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Mini‐frac (DFIT)Analysis for Unconventional Reservoirs using F.A.S.T. WellTest™

Course Outline

• Introduction• What is a Mini‐frac Test?• Why Perform a Mini‐frac Test?

• Mini‐frac Test Overview

• Analysis• Pre‐Closure Analysis• Leak‐off Types• Nolte After‐Closure Analysis• Soliman/Craig After‐Closure Analysis• ACA Modeling

• Radial Flow Example

• Linear Flow Example

• Mini‐frac Test Design2Copyright © Fekete Associates Inc.

What is a Mini‐frac Test?

• A mini‐frac test is an injection/falloff diagnostic test performed without proppant before a main fracture stimulation treatment

• The intent is to break down the formation to create a short fracture during the injection period, and then to observe closure of the fracture system during the ensuing falloff period.

3Copyright © Fekete Associates Inc.

What is a Mini‐frac Test?

• The created fracture can cut through near‐wellbore damage, and provide bettercommunication between the wellbore and true formation.

• A mini‐frac test is capable of providing better results than a closed chamber test performedon a formation where fluid inflow is severely restricted by formation damage.


Why Perform a Mini‐frac Test?

• Determine initial formation pressure (Pi) & effective permeability (k) to:– Assist production/pressure data analysis– Provide initial inputs for reservoir models– Assess stimulation effectiveness– Help quantify reserves

• Estimate fracture design parameters such as:– Fracture gradient– Closure pressure (minimum horizontal stress)– Leak‐off coefficients



For Shale/Tight Formations:

Effective Permeability (k) is very low• Matrix permeability of a few nanodarcies to a few microdarcies (when

natural fractures exist) render conventional tests impractical before stimulation

Horizontal Multi‐Frac Wells• Massive hydraulic fracture treatments• Multiple fracture stages• Multiple perforation clusters per fracture stage• Numerous fracture networks created• Difficult to quantify effective formation permeability and pressure after

stimulation6Copyright © Fekete Associates Inc.


Shut‐in Time Required to Estimate Pi & k (After Perforating)Based on Haynesville Shale Properties

Simulated Pressure Buildup After Perforating

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Pres

sure

(p

si(a

))

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Time (h)

1000Nanodarcies2Weeks

100Nanodarcies5Months

10Nanodarcies4Years!

Skin=+2



Simulated PITA Derivative After Perforating

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107

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Impu

lse

Der

ivat

ive

(

t a)2

d

/d(

t a)

((1

06p

si2/

cP)

hr)

10-1 1.0 101 102 103 104 1052 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8

Pseudo-Time (h)

Shut‐in Time Required to Estimate Pi & k (After Perforating)Based on Haynesville Shale Properties

10Nanodarcies4Years!

100Nanodarcies5Months1000Nanodarcies

2Weeks

Skin=+2



Shut‐in Time Required to Estimate Pi & K (After Mini‐frac)Based on Haynesville Shale Properties

Simulated Pressure Falloff After Minifrac

10500

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Pres

sure

(p

si(a

))

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Time (h)

1000Nanodarcies1Day



Skin=‐2.5



Simulated PITA Derivative After Minifrac

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107

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Impu

lse

Der

ivat

ive

(

t a)2

d

/d(

t a)

((1

06p

si2/

cP)

hr)

10-1 1.0 101 102 103 104 1052 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8

Pseudo-Time (h)

Shut‐in Time Required to Estimate Pi & K (After Mini‐frac)Based on Haynesville Shale Properties



1000Nanodarcies1Day

Skin=‐2.5


Mini‐frac Test Overview


Mini‐frac Analysis

Mini‐frac Test Analysis is conducted in two steps:

• Pre‐Closure Analysis (PCA)– Uses special derivatives and time functions (G‐Func on, √t)– Indentify leak‐off behaviour and closure pressure

• After‐Closure Analysis (ACA)– Similar workflow to traditional pressure transient analysis– Uses “impulse” solution to establish formation permeability (k)

and pressure (Pi)


PCA: ParametersThe following parameters are determined from the Pre‐Closure Analysis (PCA):

• Fracture Closure Pressure (pc)pc = Minimum Horizontal Stress

• Instantaneous Shut‐In Pressure (ISIP)/Propagation PressureISIP = Final Bo omhole Injec on Pressure ˗ Fric on Component

• Fracture Gradient

Fracture Gradient = ISIP / Formation Depth

• Net Fracture Pressure (Δpnet)

Δpnet = ISIP – Closure Pressure

• Fluid Efficiency: the ratio of the stored volume within the fracture to the total fluid injected


PCA: G‐FunctionThe G‐function is a dimensionless time function relating shut‐in time (t) to totalpumping time (tp) at an assumed constant rate and are based on the followingequations:

Two limiting cases for the G‐function are shown here:

α = 1.0 is for low leak‐off

α = 0.5 is for high leak‐off

The value of g0 is the computed value of g at shut‐in.14Copyright © Fekete Associates Inc.

PCA: G‐Function Analysis

Fracture closure is identified as the point where the G‐Function derivative starts to deviate downward from the straight line


G-Function

0

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Sem

ilog

Deriv

ativ

e G

dp/

dG

(psi

(a))

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First Derivative dp/dG

(psi(a))

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p (psi(a))

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52

G-function time

Semilog Derivativepdata

First Derivative

Inj. Volume 3.99 bblISIP 7930.1 psi(a)Ddatum 9650.000 ftFrac grad 0.822 psi/ft

Fracture Closure

Gc 21.014tc 159.76 minpc 7308.4 psi(a)

Fracture Closure

Gc 21.014tc 159.76 minpc 7308.4 psi(a)

Fracture Closure

Gc 21.014tc 159.76 minpc 7308.4 psi(a)

PCA: Leak‐Off TypesNormal Leak‐off: occurs when the fracture area is constant during shut‐in and the leak‐off occurs through a homogeneous rock matrix

The characteristic signatures of normal leak‐off are :1. A constant pressure derivative (dP/dG) during fracture closure.2. The G‐Function derivative (G dP/dG) lies on a straight line that passes through the

origin16Copyright © Fekete Associates Inc.

Normal Leakoff

GFunctionDerivative(Gdp/dG)

G‐Function(GTime)

• NormalLeakoff

PCA: Leak‐Off TypesTransverse Fracture Storage/Fracture Height Recession is indicated when the G‐Function derivative G dP/dG falls below a straight line that extrapolates through the normal leak‐off data, and exhibits a concave up trend

Two characteristics are visible on the G‐function curve:1. The G‐Function derivative G dP/dG lies below a straight line extrapolated through the normal

leak‐off data.2. The G‐Function derivative G dP/dG exhibits a concave up trend.3. The First Derivative dP/dG also exhibits a concave up trend.

TransverseFractureStorage/FractureHeightRecession


Fracture Height Recession

• Fracture penetrates impermeable zone

Fracture Height Recession

• Fracture penetrates impermeable zone

Transverse Storage

• Early Time – Secondary fractures open

Transverse Storage

• Late Time – Secondary fractures close

PCA: Leak‐Off TypesPressure Dependent Leak‐off (PDL): indicates the existence of secondary fractures intersecting the main fracture, and is identified by a characteristic “hump” in the G‐ Function derivative that lies above the straight line fit through the normal leak‐off data.

The characteristic signatures of pressure dependent leak‐off are:1. A characteristic large “hump” in the G‐Function derivative G dP/dG lies above the straight

line that passes through the origin..2. Subsequent to the hump, the pressure decline exhibits normal leak‐off.3. The portion of the normal leak‐off lies on a straight line passing through the origin.4. The end of the hump is identified as “fissure opening pressure”.


Pressure Dependant Leak‐off• Early Time ‐ Extra leak‐off from microfractures at high

pressure/early time

Pressure Dependant Leak‐off• Late Time‐Microfractures close, normal leak‐off resumes

PCA: Leak‐Off TypesFracture Tip Extension occurs when a fracture continues to grow even after injection is stopped and the well is shut‐in. It is a phenomenon that occurs in very low permeability reservoirs, as the energy which normally would be released through leak‐off is transferred to the ends of the fracture.

The characteristic signatures of fracture tip extension are:1. The G‐Function derivative G dP/dG initially exhibits a large positive slope that continues to

decrease with shut‐in time, yielding a concave‐down curvature.2. Any straight line fit through the G‐Function derivative G dP/dG intersects the y‐axis above the

origin. 26Copyright © Fekete Associates Inc.

Fracture Tip Extension

• Fracture Tip Extension Provides Extra Leak‐Off

After‐Closure Analysis (ACA)• ACA is performed on falloff data collected after fracture closure• Similar workflow to traditional pressure transient analysis

• Traditional PTA founded on the “constant‐rate solution” • Main ACA techniques are founded on the “impulse solution” • The “constant‐rate solution” hinges on the flow rate prior to SI• The “impulse solution” hinges on a “defined volume”


After Closure – Linear Flow

PlanView

After Closure – Radial Flow

• Radial Flow in Horizontal Plane– If linear flow is observed before radial flow, can use fracture model

PlanView– VerticalModelwithFracture

3D

After Closure

• Radial Flow in Horizontal Plane– If only radial flow is observed, can be modelled as vertical with negative skin

VerticalModelConceptualModel

PlanView

After‐Closure Analysis (ACA)

• After‐Closure Analysis (ACA) is performed on falloff data collected after fracture closure.

• Similar workflow to traditional pressure transient analysis.• Traditional PTA founded on the “constant‐rate solution”; Mini‐Frac ACA

techniques are founded on the “impulse solution”.• The “constant‐rate solution” hinges on the flow rate prior to the analyzed

shut‐in period whereas the “impulse solution” hinges on a “defined volume”.• Impulse solutions are used because of the short injection period and assume

the entire injected volume is injected instantaneously. • There are two ACA techniques available in F.A.S.T. WellTest™ (Nolte and

Soliman/Craig).


Nolte ACA

• This after‐closure analysis method is based on the work of K.G. Nolte8, and expanded on by R.D. Barree4.

• Based on the solution of a constant pressure injection followed by a falloff.

• The impulse equations are obtained by approximating the injection duration as very small.

• Uses injected volume as the impulse volume and the falloff begins at fracture closure.

• Characteristic slopes of the semi‐log derivative when plotted on the log‐log derivative plot differ from traditional PTA:

• Impulse Linear flow has a slope of ‐1/2.• Impulse Radial flow has a slope of ‐1.


Nolte ACA


Derivative

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104

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3

5

23

5

23

5

p,

Sem

ilog

Der

ivat

ive

(F L

2 2 )d

p/

d(F L

2 2 )

(ps

i(a))

10-210-11.0 2345678923456789

FL2 2

pdataDerivativedata

Impulse Radial -1

k 0.0165 md

t 38.73 hp 6652.6 psi(a)

Impulse Linear -1/2

t 15.08 hp 6750.9 psi(a)

Soliman/Craig ACA

• This after‐closure analysis method is based on the combined works of M.Y. Soliman and D. Craig1.

• Soliman’s solution is based on a constant rate injection followed by a long falloff2.

• Soliman applied superposition in Laplace space to obtain a single equation and then took the late‐time approximation to obtain impulse equations (for bilinear, linear and radial flow).

• D. Craig developed an analytical model which accounts for fracture growth, leak‐off, closure and after‐closure3.

• The late‐time approximation of Craig’s model produced impulse equations that are consistent with Soliman's solutions.

• Uses injected volume as the impulse volume.• Characteristic slopes of the impulse derivative when plotted on the log‐log

derivative plot are identical to those of traditional PTA.• Soliman/Craig's solutions facilitate the use of analytical models in F.A.S.T.

WellTest™. 35Copyright © Fekete Associates Inc.

Soliman/Craig ACA


Derivative

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104

2

46

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23

5

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4

Impu

lse

Der

ivat

ive

t (

tp +

t)

dp/d

t (p

si h

r)

10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8

t (h)

Derivativedata

Radial 0

k 0.0165 md

t 12.98 hp 6777.5 psi(a)

Linear 1/2

Xf(sqrt(k)) 1.24 md1/2ftk 0.0165 mdXf 9.676 ftsXf -2.780

t 38.13 hp 6653.5 psi(a)

ACA ‐Modelling• Once the initial reservoir pressure (Pi) and permeability (k) are estimated, a model is

generated (Soliman/Craig)to confirm these estimates. Note that the existing model does not account for the change in storage that occurs while the induced fracture is closing, and the analysis is focused on the after‐closure data.

• This is especially critical when reservoir dominated (radial) flow is not achieved within a test period, or when data scatter aggravates the analysis.


Derivative

10-2

10-1

1.0

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104

3

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3

3

3

Impu

lse

Der

ivat

ive

(

t)2

dp/

d(

t)

(psi

hr)

10-3 10-2 10-1 1.0 101 102 1032 3 4 5 6 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6

t (h)

DerivativedataDerivativemodelExt. Derivativemodel

pi (syn) 6592.0psi(a)kh 0.6138md.fth 40.000ftk 0.0153md

s' -2.731sXf -2.738Xf 9.273ft

Mini‐frac Observations from Real Data

• An example of a Mini‐frac test conducted on a vertical well at a formation depth of 10,000 ft analyzed using F.A.S.T. WellTest™ is depicted in the following slides.


History

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sure

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0

Liquid Rate (bbl/d)

1.22 1.24 1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 1.56 1.58

Time (h)

qwater

pdata

Inj . Volume 16.35 bblISIP 9444.2 psi(a)Ddatum 10100.000 ftFrac grad 0.935 psi/ft

Formation Breakdown

pdata 10942.7 psi(a)

Stop Injection

t 0.31 hpdata 9557.0 psi(a)qw -1440.00 bbl/d

Estimated ISIP

pdata 9444.2 psi(a)

Start Injection


• The pre‐closure analysis using the semi‐log and first derivative corresponding to G‐function time is shown below:

• From this plot, fracture closure is identified within the initial 3‐hours of the falloff period


G-Function

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ilog

Der

ivat

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G d

p/dG

(p

si(a

))

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First Derivative dp/dG

(psi(a))

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9500

p (psi(a))

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

G-function time

Semilog Deriv ativ epdata

First Deriv ativ e

Inj . Volume 16.35 bblISIP 9444.2 psi(a)Ddatum 10100.000 ftFrac grad 0.935 psi/ft

Analysis 1

Fracture Closure

Gc 6.233tc 166.76 minpc 7217.0 psi(a)

Fracture Closure

Gc 6.233tc 166.76 minpc 7217.0 psi(a)

Fracture Closure

Gc 6.233tc 166.76 minpc 7217.0 psi(a)


• The Nolte ACA log‐log diagnostic plot is shown below:

• The semi‐log derivative, calculated with respect to closure time, exhibits a slope of ‐1 after 5.64 hours, suggesting that radial flow has developed.

• The fluctuations in the derivative slope can be attributed to gas‐entry that is not accounted for with the bottomhole pressure calculations.


Derivative

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102

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104

2

3

57

2

3

57

2

3

5

, Sem

ilog

Der

ivat

ive

(F L

2 2 )

d

/d(F

L2 2 )

(1

06ps

i2/c

P)

10-210-11.0 2345678923456789

FL2 2

dataDerivativedata

Impulse Radial -1k 1.8577e-03md

t 23.07hp 5604.5psi(a)rinv 21.976ft

t 5.64hp 6322.9psi(a)


• The falloff data plotted with the Nolte ACA radial time function FR2 is shown below:


Minifrac Radial (Nolte)

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2500

(106

psi2

/cP)

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6800

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7200

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7600

p (psi(a))

0.000.040.080.120.160.200.240.280.320.360.400.440.480.520.560.600.64

FR1

data

Analysis 1kh 0.1115md.fth 60.000ftk 1.8577e-03mdp* 5363.9psi(a)

t 23.07hp 5604.5psi(a)rinv 21.976ft


• The log‐log plot of the derivative used in the Soliman/Craig impulse solution shows the match obtained with the model:

• The model suggests radial flow was not quite achieved during the test period, and would likely develop after ~50 hours of shut‐in.

• In this case, the transition to radial flow is sufficiently developed to yield reliable estimates of formation pressure and permeability.


Derivative

101

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104

2

4

2

4

2

4

Impu

lse

Der

ivat

ive

t a

(tp

+

t a) d

/d

t a

((10

6 psi

2 /cP

) hr)

10-3 10-2 10-1 1.0 101 1022 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7 2 3 4 5 6 7

ta (h)

DerivativedataDerivativemodelExt. Derivativemodel

kh 0.1978md.fth 60.000ftk 3.2968e-03md

Xf 1.572ftsXf -0.963pi 5461.7psi(a)

ApproachingRadial Flow

t 23.07hRadialFlowΔt=50.0h

Mini‐Frac Test Design

• Short duration injection period, followed by extended falloff period.

• Water commonly used for injection.

• Optimum injection rate/duration:

• 1 – 2 bpm (1500 – 3000 bbld)

• 2 – 3 minute injection (after wellbore fill‐up)

• sufficient to breakdown formation, while minimizing fracture growth and closure time

• Falloff duration controlled by permeability (k) and rock properties:

• minimum 2 days for k > 0.001 md (1000 Nanodarcies)

• minimum 2 weeks for k < 0.001 md (1000 Nanodarcies)


References1. "New Method for Determination of Formation Permeability, Reservoir Pressure, and Fracture Properties from a Minifrac Test",

Soliman, M.Y., Craig D., Barko, K., Rahim Z., Ansah J., and Adams D., Paper ARMA/USRMS 05‐658, 2005

2. “Analysis of Buildup Tests With Short Producing Times”, M. Y. Soliman, SPE, Halliburton Services Research Center, Paper SPE 11083 August 1986.

3. “Application of a New Fracture‐Injection/Falloff Model Accounting for Propagating, Dilated, and Closing Hydraulic Fractures, D. P. Craig, Haliburton, and T. A. Blasingame, Texas A&M University, Paper SPE 100578, 2006.

4. “Holistic Fracture Diagnostics”, R. D. Barree, SPE, and V. L. Barree, Barree & Associates, and Craig, SPE, Halliburton, Paper SPE 107877, Presented at the Rocky Mountain Oil & Gas Technology Symposium held in Denver, Colorado, USA, 16‐18 April 2007.

5. “After‐ Closure Analysis of Fracture Calibration Tests”, Nolte, K.G., Maniere, J.L., and Owens, K.A., Paper SPE 38676, Presented at the 1997 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5‐8 October, 1997.

6. "Background for After‐Closure Analysis of Fracture Calibration Tests", Nolte, K. G., Paper SPE 39407, Unsolicited companion paper to SPE 38676 July, 1997.

7. “Modified Fracture Pressure Decline Analysis Including Pressure‐Dependent Leakoff”, Castillo, J. L., Paper SPE 16417, presented at the SPE/DOE Low Permeability Reservoirs Joint Symposium, Denver, CO, May 18‐19, 1987.

8. “Determination of Fracture Parameters from Fracturing Pressure Decline", Nolte, K. G., Paper SPE 8341, Presented at the Annual Technical Conference and Exhibition, Las Vegas, NV, Sept. 23‐26, 1979.

9. "Use of PITA for Estimating Key Reservoir Parameters", N. M. Anisur Rahman, Mehran Pooladi‐Darvish, Martin S. Santo and Louis Mattar, Paper CIPC 2006 ‐ 172, presented at 7th Canadian International Petroleum Conference, Calgary, AB, June 13 ‐ 15, 2006.

10."Development of Equations and Procedure for Perforation Inflow Test Analysis (PITA)", N. M. Anisur Rahman, Mehran Pooladi‐Darvish and Louis Mattar, Paper SPE 95510, presented at 80th Annual Technical Conference and Exhibition of the SPE, Dallas, TX, October 9 ‐ 12, 2005.


Documents

Mini frac (DFIT)Analysis for Unconventional Reservoirs ... · Mini‐frac (DFIT)Analysis for Unconventional Reservoirs using F.A.S.T. WellTest ™ ... Frac grad 0.822 psi/ft Fracture