Fracture, Analogy to Balloon.

Q qLoss LpnetCH( ) ∆L/L ∆ pnet/pnet ∆Cp/Cp ∆H /H++ +( ) 1∆t-----+=



-wsrima-

sion

ureo flowcture.

ure as

or

Fracture Stiffness

Fig. 8.24 shows equations used to describe fracture stiffness,S, for both a confined height fractureand a fracture with radial geometry. For both geometries,S is proportional to the crack openingmodulus,E', and either fracture height,H, or fracture radius,R, or for a Geertsma fracture geometry, to fracture length,L. As shown in the figure for the confined height case, if the fracture grointo a bounding formation, the fracture stiffness, and thus pressure decline analysis is still prily dependent on the initial fracture height.

Knowing fracture stiffness, the fracture P-V relationship can be calculated from the expres

(8.2)

wheredpnet is the change inaveragepressure in the fracture. Unfortunately, only wellbore presscan be measured, and even though the fracture has stopped extending, fluid will continue tdown the fracture and wellbore pressure will be higher than the average pressure in the fraThus, a termβ is defined which relates wellbore pressure to the average pressure in the fract

(8.3)

Fig. 8.25 provides graphs for determiningβ for a confined height fracture. For a radial fracturea short Geertsma geometry fracture,β will be approximately 1.

Since the rate of change in fluid volume,dV/dt, is equal to the fluid loss rate,qLoss, Eq. (8.2) canbe rewritten as

, (8.4)

whereqLoss is a volume loss term and thus, negative to the system.

Fig. 8.24 - Width/Pressure Relations for Two Common Fracture Geometries.

dVdt------- A β

S---------= d pnet/dt

pavg β pwell .=

qLoss A β/S( )d pnet/dt–=



the

een

d,

e

rring,eral, ofsis of

Fluid Loss Rate

For most hydraulic fracturing situations, the rate of fluid loss is governed by linear flow intoreservoir, and expressed by the relationship

(8.5)

wherevLossis the fluid loss velocity over an incremental area of the fracture,da; C is the fluid losscoefficient; andτ(a) is the time when the area was created. The final relationship then betwfracture stiffness,S, rate of pressure decline, andC, the fluid loss coefficient, will be termed∆P*as discussed on page 8.30. Note, despite the similarity in terminology with a Horner plotP*, the∆P* value for fracture pressure decline analysis has no relation to reservoir pressure. Instea∆P*is simply related to the rate of pressure decline following an injection at fracturing rate.

Assuming linear flow or “Carter” type24 fluid loss, and referring back to Eq. (8.5), the total volumrate of fluid loss,qLoss, can be found from

(8.6)

e.g., integrating the fluid loss velocity over the entire fracture area with the factor of 2 occusince the fracture has two “sides.” Obviously, to reduce this to any usable form, the unknownτ(a)(e.g., the time when each element of the fracture area was created) must be known. In gencourse, this is not a simple, or a known function, and if this is an important factor, then analy

Fig. 8.25 - β Ratio of Average Pressure in Fracture to Wellbore Pressure, After Shut-In, for aConfined Height Fracture.

vLossC

t τ a( )–[ ]---------------------------=

qLoss A2Cda

t τ a( )–[ ]---------------------------∫=



func-ce. Forll

the fracturing pressure decline data will become of limited usefulness. However, while thistion is not known, it can be bounded and these bounds can be used to test the importanexample, as shown by Nordgren,23 Geertsma,4 and others, for very low fluid loss, fracture area wigrow approximately linearly with time,

(8.7)

while for very high fluid loss, fracture area will grow with the square root of time

(8.8)

as illustrated in Fig. 8.26.

As an example, consider a low fluid loss case,A ≈ t, or

whereA is the total fracture area created at the end of the pump time,tp, and 'a' is a small incre-mental fracture area that was created or opened at timeτ, τ < tp. This gives

or

Fig. 8.26 - Fracture Growth with Time.

A t , Low "0"( )Loss≈

A t , High "∞"( )Loss≈

Time

Are

a

aA--- τ

t p----=

saA--- t p=

qLoss2Cda

t A/a( )t p–[ ]-----------------------------------∫=



s lea-ea,

w thes freerve int very

e pres-

which can be integrated from area=“0” to area = “A” to give the rate of fluid loss,qLoss, for timesgreater than (or equal to)tp. This integration gives

or

where time,t, equalstp+ts (e.g., pump time + shut-in time) andδ = ts/tp.

Similarly, for high fluid loss, Eqs. (8.6) and (8.8) can be integrated to give

or, more generally,

(8.9)

where

and a new parameter,rp, has been added for cases where only a fraction of the fracture area ikoff area. That is,rp is the ratio of permeable area opened by the fracture to total fracture ar

The time behavior of the fluid loss rate is determined by f(δ)

and these two functions are plotted vs. dimensionless shut-in time,δ in Fig. 8.27. The similaritybetween the two time functions seen in the figure indicates that an EXACT knowledge of hofracture grew with time is not necessary for the decline analysis - so long as the fracture wato extend, e.g., no screenout condition occurred. For example, consider the dashed cuFig. 8.24, showing an ideal fracture area vs. time behavior for a treatment which screens ouearly. For this case, fracture area stops increasing early during the pumping. Thus, during th

qLoss2AC

tp-----------2 t t t p––{ }=

qLoss2AC

tp

-----------2 1 δ+( ) δ–{ }=

qLoss2CA

tp

----------- sin1– 1

1 δ+( )---------------------

=

qLoss

2CrpAf δ( )

t p

----------------------------=

δ ts/t p e.g., Shut-in Time/pump time( )=

r pPermeable Fracture Area

Total Fracture Area------------------------------------------------------------ .=

f δ( ) 2 1 δ+( )1/2 δ1/2–{ } Low Fluid Loss–=

sin1–

1/ 1 δ+( )[ ] High Fluid Loss–



ationerrone--owththus

loss

with a

avior

sure decline, all of the leakoff area is “old,” leading to lower than expected leakoff and applicof the pressure decline analysis to the postpumping pressure behavior would calculate anously low fluid loss coefficient. Finally, note that Fig. 8.27does notindicate that there is no behavior difference between high and low fluid loss cases. Merely just that the exact time-rate-of-grof the fracture while pumping is not a dominant factor, and that postfrac fluid loss rate (andpressure decline behavior) is a function of fluid loss coefficient,C, pump time,tp, and the total cre-ated fracture area,A.

∆P* - Pressure Decline Analysis

Going back to the basic pressure decline behavior Eq. (8.2) and combining this with the fluidrate from Eq. (8.9) gives

(8.10)

or

(8.11)

and this gives a definite relation between fracture stiffness,S, fluid loss coefficient, and postfracpressure decline. If pressure decline were a linear function of time (e.g.,dp/dt= constant), then therelation could be characterized with a simple “psi/minute.” For example, assume a casepump time,tp, of 20 minutes. If 10 minutes after pumping is stopped, e.g.,ts = 10 orδ = 0.5, therate of pressure decline,dp/dtwas 5 psi/minute, then, from Fig. 8.25,f(δ) ≈ 1. If the fracture stiff-ness were known, then Eq. (8.11) could be solved for fluid loss coefficient. However, the beh

Fig. 8.27 - Bounds on Rate of Fluid Loss Function (bounds are less than 10% different after shut-intime equal to 1/4 of pump time).

qLoss2AC

tp

----------- r p f δ( ) AβS

-------d pnet/dt–= =

d pnet/dt–2CS

β t p

------------ r p f δ( )=



eline.loss,

.

n-e

er-

r

is more complex than this, and a value, defined as∆P*, will be used to describe the pressurdecline behavior. Basically,∆P* is a single value which characterizes the rate of pressure decA high value indicates a rapid pressure decline, which would usually correspond to high fluidhowever, it might also correspond to a very stiff formation. Thus we see that∆P* does not directlydescribe fluid loss, but rather it will be seen to specify a relation between several variables

Unfortunately, the rate of change of pressure,dpnet/dt, is hard to measure and use, making it covenient to integrate the pressure decline,dpnet/dt, to convert Eq. (8.11) into a pressure differencform. Clearly integratingdp/dt from time =to to time =to + ∆t

gives a pressure difference

whereto (or δo) is just a convenient “marker” time or starting time for calculating pressure diffences.

Simultaneously, the right hand side of Eq. (8.11) is integrated fromto to a later time,t giving

where the “G function,”G(δo,δ), is defined as

and arises from integrating the time function,f(δ), controlling the postfrac rate of fluid loss. Foexample, for the low fluid loss (high efficiency) limit,g(δ) is given by

while, for the high fluid loss (low efficiency) limit,

Finally, redefining the variable group (πC rp S)/(2β) as∆P* gives

(8.12)

dpdt------dt–∫ ∆p p t=to( ) p to ∆t+( )+= =

∆p δo δ,( ) p δo( ) p δ( )–=

∆p δo δ,( ) p δo( ) p δ( )–pCS2β

----------- r p t p G δo δ,( )= =

G δo δ,( ) 4π--- g δ( ) g δo( )–{ }=

g δ( ) 43--- 1 δ+( )3/2 δ3/2

–{ } ,=

g δ( ) 1 δ+( )sin1– 1

1 δ+( )--------------------- δ+=

t p

∆p δo δ,( ) ∆P* G δo δ,( ) ,=



ure

ashe fol-

ant)e pres-

andurfaceafter a

-om-

indicating that the variable∆P* is simply a multiplier which best matches the actual pressdecline behavior to the theoretically perfect behavior defined by “G ,”

Type Curve Analysis

The actual value for∆P* is found by creating theoretical type curves from the “G function” (seen in Fig. 8.28) and then matching the actual data to these curves. This is illustrated in tlowing example.

Consider a case where a “minifrac” (e.g., a volume of fracturing fluid pumped without propphas been pumped down tubing while measuring surface annulus pressure. After shut in, thsure decline is measured as seen in Fig. 8.29 and tabulated in the table below.

The first step in any pressure decline analysis is to determine the fracture closure pressureclosure time. For the example here, it is assumed that pre-minifrac stress tests indicated a (sequivalent) closure stress of 1500 psi. The minifrac pressure decline reaches this pressureshut-in time,ts, of about 26 minutes - giving a closure time,tc, of 26 minutes. This gives a dimensionless closure time,δc, of 1.3, with, since no proppant was pumped, the fracture being cpletely closed at “closure time.”

Fig. 8.28 - Plot of G( δ,δo), Master Curves for Matching Pressure Differences.

∆P*πCS2β

----------- r p t p .=



Fig. 8.29 - Example, Minifrac Pressure Decline Data.

Table 8.2 - Example Pressure Decline Data.

Shut-inTime (min)

Pressure(psi)

P(to=4,t)(psi)

P(to=10,t)(psi)

P(to=20,t)(psi)

0 1658

2 1.4 1642

4 2.0 1625

6 2.47 1610 1625-1610

= 15 psi

8 2.83 1595 30

10 3.16 1582 43

12 3.46 1569 56 13

14 3.74 1558 67 24

16 4.0 1544 81 38

18 4.24 1534 91 48

20 4.47 1525 100 57

22 4.69 1515 110 67 10

24 4.90 1507 75 18

26 5.10 1498 84 27

28 5.29 1493 89 32

30 5.48 1486 96 39

32 5.66 1481 101 44

34 5.83 1476 106 49

ts∆ ∆ ∆

δc tc/t pShut-in Time at Closure

Pump Time--------------------------------------------------------------

2620------.= = =



s thanure clo-” andeis

time of” startureves) oned” to

urvestart

thecy,

the

In selecting the “start” times for the pressure difference analysis, all start times must be lesthis dimensionless closure time since the analysis has no meaning for pressures below fractsure pressure. Referring to the “type curve” of Fig. 8.28, one might select the “0.2,” the “0.5,the “1.0” curves, since the dimensionless start times,δo, for these curves all come prior to thdimensionless closure time ofδc = 1.3. For theδo = 0.2 curve, the corresponding “real” start time

e.g., dimensionless start time,δo, timespump time.

Thus a column of pressure differences is created (as seen in Table 8.2) starting at a shut-infour minutes. Similarly, a column of pressure differences is created corresponding to a “realtime of 10 minutes (to = δo x tp = 0.5 x 20) and to a “real” start time of 20 minutes. These pressdifference values are then plotted vs. shut-in-time (as three separate and independent curlog-log scales identical to the type curve scales as seen in Fig. 8.30, and the data is “matchthe theoretical curve.

Note, however, that the theoretical type curves include two “sets” of curves: three “dashed” cfor dimensionless start times ofδo = 0.05, 0.10, and 0.20; and “solid” curves for dimensionless stimes ofδo = 0.20, 0.50, 0.75, 1.0, and 2.0. The “early time,” “dashed” curves correspond tolow efficiency solution, while the “later time,” “solid” curves correspond to the high efficiene.g., low fluid loss, solution. Closure time, found by plotting the pressure decline vs.

Fig. 8.30 - Type Curve Match for Example.

to δo t× p 0.2 20× 4 minutes .= = =



ses atr aer thanea inutes)

rpolate

ion of

ses theis one timer anal-

,“sur-

0 plus

le of aking

square-root of shut-in time, is used to determine which type curves to use. If the fracture cloa dimensionless time less than 0.5 (δc < 0.5), e.g., a fracture closing in less than 30 minutes afte1 hour pump time, then the high curves (dashed) should be used. For closure times greatpump time, the low curves (solid) should be used. For cases which fall into the gray arbetween these limits (e.g., maybe a closure time of 30 minutes after a pump time of 40 minthe curves which best match the “shape” of the data should be used, and/or one might intebetween the two sets of theoretical type curves.

'G' Function Plot for ∆P*

Eq. (8.12) showed a linear relation between the pressure decline “differences” and a functshut-in time - the'G' Function. As a special case for using this equation, a “start time,”δo, of “0”might be chosen, then Eq. (8.12) could be rewritten as

whereISIP is the Instantaneous Shut-In Pressure. This leads to

or

That is, the slope of a linear plot of the shut-in pressure decline vs.'G' (as defined earlier) givesthe “match pressure”∆P* .

Since this'G' function is generally a complex function of the dimensionless shut-in time,d, the'G'Function Plot is clearly most amenable to computer generated analysis. Also, in several ca'G' function has been found to work better for very high fluid loss cases where closure timethe order of 20 to 30% of pump time or less. For cases with longer closure times, e.g., closur40% (or more) of pump time, the type curve approach discussed above often offers an easieysis.

For the previous example, the pressure decline data is plotted vs.'G' in Fig. 8.31, where, as beforeclosure stress is assumed known from minifrac tests to be 1500 psi. (Actually, this would be aface equivalent” closure pressure, with “real” closure pressure equal to 4530 psi, e.g., 150the hydrostatic head of±7000 ft of water.) At any rate, in the'G' Function Plot, the slope of thedata is taken just prior to closure pressure, though for this plot (which is an excellent examp'G' Plot) the slope is relatively constant from shut-in all the way down to fracture closure. Tathe slope of the indicated line shows a slope of -98 psi, which gives∆P* = 98 psi, essentially per-fect agreement with the earlier type curve match analysis.

∆p 0 δ,( ) ISIP p δ( )– ∆P* G 0 δ,( )= =

p δ( ) ISIP ∆P* G 0 δ,( )–=

∆P* dp/dG .–=



rere isa dis-

fluida case

effi-t.

imits,thesetween

clinef fluid

i-8.32.

This plot also shows a distinct slope change at a pressure of±1500 psi, e.g., just at closure pressuand sometimes, a'G' Function Plot can be used to determine fracture closure. The procedusimilar to a root-shut-in-time analysis for closure, a distinct slope change is taken to indicatetinct fracture behavior change, e.g., the fracture closing. Again, as with'G' Function Plot analysisin general, we have found this analysis procedure to be most useful in low efficiency (highloss) environments - though clearly this example shows a very clear 'G' Function analysis forwith closure time equal to 1.3 times pump time, e.g.,δc = tc/tp = 1.3.

A final note concerning 'G' Function Plots is - What 'G' Function should be used? For lowciency (high fluid loss) cases whereδc < 0.4 to 0.5, clearly the low efficiency function is correcSimilarly, for longer closure time cases withδc > 1, the high efficiency (low fluid loss) function asused for Fig. 8.31 is probably most correct. However, for the “gray” area between these lsome distortion and error can be introduced by the lack of a purely applicable 'G' Function. Incases, type curve analysis often proves superior by allowing easy, manual interpolation bethe two limiting theoretical solutions.

Fluid Efficiency

Fluid efficiency is defined as the fracture volume (at the end of pumping, e.g., at time =tp) dividedby the total slurry volume pumped (e.g., fluid, sand, everything). As an aid in Pressure DeAnalysis, the rate of pressure decline equation can be integrated to determine the volume olost between shut-in,tp, and the time at which the fracture closes,tp + tc. For a minifrac treatment,e.g., a small volume calibration treatment with no proppant, the volume lost betweentp andtp+tcequals the volume of the fracture attp. Dividing this volume by the total volume injected gives effciency. Thus, a relationship between closure time and fluid efficiency exists as shown in Fig.

Fig. 8.31 - ‘G’ Function Plot.



to

l fis-s-

cline

y

The efficiency,ef, obtained from this figure is used to define a new variable,ρ, which is used inthe type curve analysis and defined as

whereVf is fracture volume andVL is fluid loss volume during injection.ρ can also be determineddirectly from the type curve analysis in terms of the match pressure,∆P* , and the net fracturingpressure at shut-in,ps (e.g.,ISIP - closure pressure).

whereGo is the pressure difference function atδ = 0 (discussed on page 8.31) and equal1.57-0.238ef (within 5%, Go = 1.45), andK is a correction to the fluid loss coefficient whichaccounts for additional fluid loss only during pumping (e.g., spurt loss or opening of naturasures during injection). However,K cannot (at this time) be determined from any analytical presure decline analysis so shouldalways be set equal to “1.”

These “two” efficiency values supply a means of quality control for fracturing pressure deanalysis. First, efficiency is determined from the dimensionless time-to-close,δc and the graph inFig. 8.32. Next, the loss ratio,ρ, is determined from the type curve match pressure,∆P*, and thefinal net pressure,ps, as discussed above. This value forρ is then used to calculate an efficienc

Fig. 8.32 - Efficiency vs. Dimensionless Closure Time.

ρ V f /VL ef / 1 ef–( ), or= =

ef ρ/ 1 ρ+( ),=

ρ π ps/4Kgo∆P* ,=

go 1.57 0.238 ef (within 5%,go×– 1.45),= =



achreatergree-

the the-lose

h arealysises (forl frac-

roce-Also,e pres-

to cal-

in theted and

ssureethickrface

20,000essure

, 6-8us of

thesefluid

from ef = ρ / (1 + ρ). These efficiency values should be within 2 to 3 “percentage units” of eother, e.g., 10% vs. 12% would be good agreement as would 90 vs. 92%. If the difference is gthan this, then one might initially check the analysis, choice of closure pressure, etc. If disament persists, then it may indicate a real discrepancy between actual fracture behavior, andoretical assumptions which form the basis for decline analysis. If the efficiency from time-to-cand the chart in Fig. 8.32 is less than the calculated efficiency (e.g., calculated from∆P*), the dis-crepancy could be due to significant spurt loss and/or to fluid loss to natural fractures whicopen during injection but which close (or are closing) during the pressure decline. Decline ancannot quantify this loss, but can indicate its existence and thus allow appropriate job changexample, possibly the inclusion of 100 mesh fluid loss additive to reduce any loss to naturatures).

In addition to this quality control procedure for the decline analysis, Section 8.6 presents a pdure for determining a fracture treatment design schedule based solely on fluid efficiency.efficiency corrections are presented to account for proppant in the fracture at closure, so thsure decline after an actual propped fracture treatment can be used in a type curve analysisculate fluid loss coefficient.

Example/Guidelines

The following will present some general guidelines for fracturing pressure decline analysiscontext of reviewing an actual field example. The pressure data is the same as that presendiscussed earlier in Fig. 8.29 and Table 8.2.

Example - Pressure Decline Analysis:

Prefrac tests were conducted on a 7000 ft deep oil bearing formation with a reservoir preof 3250 psi and a formation temperature of 240°F. The formation is a thick sand-shalsequence with 5-10 ft sandstone layers (porosity of 12 to 14%) interbedded with 1 to 3 ftlayers of low porosity siltstones and anhydrites. From pump-in/flowback stress tests, suclosure pressure was found to be 1500 psi. The stress tests were followed by pumping agallon crosslinked gel minifrac (estimated viscosity of±300 cp) in 20 minutes at an averagrate of 24 bpm. At the end of pumping the ISIP was 1658 psi and the postminifrac predecline data was shown in Fig. 8.29 (listed in Table 8.2).

Lab Tests show the sand to have a Young's modulus of 4 to 5 million psi; the siltstonesmillion; and the anhydrite, 8-10 million. Based on a simple volume percentage, a modul6 million psi is assumed to be representative of the formation.

Before proceeding with the example, some general guidelines are given in Table 8.3, andguidelines will be followed (essentially step-by-step) for analyzing this data and calculating aloss coefficient.



e.e mightis oftenarticu-aring., fluidessureange

Following the general guidelines, the first step isalwaysto determine fracture closure pressurFor this case, closure pressure was known as 1500 psi from pre-minifrac stress tests and onsimply assume that the fracture closes when the pressure declines to this value. However, ita good procedure to conduct a closure stress analysis with the decline data itself. This is plarly appropriate since into a liquid saturated formation (remembering that this is an oil beformation) can locally increase pore pressure and thus locally increase closure pressure, e.gloss can generate what is often referred to as “back stress.” Since this is an oil zone, the prdecline is first plotted vs. root shut-in time as seen in Fig. 8.33. This shows a distinct slope chat a pressure of 1500 psi, e.g., for this case the minifrac has not altered closure stress.

Table 8.3 - Guidelines for Analysis.

1. Must know when fracture closes (or closes on proppant)

a. pressure = known closure pressure

b. pressure vs. plot (ts is shut-in time)

2. Find dimensionless time-to-closec = Shut-in time-to-closure / pump-time (tc/tp)

3. Select 2 or 3 o values from master curves such that o < about 2/3 c

4. Convert o to real shut-in time, to = ( o) x (tp)

5. Find pressure differences for each toe.g., P(to,t) = p(to) - p(t), t > to

6. Plot a data curve for each toe.g., plot P(to,t) vs. t on log-log paper with same scale as Master Curves

7. Draw vertical line at t = tcdo not use data for matching after fracture closure

8. Draw vertical line at t = tp (shut-in time equal to pump time)

9. Place transparency of Master over data with vertical “PUMP-TIME” line on Master aligned withvertical “t = tp“line on data

10. Only moving master vertically , find best match for corresponding to curves- give most weight for greater to curves as these are least affected by any additional fracture extension- give more weight for longer times on each curve (but t < tc)

11. After match, read P* (match pressure) from pressure difference scale on left

12. Determine efficiency from

a. Find efficiency from c and “time-to-close vs. efficiency” chart

b. Use P* from type curve match and net pressure at shut-in(ps = ISIP - closure pressure) to calculate ef.

13. Compare ef (a) and (b)If similar within a 2-3 percentage units, proceed to determine and choose correct fracture model and then calculateother variables such as fluid loss coefficient, etc.

Pitfalls

1. Using pressure data after fracture closed.

2. Using equations for wrong fracture model.

ts

δδ δ δ

δ δ

∆

∆

∆

∆

δ∆



onless

, andurvesinutesces forub-tual

differ-axis vs.whichof(low

etre at

This plot also shows closure after about 26 minutes (also see Table 8.2) giving a dimensiclosure time of

and 2/3 of this value is about 0.9 - thus, referring to the type curves in Fig. 8.28, the 0.2, 0.51.0 curves might be chosen for analysis giving real “start” times for constructing the data cof 0.2, 0.5, and 1.0 times the pump time of 20 minutes, or real start times of 4, 10, and 20 mas seen in Table 8.2. As an example, the reference time for calculating the pressure differenmatching theδo = 0.2 curve would be a shut-in time of 0.2 times 20 minutes or 4 minutes. All ssequent pressures are subtracted from the pressure at 4 minutes (1625 psi) to get the ac∆pcurve for comparison to the type curve. This same procedure is followed for theδo = 0.5 and 1.0curves, giving three curves which are “best fit” matched to the master curves. The pressureences are calculated as seen in Table 8.2 and then pressure difference is plotted on the “y”shut-in time on the “x” axis of a log-log plot (with scales the same size as the master curves)is then matched with the theoretical curves as seen in Fig. 8.30. This gives a match pressure∆P*= 100 psi, noting that since closure time is greater than pump time, the “solid” high efficiencyfluid loss) curves are used to match the data.

The dimensionless closure time ofδc = 1.3 is then used with the efficiency chart, Fig. 8.32, to ga “time-to-close” efficiency of 47%. The match pressure of 100 psi along with the net pressushut-in,ps, of 158 psi (as seen in Fig. 8.33) is used to calculate efficiency as

Fig. 8.33 - Example Pressure Decline Data - Closure.

δcShut In– Time– To– Closure–

Pump Time---------------------------------------------------------------------------------- 26 / 20 1.3 ,= = =

ρ π ps/4KGo∆P* 3.142 158×4 1 1.45 100×××-------------------------------------------- 0.86= = =



est

is

can

pres-ssary

bedsatinghe low

oftenas seen

ere

eom-

where Go is assumed = 1.45,K = 1, and ef = ρ/ (1 +ρ) = 0.86 / 1.86 = 0.46.

Note: If this calculated efficiency was significantly different from 50%, it would probably be bto use this first calculated efficiency to recalculate go = 1.57 - 0.238 *ef, and then use thisnew value ofgo to find a new efficiency. It is seldom worthwhile, however, to follow thiteration for more than one time through.

This is clearly in excellent agreement with the “time-to-close” efficiency and thus the analysisproceed with confidence, e.g., there is no indication of “unaccounted for” fluid loss.

Note that up to this point, the analysishas been independent of fracture geometry, e.g., it madeno difference whether the fracture was radial, confined height, etc. However, once the matchsure,∆P*, and efficiency have been determined and the efficiency “checked,” then it is neceto assume a fracture geometry in order to calculate a loss coefficient.

For this example, one might initially expect no height confinement based on: (1) no discretewith sufficient thickness to contain a fracture, and (2) high modulus which leads to high trepressures and thus increases any tendencies for height growth. While it is not conclusive, tnet pressure at shut-in of 160 psi reinforces this expectation since confined height fractureshave higher net treating pressures than this. Equations from Table 8.5 can then be usedbelow:

First the radius of the fracture is found from

and this radius is then used to calculate a fluid loss coefficient and fracture width

and

Taking a look at this problem from a slightly different view, assume that postminifrac logs wavailable which gave indications of a gross fracture height of 350 to 400 ft. This value for‘H' mightthen be used in the equations for a confined height fracture (e.g., a Perkins & Kern fracture getry) as seen below,

xf0.134VG E'

2πK∆P* go 1 ρ+( )----------------------------------------------

1/3=

xf0.134( ) 20 000,( ) 6 10

6×( )2( ) 3.14( ) 1( ) 100( ) 1.45( ) 1.86( )

-----------------------------------------------------------------------------1/3

211 ft= =

C ∆P* xf( )/ rpE' t

p( )[ ] 100( ) 211( )/ 1( ) 6 106×( ) 20( ) 0.0008ft/ min= = =

w 6π psxf( )/E' 6( ) 3.14( ) 158( ) 211( )/ 6 106×( ) 0.10 inches.= = =



thepro-

6) or tothangives,

test.

dentr 'proce-

here, atpost-

d:

prop-par-

ussed

e injec-pos-turenet

er ap-sed toslope

closedecline

However, it is immediately noted that this gives a tip-to-tip length of 326 ft which is less thanapproximate fracture height of 350 to 400 ft; thus, the Perkins & Kern model would not be appriate, and the calculations should move on to the radial model (as discussed on page 8.2the Geertsma model calculations (which would be for a fracture with a tip-to-tip length lessthe height). For this example, the radial model shows a predicted radius of 211 ft which woulda total, gross fracture height ofH = 422 ft, and since this would be in fair agreement with the loga radial model would probably be the most appropriate geometry model for describing the

It is important to note in these calculations that there are several uncertainties; in particular, thefinal result for fluid loss coefficient (the usual goal for the decline analysis) is strongly depenon the value of modulus. If this value is not known from core analysis then the final result foC'becomes uncertain. In many cases, however, the final analysis can be improved through adure of pressure history matching as discussed in Section 8.3.

Post-propped-Frac Pressure Decline AnalysisFracture pressure decline analysis as presented above assumes a minifrac test injection, wclosure, a fracture will be completely closed. However, the same analysis is applicable topropped-fracture treatment pressure data, so long as two important points are remembere

1. After a propped fracture treatment, fracture closure occurs when the fracture closes onpant. However, at this point, of course, the fracture is not completely closed, but is heldtially open by the proppant. Thus the time-to-close efficiency must be corrected as discbelow.

2. The pressure decline analysis assumes that the fracture was free to propagate during thtion period. When proppant is included in a real stimulation there is, of course, always thesibility that due to slurry dehydration and/or proppant reaching the fracture tip, fracextension will be halted and a tip screenout will occur. This is usually evident from thepressure behavior and if such a condition occurs, then normal decline analysis is no longplicable. Note, however, that pressure history matching as discussed below can still be uanalyze the data with the time where the screenout starts (e.g., the beginning of the “unit”on a Nolte-Smith plot, Fig. 8.16) being a good marker for history matching analysis.

The time-to-close expressions previously presented on page 8.35, assumed the fracturecompletely, e.g., no proppant. Similar analysis can be performed from the postfrac pressure d

xf0.134VG E'

4K∆P* βxgo 1 ρ+( )H2--------------------------------------------------------=

xf0.134( ) 20 000,( ) 6 10

6×( )4( ) 1( ) 100( ) 0.65( ) 1.45( ) 1.86( ) 375 375×( )

---------------------------------------------------------------------------------------------------------- 163 ft .= =



Table 8.4 - Pressure Decline Analysis Calculations.

Perkins & Kern (Confined Height) Geometry Geertsma deKlerk Geometry

Radial Geometry (Unconfined Height Growth)

NOMENCLATURE

s - See discussion on reverse side of table

K - Correction factor for spurt loss, normally K = 1

C - Fluid loss coefficient (ft/

E' - “Plain Strain” Modulus = E / (1- 2) (psi)E - Young’s Modulus, - Poisson’s Ratio

ef - Fluid efficiency = Fracture-volume-at-shut-in / Volume-injected

go - Constant approximately = 1.45, (go = 1.57 - 0.238 ef)

Hp - Permeable or leakoff height (ft)

H - Gross fracture height (ft)

P*- Pressure decline Type Curve Match Pressure (psi)

Ps - Net pressure at shut-in (psi)

- “Loss Ratio” = Fracture-Volume-at-shut-in divided by Volume-lost-during-pumping = ef / (1-ef)

rp - Ratio of permeable or leakoff area to total fracture areaFor P&K or Geertsma rp = Hp / H, for a radial geometry rp is more difficult to define and is normally set = 1

tp - Injection time (minutes)

VG - Total Injected Volume in Gallons = Vp

w - Average fracture width (inches)

xf - Fracture 1/2 length or penetration (ft) (Radius for Radial Geometry)

x f0.134 VG E '

4K∆P *βsgo 1 ρ+( )H2

-------------------------------------------------= x f0.134 VG E '[ ]1/2

8K∆P *βsgo 1 ρ+( )H----------------------------------------------=

w 6πβs psH /E '= w 12πβs psx f /E '=

C ∆P *βsH( )/ r pE ' t p( )= C 2∆P *βsx f /r pt pE '=

x f0.134 VG E '

2πK∆P *go 1 ρ+( )----------------------------------------

1/3=

w 6πpsx f( )/E '=

C ∆P *x f( )/ r pE ' t p( )=

β

min

υυ

∆

ρ



ctive

re, the

if the propped volume of the fracture is taken into account. If proppant is considered, the effefracture volume that will close,Vf', can be written as

whereVf is the total fracture volume created andVpr is the volume of proppantincluding theporosity of the proppant. In terms of an apparent fluid efficiency,ef', e.g., the efficiency that wouldbe calculated based on closure time and not corrected for the propped volume of the fractuactual fluid efficiency can be expressed as

βs - Average Pressure Correction Factor

Pressure decline analysis is based on the average pressure in the fracture, but, unfortunately, the only value thatcan be monitored is wellbore pressure, which will tend to be slightly higher than the average pressure. The valuefor this correction factor is a function of fracture geometry and fluid rheology.

Geertsma deKlerk Geometry

For a fracture with this geometry, Daneshy showed in SPE publications that βp (the correction factor during pump-ing) is ± 0.85. After shut-in, the correction factor will be higher than this, thus 0.85 < βs < 1.0. Typically, a value of0.9 is used.

Radial Geometry

For a radial geometry (or “penny” shaped fracture), βs is near unity. For convenience in simplifying the precedingequations, βs was assigned a value of

Perkins & Kern Geometry

Perkins & Kern GeometryFor a confined height fracture, the correction factor can vary from 0.5 to 0.8, with a “typical” value of 0.65. Theexact value for a particular case is a function of the non-Newtonian character of the injected fluid, and a function ofhow much viscosity degradation occurs along the fracture during pumping. The non-Newtonian nature of the fluidis characterized by the fluid’s non-Newtonian, n', and this parameter might vary between 0.5 (for very non-Newto-nian fluids such as a Nitrogen foam) and 1.0 for an essentially Newtonian fluid such as a linear gel. The amount ofviscosity degradation is qualitatively associated with “a,” where a=1 indicates no viscosity degradation along thefracture, a=1 indicates “moderate” viscosity degradation, and a=2 indicates “severe” viscosity degradation from thewellbore out to the fracture tip. The pressure correction factor is found from these two parameters by

Typical Values for this factor are given below:

T(°F) n' a βs

Linear Gel - 60-80 1 1 0.6780-120 1 2 0.57

Crosslink Gel - 80-120 0.75 0 0.78140-180 0.75 1 0.64200-250 0.75 2 0.54

Nitrogen Foam - 80-120 0.5 1 0.60140-180 0.75 2 0.54

Gelled Oil - 100-140 0.5 1 0.60150-220 0.75 2 0.54

Table 8.4 - Pressure Decline Analysis Calculations.

βs 3π2/32 0.925 .= =

βs 2n' 2+( )/ 2n' 3 a+ +( ) .=

V f ' V f Vpr ,–=



the

tce

umpede clo-

sure

ffi-

asedt. The

ined in

wherefpr is the volume fraction of proppant pumped (including proppant porosity) relative tototal slurry injected and defined as

W is the proppant weight,ρpr is the specific weight of the proppant material, e.g., 165 lb/f3,2.65 gm/cc, 22 lbs/gallon for sand,φ is the proppant porosity (typically on the order of 0.40 sinthis refers to a proppant pack with essentially “zero” stress), andVp = Vfl+W/ρpr. For example,assume a fracture treatment containing 100,000 gallons of gel and 300,000 lbs of sand is pat a rate of 30 bpm. After the end of injection, the pressure decline is monitored and fractursure is detected attc = 45 minutes. The total volume injected is

SubstitutingVp into the equation forfpr,

Total pump time was 113,636 gallons/(42 gal/bbl)/(30 bpm) = 90.2 minutes and with a clotime of tc = 45 minutes, the dimensionless time-to-close was

This value ofδc = 0.50 is used with the time-to-close/efficiency relation to give an “apparent eciency” of 28%,

However, the actual efficiency must be greater than this since this “apparent efficiency” is bon closure on proppant, and, of course, the fracture is not completely closed at this poinactual efficiency is then found from

to be equal to 41%.

This efficiency of 0.41 is now used with the pressure decline data(prior to closure on proppant)to perform a type curve analysis using the same procedures discussed previously and outlTable 8.3.

ef 1 1 f pr–( ) 1 ef '–( ) ,–=

f pr Vpr/Vp W/ ρprVp 1 φ–( )( ) .= =

Vp 100 000 gals 300 000 lbs/(22 lbs/gal),[ ]+, 113 636 gals .,= =

f pr 300 000 lbs/ 22 lbs/gal( ) 113 636 gals,( ) 1 0.40–( )[ ], 0.179 .= =

δc 45/90.2 0.50 .= =

ef ' 0.28 .=

ef 1 1 f pr–( ) 1 ef '–( )–=

1 0.179–( ) 1 0.28–( )– 0.41 .= =



storyericalthe

equa-tainties

uations.

a

by the

ac-dulus,lyterde-

8.5 Pressure History Matching

The most powerful method of interpreting/analyzing fracturing pressure data is via the himatching of actual net treating pressure (and pressure decline) data - generally with a numfracture simulator. Another method of looking at this is - Calibrating the Fracture Model forparticular formation being studied. Also, whether a numerical model is used, or the simpletions below are used, some simple pressure history matching can overcome the uncerinvolved in fracturing pressure analysis.

These uncertainties mainly arise since there are essentially more variables than there are eqThe first of the two main equations can be represented by (from Section 8.3)

where the net treating pressure (and thus the value forps used in the decline analysis) is mainlyfunction of the modulus of the formation and the gross or total fracture height,H.

The second main “equation” is the pressure decline behavior which might be represented∆P* value

where'S' is the fracture stiffness which (for any fracture geometry) is primarily a function of frture height and the formation modulus. Thus there are three main variables or unknowns, moE, height,H, and fluid loss coefficient,C. The important pointhere is that since there are basicalthree unknowns and only two “equations,” these equations and any solution for them is in

Fig. 8.34 - Pressure History Matching

Pressure Decline(Fluid Loss; Sand Schedule)

Treating Pressures(Critical Pressure)

Simulator

Improved Designs

pnetE'H----- µQL[ ]3/4

=

∆P*πCS2β

-----------r p t p .=


Pressure History Matching

ves nolculatee fluide.

ta insmallistoryg pres-eightm the

sig-new

odu-how-lativelyely,

fferent

pendent. For example, simply solving the pressure decline equations for a loss coefficient giassurance that the answer is meaningful; i.e., is the modulus and fracture height used to cathe fluid loss consistent with the net treating pressure. If these values are consistent, then thloss coefficient determined from∆P* will be a reasonable (though possibly still not unique) valu

This history matching process is illustrated in Fig. 8.34. For an example, consider the daFig. 8.35. The Nolte-Smith plot of net treating pressure shows increasing pressure with apositive slope, indicating a confined height fracture and a numerical model was used to hmatch this data and thus determine a height and modulus consistent with the actual treatinsure behavior (with the modulus also being consistent with published industry data). This hand modulus can then be used with some confidence to calculate a fluid loss coefficient frodecline analysis. At this point, however, the calculated value for'C' might be different from thevalue used in the initial numerical modeling of the treating pressure, and if this difference isnificant (e.g., greater than 20 to 30% difference), the modeling should be redone with thevalue for'C', modifying the height and/or modulus values as required. The new height and mlus would be used to calculate a revised fluid loss coefficient, e.g., one would iterate. Note,ever, that it is very seldom necessary more than one time since the net treating pressure is rein- sensitive to a precise value for'C'. Because of this relationship (that net pressure is relativinsensitive to fluid loss), the history matching shouldalwaysbegin with matching the net pressurewith the modulus and height thus determined then used to calculate a loss coefficient .

With this history match, then, one has a set of three main variables (H, E, & C) which yield a gooddescription of the minifrac test. These can then be used with some confidence to consider di

Fig. 8.35 - Case History of Pressure History Matching



valuesred toeter-agree-

ng thepos-hed-hat hastimumavail-

ations

reasessider-

,

s as

nitiallye frac-yticalr exam-

treatment designs, larger/smaller volumes, etc. Note, however, that even though the threemay be “consistent” they are still not necessarily the correct values. External data is requifully determine the problem. For example, core data for the modulus might make this a fully dmined problem. For the case in Fig. 8.35, postfrac temperature logs showed a height in fairment with the history matching, making this a fully determined problem.

Simple History Matching

The use of a numerical model for pressure history matching offers many advantages includiability to handle fairly complex geology, the ability to simulate the entire history of a test, and (sibly most important) the ability to proceed immediately to considering different treating scules, treatment volumes, etc. Since these considerations are based on a set of data taccurately described the “past,” one can simulate other treatment designs and arrive at an optreatment with some confidence. However, in many cases an appropriate model may not beable, but, rather than abandon history matching, it is often possible to use quite simple equto gain some of the benefits achievable from detailed modeling and matching.

In particular, for a confined height fracture (e.g., a case where the net treating pressure incduring a job as seen in Fig. 8.35), treating pressure is generally dominated by fluid flow conations and can often be reasonably predicted (e.g., maybe within±10%). For a confined heightfracture, net pressure can be approximated by the following equation

(8.13)

(8.14)

whereµ is the average fluid viscosity (centipoise),'VG' is the total fluid volume pumped in gallons'Q' is the pump rate in bpm,'E' is the modulus in psi,xf is the fracture 1/2 length in feet,'H' is thegross fracture height in feet, and∆P* , ρ, etc., are determined from the pressure decline analysidiscussed earlier starting on page 8.30.

For other geometries such as an unconfined, radial fracture or a case where the fracture is iconfined but then experiences significant height growth, rock mechanics considerations at thture tip begin to play a more dominant role, often precluding the use of such simple, analequations. However, such equations can be developed and may sometimes prove useful. Fople, for a radial fracture,

pnet

0.015 E3µQxf[ ]

1/4

H---------------------------------------------=

xf0.134VG E

4K∆P* βsgo 1 ρ+( )H2-------------------------------------------------------=

pnet0.0078 QµE

3[ ]1/4

xf2/3

------------------------------------------=



com-

ture 1/2

tionedthis

cture

t data

t

modu-

ate oft

ionone

e

Simple History Matching Procedure & Example

The suggested procedure for use of such equations is a type ofsingle data point history matching.That is,ps, the final net pressure (e.g., ISIP minus closure pressure) is matched to determine apatible set of'H' and 'E' values to use in calculating fluid loss coefficient,'C'. These values formodulus and height are then used in the pressure decline equations to recalculate the fraclength,xf, and the loss coefficient. If these new values for penetration and'C' are significantly dif-ferent from the first values, it might be necessary to iterate one more time. However, as menabove, it is seldom necessary to iterate more than once. If the final height determined frompressure matching is consistent with the geology and/or possibly other log indications of fraheight; or if the modulus is consistent with core data; then the final three major variables (E, H,andC) can be used with confidence.

As an example, consider the minifrac studied earlier in Section 8.4, with some of the relevanfrom that case listed in Table 8.5.

Using this data in the radial fracture geometry calculation forpnet gives a predicted net pressure ashut-in (e.g.,ps) of 240 psi, somewhat greater than the actual measured value ofps = 158 psi.Remembering that the modulus was strictly an assumed value, one might then use a lowerlus, say 4x106 psi to calculate (still using the initial value forxf) a final net pressure of 178 psi, infair agreement with the actual data. This new modulus is then used to revise the initial estimfracture radius (xf), with a new calculated value ofxf = 185 ft, and a new calculated loss coefficienof 0.0010 ft/ . With this new fracture radius of 185 ft, and the new modulus of 4 millpsi, the new calculatedps is 195 psi, which is still about 20% greater than the actual data, thusmore iteration might be in order with a modulus of maybe 3.5x106 psi. At the end of that final iter-ation, a set of the three major variables (H, E, andC) would be determined which are compatiblwith the minifrac data. In addition, since the calculated fracture radius of±190 ft (which gives a

Table 8.5 - Minifrac Analysis Data.

Test Parameters

Volume=20,000 gallons tp = 20 minutesQ =24 bpm = 300 cp

Minifrac Analysis Parameters

K =1 ef = 0.46DP* =100 psi = 0.86

Pressure Decline Analysis Initial Results(Calculations for Radial Fracture Geometry)

E' =Assumed equal to 6x106 psixf =Calculated as 211 ftC =Calculated as 0.0008 ft/

xf0.134VG E'

2πK∆P* go 1 ρ+( )----------------------------------------------

1/3= .

µ

ρ

minute

minute



able

ol ford anal-e geo-

yersata or

fiablesome-the

suchcture

re wassurejectedwn,latingom-cern-whichobser-h dis-se.

anal-ressure

ern”

gross fracture height at the wellbore of 380 ft) is consistent with fracture height logs, it is probthat these values are a very good solution to the actual in-situ conditions.

Complex Geology Effects

Pressure analysis might be considered “proven” for simple geologies, making it a practical tomany (if not most) cases. In general, even, it might be stated that where the basic theory anysis methods break down - the problems are related to some more complex geology. Theslogic complexities can further be “categorized” into cases involving: (1) multiple formation laand (2) natural fractures. In fact, the bulk of the problems in analyzing fracturing pressure din utilizing the results of such analysis can be traced to one of these complicating factors.

The effect of natural fractures was discussed in Section 8.4, and this effect is often identifrom a constant net pressing pressure on a Nolte-Smith plot (e.g., a “critical” pressure) andtimes by comparing the type curve match efficiency with the efficiency derived directly fromtime-to-close.

The possible effects of multiple formation(s) layers is more difficult to categorize sincemulti-layered geology can lead to gross distortions and changes with time of the basic frageometry. As an example, consider the case pictured in Fig. 8.36, where a hydraulic fractuinitiated in one zone, but then penetrated a barrier and “broke into” a zone with lower clostress. During the remainder of the pumping, the lower stress zone will accept most of the influid. That is the “main” fracture will not be in the zone where the fracture started. After shutdohowever, one might expect the barrier between these two zones to close rather quickly - isothe perforated interval from the “main” fracture. Thus the pressure decline behavior will be dinated by the characteristics of the perforated zone, and may give little or no information coning the redirection of the fracture geometry, or the characteristics of the lower stressed zoneaccepted most of the injection. Possibly, though, such behavior may be inferred through anvation of some decline in the net treating pressure indicating the height growth combined witcrepancies between the∆P* derived efficiency and the efficiency derived from the time-to-clo

Another example of the effect of multiple layers might be seen in the “Big” pressure declineysis problem. The problem as described and several parameters determined from the pdecline analysis are included in table Table 8.6.

Using the simple history match equations from page 8.48 (for a confined height, “Perkins & Kgeometry since the net pressure for the minifrac increased indicating height confinement),

(8.13)pnet

0.015 E3µQxf[ ]

1/4

H---------------------------------------------=



(e.g.,t pres-s than

greatert to

wouldlus ofe

,

(8.14)

and the problem definition data from Table 8.6, one calculates a final net treating pressurenet pressure at shut-in) of 688 psi, 20% less than the actual value of about 860 psi. Since nesure is most affected by fracture height and modulus, either the fracture height must be lesthe gross zone thickness (e.g., less than 150 ft), or the modulus of the formation(s) must bethan 7x106 psi, or “?”. Since it might be unexpected (but not impossible) for the fracture heighbe less than the gross formation thickness, an initial approach to history matching this dataprobably be to increase the modulus. Doing this shows, after a couple of iterations, a modu9x106 psi giving a calculated final net pressure,ps, of 885 psi, in near perfect agreement with thactual data. The new calculated values forxf and 'C' are then 802 ft and 0.00075 ft/respectively.

Fig. 8.36 - Fracture Going Out of Zone.

xf0.134VG E

4K∆P* βsgo 1 ρ+( )H2-------------------------------------------------------=

minute



psita

fness

rma-f twores-r- andassumeacturectureually

lay-essureourse,of thet bef the

Thus the pressure history matching gives a set of three major variables ofH = 150 ft, E = 9x106

psi, andC = 0.00075 ft/ , which satisfy both the final net treating pressure of about 860and the pressure decline behavior of∆P* = 260 psi and efficiency = 62%. However, since core daindicated a modulus on the order of 7 million psi, what might explain the higher apparent stifof the formation(s)?

A possible answer to this might be seen in Fig. 8.37, which illustrates the “geology” of the fotion, showing that the 110 ft net height (out of the 150 ft gross section) is actually composed odistinct sandstone layers with±30 ft of shale separating the two zones. Since the increasing psure behavior during the minifrac seems to indicate good height confinement (e.g., the oveunderlying shales having higher closure stress than the sands), it might be reasonable tothat the “separating” shale might also be a barrier (e.g., have a higher closure stress) to frgrowth. Thus this shale would “pinch” the fracture width (as seen Fig. 8.37), causing the frato behave “stiffer” than a simple, 150 ft high fracture, thus explaining the need for an unushigh modulus if the basic pressure analysis methods are to be used.

Given this more complex geology, a fracture simulator capable of treating multiple formationers might be used to history match the actual data, as seen in Fig. 8.38 for the treating prbehavior. Once the model is successfully set up to “history match the past,” it can then, of cbe used with some confidence to design future jobs. Or, in fact, where the dominant effect“multiple zones” is to just stiffen the fracture, a simple “Perkins & Kern” type procedure mighused for frac design by using the artificially high modulus value to account for the effect oshale layer on fracture width.

Table 8.6 - “Big” Pressure Analysis Problem.

Problem Definition

Volume Pumped = VG = 38,000 gallonsE = Modulus, estimated as 7 million psiGross formation thickness = H = 150 ftLeakoff Height (= net height?) = 110 ftRate = 35 bpmPump Time = 25.5 minutesFluid Viscosity estimated at 300 cp

Pressure Decline Analysis Variables

∆P* = 260 psiFinal Net Treating Pressure = ps = 860 psiEfficiency = 0.62ρ = 0.62 / (1 - 0.62) = 1.63Initial Calculations

Fracture 1/2 Length = 624 ft

C = 0.00095 ft/ minute

minute



Fig. 8.37 - Actual Fracture Geometry - Pressure Decline Analysis Problem.

Fig. 8.38 - Nolte-Smith History Match, Pressure Decline Analysis “Big” Problem.



ationf zonere fine,

th. Inof com-rly

es a

The above two brief examples have illustrated the extreme range of effects that multiple formlayers can have on fracture pressure analysis - from the case of the frac growing totally out oand almost invalidating the analysis methods; to a case where the basic analysis methods abut a slightly artificial modulus must be used in order to accurately describe the fracture widgeneral, it is this extreme range of effects that makes general statements about the effectsplex geology difficult or impossible to make. However, while multiple formation layers cleacreate problems, two recent studies (Warpinski25 and Miller and Smith22) have shown that thecombination of pressure decline analysis with numerical modeling/history matching providuseful, powerful tool for analysis of such complex geologic cases.


Proppant/Fluid Schedule From Pressure Decline

mostn andns (asen incussedovern

ablesevelopllboreasur-ssedtionedthen aially arivedtion ofmost

8.6 Proppant/Fluid Schedule From Pressure Decline

While the ultimate goal of a well stimulation treatment is to increase production using thecost effective procedures and materials, the actual, final “product” from the treatment desiganalysis consists of pumping schedules specifying volumes, proppant addition concentratioseen in Fig. 8.39), and specifying in-situ time-temperature history for the injected fluid (as seFig. 8.40 for use in selecting and specifying materials). The pressure analysis procedure disin this chapter have concentrated on measuring or determining the physical variables which gfracture growth, e.g., in-situ stresses, modulus, fluid loss coefficient, etc. With these variproperly measured, it becomes possible, through the use of a numerical fracture model, to dpumping schedules for achieving the desired goals. However, in some conditions existing welimitations, or time/budget constraints may not allow adequate time or data collection for meing the individual variables governing fracture behavior. However, it will be shown and discubelow (following Nolte14) that the final “products” (e.g., pumping schedules) are a strong funcof a single variable, thefluid efficiency for the treatment. If this single value can be determinfrom a prefrac injection test (or from experience gained on previous treatments in the area)pumping schedule can be determined directly from this one value, e.g., efficiency is essent“state variable” for the propped fracturing process. Note however, that the efficiency deschedule is developed from a preselected total treatment volume - with no direct considerafracture length, fracture conductivity, etc. (e.g., no direct consideration of creating the best orcost effective stimulation for a particular formation).

Fig. 8.39 - Treatment Schedule, Proppant Addition Concentrations.



nt of

urfaceideal

cien-actualetry

lectednsuffi-tional

) theand

expo-

Advantages of an Efficiency Derived Schedule

1. Allows development of an “optimum” pumping schedule based on a direct measuremefluid efficiency for the particular well and formation being treated.

2. The analysis requires relatively simple data collection and can generally be done from spressure information. Also, the analysis can be completed in a short time making it anprocedure for field use.

3. Final pumping schedule is not significantly affected by actual fracture geometry, thus efficy procedures can be used in formations (such as coal seams for one example) wherefracture geometry may be very complex. Also, this “independence” from fracture geommakes the procedure ideal for initial treatments in a new, “wildcat” area.

Disadvantages of an Efficiency Derived Schedule

1. Prefrac injectionmust use same fluidas planned for the stimulationand must be pumped atthe same rate as will be used for the actual propped fracture treatment.

2. Efficiency procedure assumes no knowledge of actual fracture geometry, thus the pre-setreatment volumes used as a basis for developing the final pumping schedule may be icient for achieving required production, or the volumes may be excessive, incurring addicosts and unnecessarily increasing the risks associated with completion operations.

The information generally needed for a stimulation are: (1) the fluid volume to be injected, (2injection rate, (3) the proppant addition schedule, (4) the resulting propped fracture widthlength, and (5) the amount of time that fluids will be exposed to reservoir temperature. This

Fig. 8.40 - Treatment Schedule, Fluid Temperature History.



f fluidts, or,e a rel-ally,of the

orma-uired

evel-d vol-thepic-

fully)ping)

ever,h fluidturetionture

orma-of a

y forc-r too

uringeffi-

fracta col-nd will

s haveility do

ssurestimu-d forsemple-

sure time is needed for selecting the required fluid system along with the amount and type oadditives. For a new area, the volume limitations may be determined from budget constrainfor a more developed area, volumes may be specified based on the requirements to achievative change in fracture length (or conductivity) from that achieved by prior treatments. Finpump rate is often prescribed based on horsepower limitations or pressure limit constraintswellhead and/or tubulars. While, as mentioned above, the efficiency procedure gives no inftion on propped fracture length or width, it does give the final ingredient, that being the reqpad volume and proppant addition schedule.

While lack of knowledge of final propped fracture dimensions precludes any quantitative dopment of the treatment design in terms of postfrac production; determining the required paume and pumping schedule still remains the most difficult and critical to obtain of any ofnecessary information. As an example, consider the final fracture conductivity distributiontured in Fig. 8.41. This is the results of a numerical simulation for a case which (purposeincluded an excess pad volume. As seen in the figure, at shut-down (e.g., at the end of pumthe propped fracture 1/2 length is on the order of 500 ft, which was the design length. Howdue to the excess pad volume, the created length is nearly twice as long. Since the area of higloss is located near the fracture tip, fluid continues to flow from the wellbore region of the fracout toward the fracture tip after shutdown. This “afterflow” results in a proppant redistribuleaving a relatively (undesirable) low fracture conductivity in the near well area - reducing fuproduction rates. Another example of the critical need for pad volume/proppant schedule inftion is, of course, the case of inadequate pad volume. This will result in the slurry portionstreatment dehydrating and “screening out,” reducing the propped fracture length and possibling remedial wellbore cleanout operations. Thus, even for fixed treatment volume, eithemuch, or too little pad volume is detrimental to final postfrac results.

Determining Fracture Fluid Efficiency

As discussed in Section 8.3, the fluid efficiency for a treatment can be determined by measthe time-to-close after a fracturing rate injection. Thus the most direct way to measure fluidciency for use in an efficiency design is to conduct a prefrac “calibration treatment” or “minitest.” This is the most common method when using the efficiency design techniques, and dalection and analyses for such prefrac testing are thoroughly discussed in earlier sections anot be repeated here.

However, an alternate method may be available when earlier propped fracture treatmentbeen performed in the area, and where formation properties such as thickness and permeabnot change radically from well-to-well. As an example, consider the ideal Nolte-Smith net preplot in Fig. 8.42, and assume this is a field measured curve from an offset propped fracturelation. At a pump time of 20 minutes, proppant is on the formation (e.g., pad was pumpetwenty minutes) and one hour later (e.g., at a pump time of±80 minutes) pressure starts to increaindicating that fracture growth has stopped. Probably this job would have been pumped to co



lyunlesss thansim-

-rcent-rately,ck out”

tion, since pressure only increases by±500 psi after the start of the “screenout,” with this relativesmall increase possibly not even being noted in normal surface pumping records. However,this screenout was a planned occurrence, it is probable that fracture length is much lesdesired. While unfortunate for this well, the information can aid in future treatment designs byply noting the pad percentage at the start of the pressure increase.

For this case, pressure starts increasing after±80 minutes, with a pad pump time of 20 minutesthus pad percentage for the “first part of the job” was 25%. For future treatments, the pad peage should be increased in volume to at least equal 25% of the total pump time. More accusince pad percentage is related to job size, the pad percentage of 25% could be used to “ba

Fig. 8.41 - Fracture Conductivity Redistribution Resulting from Excess Pad Volume.

Fig. 8.42 - Use of Field Data to Determine Fluid Efficiency.



sedd thisnd pad

nt, the

-

grow-

hus,starts)

pant

) andeftercture

a fluid efficiency. The fluid efficiency thus measured for the first 80 minutes of the job is then uto calculate an expected fluid efficiency for a larger treatment (as discussed below), anexpected efficiency for the total job is used to determine the new, required pad percentage avolume.

Pad Volume

Once an efficiency (or expected efficiency) has been determined for a proposed treatmerequired pad percentage for the job is found from the simple relation

(8.15)

whereef is the expected efficiency for the treatment,fp is the required pad fraction for the treatment, andfC is a “correction” term.

In developing this, consider the curve shown in Fig. 8.43. This curve illustrates fracture areaing with time (or volume). Further, consider that at some time,ftp (wheretp is the total pump timeandf is a fraction) a switch is made from pumping pad to pumping proppant laden slurry. Tthe initial fracture area created (e.g., the small element of fracture created just as pumpingis exposed to fluid loss for the entire pump timetp, with this fluid loss coming out of the pad fromtime '0' to timeftp, with subsequent fluid loss coming out of, and serving to dehydrate, the propladen slurry.

Similarly, one might consider some later element of the created fracture area,da, which is createdat time =τ (e.g., before that time it did not exist since the fracture had not reached that pointhas a total exposure time to fluid loss ofη = (tp - τ). For some fraction of that total exposure tim(τ < tp), fluid loss from this increment of the fracture area will come from the pad volume. Athat point, the slurry “front” passes and subsequent fluid loss out of that element of the fra

Fig. 8.43 - Variables for Determining Pad Percentage.

f p 1 ef–( )2f c+=



tincre-

re

idure isele-erfectachesleav-

bu-

e, theac-

quals

area will be coming out of the slurry.Assume then, that this point in time where the slurry fronpasses an element of fracture area is similar for each element of the fracture. Then for somemental area,da, total fluid loss exposure time isτ. For a fraction of this total time,fη, fluid loss isfrom the pad while for the remainder of the exposure time, fluid loss is from slurry.

The volume of fluid lost during a fraction,f, of each incremental fracture area's fluid exposutime,η, can then be found by integrating14

whereVLossis the total volume of fluid lost during the entire pump time. Thus the portion of flulost for a (constant) fraction of the fluid exposure time of each incremental area of the fractsimply proportional to . Also, if this assumption concerning the slurry “front” passing eachment of the fracture is correct, then this simple curve (dashed line in Fig. 8.43) defines the ppad. That is, the slurry front reaches the fracture tip just as pumping stops, e.g., it neither rethe tip prematurely leading to proppant bridging (a screenout), nor does it fail to reach the tip,ing a portion of the fracture without proppant or allowing harmful “afterflow” proppant redistrition during fracture closure.

Clearly then this is a possible curve for the optimum pad volume, and based on this curvdesired fraction,f = fp, is readily found. As discussed above, the volume of fluid lost during a frtion, f, of each fracture elements' fluid exposure time, equals xVLoss, whereVLoss is the totalloss volume during the treatment. For the ideal pad then this fractional lost volume exactly ethe pad volume giving

whereVp is the total volume injected during the entire pump timetp. Since efficiency,ef, is definedas fracture volume at the end of pumping divided by the total volume injected, thenVLoss, mustequal

and the ideal, theoretical pad fraction is given by

VLoss f( ) 2Cdη

η-------

0

fη

∫ da

0

A

∫=

f x VLoss=

f

f

f pxVp f xVLos=

VLoss 1 ef–( )xVp=

f p 1 ef–( )2= .



ticalrly

entage

aterary

al padoss andre)and

iencyshowsg fromight

However, reviewing the dashed (“slurry front propagation”) curve in Fig. 8.43 shows a verslope at the beginning, e.g., implying an initially infinite velocity for the slurry front. This is cleaan impossibility, and leads to a correction factor,14 fC, as shown in Fig. 8.44.

Thus, more generally, the ideal pad percentage,fp, is given by

(8.13)

where fC = 0.05, efficiency,ef, > = 0.20, =ef/4, efficiency < 0.20 .

Using this (somewhat in reverse) with the ideal case shown in Fig. 8.42 where the pad perc(prior to start of screenout) was 0.25 gives an efficiency on the order of

for the first 80 minutes pumping of that job. (Note that in this case, the final efficiency is grethan 0.20, thus the initial estimate offC = 0.05 was correct, otherwise it would have been necessto iterate on the correction term in order to find the actual efficiency.)

Of course, while the dashed curve in Fig. 8.43 represents the general character of an idestage, the assumption that each incremental fracture area element is exposed to pad fluid lslurry fluid loss in the same ratio (e.g.,'f' is a constant for each incremental element of the fractuis not proven. As one “proof,” or at least justification, for this assumption, pad percentageproppant addition schedules (as discussed in the following section) arising from the efficanalysis are compared to schedules developed from computer models in Fig. 8.45. Thisactual treatment schedules from three separate areas, representing fluid efficiencies rangin18 to 70%. The low loss, high efficiency example is for a tight gas field in Colorado where he

Fig. 8.44 - Correction Factor for Pad.

f p 1 ef–( )2= f C+

0.25 1 ef–( )2= 0.05 1 ef–( )2,+ 0.20=

ef 0.55±=



gaslossorth

ams andy deter-

)field

, have-singleure.

confinement was virtually perfect; the middle curve comes from treatment histories from afield in East Texas where some height growth generally occurred; and the third, high fluidexample, was for fracturing in a thick, moderate permeability, carbonate formation in the NSea. In each case, computer model designs were based on extensive data collection progrfield experience, and, in each case, the final proppant schedule is seen to be quite accuratelmined by fluid efficiency alone.

Proppant Addition Schedule

The average proppant concentration,cavg, for a treatment is

(8.16)

whereW is the total weight of the proppant andVp is the total slurry volume (fluid plus proppantinjected. Note here that this definition of proppant concentration differs from the normalusage of pounds-of-proppant per gallon-or-fluid. Additionally,cf is defined as the final, maximumproppant concentration pumped during a treatment, and due to fluid loss,cf must be greater thancavg. One possible design goal for a propped fracture stimulation is to, at the end of pumpinga uniform proppant concentration, equal tocf, from the wellbore to the fracture tip. This will generate a fracture with reasonably uniform conductivity along the fracture length (assuming atype of proppant is used) and will maintain fairly uniform slurry viscosity throughout the fractIn terms of the fracture volume at the end of pumping,V = ef x Vp, this final proppant concentrationcan be written as

Fig. 8.45 - Comparison with Computer Models.

cavg W/Vp=

cf W/V W/ ef Vp( ) .= =



en-

n6.

Combining this with the definition of average concentration gives

wherecD-avg is a “normalized” value for average concentration. Similarly, a normalized conctration at any point in time during the treatment is defined by

and, for convenience a new “time scale” is defined,ξ, where the new time scale starts at “0” wheproppant is started and reaches a value of “1” at the end of the job as illustrated in Fig. 8.4

In terms of this new time scale, certain fixed values for the normalized proppant schedule,cD, canbe stated

Assuming a function for the proppant schedule of the form

the exponent,∈, can be evaluated from the above limits on the function,cD, given above

Fig. 8.46 - Time Scale, ξ, for Determining Proppant Addition Schedule.

cD avg– cavg/cf ef ,= =

cD c/cf ,=

ξ t f t p–( )/ t p f t p–( ) .=

cD ξ( ) 0 ξ = 0<( ),=

cD ξ( ) 1 ξ = 1<( )=cD avg– ef .=

cD ξ( ) ξ (0 =ξ = 1)<<=∈



tions

above,otoni-nablenge ofping

s and

lumethepinghownd per-

vari-eightn forarlier,high

or after incorporating a “correction” factor discussed on page 8.62 for the pad volume calcula

Thus a “dimensionless” or “normalized” proppant addition schedule is defined by

(8.17)

and since this function satisfies the numerical end points for a proppant schedule as statedsatisfies the relation for the final average proppant concentration, and also provides a moncally increasing schedule as commonly utilized in practice - it is expected to be a reasoapproximation to an ideal schedule. As seen in Fig. 8.45, again for three cases covering a raconditions and fluid efficiency, this simple relation does indeed provide an acceptable pumschedule.

Effect of Treatment Volume

In an example considered in the discussion of Fig. 8.42, from the pad pump time of 20 minutethe time when a screenout started at 80 minutes (pad fraction,fp, of 0.25), it was found that thefluid efficiency for the first 80 minutes of pumping was±55%. Also, a minimum design criteriafor future treatments in that formation was to use a pad volume equal to 25% of the total voto be pumped. However, this fluid efficiency of 55% is applicable for the first 80 minutes ofjob and, in general, fluid efficiency is a function of job size and will tend to decrease as pumtime gets longer and longer. Thus for a job requiring a total pump time of about 2 hours as sin Fig. 8.42, the expected efficiency would be somewhat lower than 55% and the required pacentage would be somewhat greater than 25%.

Fluid efficiency is related to pump time (e.g., volume and rate), fluid loss coefficient,C, and to thefluid loss area, orrp, the ratio of loss area to total fracture area. While these are the primaryables governing efficiency, it is also slightly affected by fracture geometry (e.g., confined hvs. radial fracture growth) and fluid rheology. For a general case there is no analytical solutiofluid efficiency, however, as with the other fracturing pressure decline analyses discussed eit is possible to place certain bounds. For example, for efficiency approaching “0” (e.g., veryfluid loss), fluid efficiency is proportional to time raised to a power14

= 1 e– f .∈

= 1 ef f C/ef .––∈

cD ξ( ) ξε 0 =< ξ = 1<( ) , = 1 ef f C/ef ,––∈=

ef t**≈ n / 2n 2+( )–5n 2+( )/ 82 8+( )–

"PK"

"Radial"

GeometryGeometryGeometry

2n 1+( )/ 4n 4+( )–"GdK"



5

someiencynd, in

imes

ation-

cross-t used

-

y vol-r fluide that

where'n' is the power law exponent for a non-Newtonian fluid.'n' generally ranges between 0.and 1 for common fracturing fluids, and usingn = 0.75 (a typical value for crosslink gels) gives

While the range between these various possible fracture geometries is possibly significant incases, it is noted that the values above are for the limited case of very high fluid loss. As efficapproaches “1” (e.g., no fluid loss), then the fracture geometry does not effect efficiency, athe above form, efficiency is proportional to time raised to the “0” power, e.g.,

Interpolating between these limits gives a ratio of efficiencies between two different pump t(t2 andt1) as

but, generally, acceptable accuracy is obtained by simplifying the above ratio to a single relship

(8.18)

Example

As an example, consider a case where a “minifrac” test was pumped. The test consisted of alinked gel identical to the fluid planned for use during the propped fracture treatment. The tes25,000 gallons (595 barrels) pumped at 25 bpm with a total pump time,tp, of 23.8 minutes. Frac-ture closure was observed 28.6 minutes after shut-in, e.g.,tc = 28.6 minutes. This gives a dimensionless closure time of

And, from Fig. 8.32,δc of 1.20 gives ef = 0.45 (45).

Find Actual Job “Expected” Efficiency

Now assume that it is desired to pump an actual propped fracture treatment with a total slurrume of 100,000 gallons and a final proppant concentration of 8 ppg (pounds of proppant pegallon). The actual treatment will also be pumped at 25 bpm, and it is important to note her

ef t**≈"PK""GdK""Radial"

GeometryGeometry .Geometry

0.357–0.214–0.411–

ef t0≈ constant 1 .= =

ef 2/ef 1( ) t2/t1( ) **= 0.214 1 ef 1–( )–0.411 1 ef 1–( )–

"PK""GdK""Radial"

GeometryGeometry ,Geometry

0.357 1 ef 1–( )–

ef 2/ef 1( ) t2/t1( )1 e1–( ) 3⁄–

=

δc tc/t p 28.6/23.8 1.20= = =



tionciency

nsist of

y vol-con-

uctedn, soppant

while the minifrac efficiency can be corrected for the larger volume,it cannot be corrected forrate changes, thus in order to use simply the efficiency from the minifrac, the propped stimulatreatment must be pumped at the same rate. This gives [using Eq. (8.18)] an expected effifor the actual treatment of

Treatment Pad Percentage

The actual treatment pad percentage is then found from Eq. (8.15)

and since the total expected treatment volume is 100,000 gallons, the pad stage should co47,000 gallons.

Proppant Addition Schedule

The “proppant schedule exponent,”ε, is then found from

and the dimensionless proppant schedule is given by

and this equation is used to construct the simple table shown in Table 8.7, where the slurrumes shown are “arbitrarily” selected points which will be used to construct a curve of propcentration vs. slurry volume. It is particularly important to note that the calculations are condin terms of slurry volume and slurry concentration, e.g., pounds of proppant per slurry galloa conversion is necessary to the more common industry terminology of “ppg” (pounds of proper fluid gallon).

These conversions from ppg (pounds of proppant per fluid gallon -Cfl) to pounds of proppant perslurry gallon (Csl) have been made using the formulae

and

ef 2/0.45 4/1( ) 1 0.45/3–( )–=

ef 2 0.45( ) 4( ) 0.18–0.35 35% .= = =

f p 1 0.35–( )2= 0.05+ 0.47 ,=

ε 1 ef f C/ef–– 1 0.35– 0.05/0.35– 0.51= = =

cD ξ( ) ξε (0 =< ξ = 1),ε<= = 0.51,

Csl C fl S.G.× 8.33×( )/ Cfl S.G.+ 8.33×( )=

Cfl S.G. 8.33×( )/(S.G. 8.33× /Csl 1)– .=



con-ched-ent,e, with

treat-nt and

Finally, these calculated points might be plotted as shown in Fig. 8.47, and a smooth curvenecting the points constructed - with this curve then describing the ideal proppant addition sule. This curve might then be the final job input for a computer controlled “ramp” type treatmor the curve might be subdivided into discrete stages as seen by the dashed line in the figurthese discrete stages then being used for job control.

Time/Temperature History

The efficiency can also be used to determine an approximate time-temperature history for thement as illustrated in Fig. 8.40 as discussed by Nolte, in his paper “Determination of ProppaFluid Schedules from Fracturing Pressure Decline.”14

Table 8.7 - Application of Proppant Addition Schedule.

Total Treatment Volume - 100,000 Slurry GallonsPump Rate - 25 bpmProppant is sand - S.G. = 2.65Max Proppant Concentration is 8 ppg (5.87 pounds per slurry gallon)

Slurry Volume(gallons) ξ cD

Pounds of Propper Slurry Gal

PPG (lbs of prop perfluid gal)

47,000 0.0 0.0 0 0.0

59,720 0.24 0.48 0.48x5.87 = 2.82 3.5

72,970 0.49 0.70 4.10 5.2

86,750 0.75 0.86 5.05 6.6

100,000 1.0 1.0 5.87 8.0

Fig. 8.47 - Treatment Schedule from Efficiency.

8

7

6

5

4

3

2

1

0

PP

G

Eff, Mini-Frac = 0.45Expected Eff, Main Frac = 0.40Rate = 25 BPM

20 40 60 80 100Slurry Volume (M-gallons)



ations

8.7 Nomenclature

A Total Fracture Area created after pumping fortp minutes (ft2)

C Fluid Loss Coefficient (ft/ )

∆P Pressure Difference (psi)

∆P* Match pressure for pressure decline analysis (psi)

δ Dimensionless Shut-In Time,δ = ts/tp

δc Dimensionless Closure Time,δc = tc/tp

ef Fracture Fluid Efficiency = Fracture Volume at Shut-In (V)/Total Volume Pumped (Vp)

E Young's Modulus of Formation (psi), Typical Values - 2x106 psi to 8x106 psi

E' Crack Opening Modulus =E/(1-υ2) (psi)

f Fraction

fp Pad Fraction or Pad Percentage

fpr Proppant Fraction of Job,Vpr/Vp

H Total or Gross Fracture Height (ft)

Hp Permeable or Leakoff Height (ft)

pc Fracture Closure Pressure (psi)

pnet Net Fracturing Pressure (e.g., bottomhole treating pressure just outside the performinus fracture closure pressure) (psi)

ps Net Pressure at Shut-In (e.g.,ISIP - pc)

φ Porosity of Proppant Pack (typically on the order of 0.40)

Q Total Injection Rate (barrels/minute, bpm)

qLoss Fluid Loss Rate (bpm)

rp Ratio of permeable or leakoff area to total fracture area for P&K or Geertsmarp = Hp/ H;for a radial geometryrp is more difficult to define and is normally set = 1

ρ Loss Ratio = efficiency/(1 - efficiency)

ρpr Specific Gravity of Proppant (e.g., 2.65 gm/cc or 22 lb gal for sand)

S Fracture “Stiffness” for Pressure Decline Analysis

tc Closure Time, e.g., Shut-In Time to Fracture Closure (minutes)

tp Pump Time (minutes)

ts Shut-In Time (e.g., incremental time since pumping stopped) (minutes)

minute


Nomenclature

τ Time when an incremental element of fracture area is first exposed to fluid loss

V Fracture Volume (ft3)

VLoss Total Fluid Loss Volume During Pumping (ft3)

Vp Total Slurry Volume Pumped (ft3)

Vpr Total Proppant Volume Pumped (ft3), including porosity of proppant

Vfl Total Fluid Volume Pumped (ft3)

δ Dimensionless Shut-In Time,ts/tp or (t-tp)/tp

W Total weight of proppant pumped (pounds)

υ Poisson's Ratio for Formation (dimensionless), Typical Values - 0.15 to 0.25

µ Fluid Viscosity (centipoise)



id,”

res,”

ractur-

1, pre-

exasExhibi-

10130,

ma-

aulic

erfo-w-Per-

paper18-19.

8.8 References

1. Godbey, J. K. and Hodges, H. D.: “Pressure Measurements During Fracturing Operations,”Trans., AIME, (1958)213, 65-69.

2. Khristianovic, S. A. and Zheltov, Y. P.: “Formation of Vertical Fractures by Means of Highly Viscous LiquProc. Fourth World Pet. Cong., Rome (1955) Sec. II, 579-86.

3. Perkins, T. K. Jr. and Kern, L. R.: “Widths of Hydraulic Fractures,”JPT(Sept. 1961) 937-49;Trans., AIME 222.

4. Geertsma, J. and de Klerk, F.: “A Rapid Method of Predicting Width and Extent of Hydraulic Induced FractuJPT (Dec. 1969) 1571-81;Trans., AIME 246.

5. Veatch, R. W. and Crowell, R. F.: “Joint Research/Operations Programs Accelerate Massive Hydraulic Fing Technology,”JPT (Dec. 1982), 2763-75.

6. Nolte, K. G. and Smith, M. G.: “Interpretation of Fracturing Pressures,”JPT (Sept. 1981), 1767-75.

7. Nolte, K. G.: “Determination of Fracture Parameters from Fracturing Pressure Decline,” paper SPE 834sented at the 1979 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 23-26.

8. Schlottman, B. W., Miller, W. K. II, and Leuders, R. K.: “Massive Hydraulic Fracture Design for the East TCotton Valley Sands,” paper SPE 10133, presented at the 1981 SPE Annual Technical Conference andtion, San Antonio, Oct. 4-7.

9. Elbel, J. L. et al.: “Stimulation Study of Cottage Grove Formation,” JPT (July 1984) 1199-1205.

10. Dobkins, T. A.: “Procedures, Results, and Benefits of Detailed Fracture Treatment Analysis,” paper SPEpresented at the 1981 SPE Annual Technical Conference and Exhibition, San Antonio, Oct. 4-7.

11. Smith, M. B.: “Stimulation Design for Short, Precise Hydraulic Fractures” SPEJ (June 1985) 371-79.

12. Smith, M. B., Miller, W. K. II, and Haga, J.: “Tip Screenout Fracturing: A Technique for Soft, Unstable Fortions,” SPEFE (Feb. 1987) 95-103;Trans., AIME, 283.

13. Morris, C. W. and Sinclair, R. A.: “Evaluation of Bottomhole Treatment Pressure for Geothermal Well HydrFracture Stimulation,”JPT (May 1984) 829-36.

14. Nolte, K. G.: “Determination of Proppant and Fluid Schedules From Fracturing-Pressure Decline,”SPEPE(July1986) 255-65;Trans., AIME, 281.

15. Nolte, K. G.: “A General Analysis of Fracturing Pressure Decline With Application to Three Models,”SPEFE,(Dec. 1986) 571-83.

16. Martins, J. P. and Harper, T. R.: “Mini-frac Pressure Decline Analysis for Fractures Evolving From Long Prated Intervals and Unaffected by Confining Strata,” paper SPE 13869 presented at the 1985 SPE/DOE Lomeability Gas Reservoirs Symposium, Denver, May 19-22.

17. Castillo, J. L.: “Modified Fracture Pressure Decline Analysis Including Pressure-Dependent Leakoff,”SPE 16417, presented at the 1987 SPE/DOE Low-Permeability Gas Reservoirs Symposium,.Denver, May


References

akoffl Tech-

aulicX,

E 11064,

e ofo, Tex-

cturelsa,

18. Cooper, G. D., Nelson, S. G., and Schopper, M. D.: “Comparison of Methods for Determining In-Situ LeRate Based on Analysis With an On-Site Computer,” paper SPE 13223 presented at the 1984 SPE Annuanical Conference and Exhibition, Houston, Sept. 16-19.

19. Warpinski, N. R.: “Investigation of the Accuracy and Reliability of In Situ Stress Measurements Using HydrFracturing in Perforated, Cased Holes,”Proc., 24th U.S. Symposium on Rock Mechanics, College Station, T(June 1983) 773-86.

20. McLennan, J. D. and Rogiers, J. C.: “How Instantaneous are Instantaneous Shut-In Pressures,” paper SPpresented at the 1982 Annual Meeting of SPE, New Orleans, Louisiana, Sept. 26-29.

21. Warpinski, N. R. and Teufel, L. W.: “In-Situ Stresses in Low Permeability, Nonmarine Rocks,”JPT, April, 1989.

22. Miller, W. K. II and Smith, M. B.: “Reanalysis of the MWX-Fracture Stimulation Data from the Paludal Zonthe Mesaverde Formation,” paper SPE 19772, presented at 1989 Annual Fall Meeting of SPE, San Antonias, Oct. 8-11.

23. Nordgren, R. P.: “Propagation of a Vertical Hydraulic Fracture,”SPEJ(Aug. 1972) 306-14;Trans., AIME, 253.

24. Carter, R. D.: Appendix I to paper by C. C. Howard and C. R. Fast, “Optimum Fluid Characteristics for FraExtension,” presented at the 1957 ASME Spring Meeting, Mid-Continent District, Div. of Production, TuOK, April.

25. Warpinski, N. R.: “Dual Leakoff Behavior in Hydraulic Fracturing of Tight, Lenticular Gas Sands,”SPE Pro-duction Engineering (August 1990) 243.




References


Chapter

Wequiredized.ve our

ment-

ance ofze theation,rate,oal.nt loss

duc-ion oflationed ine madewect costust be

es then of

Economic Optimization of HydraulicFracture Treatments

9
9.1 Introduction
“After 40 years of growth in income, we are now in a period where there will be little growth.have to continue to rationalize both staff and assets to reduce our operations to the size refor expected level of (future) investment and to reduce costs so that cash flow can be maximThe fat, lazy days are over. We must continue to become leaner and meaner. We must improefficiency.” This is the charge made by the authors of a paper entitled “Petroleum ReinvestIs there a future for our Industry?”

Doom and gloom or a challenge to be overcome? These statements bring home the importproperly maximizing cash flow in the management of our oil and gas properties and emphasineed to focus on immediate opportunities to bring about revenue improvement. Well stimuleither by acidizing or through hydraulic fracture stimulation, is one method available to genevirtually overnight, improved production revenues that will assist in our accomplishing this gWell stimulation, however, is a business decision that can just as easily result in an investmeif not properly understood and applied.

Amoco Corporation has traditionally reinvested over 50% of it's total earnings in Amoco Protion Company (APC) for the sole purpose of developing reserves and the resulting productoil and gas. Over the last decade, APC has developed and applied hydraulic fracture stimutechnology worldwide, an investment that today provides over 50% of all oil and gas producour domestic U.S., Canadian and North Sea operations. Price declines in recent years havit increasingly difficult to justify investment in drilling, completing and stimulating wells. Loprices have been compounded by an increased incidence of poor economic returns and projoverruns, as summarized in Table 9.1, suggesting better risk management procedures mincluded as a part of economic analysis and stimulation optimization. This section addressmethods to follow and the pitfalls to avoid when maximizing revenue from the implementatiohydraulic fracture treatments.

Table 9.1 - Average of Gulf of Mexico Projects to 1988. 1

Production: -10%

Reserves -9%

Project Time +29%

Project Cost: +33%

Present Worth -88%

Hydraulic Fracturing Theory Manual9-1August 1992

Introduction

lance, withpro-lutions

e com-mate-is byearchRAC.g pro-when

Economic optimization of a well stimulation treatment requires that the designer carefully baa large number of parameters describing the reservoir, including its fluid and rock propertiesthe inflow performance and associated cost of providing a man-made flow conduit that willduce the largest production increase at the least incremental cost. There are usually many soto this problem because the different stimulation materials and their associated costs can bbined in many ways to produce an optimum. The challenge facing us today is to consider allrials and sensitivities, and their associated risks, to arrive at the true “optimum,” a task thatno means trivial and is best suited to today’s computer technology. Amoco Production Reshas developed an integrated fracture, reservoir, and economics program called ULTRAFThis program allows the user to assess the economic benefits and sensitivities of the fracturincess. The following sections are some of the more important considerations to be evaluatedoptimizing stimulation treatments.


Economic Optimization of Hydraulic Fracture Treatments9

turn,expen-

rfor-

tant oftlined.uatelyasures

e

ake

ecalcu-of de-ition

-uring

the ad-n be

ro.

9.2 General Economic Criteria

Provided that cash inflows may be reinvested in projects yielding some positive rate of rethere is a benefit associated with receiving cash inflows as early as possible, and delayingditures as long as possible. This is just a restatement that funds have time value. Themagnitudeandtiming of project net cash flows are important yardsticks by which to measure project pemance. Similar considerations are valid with associated costs of production.

Amoco evaluates investment projects on the basis of several standards. The most importhese will be discussed in this section, and the merits and shortcomings of each will be ouAs the discussion proceeds, it will become clear that no single measure is sufficient to adeqanalyze a project and that an evaluation utilizing a variety of measures is desirable. The meused within Amoco are defined as follows:

1. Net Present Worth or Value (PW or PV)The sum of all future cash flows discounted to thinitial time, at a stated discount rate.

2. Incremental Present Worth or Value of the Fracture (INCPVF)The Net Present Value of afracture case less the present value of the unfractured case.

3. Fracture Incremental Present Worth or Value (FINCPV)The Net Present Value of a fracturecase less the present value of the preceding case. Used to show diminishing returns.

4. Profitability Index (PI) The [continuous] compound interest rate whose discount factors mthe present worth of a project’s net cash flows equal to zero.

5. Discounted Return on Investment (DROI)The ratio of a project’s net present worth to thpresent worth of the total investments discounted at a stated rate. (The denominator islated after tax and overhead and includes investment tax credits and the after-tax effectpreciation.) In ULTRAFRAC, DROI includes capital expenses such as well costs in addto fracturing costs.

6. Fracture Discounted Return on Investment (FDROI)FDROI is defined as above only capital costs such as well costs are excluded. Only the AFIT (After Federal Income Tax) fractcosts are used in this economic analysis.

7. Incremental Discounted Return on Investment (INCDROI)INCDROI is defined as the ratioof the incremental present worth of the fracture cases to the incremental cost to achieveditional length. As a result, a DROI cutoff, consistent with Business Unit budgeting, caused to aid in determining the optimum fracture treatment.

8. Payout (PO) The time for the cumulative undiscounted cash flow of a project to reach ze

Hydraulic Fracturing Theory Manual 9-3 August 1992

General Economic Criteria

, alsooco’swithin

therercent-

year.in theavail-

lows:

utureafter

estedould

The Present Worth Concept

A concept which lies at the foundation of economic evaluation procedures is present worthcalled present value (PV). While these two expressions are interchangeable and all of Amother subsidiaries use the term present value, the term present worth is normally usedAmoco Production. Present worth is abbreviated in this text as PWi, where i is the interest rate. Theprinciple is that a dollar of income is worth more to an investor, or a firm, if received now rathan at some time in the future. This is because the dollar can be invested at some positive page rate of return (interest rate) during the intervening time.

For example, a dollar received now would, at 5% annual interest, be worth $1.05 after oneHence, to be indifferent between accepting a dollar now or a certain sum of money one yearfuture, that sum of money would have to be $1.05 (assuming 5% return is the highest returnable to investors). The future worth (FW) of a dollar after one year at 5% is calculated as fol

FW = 1.00 (1 + .05)

= 1.05

After two years, if the interest were left in the account, the future worth would be:

FW = 1.00 (1 + .05) (1 + .05)

= 1.00 (1.05)2

= 1.1025

Present worth is the value that, when invested at the given interest rate, will yield the given fworth after the applicable number of periods. Using the previous example of $1.05 receiveda year, the present worth is $1.00 (since it would grow to the future worth of $1.05 when invat 5% for one year). Another way to think of present worth is the value in current dollars you wrequire to make you indifferent between receiving that amount or the future worth.

The relationship of present and future worth can be stated generally as,

FW = PW (1 + i)n (2.1)

whereFW= future worth,PW= present worth,i = interest rate (assumed constant), andn= numberof periods over which the interest rate applies.

In general terms, present worth is found by solving Eq. (2.1) for PW.

PW = FW (2.2)

The quantity

11 i+( )n

------------------

11 i+( )n

------------------



) dis-ally

ount-

/e

ary to

tceda sit-

ar end

le dis-f this

es to

shples

is known as adiscount factor.

The form of present worth discussed so far is known as end-of-period discrete (or periodiccounting. If one assumes that the time period over which compounding occurs is infinitesimshort, the result is continuous discounting, the type employed Amoco. With continuous discing, the present worth is determined as follows:

(2.3)

wherePW = present worth,FW = future worth, e = Exponential Function,i = Interest Rate(assumed constant) andn = number of periods over which the interest rate applies

The use of tables and computer programs simplifies the calculation of the discount factor 1ni.

If more than one future amount, occurring at different times, is being discounted, it is necessalter the equation to account for multiple cash flows. Eq. (2.4) illustrates the case ofn cash flows,each assumed to occur at year end.

(2.4)

where C0, C1, ..., Cn = annual point-in-time cash flows for years 1 through n and DF1, DF2, ..., DFn

= associated continuous discount factors for years 1 through n.

The discussion of present worth thus far has centered around cash flows which occur at apoint intime. More frequently, however, cash flows occuruniformly throughout a period, rather than ayear end. An example of a uniform cash flow is revenue from an oil well. The oil is not all produon December 31, 19xx; therefore end-of-year discounting is not appropriate. An example ofuation tailored to use end-of-period discounting might be annuity payments received at yefor several years.

Table 9.2 summarizes the types of discounting and cash flows which exist and the applicabcount factor tables, which are included, along with brief instructions, in a separate section omanual. Only the continuous form of discounting is utilized by Amoco and all future referencdiscounting will be to that form.

Annual continuousdiscount factors, the type normally used by Amoco, for point-in-time caflows are listed in Table 9.3, and factors for uniform cash flows are listed in Table 9.4. Exam

Table 9.2 - Summary of Discounting and Cash Flows.

Type of Discounting Cash Flow Applicable Table

1. Discrete Point-in-timeUniform

Not applicableNot applicable

2. Continuous Point-in-timeUniform

9.39.4

PWFWeni---------=

PW Co C1 DF1( ) C2 DF2( ) ... Cn DFn( )++ + +=



. Forand

t cashtainedrth of% dis-

nitiesg the

rm is

ause-year

of present worth calculations for both uniform and point-in-time cash flows are also providedanything other than the simplest of examples, computer programs such as ULTRAFRACGEM handle the calculations.

Table 9.4 also shows an example of present worth calculation. The annual $75 M project neflow streams are assumed to result from a $100 M investment. Discounted cash flows are obby multiplying the annual net cash flows by the appropriate discount factors. The present wothe project is the sum of the discounted cash flows. Present worth has been calculated at 15count rate for point-in-time and uniform cash flows.

The significance of present worth is that, provided an investor has other investment opportuat the stated discount rate, he would be indifferent to accepting $81.1 M now or acceptinundiscounted uniform cash flows over the three years of project life. In fact, the value of a fifrequently said to be the present worth of all of its cash flows from its various projects.

Present worth is helpful in ranking projects of the same size as illustrated by Table 9.5:

In examining these projects, it is clear that an investor would favor project A over B, becProject B for the same investment ($1,000 M) yields $100 M less per year over the three

Table 9.3 Calculation of Present Worth Using Continuous Discount Factors (Amoco).

YearNet Cash Flow

($M)

Point-in-time Cash Flows

Discount Factors @ 15%Discounted Cash Flow

($M

0 -100 - -100

1 75 .8607 64.6

2 75 .7408 55.6

3 75 .6376 47.868.0 = PW15

(Point-in-Time)

Table 9.4 - Calculation of Present Worth Using Uniform Discount Factors.

YearNet Cash Flow

($M)

Uniform Cash Flows

Discount Factors @ 15%Discounted Cash Flow

($M

0 -100 - -100

0-1 75 .9286 69.6

1-2 75 .7993 59.9

2-3 75 .6879 51.681.1 = PW15

(Uniform)



pt ofmorerein-

l has

thee firm

ositiveose

jects

t fac-as the

annualoccur

s pat-se of

project life. Project A and Project C, however, each return a total of $500 M, and the concepresent worth aids in differentiating between them. Project C is preferred because it returnsof its cash earlier which leads to its having a higher present worth (the incoming cash can bevested). This once again emphasizes that both thetiming andmagnitudeof investments have tobe considered. It is interesting to note that Project B, while returning all of its investment, stila negative present value at both 13% and 15% discount rates.

If this firm’s cost of capital is 13%, it would undertake all projects with a PW13 > 0, acceptingproject A and C but rejecting B. However, if the firm were capital constrained, it would rankprojects in order of economic attractiveness and choose those which maximize the value of thwithin the imposed constraints.

Amoco has set a minimum investment criterion that those projects accepted must have a pPW15. Subject to the size of Amoco’s investment budget and manpower constraints, thprojects should be selected which maximize the present worth of the total package of proavailable.

Profitability Index

Profitability Index (PI) is defined as that [continuous] compound interest rate whose discountors make the present worth of a project’s net cash flows equal to zero. PI is also referred toproject’s internal rate of return.

The PI may also be thought of as the discount rate which sets the sum of the discountedcash inflows equal to the sum of the discounted annual cash outlays. Investments normallyat the commencement of a project, followed by a number of years of cash inflows. Where thitern is substantially altered, there may be multiple PI’s, which is a serious limitation to the uthis technique.

Table 9.5 - Project Ranking Using Present Worth Concept.

Year

Annual Cash Flows

Project A Project B Project C

0 -1,000 -1,000 -1,000

1 500 400 600

2 500 400 600

3 500 400 300

Total 500 200 500

PW13 163 -70 193

PW15 120 -104 152



end-ent

zero.

andard.

,e.

ilableld pre-o pay

lowingwherer PI.

esentnd theas fol-

An example may be helpful in explaining PI. Suppose a firm is offered a project with annualof-year point-in-time cash flows of $100 M for five years after an initial (time “zero”) investmof $350 M. The calculation of PI for such a project is shown in Table 9.6.

Recall that the PI is that discount rate which sets the present worth of the project equal toTherefore, by interpolation,

Once the PI is calculated for a proposed project, it should be compared to the established stIn the current environment for Amoco, the minimum standard is 15 PI (or ).Projectswhich yield less than a 15 PI should not generally be accepted.However, other considerationssuch as an interrelationship with more profitable opportunities, may lead to their acceptanc

Should Amoco’s supply of projects returning at least 15 PI dwindle to the point where the avamonies exceed the investment requirements for such projects, the minimum PI standard wousumably be lowered, but never less than the cost of capital. Investors would prefer that Amocout the excess funds as dividends if they can earn higher return than can be realized by pthe funds back into Amoco’s operations. Amoco might also choose to invest the funds elsewithin the consolidated corporation if projects in other lines of business could yield a highe

Discounted Return on Investment (includes Fracture Discounted Return on Investment)

Discounted Return on Investment (DROI) is the ratio of a project’s net present worth to the prworth of the total investments (after tax and overhead and including investment tax credits aafter-tax effects of depreciation), discounted at some rate. The denominator is calculatedlows:

Table 9.6 - Calculation of Profitability Index.

Time (years) Cash Flow ($M)

Present Worth @ 12% Present Worth @ 14%

DiscountFactors Present Value

DiscountFactors Present Value

0 -350 - -350.0 - -350.0

1 100 .8869 88.7 .8694 86.9

2 100 .7866 78.7 .7558 75.6

3 100 .6977 69.8 .6570 65.7

4 100 .6188 69.9 .5712 57.1

5 100 .5488 54.9 .4966 59.7

+4.0 -15.0

PI419------x 14% 12%–( ) 12%+=

PI 12.4 approximately=

PW15 0≥



esention’sthe

bsidiaryeval-nder

h thepoten-), thects tosent, as

Discounted PW of Cash Investment, After Tax =

+ (Capitalized Part of Investment), discounted at i percent

+ 0.5 (Expensed Part of Investment), discounted at i percent

+ 0.5 (0.2 x Investment), discounted at i percent

- 0.5 (Depreciation), discounted at i percent

- (Investment Tax Credit), discounted at i percent

where 0.5 = Tax Rate and 0.2 x Investment = Overhead

DROI is a measure of capital efficiency which may be viewed as the amount of after-tax prworth generated per dollar of discounted investment. It is only used within Amoco Productdomestic operations. Differing fiscal regimes in foreign countries make it difficult to definedenominator of the expression on a consistent basis, so the measure is not useful to any suhaving operations outside the United States. To understand how DROI is useful in economicuations, it may be worthwhile first to review other evaluation criteria, and the circumstances uwhich they are useful. Some of their shortcomings will illustrate the utility of DROI.

When considering two mutually exclusive projects with the same investment, the one withigher present worth should be accepted. Likewise, when considering an entire collection oftial projects with different investment requirements (such as during budget preparationpresent worth of the total package should be maximized. The decision as to which projeinclude and which to reject is complicated by the fact that not all projects offering a given prevalue require an equal capital investment. DROI is a useful tool for dealing with this problemillustrated by the following group, in Table 9.7, of potential projects available to a firm:

Table 9.7 - Utility of DROI in Project Ranking.

Project

Current YearInvestment

($MM)

After-tax PW 15Investment

($MM) PIPW15($MM) DROI15*

A 12 6 21 9 1.50

B 8 4 17 5 1.25

C 4 2 18 4 2.00

D 6 3 19 2 0.67

E 2 1 16 3 3.00

F 2 1 20 2 2.00

G 8 4 14 -2 -.50

* Assumes these are after-tax numbers and that no overhead, tax credits, or depreciationcredits exist.



turn-condi-

f the

PI

nt

ce itrally

intobove

gidrd, a

istentocket

reachg theresent

the

lows,yout,ison ofming

ot onlyure ofeded

ermin-

Assume that this year’s capital budget allows $20 MM of expenditures. Since the projects reing at least 15 PI exceed the available funds, some projects must be foregone. Under thesetions, the firm should rank its projects in such a way as to maximize the present worth opackage of projects. Ranking these projects on the basis of the highest PW15 results in Projects Aand B being selected with a combined PW15 of $14 MM. Ranking these projects on the basis ofresults in the selection of projects A, F, and D with a combined PW15 of 9 + 2 + 2 = $13 MM forthe total $20 MM investment. Ranking on the basis of highest DROI15 yields projects E, C, F, andA for a combined PW15 of 3 + 4 + 2 + 9 = $18 MM for the $20 MM investment, which is consistewith the goal of maximizing PW15 of the package of projects given the spending limitations.

The PW method of ranking fails in the situation described above because of thedifferent invest-mentsrequired to yield a given present worth. The PI method also fails to rank projects sinimplies an ability to reinvest cash thrown off by a project at the PI rate. Since this is not genethe case, the PI method does not compare projects on a consistent basis.

In summary, DROI is of use in ranking projects of different investment magnitudes. It takesaccount the time value of money and it also measure a project’s susceptibility to risk. In the aexample, a DROI15 of 1.50 is the minimum which would be accepted. Amoco in fact has no riminimum DROI criterion. In general, where a 15 PI is Amoco’s minimum investment standaDROI15 would be determined and used to rank the available investment projects. A DROI15 equalto zero will indicate that the 15 PI standard has been met. While DROI provides a consmethod of ranking projects, other factors such as payout, ROI, and maximum cash out-of-pmay be considered depending upon the investment climate.

Payout

Payout (PO) is defined as the length of time taken for the cumulative cash flow of a project tozero. For some projects payout provides a rough measure of risk, by indicating how loninvestment capital is exposed. Amoco has no specific payout time criterion. When neither pworth, PI nor DROI distinguishes between two mutually exclusive projects, the one withshorter payout is generally preferred.

The major shortcoming of the payout standard is that it fails to account for the timing of cash for to recognize cash flows after payout. If, for example, most of the project life occurs after palater cash flows are not considered by the payout criterion. Table 9.8 summarizes a compartwo projects which have identical payouts but differ in present worth and illustrates how the tiof cash flow is ignored by payout.

When used in combination with PI and present worth, payout does serve a useful purpose. Ndoes it indicate how long investment capital is at risk, but it also functions as a rough measliquidity. For instance, if Amoco’s management decided that all available capital was to be nenext year for a major expenditure, e.g., a large acquisition, then payout time could be the deting factor in ranking economically qualified projects.



flowpreci-lationWhenmentve-

y theesent

amati-ffectcash

5 PI

mple.go outoppor-thatis not

Return on Investment

Return on Investment (ROI) is defined as the ratio of the undiscounted cumulative net cashof a project to the total investments (after tax and overhead and including investment and deation tax credits). The ROI calculation is performed in the same manner as the DROI calcu(shown on page 9-8) with the exception that all values are undiscounted in the ROI equation.comparing project with similar cash flow patterns, such as a number of individual developdrilling wells, ROI, in combination with payout, can provide an indication of project attractiness.

Like payout, however, ROI does not account for the time value of money. This is illustrated btwo projects in Table 9.9 which are identical with regard to ROI. When evaluated on a prworth basis, which accounts for the time value of money, Project B is clearly preferred.

Another characteristic of ROI, which may be misleading, is that the measure increases drcally with an increase in project life. The example in Table 9.10 clearly demonstrates this efor five projects, each of which shows a 15 PI on a single $1,000 time zero investment. Thereturn is the total amount of cash to be returned to the investor at the end of the project.

All five projects are equally attractive assuming the ability to reinvest the cash in similar 1opportunities over the lives of the projects.

Amoco has no minimum ROI standard, for reasons which are apparent from the above exaThe high ROI, long-life project does have the advantage that the company does not have toand find a 15% reinvestment opportunity quite as soon, but as long as it is assumed that suchtunity canbe found, there is no need for a minimum ROI. Requiring minimum ROIs indicatesthe company does not have the ability to find reinvestment opportunities. As a result, ROIincluded in ULTRAFRAC.

Table 9.8 - Pitfalls of Optimizing Using Payout.

Year

Net Cash Flow

Project A Project B

0 -$2000 -$2000

1 1500 1000

2 500 1000

3 1000 1000

PW15 = $ 299 $ 240

PI = 23.3 21.0

PO = 2.0 years 2.0 years



en-

, theres of

). Theecause

thef

Incremental Economics

The PI standard should be employed toqualify projects for acceptance, but not to select betwemutually exclusive projects, i.e., projects such thateither Project A or Project B may be undertaken, but not both.

Incremental economics should be run in this case. If both projects return positive cash flowsis an opportunity cost in opting for one over the other. Hence, the benefit to the firm, in termincreased cash flow, is the difference (or increment) between the two cash flows.

An importance use of incremental economics is shown by the example below (Table 9.11two alternatives represent the options of developing or dropping a certain lease. Note that bAlternative A generates tax benefits with no cash expenditures, the resulting PI is infinite.

Examining either mutually exclusive option in isolation can result in an incorrect decision. Inexample, while Alternative A provides a positive PW15 due to the benefit of being able to write of

Table 9.9 - Pitfalls of Optimizing Using ROI.

Year Project A Project B

0 -200 -200

1 100 150

2 100 150

3 150 100

4 150 100

Total 300 300

ROI 1.5 1.5

PW15 138.1 158.9

Table 9.10 - ROI and Project Life Relationship.

Project Life(years)

Cash Return($) PI ROI

1 1,162 15 0.16

5 2,117 15 1.12

10 4,482 15 3.48

20 20,089 15 19.09

50 1,808,042 15 1,807.04



nt ben-

sinceof tax

in the

flowhe hor-tion.

the asset on current taxes, it is less than the PW15 of Alternative B. On the other hand, deciding oAlternative B means foregoing the option of dropping the lease (an opportunity cost). The neefit to Amoco of developing would not be $3.5 MM, but rather $0.5 million.

When considering development of a lease, it is important to examine the drop alternativedoing nothing is generally a poor alternative. Dropping the lease at least has the advantagewrite-offs. A development vs. drop analysis is ideally handled by incremental economics, asabove example. On occasion, the alternatives may both have negative (but different) PW15’s, butan incremental PW for one alternative over the other will always be positive.

Mutual exclusivity frequently gives rise to multiple PIs since the cumulative incremental cashmay have several sign reversals. In that case, the PW vs. discount rate profile would cross tizontal axis (PW=0) more than once (Table 9.12). The following example illustrates this situa

Table 9.11 - Incremental Economics.

Alternative A(Drop)

Alternative B(Develop)

PI 19

PW15 ($MM) 3 3.5

Table 9.12 - Illustration of Multiple or Dual PI.

YearProject A

(M$)

Investment Annual Cash Flows

CumulativeIncremental

Project B(M$)

Incremental(B)-(A)

0 -400 -500 -100 -100

0-1 75 150 75 -25

1-2 100 150 50 25

2-3 100 150 50 75

3-4 125 150 25 100

4-5 100 150 50 150

5-6 50 0 -50 100

6-7 50 0 -50 50

7-8 25 0 -25 25

8-9 25 0 -25 0

9-10 20 0 -20 -20

Total 270 250 -20 -20

∞



overB tohapezero

m ofvest-

licatedver,can-

relied

r

ation-PWximiz-

The incremental cash flow in this case represents the benefit to the firm of selection Project BA. The cash flow of Project A becomes an opportunity cost which is subtracted from Projectdetermine the incremental cash flow. The present worth profile would be of the general sshown on Fig. 9.1. Points C and D indicate the discount rates for which the present worth is(definition of PI).

This type of present worth profile is typical of most incremental projects. To avoid the problemultiple PIs, the present worth of the incremental cash flow stream (B-A) at the marginal reinment rate should be examined. A positive PW15 would imply acceptance of Project B.

Sometimes the incremental cash flow approach is hard to apply. On some of the more compscenarios which arise, the correct incremental cash flow stream is difficult to identify. Howethe importance of choosing the correct project alternatives and properly defining the problemnot be overstressed. Failure to do so may lead to a decision which does notmaximizethe presentworth of the total cash flows and, hence, of the corporation.

Present Worth Vs. the Profitability Index

The present worth concept is theoretically superior to PI for several reasons, and should beupon more heavily than PI.PI may lead to an incorrect ranking decision because of the implicitassumption that project proceeds can be reinvested at the PI rate.Present worth, on the othehand, assumes reinvestment at the discount rate used in its calculation. While PI serves toqualifyan investment, it does not provide the correct solution when ranking projects under capital ring or when choosing among mutually exclusive alternatives. The project offering the higher15

should instead be selected in a mutually exclusive situation, since we are concerned with maing the present value of thecash flowfrom projects as the means by which to maximize thevalueof the firm.

Fig. 9.1 - Present Worth Profile.



ccur’ cashand

ts isyear.

t ther-

h.

ingever,

Situations in which present worth and PI may rank mutually exclusive projects differently owhen the investment cost of one is larger than another, or when the timing of the projectsflows differs. Examples of mutually exclusive projects include the farm-out vs. drill decisionthe choice of 40-acre spacing vs. 20-acre spacing in the same field.

An example where PW and PI give different rankings to projects with dissimilar investmenillustrated in Table 9.13. Project A calls for the investment of $100 and yields $150 after oneIts PI would be 40.6 with continuous discounting (point-in-time cash flow) and its PW15 would be$29. Project B, in contrast, would require a $1 million investment and provide $1.25 million aend of a year. Its PI is only 22.4 but its PW15 is $75,884. The two methods rank the projects diffeently, as the PI of A is greater than the PI of B, but the PW15 of B is greater than the PW15 of A.Obviously, you would prefer project B as it returns significantly more than the present wort

An example of projects differing in the timing of their cash flows is shown Table 9.14. In rankProject C and Project D on the basis of PI, Project C would appear to be the better option. Howa closer examination reveals that Project D has the higher PW15.

Table 9.13 - Comparison of PW vs. PI for Ranking.

Year

Annual Cash Flows ($)

Project A Project B

0 -100 -1,000,000

1 150 1,250,000

PI 40.6 22.4

PW15 29 75,884

Table 9.14 - Timing of Cash Flow.

Year

Annual Cash Flows (M$)

Project C Project D

0 -25,000 -25,000

0-1 15,000 0

1-2 15,000 30,000

2-3 15,000 25,000

3-4 15,000 10,000

PI = 53 45

PW15 = 20,120 22,098



s the. Noteminesd 20-

wn inaxis.

Dualate to

at it canage is

ly, itbasisamil-dentshort-

Fig. 9.2 is a plot of present worth vs. discount rate for two mutually exclusive projects such a40-or 20-acre spacing alternatives, which shows the curves crossing at some positive PWthat the particular discount rate at which the decision is made (15% in this example) deterthe selection. At the intersection of the two curves one would be indifferent between 40- anacre spacing.

PI causes problems in reaching a decision when multiple (Dual PI) solutions occur, as shothe previous example. PI is defined as the intersection of the PW profile with the horizontalNote that in that example (Fig. 9.1), the profile has two points of intersection with the axis. InPI projects, PI should not be used as a ranking criterion. In this example, it is more appropriutilize present worth and Discounted Return on Invement in the ranking process.

Why then use PI at all? There are several advantages to the PI method. One advantage is thbe compared directly with the cost of capital and anticipated rate of return. A second advantthat, unlike the PW method, PI abstracts from the size of a project. A PW15 of $50,000 can beobtained on a $10 million investment as well as on an original outlay of $25,000. Accordingis possible to distinguish these two different sized projects on the basis of PI, but not on theof present worth. A third advantage, and not an insignificant one, is Amoco management’s fiarity with PI. If management has a basic familiarity with the method, they can feel more confiin their decision-making process. Despite these advantages, it is important to be aware of thecomings of PI, as well as those of each of the other investment criteria.

Fig. 9.2 - Present Worth Profiles.



deci-ss thanelay

o theng so

der-zero,

vs.nt out-soared.

at time

ano pastexists.

Yet-to-Spend (Point Forward Evaluation) Vs. Full-Cycle Economics

As has been noted, timing is a very critical variable in making effective economic evaluationsion. The present value of a dollar of revenue received at some future date is considerably leif it were available now. Ideally, one would prefer to receive all revenues immediately, and dall expense as long as possible

Timing enters into economic analysis in yet another way. The time of the analysis relative tlife of the project must be established. Most of the discussion of investment decision-makifar has centered around the timing and magnitude of cash flows produced by a projectas viewedat the present time.Fig. 9.3 indicates the cash flows and the point at which the analysis is untaken (time zero) for such a project. Note that the analysis and initial investment occur at timewith cash flows received later in the project life.

Not all analyses are conductedbeforethe initial investment is made. In the case of a developdrop decision on a well proposal, a reanalysis may be required after a considerable investmelay has already occurred. Perhaps estimates of reserves have fallen or operating costs haveFig. 9.4 illustrates a well reassessment made after the initial investment spending occurredt = -2. In this case, how should the economics be calculated?

The original investment of $1,000 represents asunk costand the $200 received at time t = -1 isbenefit already received. No current decision can affect past expenditures, and conversely,spending should be considered in a yet-to-spend decision. One qualifier to this statement

Fig. 9.3 - Point Forward Evaluation.

Fig. 9.4 - Full Cycle Evaluation.

0

500 600 800 600

1 2 3 4

-1,000

Project Life

200 200 500 600 800 600-2

-1,000

-1 0 1 2 3 4ProjectLife



taxes.

flowstax) isuentlyratinga PW,000itive

or not

ignedginalexplo-

Past spending, or sunk cost, may affect future economic decisions via an impact on futureSuch effects must be considered in a yet-to-spend analysis.

The rationale of yet-to-spend economics, which evaluate only current and prospective cashand disregard sunk costs, can best be illustrated Table 9.15. Assume that $500,000 (afterspent on exploration in a certain area and that two fields are found. The fields are subseqdeveloped at a cost of $600,000 per field (after tax). One field is projected to have an opecash flow, after all operating costs, royalties, and local and federal taxes, of $2,000,000, and15

of $560,000. The second field, of poorer quality, will have an operating cash flow of only $800with a PW15 of $80,000. A yet-to-spend evaluation would show that both fields have posPW15’s and PI’s of 15 or better. Accordingly, both would be developed.

If the sunk exploration costs ($250,000 per field) were considered when deciding whetherto develop the discoveries, the net cash flow and PW15 would differ, and the decision would differ.

In fact, Field B would not be developed, and all the exploration costs would have to be assto Field A. In this event, an analysis of thefull-cycleeconomics shown as Table 9.16 of developinField A (including all sunk and anticipated cash flows over the life of a project) would show a fnet cash flow of $900,000 ($2,000,000 less $600,000 development cost and $500,000 total

Table 9.15 - Rationale of Point Forward Economics.

Point Forward Economics

Field A Field B Total

Operating Cash Flow $2,000,000 $800,000 $2,800,000

Development Cost 600,000 600,000 1,200,000

Net cash Flow on Development $1,400,000 $200,000 $1,600,000

Development PW15 $ 560,000 $ 80,000 $ 640,000

Table 9.16 - Full Cycle Economics

Full-Cycle Economics

Field A Field B Total

Operating Cash Flow $2,000,000 $800,000 $2,800,000

Development Cost 600,000 600,000 1,200,000

Sunk Cost 250,000 250,000 500,000

Net Cash Flow 1,150,000 - 50,000 1,100,000

PW15 Including Sunk Costs $310,000 $-170,000 $140,000



costcashldision.

sultingered.

cash-spendsidered

ration cost) and a PW15 of $60,000 ($310,000 less Field B’s $250,000 share of the explorationat time zero). This answer is incorrect because by developing Field B, the total full-cycle netflow would be $1,100,000, with a PW15 of $140,000, which is greater than that of developing FieA only. Thus the analysis which considers sunk costs leads to an incorrect investment dec

It must be remembered that past expenditures may have a substantial effect on thefuture tax con-sequences. Previous costs may affect depreciation, cost depletion, and the gain or loss refrom sale or abandonment of the original project. As a result, future tax liabilities would be altIn analyzing future investments or other alternatives, considerations must be given to theeffects of the future tax consequences. Although sunk costs should be disregarded in a yet-toinvestment decision, except as to the resulting future tax consequences, they should be conin compiling a PIA. PIA’s will be discussed in detail in Section IV.


Elements Of Fracturing Treatment Costs

aterialtivitiescosts.mpa-

eptn, perepowere addi-and

withually

00 -p to 4

sed onervice

andosts

r time;ters, etc.

pedPrices

tiveifolds,nsferd con-

9.3 Elements Of Fracturing Treatment Costs

Fracturing treatment costs are primarily comprised of pumping and blending charges, and mcosts for fracturing fluids, fluid additives, and propping agents. In some cases associated acsuch as well pulling costs, tubular rentals, etc., contribute significantly to the total treatmentSome of the types of costs associated with fracturing treatments from stimulation service conies and other associated contractors and suppliers are presented.

Stimulation Service Company Costs

Treatment costs usually include the following service company cost components.

Fracturing Pumping Equipment: Pump truck costs base minimum charges for all trucks excpressure multiplier pumps, per well, for a period up to 4 hours continuous service, on locatiohydraulic horsepower ordered. Prices are based on pumping pressure, and hydraulic horspumping charges increase with pumping pressure increment increases. Other costs includtional pumping time over 4 hours, nonpumping service time, minimum pump truck chargesstandby pumping equipment.

Propping Agent Pumping Charge:These charges apply when propping agents are pumpedany fluid and are in addition to the fracturing pump truck charges. Prices per unit weight (us100 lbs (CWT)) are based on the type and size of the proppant.

Pressure Multiplier Pumps:These are usually required for pumping pressures in the 10,020,000 psi range. Charges include pressure multiplier pump base charges, per well, for uhours continuous service on location, per hydraulic horsepower ordered. Prices are bapumping pressure. Other costs include additional pumping time over 4 hours, nonpumping stime, minimum charges, standby unit charges, and propping agent pumping charges.

Blender Services:Base charges for continuous proportioning and mixing of propping agentfracturing fluid, based on average injection rate, first 4 hours or fraction, per well. Other cinclude blender services time over four hours, based on pumping rate, nonpumping blendeblender standby; other blender and equipment charges such as paddle mixers, densitome

Slurry Concentration Handling Service:These charges apply when propping agents are pumwith any fluid and are in addition to blender charges and propping agent pumping charges.depend on propping agent concentration.

Auxiliary Stimulation Equipment: These items include sand handling equipment, radioacmaterial for tagging sand, wellhead protective injection equipment (tree-savers, etc.), mannitrogen, CO2 equipment, flow meters, fracturing support units, special equipment (tanks, trapumps, valves, wellheads), ball sealer equipment, treating connections left on location, sancentrators, etc.



1961)

969)

s

9.4 References.

1. Campbell, J. M.,”Analysis and Management of Petroleum Invests, Risk, Taxes and Time.”

2. Prats, M.: “Effect of Vertical Fractures on Reservoir Behavior - Incompressible Fluid Case,” SPEJ (June105-18;Trans., AIME, 222.

3. McGuire, W. J. and Sikora, V. J.: “the Effect of Vertical Fractures on Well Productivity,”Trans., AIME (1960)219, 401-04.

4. Tinsley, J.M.et al.: “Vertical Fracture Height - Its Effect on Steady-State Production Increase,” JPT (May 1633-38;Trans., AIME, 246.

5. Elkins, L.E.: “Western Tight Sands Major Research Requirements,”Proc., Gas Research Inst./American GaAssn./U. S. DOE Intl. Gas Research Conference, Chicago (June 9-12, 1980).

6. Petroleum Production Handbook, T. C. Frick (ed.), SPE, Richardson, TX (1962) Chap. 38.

7. Guerrero, E. T.:Practical Reservoir Engineering, The Petroleum Publishing Co., Tulsa, OK (1968) 72-75.


References.




Chapter

Special Topics10

This chapter is divided into two sections:

10.1 Fracturing Tests starting on page 10-3 and

10.2 TerraFrac starting on page 10-29.

Hydraulic Fracturing Theory Manual10-1September 1992

Special Topics10

Hydraulic Fracturing Theory Manual 10-2 September 1992

Fracturing Tests

rstand-eters.frac-of ther coremea-

n.

o, andtech-

e andsen-gradingpertiesation.

coring

sts uti-f thehet in-situhydra-sealedUnlessg theheg thement ore per-

sticityxially

10.1Fracturing Tests

Introduction

The success of a fracture stimulation depends on the accuracy of the design theory, an undeing of the propagation or growth of hydraulic fractures, and the accuracy of design paramMany field and laboratory tests are available which allow a more accurate approximation ofturing parameters. This section covers the more widely used tests; providing a descriptiontest procedures and in some cases interpretation guidelines. Descriptions are included fotests, prefrac logs, perforation and permeability determination, bottomhole treating pressuresurements, closure stress tests, minifracs, postfrac logs, and fracture azimuth determinatio

Core Tests to Determine Mechanical Rock Properties and Fluid Loss Coefficient

Fluid Loss Coefficient Core can be analyzed to determine elastic modulus, Poisson's Ratifluid loss coefficient for use in fracture stimulation design. Core analysis is currently the bestnique available for obtaining elastic rock properties.

Full diameter cores should be cut through the interval of interest, including both the pay zonadjacent formations, with coring of adjacent formations of sufficient thickness to obtain repretative samples. In many cases, a gradation occurs from one bed to another; such as shaleinto a sandstone forming a siltstone transition bed. In a case such as this, mechanical protests performed on the transition core would not be representative of the adjacent shale formWhen available, open hole logs from an offset well should be used to determine the requiredinterval.

Core for rock properties tests should have a minimum diameter of 2-1/2 inches, since the telize a 3/4-inch diameter by 1.5-inch long plug which is cut perpendicular to the long axis ocore. The core should be peel-sealedon location. Peel-sealing the core prevents dehydration of tsamples, which provides a more accurate measure of elastic and mechanical properties aconditions. Transporting the core back to a warehouse for peel-sealing allows excessive detion of samples. Past attempts to designate specific portions of the core interval to be peel-have led to confusion, and critical portions of the core have sometimes been left unsealed.personnel familiar with the selection of samples for the specific tests can be on location durinentire coring operation, it is recommended thatall of the core be sealed on-site and shipped to tAmoco Research Department or outside laboratory for analysis. The core facility handlinsamples should be advised that the core is to be shipped straight to the Research Departlaboratory with no whole-core or plug analysis to be performed. Routine core analysis can bformed after samples have been collected for mechanical properties tests.

As discussed in Chap. 4, core is analyzed by triaxial stress-strain tests to yield modulus of ela(E). The test is performed by applying a hydraulic pressure to the core plug, then loading it a


Special Topics10

,

tative

onee

f thehe

xpla-tion on

and measuring the displacement or strain (ε). In determining modulus for fracturing calculationsthe applied hydraulic pressure is normally set equal to the mean effective stress (σ) acting on thereservoir rock, i.e., the confining stress. An additional stress is then applied which is represenof the net pressure above confining pressure required to open a fracture.E is then determined fromthe resultant stress strain curve asE = σ/ε. Fig. 10.1 shows stress strain curves for a sandstunder several confining stresses to illustrate the sensitivity ofE to confining stress. Care must btaken to estimate the confining stress correctly.

Poisson's ratio (γ) is also determined in the laboratory in a triaxial stress test.γ is the ratio of lateralexpansion to longitudinal contraction for a rock under a uniaxial stress condition. The ratio omeasured lateral strain to the axial strain isγ. Fig. 10.2 shows an example of strain data and tcalculation ofγ.

Cores are also used to perform static fluid loss tests to determine a fluid loss coefficient. An enation of the testing procedure and interpretation and use of the results is covered in the secfluid loss.

Fig. 10.1 - Modulus of Elasticity.

Confining Stress, psi7,500

3,000

0

30,000

24,000

18,000

12,000

6,000

00.00 0.20 0.40 0.60 0.80 1.00

E-02STRAIN ( ) - Percentε

Stress ( σ)psi

Example: At a confining stress of 7500 psi,

E =σ/ε = 24,000 / 0.0047 = 5.1 x 106 psi


Fracturing Tests

ervoirl, neu-t data

eforeliptical

casesbeen

ed thatre as a

ular toted tohole

Prefrac Logging Program

As a minimum, the standard suite of open-hole logs should be run for determination of rescharacteristics and lithology. This should include gamma ray and/or spontaneous potentiatron porosity and density logs, and resistivity logs. Several special logs can be run to collecspecifically related to fracturing.

Borehole Geometry Log

Borehole geometry logs measure hole eccentricity or ellipticity and its orientation, and thermust be run in open-hole. It has been noted in some fields that wellbore washouts create elcross sections, with the long axis of these noncircular sections sharing a common azimuth. Inwhere the minimum hole diameter is equal to bit diameter, such washouts or spalls havetermed “breakouts” and have been reported on from many different areas.1-3 These should not beconfused with common washouts or key seats as illustrated by Fig. 10.3. It has been theorizbreakouts are caused by shear failure induced by a stress concentration around the wellboresult of (1) unequal horizontal stress and (2) appreciable shear strength of the rock.5 Unequalstresses will cause a preferential stress concentration on the side of the wellbore perpendicthe maximum stress direction, and if the shear strength is high enough, breakout will be limithis region. In such a case, the breakout will develop with the long axis of the elliptical boreperpendicular to the expected azimuth of hydraulic fractures.

Fig. 10.2 - Poisson’s Ratio.

30,000

24,000

STRESS (s )psi

18,000

12,000

6,000

0-1.00 -0.80 -0.60 -0.40 -0.00 0.20 0.40 0.60 0.80 1.00

E-02-0.20

STRAIN (e) - Percent

LATERAL

AXIAL

Example: Poisson’s Ratio (g) = - e lat. / eaxial = -(-0.0008 / 0.0047)= 0.17


Special Topics10

ust beoodl for

sureeds

Because alternative interpretations exist for breakouts, it should be emphasized that care mtaken in utilizing this type of data to determine fracture azimuth. Although it may not be a gtechnique as a primary indicator of azimuth, borehole ellipticity could serve as a powerful tooextrapolating data where more comprehensive azimuth measurements have been made.

Long Spaced Digital Sonic Log (LSDS)

The Digital Sonic Log has shown to have application in the estimation of vertical in-situ clostress distribution.6 This data is critical in defining the differential closure stresses between b

Fig. 10.3 - Borehole Geometry Log. 4


Fracturing Tests

ssionalretical-situhe cal-

usedrger.ndardrosityss pro-

sion.the

depthf thede-idth,

per-lses,ck ofthatf the

e ce-ould bess thant maylts ob-rupturerature

for determining fracture height growth parameters. These logs measure shear and compresonic velocities, which may be used to calculate dynamic elastic rock properties, and theoclosure stress in a given horizon.7 The stresses thus calculated should be calibrated to actual instresses by measuring the in-situ closure stress in 3-4 zones in the wellbore, and shifting tculated stresses to match in-situ stresses.

Both Amoco and Schlumberger have developed a Digital Sonic Log, both of which have beensuccessfully in this technique. This log is run routinely by both Amoco and SchlumbeSchlumberger charges only slightly more for their Long Spaced Sonic Log than for the staBorehole Compensated Sonic Log. The Long Spaced Sonic Log yields as good or better pomeasurements as the Borehole Compensated Sonic, and yields information regarding strefiles as described above, along with a qualitative indication of natural fractures.

Downhole Television and Borehole Televiewer

One of the most reliable methods for determining fracture azimuth is with downhole televiThe tool is a downhole closed circuit television developed by Amoco, which directly viewsborehole wall making interpretation very simple. The disadvantages to using this tool are itslimitations, openhole requirements, and the need to deliver visibly clean fluid to the bottom owellbore.8 While TV logging cannot be done on a routine basis, it offers a reliable method oftermining fracture azimuth at the wellbore, and supplies additional data about fracture wheight, etc., as part of the process.

The Borehole Televiewer (BHTV) is a “sonic” type tool, introduced by Zemaneket al.,9 which inprincipal should be an excellent fracture identification tool. However, the tool has not alwaysformed up to its potential. The tool consists of a crystal which emits high frequency sonic puthen receives and records the reflection of these pulses from the borehole wall - with the laany reflection possibly indicating the existence of a fracture. One problem in using this tool isborehole ellipticity and/or wellbore deviation creates blind areas due to decentralization otool.10 Also, at this time, fracture width cannot be defined with this logging method.

Cement Bond Log

A cement bond log should be run in all wells to be fractured to determine the integrity of thment bond. Should poor bonding exist through the pay and adjacent beds, these zones shcement squeezed to afford a hydraulic seal between zones of potentially lower closure strethe pay. Channeling behind pipe would tend to aggravate any height growth problems thaexist and could introduce discrepancies in data to be collected later that may make any resutained meaningless. Poor cement behind casing further aggravates the problems of casingdue to poor quality casing or joints and can affect temperature behavior on postfrac tempesurveys.


Special Topics10

andhave

ulatingnding

-tem-. 10.4mper-

be in-non-

n. The

Temperature Logs

Base Temperature Logs:A base temperature log is run to determine geothermal gradientstatic bottomhole temperature. To obtain a valid static temperature survey, the well shouldbeen shut-in for at least one week prior to logging. Temperature disturbances caused by circthe well during clean-out operations, etc., require approximately 3-5 days to dissipate, depeupon individual well conditions.

Preperforation Cold Water Circulation Temperature Surveys: This technique is used to identify zones in the wellbore which are apt to exhibit temperature anomalies on postfracturingperature surveys due to thermal conductivity and/or wellbore effects, such as shown in Figand Fig. 10.5. These anomalies often are confusing and misleading and often complicate teature log interpretation for fracture height determination.

Many anomalies are usually present on postfracturing temperature surveys but may not alldicative of the presence of a fracture. This technique provides a method to “subtract out” thefracture related anomalies to improve the accuracy of postfrac temperature log interpretatioprocedure for obtaining these surveys is as follows:

Fig. 10.4 - Example of Cold Water Circulation Test.

THERMALCONDUCTIVITYEFFECTS

PRE FRACPROFILE

STATICLOG

POST FRACPROFILE

FRACTURE TOP PROFILESSEPARATE

8800

9000

9200

9400

9600

9800

10000

10200

10400

HO

LE D

EP

TH

(ft)

175 200 225 250

TEMPERATURE ( °F)

PERFS

8600

8800

9000

9200

9400

9600

PERFS

HO

LE D

EP

TH

(ft)

POST FRACLOG PRE FRAC TEMP LOG


FRACTURE TOP

FLUID MOVEMENTEFFECTS

2830

2790

2750

2710

2670

2630

HO

LE D

EP

TH

(M

ET

ER

S)

180 200 220 240 260

82 93 103 116 126

TEMPERATURE°

°

F

C


Fracturing Tests

ay to

e lim-ping

tweenshouldrvoir:

1. Run static temperature log over interval to be fractured [approximately 1,000 ft above pPlug Back Total Depth (PBTD)] at 20-30 ft/min.

2. Run tubing open-ended to 20-25 ft above PBTD.

3. Circulate water down tubing and up the annulus at maximum possible rate within pressuritations for at least 3-4 hours. Friction reducer may be added to the water to reduce pumpressure. The water may be recirculated if a significant temperature differential exists bereservoir temperature and the outlet temperature of the water at the surface. Cold waterbe added to the inlet stream when the outlet temperature rises by 25% of the initial reseinlet temperature differential.

4. Trip in with temperature tool to 1,000 ft above the pay interval.

Fig. 10.5 - Effect of Wellbore & Completion. 11

INJECTIONCURVE

INJECTION TIME2100DAYS

150DAYS

48 HRSI

11” DIAHOLE

INJECTION ZONE

75 80 85 90 95 100 105 110 1154300

4400

4500

4600

4700

4800

4900

HO

LE D

EP

TH

(ft)

TEMPERATURE ° F

75 80 85 90 95 100 105 110 1154300

4400

4500

4600

4700

4800

4900

INJECTIONCURVE

HOURS SHUT-IN3 12 48

CEMENT14” DIAHOLE

INJECTION ZONE

TEMPERATURE °F


Special Topics10

d, usu-

test maylog in-

f four

ear onentedrictionfords aeed toulate

5. Log downward at a speed of 20-30 ft/min.

6. Pull tool to 1,000 ft above pay.

7. Repeat logging runs every 30-45 minutes until temperature anomalies are well developeally 3-5 logging runs.

This technique has shown more success in some areas than others. Still, in new areas, thebe run to verify whether it shows potential to increase the accuracy of postfrac temperatureterpretation.

Perforating and Permeability Determination

The interval to be stimulated should be perforated with a casing gun at a minimum density oshots per expected bpm fracturing injection rate, using guns with 90° or 120° phasing.

Perforating with many large holes will reduce perforation friction pressure and excessive shthe frac fluids. Perforating out of phase decreases the likelihood of the perforation being oriin a line at a high angle to the fracture azimuth, as shown in Fig. 10.6, and therefore reduces fpressure and shear between the wellbore and fracture. This method of perforating also afbetter flow path to the wellbore during bottomhole pressure buildup and may reduce the nacidize the zone to attain an adequate flow rate for obtaining a buildup. If possible, do not stimor breakdown the perforations prior to flow testing.

Fig. 10.6 - The Effect of Zero Degree Phasing Perforations on a Fracture Treatment.

NarrowGap Vertical

Fracture

min

max

Cement


Fracturing Tests

one issamew the

g layers,e shaleible ins test-

for-lossost-

h and

ss testsgrowthe me-eded is“fool-ictionyieldlts are

sacker)s at the. Thepocket

oys atech-For then pro-

main

Better results are obtained in the minifrac and fracture treatment analysis if only one pay zperforated. The analysis of net pressure is complicated by fracturing multiple zones at thetime, particularly if the zones are separated by sufficient thicknesses of confining beds to allopropagation of two or more fractures at the same time.

When closure stress tests are performed in shales to measure the closure stress of boundinexperience has indicated that high density perforating with large charges could compress tharound the perforation tunnel. This added stress to the rock has made breakdown imposssome cases. Little is known at this time about the best method for perforating shales for stresing and further field research testing is required in this area.

A bottomhole pressure buildup test should be run to determine formation flow capacity. Themation permeability is used to determine optimum fracture length, to set limits on the fluidcoefficient to be used for designing the fracture stimulation, for improving the accuracy of pfracturing performance prediction, and for analyzing postfrac buildup tests for fracture lengtconductivity.

Bottomhole Treating Pressure Measurement

Three tests require the measurement of BottomHole Treating Pressure (BHTP): closure streto establish the base fracturing pressure, minifracs to determine the mechanics of fractureand to estimate fluid loss coefficient, and fracture stimulation BHTP analysis to determine thchanics of fracture growth and to evaluate the treatment. In all cases, the pressure data nethe pressure at the perforations to eliminate tubing friction pressure as a factor. To date, aproof” technique has not been developed to accurately account for all variables affecting frpressure to allow the subtraction of friction pressure from surface treating pressures toBHTP. Extensive work has been performed in this area by the industry, but at best the resuonly reliable about 50% of the time.

Three techniques are recommended for measuring BHTP.12 Fig. 10.7 shows wellbore schematicfor executing these procedures. The first requires running tubing open-ended (without a pand pumping down either the tubing or annulus. The other side is then static, and pressuresurface on the static side are a direct reflection of BHTP, corrected for hydrostatic pressuresecond technique involves the use of a surface readout pressure gauge mounted in a sidemandrel, strapping the electric line to the outside of the tubing. The third technique empldownhole recording pressure bomb placed into a simple mandrel below a packer. With thisnique, actual BHTP are recorded, but the data cannot be accessed until after the treatment.two procedures where BHTP is measured in real-time, the stimulation service companies cavide on-site computer vans which facilitate quick manipulation of the prefrac test and/ortreatment data for plotting to make on-site judgmental decisions.


Special Topics10

be-g, theas onat the

n willsmittedr waterirds,ted for

is de-

bingllowse gaugessure

Procedure for Measurement of Static Pressure Tubing/Annulus

Run tubing open ended (without packer) to within 100 ft of the perforations. When pumpinggins, tubing and annular pressure will be continuously recorded. If pumping down the tubinannular pressure is a direct reflection of BHP, with a correction for hydrostatic head. Any gthe static side (tubing or annulus) should be circulated out of the hole so that the pressuresurface will reflect true bottomhole treating pressures. Gas bubbles in the static fluid colum(1) alter the hydrostatic head of the fluid and (2) dampen the pressure response being tranthrough the fluid as the gas compresses and expands with changing pressure. Collect fousamples for determination of specific gravity at one-third points (beginning, one-third, two-thand end) of the total volume used to load and circulate the hole. Since BHTP must be correchydrostatic head to derive bottomhole closure stress, an accurate fluid density determinationsirable.

Procedure for Recording Downhole with Surface Readout

Prior to running tubing for any of the BHTP tests, a side pocket mandrel is placed in the tustring just above the packer. A port from the side pocket mandrel to the inside of the tubing ameasurement of pressure by a pressure gauge in the mandrel. The wireline for the pressuris strapped to the tubing as the string is run in the hole. The wireline is connected to the prebomb through an electrical port which is an integral part of the side pocket mandrel.

Fig. 10.7 - BHTP Measurement.

PtQt

PaQa

Qt - 0

Pt - BHP-Pnor

Qa - 0

Pa- BHP-Pn

WIRELINE

SIDE POCKETMANDRIL

PRESSURESENSOR

MANDRILPORT

PACKER

Q Q

PACKER

PERFORATEDSUB

(BLAST JOINT)

PRESSUREBOMBSEATINGNIPPLENO-GO NIPPLE

(a) (b) (c)

Open-ended Tubing Downhole RecorderWith Surface Readout

Downhole PressureMeasurement


Fracturing Tests

essureat

pe. Atmentn mea-

, (1) theero per-meterbly the

n a ma-

onto

curated frac-ute. Forusually

able fornt is

ure de-nies, thely un-

cture, toeval-e frac-essure

cture,o de-

clo-

Procedure for Downhole Pressure Measurement

Prior to running tubing and packer a special mandrel must be constructed in which to set a prbomb. The mandrel consists of (from bottom to top) a joint of tubing with a “NO-GO” nipplethe bottom, a seating nipple, a perforated sub (usually a blast joint) and a pup joint for tailpidownhole recording pressure bomb is set into the seating nipple with a slick line, and the treapumped down tubing and out the perforated sub. Pressures at the bottom of the string are thesured by the bomb.

To ensure the mandrel assembly does not cause increased fluid shear during the treatmentperforated subs should be prepared such that the perforation area is adequate to yield near zforation friction, and (2) the outside diameter of the assembly should not exceed the outer diaof the tubing to provide adequate annular space between the assembly and casing. Probaeasiest and least expensive way to prepare the perforated sub is to have the holes drilled ichine shop. This ensures all holes are open, large and properly spaced.

After the fracture treatment, the pressure bomb may be retrieved with a slick line by latchinga fishing neck on top of the bomb or by pulling the tubing string.

Pressure Measurement Devices

A number of service companies are equipped to accurately record treating pressures. Acpressure measurements are a must. The minimum pressure/time resolution for minifrac anture treatment analysis is pressure to the nearest 10 psi and data acquisition once per minclosure stress tests, pressure resolution to the nearest 1 psi and 10 sec data acquisition isadequate. Fracturing service company pressure transducers have proven to be too unrelithis type of work. Aside from the resolution of the transducers, fracturing company equipmeoften not accurately calibrated and is prone to failure. In cases where highly accurate pressvices have been used to independently monitor the same pressures as the service compatwo pressure recordings commonly differed by 100-500 psi. This level of accuracy is generalacceptable for this type of analysis.

Closure Stress Tests

Closure stress is measured to determine the minimum pressure necessary to sustain a fraallow determination of net fracture pressure during a minifrac and fracture stimulation, and touate proppant strength requirements. In the analysis of bottomhole treating pressures whilturing, closure pressure is analogous to the flowing bottomhole pressure measured in prtransient tests; i.e., it is a base pressure above which pressure analysis is performed.

Closure stress is determined by pumping a volume of fluid at a rate sufficient to create a fraand then allowing the fracture to close either by shutting-in the well and allowing pressure tcline to below closure pressure, or by flowing the well back until pressure is reduced to below


Special Topics10

eclineterminete testtypical

te. Inepend-y, low

en-stress

e. Theied ash per-t in-ring

hut-inflowre

edre pres-ed thatcreaseof for-

sure pressure.12 In either case, closure pressure is identified by a change in the pressure dcharacteristics as the fracture closes. Either test should be preceded by a step-rate test to deextension pressure, which should be within about 100 psi of closure pressure. The step-rawill also assure that a fracture exists before the closure test is attempted. Fig. 10.8 shows astep-rate test plot. The time step at each rate should be constant, e.g., 2 minute intervals.

To create the fracture requires that a sufficient volume of fluid be pumped at a sufficient rapractically all cases, pumping for 10-20 minutes at 10 bpm has proven to be adequate; but, ding on the results of the step-rate test, these guidelines may be altered. In low permeabilitleakoff formations 50 bbls at 5 bpm may be sufficient.

Any fluid, which is compatible with the formation rock and fluids, may be used for the tests. Gerally whatever base fluid is to be used for the fracture stimulation is used for the closuretest: produced formation water, 2% KCl water, etc.

Determination of closure pressure from shut-in pressure declines is operationally very simplwell is left shut-in until pressure declines to a point at which closure pressure can be identifshown in Fig. 10.9. This method of determining closure pressure is most appropriate for higmeability formations which close quickly. In this type formation, closure would occur almosstantly during a flowback test making identification of closure pressure difficult. The data, dua shut-in decline test, should be plotted real-time, if possible, to determine the length of stime. The decline data can also be plotted on a Horner type plot, Fig. 10.9, to identify radialand, thus, ensure the fracture has closed.13 Also, this plot can be used to estimate the near wellboreservoir pressure,p*. To ascertain the length of shut-in time may require a “trial” test, followby subsequent tests. The number of tests performed will depend on the agreement of closusures picked. If good agreement is evident, only 2-3 tests may be required. It has been notin liquid filled reservoirs closure pressure increases with each subsequent test due to an inin pore pressure. When this occurs, the earlier test results are probably most representative

Fig. 10.8 - Step-Rate Test.

INJE

CT

ION

RAT

E

TIME INJECTION RATE

“FRACTUREEXTENION PRESS”

“BO

TTO

MH

OLE

” P

RE

SS

.AT

ST

EP

EN

D


Fracturing Tests

e treat-

han ahich

is de-ose ofthe

ecline2wing

just-r - se-

mation closure and should be used to calculate net pressure during the minifrac and fracturment.

Closure stress determination from flowback pressures is only slightly more complicated tshut-in decline test and is more conducive for low to moderate permeability formations, wwould require extensive monitoring periods during a shut-in decline test. The flowback ratetermined by the fluid loss characteristics of the formation and the surface pressure; the purpthe flowback being to flow back at a rate on the order of the rate at which fluid is being lost toformation. For this flow back rate, a characteristic reverse curvature occurs in the pressure dat closure pressure as shown on Curve “b” in Fig. 10.11. A suggested initial flowback rate is 1-bpm. The proper flowback rate is usually determined by trial and error on the first tests, floback at different rates until the correct flow back rate is found and a good test is obtained.

To control the flowback rate, a manifold similar to that shown in Fig. 10.12 is required. An adable choke, gate valve, or automatic constant flow regulator (e.g., manufactured by Oilmaste

Fig. 10.9 - Pump-In/Shut-In Decline. Fig. 10.10 - Pump-In/Shut-In Decline.

Fig. 10.11 - Pump-In/Flowback.

SHUT-IN DECLINE

POSSIBILITIES

CLOSUREPRESSURE

“BO

TTO

MH

OLE

” P

RE

SS

tsi or t i + tsi

tsi = SHUT-IN TIME

ti = INJECTION TIMEINTO FRACTURE

P*

STARTRADIAL

“BO

TTO

MH

OLE

” P

RE

SS

LOG (tsi +ti) / tsi

tsi = SHUT-IN TIME

ti = INJECTION TIME= INTO FRACTURE

PUMP IN /FLOWBACK

a

b

c

pc

TIME“BO

TT

OM

HO

LE”

PR

ES

S a - RATE TOO LOW

b - CORRECT RATE FORpc - CLOSURE PRESS AT

CURVATURE REVERSALFROM (+) TO (-)

c - RATE TOO HIGH


Special Topics10

henof themeter.without in

chokechoken theithout

ability

ecorderbe suf-ut the

te re-wingratee, thetion.tdownest

wbackeases.

rial no. 280-390) should be installed downstream of a 1-inch and/or 2-inch flowmeter(s). Wselecting a flowmeter for measuring the flowback rate, one must keep in mind the rate rangemeter used. Service companies tend to recommend, and will usually supply, a 2-inch turbineExperience has shown that it is difficult to impossible to measure flowback rates of 1-2 bpmmeters of this size. The best choice seems to be a 1-1.5 inch turbine meter with digital readbpm. Digital readout boxes, showing flowback rate, should be positioned near the valve orfor ease, accuracy, and quickness of adjustment. To minimize the adjustment of this valve orfrom test to test, a full opening gate valve or Lo-Torque valve should also be placed betweewellhead and flowmeter(s). This valve can be used to open and close the flowback system whaving to fully close the valve downstream of the flowmeter(s).

The following procedure is recommended for closure stress tests in low to moderate permeformations:

1. Since real-time data is necessary, either open-ended tubing or a downhole pressure rwith a surface readout is required to obtain BHP. In some cases, surface pressures mayficient. Pressures and rates should be monitored and recorded continuously throughotests.

2. Perform step-rate test to determine “extension pressure” and the minimum injection raquired to fracture the formation. Utilize the step-rate test as a pump-in/flowback test, flothe well back at a constant rate of 2 bpm. Note: In latter portion of pump-in, the injectionshould be increased by an equivalent rate to the planned flowback rate. At the same timflowback manifold should be opened and the flowback rate set prior to shutting down injecThe shutdown should be slow, i.e., in 10-15 seconds be pumping at 0.5 bpm, then shucompletely. This will prevent “fluid hammer” effects in the wellbore, which could distort tresults.

3. Flowback at a constant rate until the BHP approaches reservoir pressure. To keep the florate constant will require constant adjustment to the valve as the surface pressure decr

Fig. 10.12 - Pump-In/Flowback.

WELLHEAD

FLOWBACKLINE

GATE VALVEOR LO-TORQUE

VALVE

1”FLOWMETER

2”FLOWMETER

DIGITAL READOUT

DISPOSALPIT

ADJUSTABLE CHOKEOR GATE VALUE

DIGITAL READOUT


Fracturing Tests

or are inrom theo high

ecordDo not

oxi-a frac-

frac-ment,, and.,

ystemHTP

ncy

e usedessureld be

ll pres-

s off to

ssureeters,ich is

4. Based on the required injection rate, perform pump-in/flowback test by injecting fluid fminimum of 10 minutes, e.g., if rate = 5 bpm, pump 50 bbls. Flowback using proceduSteps 2 and 3 above. Constant flowback rate may have to be increased or decreased f2 bpm in Step 2 depending on the results from Step 3. Fig. 10.11 shows examples of toand too low flowback rates.

5. Repeat Step 4 until a repeatable closure pressure is established.

6. Perform pump-in/shut-in decline using the same volume and rate determined above. Rpressure decline until pressure falls well below the closure pressure determined above.flowback during this step.

Note: In formations with relatively high permeability (>0.1 md), acid ISIPs may closely apprmate closure stress, if the acid jobs are small, pump rates are low (yet high enough to createture), and nitrogen or CO2 are not mixed with the acid.14 This will yield a first estimate of closurestress in most cases and will set an upper limit for closure stress.

Minifracs

Minifracs or “Calibration Treatments” are pumped to obtain information on the mechanics ofture propagation during the small treatment (net fracture pressures, height growth or confineetc.), and to collect data for determination of fracture geometry, time for the fracture to closefluid loss coefficient.15 This test consists of pumping a relatively small volume of fluid, i.e10-20% of the main fracture treatment depending on its size, using the main treatment fluid sand pumping at the expected main treatment injection rate. During and after the minifrac, Band the shut-in pressure decline is monitored and recorded.

The following procedure is recommended to perform the minifrac:

1. Batch mix the required amount of fracturing fluid. Batch mixing is required for gel consisteand to minimize friction pressure variations throughout the test.

2. One of the BHP measurement techniques described previously on page 10-11 should bfor measuring pumping and shut-in decline pressures. Tubing pressure and casing prshould be recorded by the fracturing service company. In addition, the wellhead shourigged with a lubricator as described under Temperature Profiles.

3. Pump minifrac at expected main treatment rate (constant rate throughout test). Record asures and rates continuously throughout the job.

4. Shut down and record pressure decline for as long as required until the pressure bleedwell below the closure stress value previously determined by the closure stress test.

Fracture geometry can be evaluated from a Nolte-Smith Log-Log plot of net fracturing pre(BHTP - closure pressure) vs. pump time as discussed previously in Chap 8. Design paramincluding the fluid loss coefficient, can be determined using the pressure decline analysis whalso presented in the Fracturing Pressure Analysis Section.


Special Topics10

out in-a stat-osureicator.ith a

lectionmpera-eraturessure

eachhew thete. Itry datatart-

racture

l heatthesetem-ation

surveyation

iffer-ute oth-ose”use an

Postfrac Logging Program

Temperature Decay Profiles

Temperature decay profile surveys should be run as soon as possible after a minifrac withterfering with the collection of pressure decline data. If bottomhole pressure is measured viaic tubing string, the lubricator can be rigged up on the wellhead ahead of time, and the clstress tests and minifrac can be pumped through a wing valve or T-connection below the lubrThe temperature tool is run in the lubricator before the job and isolated from the wellbore wvalve while pumping.

If a wireline pressure gauge is run during the prefrac tests, the pressure decline data colshould be completed and the pressure gauge removed prior to installing and running the teture tool. If bottomhole pressure is measured via a static open-ended tubing string, the temptool should not be run until after the pressure decline since running the tool will distort the predata.

A minimum of three logging runs should be made at intervals of 45 minutes from the start ofrun. No backflow from the well should be allowed prior to or during temperature profiling. Tlogs should be run from several hundred ft above the pay interval to several hundred ft belofracture bottom or plug back Total Depth (TD), logging down at a speed of about 20 ft/minuis the Amoco engineer's responsibility to see that the logging company records the necessaon the log heading, including fluid type and volume pumped, total pump time, times minifrac sed and ended, and fluid surface temperature.

This same procedure also applies to temperature decay profile surveys run after the main ftreatment.

Postfrac Temperature Log Interpretation

After a minifrac or fracture treatment, heat transfer will occur above the treated zone by radiaconduction, while over the fracture faces, heat transfer will be by linear flow. Ideally, acrosstwo areas temperature will recover at different rates following the end of pumping, causing aperature anomaly to develop which identifies the fractured zone. Unfortunately, this ideal siturarely occurs, making misinterpretation of postfrac temperature logs all too common.

As discussed earlier on page 10-8, a static base temperature log and cold water circulationmay be run to determine the temperature gradient and identify anomalies caused by formchanges, the wellbore, and the completion. Fig. 10.13 shows the conductivity effects from dent formations on both pre and postfrac logs.11 Fig. 10.5, shown previously, shows how a washobehind casing will create a cool anomaly which may be interpreted as a fractured zone. On ther hand, a washout completely filled with cement will insulate the wellbore and create a “hot non the log. Also, a change in tubular diameter, such as the bottom of tubing or casing can ca


Fracturing Tests

g and

prob-id

to an-ardthe

l downbe a

ar then truef thes ver-at best,

“offset” in the log. All of the above anomalies can be detected with the base temperature losubtracted out of the postfrac log interpretation.

Fig. 10.14 shows a warm anomaly or “hot nose” above the fractured zone and the obviouslems associated with picking the fracture top.11 It has been theorized that this is caused by flumovement after shut-in and that the “hot nose” is part of the fracture height.

Temperature crossovers are often seen below the perforated interval from one logging runother. Below the perforations, the wellbore is filled with stagnant, hot fluid; and any downwfracture growth will place cooler fluid outside the casing than inside. Thus, heat flow will be inopposite direction from that across and above the fractured zone and the wellbore may coowith time. This often results in a temperature “crossover,” as seen in Fig. 10.15, which cangood indicator of the bottom of the created fracture.

Since temperature logs are shallow investigative tools, they only see the fracture at or newellbore. If the created fracture is not vertical, but dipping at an angle somewhere betweevertical and true horizontal, temperature logs will not provide a meaningful interpretation ofractured interval as illustrated in Fig. 10.16. This same problem occurs when the fracture itical and the wellbore is deviated. Thus, under these circumstances temperature logs are,poor indicators of fracture growth.

Fig. 10.13 - Pre and Postfrac TemperatureLogs Showing Thermal Conductivity

Effects.

Fig. 10.14 - Temperature Log ShowingWarm Anomaly Above Treatment Zone.

8800

9000

9200

9400

9600

9800

10200

10400

PERFS

10000

80 93 108 121 135

175 200 225 250 275

° C

° FTEMPERATURE

3170

3110

3050

2990

2930

2870

2810

2750

2690

STATICLOG

PRE FRACPROFILE


POST FRACPROFILE

FRACTURE TOP PROFILESSEPARATE

HO

LE D

EP

TH

(ft)

HO

LE D

EP

TH

(m

eter

s)

TOP

POST FRACTEMP LOG

TOP?

TOP?3750

3720

HO

LE D

EP

TH

(m

eter

s)

PERFS

190 200 210TEMPERATURE

88 93 98

°F

°C

GRSP

12200

12300

HO

LE D

EP

TH

(ft)


Special Topics10

ryble in, the

In a well which “goes on vacuum” after a stimulation, the falling fluid level will continually carwarm fluid down into the fractured zone, obscuring the temperature anomaly. This is possiinjection well stimulations and on pumping wells with low reservoir pressure. In such casesfluid level should be allowed to stabilize prior to running the logs.

Fig. 10.15 - Crossover Below Perfs.

Fig. 10.16 - Fracture - Wellbore Communication.

#1#4

4 1

TOP

TEMPLOG

GR

Fracture CommunicationWith Wellbore

Vertical FractureStraight Wellbore

Dipping FractureOr Deviated Wellbore


Fracturing Tests

ctureations,

e ofd ma-

diatelyow-

theyropor-

Thuse an-

nd ahannelcturedosited

e log.f the.fact,

ludely ac-

Postfrac Gamma Ray Logs

In addition to temperature logging, postfrac gamma ray logs are often run to evaluate fraheight. Fracturing proppant is tagged with radioactive-traced proppant, the tracer concentrshown in Table 9.1, have proven to give good results:16

Noting the variation in half-lives, a postfrac gamma ray log should be run early in the half-lifthe tracer used. Also, for the most definitive results with regard to fracture height, the taggeterial should be added throughout the stimulation.

One advantage of gamma-ray over temperature logs is that they do not need to be run immeafter a stimulation, allowing wellbore fill below perforations to be removed before logging. Hever, the other restrictions on the temperature logs apply equally to radioactivity logs - that isare shallow investigative tools (shallower, even, than temperature logs), the response is ptional to fracture width, and the wellbore and completion can effect the resultant log profile.while the two logs are often used in combination, the potential exists for them to confirm onother and still not yield reliable results.

One disadvantage of radioactivity logs is their inability to distinguish between a fracture asmall channel behind casing. The temperature response due to a small amount of flow in a cor annular space behind casing may not alter the radial flow heat conduction around unfraportions of the wellbore and does not affect the temperature logs. However, any material depin a channel is indistinguishable from tagged material in a fracture.

Fig. 10.17a shows a good example of pre and postfrac gamma ray logs.11 The radioactive materialindicates the top and bottom of the fracture and correlates well with the postfrac temperaturA second example, shown in Fig. 10.17b, utilized radioactive material in only the later pact ofracture treatment, thus radioactive material showed up only through a portion of the fracture11 Inthis same figure, radioactive material shows up across the “hot nose” indicating this to be, inpart of the fracture height.

Fracture Azimuth Determination

Currently, the four most common techniques available for determining fracture azimuth inctiltmeters, borehole geophones, oriented core, and borehole geometry. The two most wide

Table 9.1 - Tracer Concentrations.

Tracer Half-LifeRecommendedConcentration

Iodine 131 8 days 2 mc/10,000 lbs

Iridium 192 74 days 1 mc/10,000 lbs

Scandium 46 85 days 0.5 mc/10,000 lbs


Special Topics10

re anal-

ble”oped tose intiltme-at thedrau-

asure-..

l, at ad in ate the

cy onf themagni-

cepted techniques are tiltmeters and geophones, with increasing acceptance of oriented coysis generated through recent consistent results from strain relaxation measurements.

Tiltmeters

Tiltmeters are highly sophisticated, extremely accurate bi-axial instruments which utilize “bubsensors to measure the change in angle of a surface. These devices were originally develaim intercontinental missiles, and were later employed by the U.S. Geological Survey for uthe study of earth movements associated with earthquakes and volcanic activity. The use ofters to monitor hydraulic fractures, at depths up to 10,000 ft, is based on the assumption thearth will respond in a “more or less” elastic manner to deformations caused by opening a hylic fracture. In that case, the surface of the earth will deform in a predictable manner and mements of this deformation can be interpreted to obtain data with respect to fracture geometry17,18,19

Fig. 10.18 illustrates surface deformations associated with fractures of several orientations

A typical tiltmeter array consists of 12-16 instruments evenly spaced radially around the weldistance of about 0.4 times the depth of the zone to be fractured. Each instrument is installeshallow cased hole, usually 10 to 20 ft deep, and packed into position using sand to insuladevice from surface weather and noise effects.

The tiltmeter instruments are capable of measuring changes in tilt of a surface with accurathe order of 1 x 10-7 radians. Due to the sensitivity of the measurements, changes in the level oearth's crust due to solid earth tides cause changes in the surface angle which are orders of

Fig. 10.17 - Comparison of Postfrac Gamma-Ray and Temperature Logs.

POSTFRACTEMPPROFILE

BASEGR

POST FRACGAMMA RAY

FRAC ZONE

PERFS

9200

9300

9400

9500

9600

HO

LE D

EP

TH

(ft)

(a)

POST FRACGAMMA RAY

WARMNOSE

RADIOACTIVE SANDIN WARM NOSE

POSTFRACTEMPPROFILESP

9100

9200

9300

9400

9500

HO

LE D

EP

TH

(ft)

2780

2810

2840

2870

2900

HO

LE D

EP

TH

(m

eter

s)

(b)


Fracturing Tests

short-lteringateda tilthows

ombi-oducel and

andhas

place.22.

tude greater than the fracture treatment. Fortunately, the period of the fracture event is mucher than the “tidal noise” and can be separated by post-analysis using frequency domain fiand/or tidal filtering. The residual from this filtering is then used to measure the tilt signal relto hydraulic fracturing. The signals from both channels of a tiltmeter are combined to formvector which embodies direction and magnitude of the tilt measured at that site. Fig. 10.19 sthe recorded response for one channel from a single site.

To analyze the data, observed tilts are compared with theoretical values for many possible cnations of fracture azimuth and dip; and thus, the azimuth and dip are determined which prthe least error. An example shown in Fig. 10.20 shows theoretical tilt responses for verticahorizontal fractures and Fig. 10.21 shows a least error fit for observed vs. theoretical data.

Just as the pattern, or direction of the tilt vectors is related primarily to the fracture azimuthdip, the magnitude of the vectors is principally a function of fracture volume. Recent workbeen performed which combines fracturing pressure analysis with tilt vector magnitude tobounds on created fracture dimensions for wells shallower than 4000 ft, as seen in Fig. 10

Fig. 10.18 - Surface Tiltmeter Monitoring.

DIP = 90°

DIP = 60°

DIP = 30°

DIP = 0°


Special Topics10

periodprep-

olvedthese

g frac-ire-ent

otherset offm of

Because extensive site preparation is required to install the tiltmeter array and a site “aging”is required, scheduling should begin far in advance of the hydraulic fracture treatment. Sitearation should begin a minimum of three weeks prior to the treatment. District personnel invin this testing should work closely with the Research Department in setting up and executingtests.

Borehole Geophones

Borehole geophones measure the sonic energy, or noise, produced while a formation is beintured.21-,25A set of three geophones is typically installed in the wellbore on a single conductor wline prior to the well being fractured. Since a wireline is in the hole while fracturing, the treatmis usually a small gelled-water minifrac without proppant. One geophone is vertical and thetwo are horizontal. The orientation of the geophone tool is determined using surface shotsin strategically located sites in an array with a radius equal to the depth of the tool. A minimu

Fig. 10.19 - Typical Tiltmeter Record for a Hydraulic Fracture.

CHANNEL 9 - RAW DATA1.7670

1.7537

1.7404

1.7270

1.7137

1.7004

1.6871

1.6738

1.6604

1.6471

1.6338317.53 317.56 317.61317.58317.51 317.55 317.59 317.62 317.64

VOL1

Tilt Signal

11:12:11:58:05 TO 11:12:15:40:31

READING ARE FROM CHANNEL 9 PROJ: 84-28TOTAL OF 217 POINTS PLOTTEDSTARTING TIME IS 11:12:11:58:05ENDING TIME IS 11:12:15:40:31STARTING TIME IN JULIAN UNIT IS 317.49867ENDING TIME IN JULIAN UNIT IS 317.65314


Fracturing Tests

Fig. 10.20 - Theoretical Tilt Vectors.

Fig. 10.21 - Observed vs. Theoretical.

VERTICAL FRACTURE

(mirror symmetryrelative to the strikeof the fracture)

HORIZONTAL FRACTURE(radial symmetry relativeto the wellbore)

Theoretical

Observed

Well B DIP = 50 AZIMUTH=29


Special Topics10

at equalurce

gatedrrivale sonicsults

.e cor-red tofield,anal-swerthe di-

four shots are detonated, one at a time, using dynamite. The sites are 20 ft deep and locatedintervals of 45°. The recorded arrival time of the shock wave indicates the direction of the sowith respect to the geophones.

Fracture azimuth is determined by analyzing the arrival times of sonic waves being propathrough the formation as the rock cracks and the fracture extends in length. The variation in atimes between the three geophones is analyzed to determine the direction of the source of thwaves (the tip of the fracture) from the wellbore. Fig. 10.23 shows an example of the type of reobtained.

Oriented Core Analysis

The use of oriented cores to predict fracture azimuth has been suggested for many years3,5 Thechief advantage of core analysis for fracture azimuth is its ease of application. During routining operations, the additional work required to orient and analyze the core is small compaother azimuth measuring procedures. Also, since most coring is done early in the life of thethe azimuth data collection is very timely. The biggest disadvantage to common oriented coreysis is the fact that this is an indirect measurement, and it is difficult to be certain that the anis correct. The most successful core analysis, which has only recently gained acceptance, isrect on-site measurement of strain relaxation.26

Fig. 10.22 - Fracture Dimensions.

R = 330 ft

R = 1000 ft

R = 570 ft

Fracture Volume

Err

or in

Fil

(%)


Fracturing Tests

kniveszimuthh that

en thee is torien-

-, or a

acturepurelyheours.can be

after there goodto pre-

mple tore then

The indirect oriented coring process uses a shoe on the bottom of the core barrel with threeto cut grooves in the core. One of these is the reference groove at a known orientation to an alug attached to the inner core barrel. An orientation tool is mounted above the core barrel sucthe orientation lug is visible when the tool photographs the compass. The correction betwereference knife and the orientation lug can be pre-set in the shop, but a preferred techniquhoist the barrel in the derrick and use an optical aligning device to determine their relative otation; this is then recorded for future calculations.27 Since this tying of orientation to depth is indirect, the biggest sources of error come from incomplete core recovery, breaks in corespiraling reference groove.

The technique of direct on-site measurement of strain relaxation from cores to determine frazimuth is based on laboratory observations that the stress-strain behavior of rocks is notelastic, but is a function of loading rate and time.28 In such a case, strains stored in the rock by tin-situ stresses will not be released instantly when the core is cut, but will relax over many hIf the core can be recovered and instrumented during this time, the orientation of stressesdetermined by measuring relaxation in different directions.

The strain relaxation process involves selecting several core samples as soon as possiblecore reaches the surface. The samples should be selected from intact core sections to ensuorientation data, then removed to a reasonably constant temperature environment, sealedvent moisture evaporation, and then tested by attaching the deformation gauges to the sarecord strain relaxation (and temperature) data from 12 to 24 hours. These measurements aused to calculate the orientation of the in-situ stresses.29 Fig. 10.24 shows typical data taken fromstrain relaxation measurements on a shale sample.30

Fig. 10.23 - Borehole Geophones.

X

Y

Z

SIG

NA

LA

MP

LIT

UD

E

Time

Typical microseismic event recorded on threeorthogonally mounted seismic detectors. Thetime marks are 0.017 sec. apart.

N

EW

S

Polarization of “single-phase” events recorded withthree-axis geophone package.downhole


Special Topics10

o mea-e-

and a

near

a canfferentbore-geom-uthwith aincor-pre-of the

The strain relaxation technique has proven accurate in several tests where azimuth was alssured with other procedures.21,26,31,32These include tests in a volcanic tuff in Nevada; a low permability Mesa Verde Sandstone; a low permeability gas sand in the Cotton Valley Formation;high porosity, high permeability sandstone in Oklahoma.

Borehole Geometry

The geometry of the borehole (ellipticity) may be affected by the stresses in the earth in thewellbore region. The fracture azimuth is also affected by these stresses.1-5 Therefore, a simple cor-relation might be made between borehole ellipticity and azimuth if conclusive supporting datbe obtained. As discussed earlier on page 10-5, borehole ellipticity measurements in two diareas indicate that fracture azimuth is either parallel to or perpendicular to the long axis of thehole. By combining the results of the azimuth measurements discussed above with boreholeetry, a correlation might be made for a given field which would greatly simplify fracture azimdetermination. Borehole geometry must be obtained in open-hole, and can be measuredBorehole Geometry Log as previously discussed on page 10-5, or from the oriented caliperporated into the Dipmeter Log. The Dipmeter Log yields information useful in geologic intertation, whereas the Borehole Geometry Log describes only the orientation and dimensionsborehole.

Fig. 10.24 - Strain Relaxation.

Elastic Strain

Time-Dependent Strain

C

C'

B

A

to t1 t2TIME

ST

RA

IN

Core Recovered and Instrumented at C'

Det1 - t2


Introduction To TerraFrac

mer-since

in thecess-

is notof datadevel-s. It can

frometry.

eome-redicta nu-d be-. Thetop ofmp-

mplesthese

eudooweverplestC,

cien-f frac-nfining, etc.to use

nding

e well-

10.2Introduction To TerraFrac

TerraFrac is a three dimensional fracturing simulator that is probably the most advanced comcially available hydraulic fracturing simulator presently available. It has been in use by TRC1983 to address nonstandard fracture design problems. Fracturing design problems in wellsValhall Field in the North Sea, as well as exploration wells all over the world, have been sucfully addressed using the TerraFrac Simulator.

TerraFrac is installed on the IBM mainframe computer at the Research Center; however ityet released for general use because of the complexity and time-consuming requirementsinput, code execution, and the requirement of output analysis. The code is still undergoingopment and possesses very advanced capabilities such as thermal and poroelastic effectalso be applied in fracture designs where the fracture may migrate considerably up or downthe point of initiation, to study the effects of perforation placement on resulting fracture geom

TerraFrac solves the fracturing problem, in a general sense, i.e., it determines the fracture gtry as part of the solution process. A three-dimensional simulator is a simulator that can pfracture shape (width and height at any point along the fracture’s length). However, this ismerically demanding problem which is strongly nonlinear because of the coupling requiretween the fluid pressure distribution in the fracture with the stiffness of the opening fracturesolution of the problem may lead to fracture shapes that are complex, like the one at theFig. 10.25, which are relatively realistic even though they employ certain simplifying assutions, e.g., planar fractures. The schematics in the lower part of Fig. 10.25 represent the simodels which are still used throughout the industry for simulating fracture treatment design. Tare idealistic versions of what may be happening downhole.

There is a category of fracturing simulators of intermediate complexity referred to as psthree-dimensional simulators. These simulators can also predict the shape of the fracture, hthey still apply some simplifying assumptions on fracture propagation derived from the simmodels. The majority of practical fracture design simulators (e.g., STIMPLAN, MFRAFRAC-HT, etc.) fall in this category and are widely used because of their computational efficy. However, they do not replace the need for a 3-D simulator, especially when estimation oture shape is crucial, e.g., for fractures near water bearing zones in the absence of strong cobarriers, unconventional location of the perforations within adjacent layers to the pay zoneTherefore, depending on the fracture design problem, the engineer has a wide range of toolsand obtain the proper solution, the most important of which is sound judgment and understaof the governing physical phenomena.

General Description of the TerraFrac Simulator

The TerraFrac simulator assumes that the fracture is planar and symmetric with respect to th


Special Topics10

blem

“ulti-lanarorous

bore. It determines fracture geometry from the solution of a complex nonlinear interaction proof:

• 3-D Rock Deformation assuming Elastic Layered Formation;

• Fluid flow in the Fracture with Proppant and Thermal Effects on Rheology;

• Fracture Propagation using Linear Fracture Mechanics;

• Leakoff;

• Simplified (One Dimensional) Thermo-poroelastic Effects;

• etc.

In this sense TerraFrac is a fully three-dimensional fracturing model. However, it is not themate” model! Our desire is for a “super” simulator which can determine the shape of nonpfractures and account for other phenomena such as formation nonlinearity (plasticity) rig

Fig. 10.25 - Models to Better Simulate “Actual” Fracture Behavior.

Actual?R

wfPenny

Area of Largest

Approximately EllipiticalShare of Fracture

Flow Resistance

wf

wf

xf

xf

hf

Perkins & Kern Geertsma & deKlerk



res-s, this

frac-frac-ed. Ite per-ablyssurefluidforma-cture

e theke asticcan beat thee elas-

hich

elasticritical

f thecturenforce-

ementfrac-

cture

n ofrme-

o re-solve

modeling of the formation-fracture interaction (coupled thermo-poroelastic interaction of theervoir and the propagating fracture), etc. Although much work has been done in these areatype of simulation capability is not yet available.

A short account of how the model works is as follows: TerraFrac determines the shape of theture in an iterative way. It starts from an assumed fracture shape which is small relative to theture dimensions after the treatment has ended. An initial pressure distribution is also assumis recommended to start the simulation with a small penny shaped fracture at the center of thforations. If the perforation interval is large with varying closure stresses, one would probchoose to initiate the fracture at a point where the closure stress is minimized. The fluid preis assumed (handled internally) initially to be constant. The fracture width is dependent onpressure distribution and fracture shape, and can be calculated from an elastic 3-D rock detion solution. TerraFrac has the capability to calculate fracture width for a general shaped frawith arbitrary fluid pressure distribution. The widths from this solution stage are used to solvfluid flow problem in the plane of the fracture. The fracturing fluid is assumed to behave lipower law fluid in laminar flow between parallel plates. The widths determined from the elasolution are used as the distance between the parallel plates. The fluid pressure distributioncalculated by satisfying the momentum and continuity equations with appropriate conditionsboundaries. Then the fracture widths can be derived using this pressure distribution from thtic solution. In this way, an iteration can be performed to derive the pressures and widths ware mutually consistent.

The tendency of the fracture to propagate can be quantified using the closure stress profile,constants, toughness, the fluid pressure distribution, and the pre-existing fracture shape. A CFracture Width is calculated internally (Fracture Propagation Criterion), and, if the width ofracture at some given distance behind the front exceeds the critical fracture width, the frapropagates. The distance of propagation is calculated from a combination of mass balance ement and the amount by which the widths near the front exceed the critical fracture width.

During the propagation, leakoff is assumed to occur according to Carter's model. The enforcof the continuity equation dominates the propagation and is given priority. In this sense, theture Propagation Criterion is satisfied within broad tolerances, while continuity near the frafront is satisfied more accurately.

Input To Terrafrac

The downhole schematic of Fracturing Configuration of Fig. 10.26 gives a pictorial definitiothe input to TerraFrac. For each formation layer, it is required to define reservoir (porosity, peability, thermal conductivity), and elastic (modulus, Poisson’s ratio, toughness) properties.

Input relative to model discretization, convergence limits, input, output, and plotting are alsquired. The model uses a combination of finite element and boundary element methods to


Special Topics10

eralses in10.28.scope

l lay-from

main-

mem-finedTer-

ff andts theloped

the coupled elastic-fluid flow problems. The fracture’s boundary is subdivided into quadrilatwhich are further subdivided into four triangles. All calculations are performed on the trianglterms of the pressures and widths at the nodes. A typical plot of the mesh is shown on Fig.A detailed explanation of the input and the numerical techniques employed are beyond theof this manual.

Note that the original TerraFrac formulation required the elastic properties to be uniform in alers; however, an approximate way to account for the first order effects of modulus changeslayer to layer has been recently implemented by TerraTek and has been installed on our IBMframe computer.

Terrafrac Simulation Runs

Confined Fracture Growth

The TerraFrac model can be applied for confined fracture growth. However, it should be rebered that confined fracture growth is not the target of the TerraFrac capabilities. For confracture growth, Perkins and Kern (PKN) type model programs are much more efficient thanraFrac.

The confined height example of Fig. 10.27 was devised to demonstrate the influence of leakoclosure stress gradient during the initial stages of fracture evolution. Furthermore, it acquainreader with typical plots of the TerraFrac results produced by the plotting postprocessor deve

Fig. 10.26 - Schematic of the Hydraulic Fracturing Configuration.



metersfractureem-nfin-

025 ftr 4 is

frac-wn inthen

itional

by the Frac Group. The mesh used for this analysis is shown on Fig. 10.28.

The fracture shape evolution gives an appreciation of the delicate balance of the in-situ paraand their influence on fracture shape. Note that steep closure stress gradients push thegrowth upwards, while low leakoff zones encourage fracture growth in them. This is clearly donstrated in Fig. 10.29 which shows fracture evolution until the fracture reaches the lower coing layer (layer 5). The fracture was initiated as a penny shaped fracture of 20 ft radius at 8depth. The fracture initially propagates as a penny in layer 3. Later, the small leakoff of layeattracting the fracture more than the closure stress gradient of 0.848 psi/ft of layer 2 and theture grows downwards until it reaches layer 5. The remainder of the fracture evolution is shoFig. 10.30. The fracture, being confined below, grows upwards until it reaches layer 1. Fromon, we have confined fracture growth and the TerraFrac analysis does not offer anything addto a PKN program analysis.

Fig. 10.27 - TerraFrac Example (Demo 2).

Depth-Feet

LAYER 1 C = 0.0

LAYER 2 0.848 psi/ft C = 0.0025 ft/min

LAYER 3 C = 0.0025 ft/min

C = 0.0005 ft/min

LAYER 5 C = 0.0

7200 7300 7400 7500 7600

1 - 2

2 - 33 - 4

4 - 5

PERFORATIONS

FORMATION PROPERTIES

E = 1.26x106 psiυ = 0.35

FLUID VISCOSITYµ = 90 cp

PUMPING RATEQ = 16 bbl/min

CLOSURE PRESSURE - PSI

-7900

-8000

-8100

-8200

CLOSURE STRESS

LAYER 4


Special Topics10

Fig. 10.28 - Step 50 Fracture Grid.

Fig. 10.29 - Fracture Evolution Steps 0-40.

X (FEET)

Y (

FE

ET

)Y

(F

EE

T)

X (FEET)



greate firstof in-efore,

vol-e dur-uld beressureith ref-

lesserlow the

theseis ex-

onver-urioust sen-

Fig. 10.31 shows the plot of the step number vs. injected volume. From this plot we see that aamount of steps (and computing time) is spent during the initial propagation stages. During th40 steps only 23 barrels of treatment volume were injected. Consequently, a small amountjected volume propagates the fracture rapidly to a confined mode of fracture extension; thera PKN analysis is essentially applicable for the entire fracturing propagation process.

Fig. 10.32, Fig. 10.33, and Fig. 10.34 show plots of the evolution of leakoff volume, fractureume, fracture width, and fracture dimensions. Fig. 10.35 shows the variation of fluid pressuring the fracture treatment. The “kinks” in the pressure are due to numerical reasons and shosmoothed out (see next paragraph). The maximum pressure reflects the slightly increasing ptrend of confined fracture extension. The pressure at the perforations (depths are plotted werence to the center of perforations referred to as 0.0 ft) shows this increasing tendency to adegree. Note that hydrostatic head in the fracture forces the maximum pressure to occur beperforations.

Fig. 10.36 and Fig. 10.37 show the error distributions of the iteration scheme. Comparingfigures with Fig. 10.35, we see that the pressure distribution is sensitive to these errors. Thispected due to the strong nonlinearity of the problem. Consequently, despite the stringent cgence error of 1%, the TerraFrac user should be able to distinguish real behavior from spnumerical behavior of the solution. This is valid especially for pressures which are the mossitive.

Fig. 10.30 - Fracture Evolution Steps 41-80.

Y (

FE

ET

)

X (FEET)


Special Topics10

Fig. 10.31 - Evolution of Leakoff Volume, Fracture Volume, Fracture Width, and FractureDimensions.


REFERENCE DEPTH (ft): 8.025000E+03REFERENCE PRESSURE (psi): 7.300000E+03

100

80

60

40

20

00 200 400 600 800 1000

TOTAL VOLUME INJECTED (bbl)

ST

EP

NU

MB

ER

STEP NUMBER


800

600

400

200

00 200 400 600 800 1000

BA

RR

ELS

TOTAL VOLUME INJECTED (bbl)TOT. FRACTURE VOL (bbl)

TOT. LEAKOFF VOL (bbl)



drops

takenwell

nity it.

st esti-closure50 psierfo-90 cp

75 psi.

ed be-treat-

th theplexents as

Fig. 10.38 shows the efficiency of the treatment. We see that the efficiency of the treatmentto approximately 20% while 80% of the volume injected leaks into the formation.

Unconfined Fracture Growth

Two examples of unconfined fracture growth are briefly discussed in this section. They werefrom a real case analysis of fracturing treatment for the Upper Hod formation of the 2/8A-17in Valhall. These examples illustrate the capabilities offered by TerraFrac and the opportuoffers to enhance understanding of the fracturing process for complicated in-situ conditions

Fig. 10.39 shows the two closure stress profiles considered; they were derived from our bemates of the in-situ conditions. Case A represents the base case; case B has a 200 psi lowerstress in the Tor relative to case A (due to reduced reservoir pressure after production) and ahigher closure stress in the “Dense zone” to account for its higher confining capacity. The prations are located directly below the dense zone. A constant 15 bbl/min pumping rate and adownhole viscosity fracturing fluid were assumed. The reservoir pressure was taken as 62

Completion experience in Valhall has established that the Tor should not be directly perforatcause it produces solids and plugs the well. The Upper Hod is perforated instead. Upper Hodments have the dual purpose of stimulating the poorer Hod formation and communicating wi“rich” Tor formation. Fracture height growth is not confined and fracture shapes may be comdependent on the in-situ conditions. It has been the practice to design such fracture treatm



0.30

0.25

0.20

0.15

0.10

0.05

0.000 200 400 600 800 1000

INC

HE

S

TOTAL VOLUME INJECTED (bbl)MAX FRAC WIDTH (in)WIDTH (in) AT 0.0000C+00 ft


Special Topics10


Fig. 10.35 - Variation of Fluid Pressure During the Fracture Treatment.


600

500

400

300

200

100

0

FE

ET

0 200 400 600 800 1000TOTAL VOLUME INJECTED (bbl)

MAX FRAC LENGTH (ft)MAX FRAC HEIGHT (ft)MAX HEIGHT ABOVE CNTR (ft)MAX DEPTH BELOW CNTR (ft)


350

300

250

200

150

100

500 200 400 600 800 1000

PS

I

TOTAL VOLUME INJECTED (bbl)MAX PRESSURE (psi)PRES (psi) AT 0.0000F+00 ft



deter-adient,imu-

nd Boriginough

erent.con-

andleakoff

casecaseevel-of the

“penny” shaped fractures for lack of a better alternative. However, using TerraFrac we canmine fracture shape and study the effects of closure stress profile, actual closure stress grleakoff variation, and position of perforations. It is this capability that makes the TerraFrac slator so useful for Valhall field and other fields where no significant confining barriers exist.

Fig. 10.40 shows the fracture evolution for case A. The fracture was initiated (for both A acases) as a small penny (of 10 ft radius) located at the center of the perforations, which is theof the Y-axis. Note that in case A the fracture essentially remains approximately a penny, althsome confinement can be observed at the shale-Tor interface.

Fig. 10.41 shows the fracture evolution for case B. For this case the shape is drastically diffIt grows mainly in the Tor where closure stress is low. The lower part of the fracture simplynects the perforations. This type of behavior can only be quantified by numerical simulationrepresents a delicate balance of the in-situ values of closure stress, closure gradients, andas well as the location of the perforations and fluid rheology.

Fig. 10.42 compares the fracture width profiles along the wellbore for both A and B cases. InA, the maximum fracture width occurs close to the perforations (the origin of the Y-axis). InB, the fracture grows “unsymmetrical” with respect to the perforations and a pinching point dops. Width pinching near the perforations may cause a screen-out during the early stagestreatment.

Fig. 10.36 - Error Distributions of the Iteration Scheme.


1

0.8

0.6

0.4

0.2

CO

NV

ER

GE

NC

E E

RR

OR

(%

)

0 200 400 600 800 1000TOTAL VOLUME INJECTED (bbl)

CONVERGENCE ERROR (%)


Special Topics10

d these A,olumelumectureimatelyrema-nger oftreat-of the

istoryso that

mayximum

own inhavior.ed vol-Due to

Fig. 10.43 shows the fracture width history for both cases. The maximum fracture width anfracture width at the perforations (i.e., at 0.0 ft) are plotted vs. the total injected volume. In cawe see no significant difference between these two values, both of which increase with the vof the fracturing treatment. In case B, the max width occurs in Tor and increases with the voinjected as expected. However, the width at the perforations initially increases (while the frais still a penny) and subsequently decreases at about 200 bbl, to remain constant at approx0.10 inches for the remaining of the treatment. This pinching effect may be the reason for pture screen-out. For such a case, an increased pad volume does not diminish the dascreen-out. More viscous fluid and small proppant may be required to pump the fracturingment successfully. Note that the width at perforations can actually decrease during pumpingtreatment, especially when unconfined nonsymmetric fracture growth occurs. The width hplot may by used to estimate the volumes of the pad and the total volume of the treatment,proppant is introduced when the fracture attains sufficient width. The maximum proppant sizealso be estimated. For example, case B allows a 20/40 proppant to be pumped with a maproppant diameter of 0.0331 inches.

The character of the pumping pressure behavior for the two cases is also different as shFig. 10.44. These pressure histories are sufficiently smooth to represent real pressure beThe maximum pressure and the pressure at the perforations are plotted vs. the total injectume. Note that the pressures plotted are in addition to the reference pressure of 7084 psi.

Fig. 10.37 - Error Distributions of the Iteration Scheme.


10

8

6

4

2

0

-2

-4

PE

RC

EN

T

200 400 600 800TOTAL VOLUME INJECTED (bbl)

STEP VOLUME. BAL. ERROR (%)TOTAL VOLUME BAL. ERROR (%)CONVERGENCE ERROR (%)



trates ath of

ng stag-onfines

ring the

ctureht areal androws

ade

es.

.

hydrostatic pressure the maximum pressure occurs below the perforations. Case A demonstypical pressure decrease during pumping which is characteristic of unconfined fracture growa penny shaped fracture. Case B shows a complicated pressure behavior at the early pumpies. This is due to the presence of the pressure barrier in the dense zone which temporarily cthe fracture.

In some cases the pressure plot may be used as a closure stress diagnostic tool by compasimulated pressure with the actual pumping pressure during a minifrac test.

Fig. 10.45 shows the evolution of the fracture dimensions. Maximum fracture length, fraheight above perforations, fracture depth below perforations, and maximum fracture heigplotted vs. the total volume injected. In case A, the fracture propagates in both the horizontvertical directions. In case B, the fracture is essentially confined height-wise and glength-wise in the Tor formation. An estimate of the total fracture treatment volume may be mfrom this plot, based on the desired dimensions of the fracture.

Summary

TerraFrac is be a valuable simulation tool both for research and design of hydraulic fractur

1. It can be used to determine the fracture shape for given in-situ and pumping conditions

Fig. 10.38 - Efficiency of Treatment.


1

0.8

0.6

0.4

0.2

00 200 400 600 800 1000


TOTAL FRAC VOL/VOL INJSTEP LEAK VOL/INJ VOL


Special Topics10

blems

c pres-

istoryracture

2. It can be used to study the effect of the location of the perforations and the associated proof width pinching.

3. It may be used to diagnose in-situ closure stress features by comparing the actual minifrasure with simulated pressure.

It is possible, however, to make some overall proppant scheduling judgements using the hplots. For example, the proppant volume at screen-out conditions should be less than the fvolume at any instant, and this leads to an upper limit for proppant loading per fluid gallon.

Fig. 10.39 - Valhall A-17 Cases A and B.

6700 6800 6900 7000 7100 7200

DE

PT

H (

ft)

CLOSURE PRESSURE (psi)

min

-8200

-8300

-8400

-8500

-8600

SHALE C=0 0.75 psi/ft

TOR

C=0.005 ft/

0.68 psi/ft

0.66 psi/ft

DENSE ZONE C=0.002 ft/ min

PERFORATIONS

U. HOD minC=0.002 ft/

L. HOD C=0.002 ft/ min

0.64 psi/ft

0.64 psi/ft

FORMATION PROP.E = 1.26 X 106 psiaν = 0.4FLUID VISCOSITYµ = 90 cpPUMPING RATEQ = 15 bbl/min

CLOSURE STRESS ACLOSURE STRESS B



Fig. 10.40 - Fracture Evolution A17A.

1338 bbl896 bbl

570 bbl

346 bbl201 bbl

113 bbl

U HOD

DENSE ZONE

TOR

SHALE

0 50 100 150 200 250 300

150

125

100

75

50

25

0

-25

-50-75

-100

-125

-150

X FEET

Y F

EE

T


Special Topics10

Fig. 10.41 - Fracture Evolution A17B.

SHALE

631 bbl

442 bbl

298 bbl

128 bbl

TORDENSE ZONE

U HOD138 bbl

87 bbl

0 40 80 120 160 200

140120100806040200

-20-40-60-80

X FEET

Y F

EE

T

SHALE

1424 bbl

1012 bbl

751 bbl

DENSE ZONE

U HOD

0 50 100 150 200 250

175150125100

755025

0-25-50-75

-100

Y F

EE

T

X FEET

TOR



Fig. 10.42 - Fracture Width at the Wellbore.

A17A

A17B

150

125

100

75

50

25

0

-25-50

-75

-100-125

-150

140

120

100

80

60

40

0

-20

-40

-60

-80

20

0.00 0.05 0.10 0.15 0.20 0.25

0.00 0.05 0.10 0.15 0.20

1338 bbl

631 bbl

WF IN

Y F

EE

T

WF IN

Y F

EE

T


Special Topics10

Fig. 10.43 - Fracture Width, A17A and A17B.

A17A

A17B

0.25

0.20

0.15

0.10

0.05

0.000 500 1000 1500 2000

INC

HE

S


0.30

0.25

0.20

0.15

0.10

0.05

0.000 400 800 1200 1600

INC

HE

S


MAX FRAC WIDTH (in)WIDTH (in) AT 0.0000E+00 ftX



Fig. 10.44 - Pumping Pressure.

AMOCO REPORT NO. A17A500

400

300

200

100

00 500 1000 1500 2000

PS

I


AMOCO REPORT NO. A17B500

400

300

200

100

0

PS

I

-1000 400 800 1200 1600


REFERENCE DEPTH (ft):

REFERENCE PRESSURE (psi):7.084000E+03

8.366000E+03

MAX PRESSURE (psi)PRES (psi) AT 0.0000E+00 ftX


Special Topics10

Fig. 10.45 - Fracture Dimensions.

A17A

A17B

400

300

200

100

00 500 1000 1500 2000

FE

ET


600

400

200

00 400 800 1200 1600

FE

ET


X

X MAX DEPTH BELOW CNTR (ft)

MAX HEIGHT ABOVE CNTR (ft)

MAX FRAC HEIGHT (ft)

MAX FRAC LENGTH (ft)


References

the Ne-7.

atedchnical

ells,”

ela-Play,”

pany

10965,

pes

sin,

d at the

Val-Vegas,

resent-

Re-

10.3References

1. Gough, D. I. and Bell, J. S.: “Stress Orientations from Oil Well Fractures in Alberta and Texas,”Cdn. J. EarthSci. (1981)18, 638.

2. Thorpe, R. and Springer, J.: “Relationship Between Borehole Elongation and In Situ Stress Orientation atvada Test Site,” paper presented at the 1982 U.S. Rock Mechanics Symposium, Berkley, CA, Aug. 25-2

3. Babcock, E. A.: “Measurement of Subsurface Fractures from Dipmeter Logs,”AAPG Bull.(July 1978)62, 1111.

4. Brown, R. O., Forgotson, J. M., and Forgotson, J. M. Jr.: “Predicting the Orientation of Hydraulically CreFractures in the Cotton Valley Formation of East Texas,” paper SPE 9269 presented at the 1980 SPE TeConference and Exhibition, Dallas, TX, Sept. 21-24.

5. Bell, J. S. and Gough, D. I.: “Northeast-Southwest Compressive Stress in Alberta: Evidence from Oil WEarth and Planetary Sci. Letters,45, 475-82.

6. Dutton, R. E., Nolte, K. G., and Smith, M. G.: “Use of the Long-Spaced-Digital-Sonic Log to Determine Rtionships of Fracturing Pressure and Fracture Height for Wells in the East Texas, Cotton Valley Tight GasAmoco Production Company Report F82-P-12 (February 15, 1982).

7. Beaudoin, G. J.: “Interpretation and Use of 3-D Sonic Data: A Preliminary Study,” Amoco Production ComReport F80-E-13 (September 1980).

8. Smith, M. G., Rosenberg, R. J., and Bowen, J. F.: “Fracture Width: Design vs. Measurement,” paper SPEpresented at the 1982 SPE Annual Technical Conference and Exhibition, New Orleans, Sept. 26-29.

9. Zamenek, J.et al.: “The Borehole Televiewer - A New Logging Concept for Fracture Location and Other Tyof Borehole Inspection,”JPT (June 1969) 762-74;Trans., AIME, 246.

10. Bredehoeft, J. D.,et al.: “Hydraulic Fracturing to Determine the Regional In Situ Stress Field, Piceance BaColorado,”Bull., GSA (Feb. 1976)87, 250-58.

11. Dobkins, T. A.: “Improved Methods To Determine Hydraulic Fracture Height,”JPT (April 1981) 719-26.

12. Nolte, K. G.: “Fracture Design Considerations Based on Pressure Analysis,” paper SPE 10911 presente1982 SPE Cotton Valley Symposium, Tyler, TX, May 20.

13. Nolte, K. G.: “Analysis of Pump-In/Shut-In Tests for Closure Pressure,” Amoco Document.

14. Rosepiler, J. M.: “Determination of Principal Stresses and Confinement of Hydraulic Fractures in Cottonley,” paper SPE 8405 presented at the 1979 SPE Annual Technical Conference and Exhibition, LasSept. 23-26.

15. Nolte, K. G.: “Determination of Fracture Parameters from Fracturing Pressure Decline,” paper SPE 8341 ped at the 1979 SPE Annual Technical Conference and Exhibition, Las Vegas, Sept. 23-26.

16. Heidt, J. H., Nolte, K. G., and Smith, M. B.: “Fracturing Field Research Programs,” unpublished Amocosearch document, September 1981.


Special Topics10

atedand Ex-

ssure

Earth

r SPE

lation

ience

0 pre-

Ori-

n Dia-

11624

evo-v. 9-11.

nt-84 An-

ent.Sympo-

17. Wood, M. D., Pollard, D. D., and Raleigh, C. B.: “Determination of In-Situ Geometry of Hydraulically GenerFractures Using Tiltmeters,” paper SPE 6091 presented at the 1976 SPE Annual Technical Conferencehibition, New Orleans, Oct. 3-6.

18. Wood, W. D.: “Method of Determining Change in the Subsurface Structure Due to Application of Fluid Preto the Earth,” U.S. Patent No. 4,272,696, (1981).

19. Davis, P. M.: “Surface Deformation Associated with Dipping Hydrofracture,”J. Geophysical Res.(1983)881,No. 87, 5826.

20. Pollard, P. O. and Holzhausen, G.: “On the Mechanical Interaction Between a Fluid-Filled Fracture and theSurface,” Tectonophysics (1979)53I, 27.

21. Lacy, L. L.: “Comparison of Hydraulic-Fracture Orientation Techniques,”SPEFE(March 1987) 66-76;Trans.,AIME, 283.

22. Schuster, C. L.: “Detection Within the Wellbore of Seismic Signals Created by Hydraulic Fracturing,” pape7448 presented at the 1978 SPE Annual Technical Conference and Exhibition, Houston, Oct. 1-3.

23. Pearson, C.: “The Relationship Between Microseismicity and High Pore Pressure During Hydraulic StimuExperiments in Low Permeability Granite Rock,”J. Geophysical Res.(Sept. 1981)86, 7855-64.

24. Albright, J. N. and Pearson, C. F.: “Acoustic Emissions as a Tool for Hydraulic Fracture Location: Experat the Fenton Hill Hot Dry Rock Site,”SPEJ (Aug. 1982) 523-30.

25. Dobecki, T. L.: “Hydraulic Fracture Orientation by Use of Passive Borehole Seismics,” paper SPE 1211sented at the 1983 SPE Annual Technical Conference and Exhibition, San Francisco, Oct. 5-8.

26. Teufel, L. W.: “Prediction of Hydraulic Fracture Azimuth from Anelastic Strain Recovery Measurements ofented Core,”Proc., 23rd U.S. National Rock Mechanics Symposium (1982) 238-46.

27. Rowley, D. S., Burk, C. A., and Manual, T.: “Oriented Cores,” Christensen Technical Report, Christensemond Products (Feb. 1981).

28. Robertson, E. C.:Viscoelasticity of Rocks in State of Stress in the Earth’s Crust, W. Judd (ed.), (1964) 181-224.

29. Blanton, T. L.: “The Relation Between Recovery Deformation and In-Situ Stress Magnitudes,” paper SPEpresented at the 1983 SPE/DOE Low-Permeability Gas Reservoirs Symposium, Denver, March 14-16.

30. Blanton, T. L. and Teufel, L. W.: “A Field Test of the Strain Recovery Method of Stress Determination in Dnian Shales,” paper SPE 12304 presented at the 1983 SPE Eastern Regional Meeting, Champion, PA, No

31. Teufel, L. W.et al.: “Determination of Hydraulic Fracture Azimuth by Geophysical, Geological, and Orieed-Core Methods at the Multiwell Experiment Site, Rifle, Colorado,” paper SPE 13226 presented at the 19nual Technical Conference and Exhibition, Houston, Sept. 16-19.

32. Smith, M. B., Ren, N. K., Sorrels, G. G., and Teufel, L. W.: “A Comprehensive Fracture Diagnostic ExperimPart II. Comparison of Seven Fracture Azimuth Measurements,” paper SPE 13894 presented at the 1985sium on Low-Permeability, Denver, May.


Hydraulic Fracturing Theory Manual11-1

Chapter

July 1999

11.1 Perforating

Proper selection and execution of a perforating program is essential to the success of a fracturetreatment completion. Consideration must be given to perforation diameter, shot density, phasing,location and length of the perforation interval, and, in some special cases, perforation orientation.While most of that presented in this section applies to both vertical and deviated wellbores, partsalso deal specifically with perforation patterns and procedures for deviated or horizontal well frac-turing.

Hole Diameter

Perforation hole diameter directly affects the proppant size and maximum concentration that canbe pumped during a fracturing treatment. Perforations must be large enough relative to the maxi-mum proppant diameter to prevent bridging. Fig. 11.1 shows the minimum recommended perfo-ration size necessary to inject various size proppants at different concentrations. For example, topump 20/40 mesh sand at 10 ppg, a minimum perforation diameter of 0.20 in. is recommended.

“RULE-OF-THUMB”: Perforation diameter should be at least six times the maximumproppant diameter to prevent bridging.

Another consideration in perforation sizing is fracturing fluid degradation. If perforation diameteris too small, high shear-rates in the perforation tunnel can irreversibly destroy gel structure. Thiswill result in a reduction in the gel’s ability to carry proppant and a screenout can ensue.

Entry hole diameter can be affected by several variables, including

• casing grade

• stand-off of the perforation gun with the casing,

• charge design (big hole versus deep penetrating),

• charge alignment, and

• casing thickness.

API charges are tested in casing from K-55 to L-80. When using P-110 and harder casing, theentrance hole size will be reduced by as much as 20%.

Fracture Stimulation Guidelinesand

Quality Control11


11

Figure 11.1 Minimum Perforation Diameter v. Proppant Size and Concentration.

The “ideal” stand-off to obtain maximum performance from a perforating gun is approximately1/ 4 in. to 3/4 in., depending on gun size and charge design. If stand-off is significantly greaterthan this, hole diameter and penetration will be reduced. Also, if the jet charges do not exit theport plugs of the gun through the near center of the plug, perforation performance can bedramatically reduced. Following a perforation job, all guns should be inspected to determinewhat percent of charges fired and any misalighned firing through the port plugs.

Table 11.1 provides a very approximate chart of gun type/size, casing/tubing size, and weightcharge versus perforation entry hole diameter. These diameters were generated by various servicecompanies using the API recommended cement target. Results from different service companiescan vary dramatically; thus, this chart should only be used as a rough reference. Whendetermining the most appropriate perforating gun and weight charge, the service company shouldbe consulted to obtain the most recent data and recommendations.

Hydraulic Fracturing Theory Manual

Perforating

11-3July 1999

Number of Perforations

In addition to perforation size, the number of holes open affects the injection rate at which a frac-ture treatment can be pumped. To determine the number of perforations required for a specifictreatment design, the following equation can be used

(11.1)

where, is the specific injection rate per perforation (bpm/perf), is perforation friction

(psi), is perforation diameter (in.), is the perforation coefficient (usually 0.9), and is the

maximum fracturing fluid (slurry) density (lbs/gal). is an efficiency number that corrects forthe fact that all perforations are not perfectly circular or smooth orifices. Assuming minimal per-foration friction, a value of 100 psi is normally used in the equation.

Table 11.1 - Approximate Chart of Gun and Casing/Tubing Sizes Versus Charge Size and Entry Hole Diameter for Various Type Perforating Guns.

Gun TypeGun OD

(in.)Casing OD

(in.)Entry Hole Diameter

(in.)Charge Wt.

(grams)

HollowSteel Carrier

3-1/83-3/83-5/8

44

4-1/24-1/24-1/25-1/2

7

0.31-0.390.380.40

0.34-0.500.38-0.46

101410

10-22.719-22.7

ExpendableRetrievable

Carrier

11-1/4

1-11/161-11/161-11/16

2-1/82-1/82-1/8

4-1/22-3/82-3/82-7/85-1/22-7/85-1/2

7

0.150.300.360.380.270.43

0.33-0.490.32-0.44

25

131313

22.722.722.7

Expendable 1-1/41-11/161-11/161-11/16

2-1/82-1/82-1/83-3/43-3/43-3/4

2-3/82-7/84-1/25-1/22-7/85-1/2

74-1/25-1/2

7

0.300.360.510.300.440.410.420.660.670.71

513

13.513

22.722.722.7909090

NOTE: Entry hole diameters generated with API Concrete Target test.

ipf

Ppf( ) dpf( )4 α( )2

0.2369 ρ( )--------------------------------------

1/2

=

ipf Ppf

dpf α ρ

α


11

11-4 July 1999

While Eq. (11.1) can be used to calculate the minimum number of holes required for desired treat-ment parameters, normally some holes may be plugged, some charges may have misfired, and/or the holes may be substandard due to misaligned firing or poor gun stand-off. The following is rec-ommended to compensate for this:

“RULE-OF-THUMB”: Either a perforation coefficient of 0.5 should be used in Eq. (11.1)or the number of holes, determined with a coefficient of 0.9, should be doubled to insure thatenough, good quality holes are open for the treatment.

If a well has already been perforated before the fracture treatment design is formulated, which isusually the case; Eq. (11.1) can be used to determine the maximum injection rate through theavailable perforations or decide if additional perforations are required. An example of this isshown in Table 11.2 for a well that was perforated and tested and found to have much higher per-meability and skin than anticipated. Initially, the well was shot 2 spf over the 20 ft pay interval witha hole diameter of 0.38 in. From testing, the well appeared to have a permeability of 200 md anda skin of +20. Based on fracture modeling, a treatment rate of 40 bpm was desired, limited by theworkstring, and to obtain good conductivity through the damaged region, a maximum proppantconcentration of 10 ppg 20/40 mesh sand was required. As seen in Table 11.2, the minimum num-ber of perforations required for this treatment was about 110 or 70 more than available. Thus, thewell had to be either reperforated prior to fracturing or the maximum injection rate reduced to 15-20 bpm, the later probably not feasible given the expected high fluid leak-off.

Perforation Phasing

When perforating for a fracture treatment smaller phasing angles are better, i.e., 90 or 120° phas-ing better than 180 or 360° (same as 0°) phasing. As shown in Fig. 11.2, if enough of the perfora-tions are not in the near direction of the preferred fracture azimuth, the fracture must traversearound the outside of the cement to reach this orientation. Since the fracture will propagate perpen-dicular to the least principle stress, the portion of the fracture which travels around the wellborewill be subjected to higher stress, resulting in a narrower width or “pinch-point” . This causes ahigh fluid shear environment and can result in fluid degradation and proppant bridging and anensuing screenout. This type environment is the most common cause of “tortuosity” or a tortuousfracture path caused by some near-wellbore restriction such as described above. Most cases of tor-tuosity can be cured with proper perforating to insure good communication between the wellboreand main fracture body. This will also, typically, result in reduced treating pressures (lower HHPcosts) and better post-frac performance.

Perforating for Deviated/Horizontal Well Fracturing

There is nothing good about the effect of well deviation on fracturing, and, when possible, thisshould be avoided. However, many situations exist where fracturing deviated wells is either desir-able or dictated by other concerns. One example might be multiple completions from long reachwells, with another being workover or recompletion operations in existing wellbores. Perforation


Perforating

11-5July 1999

patterns can play a dominant role in fracturing from non-vertical wellbores. To better under-stand this, the following briefly describes possible fracture to wellbore patterns in deviated wells.

While current “state-of-the-art” does not allow complete quantification of the effects of well devi-ation on fracturing, it is clear that these effects are related to two angles: (1) the well deviation fromvertical, α, (assuming a vertical fracture) and (2) the difference in direction between the wellboreand the preferred fracture azimuth, β, as shown in Fig. 11.3. Best communication will exist whenthese two angles are minimized. Basically, there are five possible patterns of wellbore to frac-ture communication for deviated wells (and vertical fractures). First is when the wellbore isparallel to the maximum horizontal stress direction, i.e., parallel to the preferred fracture azimuth,and the fracture follows the wellbore. This is the only “good” scenario and fracture behavior canbe expected to be similar to behavior for a vertical well. The remaining four patterns are illustratedin Fig. 11.4, and in order of increasing “badness”, include (1) a single fracture along the wellboreturning gradually to the preferred orientation, (2) a single fracture parallel with the well but then

Table 11.2 - Example Calculation of Number of Perforations Required or Maximum Rate Obtainable for Fracturing Treatment Design.

Determine the number of perforations required to inject at 40 bpm or the maximum injection ratepossible with the existing 40, 0.38 in. holes. Assume a perforation friction of 100 psi. The max-imum planned slurry design is 14.59 lbs/gal.

1. To safely inject at 40 bpm:

holes required = (40 bpm/0.7) x 2 = 114 holes

Using = 0.5, instead of 0.9, in the above eq.:

= 0.39 bpm/perf

holes required = 103 holes

* REPERFING REQUIRED TO ADD ABOUT 70 MORE HOLES!

2. Maximum rate achievable without perforating:

(0.39 bpm/perf)(40 perfs) = 16 bpm

i pf

Ppf( ) dpf( )4 α( )2

0.2369 ρ( )--------------------------------------

1/2

=

i pf100( ) 0.38( )4 0.9( )2

0.2369( ) 14.59( )-----------------------------------------------

1/2=

i pf 0.7 bpm/perf=

α

i pf


11

11-6 July 1999

turning sharply to follow the preferred azimuth, (3) a single fracture crossing the well, and (4) mul-tiple fractures crossing the well. In each of these cases,high “apparent” downholefriction maybe caused by near-wellbore fracture width restrictions (tortuosity).

For the “most” awful case, i.e., multiple fractures crossing the wellbore, asmall clusteredgroupof perforations is often used as shown in Fig. 11.5, though this may not totally eliminate multiplefractures. To totally eliminate the possibility of multiple fractures,a single “plane” of perfora-tions is desired, or even better a“notched” casingusing abrasive techniques. Some perforationpatterns may maximize the chances of creating the preferred single fracture along the wellbore. Inparticular,two “lines” of perforations (0-180° phasing), properly oriented, with a minimumspacing between holes, should maximize the chances of this occurring. The fracture, though, maythen still have to turn to follow the preferred azimuth. Any real calculation of an “optimal” perfo-

Fig. 11.2 - Effect of Perforation Phasing on Fracture - Wellbore Communication.


Perforating

11-7July 1999

Fig. 11.3 - “Wellbore Orientation with Respect to Hydraulic Fracture.

Fig. 11.4 - “Bad” to “Awful” Patterns of Wellbore to Fracture Communication for Deviated Wells(and Vertical Fractures).


11

11-8 July 1999

rating pattern for deviated or horizontal wells requires extensive knowledge of the in in-situstresses.

Over-Pressured Perforating

Another procedure first introduced in Prudhoe Bay, is thecombination of “in-line” perforationswith super over-pressureperforating . ARCO has shown that a rapidly propagating fractureturns much more slowly and smoothly to follow its preferred direction than a hydraulic fracturepropagating at a “normal” speed. The followingperforation procedure is followed: (1) a smallvolume of water is placed in the bottom of the well, (2) the perforation guns are then positionedand the remainder of the well filled with nitrogen at relatively low pressure, (3) water is theninjected into the top of the well to compress the gas and increase bottomhole pressure to a level farbeyond the fracture closure stress, and (4) the perforating guns are fired, opening perforations inthe pipe and creating and rapidly propagating a fracture (downhole injection rates on the order of100’s of bpm have been measured during the initial breakdown following perforating). Since thefracture is being created with pressure greater that the “other” in-situ stresses, a fracture can openand propagate at unfavorable angles. This high pressure, combined with dynamic effects of rapidpropagation cause a smooth, slow turning to the favorable fracture orientation, e.g., case “1” inFig. 11.4. Thus, in principal, this procedureshouldproduce the “least non-ideal” deviatedwell

Fig. 11.5 - Perforation Patterns for Deviated Well Fracture.


Perforating

11-9July 1999

fracture , though of course for certain combinations of wellbore orientation and in-situ stresses,the same procedure could cause the very undesirable, multiple, crossing fractures, with the criticalconditions where this might occur again being related to the differences in the three directional in-situ stresses. Since the directions and magnitudes of all in-situ stresses is usually not known, deter-mining the proper conditions for this type of completion becomes subject to field “experiments”.

Other Considerations

Thelocation and length of the perforated interval needs to also be considered under certain cir-cumstances. For example, if a large pay zone is bounded above by a zone of similar stress, it maybe more conducive to perforate only the lower half of the pay to obtain more complete vertical cov-erage. With the entire pay perforated, the fracture would tend to initiate in the top half and mightgrow more in an upward direction and place a large portion of the treatment in non-pay. Similarperforating strategy might also be appropriate when an oil-water or gas-oil contact is in the nearproximity to the pay zone.


11

11-10 July 1999

11.2 WELLBORE CONFIGURATION

The three most common wellbore configurations used to pump fracture treatments (Fig. 11.6) are

• down production casing,

• down tubing with a packer, and

• down open-ended tubing.

Performing a fracture treatment down casing can be quite beneficial, this configuration allowinghigher injection rates and lower surface treating pressures and, in turn, requiring less fluid andhydraulic horsepower to perform the treatment. In certain situations, though, it may be necessaryto pump down tubing with a packer to isolate the annulus, i.e., when the casing is not strong enoughto withstand fracturing pressure or shallower perforations exist. The third configuration, i.e.,pumping down open-ended tubing, allows fracturing BHP to be obtained via the open annulus andthis can be a very valuable tool in determine fracturing behavior, especially on early wells in adevelopment program. The disadvantages to this configuration, however, are that the casing mustbe strong enough to withstand fracturing pressure and pumping down tubing lowers the injectionrate and/or increases the surface treating pressure. This and alternative methods of measuring frac-turing BHP are presented later. First, though, the following discusses the pressure limitations ofeach configuration and briefly how to determine them.

Fig. 11.6 - Common Wellbore Configurations for Hydraulic Fracture Treatments.


WELLBORE CONFIGURATION

11-11July 1999

Fracturing Down Casing

Fracture treatment conditions should be considered in the casing design, when possible. Whenfracturing down casing, one must design the treatment to keep the surface treating pressure belowthe “burst pressure” of the casing. The worst conditions will occur if the treatment screens-outand surface pressure reaches a predetermined maximum value. One can eitherdesigna casingstring to withstand the expected maximum surface treating pressure under screenout conditions orlimit the maximum surface pressure if the casing has already been set.

Treating pressure conditions can be calculated by the equation

(11.2)

where, BHTP is the expected bottomhole fracturing pressure, is hydrostatic pressure, is pipe

friction, and is perforation friction. While and are easily calculated or data exists, often

times BHTP and are unknown at onset of a treatment. In an exploratory or new developmentwell, a minifrac may be in order to determine these values, along with in-situ stress and fluid leak-off data.

Casing burst values can be found in most service company or casing design handbooks. To deter-mine a safe surface treating pressure, a burst safety factor of 1.1 is recommended for fairly newcasing. For older casing, this should be increased. Assuming a 2000 psi “sudden” increase in pres-sure if a screenout occurs, thedesign treating pressureshould not exceedthe safety factorreduced casing burst pressure minus 2000 psi.

Pop-offsor pressurerelief valveshould always be installed on the injection line(s) and set/testedto just below the predetermined maximum surface treating pressure.

Fracturing Down Tubing with a Packer

As for a casing treatment, the maximum allowable surface fracturing pressure for this configura-tion must be determined from theburst pressureof the tubing string. With this setup where theannulus is isolated,backsideor annulus pressurecan be held to allow increased maximum sur-face treating pressure. In addition to the burst pressure of the tubing, other factors must also be con-sidered; includingforces on the packer when the tubing is anchored in the packer, andtubingmovement when a locator seal assembly is used.

When thetubing is latchedor anchoredin the packer, disallowing tubing movement, forces onthe packer should be calculated to select a packer strong enough to withstand these forces.Tubingpressurewill cause anupward-acting force below the packer, and theannular pressurewillcause adownward-acting force above the packer. This can be computed by the equation

(11.3)

ps BHTP ph– pf ppf+ +=

ph pf

ppf ph pf

ppf

Fa Ap Ao–( ) po[ ] Ap Ai–( ) pi[ ]–=


11

11-12 July 1999

where is the area of the packer bore, is the area based on the tubing OD, is the area based

on the tubing ID, is the annular pressure at the packer, and is the injection pressure at the

packer. The injection pressure, , should be calculated based on the maximum allowable surfacetreating pressure under screenout conditions with the maximum slurry density in the tubing.

When alocator sealassemblyis used, allowing tubing movement, the forces and length changeson the tubing must be calculated to determine thelengthof sealsto run andslack-offwhen landingthe tubing. The four different effects that cause these forces and length changes are

1. piston effect,

2. buckling effect,

3. ballooning effect, and

4. temperature effect.

Thefirst threearecausedby pressurechangesand thelastby temperaturechangesin the well-bore. Table 11.3 includes the equations used to calculate these to determine the length of sealsrequired and tubing slack-off for fracturing conditions. Again, screenout conditions need to alwaysbe considered in designing the tubing/packer configuration.

Fracturing Down Open-Ended Tubing

When designing this type configuration for a fracture treatment, theburst pressurefor both thecasing and tubing must be considered. Since this configuration is normally used to obtain BHTPvia the live annulus, no additional pressure is applied on the annulus side at the surface. Thus, themaximum surfacetreating pressureshould be limited to keepthe surfaceannulus pressurebelow the safety factor reduced casingburst. Since the tubing burst will normally be greaterthan the casing, this configuration will not allow as high a treating pressures as would be possiblewith a packer and the annulus isolated.

This configuration also allows pumping of a fracture treatment down the annulus and monitoringthe BHTP on the tubing side. When pumping down the annulus, a blast joint should be used at thetop of the tubing string to prevent erosion. Again, the maximum surface treating pressure shouldnot exceed the safety factor reduced burst pressure of the casing. Also, screenout conditions shouldalways be considered in determining the maximum treating pressure and pressure relief valves setto just below this pressure on all injection lines.

Methods of Obtaining Fracturing BHP

Several methods exist to obtain BHTP during a fracturing treatment, including

• open-ended tubing,

Ap Ao Ai

po pi

pi

Hyd

rau

lic Fra

cturin

g T

he

ory M

an

ua

l

WE

LL

BO

RE

CO

NF

IGU

RA

TIO

N

11-13Ju

ly 19

99

Table 11.3

Tubing Forces and Length Changes Nomenclature

PISTON EFFECT:

(11.4)

(11.5)

HELICAL BUCKLING:

(11.6)

(11.7)

BALLOONING EFFECT:

(11.8)

(11.9)

TEMPERATURE EFFECT:

(11.10)

(11.11)

SLACKOFF EFFECT:

(11.12)

TOTAL EFFECT:

(11.13)

(11.14)

ACTUAL FORCE:

(11.15)

Ai = area based on tubing ID, in**2 [cm**2]

Ao = area basing on tubing OD, in**2 [cm**2]

Ap = area of packer bore, in**2 [cm**2]

As = area of steel in pipe body, in**2 [cm**2]

E = Young’s modulus for steel, 30x10**6 psi [207x10**6 kPa]

Fa = actual force, lbf [N]

Fm = mechanical force, lbf [N]

Fp = total force at packer, lbf [N]

F1 = piston force, lbf [N]

F2 = helical force, lbf [N]

F3 = ballooning force, lbf [N]

F4 = temperature force, lbf [N]

I = moment of inertia, in**4 [cm**4]

L = length of tubing or casing, in. [cm]

dLm = length change due to mechanical force, in. [cm]

dLt = total length change due to changes in pres. & temp., in. [cm]

dL1 = length change due to piston force, in. [cm]

dL2 = length change due to buckling, in. [cm]

dL3 = length change due to ballooning force, in. [cm]

dL4 = length change due to temperature force, in. [cm]

dpi = change in pressure in tubing at packer, psi [kPa]

dpo = change in pressure in annulus at packer, psi [kPa]

dr = clearance between casing ID and tubing OD, in. [cm]

dT = change in average temperature, deg F [deg C]

Wi = weight of fluid inside tubing, lbm/in. [kg/cm]

Wo = weight of fluid in annulus displaced by tubing, lbm/in. [kg/cm]

Ws = weight of steel, lbm/in. [kg/cm]

F1 Ap Ao–( )dpo[ ] Ap Ai–( )dpi[ ]–=

dL1F1( ) L( )E( ) As( )

-----------------=

F2 0=

dL2dr**2( ) Ap**2( ) dpi dpo–( )**2

8EI Ws Wi Wo–+( )-------------------------------------------------------------=

F3 0.6 dpo( ) Ao( ) dpi( ) Ai( )–[ ]=

dLm0.2L

1.0 10**7×--------------------- R**2 dpo dpi–( )

R**2 1–--------------------------------=

F4 207 As( ) dT( )=

dL4 0.0000069 L( ) dT( )=

dLmFm( ) L( )E( ) As( )

------------------ dr**2( ) Fm**2( )8EI Ws Wi Wo–+( )----------------------------------------+=

Fp F1 F3 F4 Fm+ + +=

dLt dL1 dL2 dL2 dL3 dL4 dLm+ + + + +=

Fa Ap Ao–( ) po[ ] Ap Ai–( ) pi[ ]–=


11

11-14 July 1999

• gauges in a tail-pipe below a perforated joint below the packer,

• placing gauges in the rat-hole, and

• through a telemetry acquisition system.

To obtain fracturing BHP withopen-endedtubing, the annulus must be kept full of a known den-sity fluid and the annulus surface pressure measured. The main advantage of this system is thatcanbe monitored real-time. To insure that the annulus is full of the same density fluid, the wellboreshould be circulated prior to the fracture treatment and the density of the fluid measured.

Gaugesare often times placed in a nipple in atail-pipe configuration below a perforated tubingjoint below the packer. This is agoodmethod for obtaining fracturing BHPwhen the annulusmust be isolated. While proppant may fall down around the gauges, making retrieval with wire-line difficult, the data can still be retrieved by pulling the tubing string. When possible, a fishingneck should be installed on top of the gauges and the location of the gauge landing nipple placedso that the fishing neck extends into the perforated joint. Proppant is less likely to pack around thefishing neck, making wireline retrieval of the gauges more likely.

Gaugescan be placed in therathole, but this requires going in and washing out proppant settledfrom the under-flush to retrieve them.

A recent advance in BHTP measurement during a fracturing treatment is atelemetry acquisitionsystempatented by Real Time Diagnostics, Inc. A sensor placed in the bottom of the well detectspressure and temperature and transmits this data to the surface in the form of electromagneticwaves. A receiver at the surface captures, interprets, and records the data. The advantages of thissystem are (1) thatis acquired nearly real-time to make informed decisions during the fracturetreatment and (2) that itallows the treatment to be pumped down casingat higher rates withoften times less fluid. The only disadvantage would be possible difficulty in retrieval of the bot-tomhole sensor.

Measurement of fracturing BHP can be a valuable tool in evaluating fracturing behavior, espe-cially on early development wells in an area. The best method of retrieving this data must be deter-mined as a function of the wellbore configuration and the requirements of the treatment.

Considerations for Frac-Pack Completions

In addition to the forces placed on the workstring and packer during a fracturing treatment, otherthings must be considered when fracturing through gravel-pack tools. Typically, frac-packs arepumped throughmulti-positional gravel-pack tools upgraded to allow for high-pressure, high-rate injections. Normally, the tools have three positions, includingsqueeze,circulate, and reverseas shown in Fig. 11.7. When injecting into the formation, the tool is in the squeeze position andthe fracturing slurry exits the workstring through ports in the tool. Most tools have either two orthree ports, sized and positioned to allow for a large flow area to prevent tool erosion. Theport


WELLBORE CONFIGURATION

11-15July 1999

sizeand number haveto beconsideredwhendetermining the designinjection rate to preventtool erosion and shear-thinning of the fracturing fluid.

The diameter of the tool ports must also be large enough to preventproppant bridging and even-tual treatment screenout in the gravel-pack tool. The previous section discussed proppantbridging in perforations and the same applies here. Depending on the number and port diameter,thedesign maximum proppant concentration may have to be limited.

Another consideration deals with theblank pipe normally used to extend from the top joint ofscreen to the bottom of the gravel-pack tool assembly. This must be of a sufficientlyhigh enoughgrade to withstand maximum collapseforces during a frac-pack operation. This needs to bedetermined under screenout conditions.

Fig. 11.7 - Multi-Positional Gravel-Pack Tool Commonly Used for Frac-Packs


11

11-16 July 1999

11.3 PRE-TREATMENT PLANNING

Pre-treatment planning encompasses many aspects including data collection, preliminary treat-ment design, preparation of the frac “brief”, and service company/operator interaction. The suc-cess or failure of most treatments can be traced to (1) the availability and judicious use of datanecessary to optimize the treatment design, and (2) improper planning by and interaction betweenthe service company and operator.

Data Collection Requirements

With respect to data requirements, three technical areas need to be addressed, these being wellpotential, fracture geometry, and treatment fluids and proppants. Proper evaluation of each of theseareas requires the knowledge of various rock and fluid properties. In practice, it is not possible oreconomical to collect data from every desirable source. In general, optimization of the data gath-ering should be done on the basis of whether the well is early or late in a development program. Inan initial development well, effort should be made to fully understand the well from all perspec-tives. However, knowledge gained from exploratory or early development wells can be applied tosubsequent wells in a localized area provided there is a good understanding of the local geology.

Formation Flow Potential. To justify a stimulation treatment, the formation flow potential fromfracturing must first be critically evaluated. The important data and parameters that fall into thiscategory include

• porosity (logs),

• water saturation (logs),

• permeability (logs/core),

• petrographic description of minerals (core),

• reservoir pressure (pressure transient testing), and

• gas/oil, water/oil contacts (logs).

In an early development well these would need to be measured or determined directly. In laterdevelopment wells, though, it might be possible to extract reasonable estimates from offset wells.This again would depend, to a great degree, on the spacing of the wells, the complexity of the local-ized geology, and the number and behavior of previous treatments in the area.

Fracture Geometry. After it has been established that a fracture stimulation will provide suffi-cient economic recovery, certain data and parameters are required to ascertain what size treatmentis required to optimize recovery. For fracture length, width, and height determination, the follow-ing data is required.


PRE-TREATMENT PLANNING

11-17July 1999

• minimum horizontal stress (pre-frac injection testing),

• Young's modulus (core),

• overburden stress (integrate density log),

• pore pressure (pressure transient testing),

• reservoir temperature (logs, static measurement),

• an estimate of fluid leak-off properties (core, minifrac injection), and

• treatment fluid injection rates, viscosity, and proppant density.

Again, the extent to which this data is collected should depend on when the well is drilled in adevelopment program, the availability of data from previous wells, the complexity of geology, andthe number and behavior of previous treatments. For example, injection/decline tests and minifracsmay only be required on a select few wells early in a development program to ascertain formationstresses and leak-off. Also, overburden stress and Young's modulus values should only be requiredon early wells, unless the geology varies significantly from one area to another in the developmentregion.

Treatment Fluid and Proppant Evaluation. The areas that need to be addressed when optimiz-ing treatment fluid and proppant requirements are

• ability of the fluid to carry the proppant the desired distance out in the fracture,

• fluid loss control,

• minimum impairment to proppant-pack conductivity by the fluid, and

• the strength and size of the proppant to provide the necessary fracture conductivity.

Laboratory testing by the service company may be required early in the life of a development pro-gram to choose the most appropriate fluid and proppant.

Preliminary Treatment Design

Using the available data, a “preliminary” treatment design should be formulated at this point to aidin pre-treatment planning. While this might not be the final design pumped, this will provide esti-mates of treatment requirements including

• fluid/chemical/proppant amounts,

• on-site storage,

• equipment,

• location sizing, and


11

11-18 July 1999

• personnel requirements.

The expected treatment schedule should be reviewed by the service company at the earliest pos-sible date to insure that these requirements can be met. Often times, in remote areas, chemicals orproppant may have to be ordered weeks or even months in advance. Also, additional equipmentmay have to be brought in from other areas or scheduled.

Frac “Brief” Procedure

To aid in pre-frac planning and treatment execution a fracturing procedure should be preparedeither by the operator or jointly by the operator and service company for each treatment and shouldinclude at a minimum the following:

• pertinent wellbore information includingcasing/tubing depth, size, weight, and grade;packer type and depth;plug-back TD;perforation interval; andperforation size, density, and phasing.

• pertinent reservoir information includingformation name and type,reservoir pressure, andreservoir temperature.

• treatment pump schedule includingstage volumes, rates, proppant concentrations,fluid and proppant types,special chemical addition, e.g., breaker scheduling, and displacement fluid and volume.

• pressure requirements includingmaximum allowable surface pressure (tubing/casing) and anticipated treating pressure.

• maximum HHP requirements.

• standby equipment requirements.

Service Co./Operator Interaction

In an“Alliance” environment, more responsibility for designing, setting-up, executing, and eval-uating fracture treatments has been placed with the service company partner. There are certainareas, however, where the operator and service company need to interact to help insure a successfultreatment. The first obvious area is in thedesignphase. The operator will need to furnish the ser-vice company with all available well and reservoir data. If sufficient data is not available, both par-ties should discuss and determine what additional data is required and how it can be most cost-


PRE-TREATMENT PLANNING

11-19July 1999

effectively acquired. Regardless which party takes on the bulk of responsibility for the design, alldesigns should be reviewed by the other partner to insure there are no differences or questionsbefore proceeding to the field. When prepared, thefrac “brief” should also be reviewed andapproved by both parties since, ultimately, safety issues are still the responsibility of Amoco.

Once the design and procedure have been prepared, under the alliance arrangement it is the servicecompany's responsibility toimplement the treatment. This includes making sure the location sizeis adequate, that adequate storage tanks are provided, and that sufficient fluid, chemicals, proppant,equipment, and personnel are available to fulfill the requirements of the treatment. Certain phasesof this will require interaction with the operator representative, e.g., enlargement or grading of thelocation.

During the treatment it is the ultimate responsibility of the service company to insure that thematerials pumped meet design specifications and that proper quality control procedures have beenimplemented to insure this. Periodically, the service company should be called upon to demon-strate to the operator the quality of the fluids and proppants on-site. It is also the service company'sresponsibility to see that the treatment is pumped as close to design as possible, adhering to safepractices as dictated by both parties. An operator representative should be present for the pre-treat-ment safety meeting and treatment execution and should be allowed to interject comments or makechanges to the treatment if deemed necessary to insure completion of the treatment or to preventan unsafe situation.

Post-treatmentappraisal should include both parties. Any deviations from the design and prob-lems encountered with equipment or fluids should be documented and contingencies formulatedto help prevent reoccurrences.


11

11-20 July 1999

11.4 FRACTURING FLUID QC

Several types of fracturing fluids are available for use on today's fracturing treatments, includingwater-based fluids, oil-based fluids, alcohol-based fluids, emulsion fluids, and foam-based fluids.It is important that the design engineer choose the best fluid to achieve successful and the mostcost-effective stimulation of his/her well. While this is a design issue, it is also the first step in aproper fluid quality control program. Compatibility of the fracturing fluid with the formation mate-rial/fluids is essential to prevent such things as clay swelling and pore throat plugging, the creationof emulsions and/or sludging of crude oil, the degradation of matrix cementation, etc. An idealfracturing fluid should have certain physical and chemical properties that include:

• Compatibility with the formation materials/fluids.

• Sufficient viscosity to develop the necessary fracture width and transport proppants thedesired distance into the fracture.

• An efficient (i.e., low fluid loss) fluid to minimize the amount of fluid required.

• Easy to remove from the formation with minimal damage to the formation and proppant pack.

• Low friction pressure in the tubulars.

• Easy preparation of the fluid and quality control in the field.

Choosing a fracturing fluid will require compatibility testing by the service company with forma-tion core/fluids and rheology testing with the actual base (source) mixing fluid. In a new area orformation, where no historical data exists, these tests should always be performed. Starting withthis step, a proper fluids quality control program should include the following:

• Choosing the appropriate gel system and familiarity with this system.

• Base fluid and gel rheology testing.

• Base fluid delivery, filtration, and storage on-location.

• Gel pilot testing on-location.

• Final gel preparation.

• Sampling.

Since most treatment today are performed with water-based, oil-based, or foam-based fracturingfluids, the following focuses on quality control measures for these.

FRACTURING FLUID QC

July 1999 11-21 Hydraulic Fracturing Theory Manual

Base Mixing Fluid

Prior to moving any equipment on location for a fracturing treatment, the service companyshould be confident that the base mixing fluid will be compatible with the formation and thechosen gel system. In a new area and/or formation, where there are significant changes to jobsize, and/or the source water changes, the base mixing fluid should always be tested by theservice company in the lab and a base set of rheology values generated. At the other end of thespectrum, where a particular water source has been tested and used routinely with success, this isnot necessary on every treatment; but, should still be periodically spot checked.

When a water-based gel is used, it is imperative that a fresh, clean water be used and that the ser-vice company check the ion content and bacteria count. Certain ions, bacteria, and other foreignmaterials can interfere with the proper building of a quality fracturing fluid. One example of thisis a source water used in Australia where the natural borate content is high and causes a weakcrosslink of the base gel if the pH is lowered. This was discovered through laboratory testing andprevented a potentially nasty situation, i.e., crosslinking of the base gel in the frac tanks. Insteadthese jobs are successfully pumped by adding the pH reducing chemicals on-the-fly.

Table 11.4 is an example form for testing the base mixing water. The three most important com-ponents of a base mixing water are the iron content, pH, and bacteria count. For most water-based gel systems, the total iron content should be less than 25 mg/liter. Excess iron canreduce the temperature stability of the gel as well as causing the gel to be more shear-sensitivewhen crosslinked. Excessive iron is usually introduced into the system through rusty frac tanksor transports delivering the water to location.

The pH of the base mixing water should be in the 6 to 8 range. A pH higher than 8 can causepoor gel hydration and a ph less than 6 can cause gel lumping and “fish eyes”. It is desirable tostart with a base mixing water pH close to a 7. A pH buffer, acid, or base can be used to bring thepH into this desired range.

One of the more common sources of gelation problems is bacterial contamination of the basewater. Certain types of bacteria thrive on gel as a food source, destroying the gel structure bybacterial enzymes. Sulfate reducing bacteria are most common, converting sulfates in the fluidand reservoir to sulfide, a detrimental formation blocking agent. This type of bacteria ischaracterized by a blackening of the water and a strong hydrogen sulfide odor.

Bacteria presence is most common during summer months when temperatures exceed 80°F.During hot periods, bacteria growth accelerates in stagnant water such as that stored in frac tanksfor an extended period (as little as a few days). As a preventative, bactericide should always beadded to the frac tanks prior to filling. This measure is more effective and less expensive thancombating the bacteria after it has flourished. If the water becomes contaminated, dispose of thewater, re-clean the tanks, and re-fill with bactericide treated water. Adding bactericide to acontaminated tank will not solve the problem. This will only kill the bacteria, but the bodiesand enzymes will remain.


11Table 11.4 - Sample Form for Testing Base Mixing Water for Hydraulic Fracturing

In many cases, the water should be filtered through a 10 micron filtering system. While thisis more costly and time consuming, it can prevent much larger costs incurred if the gel cannot beproperly mixed and has to be disposed of. When city water is routinely used, filtering should notbe required. The service company/operator must make sure, though, that the source water deliv-ered to location is the same as that requested and not contaminated in transit. Visual inspectionof the water in the frac tanks should be a routine step prior to mixing any gel. This may helpdetect contaminants in the water and, possibly, the improper filtration of the water.

When oil is the base fluid, usually lease crude or diesel, compatibility/stability tests should beperformed with the gel system chemicals (preferably those to be used during the treatment). Mostsystems will not gel as easily with crudes having an API gravity of 30° or higher. Also, somediesels may contain detrimental components. The content of diesel will vary with supplier,refinery, and seasonal changes. Special additives are included in extreme cold regions to preventdiesel freezing and these can be detrimental to the gelling and gel breakage process. Oil-basedfluids are more difficult to mix than water-based gels and by knowing the properties of the oiland performing early pilot tests, the first step has been taken to insure the fluid can be preparedon-site with the least amount of difficulty.

WATER QUALITY TEST

Date: _________________________________________________________________

Water Source: __________________________________________________________

Company/Person Testing: ________________________________________________

TESTS: Recom’d Level Conc. ppm, mg/l

Temperature 40-100 deg F SG Corrected to 60 deg F <1.038 pH 6 - 8 Total Iron <20 ppm

Ferrous Iron (Fe+2) Ferric Iron (Fe+3)

Total Phosphorous (PO4-3) <5 ppm Sulfite (SO3-2) Sulfate (SO4-2) Calcium-Magnesium Hard (CaCO3) <1000 ppm Total Reducing Agents 0 ppm Total Bacteria Count <10**5 ppm

Aerobic Anaerobic

Boron

FRACTURING FLUID QC


Table 11.5 - Testing of Base Mixing Fluids for Hydraulic Fracturing

Transport and Storage of Fluid

All transports bringing the base mixing fluid and all frac tanks used for storage on locationshould be very clean and free of rust and other chemical contaminants. Transports and frac tanksshould be thoroughly drained, steam cleaned, and flushed with clean water prior to loading themixing fluid. If oil or diesel is to be shipped and stored, all water must be removed prior tofilling. Less than 1% water in a gelled-oil system can cause severe gelation problems.

If frac tanks are showing signs of excessive rust and wear, the valves do not operate freely,and/or the tanks are not thoroughly clean they should be rejected. This will require an inspectionby the service company and/or operator. Ultimate care should be taken to insure that the transportand on-site storage of the base-mixing fluids results in a clean fluid to start with in mixing thefracturing fluid. Of all the quality control measures, this is one of the most important topreventing gelation problems. “ Prevention far exceeds the cure.”

BASE MIXING FLUID

• Obtain 3 Samples from Source- Composition / Compatibility Testing (Svc Co.)

WATER-BASE FLUID:

• Iron Content <20 mg Fe/liter- Reduce Temp. Stab. of Gel- Transports / Frac Tanks

• pH between 6.0-8.0- >8.0 Poor Gel Hydration- <6.0 Lumping or “Fish-Eyes”

• Bacteria- Most Common Above 80 deg F- Will Destroy Gel Structure- Hydrogen Sulfide Odor

OIL-BASE FLUID:

• Lease Crude or Diesel

• deg API Gravity or Lower Best

• Diesel Content Change with Supplier, Refinery, and Seasonal Change• Compatibility Test is a Must


11Quality Controlling Water-Based Gels

Water-based fluids can be broken into two categories, i.e., linear and crosslinked gels. Linear gelis water thickened with a viscosifier, the more common viscosifiers being guar, hydroxypropalguar (HPG), hydroxyethylcellulose (HEC), and carboxymethyl HPG (CMHPG). With linear gelsthe only means of increasing the viscosity is to increase the polymer loading. Crosslinked fluidson the other hand start with a linear gel and a borate or metal (zirconate or titinate) crosslinker isadded which ties or bonds the polymer molecules together, resulting in a pseudoplastic fluid withmuch higher viscosity than obtainable with simple linear gel systems.

Quality control procedures for linear gels are fairly straight forward and include checking thefollowing:

• Base gel viscosity.

• pH of the fluid.

• Consistency and appearance of the gel.

• Breakage of the fluid.

Prior to mixing any gel in the frac tanks, pilot tests should first be performed with the base-mixing water from each tank. Minimum equipment requirements to perform these tests, whichshould be supplied by the service company, include:

• Fann 35 viscometer.

• Properly calibrated scale.

• pH meter.

• Thermometer.

• Waring blender or similar mixing devise.

• Heat bath capable of reaching 180-200°F.

All pilot tests should be performed using samples of the chemicals supplied on-location for thetreatment. The following procedure should be followed and all phases recorded:

• Visually check the base water for signs of bacteria or contaminants.

• Measure the pH of the base mixing water.

• Mix the gel sample to include all chemicals planned for the treatment, including the breaker.

• Measure the temperature and pH of the final gel sample.

FRACTURING FLUID QC


• Measure the viscosity of the gel, taking Fann readings at 100, 300, and 600 rpms.

• Immerse the gel sample in the heat bath.

• Measure and record the viscosity of the fluid in the heat bath every 30 minutes or so todetermine viscosity degradation for use in the design model and to evaluate breakage of thefluid. (At a minimum, the fluid should be heated and sufficient breaker added to insure thatthe breaker on-site works.)

Fig. 11.1 and Fig. 11.2 are Fann viscometer readings for various linear HPG gel loadings andtemperatures at a shear-rate of 511 sec-1 (corresponds to Fann 35 - 300 rpm reading). The sameare provided for linear HEC gel in Fig. 11.3 and Fig. 11.4 . These can be used as a guide inchecking the initial gel viscosity at surface temperature. Some tolerance should be allowed, i.e.,a few cp either side of the values shown in the plots, since there will be some variance in themixing of each tank, e.g., for a 50 lb HPG gel loading an acceptable range of Fann readings at70°F might be 45-53 cp. If the gel viscosity falls much outside this range, another sample shouldbe caught from the tank and re-checked. If it is still outside this range, then corrective measuresmust be taken to bring it into spec if it can not be used in the tail-end of the treatment when theformation is coolest

Fig. 11.8 - Hydroxypropylguar (HPG) - Fann Viscosity v. Polymer Concentration in 2% KCIWater @ 60°F.

When performing break tests, it is usually necessary to mix several samples with differentbreaker concentrations to determine the final breaker loading. The breaker loading should betailored so that the maximum effective loading is added throughout the treatment to insure


11

Fig. 11-9 - Hydroxpropylguar (HPG) - Fann Viscosity v. Temperature for Various Polymer Loadingsin 2% KCI Water.

eventual complete degradation of the gel. When the expected BHT exceeds the achievabletemperature of field heat baths, the breaker scheduling will have to be determined in thelaboratory (also required when go into a new area or formation or where significant changes aremade to the treatment size and/or the fracturing fluid or water source is changed).

Different breaker concentrations may be required for different fluid systems. Also, thereservoir BHT will dictate the amount of breaker that can be added so the gel degrades in thetime required. Two general types of breakers are available for use, i.e., raw (oxidizing orenzyme) breaker and encapsulated (delayed) breaker. It has been shown in industry studies thatup to a point more breaker is better from the standpoint of degrading the gel filter-cakeformed on the fracture walls and removing the gel residue from the proppant pack. A “ roughrule-of-thumb” is to design the breaker schedule so the pad fluid is completely broken intwice the expected pump time and the tail-end fluid is broken in about an hour after shut-down. For example, as shown in Table 11.3, on a 1-hour or less treatment, sufficient breakershould be added to the pad to break the fluid in approximately 2 hours and the breaker scheduleincreased so the tail-end fluid breaks within 1 hour after shut-down. Depending on the reservoirtemperature and gel loading, only encapsulated (delayed) breaker may be required in the pad,whereas in the later stages the raw breaker concentration may be increased and the encapsulatedbreaker concentration decreased. When feasible, the breaker schedule should be

FRACTURING FLUID QC


Fig. 11.10 - Hydroxyethlcellulose (HEC) - Fann Viscosity v. Polymer Concentration in 2% KCI Water@ 60°F.


11

Fig. 11.11 - Hydroxyethylcellulose (HEC) - Fann Viscosity v. Temperature for Various PolymerLoadings in 2% KCI Water.

designed/evaluated on-site based on pilot test ing with the actual mix fluid and breakerstock provided for the treatment. Ineffective batches of breaker have been known to exist!

Table 11.6 - Sample Fracture Treatment Schedule with Raw and Encapsulated Breaker Ramps.

Fluid Type Fluid Vol(gals)

Raw Brkr(#/Mgal)

Enc. Brkr(#/Mgal)

Prop Conc(ppg)

Rate(bpm)

30# Borate XL 3500 0.0 5.0 0.0 20.0

30# Borate XL 500 0.0 5.0 1.0 20.0

30# Borate XL 300 0.5 4.0 2.0 20.0

30# Borate XL 300 0.5 4.0 3.0 20.0

30# Borate XL 300 1.0 3.0 4.0 20.0

30# Borate XL 300 2.0 3.0 5.0 20.0

30# Borate XL 300 3.0 2.0 6.0 20.0

30# Borate XL 400 4.0 2.0 7.0 20.0

30# Borate XL 600 5.0 2.0 8.0 20.0

Note: Raw breaker ramped up and encapsulated breaker ramped down based on field-generated lab testsin heat bath at expected BHT.

FRACTURING FLUID QC


Quality control procedures for crosslinked gels are much the same as for linear gels with theexception of checking the ability of the fluid to crosslink, it's crosslinked consistency, andcrosslink time. The same procedures as above should be followed to prepare and test the baselinear gel prior to crosslinking. Crosslinked gel systems generally fall in one of two categories,i.e., instantaneous crosslink and delayed crosslink. The crosslink time can be controlled by anumber of methods. Some companies control crosslinking by adjusting pH, others vary crosslinktime by changing the crosslinker concentration or by blending crosslinkers, while still others useretarders or accelerators to control the time to crosslink without changing the crosslinker or pH.

Again, pilot testing is very important in determining if the gel is properly crosslinking and howlong it takes to crosslink. Generally, the best way to test this is to obtain a sample of thecrosslinker on-site and observe the crosslinking of the linear gel in a blender. The speed of theblender should be set just high enough so a vortex forms in the center of the linear gel sample.The crosslink time is then measured from the time the crosslinker is added until the vortex closesand a mushroom forms on top of the sample - this termed the “ Vortex closure time” . Forinstantaneous crosslink systems, the gel should form a bonded structure very quick. For adelayed system, though, this may take some time, depending on the temperature and pH of thefluid. When testing a delayed crosslinked gel, it is best to heat the base gel to the expectedaverage wellbore temperature during the treatment to perform the pilot tests. The delay time forthe crosslink is determined by the expected residence time in the pipe, i.e., the gel should ideallybe crosslinking just outside the perforations. This will minimize pipe friction pressure andminimize the shear on the gel before it enters the fracture.

A good crosslinked gel should exhibit a strong bonding with a smooth texture that can be lippedout of the sample container and returned as a whole unit. If a gel is under-crosslinked it willexhibit a weak, slimy, runny appearance absent of strong bonding. At the other end of thespectrum an over-crosslinked gel will exhibit a chunky, rough, “brittle” appearance. This typefluid, while viscous in appearance will have poor temperature stability.

If crosslinking problems occur, several things can be investigated including:

• The crosslinker itself. Catch another sample from a different drum on-site.

• The pH of the fluid if the crosslinker is being controlled by pH.

• The crosslinker concentration.

In special cases where the gel simply will not crosslink properly, it may be due to contaminantsin the base gel. This, however, can be prevented if proper laboratory and pilot testing (including


11

11-30 July 1999

crosslinking) is performed prior to mixing the tanks of gel. If crosslinking is a problem in only onetank and sufficient excess is available or can be mixed, then that particular tank may have to beutilized as prepad or flush or disposed of. Do not pump any gel as part of the main treatment thatis suspect.

Again, as for the linear gel systems,breaker schedulingis very important for crosslinked gel sys-tems. There is nothing worse than pumping a crosslinked gel into a reservoir that might not break.Undoubtedly many wells have been ruined this way. If possible, breaker tests should be performedin a heat bath on-site to determine the optimum breaker schedule. If the reservoir temperatureexceeds 200°F, the upper limit for most conventional heat baths, then extensive laboratory testingshould be performed by the service company with the actual mixing water and preferably thechemicals from the treatment stock to determine the best breaker schedule for the desired timeperiod.

When utilizing resin-coatedproppants, these can have a dramatic affect on the crosslink andbreak time of crosslinked gel systems. Some of the crosslinker and breaker are neutralized by theresin, requiring that additional amounts of these chemicals be added to achieve the same gel.Again, this requires extensive testing by the service company to determine the adjustmentsrequired. This is generally a hard thing to quantify and impossible to determine on-site. A newencapsulated curable resin-coated proppant has just recently been introduced on the market whichstill bonds in the fracture with closure stress yet is inert to fracturing fluids and chemicals. If itproves to work as advertised, it should eliminate the problems associated with the interaction withcrosslink gel chemicals and breakers.

All pilot test results done on-site should be recorded on a form similar to Table11.7.

Quality Controlling Oil-Based Gels

Some formations, although these are few and far apart, simply do not lend themselves to water-based fracturing. These might have large quantities of swelling or migrating clays, imbibe largeamounts of water, and/or the rock matrix structure is weakened by water. In these cases, oil-basedgel may be the preferred fracturing fluid. Due to difficulties in properly mixing and quality con-trolling this system, in addition to the safety hazards, gelled-oil should only be used as a last resortafter careful reservoir and laboratory evaluation.

Mostgelled-oil are made up of the followingcomponents:

• Lease crude or diesel as the base fluid.• Gelling agent.• Activator additive.• pH control additive.• Breaker.• Fluid loss additive.


FRACTURING FLUID QC

11-31July 1999

Mostcrude oil from 28°F API and higher can be gelled with this system; however, the particularcrude must be tested for gelation prior to a decision being made on its use. Testing should also beperformed with eachdieselsource to determine its suitability. The content of diesel may vary withsupplier, refinery, and seasonal changes. Special additives included to prevent diesel freezing canhave a detrimental affect on the gelation and breakage of a gelled-oil system.

The concentration ofgelling agent(aluminum phosphate) is the controlling factor in determiningthe viscosity of the gel. This concentration will depend on the desired viscosity at BHT. Typicalviscosities achievable with this system are 50-300 cp (170 sec-1) at 80-190°F and 50-150 cp at200-250°F. Theactivator (sodium aluminate or other base) is normally held to a constant ratiowith the amount of gelling agent, e.g., if 8 gals/Mgals gelling agent is used, 3 gals/Mgals of acti-

Table 11.7- Fracturing Fluid Quality Control Form.

Well / Field:________________________________ Date:_________________

Location: ________________________________ Tested By: ___________

TankNo.

Gel Type/ Conc.

Gauge /Pump

VolumeFluidTemp.

Vis. @300rpm pH

XLTime

BreakTime Appearance


11

11-32 July 1999

vator is added; with 6 gals/Mgals of gelling agent the activator concentration is around2.3 gals/Mgals.

The concentration ofpH control additive is dependent on the pH of the particular oil. Lab testing,through trial and error, is required to determine the correct concentration of pH control additive.In lab testing the gelling agent and activator are added first and then the pH control added dropwise until gel viscosity is observed.

Breakersused for gelled oil systems include sodium bicarbonate (baking soda) and slaked lime orcalcium hydroxide. The sodium bicarbonate is used on most treatments unless the BHT is very lowor a short break time is desired. Typical concentrations of breaker range from 10-75 lbs/1000 Mgals depending on the BHT, pump time, and the desired break time. As noted forthe water-based gel systems, it is preferable to add as much breaker as lab tests indicate possiblewhile still maintaining sufficient viscosity to safely complete the treatment. Cases have been sitedwhere no or an insufficient amount of breaker were added and the gel did not break, causing thetreatment to be ineffective and plugging of the formation.

In a gelled-oil system, the sodium bicarbonate breaker also acts as afluid lossagent, this being ina free flowing powder form. Other additives such as Adomite Aqua and silica flour can be used,however, these are not recommended unless absolutely necessary.

On-site quality control test procedures for gelled-oil systems should include the following:

• Roll each frac tank of oil thoroughly.

• Sample the base oil from each tank.

• Add the gelling agent and activator to the sample(s) at the prescribed concentrationsrecommended by the service company and previous lab testing.

• Determine the amount of pH control additive by adding drop-wise until viscosity develops.

• Test the viscosity of the fluid with a Fann 35 viscometer. If the viscosity is within the desiredrange, proceed with the next step. If it is too high or too low, prepare another sample, adjustingthe gelling agent and activator concentration and going through the pH additive test again.Continue to retest until the desired viscosity is obtained or the best gel obtainable is achieved.

• After the gelling agent, activator, and pH additive concentrations have been fine-tuned, mixseveral more samples with varying concentrations of breaker and immerse these in a heat bathto monitor the gel degradation and break time. The gel should have sufficient viscosity tocomplete the treatment safely and then break back to less than 10 cp at a Fann 300 rpm reading.An example of the results of this type testing are shown in Fig. 11.12. In this case, it wasdetermined that 40 lbs/Mgals of breaker was optimum for completing the short pump timetreatment and getting a good break within a reasonable time after the treatment.


FRACTURING FLUID QC

11-33July 1999

These tests should be performed for each tank of oil as some may react differently than othersrequiring slight alterations to the chemical additive combination.

Safety precautions associated with handling gelled-oils include:

• Wearing rubber gloves and safety goggles when handling all chemicals. Some are acidicand some alkaline and can cause severe burning.

• Take the necessary precautions associated with a highly flammable fluid, i.e., ground theblending and pumping equipment, no smoking on location, use of shrouds on high pressuredischarge lines, and proper fire fighting equipment.

Quality Controlling Foam Fracturing Fluids

Foam fracturing fluids are sometimes an alternative to oil-based gels to minimize the amount offluid placed on the formation. Their most common application, though, is in fracturing underpres-sured reservoirs where the entrained gas in the fluid results in improved and rapid cleanup. Virtu-ally any liquid can be foamed, including methanol, methanol/water mixtures, hydrocarbons, andwater. The most commonly used system is comprised of a 20-40 lb/Mgal linear water-based geland 65-80% CO2 or N2, i.e., a 65-80 quality foam. This means that 65-80% less water is used ascompared to conventional treatments. The advantages of using CO2 over nitrogen as the gas phase

Fig. 11.12 - Results of Field Break Test for Oil-Base Gel, Using a Fann 35 Viscometer and Heat Bathto Determine Optimum Breaker Concentration.


11

11-34 July 1999

is (1) that CO2 can be pumped as a liquid, it not turning into its gas phase until reaching reservoirconditions, and this resulting in lower treating pressures and (2) the liquid CO2 is soluble in water,thus as it turns into a gas in the reservoir it will not dissipate into the formation as might be the casewith a less soluble gas such as nitrogen. The use of nitrogen, though, can be considerably cheaperwhen the expected treating pressures are low. Some of the disadvantages of using foam fracturingfluid are (1) that job execution must be precise - small variations in water or gas mixing rates cancause loss of foam stability and (2) downhole proppant concentrations are generally limited toabout 8 ppg since all of the proppant must be added to the liquid phase which comprises only about1/4 of the total foam fluid.

Since most foam treatments use a water-based linear gel for theliquid phase, the samequalitycontrol proceduresoutlined previously for this type gel should be applied here. Generally, thesewould again include checking the base gel viscosity, pH, and temperature to make sure the gelmeets design specifications. Little can be done in regard to quality controlling the gas phase, asidefrom checking to make sure sufficient quantity is on-site to conduct the desired treatment.

Because foam fracturing treatments are more complex to perform than single-phase treatments, itis important that the service company treater and engineer fully understand the surface proppantschedule and liquid/gas rates to obtain the desired concentrations and rate downhole. A plan shouldbe carefully laid out with a table such as shown in Table 11.8 for all to follow during the treatment.

Additional Fluid Quality Control Measures

• Inventory all chemicals and fluids/gas on location at the earliest possible time to make sure theright materials in the right amounts are available for the treatment.

Table 11.8 - Sample Schedule Prepared for Constant Clean Side and Nitrogen-Rate Foam FractureTreatment.

FoamVolume,

gal

LiquidVolume,

gal

FOAM FRAC PUMPING SCHEDULE

Time,min:sec

Proppant Slurry Volume Pumping Rate

Foam,ppg

Liquid,ppg

Totallb

Foam,gal

Blend,gal

Nitrogen,scfm

Liquid,bbl/min

Sand,*bbl/min

Totalbbl/min

35,000

25,000

30,000

12,500

10,000

7,500

1,800

TOTALS:

121,800

10,500

7,500

9,000

3,750

3,000

2,250

540

36,540

0.0

1.0

2.0

3.0

4.0

5.0

0.0

0.0

3.3

6.7

10.0

13.3

16.7

0.0

0

25,000

60,000

37,500

40,000

37,500

0

200,000

35,000

26,130

32,712

14,195

11,808

9,195

1,800

130,840

10,500

8,630

11,712

5,445

4,808

3,945

540

45,570

13,820

13,820

13,820

13,820

13,820

13,820

13,820

4.5

4.5

4.5

4.5

4.5

4.5

4.5

0.0

0.7

1.4

2.0

2.7

3.4

0.0

15.0

15.7

16.4

17.0

17.7

18.4

15.0

55:33

39:37

47:29

19:53

15:53

11:54

2:51

193:10

Foam quality: 0.70

Total Nitrogen required: 2,669,563 scf (calculated as scf/min x total time)

2,671,480 scf (calculated as total bbl nitrogen x scf/bbl space)

*Rate of sand, bbl/min = ppg x bbl/min x 0.0452


FRACTURING FLUID QC

11-35July 1999

• Perform pilot tests as soon as possible on-site to insure that the available chemicals all workand that the base mixing fluid is not contaminated.

• Take tank dips before and after the treatment to help in evaluating the accuracy of meteringduring the treatment and to access what was actually pumped.

• Set up a sampling program during the treatment to determine that the system is acting as pilottesting predicted it would. On a relatively small treatment, this might include catching 1-2samples during the pad and 2-4 samples during the proppant stages. On a larger treatment, witha pump time of several hours, several samples should be caught during the pad and, preferably,one sample per proppant stage. In the most severe case on a crosslinked gel treatment, wherethe gel is not properly crosslinking and this can be detected before proppant is started, thetreatment should be aborted and the problem remedied before a reattempt of the treatment.

• Immerse half of the treatment samples in a heat bath to determine the gel break time and todetermine the earliest possible time at which the well can be flowed back. The remainingsamples should be retained for a period of time after the treatment until the well has cleanedup. Also, if gelation problems occur during the treatment, these samples may help determinethe cause.

• Record all phases of the gel pilot testing, inventory, mixing, and results of treatment sampling.


11

11-36 July 1999

11.5 PROPPANT QC

The selection and quality of a proppant agent is very important to the outcome of a fracturing treat-ment. Production increase is a function of fracture conductivity, and fracture conductivity isdirectly related to the insitu proppant characteristics and confining (closure) stress on the proppant.Factors affecting fracture conductivity include:

• Closure stress and proppant strength.

• Proppant particle size.

• Proppant concentration.

• Proppant grain shape - roundness/sphericity.

• Amount of fines generated.

Many of these variables can be controlled to varying degrees through proper quality control prac-tices.

Closure Stress and Proppant Strength

The stress transmitted from the earth to the proppant pack at fracture closure can cause proppantcrushing and embedment of the proppant into softer formation, both of which reduce the effectivefracture conductivity. In selecting a proppant it is very important to know the approximate stress,the stress on proppant being equivalent to the closure stress minus the bottomhole flowing pres-sure. The maximum potential for proppant damage will usually occur early in the life of a wellwhen the reservoir and closure pressures are high and the BHFP is low.

Fig. 11.13 illustrates the affect closure stress has on several types of proppants, showing that athigher stresses, higher strength proppants will be required to provide adequate fracture conductiv-ity. If closure stress is unknown, this parameter should be measured through injection/decline test-ing. A list of currently available proppants and their recommended stress limitations are shown inTable 11.9, including sand, intermediate-strength, high-strength, and resin-coated proppants.

Industry studies over the past 10-15 years have shown that when proppants are subjected to stressand temperature for longer periods of time, conductivity decays with most of this decay occurringover the first 100 hours. Fig. 11.14 shows examples of this for several different type proppants. Indesigning the fracture treatment,long-term conductivity data should be obtained from the ser-vice company and used instead of the more typically published short-term data.

Proppant Particle Size

Proppant particle size selection is a design consideration and dependent on the stress level, desiredconductivity, and proppant transport (i.e., achievable fracture width). In most cases, either 20/40,


PROPPANT QC

11-37July 1999

Fig. 11.13 - Effect of Proppant Type on Proppant-Pack Permeability (Conductivity). RelativePerformance of Various Proppant is Demonstrated for 20/40 Mesh Size.

Table 11.9 - Fracturing Proppant List

Proppant Manufacture SpecificGravity

Application Limitations/Alternative

AcFrac CR-5000 Acme Borden 2.59 Curable resin coated whitesand. Less resin thanAcFrac CR. Closure stressto 6,000 psi.

AcFrac CR Acme Borden 2.59 Curable resin coated whitesand for flowback control.Closure stress to 8,000 psi.

AcFrac CR-100 Acme Borden - Curable resin coated100 mesh sand.


11

11-38 July 1999

Super TF Santrol 2.60 Low cost low resin content(2%) for bonding and flow-back control. A true 20/40mesh white sand. Closurestresses up to 6,000 psi.

Super LC Santrol 2.60 Low cost low resin content(2%) for bonding andflowback control. Whitesand. Closure stresses upto 6,000 psi.

Super DC Santrol 2.57 Dual-coat, half-cured andhalf-uncured resin coatedwhite sand for strength andflowback control. 4% resin.Closure stresses up to8,000 psi.

Super HS Santrol 2.54 High strength, dual-coat,resin coated white sand forstrength and flowbackcontrol. 5% resin. Closurestresses up to 8,000 psi.

Tempered TF Santrol 2.60 Identical to Super seriesexcept precured rather thancurable.

Tempered LC Santrol 2.60 Identical to Super seriesexcept precured rather thancurable.

Tempered DC Santrol 2.57 Identical to Super seriesexcept precured rather thancurable.

Tempered HS Santrol 2.54 Identical to Super seriesexcept precured rather thancurable.

EconoFlex Santrol 2.55 Resin coated EconoPropceramic proppant. Closurestresses to 14,000 psi

White Sand 2.65 Used to prop open createdfracture to conducthydrocarbons to thewellbore. Closure pressureto 4,500 psi. Ranked 1stamong sands.

Low closure stress.

Table 11.9 - Fracturing Proppant List (Continued)




PROPPANT QC

11-39July 1999

EconoProp Carbo Ceramics 2.65 Economical intermediatestrength ceramic proppant.Closure stress 3,000 to8,000 psi.

Lower closureapplication. Onlyoffered in 20/40mesh. Competeswith LWP 1.

Carbo-Lite Carbo Ceramics 2.73 Intermediate strengthceramic proppant. Closurestress 4,000 to 9,000 psi.

Competes withLWP Plus.

Carbo-Prop HC Carbo Ceramics 3.17 Intermediate strengthbauxite. Closure stress upto 15,000 psi.

Competes withInterProp Plus.

Carbo ISP-1 Carbo Ceramics 3.16 Intermediate strengthbauxite. Closure stress upto 15,000 psi. Lessexpensive than Carbo-PropHC. Broader sizedistribution.

20/40 mesh only.Competes withInterProp 1.

LWP 1 Norton-Alcoa 2.64 Economical intermediatestrength ceramic proppant.Closure stress 3,000 to8,000 psi.

Lower closureapplication. Onlyoffered in 20/40mesh. Competeswith EconoProp.

LWP Plus Norton-Alcoa 2.60 Intermediate strengthceramic proppant. Closurestress 4,000 to 9,000 psi.

Competes withCarbo-Lite.

InterProp Plus Norton-Alcoa 3.15 Intermediate strengthbauxite. Closure stress upto 15,000 psi.

Competes withCarbo-Prop HC.

InterProp 1 Norton-Alcoa 3.15 Intermediate strengthbauxite. Closure stress upto 15,000 psi. Lessexpensive than InterPropPlus and Carbo-Prop HC.Broader size distribution.

Competes withCarbo ISP-1.

InterProp 1 RCP Norton-Alcoa 3.06 Same as above with resincoating for flowback control.

Same as above.

UltraProp Plus Norton-Alcoa 3.49 High strength bauxite.Closure stress up to 20,000psi.

Expensive.

AcFrac SBULTRA

Acme Borden 2.56 Partially cured white sand,requires stress for bonding.For flowback control andstrength. Will not set up inwellbore in screenout.Closure stress to 8,000 psi.

More compatiblewith oxidizingbreakers.





11

11-40 July 1999

16/20, or 12/20 mesh proppant is used. Particle size distribution can have a measurable affect onfracture conductivity. For example, as shown in Fig. 11.15, one sand having 90% of the grains fall-ing between the designated 20/40 mesh sieve screen sizes, as compared to another having only60% of the grains within the required range, will exhibit much higher conductivity and the contrastwill increase as the closure stress increases.

Testingof proppant sizedistribution requires a sieve analysis and should be routinely performedas a quality control practice on most fracture treatments. The American Petroleum Institute (API)provides several publications detailing tests for sands and intermediate- and high-strength prop-pants. Shown in Table 11.10 is an excerpt from API RP 56 showing the range of various frac sands(6/12 to 70/140) and the nest of sieve screens recommended for testing. A minimum of 90% of thetested sand sample (also generally applies to other proppant types) should fall between thedesignated sieve sizes correlative to the indicated mesh size, i.e., 6/12, 12/20, 20/40, etc. Not over

AcFrac Black(PRB)

Acme Borden 2.55 Precured white sanddesigned for strength duringclosure. Closure stress to8,000 psi.

AcFrac PR-5000 Acme Borden 2.59 Precured white sanddesigned for strength duringclosure. Closure stress to8,000 psi.

Brown Sand 2.65 Brady sand. Used to propopen created fracture toconduct hydrocarbons tothe wellbore. Closurepressure to 4,500 psi.Ranked 2nd among sands.

Low closure stress.

Colorado Sand 2.65 Used to prop open createdfracture to conducthydrocarbons to thewellbore. Closure pressureto 4,500 psi. Ranked 3rdamong sands.

Does not meet anumber of API RP-56 guidelines.

Arizona Sand 2.70 Used to prop open createdfracture to conducthydrocarbons to thewellbore. Closure pressureto 4,500 psi. Ranked 4thamong sands.

Does not meet anumber of API RP-56 guidelines.

Sinter Ball 3.60 Sintered bauxite fromBrazil. Used for high closurepressure conditions tooextreme for ceramics.

Exxon license feerequired for wellsdeeper than 7,150feet.





PROPPANT QC

11-41July 1999

0.1% of the total proppant sample should be larger than the largest sieve screen mesh and not over1.0% should be smaller than the smallest sieve screen mesh.

Proppant Grain Shape

Proppant particle“roundness” and “sphericity” are measures of grain shape. Roundness is ameasure of the relative sharpness of grain corners or grain curvature and sphericity is a measure ofhow close a proppant grain approaches the shape of a sphere. Because the surface stresses are moreuniform, a well-rounded, spherical particle is capable of carrying higher loads without crushing.Therefore, at higher stress levels, a higher degree of roundness and sphericity contribute to higherproppant-pack conductivity.

A visual comparator, shown in Fig. 11.16 from API RP 56, is the most widely used method ofdetermining grain shape. For sands, the API recommends a minimum sphericity of 0.6 and a min-imum roundness of 0.6 (1.0 being a perfect sphere). For intermediate- and high- strength proppantsa minimum sphericity and roundness of 0.7 is recommended.

Fig. 11.14 - Example of Long-Term Permeability (Conductivity) Data for Various 20/40 MeshProppants Tested @ 275 °F and a Proppant Concentration of 2 lbm/sq. ft.


11

11-42 December 1995

Fig. 11.17 shows the effect on fracture conductivity for two sands at stresses of 5000 and10,000 psi, one exceeding API specs and other falling below the recommended roundness/spheric-ity. From this, it is obvious that the rounder, more spherical proppant results in much higher con-ductivity, i.e., 61% higher at 5000 psi and 300% higher at 10,000 psi stress.

Proppants routinely used and/or new proppants being considered for use should be subjected tograin shape testing under a microscope by the service company and/or operator.

Proppant Fines

The presence of silts, clays, and other fine particles in the proppant can also reduce fracture con-ductivity. Fine particles can be detected through an API recommendedturbidity teston-site. Therecommended procedure for this test is:

• Using a black marking pen, record the proppant sample identification on one side of a clearglass 4-ounce prescription bottle (100 ml in 10 ml increments) in characters approximately1/2” high.

• Place the proppant sample in the container and fill to the 20 ml mark, gently tapping andleveling the sand and further fill to bring to but not exceed the 20 ml mark.

• Add turbidity-free water (distilled water, if available) to the 100 ml mark.

• Cap the bottle and shake vigorously for 10 seconds.

• Hold the bottle at arm's length toward a moderate light source with the side of the bottle withthe identification mark facing the light source.

Fig. 11.15 - Effect of Proppant Particle Size Distribution on Fracture Conductivity for 20/40 MeshSand at Proppant Stresses of 5,000-10,000 psi.


PROPPANT QC

11-43December 1995

Interpretation

• If the sample ID can be read through the water phase, the proppant should be judged cleanand suitable for use.

• If the sample ID can not be read, the proppant sample should be judged dirty and unsuitablefor use.

Table 11.10 - Recommended API Proppant Specifications for Frac Sand and ManufacturedProppants.

Recommended Mesh Size Requirements

A minimum of 90% of the tested sample should fall between the designated sieve size. Not more than0.1% of the tested sample should be larger than the first sieve size. Not over 1% should be smaller thanthe last sieve size.

Recognized Proppant Mesh Sizes

Frac Sand SizeDesignation

+6/12

+8/16

*12/20

+16/30

*20/40

+30/50

*40/70

+70/140

USA Sievesa

Required for Testing

4 6 8 12 16 20 30 50

6 8 12 16 20 30 40 70

8 12 16 20 30 40 50 100

10 14 18 25 35 45 60 120

12 16 20 30 40 50 70 140

16 20 30 40 50 70 100 200

Pan Pan Pan Pan Pan Pan Pan Pan

* Primary Mesh Size+ Alternate Mesh Sizea USA Sieve Series as defined in ASTM E 11-70

Frac Sand Manufactured

Roundness: 0.6 value or greater 0.7 value or greater

Sphericity: 0.6 value or greater 0.7 value or greater

Turbidity: 250 FTU or less not specified

Silica: greater than 98% by weight not specified

Acid Solubility Hydrochloric acid solubility - lessthan 0.3%. 12% hydrochloric - 3%hydrofluoric acid solubility - 6/12through 30/40 mesh - 2.0%maximum allowable, 40/70 through60/140 mesh - 3.0% maximumallowable percentage.

Hydrochloric acid solubility - notspecified. 12% hydrochloric - 3%hydrofluoric - not specified.


11

11-44 December 1995

• If the sample ID can be read but with some difficulty, let the sample stand for 10 minutes andrepeat the test. If the ID still cannot be read, the sample should be judged unsuitable for use.

The most suitable time to perform the turbidity test is when the proppant bins or trucks areloaded in order to get a representative sample from a moving stream. Also, performing the test at

Fig. 11.16 - Chart for Visual Estimation of Roundness and Sphericity for Proppants Used inHydraulic Fracturing (from Krumbein and Sloss, 1955).

Fig. 11.17 - Effect of Proppant Roundness and Sphericity on Fracture Conductivity for 20/40 MeshSand at Proppant Stresses of 5,000-10,000 psi.


PROPPANT QC

11-45December 1995

this early time in the operation will allow for corrective measures to be taken if necessary withoutundue delay to the treatment.

Proppant fines can also be generated in the fracture if the proppant strength is not high enough towithstand formation stresses.Crush resistancetesting should be performed periodically on rou-tinely used proppants and all new proppants being considered for use, using the recommended pro-cedure in API RP 56. Testing of this nature can be performed by the service company, the AmocoTulsa Technology Center, or by commercial core laboratories. Table 11.11 includes the recom-mended test cell loads and maximum allowable fines for frac sand.

Additional Proppant Quality Control Measures

• Obtain weight tickets from the service company on the amounts and types of proppantdelivered and loaded on location.

• If using more than one type or size of proppant on a treatment, know where each proppant isloaded in the proppant storage bins on location and discuss with the frac operator in what orderthese are to be run.

• Catch samples of the proppant during various stages of the treatment and label these accordingto size/type proppant and when they were caught.

Table 11.11 - Stress to be Applied and Suggested Maximum Fines for Frac and Sand CrushResistance Tests (API RP 56).

Mesh SizeLoad on Cell*

(lb force)Stress on Sand

(psi)Suggested Max. Fines

(% by weight)

6/12 6,283 2,000 20

8/16 6,283 2,000 18

12/20 9,425 3,000 16

16/30 9,425 3,000 14

20/40 12,566 4,000 14

30/50 12,566 4,000 10

40/70 15,708 5,000 8

70/140 15,708 5,000 6

NOTE: Indicated loads are for cells with a 2” diameter piston. For cells of othersizes, the cell load should be adjusted by the factor:(diam. of cell, in./2)**2.


11

11-46 December 1995

11.6 TREATMENT EXECUTION

Successful execution of a fracturing treatment requires good lines of communication, followingsafe working practices, and having contingencies in place for mechanical and/or abnormal pres-sure behavior problems.

Lines of Authority and Communication

• The operator should have only one person in charge of communicating changes or decisions tothe service company.

• Key personnel from the operator and service co. should have a final review meeting to go overthe treatment pump schedule, maximum treating pressures, lines of authority, contingencyplans in case of mechanical/pressure problems, and safety issues.

• Service co. should supply properly working radios and headsets to all personnel at keyequipment focal points, i.e., blender, pumps, sand delivery, frac tanks, valve operator, and fracoperator in control van.

• Prior to pressure testing, the service co. should perform a radio check to make sure all radiosand headsets are fully functional. If an insufficient number of “working” radios are notavailable, the treatment should not be performed until this is remedied.

Safety Meeting

The safety meeting should be conducted by the frac operator with all personnel on-site and shouldinclude the following:

• An outline of the job procedure.

• Maximum treating pressures and rate.

• Pressure testing.

• Operator responsibilities.

• Operator safety gear, including safety glasses, hard hats, safety boots, and proper clothing.

• Chemical hazards.

• Location and use of fire extinguishers, eye wash facilities, first aid kits, and other safetyequipment.

• Other emergency procedures, including fire, leaks, other accidents.

• Smoking restrictions.


TREATMENT EXECUTION

11-47December 1995

• Normal and emergency shut-down procedures.

• A sign-up list of all personnel on-location during the treatment.

• A designated safe assembly area in case of an emergency situation.

Pressure Testing

Prior to every fracture treatment, all injection lines and valves should be pressure tested and“pop-offs” or pressure relief valves set. All lines should be properly staked and all personnel notdirectly involved in the pressure test should move well clear of the area surrounding the lines, well-head, and fracturing equipment. All lines should be tested to just above the determined maximumtreating pressure set by the operator, with this pressure being held and recorded for a minimum of5 minutes. If treating down tubing, with the plan to hold back-pressure on the annulus, both tubingand annulus lines must be tested. All leaks should be eliminated prior to proceeding with the treat-ment.

Pressure relief valves should always be installed on injection lines and set and tested to just belowthe determined maximum treating pressure.

Treating Problems

Oftentimes, treating problems arise during the job that must be dealt with, the most common beequipment failures, gel not properly crosslinking, proppant delivery problems, and abnormal pres-sures. These can be very disruptive to the successful completion of a treatment if proper planningand contingencies have not been put in place. Some of the more common problems are as follows:

• Blender failure dueto mechanicalproblem - In most cases, it is advisable to have a standbyblender rigged-up and operational. While blender failures are rare, the cost of standby isminimal compared to the costs that might be incurred if the treatment has to be prematurelyaborted. Hoses should be run from the standby to the frac tank manifold, the standby blendertub filled with gel, and sufficient chemicals installed on this blender to complete the job if needbe. Also, when a standby blender is installed, provisions need to be made to change the sanddelivery over to this second blender.

On small treatments, where leak-off is expected to be high, fracture closure time may notallow sufficient time to switch to a standby blender. If this is the case, a standby serves nopurpose.

• Sanding-up” the blender tub - This is caused when fluid cannot be transferred to the blenderat a fast enough rate, blender operator error (i.e., letting tub fluid level get too low), and/orthe proppant feed rate into the tub is too high. If this occurs, switch immediately to thestandby blender and resume the treatment. If no provision has been made for a standby, thetreatment may have to be terminated. With a single blender, opening multiple fluid tanks mayincrease the feed rate to the blender. If problems are encountered early in the treatment in


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11-48 December 1995

sucking fluid fast enough from the tanks at the desired injection rate, and a standby blender isavailable; then both blenders may have to be employed to keep up with the rate. This, though,takes careful planning.

• Inadequatefluid transfer from tanks to blender - This can be caused by the inability of thecentrifugal pump on the suction side of the blender to draw fluid from the tanks, especiallythose a significant distance from the blender; partially closed valves; and/or plugged or kinkedsuction hoses. Adequate suction lines of proper sizing must be installed to achieve the desiredrate. On extremely large treatments, transfer blenders may be required to transfer fluid fromremote tanks to the primary blender.

• Proppant delivery systemfailure - This is usually the weak link on any treatment. On smallertreatments, there is seldom any way to provide backup for the proppant delivery system. If thisfails, the treatment should be flushed. On larger treatments, however, dual-belt proppantconveyor systems are available, which allow the treatment to be continued if one belt bogsdown or the hydraulics on one side fail. It is important that the proppant delivery system usedbe capable of delivering the desired pounds per minute with adequate safety margin.

• Pump failures - This is one of the more common occurrences and should be dealt with byhaving adequate standby. The amount of standby is usually determined by the nature of thetreatment. Long, high-pressure treatments, where an abrasive proppant such as bauxite ispumped, should have a minimum of 100% standby. On other treatments, 50% standby isusually sufficient.

• Inaccurate metering - Flowmeters, densimeters, and pressure transducers can sometimes fail.It is advisable to have at least two of each type meter/gauge in the main injection line. Allshould be properly calibrated prior to the treatment, and early in the treatment, they should bechecked against other gauging methods, e.g., the flowmeter checked against tank dips and thedensimeter checked against sand screw RPM's. Prior to and immediately following thetreatment, the fluid, chemicals, and proppant should be inventoried to determine what waspumped and how this compares with the treatment metering.

• Loss of power or electronics to treatment van - This can present a very dangeroussituation if not dealt with properly. A proper contingency plan is required to avoid this. Thiswould include good communication with the operators and material gaugers - the volume andrate obtained from the tank gaugers, the sand concentration determined from the blender sandscrew RPM's, and the pressure monitored on the pump trucks.

Fluctuations in treating pressurecan often signal quality control problems. Pressure changes canbe caused by mechanical problems, a change in gel properties, varying proppant concentration, andformation responses.

• Abnormal pressuresfrom wellbore conditions - The more common pressure problemscaused by wellbore conditions are excessive pipe or perforation friction, and downholeequipment failures or leaks. An ISIP early in the treatment or during pre-frac testing can detect


TREATMENT EXECUTION

11-49December 1995

whether or not pipe and/or perforation friction is a problem. Without bottomhole pressure data,though, it can be difficult to tell the difference between perforation friction and excessivepipe friction due to improperly mixed frac fluids. One common reason for excessive pipefriction on crosslinked gel treatments is that the fluid is crosslinking too quick or thecrosslinker addition is incorrect. Also, different tanks of base gel may result in slightlydifferent crosslinked gel frictions. This should be checked as a first line of action. If the fluidmixing is not a problem and the treating pressure is excessively high, the treatment should beaborted. Re-design of the treatment at a lower rate may be required or the well re-perforated oran acid ball-out performed. Proper pre-frac testing with BHP, including a gel minifrac, canusually detect these types of problems so they can be remedied prior to performing thetreatment.

When the treatment is pumped down tubing, below a packer, positive annulus pressure shouldalways be held to immediately detect any communication through a tubing leak or packerfailure. If this occurs, the treatment should be terminated.

• Abnormal pressuresfrom formation response- The two most common abnormal pressureresponses caused by the formation are usually a result of fracturing out of zone or pressuringout (screening-out). If the fracture grows out of zone into a lower stressed interval, a suddendrop in pressure may be apparent. This, however, is often hard to detect at the surface due tochanging friction and hydrostatic pressures. Pressure increases preceding a screenout mayserve as an early warning signal to flush the treatment. Often, though, this is also masked bythe changing friction and hydrostatic pressures and it is not until a complete screenout occursthat it is apparent at the surface.

The service companies have developed means of calculating BHTP from surface pressure andfriction correlations to use in detecting downhole pressure changes. Due to the oftentimesinaccuracy of these correlations, though, thecalculated BHTP can be misleading and hasresulted in premature flushing of treatments when, in fact, the rising pressures were nothingmore than poor gel quality and increased friction pressure. As a rule-of-thumb, calculatedBHTP's can not be relied on and should not be used to make real-time decisions during afracturing treatment. The only time when they may provide valuable information is whenpumping down large tubing or casing where friction is not a factor and the proppant stages arelarge enough that the pipe contains all one slurry.

Flushing the Treatment

Special attention should be given the flush procedure to avoidover-flushing the proppant awayfrom the wellbore. Flush should be initiated from anear-wellheaddensimeter, to avoid major dis-crepancies in the treatmentline volume. Using this method, the flush volume can be calculated byadding (1) thewellbore volume to the top perforation to (2) the volume from thenear-WH den-simeter to the wellhead, and subtracting (3) the desiredunder-displacement. Flowmeters areusually only accurate to within 5% and this should be used as a “rule-of-thumb” in determining theunder-displacement, unless the flush volume is relatively small to begin with. All treatments


11

11-50 December 1995

should always beunder-flushedby at least2 bbls unless the 5% rule dictates more. When calcu-lating the flush volume, several people should go through this exercise to insure there are no mis-takes.

The flush counter should be immediately zeroed at the time the proppant concentration from thewellhead densimeter starts to fall off from the maximum slurry concentration. This will generallyresult in leaving the maximum proppant concentration in the fracture at the wellbore. Performingthe flush this way, though, will also result in a“tail-off” of proppant left in the wellbore abovethe point of flushing, this tail-off being that in the lines and blender tub behind the wellhead den-simeter. If adequate rat-hole is not available to accommodate this, the wellbore may have to becleaned out.

Another method to prevent some of the proppant tail-off is toby-passthe blender tub. While thisprevents the blender contents from being pumped into the well, there are certain problems that canoccur in switching to the by-pass, the most common of these being a loss of prime on the pumps.While this method is attractive, it is not recommended.

It is not advisable to flushFoam fracturing treatments with foam. To accurately determine afoam flush volume, the bottomhole conditions (temperature and pressure) must be accuratelyknown and this is seldom the case. After a foam fracturing treatment, the reservoir should becharged up enough to unload a column of water, provided the flowback is initiated in a timely fash-ion.

When to Flowback

Following a non-foam type fracturing treatment, the well shouldremain shut-in long enoughforthe fracture to closeand the tail-end gel to fully break. If closure time is expected to be short,this can be monitored from surface pressure in the frac control van. In tighter reservoirs, the shut-in time may be as much as 24 hours. Samples caught during the treatment, should be placed in aheat-bath immediately after the treatment to monitor the break time. Depending on the size of treat-ment, it will take some time for the reservoir in the proximity of the fracture to recover to originalBHT. This needs to be taken into consideration to allow some safety margin prior to initiatingflowback.

Where a foam fracturing treatment has been performed, the primary objective is usually to flowthe well back in a relatively short time frame to aid in cleanup from under-pressured reservoirs.Typically, this is done within 1-2 hours following the treatment and, in most cases, this is sufficienttime for the foam to degrade, i.e., foam half-life generally less than 1 hour. Initiating flowbackimmediately after a non-foam type treatment, i.e.,“forced closure”, is not recommended. Duringflowback, the fracture will try to close in the near-wellbore region and, if the proppant is still sus-pended in viscous fluid, much of the proppant in this region of the fracture may be pulled back intothe wellbore. If this happens, as suspected, the result could be poorer near-wellbore fracture com-munication. Only in cases where the closure time is very long and proppant may tend to settlebeneath the primary pay zone, should forced closure even be considered.


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11-51December 1995

11.7 POST-FRAC LOGGING

Post-frac logs are often run to help in evaluating whether or not model-predicted fracture geometrywas obtained. These independent measurements, when coupled with pressure analysis and post-frac modeling, can help to verify and/or modify the calculation procedure for future treatments inan area. The two most common post-frac logging tools are the temperature and gamma-ray logs.While both are shallow investigative tools and can have interpretation problems, they can providevaluable information when run correctly in a proper environment.

Temperature Logs

Post-frac temperature logs are the most common method of measuring fracture height due to theiroperational ease of use. They are easy to run, can be run in cased- or open-hole, and have minimalimpact on operations since the well is typically shut-in for several hours after a stimulation.

Procedure. The most reliable procedure for running post-frac temperature logs is to first run a base(pre-fracture) log to determine the undisturbed temperature gradient of the formations, then two tothree additional logs following the fracture treatment as shown in Fig. 11.18. The best results areobtained by logging down, so the temperature sensor is always entering undisturbed fluid, at aspeed of 20-30 fpm. The best time to obtain the base log is prior to any other completion phase,e.g., perforating, running tubing, etc. This, however, might not always be possible or cost-effectiveand the next best method is to run the base log the day before the fracture treatment. The post-fraclogs should be run shortly (1-3 hours) after the treatment and multiple passes made with a mini-mum of 3/4 to 1 hour between logging starts. No flowback from the well should be allowed priorto logging, but if this is necessary, it is usually possible to obtain a good log by allowing a coupleof hours for the temperature to re-stabilize following the flow back. In the case of an under-pres-sured reservoir where the fluid level might continue to fall after the treatment, the fluid level shouldbe allowed to nearly stabilize prior to running the post-frac logs.

When To Log. Post-frac temperature logs are typically run when there is a question about thedegree of fracture height containment that occurred as compared to model predictions. Fractureheight determination is generally more applicable when stimulatinglow permeability zones,where the objective is to achieve long fracture half-lengths. In particular, innewareaswith wellshaving virgin reservoir pressure where little is known of the boundary stresses, it is usually appro-priate to conduct a minifrac and run post-minifrac logs to “calibrate” the model stress profile forfinal design determination. Temperature logs may then also be run after the main treatment to con-firm or verify model predictions. Inmoderateto high permeability zonesusually the main objec-tive is to by-pass near-wellbore damage and fracture height is not as critical. For these type zones,though, temperature logs might still be appropriate following a minifrac if theobjective is to stayout of alternative pay zonesor water-bearing intervals in close proximity to the target zone.Also, when fracturingthick intervals of moderate to high permeability, wheremultiple layersexistwith varying permeabilitiesand stresses, temperature logs might be appropriate followinga minifrac and/or treatment to evaluate how much of the interval was treated.


11

11-52 December 1995

Limitations . Ideal logs, such as shown in Fig. 11.18, are rare and may be in error when they dooccur. To help in evaluating when temperature logs should be run and how best to interpret them,it is important to understand their limitations. The two primary factors affecting temperature loginterpretation are thecreatedfracture width and wellbore conditions. Low-stressand/or low-moduluszonescan have significantly greater fracture width and will accept the majority of fluid.This results in more cooling across this region(s) and the largest temperature anomaly. This isbotha strength and weakness: a strength because the log is indicating where the bulk of fluid went anda weakness because the larger anomaly can mask height growth into higher stress/modulus zones,leading to misinterpretation of fracture height and geometry.

Wellbore conditions can also affect temperature log interpretation, these includingplacementofthe downholeassemblyand wellbore deviation. Pumping down tubing will create a temperatureanomaly immediately below the tubing because of the difference in radial heat flow rates for a tub-ing/casing configuration compared with fluid flow just inside the casing.

• When post-frac temperature logging is planned, the tubing/packer/tail-pipe assembly should bepositioned far enough above the highest point of expected fracture growth to preventinterpretation problems.

Wellbore deviation can also significantly impact temperature log interpretation. Generally, wherethe wellbore is vertical and the fracture grows vertically, there is complete communication of thefracture along the wellbore. However, when the fracture grows vertically from a deviated wellboreor a non-vertical fracture grows from a vertical wellbore, the fracture will (in most cases) leave thewellbore. And, because the temperature tool is a very shallow investigative tool, it will not identify

Fig. 11.18 - Base and Post-Fracture Temperature Logs: Runs #1 - 8 hrs after Injection and Run #2 -18 hrs after Injection.


POST-FRAC LOGGING

11-53December 1995

that portion of the fracture not in direct contact with the wellbore. Thus, in situations such as this,temperature logs have limited application.

• Temperature logs have very little to no application in deviated well fracturing, unless they areused to determine whether vertical or horizontal fracturing is occurring. Even for thisapplication, their interpretation may be questionable.

Interpretation . While temperature logs, when used as a stand-alone tool, can be difficult to inter-pret, they can yield valuable information when interpreted correctly. Several analysis techniqueshave been developed to aid in this. One of these is acold-water circulating test to assist in anal-ysis. This involves circulating down tubing and up the annulus to cool the wellbore without creat-ing a fracture. Post-circulation logs then indicate perturbations caused by thermal conductivitychanges and wellbore effects, such as washouts. Post-frac logs can then be compared to this pre-frac log to identify fluid movement outside the pipe and thus the presence of fracture heightgrowth. An example of this is shown in Fig. 11.19. For the particular case of a“warm nose”aboveperforations, further evidence of the correctness of this interpretation was given by comparingpost-frac temperature and gamma-ray logs, as shown in Fig. 11.20.

Fig. 11.19 - Example of Post-Cold-Water-Circulation Test Log with Post-Fracture Log.


11

11-54 December 1995

Running ofmultiple post-frac logsalso improves the temperature log interpretation. Fig. 11.21shows an example where the temperature profile changed with later logs, giving a much easierinterpretation.

Downward fracture growth is difficult to determine with a temperature log. Typically, at the con-clusion of a fracture treatment, the wellbore fluid below the perforated interval is very near staticreservoir temperature. Thus, the temperature log will show a sharp break at this point and this isoften misconstrued as the fracture bottom when, in fact, this is only indicating stagnant fluid in therathole. If the fracture has grown downward, the fluid outside the wellbore will be cooler than thatinside the rathole and post-fracture cooling below the perforated interval may be observed, result-ing in a“temperature cross-over”as shown in Fig. 11.22. This is a clear indication of downwardfracture growth and the point of cross-over is interpreted as the fracture bottom.

Gamma-Ray Logs

Gamma-ray logs are another common method of measuring fracture height. These are conductedby inducing artificial radioactivity in the fracture by including tagged proppant or tagged liquid inthe normal fracturing proppant or fluid, followed by post-treatment gamma-ray logs. Oneadvan-tage of gamma-ray logsover temperature logs is that they need not be run immediately afterstimulation, allowing wellbore fill below perforations to be cleaned out before logging. Theotherrestrictions on temperature logs,however,apply equally to radioactive logs, i.e., they are shal-

Fig. 11.20 - Comparison of Post-Fracture Temperature Log and Post-Fracture Gamma-Ray Log.


POST-FRAC LOGGING

11-55December 1995

low investigative tools (shallower even than temperature logs) and the response is proportional tofracture width. Thus, while the two logs are often used in combination, the potential exists for themto confirm one another and still not yield totally reliable results.

Procedure. Radioactive materials are added to the fracturing slurry stream with proper injectionand metering equipment supplied by the radioactive tracer company. Both high-pressure and low-pressure equipment is available for adding the radioactive material either upstream or downstreamof the high pressure pumps. As mentioned earlier, tracers can be added either in a solid (proppant)form or a liquid form.Zero-washtracers, patented by ProTechnics, should be used whenever pos-sible. This minimizes the residual radioactive material left in the wellbore and eases the interpre-tation of post-frac gamma-ray logs. Table 11.12 lists theavailable types of tracers, theirrecommendedapplication, the morecommonly usedisotopes, meshsizesfor solid tracers, andcrush resistancelimitations. Typically, for a fracturing treatment, proppant embedded with Sc-46(Scandium), Sb-124 (Antimony), and/or Ir-192 (Iridium) are used as solid tracers. These same iso-topes can also be used in liquid form.Typical tracer concentrations are 0.15-0.8 mCi per1000 gals of fluid or pounds of proppant, depending on the gamma-ray tool size planned for use.For a 1-11/16 in. tool, the recommended concentration is 0.35-0.8 mCi/1000 gals or lbs and for a3-5/8 in. tool, it is 0.15-0.30 mCi/1000 gals or lbs. The types and concentrations of isotopes usedis dependent on the program objectives and the time before post-frac logs will be run, some iso-

Fig. 11.21 - Example of Temperature Profile Changing with Time, Later Log Showing a “Clearer”Interpretation.


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topes having longerhalf-lifes than others, i.e., Au-198 (gold) - 3 days, Sb-124 - 60 days, Ir-192 -74 days, and Sc-46 - 84 days. The tracer service company should be consulted to obtain recom-mendations for a specific application.

A proper gamma-ray logging program for fracture treatment evaluation should always include apre-treatment log to identify naturally occurring isotopes in formation layers and to provide abaselog for comparison to the post-frac log. Comparing these two greatly enhances the interpretationof post-frac logs.Spectral gamma-ray tools are available for use in distinquishing multiple iso-tope tracing.

Application . Some of the more common applications of tracer logs are:

• Minimum fracture height. Radioactive tracers can identify the minimum height of themedium pumped - either hydraulic height (liquid tracers) or propped height (proppant tracers).In many cases, this minimum height may be equal to or very close to the created height; but,

Fig. 11.22 - Example of Temperature Crossover Below Perforations.


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Table 11.12 - General Description and Properties of ProTechnic’s Patented ZERO WASH TracerProducts.

SOLIDS

• PTI-ZW ZERO WASH -- Intermediate strength ceramic bead embeddedwith Sc-46 (2.65 s.g.), Sb-124 (2.60 s.g.), or Ir-192 (2.64 s.g.).Color: Various shades of gray.Mesh Size: 40/70 (will not flow through 20/40 or 12/20 sand pack).16 through 80 mesh available.Crush Strength: >8000 psi

• PTI-ZWLD ZERO WASH LD -- low density ceramic bead that is embeddedwith Sc-46 (1.29 s.g.), Sb-124 (1.48 s.g.), or Ir-192 (1.34 s.g.).Designed for acidizing applications and low matrix injection rates.Color: Dark green to brown.Mesh Size: 40/70 (will not flow through 20/40 or 12/20 sand pack).30 through 100 mesh available.Crush Strength: <2000 psi

• PTI-LZW LIQUID ZERO WASH -- Resin micro embedded with Sc-46(3.17 s.g.) or Sb-124 (4.17 s.g.). Designed to emulate a fluid.Color: Ranges from light brown to white.Mesh Size: 5-50 micronsCrush Strength: N/A

Custom irradiated High Volume Zero Wash products are available by special order.

LIQUIDS

Most tracers can be made both oil and water soluble. Specific chemical additives can be usedto balance the pH of the fluid to enhance adsorption on the formation or to reduce “plating out”on tubulars.

TRACER CONCENTRATION GUIDELINES

MINI-TOOL (1-11/16”)

Water Based Fluids: 0.35 - 0.80 mCi/1000 gals or lbsAcids: 0.50 - 1.50 mCi/1000 gals or lbs

LARGE TOOL (3-5/8”)

Water Based Fluids: 0.15 - 0.30 mCi/1000 gals or lbsAcids: 0.40 - 1.25 mCi/1000 gals or lbs


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11-58 December 1995

in other cases, due to width restrictions in higher stress layers, this height may be considerablyless than the actual created height.

• Proppant distribution at the wellbore. By placing multiple tracers staggered throughout afracturing treatment, it may be possible to determine whether proppant in an interval wasplaced early or late in the treatment, i.e., are all perforation sets effectively propped at thewellbore. Fig. 11.23 shows an example of this type application. In this treatment, Sb-124(medium shading) was used in the first 18,000 lbs (1-3 ppg), Sc-46 (white) in the middle30,000 lbs (4-6 ppg), and Ir-192 (dark shading) in the last 48,000 lbs (6 ppg). From this log,the lower perforated interval took only the lower concentration slurry, while the higherconcentration slurry went primarily in the upper sets of perforations.

• Proppant settling. The effects of proppant settling to the lower part of the perforatedinterval or out of the desired zone can be seen with radioactive logs.

• Stagingefficiency. In many cases, the need to separate a fracture treatment into multiple stagesis apparent from tracer analysis. There may be a larger stress or pore pressure contrast betweenlayers than assumed causing inefficient stimulation in a single stage treatment. Conversely,multiple stage treatments may be determined to be unnecessary with tracer analysis. Fig. 11.24shows an example where very little proppant was placed in the upper three sets of perforationswith the initial treatment and post-frac performance was disappointing. A second treatment(refrac) was performed after isolating the bottom perforations with a bridge plug. As shownfrom the second log, after the refrac which was tagged with a different isotope than used on thefirst treatment, the upper sets of perforations were stimulated. Post-frac performancedoubled.

When Applicable to Run. Table 11.13 lists some of the more common circumstances underwhich tracer logs might have an application in helping to define fracture treatment effectiveness.


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11-59December 1995

Fig. 11.23 - Example Gamma-Ray Log Where Three Isotopes Were Used to Tag Proppant - Sb-124(1-3 ppg), Sc-46 (4-6 ppg), and Ir-192 (6 ppg). Note Bottom Zone - Lower Concentrations Only, with

High Concentration in Top Zone Only.


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Fig. 11.24 - Example Gamma-Ray Logs Where (1) the Initial Fracture Treatment Only Propped theBottom Zone and (2) Successful Propping of the Upper Zones with a Second Treatment.


POST-FRAC LOGGING

11-61December 1995

Table 11.13 - Some Criteria for Tracer Addition and Gamma-Ray Logging.

• If, Due to Size of Gross Interval, Total Zone Coverage is in Doubt.

• If Stress Contrast Between Zone and Barrier is < an Amount That Might Allow Growth Outof Zone.

• If Limited Entry Perforating is Used.

• If These are Multiple Perforation Sets.

• If the Perforated Intervals is Within the Vicinity of an Undesirable (Gas/Oil/Water), FluidContrast in the Reservoir.

• If the Permeability Varies by a Factor of Some Significant Percentage or More Per Stage.

• If Specialty Proppants are “Tailed In.”

• If the Well has Questionable Cement Quality or Casing Integrity.

• If You Are Using Diversion in Completion.

• If Stress Contrast is > Some Significant Pressure Psi Between Perforated Layers.


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School Problems

FRAC School Problem No. 1

Use the Quick Worksheet to complete the following table.

CostM$

SlurryVol

(mhsld)Net

PressureAverage

WidthFluid

Efficiency FCD FOI

xf = 250

xf = 500 *

xf = 750

H = 50'

H = 100' *

H = 150'

C = .005

C = .0015 *

C = .0025

Q = 20

Q = 35 *

Q = 40

E = 4

E = 8 *

E = 12

P-1 Hydraulic Fracturing Theory ManualApril 1994

School Problems

ationrval ismadember of

use the

alysiscludeill beildingized,the

sand.ave ahowse toterval

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ate ofssurestable

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Evaluation of a recompletion to a moderate permeability gas sand.

Abstract

The Workshop No 2. was drilled as an infill producing well to a deeper horizon. Repeat FormTest (RFT) pressure data and dipmeter log, however, indicate the planned completion intein a fault block already being depleted by at least two offset wells. As a result, plans are beingto complete a porous and permeable gas sand at 5300 ft. This sand has been seen in a nuwells in the area and appears to be fairly continuous over at least an entire section. Becasand is in a known regulatory horizon, it will be completed as a development well.

Purpose

This problem illustrates the benefits associated with the application of fracture pressure antechniques to the design and optimization of fracture stimulations. The techniques utilized inthe analysis of closure stress, step rate, flowback, and minifrac tests. Analysis of this data wused to develop an understanding of the fracture characteristics. This will be done through buan ULTRAFRAC data file and history matching minifrac data. Once the fracture is characterULTRAFRAC will be run in DESIGN Mode to determine the optimum treatment design fornew horizon in the well in question.

Description

A calculated log section over the potential completion shown in Fig. P.1 highlights the payIn addition, a Long-Spaced-Digital-Sonic (LSDS) log over the section showed the sand to hcompressional wave sonic travel time of approximately 65 micro-seconds per foot. Fig. P.2 sa plot of acoustic travel time vs. Young’s Modulus, E, for various rock types. Use this figurformulate initial estimates. The maximum bottomhole temperature recorded over the sand inwas 170 F.

Reservoir pressure in the sand is unknown, though, the deeper target sands have been founormally pressured (e.g., 0.433 psi/ft of depth). The interval in question was drilled with 9.5 lmud with no significant gas shows. Assuming a normal pressure gradient indicates a reservopressure of 2295 psi at 5300 ft. The well was completed in 5.5 inch casing with 2 7/8 inch tulanded at 5130 ft. The well was perforated with 2 shots/ft and produced for 24 hours at a r520 mscfd. The production stream was dry gas. A build up test was run but bottomhole pregauge failure precluded the build up interpretation. Surface pressure data indicated fairlywellhead pressure of 1200 psi.

Some core data exists from a nearby exploration well which indicated the interval in questioa clean sandstone with a porosity between 11.2 and 14.7%. Core permeability tests showedability to air (no confining stress) of 0.44 to 0.55 md. Generally, core permeability is reducedfactor of approximately 5 to represent in-situ gas permeability.

°

P-2Hydraulic Fracturing Theory Manual April 1994


Fig. P.1 - Log Section.


School Problems

0 psiUnitper-

ted toas mea-er withn esti-

d 170

bpmhows

ervoir

Production plans include compression which will allow a surface producing pressure of 10with a flowing bottomhole pressure of approximately 450 psi. The Gas Marketing Businessindicates that it will cost nearly 0.15 $/mcf to transport the gas to the delivery point. Annual oating costs are $6,000 per well in the area.

Because of the limited rock property data a series of injection flowback tests were conducdetermine formation closure pressure. During these tests, bottomhole treatment pressure wsured with a gauge set at 5375 ft. The closure stress tests were conducted with 2% KCl watfriction reducer. This data is used to find the fracture closure stress, and possibly to give amate of reservoir pressure.

Reservoir fluid data assuming a gas gravity of 0.65, a reservoir pressure of 2295 psi, andegrees is calculated in the fluid property section of ULTRAFRAC to be:

• Gas Viscosity: 0.0174 cp

• Z-Factor: 0.85696

• Gas Compressibility: 455.6 x 10-6 psi-1

The closure stress tests consisted of:

A. Pumpin/Shutin Test

An injection/shutin pressure decline test conducted by injecting 25 bbl of KCl water at 10(tp = 2.5 minutes) and then recording the pressure decline as shown in Fig. P.3. Fig. P.4 sa plot of pressure vs. horner log time extrapolated to give a rough approximation of respressure.

Fig. P.2 - Young’s Modulus (E) vs. Acoustic Travel Time.

Aco

ustic

Tra

vel T

ime

mic

rose

cond

s/ft

Sand

DolomiteLime

E x 106 - psi



Fig. P.3 - Pressure Decline Analysis.

Fig. P.4 - Pseudo-Pressure Estimation.

Injection/Decline Test4250.000

4000.000

3750.000

3500.000

3250.000

3000.000

2750.000

Closure Pressure =

0.0000 0.5000 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.00

SQRT [dt] (min**0.5)

Pw

s ps

ia

psi

Start of Pseudo-Radial Flow Effects

P* = Reservoir Pressure = 2280 psi

1.00 10.00

4250.000

4000.000

3750.000

3500.000

3250.000

3000.000

2750.000

Log [(tp + dt)/dt]

Pw

s ps

ia

Plot Horner Plot as QC for Shut-OIn Decline Analysis

File: PROBLEM.FRACompany:Well:Field:

Test Date:Test Type:Perforations, Top:

Bottom:

Extrap. p# 2271.921


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line., andinute

back

flu-andcal-eown

B. Step Rate Inject Test

A step rate injection test was then performed immediately following the pressure decthe step rate test consisted of pumping KCl water at rates of 0.5, 1, 2, 3,4, 5, 7, 10, 1215 bpm for two minutes at each rate. The rates and pressures at the end of each two mstep are shown in Fig. P.5.

C. Pumpin/Flowback Test

At the end of the step rate test the rate was increased to 17 bpm, the well was then flowedat a rate of 2 bpm. The resulting pressure decline is shown in Fig. P.6.

D. Minifrac Test

A gel minifrac was pumped by injecting 38,000 gallons of 40 lb/1000 gals crosslinked fracid down tubing at an average rate of 35 bpm (injection time approximately 25.5 minutes),then flushing the well with 2% KCl water. Analysis of the pumping decline data is used toculate the fluid loss coefficient. The minifrac data both injection and pressure decline arshown in Fig. P.7. A plot of net pressure versus time for the minifrac injection period is shin Fig. P.8.

Fig. P.5 - Step-Rate Injection Test.

Extension Pressure = psi

4500

4000

3500

3000

2500

20000 5 10 15 20

Inj Rate (bpm)

Bot

tom

hole

Pre

ss (

psig

)



Fig. P.6 - Pumpin Flowback Test.

Fig. P.7 - Minifrac Pressure Data.

File: PROBLEM.FRACompany:Well:Field:

Test Date:Test Type:Perforations, Top:

Bottom:

Clos Time Tc.: 6.874Clos press Pc.: 3434.801

4200.000

4000.000

3800.000

3600.000

3400.000

3200.000

3000.00030.000 32.000 34.000 36.000 38.000 40.000 42.000 44.000 46.000 48.000 50.000

Clock Time (minutes)

Pre

ssur

e ps

ia


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Fig. P.8 - Nolte-Smith Net Pressure Plot.




Procedure:

Step 1: Update economic and reservoir data.

Step 2: Develop geomechanical input from porosity and sonic log data.

Step 3: Evaluate injection/decline, step rate test, and pumpin flowback test data for closurepressure.

Step 4: Input closure pressure data into geomechanical panel.

Step 5: Evaluate minifrac test for fluid efficiency and leakoff coefficient.

Step 6: Enter leakoff into ULTRAFRAC.

Step 7: Enter Framode in Analysis and enter minifrac volume of 38,000 gallons.

Step 8: Save file.

Step 9: Enter Quick Worksheet and history match net pressure, P*, and efficiency by alter-ing fluid loss coefficient and Young’s Modulus.

Step 10: Once history match obtained with Quick Worksheet, execute fracture model andmatch net pressure data.

Step 11: Once matched, change FRACMODE to design and conduct an optimization study.Note both optimum length and conductivity.

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Workshop Problem 3

Understanding the reservoir response to fracturing through the evaluation of a Tight Gas Well.

Abstract

The Nowayds No. 1 was drilled as a 640 acre location in the East Texas Cotton Valley Field. Con-ventional fracture stimulations in the Cotton Valley have consisted of 415,000 gallons of 40 lbcrosslinked frac fluid and 1 MMlb of 20/40 sand. A service company representative showed up oneMonday morning recommending a significantly larger fracture treatment using carbo prop plus.

This problem illustrates the importance of understanding the reservoir response to hydraulic frac-turing (i.e., the importance of FCD). The problem also highlights the benefits of optimizing fracturetreatments in the East Texas Cotton Valley.

Description

The Cotton Valley Sand Formation is upper Jurassic in age and is bounded by the Bossier Shalebelow and the Travis Peak Formation above. The formation is approximately 1,400 ft thick and istypically found at depths ranging from 8,000 to 10,800 ft and covers nearly all of Panola, Rusk,and Harrison Counties in East Texas. The Cotton Valley is basically a transgressive-regressivemarine sequence. The Taylor Zone, the lowermost sand member in the Cotton Valley is an offshorebar-shoreface transition and consists of a series of small bars and shales. The Taylor Sand is nearly250 ft in gross thickness in the Nowayds No. 1. Above the Taylor interval lies 200 ft of shale whichgenerally confines a 2,500 ft fracture.

The Taylor sand, in the Cotton Valley trend, has an average permeability of approximately0.005 md. Buildup tests in the vicinity of the Nowayds No. 1 indicated an average reservoir pres-sure of 4,300 psi. Production from the Taylor is a dry gas at about 265°F. Table P.1 summarizestreatment and design data important to this analysis, while Table P.2 shows a conventional pumpschedule used in this area. Average porosity and water saturation for the Taylor Sand is 6% and55%, respectively. Fig. P.1 shows a log section of the Nowayds No. 1. Fig. P.2 shows plots of netpressure during a fracture treatment performed in offset wells using the conventional treatmentdesign. Fig. P.3 shows a dimensionless closure time to injection time plot to be used in this analysisto determine fluid efficiency.

Objective

Your job is to compare the conventional Cotton Valley treatment design (Table P.1.) to the servicecompany recommendation shown in Table P.3. Develop an ULTRAFRAC data set and evaluatethe two designs in the ANALYSIS Mode. Compare and contrast the economic results of the twotreatments. How do these results compare to your optimum design (DESIGN Mode).

Workshop Problem 3


Procedure:

Step 1: Using the default file in the ULTRAFRAC database, Table P.1 and Figure P.1,update the geomechanical data, calculate leakoff, set fracmode to analysis and inputconventional schedule.

Step 2: Save file.

Step 3: Execute Fracture Simulation.

Step 4: Look at fracture output and determine fluid efficiency.

Step 5: Compare efficiency to that determined from analysis of Figure P.3 and Table P.1.

Step 6: Modify leakoff and rerun trying to match efficiency, repeat until matched.

Step 7: Save file.

Step 8: Print/Save Fracture output and economic summary output.

Step 9: Modify schedule (Table P.3) and save as.

Step 10: Execute fracture simulation.

Step 11: Compare results.

Step 12: Set Fracmode to design.

Step 13: Run and determine optimum (optional) fracture length and conductivity.

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Table P.1 - Data for Example Well Analysis

Treatment Volume (MGALS) 360

Treatment Rate (bpm) 75

Treatment Time (min.) 178

Closure Time (min.) 356

Fluid Type Crosslink

Reservoir Depth (ft) 10000

Temperature (°F) 265

Permeability, (md) .005

Fracture Height (ft) 300

Fluid-Loss Height (ft) 280

Formation Modulus (106 psi) 8

Proppant Concentration (lbs/gal) 9

P-12Hydraulic Fracturing Theory Manual

Table P.2 - Conventional/Schedule

Stage VolumeSand

lbs/gal

Pad 72,000

1 31,200 1

2 4,875 2

3 12,000 3

4 28,000 4

5 35,000 5

6 40,000 6

7 42,000 7

8 50,000 8

9 45,000 9

April 1994

Workshop Problem 3


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Table P.3 - Pumping Schedule Recommended by Service Company

Job Description Information

Stage NamePump Rate

bbl/min Fluid NameStage Field Vol

gal Prop Conc lb/galProppant Type

and Mesh

Pad4 PPA6 PPA8 PPA

10 PPA12 PPA

12 PPA/RFlush

7575757575757575

YF540HTYF540HTYF540HTYF540HTYF540HTYF540HTYF540HTWF120

900003000034000316002960069400100009482

04681012120

ISP 20/40ISP 20/40ISP 20/40ISP 20/40ISP 20/40ISP 20/40ISP 20/40

Job Totals

Fluids Prop

44500 gal of WF120359000 gal of YF540HT

2390000 lb of 20/40 ISP


Workshop Problem 4

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abilitylargeonateffects

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Workshop Problem 4

Application of fracture optimization to a multilayer reservoir, North Cowden Unit, Ector CounTexas.

Abstract

Fracture treatment optimization techniques have been developed using Long-Spaced-DSonic (LSDS) logs, pumpin-flowback, pumpin-shutin, minifrac, and downhole treating presdata. These analysis techniques have been successfully applied to massive hydraulic fra(MHF) of tight gas wells and short highly conductive fractures in moderate permeability reseralike.

Purpose

This problem illustrates the application of fracture analysis techniques to a moderate permereservoir. These techniques will be used to develop an ULTRAFRAC data set and identifyzonal variations in rock properties and pore pressure which result from the complex carbgeology. The inclusion of geologic factors in fracture treatment design and their resulting eon fracture geometry will be highlighted.

Geologic Setting

The North Cowden Unit produces from the Permian Age Grayburg Formation at an averageof 4,300 ft. The Grayburg, which is bounded by the Queen and San Andres Formations, coof varying percentages of dolomite, anhydrite, and sand as shown in Figure P.11. Gross payness is 450 ft with a net pay thickness of approximately 200 ft. The average porosity is 9%permeability ranges from 0.1 to 50 md with an average of 2 md the average water satura50%. The Grayburg Formation is informally subdivided into nine zones. Zones that are primsand are identified as S-1 through S-3. Figure P.12 shows a CNL/FDC typelog of the Grasequence with an additional S-4 interval, which is present in portions of the field.

The Grayburg Formation exhibits a great diversity of carbonate lithologies ranging from supramudstones to fusulinid wackestones representing subtidal conditions. Interfingered with thesbonates are terrigeneous felspathic quartzarenites. The carbonates and sands have been exdolomitized with all sediments having varying degrees of anhydrite infilling and/or anhydritefilling and cementation. Although there is a lack of any distinct trend, localized areas of relathigh pore volume and flow capacity do exist and generally correspond to sand developmentmost notable the S-2 horizon as shown in the velocity profile, Figure P.13.

Description

The North Cowden Unit was in the early stages of an extensive infield development prodesigned to densify from 80 acre to 40 acre development. One hundred and fifty infield prodwells have been identified for drilling at a capital investment of $250 M per well with an additio


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drill

cersin thewhichcturer and

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fieldsis asphys-

Anal-hows aorizone an

ationsargedmax-

$50,000 per well to complete. The North Cowden Unit budget for 1992 totals $15 MM (i.e.,and complete 50 wells).

The production engineer, while reviewing historical NCU performance, found that NCU produdid not perform as well as their offset competitors. It was also determined that treatmentsUnit consistently exhibited increasing net pressure during stimulations (see Figure P.14)was inconsistent with the presumed radial fracture propagation. An ivnestigation of NCU fratreatment designs showed that, historically, 30,000 gallons of 30# crosslinked gelled wate30,000 lbs of 8/12 mesh sand were pumped down 2-7/8 inch tubing at rates of 15 bpm asin Table P.4. Prefrac production rates average 150 BOPD x 150 BWPD with a 6% produdecline. The economic limit is 5 BOPD.

Additional data available includes a long-spaced-digital-sonic log from a nearby well in thewhich was used to determine Young’s Modulus and Poisson’s Ratio on a foot by foot bashown in Figure P.15. Table P.5 shows the comparison of LSDS derived rock properties toical core measurements.

Further in-situ test data available includes closure test data from the S-2 and D-2 horizons.ysis of these test are included as Figure P.16 and Figure P.17, respectively. Figure P.18 sdimensionless pressure match of post-frac pressure decline data which indicates a D-5 hfluid leakoff coefficient of 0.00025. The sand intervals in the unit should be expected to haveven higher fluid loss coefficient.

Also shown for completeness (Figure P.19 - Figure P.21) are net pressure plots of stimulconducted in the D-2, S-2, and D-5 intervals, respectively. The production engineer was chwith evaluating this treatment schedule to ensure that it was the optimum treatment design toimize the present value of the infield development program.


Workshop Problem 4


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Workshop Problem 4

Table P.4 - Conventional NCU Fracture Stimulation Design

Pump 30,000 gallons of 30 lb/m gal. crosslinked gelled water and 30,000 lb of8/12 mesh sand

10,000 gallons pad

2,000 gallons w/ 1/2 lb/gal 8/12 sand

4,000 gallons w/ 1 lb/gal 8/12 sand+

6,000 gallons w/ 1-1/2 lb/gal 8/12 sand

8,000 gallons w/ 2 lb/gal 8/12 sand

Flush

Table P.5 - Comparison of Young’s Modulus

Zone Core (10 ° psi) LSDS (10 ° psi)

D-1 8.019.02

D-2 8.84 9.00

D-3 6.367.31

9.259.25

S-2 4.774.54

5.005.00

D-4 7.999.75

9.59.5

S-3 9.08 10.0


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Workshop Problem 4


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Workshop Problem No. 5



Fracture design in a moderate permeability reservoir in the North Sea.

Abstract

The NS25 was drilled and completed as a horizontal well. Production from the 5000 ft horizontalsection averages 500 BOPD well below expectations. In addition, the well produced slugs of chalk(formation). Wellbore stability is reasoned to be the cause for the under performance of the lateralsection. Therefore, to minimize both proppant or formation flowback problems resin coated prop-pants are used in fracture stimulations. To aid in the design and execution of the fracture stimula-tion, a minifrac was conducted utilizing 56,000 gallons of a water based crosslinked borate systempumped at 35 BPM which is the maximum achievable rate from the stimulation vessel.

This problem illustrates the benefits of utilizing minifrac data to design treatments at the well site.This will be accomplished by first analyzing the minifrac data and then utilizing design techniquescaptured in an EXCEL spreadsheet program to design and implement a treatment.

Description

The NS25 produces from the TOR Formation as shown in Figure 1. The Tor, as shown, is some75 ft thick in the NS25. Rock properties testing has indicated that the chalk formation has aYoung’s modulus of 500,000 psi and a poisson’s ratio of 0.3. Because of the softness of the chalk,the resistance to the creation of a fracture is great and as a result, fracture toughness is on the orderof 15,000. The reservoir is normally pressured and has a permeability of 10 md and a porosity of30%.

The stimulation vessel from which the fracture stimulation was to be performed was fully loadedwith 1 million pounds of resin coated proppant and 329,000 gallons of 30# crosslinked borate frac-turing fluid. In additional to conventional land based materials costs an additional $300,000 boatservice charge is required to stimulate this well.

Objective:

Your job is to utilize the results of the minifrac test to optimally place all of the fluid and proppantloaded on the boat. Secondly, test this design with ULTRAFRAC and determine the fracture lengthand conductivity of the fracture stimulation. Also note the in-situ pounds per square foot of prop-pant in the fracture. Finally, utilize this information to determine the post-frac production rate andpayout of the stimulation.

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Procedure:

Step 1: Interpret the minifrac test and determine fluid efficiency, closure pressure, and clo-sure time.

Step 2: Build an ULTRAFRAC file by first adding the boat service charge to miscellaneouscosts in the economic section.

Step 3: From the log generate a geomechanical data set.

Step 4: Estimate leakoff and check with respect to the minifrac analysis.

Step 5: Simulate minifrac and match final pressure and fluid efficiency

Step 6: In design mode, determine the optimum fracture length and conductivity.

Step 7: In analysis mode, select optimum design schedule and execute fracture simulationto determine length, conductivity, and in-situ pounds per square foot.

Step 8: Use Quick Worksheet or Prats curve to estimate Post-Frac Folds of Increase, FOI.

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2200'.the

n hasly, so

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el runsil pro-ooks,

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icientss ofstmentture

Water Injection Well Problem 6

The El Marginalo Field is a mature waterflood of a sandstone reservoir located at a depth ofInjection rates have declined due to fillup, and from the development of positive skins frominjection of some unfiltered water. This skin is not removable by acid washes, and the decisiobeen made to fracture stimulate all injection wells. For tax purposes, this must be done quickthere is no time to field evaluate various stimulation procedures. Therefore, it is imperatiarrive at an optimum stimulation design quickly since almost a hundred wells are involved.

A candidate well for the first stimulation has been selected. The well was shut in and the prefalloff measured; three closure stress tests were run; then 200 bbl of fracturing fluid were injdown tubing with the surface annulus pressure measured during injection and during the prdecline after injection (Note: Due to possible problems with old casing, all the stimulationsbe pumped down tubing.) The data from these tests, along with some open hole logs are inas attachments.

Also included is the present worth of increased injection. This was developed based on modfor various fracture lengths and conductivities. The chart is the present worth of increased oduction only, and does not include the fracturing costs. Based on service company price bstimulation costs should be about $1.00/gal for fluid, $0.08/lb for sand, and $2500.00 for milworkover rig time, etc.

Your assignment - should you decide to accept it - is to design a stimulation program, in suffdetail to allow field execution. Since there will be no time to evaluate long-term effectivenedifferent procedures, the job should be designed to maximize the discounted return on inve(DROI). Also, fracture length should not interfere with reservoir sweep, since hydraulic fracazimuth is totally unknown in this field.

Pressure Falloff Test

Reservoir Properties -

= 0.15 , Residual Oil Saturation = 0.20

= 1 (cp) , C = 9 x 10-6 (1/psi)

BHST = 100°F

Test Parameters -

rw = 0.40 (ft) , Injection Rate = 280 BWPD

Injection Pressure = 1340 psi

Average Reservoir Pressure = 700 psi:

φ

µ




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OPEN HOLE LOGS FOR WATER INJECTION WELL EXAMPLE




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“Mini-Frac” Pressure Data

Data measured on static, open annulus while injecting down tubing.Pump time was 25 minutes, pumping 200 bbl at an average rate of8 bpm (rate was reasonably constant).

Time Since PumpingStarted (min) Pressure (psi)

0.5 4001.0 4032.0 4183.0 4254.0 4305.0 4356.0 4387.0 4438.0 44910.0 45812.0 46315.0 46817.0 47120.0 47922.0 48024.0 48225.0 483

Shut-in at 25.0 minutes26.0 1 1 43427.0 2 1.41 40628.0 3 1.73 39229.0 4 2.00 38030.0 5 2.24 36931.0 6 2.45 35932.0 7 2.65 35033.0 8 2.83 34134.0 9 3.00 33235.0 10 3.16 32437.0 12 3.46 30739.0 14 3.74 29041.0 16 4.00 27443.0 18 4.24 258




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CLOSURE STRESS TESTS FOR WATER INJECTION WELL EXAMPLE

280

250

250

Tight Gas Problem 7

-

Tight Gas Problem 7

320 acre wells; 4-1/2 casing; frac orientation N 80 EReservoir: Estimate 5-10 d; P = 3000 psi; = 0.10, Sw = 0.50

T = 260°F

Other Information1. Open hole log (attached)2. Calibration Treatment Decline (attached)3. Offset BHTP (attached)4. Well Cost $275M5. Frac Costs: $0.75/gal; Sand: $0.06/lb; IDP: $0.60/lb

PW(15) Production Only Triaxial Lab TestXf kfw PW($MM) Stress(psi) Strain(10-6in/in)

1000 100 0.40 500 1252000 100 0.63 1000 2553000 100 0.79 1500 3854000 100 0.91 2000 520

2500 6301000 300 0.45 3000 8102000 300 0.75 3500 9803000 300 0.99 4000 11704000 300 1.10

1000 1000 0.462000 1000 0.803000 1000 1.094000 1000 1.25

(From 2DMHF and GEM)

Prepare: Optimum Fracture Design with sufficient detail that an Experienced Field Foreman could execute the treatment with the results you expected.

µ φ


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Tight Gas Problem 7

TIG

HT

GA

S W

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BOTTOM-HOLE TREATING PRESSURES FOR WELLS OFFSETTINGTIGHT GAS WELL

Oil Well Problem 8

in thewas35%b testsment.

ctionDes-

endationtionalbeentreat-

n in4 and

/sq ft

al forping

Oil Well Problem 8

Desperate Energy Co. is evaluating the drilling of a 160 acre spacing development wellHopeful Field to a total depth of 2610 meters (M). The target chalk formation of an offset wellfound from 2500 M to 2565 M as shown on Attachment 1, and had an indicated porosity ofand an average oil saturation of 60%. Core obtained from the same well was subjected to lawhich revealed the chalk to be water sensitive, very soft, and conducive to proppant embedA pressure buildup test from the offset is shown in Attachments 2 and 3.

The cost of drilling and setting casing on this well is estimated to be $5 MM. Based on produfrom other ells in the field, the unstimulated, damaged PW(15) is estimated to be $2.5 MM.perate Energy management wants you, the engineer, to evaluate data and make a recommwhether the well should be drilled and what the optimum fracture design would be. Convenfracture treatment designs, provided by the service company for other wells in this field, haveunsuccessful in obtaining economic production rates. Unfortunately, the records for thesements are not available. The wellbore configuration normally used in this field is showAttachment 1. Data from pre-frac tests performed on the offset are included in Attachments6.

Other Pertinent Information

1. The zones above and below the pay interval are also chalk.

2. Due to proppant embedment in the soft chalk, an in-situ proppant concentration of 2 lbsmust be achieved.

3. If a fracture treatment is performed, the cost for doing the treatment will be $3.50/slurry ggel “Ottawa” sand or $.25/slurry gal for gel + intermediate proppant. Equipment and pumcharges are figures in as part of the material costs.

Pressure Build-Up Data from Offset Well


C = 9 x 10-6 (1/psi) , = 2.0 (cp) = 0.35 , B = 1.1 (bbl/bbl)

Net Pay = 200 (ft)

Parameters -

rw = 0.40 (ft)Test Data -Flow Time - 6 (hrs) , Rate = 582 BOPDFinal Flowing Pressure (BHFP) = 2334 (psia)

µφ


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, the

Results from Minifrac Treatment

Injected 20,000 gals of 90 cp gel at an average injection rate of 7.94 BPM. Following injectionshut-in BHP was monitored for 14 minutes.

SI TIme (min) BHP (psi)

0 7200

1 7194

2 7169

3 7157

4 7146

5 7136

6 7128

7 7121

8 7114

10 7100

12 7087

14 7074


Oil Well Problem 8


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Oil Well Problem 8

Net Treating Pressure During Minifrac

(Time = 0 when gel on performations)

OIL WELL PROBLEMATTACHMENT 5


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Bili near FLow Problem 9

wellwed atativeons?

Fcd,

both

of theb was

the first


An oil field, fully developed on 80 acres is being considered for a re-stimulation program. Onewas fractured and a post-frac build up test run. Plotting the data on a log-log type curve sho1/4 slope, and a plot of build-up vs. fourth root of shut-in time is attached. Based on a qualiexamination of this plot, can any general recommendations be made about future stimulati

Using the plot and the following reservoir properties, find fracture conductivity and length,and steady-state folds of increase (FOI) resulting from this stimulation.


k = 3.3 md , = 0.10 , Ct = 9 x 10-6 (1/psi) = 3.0 cp , h = 200 ft , q = 290 BPD , B = 1.2

Calculations -

kfw = (eqn. 6, p. 11)

xf = (eqns. 13-15, p. 16)(Note: These equations can be solved in several ways, one way is graphically, plottingsides of the equation vs. length, since both sides are functions of xf.)

Fcd =

Steady-State FOI =

Based on extrapolating from 3 months production, it has been determined that the PW(15)increased production resulting from the stimulations is $390,500. The cost of the fracture jo$35,500. Calculate the discounted return on investment for this stimulation.

DROI =

Fracture design calculations were done based on analysis of post-frac pressure data fromwell. These were used to develop a price table for changes in the stimulation design:

φµ


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OI fore cases

Using these prices and steady-state calculations for folds of increase (FOI), calculate the DRthe various stimulation designs. Should a change in design be recommended? Should morbe considered?

(Costs in $1,000.00)

xf = kfw 0.5 * base base case 2 * base

0.5 * base 24 34 48

base case 25 35.5 51.5

2 * base 27 39 59

DROI

xf = kfw 0.5 * base base case 2 * base

0.5 * base

base case

2 * base




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Index
AAccelerated settling 6-13Acid Fracturing 3-22Activator and gellant 6-8Additive(s)
chemical 6-7clay control 6-6diesel fluid loss 6-14fluid loss 5-23particulate fluid loss 6-14

Advantagesfoamed frac fluids 6-41gelled hydrocarbons 6-48methanol gels 6-49polymer emulsion fluid 6-40

Aluminumantimony and boron 6-32crosslinked orthophosphate esters 6-47

Anaerobic bacteria 6-6Analysis of bilinear flow data 3-46Anderson and Stahl 1-4Anionic surfactants 6-6Antimony, boron and aluminum 6-32Apparent productive length 5-36Appropriate viscosity 6-11Aqueous

fluids 1-4foam 6-1

Auxiliary stimulation equipment 9-20Axial

strain 4-2, 4-3stress 4-2

Azimuth 3-8

BBacteria, anaerobic 6-6Base temperature logs 10-8Bedload, transport 6-12BHTP

gauge tailpipe assembly 8-23measuring devices 8-23measuring techniques 8-22

Bilinear flow 3-25, 3-27data analysis 3-35equations 3-28graphs 3-41

Binary foam 6-43, 6-46Bingham plastic fluid 5-29Biocides 6-7Blender 1-8

services 9-20Blocks,water 6-7

Borategels and foams 6-9ores 6-34

Boreholegeometry log 10-5televiewer 10-7

Boron, aluminum and antimony 6-32Bottomhole

pressure 5-15treating pressure 8-14, 8-22

Bounding beds 5-3, 5-4, 5-12, 5-13, 5-15Breakdown pressure 8-4Breaker(s)

crushable 6-20encapsulated 6-7, 6-20enzyme 6-7, 6-20gel 6-20release, crushable and controlled 6-21

CCapacity

finite 3-4infinite 3-4variable finite 3-4

Capillary tubingfield nominal shear rates 6-51nominal shear rates 6-51

Carboxymethylcellulose (CMHEC) 6-30hydroxypropyl guar (CMHPG) 6-30

Cationicpolymeric clay stabilizers 6-6surfactants 6-6

Cement bond log 10-7Ceramic proppants 7-1Chemical stabilizers 1-5Clay

control additives 6-6swelling or migrating 6-6

Cleanup, flow back and 6-18Closure

pressure 5-13stress 5-3, 5-4, 5-11, 5-13

differentials 5-15profile 5-3tests 5-14

Clump 6-13CMHEC (carboxymethyl cellulose) 6-30CMHPG (carboxymethyl hydroxypropyl guar) 6-30CO2 foams 6-9Cochran, Heck and Waters 1-4Coding system

Dowell Schlumberger 6-53

Hydraulic Fracturing Theory ManualI-53

Index

Halliburton’s 6-52Western Company 6-53

Cold water circulation temperature surveys 10-8Compatibility

formation, formation fluids and chemical additives 6-6safety and environmental 6-5

Compression test 4-2, 4-3Computer control console 1-9Concentrates, polymer 6-30Concentration, effective polymer 6-20Conditions

dynamic 4-2quasi static 4-2

Conductivity of proppant 7-19Consistency Index 5-29Constant

formation facepressure 3-29, 3-42, 3-44rate 3-28, 3-41

internal phase 6-40Continuity equation 2-1, 8-17, 8-19, 8-25Continuous

mixed fluid systems 6-8proportioner 1-8

Controlling fracture height 5-2Core

bulging 4-2, 4-4flow tests 6-6tests 10-3

Cost(s)pumping 6-23pumping hp 6-11

Criteria, fluid selection 6-3Critical

concentration 6-9pressure 8-1, 8-20strain energy release rate 4-7stress intensity factor 4-7

Cross reference of similar additives 6-54Crosslinked

aluminum orthophosphate esters 6-47delayed fluids 6-38delayed systems 6-8dual functionality 6-34gels 6-14hydrocarbon 6-2ideal delayed fluid 6-38polymer solutions (gels) 6-1

Crosslinkingagents 1-5fast 6-32fast, water-base gels 6-32

Crushable breakers 6-20

Hydraulic Fracturing Theory Manual I-5

DDelayed crosslinked systems 6-8Density log 10-5Depth 5-40Design package, integrated 6-23Desired fracture half-lengths 1-12Devonian shale 6-11Diesel fluid loss additive 6-14Dimensionless fracture

capacity (FCD) 3-1conductivity (FCD) 1-12

Disadvantagesfoamed frac fluids 6-46gelled hydrocarbons 6-48methanol gels 6-49polymer emulsion fluid 6-40

Discounted return on investment (DROI) 9-3, 9-8Dowell Schlumberger coding system 6-53Downhole

flow, turbulent conditions 6-51television 10-7

Dragcoefficient, particle 6-12reducing 6-9

DROI (discounted return on investment) 9-3Droplet-size 6-41Dynamic

conditions 4-2fluid loss 6-18moduli 4-2modulus 4-5

EEconomics 6-23Effect of

flow restrictions 3-37wellbore storage 3-37

Effectiveparticle shear rate 6-12porosity 5-21wellbore radius (r’w) 3-10

Elastic modulus 10-3Elasticity equation 2-1Emulsifying 6-8Emulsions 6-7Encapsulated

breaker(s) 6-7, 6-20Environmental and safety compatibility 6-5Enzyme breakers 6-7, 6-20Equation

continuity 2-1elasticity 2-1fluid flow 2-1

Equilibrium bank(s) 6-11

4

Index

FFatty-acid soaps 6-47FCD

dimensionless fracture capacity 3-1dimensionless fracture conductivity 1-12

FDROI (fracture discounted return on investment) 9-3Filtrate 5-20FINCPV (fracture incremental present worth or value) 9-3Finite capacity 3-4Flash points 6-5Flow

back and cleanup 6-18behavior index 5-29

Fluid loss 6-14addtives 5-23coefficient 5-20, 10-3foams 6-15oil base gels 6-15rate 8-27test 5-22

Fluid(s)affected by fluid flow loss 6-18aqueous 1-4bingham plastic 5-29classification 6-1crosslinked delayed 6-38degradation 5-39description of fracturing types 6-30dynamic loss 6-18efficiency 5-37, 8-36, 8-44, 8-55flow equation 2-1foamed frac 6-41hydrocarbon-base 6-23ideal delayed crosslinked 6-38low loss 6-14napalm-type 6-47optimal scheduling for 6-70polymer emulsion 6-40power law 5-29pressure calculating 5-15rheological testing of fracturing 6-49scheduling 6-70scheduling given the fluid rheology 6-70scheduling using contained rheology 6-71selection 6-1selection criteria 6-3viscosities, proppant transport 6-11viscosity 5-27volume 5-37

Fluid-elementexposure time 6-70rheology 6-70time at temperature vs. volume pumped 6-72

Fluidized layer of sand 6-12Fluorocarbon, surfactants 6-7

Foam(s) 6-15aqueous 6-1binary 6-43, 6-46CO2 6-9friction pressure data 6-43hydrocarbon 6-2hydrocarbon-base 6-23nitrogen 6-9

viscosity data 6-43texture 6-43

Foamed frac fluidsadvantages 6-41disadvantages 6-46

Foaming potential 6-8FOI (folds of increase) 1-12, 3-5, 3-10Folds of increase (FOI) 1-12, 3-5, 3-10Formation

elastic properties 4-1fluid 5-22linear flow 3-27permeability 3-1wettability of 6-6

Frac Heightvariables affecting 5-15

Fracture 5-36closure pressure 5-11closure stress 8-4determining fluid efficiency 8-58discounted return on investment (FDROI) 9-3early design 1-8extension pressure 8-4flow capacity 3-1, 3-2, 3-3geometry 5-16half-length 3-2, 5-36height 5-1, 5-3, 5-15, 5-16

controlling 5-2growth 5-1, 5-3

incremental present worth or value (FINCPV) 9-3initial height 5-3length 3-1, 5-16linear flow 3-27orientation 1-3, 3-8radius 5-36stiffness 8-26stimulation

critical factors to optimum 1-11design 1-12

toughness 4-7treatment 1-6

design 5-15width 5-15, 5-16

Fracturingeffect of modulus on 4-4fluid(s) 1-4

compatibility with its additives 6-7


Index

components, toxicity 6-5costs 6-23friction pressure 6-9gelled diesel 6-9

pressure analysis 8-1pumping equipment 9-20stimulation treatments 1-1

Frictionpressure 5-40

data for foams 6-43fracturing fluids 6-9various frac fluids 6-10wellhead and horesepower requirements 6-9

reducersoil-base 6-9water-base 6-9

Friction-loss pressures 5-37Friction-outs 6-40Full-cycle 9-18

economics 9-17

GG function 8-35Gamma ray log 5-13, 5-17, 5-18, 10-5Gas-constant

pressure 3-47rate 3-47

GDK (Geertsma and de Klerk model) 2-4, 5-16Gear pump, Jabsco 6-51Geertsma and de Klerk model 2-4, 5-10, 5-16Gel

breakers 6-20crosslinked 6-14crosslinked polymer solutions 6-1determining rheology of 6-51fast-crosslinking water-base 6-32filter cake 6-14high temperature 6-13oil base 6-15organometallic crosslinked 6-13polymer concentrates 6-37quality control of continuous-mix jobs 6-8stabilizers 1-5systems, high temperature behavior 6-13testing organometallic crosslinked 6-14uncrosslinked 6-14viscosities, hydrocarbon 6-8viscosity uncrosslinked 6-8

Gelatin model 1-4Gellant and activator 6-8Gelled

diesel fracturing fluid 6-9hydrocarbons 6-46

advantages 6-48disadvantages 6-48


high-temperature 6-47methanol 6-2, 6-48

Gradients, hydrostatic 6-9Growth, fracture height 5-1Guar gum 6-30Guideline 6-73

pad fluids 6-74viscosity 6-70

HHalf-length 2-4, 5-36Halflife 6-8Halliburton

coding system 6-52Oil Well Cementing Company 1-2

Hardness 4-1HEC (hydroxyethyl cellulose) 6-30Height

confinement 5-13, 5-14growth 5-11, 5-12, 5-13, 5-15, 5-16vertical growth 5-16

hhp prices and fracturing chemical 6-23High temperature

stability 6-13stabilizers 6-13

Hindered settling 6-13History

matching 5-15of hydraulic fracturing 1-1

Horizontal closure stress 4-3Horner plot 8-8Horsepower 5-37

requirements, friction and wellhead pressure 6-9Howard and Fast 1-8hp, pumping (cost) 6-11HPG

hydroxypropyl guar 6-30solution viscosity behavior 6-32

Hugoton 1-2, 1-7Hydraulic

fracture treatments 1-1fracturing developments 1-3fracturing history 1-1horsepower 1-6

HydrocarbonAromatic with surfactants 6-14crosslinked 6-2foams 6-2gel viscosities 6-8gelled 6-46gels, viscosity 6-48recovered, value of 6-23slick 6-2

Hydrocarbon-basefluids or foams 6-23

6

Index

fracturing fluid systems 6-2Hydrostatic, gradients 6-9Hydroxyethyl cellulose (HEC) 6-30Hydroxypropyl guar (HPG) 6-30Hydroxypropylcellulose 6-49

IINCDROI (incremental discounted return on investment) 9-3INCPVF (incremental PW or value of the fracture) 9-3Incremental

discounted return on investment (INCDROI) 9-3economics 9-12present worth or value of the fracture(INCPVF) 9-3

Infinitebounding beds 5-3capacity 3-4thickness 5-3

Initial fracture height 5-3In-situ

closure stress 5-12closure stress profile 5-15stress 5-12stress profile 5-13stress tests 8-4stresses 5-15

Insoluble residue 6-20Integrated design package 6-23Interface slip 5-11Ionic surfactants 6-6ISIP (instantaneous shut-in pressure) 8-4

JJabsco gear pump 6-51Jet mixer 1-7

KK (Geertsma and de Klerk model) 2-4kfw (fracture flow capacity) 3-2Khristianovic model 2-4

Perkins and Kern comparison of 2-5

LLateral

strain 4-2Lateral strain 4-2, 4-3Leakoff

driving pressure 6-15, 6-18resistance in the reservoir rock 6-15

Liquid-constantpressure 3-36rate 3-35

Lithology changes 5-12Load recovery 6-8

Log(s)base temperature 10-8borehole geometry 10-5cement bond 10-7density 10-5gamma ray 5-13, 5-17, 5-18, 10-5long spaced digital sonic 10-6LSDS 10-6neutron porosity 10-5resistivity 10-5spontaneous potential 5-18, 10-5static temperature 10-9temperature 5-18

Long spaced digital sonic log (LSDS) 10-6Low

fluid loss 6-14pumping pressure 6-9

MMass balance equation 8-17Massive hydraulic fracturing (MHF) 1-7Material Safety Data (MSD) 6-5Mechanical properties in fracturing 4-1Methanol 1-5, 6-7

gelled 6-2, 6-48gels

advantages 6-49disadvantages 6-49used with CO2 6-49

viscosify 6-49MHF (Massive hydraulic fracturing) 1-7Microfrac 8-4

tests 8-4, 8-7Minifrac 8-2

calibration treatments 1-10Mixing, simulated field 6-51Model 35 Fann viscometer 6-8Models, Pseudo 3-D 5-16Moduli

dynamic 4-2static 4-2

Moduluseffect on fracturing 4-4of elasticity 4-1, 4-3, 4-4, 10-3plane strain 4-1

MSD (Material Safety Data) 6-5

NNapalm 1-2Napalm-type fluids 6-47Net

fracture pressure 5-3, 5-4, 5-15fracturing pressure 4-4present value of post-frac production 6-23


Index

present worth or value (PW or PV) 9-3pressure 2-5, 5-11, 5-16, 8-14

Neutron porosity log 10-5Newtonian fluid 5-29Nitrogen foams 6-9Nolte-Smith log-log interpretation 8-14Nomenclature, service company fluid system 6-52Non-darcy flow 7-29Nonemulsifier 6-8Nonionic surfactants 6-6Nordgren 2-4

OOil-base

friction reducers 6-9gels 6-15

Open-ended tubing 8-22Organo titanates and zironates 6-32Organometallic

crosslinked gels 6-13delayed-crosslinked gels 6-39

Orientation fracture 3-8Overburden weight 5-11Overpressured reservoirs 6-9

PPad

fluids guideline 6-74volume 8-59

Pan American Petroleum Corporation 1-2Particle

clumping 6-13drag coefficient 6-12generalized, Reynolds 6-12single settling 6-13terminal settling velocity 6-11

Pay zone 5-3, 5-4, 5-13Payout (PO) 9-3, 9-10Perforating 10-10Perkins and Kern model 2-4, 5-16

Khristianovic model comparison of 2-5Permeability 5-20

formation 3-1impaired proppant pack 6-21of proppant 7-19proppant 7-5reservoir 3-2

pH 6-8PI (profitability index) 9-3Pilot tests 6-7Pinch outs 6-11PK (Perkins and Kern model) 2-4PKN (Perkins and Kern model) 2-4, 5-16Plane strain modulus 4-1

PO (payout) 9-3Point forward evaluation 9-17Points, flash 6-5Poisson’s ratio 4-1, 4-3, 5-13, 10-3Polyacrylamides 6-30Polyemulsion, see polymer emulsionPolymer

(gel) concentrates 6-37concentrates 6-30effective concentration 6-20emulsion 6-1, 6-14, 6-23

fluid 6-40fluid advantages 6-40fluid disadvantages 6-40viscosity 6-41

natural water soluble 6-30solutions

crosslinked (gels) 6-1uncrosslinked 6-1

Porepressure 5-11, 5-12, 5-13

variations 5-12Power law

exponent 5-29fluid 5-29

Prefrac stress tests 1-10Preparation and quality control 6-7Present worth 1-1, 9-4, 9-14Pressure

bottomhole treating 8-14closure 5-13critical 8-1, 8-20decline 8-2decline analysis 8-25, 8-30

example/guidelines 8-38post-propped-frac 8-42

differential 5-21fracture closure 5-11History Matching 8-46leakoff driving 6-15, 6-18multiplier pumps 9-20net 5-16, 8-14net fracture 5-3, 5-4net fracturing 4-4reservoir closure 5-13

Prices fracuring chemical and hhp 6-23Problem proppant and fluid scheduling 6-78Products

modified natural 6-30synthetic 6-30

Profitabilityindex 9-7, 9-14index (PI) 9-3

Propagation criterion 2-1Proppant fall correction factor (PFCF) 7-26


Index

Proppant(s) 1-5acid solubility 7-11addition schedule 8-62, 8-66and fluid scheduling problem 6-78bulk and grain density 7-11ceramic 7-1concentrations 8-55crush resistance 7-9damage factor 7-23design techniques 1-5fluid schedule from pressure decline 8-55hardness 7-4high strength - see Proppant(s), ceramicimpaired pack permeability 6-21intermediate strength - see Proppant(s), ceramiclong-term conductivity 7-20permeability 7-5PREDICTK 7-23resin-coated 6-7, 7-1, 7-16sand 7-1sieve distribution - see size distributionsingle-grain test 7-4size distribuiton 7-5sphericity and roundness 7-4stress 7-1temperature effect on conductivity 7-21transport 5-39

fluid viscosities 6-11fluid viscosity 6-11from viscous drag 6-11using thin fluids 6-11

turbidity 7-13volume fraction 5-33

Proppingagent pumping charge 9-20agents 1-5

Pseudo 3-D model 5-16Pseudo-Radial Flow 3-27Pump

Jabsco gear 6-51rate 5-36time, estimated 6-70

Pump-in/declinetest 8-4, 8-7

Pump-in/flowback test 8-9Pumping

cost 6-23hp (cost) 6-11

PV (net present worth or value) 9-3PW (net present worth or value) 9-3

QQualitative checks on water-base gel crosslinking 6-8Quality 6-43

control

and preparation 6-7aspects of 6-9gel continuous-mix jobs 6-8

Quasi static conditions 4-2

RRadius 5-36Recovery, load 6-8Reservoir

closure pressure 5-13naturally fractured 6-14, 6-17overpressured 6-9permeability 3-2rock leakoff resistance in 6-15Temperatures 5-32underpressured 6-9

Residueconcentrates at the fracture wall 6-21insoluble 6-20uniformly distributed 6-21

Resin-coated proppant(s) 6-7, 7-1, 7-16compressive strength 7-17

Resistivity log 10-5Return on investment 9-11Reynolds generalized particle 6-12Rheological data 6-72Rheology

determining for titanium and zirconium gels 6-51of uncrosslinked polymer solutions 6-30

Rock hardness 4-10

SSafety and environmental compatibility 6-5Sand 7-1

fluid proportioner 1-8Scaling 6-7Scheduling

fluid 6-70given the fluid rheology 6-70optimal for fluids 6-70using contained rheology 6-71

Screen outs 6-11Secant Modulus 4-3Service company

fluid system nomenclature 6-52trade names 6-52

Settlinghindered 6-13single particle 6-13Stokes 6-12terminal, velocity of a particle 6-11velocities 6-12

Shear rate 5-27Silica flour 6-14, 6-17


Index

Simple history matching 8-48Simulated field mixing 6-51Slick

hydrocarbon 6-2water 6-1, 6-11

Slip flow 6-51Slurry concentration handling service 9-20Solutions

polymer crosslinked (gels) 6-1polymer uncrosslinked 6-1

Spontaneouspotential log 10-5potential logs 5-18

Spurt loss 5-20, 6-17SRT (step-rate injection test) 8-10Stability of foam 6-43Stabilizers

cationic polymeric clay 6-6chemical 1-5gel 1-5high temperature 6-13viscosity guideline 6-74

Stanolind Oil and Gas Corporation 1-2Static

moduli 4-2temperature

log 10-9temperature gradient 5-32

Step-rate injection test (SRT) 8-10Stokes

Law, Proppant Transport 7-26settling 6-12

Strainaxial 4-2, 4-3critical enery release rate 4-7lateral 4-2, 4-3volumetric 4-2, 4-3

Stressaxial 4-2closure 5-3, 5-11, 5-13, 5-15critical intensity factor 4-7differential 5-3horizontal closure 4-3in-situ 5-12, 5-15

closure 5-12closure profile 5-15

profile 5-15proppant 7-1vertical 5-11

Surfacerecorded BHP gauge 8-22treating pressures 1-7, 6-11

Surfactants 1-4, 6-8anionic 6-6aromatic hydrocarbons with 6-14


cationic 6-6fluorocarbon 6-7ionic 6-6nonionic 6-6

Suspensionflows 6-11transport 6-12

Syntheticproducts 6-30water soluble polymers 6-30

Systemsdelayed crosslinked 6-8dual crosslinker 6-38fluid, continuous mixed 6-8hydrocarbon-base fracturing fluid 6-2water-base fracturing fluid 6-1

TTangent modulus 4-3Temperature

and time, viscosity affected by 6-13high

gel system behavior 6-13gelled-hydrocarbon 6-47gels 6-13

logs 5-18time at 6-72

TerraFrac 5-15Test(s)

closure stress 5-14compression 4-2, 4-3core 10-3

flow 6-6fluid loss 5-22in-situ stress 8-4microfrac 8-4, 8-7pilot 6-7procedures 6-51pump-in/decline 8-4, 8-7pump-in/flowback 8-9step-rate injection 8-10triaxial stress-strain 10-3vortex closure 6-8

Testingorganometallic crosslinked gels 6-14rheology, of fracturing fluids 6-49

Texture 6-43, 6-463-D models 5-15Time at temperature 6-72Time-temperature

history 8-67for fluid 8-55

Titanium, determining rheology of 6-51Toxicity, fracturing fluid components 6-5Trade names, service company 6-52

0

Index

ire-

Transient Reservoir Response 3-24Transport

bedload 6-12suspension 6-12

Treatmentpad percentage 8-66volume, effect of 8-64

Triaxial stress-strain tests 10-3Type curve(s) 8-32

analysis 8-32

UUncrosslinked

gels 6-14polymer solutions 6-1viscosity gels 6-8

Underpressured reservoirs 6-9

VValhall chalk 4-3Variable(s)

affecting frac height 5-15finite capacity 3-4

Verticalfracture width profile 5-16stress 5-11

Viscometer, Model 35 Fann 6-8Viscosify, methanol 6-49Viscosity 6-39

affected by temperature and time 6-13appropriate 6-11data for nitrogen foams 6-43effective 6-70fluid, proppant transport 6-11guideline 6-70hydrocarbon gels 6-48of foam 6-43polymer emulsion 6-41proppant transport 6-11stabilizer guideline 6-74sufficient to create wide fractures 6-11Ti and Zr continuous-mix gels 6-14uncrosslinked gels 6-8

Volumetric strain 4-2, 4-3Vortex closure tests 6-8

WWall building 5-23

effect 5-22Water

blocks 6-7slick 6-1, 6-11soluble polymers, natural 6-30

Water-base

fast crosslinking gels 6-32fracturing fluid systems 6-1friction reducers 6-9

Wellhead pressure, friction pressure and horsepower requments 6-9

Western Company coding system 6-53Wettability of formation 6-6Width

create conductive proppant pack 6-11fracture 6-11prevent pinch outs 6-11

YYet-to-spend 9-17Young’s modulus 4-1, 4-3

ZZirconium, determining rheology of 6-51Zironates and organo titanates 6-32
