OverviewThis Appendix to Chapter 5 reviews the evolutionof hydraulic fracturing design and evaluationmethods. Complementary reviews are the applica-tion of fracturing by Smith and Hannah (1996) andfracturing fluids by Jennings (1996). This review ofdesign and evaluation considers three generations offracturing: damage bypass, massive treatments andtip-screenout (TSO) treatments.

The first two generations of fracturing and theirlinks to practices are emphasized because these con-tributions are not likely well known by the currentgeneration of engineers. The review focuses onpropped fracturing and does not explicitly consideracid fracturing. Although the principles governingthe mechanics of both are essentially the same, thefluid chemistry for obtaining fracture conductivity is quite different (see Chapter 7). These principleshave their roots in civil and mechanical engineering,more specifically in the general area of appliedmechanics: solid mechanics for the rock deforma-tion and fluid mechanics for the flow within thefracture and porous media. For the porous mediaaspects, fracturing evaluation has benefited greatlyfrom the reservoir engineering practices discussed in Chapters 2 and 12.

This review reflects the authors perspective andbias in interpreting the impact of past contributions,and therefore parts of this review should be antici-pated to raise objections from others with an exten-sive knowledge of fracturing. In addition to thisvolume, the Society of Petroleum Engineers (SPE)Monograph Recent Advances in Hydraulic Frac-turing (Gidley et al., 1989) provides balanced,detailed coverage of the diverse areas of fracturingfrom the perspectives of more than 30 fracturingspecialists.

This review concludes with speculation concern-ing a future generation, in which fracture design andreservoir engineering merge into fracturing for

reservoir management (i.e., control of both the verti-cal and horizontal flow profiles within the reser-voir). Similar speculation in a 1985 lecture sug-gested that development of the technical foundationfor the TSO generation would quickly bring higherpermeability formations into consideration as typicalfracturing candidates (i.e., moderate k (2) onAppendix Fig. 1a, with 2 indicating a target forfolds of increase [FOI] in the production rate, incontrast to 10 for tight gas and massive treat-ments). However, the advent of this generation wasconsiderably delayed because of two factors thathave generally dominated technical considerationsduring the history of fracturing. These dominatingfactors are hydrocarbon prices and resistance to try-ing something new until established practices fail toallow the economic development of a prospect.

The cycles of fracturing activity in Appendix Fig.1a clearly reflect the timing of the first two fractur-ing generations. Appendix Fig. 1b identifies eco-nomic drivers for corresponding cycles in the U.S.rig count. The first surge of activity resulted whenrotary drilling was introduced, which enabled thedevelopment of deeper reserves. Fracturing activityfollowed this trend soon after its commercializationin 1949 because it was found to be an effective,low-cost means of mitigating the resulting drillingmud damage to reservoir sections (i.e., the damagebypass generation). Both drilling and fracturingactivities began a long-term decline after 1955because of degrading prices caused by imported oiland regulated gas prices. Similarly, both activitiesbegan a rapid increase at about 1979 as pricesincreased because the Organization of PetroleumExporting Countries (OPEC) reduced its oil suppliesand a natural gas shortage developed in the UnitedStates. The gas shortage, and its 10-fold-plusincrease in price, encouraged the development oftight gas reserves and an associated demand formassive fracturing treatments to develop the tightreserves. The failure of past fracturing practices for

Reservoir Stimulation A5-1

Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

K. G. Nolte, Schlumberger Dowell

large treatments spurred a significant research anddevelopment effort that beneficially impacted everyaspect of fracturing and essentially developed thefracture design and evaluation framework presentedin this volume. The industrys rapid contraction dur-ing the early 1980s resulted again from OPEC, butthis time because of OPECs failure to maintain arti-ficially high prices. The TSO treatment for creatingthe very wide propped fractures required for highpermeability evolved during this time. This tech-nique allowed the development of a troublesomesoft-chalk reservoir in the North Sea by fracturing.However, the significant potential of the TSO gener-ation did not materialize until about 10 years later,when its application was required on a relativelylarge scale to achieve viable economics for two high-permeability applications: bypassing deep damage inthe Prudhoe Bay field and its coupling with gravel

packing to achieve low-skin completions for a signif-icant venture in the Gulf of Mexico.

The potential for a future reservoir managementgeneration was demonstrated in 1994 for the Nor-wegian Gullfaks field. The potential is to use TSOtreatments and indirect vertical fracturing forincreased reserves recovery, formation solids controland water management. However, the unique bene-fits and favorable economics for this differentapproach to reservoir plumbing were slow tomaterialize because of the industrys comfort withdeviated drilling and more traditional completions.

Another observation from this historical perspec-tive is the 1985 forecast of a flat drilling level(Appendix Fig. 1b). However, activity continued todecrease rapidly, to less than one-half of the forecast,and subsequently declined by another one-half. Stableactivity levels within the petroleum industry are notseen in the historical cycles and remain the product of wishful thinking.

The beginningThe concept of hydraulic fracturing within the petro-leum industry was developed during the last half ofthe 1940s within Stanolind (now BP Amoco; e.g.,Clark, 1949; Farris, 1953; Howard and FastsHydraulic Fracturing Monograph, 1970) by buildingon the industrys experience with injection tech-niques that had experienced increased injectivity by fracturing: acidizing (Grebe and Stoesser, 1935),squeeze cementing and brine injection wells. A re-issued patent was granted (Farris, 1953, resultingfrom an initial filing in 1948) that was comprehen-sive in scope and covered many recognized practicesand products: proppant, gelled oil, breakers, fluid-loss additives, continuous mixing, pad-acid fractur-ing, emulsified acids and the use of packers for frac-turing multiple zones. Several aspects of the patentthat later became important included the implicationthat fractures were horizontal and the use of a low-penetrating fluid or with viscosity > 30 cp.

The first experimental treatments were performedin 1947 on four carbonate zones in the Houghtonfield in Kansas (Howard and Fast, 1970). The zoneshad been previously acidized and were isolated by acup-type straddle packer as each was treated with1000 gal of napalm-thickened gasoline followed by2000 gal of gasoline as a breaker. These unpropped

A5-2 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

Appendix Figure 1. (a) Trends in fracturing activity treat-ments per month (courtesy of K. G. Nolte and M. B. Smith,19851986 SPE Distinguished Lecture). (b) U.S. drilling rigactivity shows five major trends (updated from Oil & GasJournal, 1985).

1950 1955 1971 1981Year

4000

0

Trea

tmen

ts

Rem

ove

dam

age

Tight

gas (1

0)

Mod

erat

e k (

2)

High

cond

uctiv

ity

Unde

rstan

ding,

mater

ials,

equip

ment

?

45004000350030002500200015001000500

01940 1950 1960 1970 1980 1990 2000

Year

Annu

al a

vera

ge ro

tary

rig

coun

t

1985 forcast flat

OPEC overextendsPrices fallU.S. gas prices regulated

Middle East discoveries

U.S. production peaks OPEC developsprice authority

Rotary displacescable tool drilling

Up 9.

9%/ye

ar

Up 1

5.1%

/year

Down 6.1%/year

Down 25.5%/year

(a)

(b)

treatments did not increase production and led to theincorrect belief for some time that fracturing had nobenefit over acidizing for carbonate formations.

A subsequent treatment of the Woodbine sand inthe East Texas field was highly successful. It con-sisted of 23 bbl of gelled lease crude, 160 lbm of 16-mesh sand at 0.15 ppa and 24 bbl of breaker(Farris, 1953). Halliburton originally obtained anexclusive license from Stanolind and commercial-ized fracturing in 1949. Activity rapidly expanded toabout 3000 treatments per month by 1955 (AppendixFig. 1a). Before a universal license was granted toother service companies, water or river fracturingbecame popular in lower permeability areas such asthe San Juan basin (C. R. Fast, pers. comm., 1997).As implied by the name, the treatments used riverwater and sand. The water was outside the definitionof a nonpenetrating fluid within the patents specifiedfiltrate rate through filter paper or viscosity greaterthan 30 cp.

The first generation: damage bypassApplications of first-generation fracturing were pri-marily small treatments to bypass near-wellboredrilling fluid damage to formations with permeabilityin the millidarcy range. An inherent advantage ofpropped fracturing, relative to matrix treatment fordamage removal, is that a fracture opens the com-plete section and retains a conductive path into thezone. The complete opening overcomes the diversionconsideration for matrix treatments (see Chapter 19),but adds the consideration of producing from bot-tomwater or an upper gas cap. For lower permeabilityformations, large amounts of produced water aregenerally not a problem. For higher permeability for-mations, water production can be significant, whichprovided the historical preference for matrix treat-ment in higher permeability applications. However,the precision of fracturing improved significantly,and TSO treatments have been routinely performedin Prudhoe Bay oil columns only 50 ft thick andabove very mobile water (Martins et al., 1992b).

The technology for this fracturing generation issummarized in the Howard and Fast (1970) Mono-graph. The breadth of this volume is shown by itscomprehensive consideration of candidate selection(see Chapter 1) and optimal design based on eco-nomic return (see Chapters 5 and 10). Other note-

worthy design and evaluation methods from this gen-eration are fracture orientation (horizontal or verti-cal), in-situ stress and fracture width models, FOIprediction and fracture conductivity in productionenhancement.

Fracture orientation and in-situ stressThe application of mechanics to fracturing was cat-alyzed by the horizontal orientation of fracturesimplied in the Stanolind patent and the desire of sev-eral operators to avoid paying the nominal patentroyalty of $25$125, based on volume (C. R. Fast,pers. comm., 1997). Significant research activity wasconducted to show that fractures can be vertical, as isnow known to be the general case for typical fractur-ing conditions. The fracture orientation debate even-tually led to a lawsuit that was settled before the trialended. The settlement accepted the patent and nomi-nal royalty payments and stipulated that other servicecompanies receive a license to practice fracturing.However, the royalty benefits were more than nomi-nal to Stanolind because about 500,000 treatmentswere performed during the 17-year period of thepatent (C. R. Fast, pers. comm., 1997). Key to the favorable settlement for Stanolind was its well-documented demonstration of a horizontal fracture in the Pine Island field (see fig. 7-1 in Howard andFast, 1970).

The central issue in the orientation debate was thedirection of the minimum stress. The pressurerequired to extend a fracture must exceed the stressacting to close the fracture. Therefore, the fracturepreferentially aligns itself perpendicular to the direc-tion of minimum stress because this orientation pro-vides the lowest level of power to propagate the frac-ture. The minimum stress direction is generally hori-zontal; hence, the fracture plane orientation is gener-ally vertical (i.e., a vertical fracture). The preferencefor a horizontal fracture requires a vertical minimumstress direction.

In the following review, the orientation considera-tion is expanded to also cover the state of stress inmore general terms. The stress at any point in the var-ious rock layers intersected by the fracture is definedby its magnitude in three principal and perpendiculardirections. The stress state defines not only the frac-ture orientation, but also the fluid pressure required topropagate a fracture that has operational importance,vertical fracture growth into surrounding formation

Reservoir Stimulation A5-3

layers and stress acting to crush proppant or to closeetched channels from acid fracturing. The crushingstress is the minimum stress minus the bottomholeflowing pressure in the fracture. The orientationdebate resulted in three papers that will remain signifi-cant well into the future.

The first paper to be considered is by Harrison etal. (1954). Some of the important points in the paperare that the overburden stress (vertical stress v) isabout 1 psi per foot of depth, fracturing pressures aregenerally lower than this value and therefore frac-tures are not horizontal, and an inference from elas-ticity that the minimum horizontal stress is

(1)

where Ko = /(1 ) = 13 for = 14 (see Eq. 3-51).Using Poissons ratio of 14, Harrison et al. con-

cluded that the horizontal stress is about one-third ofthe vertical stress and therefore fractures are vertical.Appendix Eq. 1 provides the current basis for usingmechanical properties logs to infer horizontal stress,with Poissons ratio obtained from a relation basedon the shear and compressional sonic wave speeds(see Chapter 4). Another assumption for AppendixEq. 1 is uniaxial compaction, based on the premisethat the circumference of the earth does not changeas sediments are buried to the depths of petroleumreservoirs and hence the horizontal components ofstrain are zero during this process. Therefore, Ap-pendix Eq. 1 provides the horizontal stress responseto maintain the horizontal dimensions of a unit cubeconstant under the application of vertical stress.

However, there is one problem with this 1954 conclusion concerning horizontal stress. AppendixEq. 1 is correct for the effective stress but not forthe total stress that governs fracture propagation: = p, where p is the pore pressure, which alsohas a role in transferring the vertical stress into hori-zontal stress as explicitly shown by Appendix Eq. 2.Harrison et al. (1954) correctly postulated that shaleshave higher horizontal stresses and limit the verticalfracture height. The general case of higher stress inshales than in reservoir rocks was a necessary condi-tion for the successful application of fracturingbecause fractures follow the path of least stress. Ifthe converse were the general case, fractures wouldprefer to propagate in shales and not in reservoirzones.

Harrison et al. also reported the Sneddon andElliott (1946) width relation for an infinitely extend-ing pressurized slit contained in an infinitely extend-ing elastic material. This framework has become thebasis for predicting fracture width and fracturingpressure response (see Chapters 5, 6 and 9). Theyused the fracture length for the characteristic, orsmaller and finite, dimension in this relation. Sel-ecting the length for the characteristic dimensionresulted in what is now commonly termed the KGDmodel. Selecting the height, as is the case for a verylong fracture, is termed the PKN model. These mod-els are discussed in the next section and Chapter 6.Harrison et al. considered a width relation becauseof its role in fracture design to determine the fluidvolume required for a desired fracture extent.

The role of volume balance (or equivalently, thematerial balance in reservoir terminology) is anessential part of fracture design and fracture simula-tion code. As shown schematically on the left side ofAppendix Fig. 2, each unit of fluid injected Vi iseither stored in the fracture to create fracture volumeor lost to the formation as fluid loss. (However,Harrison et al.s 1954 paper does not discuss fluidloss.) The stored volume is the product of twice thefracture half-length L, height hf and width w. If thelatter two dimensions are not constant along the frac-ture length, they can be appropriately averaged overthe length. The half-length is then obtained by sim-ply dividing the remaining volume, after removingthe fluid-loss volume, by twice the product of the

A5-4 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

h o vK= ,

Appendix Figure 2. Volume balance for fracture place-ment (equation from Harrington et al., 1973) (adaptedcourtesy of K. G. Nolte and M. B. Smith, 19841985 SPEDistinguished Lecture).

Geometry

hf 2L w

Fluid lossCL t

Volume

Prop

pant

Pad

Proppant(% area = )

=2hfwL

Vi

L =Vi

2hf(w + CL 8t )

average height and the average width. The fluid-lossvolume depends on the fluid-loss surface area, or aheight-length product. Furthermore, as shown on theright side of Appendix Fig. 2, the ratio of stored tototal volume is termed the fluid efficiency and dir-ectly affects the proppant additional schedule (Har-rington et al., 1973; Nolte, 1986b) (see Sidebar 6L).

The second paper to be discussed from the orienta-tion era is by Hubbert and Willis (1957). The lessonsfrom this paper extend beyond fracturing and intothe area of structural geology. This work providessimple and insightful experiments to define the stateof in-situ stress and demonstrate a fractures prefer-ence to propagate in the plane with minimum stressresistance. For the latter experiments, the forma-tion was gelatin within a plastic bottle preferentiallystressed to create various planes of minimal stress.

They also used simple sandbox experiments todemonstrate normal and thrust faulting and to definethe state of stress for these conditions (see Sidebar3A). They showed that Ko, or equivalently the hori-zontal stress, within Appendix Eq. 1 is defined bythe internal friction angle ( = 30 for sand) and is 13 for the minimum stress during normal faulting and3 for the maximum stress during thrust faulting. Forthe normal faulting case and correctly including porepressure in Appendix Eq. 1, the total minimum hori-zontal stress becomes

(2)

where Ko = 13 with = 30. For this case the horizon-tal stress is much less than the vertical stress exceptin the extreme geopressure case of pore pressureapproaching overburden, which causes all stressesand pore pressure to converge to the overburdenstress. For the thrust faulting case, the larger horizon-tal stress (i.e., for the two horizontal directions) isgreater than the overburden and the smaller horizon-tal stress is equal to or greater than the overburden.Both the extreme geopressure case and an activethrust faulting regime can lead to either vertical orhorizontal fractures. The author has found AppendixEq. 2 to accurately predict the horizontal stress in tec-tonically relaxed sandstone formations ranging frommicrodarcy to darcy permeability. The accuracy at the high range is not surprising, as the formationsapproach the unconsolidated sand in the sandboxexperiments. The accuracy obtained for microdarcy-permeability sands is subsequently explained.

Hubbert and Willis also provided an important setof postulates: the rock stresses within the earth aredefined by rock failure from tectonic action and theearth is in a continuous state of incipient faulting.From this perspective, the stress is not governed by the behavior of the intact rock matrix, but by anactive state of failure along discrete boundaries (e.g.,by sand grains within fault boundaries, whichexplains the application of Appendix Eq. 2 to micro-darcy-permeability sandstones). This insightful con-clusion about the role of failure is at the otherextreme of the behavior spectrum from the elasticassumptions that Poissons ratio (Appendix Eq. 1)governs the horizontal stress and that failure has noeffect on the stress. This extreme difference in theassumptions for Appendix Eqs. 1 and 2 is oftenoverlooked because of the similar value of Ko = ~13obtained in the case of a tectonically relaxed regionand Poissons ratio near 14. However, the role of elas-ticity becomes important in thrusting areas (seeSection 3-5.2) because of the difference in horizontalstress resulting for layers with different values ofYoungs modulus (stiffness). More of the tectonicaction and higher levels of stress are supported by thestiffer layers.

Additional considerations for horizontal stress out-lined by Prats (1981) include the role of long-termcreep. Creep deformation allows relaxation of thestress difference between the overburden and hori-zontal stresses, thereby enabling the horizontal stressto increase toward the larger vertical stress governedby the weight of the overburden. This effect is wellknown for salt layers that readily creep and can col-lapse casing by transferring most of the larger over-burden stress into horizontal stress. The role of stressrelaxation is an important mechanism for providingfavorable stress differences between relatively cleansands governed by friction (i.e., Appendix Eq. 2) withminimal creep and sediments with higher clay con-tent. In the latter case, the clay supports some of theintergranular stresses. The clay structure is prone tocreep that relaxes the in-situ stress differences andincreases the horizontal stress for a clay-rich formation.

Hence, both clay content and Poissons ratio pro-duce the same effect on horizontal stress. Becauseclay content also increases Poissons ratio, there is a positive correlation of clay content (creep-inducedstress) to larger Poissons ratios (and elastic stress,from Appendix Eq. 1) inferred from sonic velocities.The implication of the correlation is that clay-rich

Reservoir Stimulation A5-5

h v p= +( ) ,2 3

formations can also have horizontal stresses greaterthan those predicted by either Appendix Eq. 1 or 2,which is consistent with the general requirement tocalibrate elastic-based stress profiles to higher levelsof stress (e.g., Nolte and Smith, 1981). The correla-tion of clay and Poissons ratio links the conclusionsof Hubbert and Willis and Prats that horizontal stressis governed primarily by nonelastic effects and thegeneral correlation between the actual stress andelastic/sonic-based stress profiles.

The third significant paper from this period is byLubinski (1954). He was a Stanolind researcher whointroduced the role that poroelasticity can have ingenerating larger stresses during fracturing. (Poro-elasticity could increase horizontal stress and lead to horizontal fractures, as in the Stanolind patent.)Lubinski presented poroelasticity within the contextof its analogy to thermoelasticity. His use of the ther-mal stress analogy facilitates understanding the poro-elastic concept because thermal stresses are generallymore readily understood than pore stresses by engi-neers. The analogy provides that when pore pressureis increased in an unrestrained volume of rock, therock will expand in the same manner as if the tem-perature is increased. Conversely, when the porepressure is lowered, the rock will contract as if thetemperature is lowered. When the rock is con-strained, as in a reservoir, a localized region of porepressure change will induce stress changes: increas-ing stress within the region of increasing pore pres-sure (e.g., from fracturing fluid filtrate or water

injection) and decreasing stress within the region of decreasing pore pressure (e.g., production). Thelong-term impact of Lubinskis paper is that theimportance of poroelasticity increases as routinefracturing applications continue their evolution tohigher permeability formations. This is apparentfrom the thermal analogyas the area of expansionincreases the induced stresses also increase. Forporoelasticity, the area of significant transient changein pore pressure increases as the permeabilityincreases (see Section 3-5.8).

Appendix Fig. 3 shows an example of significantporoelasticity for a frac and pack treatment in a 1.5-darcy oil formation. The time line for the figurebegins with two injection sequences for a linear-gelfluid and shows the pressure increasing to about7500 psi and reaching the pressure limit for the oper-ation. During the early part of the third injectionperiod, crosslinked fluid reaches the formation andthe pressure drops quickly to about 5600 psi (thenative fracturing pressure) and remains essentiallyconstant during the remainder of the injection.

The first two injections, without a crosslinked-fluidfiltrate (or filter cake) to effectively insulate the for-mation (as in the thermal analogy) from the increas-ing injection pressure, resulted in pore pressureincreases of significant magnitude and extent withinthe formation. The pore pressure increase provides upto a 1900-psi horizontal and poroelasticity stressincrease that extends the fracturing pressure beyondthe operational limit, leading to the shut-in for the

A5-6 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

Appendix Figure 3. High-permeability frac and pack treatment (Gulrajani et al., 1997b).

10,000

8000

6000

4000

2000

0

Botto

mho

le p

ress

ure,

BHP

(ps

i)

50

40

30

20

10

0

Injec

tion r

ate (b

bl/mi

n)

0 0.5 1.0 2.0 13.0 13.5 14.0

Time (hr)

Linear gel

Linear gel Crosslinked gel

Step rateInjection

BHPInjection rate

Step rate Minifracture Propped fractureInjection

second injection. This increase is about one-third ofthe native stress. However, during the two subsequentinjections the insulating effect of the crosslinkedfluids internal cake and filtrate allows fracture exten-sion within essentially the native stress state. Thepressure drop supported by the cake and filtrate isabout 1300 psi, as reflected by the rapid pressuredecrease after the third injection. This decreaseoccurs because of the rapid closure and cessation offluid loss (that activated the pressure drop), which isthe same reason that surface pressure decreases at thecessation of injection and loss of pipe friction. Thelast injection for the proppant treatment is also ofinterest because of the absence of a poroelastic effectduring the initial linear-gel injection. This observationindicates that the insulating effect remained effectivefrom the prior injection of crosslinked fluid.

For a normally pressured and tectonically relaxedarea, the maximum increase in horizontal stressbefore substantial fracture extension is about one-third of the native horizontal stress (Nolte, 1997), as was found for the case shown in Appendix Fig. 3. Also, for any pore pressure condition in a relaxedarea, the stress increase will not cause the horizontalstress to exceed the overburden (i.e., cause horizontalfracturing). However, as the example shows, withoutfluid-loss control, poroelasticity can significantlyincrease the fracturing pressure and extend it beyondoperational limits for high-permeability reservoirs.

Width modelsThe first rigorous coupling of fluid flow and the elas-tic response of the formation was reported byKhristianovich and Zheltov (1955). They used a two-dimensional (2D) formulation based on a complexvariable analysis. Their formulation was equivalentto the length becoming the characteristic, or smaller,dimension and provides the initial K for the KGDwidth model discussed later and in Chapter 6. Inaddition to being the first paper to provide the cou-pling of fluid flow and rock interaction that is theembodiment of the hydraulic fracturing process, thepaper also identified the role for a fluid lag region atthe fracture tip. This low-pressure region, beyond thereach of fracturing fluid and filling with pore fluid,has a large, negative net pressure and acts as a clampat the fracture tip. The fluid lags clamping effectprovides the natural means to lower the potentially

large tip-region stresses to a level that can be accom-modated by the in-situ condition. The presence ofthe lag region has been demonstrated by field experi-ments at a depth of 1400 ft at the U.S. Department ofEnergy (DOE) Nevada Test Site (Warpinski, 1985).

Appendix Fig. 4 compares the Khristianovich andZheltov analytical results for width and pressure tothe corresponding parameters from the Warpinskifield results. For the analytical results, decreasingvalues of the complex variable angle 0 toward theright side of the figure correspond to relativelysmaller lag regions and larger differences betweenthe minimum stress and pressure in the lag region(i.e., generally deeper formations). The width pro-files clearly show the clamping action at the tip, andthe field data appear to be represented by a 0 valveof about /8 for the analytical cases. Also notewor-thy of the experimental results is that tests 4 through7 with water and test 9 with gel show similar behav-ior when test 4, which had a relatively low injectionrate, is ignored. Tests 10 and 11 were with a gelledfluid and clearly show progressively different behav-ior from the preceding tests because of the altered tipbehavior resulting from prior gel injections and theresidual gel filter cakes that fill the fracture apertureafter closure. The cakes have the consistency of sili-con rubber and functionally provide an analogoussealing affect for subsequent tests.

The practical importance of the lag region cannotbe overemphasized. The extent of the region, whichis extremely small in comparison with commercial-scale fractures, adjusts to the degree required toessentially eliminate the role of the rocks fractureresistance or toughness (e.g., see SCR GeomechanicsGroup, 1993) and to isolate the fluid path from allbut the primary opening within the multitude ofcracks (process zone) forming ahead of the fracture(see Chapters 3 and 6). The field data show thewidth at the fluid front is well established (i.e., gen-erally greater than 5% of the maximum width at thewellbore) and that fluid enters only a well-establishedchannel behind the complexity of the process zone.These aspects of the lag region provide great simpli-fication and increased predictablility for applyingcommercial-scale hydraulic fracturing processes.

A paper by Howard and Fast (1957), and particu-larly the accompanying appendix by R. D. Carter,provides the current framework for fluid loss. Thepaper identifies the three factors controlling fluidloss: filter-cake accumulation, filtrate resistance into

Reservoir Stimulation A5-7

the reservoir and displacement of the reservoir fluid(see Fig. 5-17 and Chapters 6 and 8). All three fac-tors are governed by the relation 1/ t (where t istime) for porous flow in one dimension. The coeffi-cient for this relation was termed the fluid-loss coef-ficient CL. The authors also provided the means todetermine the coefficient for all three factors usinganalytical expressions for the filtrate and reservoircontributions and to conduct and analyze the filter-cake experiment, which is now an American Petro-leum Institute (API) Recommended Practice.

Also of significance was presentation of the Carterarea equation, with area defined as the product of the

height and tip-to-tip length. This equation, based onthe assumption of a spatial and temporal constantfracture width, provided the first rigorous inclusionof fluid loss into the fracturing problem (see Chapter6). Equation 6-18, which is solved by Laplace trans-formation, is in terms of exponential and comple-mentary error functions and is not engineer friendly.This difficulty was soon overcome by developing atable for the more complicated terms in the equationusing a dimensionless variable (see Eq. 6-19) that isproportional to the fluid-loss coefficient (loss vol-ume) divided by the width (stored volume) andhence also related directly to the fluid efficiency

A5-8 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

Appendix Figure 4. Comparison of Warpinski (1985) field data (left) and Khristianovich and Zheltov (1955) analysis(right). wo and po are the wellbore values of width and pressure, respectively; x is the distance from the well.

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

w/w

o

0.6

0.5

0.4

0.3

0.2

0.1

0

w/w

o

1.0

0.8

0.6

0.4

0.2

0

p/p o

1.0

0.8

0.6

0.4

0.2

0

p/p o

45679

1011

Test

45679

10

Test

Width atfluid arrival

0.25 0.20 0.15 0.10 0.05 0Normalized distance from tip, (L x)/L

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Normalized distance from well, x/L

0.5 0.4 0.3 0.2 0.1 0Normalized distance from tip, (L x)/L

0 0.2 0.4 0.6 0.8 1.0Normalized distance from well, x/L

0 = 4

0 = 8

0 = 16

0 = 316

0 = 38

0 = 4

0 = 8

0 = 16

0 = 316

0 = 38

illustrated in Appendix Fig. 2. Nomographs for the complete equation were also developed (e.g., figs. 4-17 and 4-18 of the Howard and Fast Mono-graph). Eventually a simple and approximate expres-sion (Harrington et al., 1973) for the Carter equationprovided the basis for fracture design into the 1980s.The approximate expression is based on the relationat the top of Appendix Fig. 2. For these applications,the average width was first determined from either theKGD or PKN model, as discussed in the following.

Another 1957 paper was by Godbey and Hodges(1958) and provided the following prophetic phrases:By obtaining the actual pressure on the formationduring a fracture treatment, and if the inherent tec-tonic stresses are known, it should be possible todetermine the type of fracture induced. . . . Theobservation of both the wellhead and bottomholepressure during fracturing operations is necessary toa complete understanding and possible improvementof this process. These statements anticipated two ofthe important enablers for the second generation offracturing: the use of pressure in an manner analo-gous to well test characterization of a reservoir andemployment of a calibration treatment to improvethe subsequent proppant treatment (see Chapters 5, 9 and 10).

In 1961 Perkins and Kern published their paper on fracture width models, including the long aspectratio fracture (length significantly greater than height)and radial model (tip-to-tip length about equal toheight) as described in Section 6-2.2. They considered,for the first time, both turbulent fluid flow and non-Newtonian fluids (power law model) and providedvalidating experiments for radial geometry and therole of rock toughness.

Perkins and Kern also discussed fracture afterflowthat affects the final proppant distribution within thefracture. After pumping stops, the stored compres-sion in the rock acts in the same fashion as com-pressible fluids in a wellbore after well shut-in. Afterfracture shut-in, fluid flow continues toward the tipuntil either proppant bridges the tip or fluid lossreduces the fracture width and stored compression to the extent that the fracture length begins to recedetoward the wellbore (Nolte, 1991). The magnitude of the fracture afterflow is large compared with thewellbore storage case, as discussed later forAppendix Eq. 4.

The one shortcoming acknowledged by Perkinsand Kern was not rigorously accounting for the flowrate change in the fracture required by continuity(i.e., material balance). They assumed that the volu-metric flow rate was constant along the fractureslength, which does not account for the effects offluid loss and local rates of width change (storagechange). This assumption was later addressed byNordgren (1972), who provided closed-form equa-tions for the bounding cases of negligible fluid lossand negligible fracture storage (i.e., most fluidinjected is lost during pumping) for a long-aspectfracture and Newtonian fluid (see Section 6-2.2). Theinitial letters of the last names of the authors of thesetwo papers form the name of the PKN model.

The remaining paper of historic importance forwidth modeling is by Geertsma and de Klerk (1969).They used the Carter area equation to include fluidloss within the short-aspect fracture, as previouslyconsidered by Harrison et al. (1954) and Khristian-ovich and Zheltov (1955). Their initials coupled withthose of the authors of the latter paper form the nameof the KGD (or KZGD) width model.

Reservoir response to a fractureUntil the advent of numerical simulators, productionmodels for a fracture did not consider transient floweffects and were based on the FOI relative to thereservoirs radial flow response with no damage (skineffect = 0). The increase in production, relative to thecase before fracturing, can be significantly greaterthan the FOI measure because fracturing also by-passes near-wellbore damage. The enhanced stimula-tion benefit increases as the magnitude of the damageincreases. For example, removing a skin effect ofabout 25 increases production by about a factor of 4,whereas during the first generation a typical FOI targetwas about 2, relative to zero skin effect.

Papers considering finite-conductive fracturesbegan to appear in 1958 and are summarized in chap-ter 10 of the Howard and Fast (1970) Monograph.Craft et al. (1962) considered the combined effects offracture stimulation and damage bypass. Also of his-torical interest is that most of this work was per-formed on analog computers with electrical circuitsrepresenting the reservoir and fracture components.Recognition of the role of conductivity was importantbecause the idealized assumption of infinite conduc-

Reservoir Stimulation A5-9

tivity, with no pressure loss in the proppant pack,cannot result from an economics-based optimizedtreatment. The incremental production increase, byachieving the infinite-acting case, would not offsetthe operational cost for the additional proppant.

McGuire and Sikora (1960) presented a significantstudy of the production increase in a bounded reser-voir for a fracture with a finite conductivity kfw forthe proppant pack, where kf is the fracture permeabil-ity. The boundary and conductivity effects are sum-marized in the set of pseudosteady-state curvesshown in Appendix Fig. 5. The curves reflect differ-ent ratios of the fracture length relative to thedrainage radius re, with the vertical axis reflectingthe FOI as J/Jo and the horizontal axis reflectingdimensionless conductivity based on the drainageradius. The McGuire and Sikora curves were the pri-mary reservoir tool for fracture design and evalua-tion until the late 1970s.

Prats (1961) used mathematical analyses to con-duct a comprehensive consideration of finite-conduc-tivity fractures with the assumption of steady-stateflow (i.e., constant-pressure boundaries). He intro-duced a dimensionless conductivity that is essen-tially the inverse of the dimensionless fracture con-ductivity commonly used for transient analyses (i.e.,CfD = kfw/kxf = /2). Prats also introduced the con-cept of an effective (or apparent) wellbore radius rw.The effective radius allows describing the fractureresponse in terms of an enlarged wellbore radiuswithin the radial flow equation. This concept is illus-trated in Appendix Fig. 6 for pseudoradial flow(adapted from Cinco-Ley and Samaniego-V., 1981b).

The effective wellbore radius, coupled with the radialflow equation, provides a powerful tool for efficientlycalculating the FOI, or negative skin effect, providedby the fracture. Prats also considered fracture facedamage (or skin effect) and provided an optimizedtreatment based on a fixed amount of proppant.

Treatment optimizationOptimizing a fracture treatment is an essential part of maximizing its benefit (see Chapters 5 and 10).For this reason Prats (1961) optimization considera-tion is of historic importance, although proppant vol-ume is generally not a realistic criterion becauseproppant cost is only part of the investment for afracture treatment (e.g., Veatch, 1986; Meng andBrown, 1987). Prats proppant optimization condi-tion at CfD = 1.26 could be a practical target forhigh-permeability reservoirs; however, this value isabout an order of magnitude lower than the optimumcase for the long transient period of a very low per-meability reservoir.

Additional lessons are also provided by the appar-entwellbore concept. The first is that a fracture isequivalent to enlarging the wellbore and not increas-ing the formations global permeability. Incorrectlyconsidering a fracture to be a permeability increasecan lead to incorrect conclusions concerning reser-voir recovery and waterflood sweep. Another insightis the generally favorable economics for an effec-tively designed and executed fracture. A fracture

A5-10 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

Appendix Figure 5. McGuire and Sikora (1960) curves forfolds of increase (J/Jo) in a bounded reservoir of area A(acres).

14

12

10

8

6

4

2

0102 103 104 105 106

Relative conductivity, kfw 40k A

(

)(J/

J o)

7.

13ln

0.4

72r e r w

0.90.80.70.60.50.4

0.30.20.1

L/re = 1

Appendix Figure 6. Effective wellbore radius versusdimensionless fracture conductivity (Nolte andEconomides, 1991, adapted from Cinco-Ley andSamaniego-V., 1981b).

1.0

0.5

0. 1

0.010.1 1.0 10 100

Dimensionless fracture conductivity, CfD

Effe

ctive

wel

lbor

e ra

dius

, rw/x

f

CfD = 30

CfD = 0.2CfD =

kfwkxf

rw = 0.28 kfwk

rw = 0.5xf

11

treatment is equivalent to excavating a very largediameter borehole (e.g., hundreds of feet in mostcases) and therefore is an extremely cost-effectiveway to provide an equivalent excavation.

The most important optimization lesson is foundin Appendix Fig. 6 for the roles of conductivity kfw(achieved by proppant cost) and fracture penetration(achieved by fluid and other additive costs; seeChapter 7). The figure indicates that as CfD increasesbeyond 10, the effective wellbore radius approachesone-half of the fracture length and there are dimin-ishing returns for additional increases in conductivity(i.e., incurring proppant costs without an effectiveincrease in production rate). For this part of Appen-dix Fig. 6, the effective radius is constrained only by length and is termed the length-limited case.However, increasing both fracture length and con-ductivity to maintain a constant CfD achieves themost efficient conversion of length into an effectivewellbore radius. This conversion is the basis foreffectively fracturing low-permeability formations.

The practical limits for the length-limited case arereaching the drainage radius, increasing conductivitywithin the limits of achievable fracture width andefficiently extending a fracture when the pressurereaches the formation capacity, as discussed later. Aspermeability increases, and proportionally decreasesCfD, the ability to increase conductivity becomes the constraint. As CfD progressively decreases, theconductivity-limited case is reached. The figure indi-cates that as CfD decreases below 1, a log-log unitslope is approached that relates rw to kfw/k, with theobvious absence of an effect from length. When theunit slope is reached, near a value of 0.2, the well-bore drawdown completely dissipates within thefracture before reaching the tip, and the extremitiesof the fracture cannot provide a production benefit.For the conductivity-limited condition, the produc-tion rate can be increased economically only by pro-viding more conductivity kfw, with an obvious con-straint from the available fracture width developedduring the treatment. This constraint was significantlyextended by the third fracturing generation of TSOtreatments, which is discussed toward the end of thisAppendix.

Transition between the first and second generationsBy 1961, the design and evaluation tools for most of the next two decades had been established by thecontributions discussed. Incremental development ofthese tools slowed because fracturing was considereda mature technology. Also affecting technical devel-opment was the degrading economics for lower qual-ity reserves as oil import-export increased and frac-turing activity decreased (Appendix Fig. 1). Thiscondition did not change until the mid-1970sbrought natural gas shortages and higher gas pricesto the United States. Higher prices produced theincentive to develop extensive regions of tight gasreserves with fractures targeting the FOI = 10 rangeof the McGuire and Sikora curves (Appendix Fig. 5).Before this period, typical fracturing targets were oilreservoirs with an FOI of about 2, with FOI relativeto an undamaged wellbore. However the FOI = 10target required about an order-of-magnitude increasein the volume and cost for a typical treatment andwas hence termed massive hydraulic fracturing.

This new target introduced higher temperaturereservoirs, typically of tight gas, that generallyexceeded the performance limits for fracturing fluidsystems. These conditions stretched the so-calledmature technology in almost every conceivable wayand resulted in a bumpy journey because of the pro-portionally large economic penalty when a treatmentfailed to meet expectations. However, reports of suc-cessful field development (e.g., Fast et al., 1977)encouraged continued interest in tight gas develop-ment.

Realistic estimate of conductivityCooke (1975) reported realistic experiments for char-acterizing the conductivity of proppant packs. Hisprocedure formed proppant packs from a slurry com-posed of polymer-based fluids by using a cell withrock faces that allowed fluid loss and the subsequentapplication of closure stress. The Cooke cell is nowa standard apparatus for a fracturing fluid laboratory

Reservoir Stimulation A5-11

(see Chapter 8). The experiments showed that theretained pack permeability could be very small.These results were unexpected because prior testingprocedures did not use fracturing fluids or stress lev-els for deeper gas reserves. The primary differenceresulted because the rock acts as a polymer screen at moderate and smaller permeability levels, whichsignificantly increases the polymer concentrationremaining within the proppant pack porosity afterfracture closure.

Cooke also provided a simple mass-balance rela-tion for this important consideration. The concen-tration factor for the polymer and other additivesremaining in the fracture relative to the originalconcentration can be expressed as

(3)for a typical proppant pack porosity of 0.33 andproppant specific gravity (s.g.) of 2.65. The relationdepends on the average concentration definedas the total pounds of proppant divided by the totalgallons of polymer-based fluid. This relation indicatesa polymer concentration increase of 20 or greater fortypical treatments at that time (e.g., of 1 to 2 lbm). This unexpected discovery of a significantreduction in retained permeability, coupled with theprior discussion on conductivity and effective well-bore radius, partly explains the difficult transition tomassive treatments.

Cookes pioneering work had obvious effects onproppant schedules for treatments and laboratorytesting procedures. Equally important, the work initi-ated substantial product development activities, asdiscussed in Chapter 7. These include improvedproppants, beginning with Cookes work on bauxitefor high crushing stress, improved breaker chemistryand breaker encapsulation, large reductions of poly-mer concentration for crosslinked fluids, foams andemulsions, and residue-free viscoelastic surfactantsystems. The evolution of fracturing fluid chemistrywas reviewed by Jennings (1996).

Height growth and proppant transportSimonson et al. (1978) presented the mechanics gov-erning fracture growth into a layer with higher stress,complementing the postulate by Harrison et al. (1954)concerning the role of stress for height confinement.The analysis considered a three-layer case for twosymmetric barriers (i.e., two barriers extending

infinitely above and below the pay section with eachbarrier having the same magnitude of stress). Thethree-layer case provided insight into how to adaptmore general relations to any number of layers (e.g.,Nolte and Smith, 1981; chapter 3 of Gidley et al.,1989). These relations led to the calculations employedin pseudo-three-dimensional (P3D) fracture simulators(see Section 6-3.2).

Novotny (1977) outlined a comprehensive basis forproppant transport calculations and in particular identi-fied the important roles of channel shear rate and frac-ture closure in determining the ultimate placement ofproppant (see Section 6-5.3. Both effects produce moreproppant fall. For non-Newtonian fluids, the effectiveviscosity for sedimentation is determined from the vec-toral sum of the shear rate in the channel and thatcaused by proppant fall (as for stagnant fluid). Thissum is generally dominated by the channel flow and is much greater than that for a particle in stagnant fluid(i.e., higher shear rate and lower viscosity). In addition,the closure period prolongs the time for proppant falland maintains the channel flow to reduce the effectiveviscosity. Novotny also provided a brief analysis of thevolume balance during closure, which is the essentialingredient for the fracturing pressure decline analysis(e.g., Nolte, 1979) that is used for calibration treat-ments (see Section 9-5).

Transient reservoir responseThe FOI consideration for fracture production wasfound to be completely inadequate for the substantialperiod of transient flow that occurs in tight formations(see Section 12-2). The first tool for finite-conductivitytransient flow was type curves provided by Agarwal et al. (1979). Although these curves were developedfrom numerical simulators, access to computers wasgenerally outside the reach of most engineers. Theseand similar type curves became the standard evalua-tion tool to assess production from a fracture treat-ment. Type curves were also used for optimizing treat-ment design. By the mid-1980s, as general access tocomputers increased, the use of type curves began todecrease accordingly.

Cinco-Ley and Samaniego-V. (1981b) providedseveral advancements for understanding and quanti-fying the transient behavior of a reservoir fracturesystem. In addition to advancing the effective well-bore concept (e.g., Appendix Fig. 6) and type curves,they identified and provided comprehensive descrip-

A5-12 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

CF ppa= 44 / ,

tions for the distinctive transient regimes resultingfrom a finite-conductivity fracture (see Section 12-2).

The bilinear flow regime, generally the first tooccur during production or a well test, was para-mount for bridging the gap between fracture designand subsequent evaluation based on production orwell tests. For permeability in the range of 10 d, thebilinear period can last on the order of a year or morefor a long fracture (>2500 ft from the well). Duringbilinear flow the stabilized pressure drawdown pro-gresses along the fracture length. During this period,it is not possible to determine the length of the frac-ture from a well test or production data because thetotal length has not had time to effectively experiencethe wellbore drawdown. Therefore, a meaningfulevaluation for fracture length cannot be obtained untilthe bilinear period ends and the transient responseprogresses toward pseudoradial flow (potentially sev-eral years). An obvious implication in this case is thata standard well test cannot be used to determine frac-ture length; the length can be determined only fromlong-term production data. They also identifiedanother important aspect of bilinear flow that occursbecause of the transient flow condition within theproppant pack: the fracture conductivity can be char-acterized, independent of length and hence most reli-ably, by the slope of a plot of pressure versus thequarter-root of time.

Recognition of these consequences for bilinearflow also explains the difficult transition to the suc-cessful application of massive treatments. Well testinterpretations misinformed instead of informed.They indicated relatively short fracture lengths thatwere assumed to be treatment placement failures andled to the common and contradicting result: how can1 million lbm of sand be contained in a fracturelength of only 100 ft? Much longer propped lengthswere later substantiated by production data after thebilinear period had ended (e.g., values of fracturehalf-length xf > 5000 ft; Roberts, 1981). Anothercontribution to incorrect interpretations was ignoringCookes (1975) report of very low retained-pack per-meability, which led to overly optimistic estimates ofconductivity and proportionally pessimistic estimatesof length. The coupling of these two factors pro-duced incorrect and negative assessments for manyearly attempts to establish massive fracturing as aviable means of developing tight gas formations.

These advancements and insight from Bennett et al. (1986) for layered formations provide a solidfoundation for the reservoir response to fracturing.

The second generation: massive fracturingAs indicated in the preceding section, the bumpyroad to successful massive fracturing also includedmassive penalties because the cost of a fracture treat-ment could become equivalent to the well cost. Thecombined effect of many companies experiencing$500,000 treatments that did not provide commercialwells resulted in a significant investment for fractur-ing research. One result of this effort is the SPEMonograph Recent Advances in Hydraulic Frac-turing (Gidley et al., 1989). The manuscripts for thiscomprehensive volume, with more than 30 contribu-tors, were completed in 1984, only five years afterthe 1979 SPE annual meeting provided the firstmeaningful number of papers from this researcheffort. The papers presented at this meeting weresignificant also because they presented a key thatenabled the reliable application of massive fracturingand rapid progression of the treatment size recordfrom 2 million lbm in 1979 to more than 7 millionlbm by 1986.

The key was that, for the first time in its 30-yearhistory, fracturing was considered in a frameworksimilar to that used for reservoir characterization.The reservoir framework consists of pressure tran-sient analysis for the flow characteristics, wirelinelogs for the formation parameters and geophysics for the macroview. The 1979 papers include the fol-lowing (a different reference year indicates the publi-cation date): Logging: Rosepiler (1979) introduced application

of the long-spaced sonic tool to infer stress in dif-ferent layers (see prior discussion of stress con-cerning Appendix Eq. 2 and Chapter 4). Dobkins(1981) presented improved cased hole loggingprocedures for inferring the fracture height thatwere also used by Rosepiler to qualitatively vali-date his novel use of mechanical property logs.

Pressure transient analysis (PTA): Nolte and Smith(1981) introduced the role of pumping pressures by

Reservoir Stimulation A5-13

using a log-log plot as a diagnostic tool (similar toPTA practice) for fracture growth characteristics,the role of pressure simulation for quantifyinggeometry (including height growth) and the role ofcalibrated stress profiles obtained from mechanicalproperty logs. Nolte (1979) introduced the role ofpressure during the postinjection closing period toquantify fluid loss and predict fracture width andlength by using a specialized time function in amanner analogous to the Horner plot. The combi-nation of these two papers provided a foundationfor the common use of the calibration treatmentand pressure-history matching for defining designparameters (see Chapter 9). Appendix Fig. 7 illus-trates the fracturing pressure for three distinct phas-es: pumping, closing and the after-closure period.

Geophysics: Smith (1979) introduced the role ofmapping fracture trajectories by using surface tilt-meters and borehole passive seismic techniques toimprove reservoir recovery by the correct place-ment of infill wells (see Section 12-1).A companion paper in 1980 showed the synergis-

tic benefit when these individual considerations areunified for tight gas exploitation (Veatch andCrowell, 1982).

Fracturing pressure: analog of reservoirresponseAn important component of fracturing pressureanalysis is the closure pressure. The closure pressureis the datum for the net pressure that constrains the

width prediction, provides an analog of the reservoirpressure and reflects the height-averaged minimumstress for the pay zone (see Sidebar 9A). The frac-ture width is proportional to the net pressure. Thedata in Appendix Fig. 7, one of the first recordingsof bottomhole pressure during a treatment, are simi-lar to the reservoir response for an injection test witha pressure increase (pumping) and subsequent falloff(closing). The injection pressure is governed by theevolving fracture geometry, and the closure data aregoverned by the fluid loss. These two conditions,respectively, enable characterizing the stored and lostcomponents of the volume-balance equation shownin Appendix Fig. 2. After closure, the pressure isindependent of the fracture parameters and dependson the reservoir response to the fluid lost during thetreatment.

The fundamental analogy between reservoir andfracturing behavior results because a diffusion-typeprocess governs both behaviors. The respective reser-voir and fracturing equivalents are kh/ w2h/(transmissibility), where k is the permeability, h is thereservoir thickness, w is the width, and is theappropriate fluid viscosity, and ct h/(wE) 1/pnet(storage capacity of the reservoir), where is theporosity, ct is the total system compressibility, and Eis the formations elastic modulus. The last expres-sion for storage contains an inverse proportionality tothe net fracture pressure pnet. This can be written interms of the fracture volume Vf, fluid pressure pf andclosure pressure pc.

(4)

(5)

This equation implies that the elastic formation,compressed to contain the fractures volume, pro-duces a system compressibility analogous to an equalvolume of perfect gas at a pressure equal to the frac-tures net pressure. The result is a significant storagecapacity considering typical conditions with morethan 1000 bbl for fracture volume and only hundredsof pounds per square inch for net pressure. The laststorage relation, for constant lateral dimensions, isimportant for a TSO, as discussed later.

A5-14 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

Appendix Figure 7. Bottomhole fracturing pressure(Nolte, 1982).

38 40 42 44 46 48 50 56 58

9000

8000

7000

6000

5000Botto

mho

le p

ress

ure,

pw

(ps

i)

Clock time (hr)

Fracturetreatment Fracture

closingTransient reservoir

pressure near wellbore

Pressure decline

Net fracturepressure

pnet = pw pc

Fracture closes on proppant at well

Closure pressure pc = horizontal rock stress

Pressure from bottomhole bombInferred pressure

Reservoir pressure

1 1 1V

dVdp p p pf

f

f net f c= =

1w

dwdp p

h Lnet net

= 1

for constant and .

Fracture simulatorsDescribing a hydraulic fracture produces a signifi-cantly more complex role for the diffusive processthan the reservoir case because the basic parametergroups change continuously with time, with a nonlin-earity for the equivalent permeability, and the far-field elastic coupling between width and pressureproduces local parameters that have a general depen-dence on the pressure everywhere within the frac-tures unknown boundaries. For these reasons, frac-ture simulators that rigorously and robustly couplethese parameters in a general manner (see Section 6-3) have not progressed at the same rate as reservoirsimulators.

The modeling difficulties led to widespread use ofsimulators based on P3D assumptions that partiallycircumvent the far-field elastic-coupling condition.The two most common means were relaxing the lat-eral coupling in the long direction of the fracture (asfor the PKN model) to allow a cellular representationand vertical height growth of the cells (e.g., Nolte,1982) or prescribing the boundary and width profilesby elliptical segments and a lumped dependence onthe governing parameters (e.g., Settari and Cleary,1986). P3D models, or more precisely P2D models,evolved to include automated proppant schedulingand the temperature-exposure history for polymer andadditive scheduling (e.g., Nolte, 1982), acid fractur-ing (e.g., Mack and Elbel, 1994), economic optimiza-tion for treatment design (e.g., Veatch 1986; Mengand Brown, 1987), automated pressure-history match-ing (e.g., Gulrajani and Romero, 1996; Gulrajani etal., 1997b) and rigorous 2D slurry flow (e.g., Smithand Klein, 1995).

Originally restricted to in-office use, these modelsmerged with on-site fracture monitoring systems toprovide treatment evaluation and simulation in real-time mode. An equally important advance was theparallel evolution of process-controlled mixing andblending equipment for reliable execution of moredemanding treatment schedules and progressivelymore complex chemistry that requires precise pro-portioning (see Chapters 7 and 11).

Fracture mapping and model validationAn important achievement was the definition of frac-ture length, height and width by employing passiveseismic measurements and tiltmeters in observation

wells (Warpinski et al., 1996; see Section 12-1). Theimportance of these measurements for fracture designand evaluation cannot be overemphasized. Indepen-dent measurements for each component of the frac-ture volume (Appendix Fig. 2) provide a long-awaitedbenchmark for validating fracture models.

Like the first generations failure to find a consen-sus for width models (e.g., Perkins, 1973), pressure-history matching could not resolve the second gener-ations conflicting adaptations of the P3D framework(see Chapter 6). The convergence of modelingassumptions failed for several reasons. The first wasfundamental to the pressure-matching process andresults because of the multitude of opportunities fornonuniqueness. Another reason was the failure toachieve a dominant industry opinion on either thetechnique or procedures for a specific technique todefine closure pressure (e.g., Plahn et al., 1997). Thisstate of affairs allowed selecting a closure pressureprocedure to validate particular modeling assump-tions and therefore justify relatively arbitrary and adhoc modeling assumptions. Techniques to determinethe closure pressure are discussed in Section 3-6 andthe Appendix to Chapter 9.

Because of nonuniqueness in the reservoir responseand the basing of reservoir models on overly idealizedmodeling assumptions for a fracture, the reservoirresponse cannot generally provide an effectiveconstraint on the achieved fracture length (Elbel andAyoub, 1991; Nolte and Economides, 1991). Mappingconstraints on all three fracture dimensions provide aunique, objective test of the geometry model assump-tions (e.g., Gulrajani et al., 1997a) and a basis forrationally judging and selecting the model complexityappropriate for the specific application, available dataand simulation resources.

Treatment design and evaluationThe primary fracture evaluation advance from themassive treatment generation is the calibration treat-ment performed before the proppant treatment todefine placement parameters. Combining the calibra-tion treatment and the purpose-designed TSO treat-ment produced the primary treatment innovation ofthe second generation. The calibrated TSO treat-ment, developed by Smith et al. (1984), became thekey to the third fracturing generation (discussedlater) and essentially removed width as a constraintfor the conductivity required to successfully fracture

Reservoir Stimulation A5-15

very high permeability formations. This capabilityand timing produced the overly optimistic predictionin 1985 for the beginning of the TSO generation, asindicated by Appendix Fig. 1a.

Transition between the second andthird generationsThe following paragraphs link several aspects of themassive and TSO generations by using the informa-tion available from the diagnostic log-log plot forfracturing in Appendix Fig. 8. Appendix Table 1 liststhe interpretations for various slopes exhibited in thefigure by the net pressure during fracturing. The dataare from two massive treatments in tight gas forma-tions. The top curve is a treatment in the Wattenbergfield, the first microdarcy-permeability field develop-ment (Fast et al., 1977). The behavior shown by thelower treatment curve, which was designed by thisauthor, provided insight for developing the TSOtreatment that enables successfully fracturing darcy-scale oil formations. The treatment related to thelower curve was not particularly successful. How-ever, it was one of the first 2 million lbm treatmentsand hence functioned better as a sand-disposaltreatment than a gas-stimulation treatment. The sandwas disposed of with 900,000 gal of crosslinked fluidcontaining 90 lbm/1000 gal of polymer, or approxi-mately 80,000 lbm of polymer.

The marginal success of the treatment is readilyunderstood by considering Appendix Eq. 3. For thetreatment average of 2.1 ppa, the equation predicts1900 lbm/1000 gal crosslinked fluid (in reality, asolid) remaining in the proppant pack porosity afterthe treatment. However, the size and viscosity forthis treatment provided an ideal test condition ofhow a formation responds to fluid pressure and anexcellent illustration for the concept of formation

capacity. The capacity (Nolte, 1982) defines the pres-sure limit for efficient fracture extension and is anal-ogous to the pressure-capacity rating for a pressurevessel. The cited reference has an unsurprisingtheme of the negative effects of excesses of pressure,polymer and viscosity.

Three mechanisms for a formation can define itspressure capacity before rupture accelerates fluidloss from the formations pay zone. The subsequentfluid loss also leaves proppant behind to furtherenhance slurry dehydration and proppant bridging.Each mechanism is defined by the in-situ stress stateand results in a constant injection pressure condition,or zero log-log slope, when the net pressure reachesthe mechanisms initiation pressure. The mecha-nisims are

A5-16 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

Appendix Figure 8. Log-log diagnostic plot for fracturing(Nolte, 1982).

*x

2000

1000

500

[5 MPa]

Net p

ress

ure,

pne

t (psi)

log

p net

40 60 100 200 400 600 1000Time (min)

log time or volume

Idealized Data

Field Data

III

II

II

III-a

III-a

III-b

IV

Inefficient extension for pnet formation capacity pfc

I

Proppantbegins

Proppantbegins

Variable injection rate

III-a

III-bII

IIV

Appendix Table 1. Slopes of fracturing pressures and their interpretation in Appendix Fig. 8.

Type Approximate log-log slope value Interpretation

I 18 to 14 Restricted height and unrestricted expansionII 0 Height growth through pinch point, fissure opening

or T-shaped fracture

III-a 1 Restricted tip extension (two active wings)III-b 2 Restricted extension (one active wing)IV Negative Unrestricted height growth

opening the natural fissures in the formation, gov-erned by the difference in the horizontal stresses

extending the height through a vertical stress bar-rier and into a lower stress (and most likely per-meable) zone, governed by the difference in thehorizontal stress for the barrier and pay zone

initiating a horizontal fracture component whenthe pressure increases to exceed the level of theoverburden stress.An important observation for the pressure capacity

is that it depends on the in-situ stress state and there-fore does not change for the formation in other welllocations unless there are significant local tectoniceffects. As a result, all future treatments for the fieldcan generally be effectively designed on the basis ofonly one bottomhole pressure recording and itsdetailed analysis (see Section 9-4).

The upper curve on Appendix Fig. 8, for theWattenberg treatment, illustrates the fissure-openingmechanism with the Type II zero slope occurring at a net pressure of 1700 psi. This value provides one ofthe largest formation capacities ever reported. The fis-sure opening is preceded by restricted height growthand unrestricted extension (Type I slope) that providethe most efficient mode of fracture extension. There-fore, conditions in this formation are favorable forpropagating a massive fracture; not by coincidence,this was the first field successfully developed in themassive treatment generation (Fast et al., 1997), and itprovided incentive to continue the development ofmassive treatment technology. Returning to AppendixFig. 8, after the period of constant pressure andenhanced fluid loss, a Type III-a slope for a fracturescreenout occurs because slurry dehydration formsfrictional proppant bridges that stop additional exten-sion (i.e., a generally undesired screenout for a tightformation requiring fracture length over conductivity).After the penetration is arrested, the major portion ofthe fluid injected is stored by increasing width (seeAppendix Eq. 4) and the net pressure develops the unitslope characteristic of storage. The amount of widthincrease is proportional to the net pressure increase.

The Wattenberg treatment consisted of 300,000 galof fluid and 600,000 lbm of sand with an averageconcentration of 2 ppa, similar to the previous exam-ple. However, the treatment was successful becausea polymer-emulsion fluid with low proppant packdamage was used. After the treatment defined theformation capacity, model simulations indicated that

the required penetration could be obtained by notexceeding the formation capacity. A subsequent treat-ment designed using 150,000 gal and 900,000 lbm ofsand (an average of 6 ppa) became the prototype forthe remaining development of the field (Nolte, 1982).

The lower curve on Appendix Fig. 8 is for theaforementioned sand-disposal treatment in the Cot-ton Valley formation of East Texas. As previouslydiscussed, the treatment provided an opportunity toobserve a large range of fracturing behavior with fivetypes of interpretive slopes occurring, including Type I indicating extension with restricted height

growth

Type II defining this formations lowest pressurecapacity at 1000 psi for the penetration of a stressbarrier

Type IV, with decreasing pressure, indicating unre-stricted vertical growth through a lower stresszone after the barrier was penetrated.The Type IV condition continued until proppant

was introduced. Almost immediately after proppantentered the fracture the pressure increased, mostlikely because the proppant bridged vertically in thewidth pinch point formed by the penetrated stressbarrier and restricted additional height growth.During the preceding 6-hr period of significant verti-cal growth, the horizontal growth was retarded. As aresult, the very high polymer concentration formed athick polymer filter cake at the fracture tip that proba-bly restricted further horizontal extension. Thus, theextremities of the fracture were restricted either byproppant or polymer cake, and continued injectionwas stored by increasing width indicated by the TypeIII-a unit slope. After a significant increase in pres-sure, the pressure became constant for a short periodat 1200 psi with a Type II slope that probably resultedfrom opening natural fissures to define a second,higher capacity. Subsequently the slope increased toan approximately 2:1 slope indicated as Type III-b.This latter slope for a storage mechanism indicatesthat about one-half of the fracture area had becomerestricted to flow, which could have resulted from onewing of the fracture being blocked to flow near thewell because of slurry dehydration from the fissurefluid loss. The wellbore region experiences the largestpressure and is most prone to adverse fluid-losseffects from exceeding a capacity limit.

Reservoir Stimulation A5-17

Subsequent treatments were improved after under-standing the formations pressure behavior as in theWattenberg case and for this area after understandingthe implications of Appendix Eq. 3 for concentratingpolymer. In addition, the observation that proppantbridging could restrict height growth was developedfor treatments to mitigate height growth (Nolte,1982). An effective and relatively impermeablebridge can be formed within the pinch point to retardheight growth by mixing a range of coarse and finesand for the first sand stage after the pad fluid.

Smith et al. (1984) later sought a means to signifi-cantly increase fracture width for the development ofa chalk formation within the Valhall field in theNorwegian sector of the North Sea. The additionalwidth was required because laboratory tests indicatedthe likelihood of substantial proppant embedmentinto the soft formation that would lead to the loss ofeffective propped width. Fracturing was consideredfor this formation because other completion tech-niques would not sustain production because of chalkflow. The resulting treatment design was based on thebehavior on the log-log plot in Appendix Fig. 8 forthe sand-disposal treatment: a purpose-designed TSOtreatment. For the disposal treatment, they observedthat after the initial screenout occurred, 2 million lbmof proppant could be placed, and the net pressureincrease indicated that this occurred by doubling thewidth after the screenout initiated.

Smith et al. designed and successfully placed aTSO treatment in which proppant reached the tip andbridged to increase the width by a factor of 2 duringcontinued slurry injection after the purpose-designedTSO occurred. This design, with successful place-ment of progressively larger propped width increases,became the tool that enabled the development of thisformation. The ability to significantly increase thewidth after screenout results from the large storagecapacity of a fracture, as detailed in the discussionfollowing Appendix Eqs. 4 and 5. Additional discus-sion on the fracture completion in Valhall field andthe TSO treatment is in the Reservoir and WaterManagement by Indirect Fracturing section.

As a historical note, a similar concept for a TSOwas disclosed in a 1970 patent (Graham et al.,1972), with the bridging material consisting of petro-leum coke particles (approximately neutral density toensure transport to the extremities). The patents goalwas increased width to enable placing larger sizeproppant in the fracture.

The third generation: tip-screenouttreatmentsA proper historical perspective of this third genera-tion requires perspective from the next generations;however, several of its developments are reviewedhere. A more comprehensive presentation and refer-ence are by Smith and Hannah (1996).

Demonstration of the ability to routinely place asuccessful TSO treatment opened the door for effec-tive fracture stimulation of higher permeabilityformations. Another component for the successfulfracturing of high permeability was the continueddevelopment of synthetic proppants that can producea cost-effective 10-fold increase in permeability rela-tive to sand for higher closure stresses (see Chapter7). Coupling this increase in permeability with thesimilar increase for propped width achieved by aTSO treatment in a moderate- to low-modulus for-mation provides about a 100-fold increase in con-ductivity over a conventional sand fracture. Theconductivity increase also translates into a 100-foldincrease of the target permeability for fracturing, asimplied by Appendix Figs. 5 and 6. The increases forwidth and conductivity also mitigate nondarcy (orturbulent) flow effects in the fracture for high-ratewells, particularly gas wells (see Sections 10-7.3 and12-3.1).

However, the anticipated growth rate shown onAppendix Fig. 1a was slowed not only by the unan-ticipated, extensive contraction of activity in general,but also by two prevailing mind sets: high-perme-ability formations cannot be successfully fracturestimulated and why fracture a commercial well?Additional field proof for the benefits of a TSO treat-ment came from two successful programs: a signifi-cant improvement over conventional fracture treat-ments for the Ravenspurn gas field in the southernNorth Sea (Martins et al., 1992b) and high-perme-ability applications in the Prudhoe Bay field (Hannahand Walker, 1985; Reimers and Clausen, 1991;Martins et al., 1992a).

Deep damageFracturing in Prudhoe Bay was particularly successfulbecause deep formation damage induced by prior pro-duction (i.e., beyond the reach of matrix treatments)facilitated sidestepping the mind set of not applying

A5-18 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

fracturing to high permeability. The incremental pro-duction from only one year of the fracturing programwould have ranked as the 10th largest producing fieldin the United States (e.g., Smith and Hannah, 1996),without including similar results achieved by anotheroperator in the other half of the field. Another signifi-cant aspect of the Prudhoe Bay application is that thefractures were routinely placed in a relatively small oilzone above a rising water zone without entering thewater zone (Martins et al., 1992a), which demon-strated that fracturing is a viable, potentially superioralternative to matrix treatments in high-permeabilityformations. This precise fracturing was achieved bycoupling an initial detailed fracture modeling studywith a calibration treatment before each proppanttreatment.

Frac and packThe frac and pack completion consists of a TSOtreatment before a conventional gravel pack. Duringthe early 1990s, frac and pack treatments wereapplied on a limited basis around the world, notablyoffshore Indonesia. Prior to the TSO treatment era,this technique was tried at various times but withoutsustained success. The large propped width from aTSO treatment was a necessary ingredient for suc-cessful frac and pack applications, as discussed later.

The frac and pack boom was in the Gulf ofMexico. The first successful application beganbecause of economic considerations and thereforeovercame the mind set of not fracturing a commer-cial well. A significant field development was notmeeting production expectations because standardgravel-packed completions could not consistentlyachieve a low skin effect; the skin effect rangedbetween 7 and 30. The skin effect was 10 after thefirst frac and pack treatment and progressivelydecreased to near zero from improvements in thetreatment design and the use of larger size proppant(Hannah et al., 1994).

The threefold-plus increase in production rate, byeliminating the skin effect, resulted from more thanjust adding a TSO treatment to the procedure. Animportant feature of a frac and pack is reduction ofthe inherent flow restriction around and through theperforations. The ring of proppant around the casing(Appendix Fig. 9) acts as an excellent external gravelpack for reducing the pressure drop through the per-forated region. The ring results from the large TSO

fracture width that mechanically must continuearound the wellbore; i.e., if the formation is pushedapart 2 in. over the large surface area of the fracture,the rock around the wellbore must be displacedaccordingly. For a well-designed and executed fracand pack, the initiating screenout at the tip is pro-gressively packed back to the well to completelypack the resulting ring.

The continuing success of the initial frac andpacks started a rapid conversion to this completion,with the frac and pack becoming the preferred Gulfof Mexico sand control completion. In addition tocontinued use offshore Indonesia, technology trans-fer resulted in a wider geographical distribution forthis sand control technique (e.g., West Africa,Gulrajani et al., 1997b).

As for other applications of TSO treatments, on-siteredesign after a calibration treatment became a stan-dard frac and pack practice. An important observationis that the same analysis procedures and design mod-els introduced for the massive treatments of tight gasformations in the late 1970s were transferred directlyto frac and pack treatments in soft formations.

Reservoir and water managementby indirect fracturingAnother application of TSO treatments is reservoirmanagement. The prototype example for this applica-tion was in the Norwegian Gullfaks field (Bale et al.,1994a, 1994b). The reservoir section had a multi-darcy-permeability upper zone that graded downwardto a permeability of about 100 md. The standard com-pletion was to perforate and gravel pack the upperzone. However, an edge-water drive would encroachthrough the high-permeability zone and turn a prolificoil well into an even higher water producer.

Reservoir Stimulation A5-19

Appendix Figure 9. Successfully packed-back TSO treat-ment.

Casing

Packed-backfracture

External gravel packconnecting all perforationswith propped fracture

A solution was found from the pioneering work of the Valhall TSO treatment discussed for AppendixFig. 8. This application in the early 1980s was formore than mitigating proppant embedment. The pri-mary objective was for controlling chalk productionfrom the primary producing zone above where theTSO treatment was placed. The upper chalk zonewas very soft with high porosity and composed ofalmost as much oil as chalk. When this zone was puton production, chalk filled the tubing and led to cas-ing collapse. The zone was produced by placing theTSO treatment in the more competent zone belowand extending the fracture height into the bottom ofthe very high porosity formation. This completionenabled chalk-free production from both the upperand lower zones (Smith et al., 1984).

This indirect access to the primary producing zonehas come to be known as an indirect vertical fracturecompletion (IVFC) and is illustrated in AppendixFig. 10. The technique of perforating and fracturingonly from competent sections and producing fromincompetent sections is a robust method for control-ling the production of formation material andincreasing recovery from the lower permeabilityzones by fracture stimulation. From this perspective,a TSO-IVFC becomes a solids control and reservoirmanagement application (see Section 5-1.2).

The Gullfaks adaptation by Bale et al. (1994a)also placed a TSO-IVFC in a lower competent partof the formation. In addition to providing sand con-trol and managing reservoir depletion, it was a watermanagement treatment because it delayed waterbreakthrough and greatly increased reserves recovery

from the lower sections by fracture stimulation and a significant increase in drawdown. This applicationcompletes the link between the sand-disposal thightgas treatment in Appendix Fig. 8 to reservoir andwater management with the intermediate develop-ment of the TSO-IVFC for solids control in theValhall field.

Screenless sand controlAnother apparent role of the IVFC is to eliminate theneed for a screen in many sand-control environmentsby selecting and perforating only competent sectionswithin or near the unconsolidated sections of the for-mation. The zone selection method can potentially beenhanced by a sonic log application. This applicationtakes advantage of the generally considered negativeeffect of near-wellbore refracted and relatively slowerwaves caused by the wellbore mechanical damagethat routinely occurs in weak or highly stressed for-mations (Hornby, 1993). However, for screenlesscompletions, the negative effect becomes a positiveeffect because the change in the wave speed for therefracted wave is a direct indication of the state ofrock failure around the well, which is caused by thewellbore stress concentration within the in-situ stressfield. Therefore, the layers with a minimal near-wellchange in wave speed relative to the far-field speedare the more competent candidate zones for perforat-ing and applying a TSO-IVFC to achieve screenlessformation-material-controlled production.

A second method of achieving a screenless sand-control completion is applied without strategicallyplaced perforations (e.g., Malone et al., 1997). Thismethod couples the proppant ring around the casingfrom a TSO treatment and proppant with effectiveflowback control (e.g., fibers, curable-resin-coatedproppant or both). The combination with a success-ful packed-back TSO achieves an external gravelpack of stable proppant (i.e., an external formation-material screen as illustrated by Appendix Fig. 9).Perforation and completion considerations areaddressed in Section 11-3.5.

The screenless completion obviously eliminatesthe cost of the screen and related tools, but moreimportantly it enables economic development of sig-nificant behind-pipe reserves that do not warrant themobilization and operational costs for a rig on anoffshore production platform, as generally requiredfor a standard gravel-pack completion.

A5-20 Chapter 5 Appendix: Evolution of Hydraulic Fracturing Design and Evaluation

Appendix Figure 10. Indirect vertical fracture for reservoirmanagement (Bale et al., 1994a).

Proppedfracture

Highpermeability

Low or moderate

permeability

A future generation: fracturing andreservoir engineering merger?The previous discussion of the TSO generation clearlyshows the blurring of what can be controlled on theinside and outside of the casing and of what havebeen the traditional roles of a fracture design engineerand a reservoir engineer. This blurring of past distinc-tions provides prospects for additional innovationsand the advent of a fourth fracturing generation.

Optimal reservoir plumbingFrom a broader viewpoint, the IVFC and strategicallyplaced perforations provide the means to extend opti-mized plumbing into the reservoir. Optimized plumb-ing, through a NODAL analysis, is generally practicedonly for the surface facilities and within the wellbore.Extended optimization requires additional considera-tions for designing the plumbing system provided bythe fracture in the reservoir and also within the frac-ture itself.

The outline for these considerations was defined byBale et al. (1994b) for the Gullfaks application. Theyconsidered the role of the permeable fracture plane onthe reservoirs 3D flow pattern and how tailoring thedistribution of conductivity can advantageously affectthis flow pattern (e.g., reducing the conductivity as thefracture approaches the high-permeability upper zoneto delay water production while increasing the con-ductivity in the lower permeability zone and applyinga large drawdown to accelerate production from thiszone; see Section 5-1.2). Therefore, the analysis anddesign tools have evolved for considering the role offractures in NODAL analysis for reservoir, formationmaterial and water management.

Achieving full potential for horizontal wells and laterals The preceding discussion of the IVFC is in the con-text of single, essentially vertical wells. The potentialfor innovative strategies to drain a reservoir increasesseveral fold by adding consideration of horizontal andlateral wells. These highly deviated wellbores are typ-ically placed without cemented casing because of eco-nomic considerations and therefore do not generallyreach their full potential because they lack an effectivetechnique to remove wellbore damage. The solution

of using cemented casing for effective treatmentdiversion tends to be overlooked because of an appar-ent failure to appreciate lifecycle economics or theeffectiveness of good cementing