SPE-14085-MS

SPEfkK=140f~~

SPE 14085

An Overview of Recent Advances in HydraulicFracturing Technologyby R.W, Veatch Jr,and Z,A,Moschovidis,Amoco Production Co.SPE Members

~~t 1SSS.societyofPetroleumEngineersThispaperwaspresentedattheSPE19S6ImernationalMssIiwlonPelroieumEwin-iwhewInSeiiing,ChinaMarch17-20,1986.Them=!erialisS@jSCI10oorracrbnbytheauthor.Permiesbntocopyiarestricted10anSbStrSCtofnotmorethan300words.WriteSPE,P.O.Sox833S.36,Richardson,Texas7WS%SS3S.Telex:7S0SSSSPEDAL.

ABSTRACT is a rather generaloverview of the recent advance-ments in technologyand the applicationby the

There have been significantadvancee in the industry. For the sake of continuity,many of theapplicationand developmentof hydraulic fracturing referencescontainedin the previouspapers aretechnologyin the past several years. Thi9 paper includedalong with refertincesof recent work. Thispiesents an overviewof some of these advances to providesthe interestedreader a rather comprehen-provide the reader with a perspectiveof the current sive resourceto a more in-depthexplorationof thefracturingstate of the art. The discussion technologyof fracturing.addresseeeconomic design considerations;fracturingmaterial behavior (pt~ppingagents? fractureconduc- The work presentedhere primarilycoverstivity, fluid loss, fluid rheology and proppant hydraulic fracturing treatmentapplicationsandtrang~rt); field acquired fracturedesign. diag- design. There is minimal referenceto the reservoirnostic and analysis technology(in-situ stressesand performanceanaLysis technologyassociatedwithstress profiling,downhole fracturingpressureand fracturing. The discussionemphasizes(1) economicpressure decline analysis,real-timeon-site moni- design considerations;(2) fracturingmaterialtoring and control,and fracturemapping);and behavior includingproppinglgents and fracturecon-three-dimensionalfracturepropagationsimulation. ductivity,fluid loss, fluid rheology,proppantA ccaprehemsivebibliographyis provided ls a transport,lnd new data on feastedfracturingfluids;resource for in-depthperusal of each area by the (3) field acquireddata for fracturedesigninterestedreader. includingin-situstress data and profiling,diag-

INTRODUCTIONnostic data from downhole fracturingpreasureaanlfrom pressuredecline, real-timeon-site monitoringand control capabilities,and fracturemapping tl:ch-

In 1982 at the InternationalMeeting on Petro- nology; and (4) three-dimensionalfractureprop#ga-Leum Engineeringin Beijing,China, Veatchl pre- tion simulationmodels.sented an overview of the status of hydraulicfracturingtreatmentand design technology. Uany of FRACTURINGECONOMICOPTIMIZATIONthe facets of this paper were updated in a subse-quent paper in 1983.2 Tlteconcept af optimizingfracturingtreatment

designs,generallyspeaking,has three basic steps:During the past 2-3 years, fracturingtech- The first (upperleft portion of Fig. 1) is to eval-

nology and its applicationthroughoutthe industry uate the increasedincome which might be expectedhave made significantprogress.This paper focuses from oil or gas producing performanceresulting ~romon many of the recent advancementswhich have devel- various fracturelengths and conductivities;theoped since the previouspapers were published. It second (lower left portion of Fig. 1) is to deter-attempts to provide the reader with a perspectiveof mine the costs required to achieve the variousthe current state of the art of fracturing. The Lengthsand conductivitiea;and the third (rightdiscussion surveys the many aspects of fracturing, side of Fig. 1) is to evaluate the net revenuetouching onLy briefly on each. It is outside the (i.e., incomeminui costs) versus fracture length toscope of the paper to present an in-depthcoverage determinethe treatmentdesign that yields the max-of all the detaiLs of the technology. What is given imum net revenue, i.e., the optimum design. The

specificproceduresused for determiningthe optimumReferencesand illustrationsat end of paper.

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AN OVERVIEWOF RECEWT ADVANCES IN HYDRAULICFRACTURING2 TECHNOLOGY 14085

fracturingtrestmentdesign for a given formationmay not always conform preciselyto these conceptualsteps. But they will always involve some type ofbalance between treatmentcosts and revenue>gener-ated from the prduction response associatedwith atreatment.

It has been generaLLy recognizedthat the frac-ture Length ~equirementsdepend greatly on reservoirpermeabilityand fractureconductivity,such aa isshown by Elkins3 in Fig. 2. Here, we see thatextremelyLow permeabilityformations(k =0.000md) may require half-Lengthsas long as3500-4500ft (see shaded area). However? Length andcondueti~itymay not be the only parameterswhichaffect fracturingdesign optimization. This issometimesnot obvious in parametricfracturingstudieswhere the primary focus is on formationpermeability,fracturepenetrationand conductivityrequiremeri:s.In some cases, other factors (e.g.,net pay, fractureheight, etc.) can become importantconsiderationsin fracturingeconomics. Theirincrementaleffects can be very significant. Forexample,considerthe effect of net pay on fracturepenetrationrequirementsto optimize the net presentworth of a treatment(i.e., the present worth of thehydrocarbonproductionfor the fracturedformationminus the presentworth of the hydrocarbonproduc-tion for the unfracturedformationminus treatmentcosts). The resultsof an example case, as shown inFig. 3, depict the percent increase in net presentworth (i.e.,net presentworth for the fracturedcase expreesedl s a percent of the unfracturedcasepreeentworth) versus fracturepenetrationfor netpays which rmge from 2 to 100 ft (0.6 to 30.6 m) ina 5-redformation. Here, fracture conduc~ivityis6000 md-ft (1829 red-m)lnd the wells lre on160 acres/wellspacing. Figure 3 shows that theoptimum fracturepenetration(i.e., the penetrationat which the maximum net present worth increaseoccurs) gets longer l s net pay increases. Theresults for this case and two other formationperme-ability levels (1 and 10 md) are sunsnarizedinFig. 4 which shows the optimum fracturepenetrationpLotted versus net pay. Here we see optimum frac-ture lengthswhich range from 200 to 1320 ft for the5- and 10-md formations,and an almost constantoptimum length for the l-redformation. This showsthat optimum lengthscan vary widely for a givc~permeabilityand fractureconductivity,depending onthe net pay magnitude.

Addressingfractureheight from an economicstandpointreinforcesthe need for having reliableheight data when designing treatments. In additionto the obvious increasein costs, fractureheightcan have a significantimpact on optimum economicpenetration,which in turn could affect well spacingrequirements. As an example, cases were run for a1 md formationwith 10 ft (3.0 m) of net pay, a2000 md-ft fracture,and 160 acres/wellspacing.Fractureheights from 180 to 720 ft (55 to 219 m)were investigated. The resultingoptimum fracturelengths and treatmentvolume requirementsare shownin Fig. 5. The optimum values were those whichyielded the maximum net present worth for each givenheight. As can be seen, the optimum treatmentvolume requirementsdid not change dramaticallyoverthe wide range of fractureheights, but the optimumLengths did. At a height of 180 ft, the optimum

fracturepenetrationapproachesthe drainageboundary (i.e., 1320 ft); at heights on the order of600-700ft(183-213m),300-400 ft (91-122m).need to invest;,ateI:hespacing for su..hsituat

Waremlvurgfet al.study on three examplesimportantfactors that :

the optikm lengthswereThis suggests that one mayeconomicsfor closer weltons.

4 ~resentedan economicand addressed severaL otherhould be considered for

op~imizingtreatmentdesigns. These included:(1) the tiurationof the productionforecast fromwhich net presentworth is calculated,(2) the netdiscountedproductionrevenue,and (3) the amouct ofinvestmentrequiredto achieve the design option.Other factcrs,such as hydrocarbonprice, interest(discount)factors,tech.lology~eveL and risk asdiscussedby Rosenberg,et al,, and Brashear,et al.,s have also been shown to play a criticalrole in economicoptimization.

PROPPINGAGENTS AND FRACTURECONDUCTIVITY.

There has been considerableprogress in thedevelopmentof intermediatestrengthpropping agents(sometimescalled intermediatedensity proppants,IDP) to supplementsinteredbauxite for high in-situstress applications. Various supplementalindustrytests on a,wide spectrumof proppingagents (sands,intermediates,sintered bauxites,resin-coatedsands, etc.) and recent investigationson fractureconductivityhav~ considerablyextended previouslypublishedwork. 1s

Studies by Philli s and Anderson,16Larsen andSmith,17 8ecq, et al.,!8 and Norman, et al.,19 plusrecent comprehensivedati!sets published by the sti-mulation sa~~ie companit!sand propping agent manu-facturers, provide m extensiveresource forfractureconductivitylaboratorytest results.

Phillipsand Anderson deamnstratea method tomodify the traditionalconductivityversus closurestress data to include the cost for various types ofproppantsas is shown by the curves in Fig. 6.These representthe cost/unitfracturearea/unitofconductivity($/ft2/Da~cy-ft)over a wide range ofclosure stresses. They account for a proppant packdamage factor of approximately20-25%. The authorssuggestedprescribingdamage factor values to adjustlaboratorytest data to representa more realisticestimateof in-situ field performance. Graphs suchas these can be constructedfor a given fracturingfluid from current proppant price schedules,labora-tory conductivitytest data, and estimates of prop-pant pack damage factors for a given fluid. Whenconstructingthese graphs, one is cautioned to useproppantperformancedata tested by consistentproceduresfrom one teeting laboratorybecause datafrom different sourcesmay not be accurately com-pared.

There has been some work conducted on proppantpack damage and plugging. Kim, et al.,26 conductedproppantpack damage tests on 20/40 mesh sand fordifferentfracture fluids eve* a wide range of cLo-sure stressesand at different temperatures. Theresults showed that fractureconductivitiescould bereducedby 40-60 percent just from plugging by thegel residue. Cheung2 reportedthat various concen-

.

.14085 RALPH W. VEATCH. JR. AND ZISSIS A. MOSCHOVIDIS 3

trationsof HCL/HF acid solutionscan dissolve a of Fig. 10 are given in TabLes 1 and 2. The resultssignificantamount of proppantand this would reduce demonstratethe significanteffect that dynamics canconductivity. Unpublishedwork sponsoredby have on fluid LOSS behavior for fluids flowing in aNorten-AltoCompany suggeststhat highly siliceous fracture. The studies by Roodhartand by Harris andproppantsmay degrade seversly in brines at high Penny also showed that fluid loss (i.e.,both spurttemperatures. Almond and Bland28 reportedon var- Loes and fluid loss coefficient)behaviorisious ways that break temperatureand breaker affectedby fluid flow dynamics.mechanism (i.e., oxidizsrs,enzymes,etc.) play animportantrole in 20/40 m?.ehsand proppantpack flow Some ~ther interestingobservationshave beenimpairmentfrom guar, deri~atizedguar, and cellu- reported. Roodhartstests demonstrateda signifi-lose basad fluids. To mitigate water blocking prob- cant effect of pressuredifferentialon walllems, Phillipsand Wilsons showed that using a building fluid loss coefficient,C . This is shownsolvent in the pad fluids with a surfactantin the in Fig. 11 for both a crosslinked~PC fluid with arest of the fluid reduceswater blockingin the 5% diesel and a hydroxyethylcellulose(HEC) basedfractureand significantlyenhancesfracturingfluid fluid with silica flour. Here we see a significantrecoveryand production. increasein C at higher pressuredifferentials.

w

A comprehensivefractureconductivity/reservoir Harris and Penny observedan ~ffect ofperformancestudy by Britt30 addressesoptimiz~!tion increasedviscosityin the flowing fluiddue toof fracture conductivityfor an oil reservoirunder. dehydrationfrom fluid loss. This phenomenonisboth primary and secondarydepletion. It showed the shown in Fig. 12, by the continuallyincreasingvis-economicbenefitsof high conductivitysh~rt frac- cosity for a test in a radial flow cell (Fig. 9)tures for moderatelypermeable (i.e., 1-10 md) for- where fluid loss is occurring. It suggeststhat themations. The resultsdepicted in Figs. 7 and 8 show gel is thickeningbecauseof fluid loss. The otherthe impactof differentfractureLengthsand conduc- curve shows that viscositydecreases from shear andtivitie:on incrementalpresentworth. By devel- temperaturedegradationwhen fluid leakoffis pre-oping curves such as these, one can determine the vented by replacingthe core with an impermeableappropriatefracturec..nductivity/lengthreLation- blank. Observationssuch as these emphasizetheship requiredto maximize economicreturns for a need for a better understandingof in situ fluidgiven reservoir. Loss behaviorand its effects on rheologyand prop-

pant transport. This is particularlyimportantStudiee by Slbe131 and Hontgomaryand becauae of the significantrole that fluid loss

Steanson32addressmethods for using reservoirper- plays, being one of the more dominant parametersformancetype curves and computerizedsimulatorsto controllingthe fracturingprocess.determinethe appropriatefracturecmductivitydesign requirementsfor various reservoirperme- . Culbis work indicatedthat at shear ratesability levels. Elbel supportspreviousfindingeby below 80 sec1, dynamic and static fluid lossBennett,et al.33 that a varying conductivityin the behaviorwas similar. Observationsby Penny, etfracturefrom the wellbore to the tip can signifi- al., showed correspondingresultsat shear ratescantly affect productionrates. Studies such as below 40 see-l. However,at high she~54rates,theythese can be very importantwhen determiningprop- suggeatedthat fluid loss followsa1}2 trendpant placementand schedulingprogramsfor a treat- rather than the consnonlyobserved t for staticment design to assure that the lppropriate tests.distributionof conductivityin the fracture isachieved. Work by the previouslymentioned invesciga-

turs42-40all supportedearlier studieswhich showedFLUID LQSS that a hydrocarbonphase (e.g., 5% diesel) could

significantlyreduce fluid Loss, especiallyif mixedlluchof the recent interestin fluid loss has with siLica flour (or other fine mesh particulate)

focusedon (1) dynamic fluid loss behavior, and a surfactant. This was especiallyeffective in(2) in situ measurements,and (3) fluid loss control fracturedcores as is shown by the example infor naturallyfracturedformations. Recent labora- Fig. 13. Culbis reportedthat the effectsof thetory and field studieshave extendedthe findingsaf hydrocarbonphase/silicaflour additiveson reducing

34-41 for both static andprevious investigators fluid loss were Less pronouncedin dynamic testsdynamic fluid loss behavior. than in the static ones.

Recent dynamic fluid loss, studiesby Gu~gis,42 Fluid Loss From Field Data: Several investiga-

;:;:,a:: :~ii4: :nny t aL*24 ~odhar: andtorahave supplementedthe literaturewith methods

lndlcatedthat dynamic fluid loss to infer fluid ioss from field data since Nolte37tests can yield different results than static tests introducedthe pressuredecline method in 1979.do and that shear rate and shear history can affectthe tests significantly. Figure 9 shows a typicalflow system with the fluid loss cells, rheology Loop

Nierode47proposeda differentapproach fordeterminingfluid loss using measurementsof

and heating capabilitiesused by most of the inves- increasinginstantaneousshut-in pressure (ISIP)tigators. Figure 10 shows the differentfluid Loss data during the treatment. This work is based onbehaviorsobserved by Culbis for differentshear the relationshiprates, shear historiesand temperatures. Thesetests were run on the same fluid, i.e., a Hydroxy-propyl.Cuar (HPG) fluid, crosslinkedwith a titaniumcompound. The test conditionsshown in the legend

AN OVERVIEWOF RECSNT ADVANCES IN HYDIUWLICFSACTURING4 TECHNOLOGY 14085

FG(t2) = FG(t1)[l+A(C~~8] ............(1)

where FC(t) is the ISIP fracturegradient (ISIP/depth) at time t (psi/ft);tl is the time.of firs!shut-in pressuremeasurement,(Mins); tof later shut-inpressuremeasurement,?::s;e:zB are empirical fit constants;and C is the fluidloss coefficient(ft/Jmin).

Nierode proposedthe values A = 0.19C43 and B =0.46767 for a Kristianovich-Geertsma-deKlerk, KGD(sometimescalled Kristianovich-Zfaltov,KZ4s) shapedfracture;and A = 0.20233 and B = 0.47850 for aPerkins-Kern-Nordgren,49*5O pm, shaped fracture.These values servedas the basis for deve~opingthecurves shcwn in Fig. 14 for using ISIP increaseandpumping time since the first shut-in to estimatefluid loss coefficient.

Cooper, et aL.,sl presentedthe results of acomprehensivefield study comparingthe rtethodsofNolte and Nierode with theoreticalexpressionsofSmith52 and of Williams,et al.41 The theoreticalexpressionsemploy the three types of linear flowleakoffmechanisms:

(1) fluid viscosityand permeabilitycontrolledcoefficient

[[email protected]

C1 = 0.0469 : .................(2)P

(2) reservoir fLuid compressibilitycontrolledcoefficient,

r]1$k Cf 5cII = 0.0374Ap P ; .............(3)Fo(3) wall buildingcontrolledcoefficient,

CIII =0.0164~ . .......0.....0..........(4)

In Eqs. (2)-(4),Ap is the bottomholefracturingpressureminus reservoirpressure,(psi); $ is theformationporosity,(fraction);k is the formationpermeability,(Darcies);p is the fracturingfluid

.

:;:;;;;t~p:;~i;;cbis the reservoirfluid compressi-is the reservoirfluid vis-

cosity, (cp); m isF?he slope of the fluid lossversus square root of time plot, (cc/~min);and a isthe area of the fluid Loss paper or core, (cm*).

To compute a total fluid loss coefficient,Ct,.Smith combined the terms in the form

C++i++r*******and Williams, et al., proposed the form

Ct = 2CICIICIII ...(6)+(C*112C17+4C11%C12+C111CICIII 2))o*5

The results of Cooper, et al., are given in Table 3.In general, it ap eared that the theoretic~lvalues

7[Eqs. (5) and (6) were lower than those computedbyeither NoLtes or Nierodesmethods. There wereseveralcases where close agreementwas obtained forthe 0.1 md formations. However, some of the otherdata exhibiteda wide divergence;and if one ;Sfaced with this dilemma (and it cannct be statisti-cally remedied),it may be necessary to conduct sen-sitivity studiesusing a wide range of leakoffvalues to investigate the impact that the differentvalues will have on a fract~re treatmentdesign.

FRACTURINGFLUID RHEOLOCY

Theologicalcharacterizationof crosslinkedfracturingfLuids remains a difficultand elusivechallenge. However, some additional insightshavebeen developedto extend the work of previous inves-tigators.3 9 Studies by Cuillot and Dunand80andPrudhonsme61have demonstratedthe use of Laser Ane-&mstry to observe velocity profiLes for investi-gating wall slip phenomena. GuiLlot and Dunand,using a circularcross-sectionalflow apparatusreportedthat at low shear rates aqueous HPG solu-tions exhibitedvelocity profilesmuch differentthan what known power Law parametercalculationswould indicate. Prudhonmeswork in a coaxial cyL-inder apparatusexhibitedbehavior anomalousto con-ventionallyknown flow models. Furtherwork isnecessary to resolveor expLain the occurrenceofthese anomalies.

Laboratorystudies using oscillatoryviscome-ters by Prudhousnelnd by KnoLl,u2 provided insightinto methods for investigatinggel structure,wallslip, and the significantrole that mixing proce-dures play in testingof crosslinkedfLuids.Figure 15 shows a schematicof Knolls apparatus.It includeda RheometricsPressure Rheometer (RPR)which is capableof both steady and oscillatoryshear. Per discussionsby Prudhommeand Knoll.,thephysicalnature of fluids can be demonstratedexper-imentallyby oscillatoryshear measurementswhichevaluate the elastic and viscous behaviorof a fLuidor gel. The elastic or storage modulus, C, asdeveLopedfrom classicalnetwork theory of macromo-lecules, is indicativeof crosslinkdensity. Theviscous or loss modulus, G, describes polymerbehavior for these materials. By determiningC andG behavior as a functionof strlm (deformatix?)and frequency(rate), the structureof a materialcan be analyzed. Thus, it was possibLe to investi-gate the viscoelaaticnature of a fluid. The RPRapparatuswaa also capable of dynamic mixing and

424

.14085 RALPH U. VEATCH, JR. AND ZISSIS A. ilOSCHOVIDIS 5

. crosslinkingof polymer. FiSure 16 shows the These valueswere comparedwith measuredfric-differencesin ElasticFlodulus(C) and Viscous tion factors (fm) computedby Eq. (8) from measured140dulus(c), l s measuredon the RPR? for an pressure Leases,uncroaslinkedHPG solutionand an MPG gel cross-Linkedwith a titaniumbased crosslinker. The inde-pendenceof G to oscillatoryfrequency,observed lt3h; W3 Apfor the crosslinkedHPC, suggestsa three- fm . ;*****.******************(8)dimension-l,gel-likestructurewhere the material 64PQ2AXcannot relax over any time period within the fre-quency range of the tests. This is not observed forthe uncrosslinkedfluid. Test proceduressuch aa where h ia the fractureheight;w is the fracturethose conductedby Knoll and by Prudhonsnahave shed width$ & ia the volumetricflow rate; and Ap/Ax isconsiderablelight on investigatingthe conditions the pressuregradient. The resultsgiven in Table 4under dhich gels will form and their degree of show that pressurelosses llong the fracturewerecrosslinking. much larger than what would be predictedby viscous

theory which is currentlyused in most of the aimu-Knoll also demonstratedthe variationsone lation models throughoutthe industry. The causes

might expect to observe between tests on blender for this are not identifiedto the degree that onepreparedgels with those which are dynamicallypre- can do more than make empiricalcorrections. Theypared (i.e., crosslinkedwhile flowing). An example are thought to result from tortuosity,secondaryin Fig. 17 shows the different stressesfor various flow, multiple fracturestrands,sharp turns (cor-shear rates that resultedfrom using different prep- ners), etc., due to the irregularityof the fracturearationprocedures. This supportsreports of many faces.of the previouslyreferencedinvestigatorswho madesimilarObservatima and emphasizesthe complex PROPPANTTRANSPORTAND PROPFANTSETiLINCnature of charactetiizingfracturingfluid rheology.

There have been several studies recentlytoRecent studies in pipe flow or capillaryequip- supplegentthe technologyof previous investiga-

ment by Prudhomne,Royce, et al. 63 Shah and Wat- tors67 77 in the area of proppant transportandset-ters,64and Gardner and Eikerts,g have yielded tling for both power law and viacoelasticFracturingadditionaldata on the effectsof shear, temperature fluids.and time for differentfluids and crosslinkingsys-tems. It has been well recognizedfrom previous Biot and Hedlin7sand ?ledlin,et ll.,79 con-invsstigatorsthat a high shear environmentcould ducted a comprehensivetheoreticaland experimentaldestroya gel if it was sheared severely after investigationon proppant transportin thincrosalinking. Observationsby Gardnerlnd Eikerta (uncrosslinked)fluids. In the apparatuashown inindicatethat high levels of shear prior to crosa- Fig. 19, they observed four regions of transportlinkinghave little effect on overall performance, phenomena,as depicted in Fig. 20. Here Region I isand that temperaturewill activate the crosslinking a settled bank where the concentrationia l functionmechaniam. Figure 18 shows the compositeof a of the proppantpacking characteristics;Region 11,series of their tests on HPO and carboxymethyl- HPG called the bad Load, is l fluidizedlayer of reLa-(CliNffi)systems croasLinkadwith l zirconiumco!a- tively small height; Region III ia l zone of viscouspound. Curve C shows the improvaisantin viscosity drag transportwhere the proppantconcentrationisperformanceof a delayed system over that of compa- more or leas constant;and Region IV is a zone ofrable nondelayedsystems (e.g., Curves A and S). turbulent transport throughwhich the concentrationOther investigationshave supportedsimilar phe- declines to zero. Their theoreticalapproachesnomena. As a result of such findingsthe industry closely modeled experimentalfindingsand their con-is moving to the use of delayed crosslinksystems elusions indicatethat nearly all transport for thinwhich are formulatedto activate after the fluid has fluids is by viscous drag.been pumped::,~wnthe tubularsand through the perfo-rations. This has been one of the significant Wcrk by Roodhartaoand Acharya81addreaseddevelopmentsin current fracturingfluid technology. proppan-.transportand settlingin flowingviscoe-

Lastic fv~cturingfluids; and Kirkby and Rocke-Warpinski86conductedexperimentson fluid flow felLer82 luvestigatedsettling in nonflowing

throughactual in-situfracturescreatedat the slurriesof both viscous and viscoelaaticfluids.Departmentof EnergysNevada Test Site. The frac- Both Roodhartand Acharya used vertical parallelture was instrumentedfrom a tunnel at a depth of1400 ft (427 m).

plate type equipmentsomewhatsimilar to HediinsTheoreticalfrictionfactors (fth) apparatus. And both developed theoreticalexpres-

were computedby Eq. (7)? sions for aettLingvelocitiesunder differentflowconditions. Some of the conclusionsof Acharyas

64 Pa work are paraphrasedbelow.

f DHvpth= ..l .l .......l .l ...l .........(7) 1. Correlationswere developed for proppantset-tling rate in inelastic(power law) and viscoe-lastic fracturingfluids for Low and

where pa is the apparent fluid viscosity;DH is the intermediateReynolds number (NRe) flowhydraullcdiameter of the fracture;v is the fluid regimes. They are as follows:velocity;and p is the fluid density.

..-..-4d3

AN OVERVIEW OF RECENT ADVANCESIN HYDRAULICFRACTURING6 TECHNOLOGY 14085 -

(a) For NRe < 2, A(Um/d );b-n)Wi =

K ..............(14)

[1 *+1l/n(pp-~)gdpu= ..........(9) is the Weissenbergnumber.where A and b aremINEL 18K F(n) material parameters,and K is the consistencyindex for pover law fluids.where 2. In the intermediateReynoldsnumber region

(2

14085 RALPH W. VEATCH, JR. AND ZISSIS A. UOSCHOVIDIS, 7

FOAMED FRACTURINGFLUIDS high proppantconcentrationsin the final gas/liquidmixture. However, recentLydevelopedtechnologyof

There has been considwable interestin the use csing proppantconcentratorshas alleviatedthisof foamed fracturingfluids in the past 3-4 years. problem to some degree.Several laboratorieshave constructedequipmentespeciallyfor teeting foam rheologyand fluid loss. IN-SITU STRESS MEASUREMENTAND PROFILINGResults of recent tests from these various sourceshave significantlyextended the databaseestablished There has been significantprogress in theby previous~nvestigators.Se-ss In particular,work measurementand profiling of in-situstressestoby Herris,sg90 Harris and Reidenbach,1 Reidenbach,

2 Watkins, et al.extend the technologyintroducedb

To!:;::ous nves-93 Wendorffand Earl,g tigators.97-102 Recently, Teufelet al.,and Craighead,et al., s48 have shown foams to have Blanton,lOsBlanton and Teufel,1069107and Teufelextremelygood theologicaland fluid loss perform- -log have enjoyed some success in deter-and Warpinsklante under a fairly wide range of conditions. Most mining both the magnitudeand directionof in-situof the Laboratorysystems used to test foams are stressesusing anelastic strain recoverydata fromsimilarto the one describedby Wendorff and Earl. orientedcores. Host of the successhas beenBasicallythey are high-pressuresystemswith foam related to the directionalaspect. The work per-generators,foam viewing chambers,heated rheology taining to magnitudehas been Less fruitful.loops, inline fluid loss cells, and fracture simula- Figure 27 shows an example of the type of testtion chambers,and are quite similarto the equip- results recordedby their metho.is.Maximum and min-ment depicted in Fig. 9. imum horizontalstressesare computed as proposedby

Blanton, i.e.,Harrisag recentlyconducteda comprehensive

study to investigatehow foam texture relates torheology. Some of the conclusionsresultingfrom (l-~~a)A&x+(~i+u~a)A&+(1+VI)P2ACZthis work are as follows: (1) foams are shear his- Ux=aUz (l+Pl)[(l-Pl)A&z+~2a(A&x+A&y)] (15)tory dependent fluids; (2) the viscosity of foam isdeterminedprimarilyby its quality and liquid phaseproperties,and is influencedto a lesser extent byits texture; (3) higher surfactantconcentrations andproduce finer texture foams; (4) viscositymeasure-ments at low pressuremay not adequatelysimulatefield usage at high pressure;(5) the chemical type (1-u~a)AS+(ul+v~a)A&x+(l+u)V Acof the liquid phase influencestexture;and (6) the Oy=ao 1 2 z (16)larger bubbles of hydrocarbonand methanol foams z (l+vl)[(l-ul)A&z+v2a(A&x+A&y)]result in sensitivityto degradationat high shearrates.

where a = D2(t)/Dl(t);Dl(t) lnd D*(t) are trans-Laboratorytests have shown that both nitrogen versely isotropiccreep compliance; t is time; Acx,

lnd CO* foam lxhibit good theologicaland fluid AS , and A& lre differentialprincipalstrainloss propertiesover a relativelywide range of con- re~overies;zVland V* are transverselyisotropicditiona. Bxamplesof the effects of foam quality Poissonsratios; and Ox, o , and u are in-situlnd gel concentrationon apparent viscosityduring principalstress magnitudes? The r~suLts of severaLtests by Harris and Reidenbach91are shown in of these tests have been compared to in-situmeas-Figs. 23 lnd 24. Here we see very good viscosities urements from small volume pump in tests (eithereven at high temperaturesfor high quality foams pump-in/shut-inor pump-in/flow_back). Teufe1104with 40-60 lbs/1000gal gel concentrations. Typical concludesthat, in general, the techniqueis reli-foamar concentrationsrequired to maintain a stable able for estimatingthe direction,but not as reli-foam with these good viscositiesat different tem- able as pump-in tests for determiningthe magnitudeperaturesare shown in Fig. 25. Note that the of principlestresses.requirementsare not too severe even at high temper-ature. Data from dynamic fluid Loss tests by Wat- Pump-inmethods (pump-in/shut-inpressurekins, et al., such as those in Fig. 26 show that in decline, ISIP, pump-in/flow-back,step rate testslow permeabilityformations,leakoffcoefficients and etc.) have essentiallybecome the most preva-for some foams can be Lower than those of cross- lent proceduresfor measuring in-situ stresses.Linked a ueous fracturingfluids. Craighead,

91Techniquessuch as those proposedby Warpinski,

et al., conductedproppant settliwgstudies on a et al.,lOg have refined the method to yieLd rela-foam generatedwith delayed crossLinkedgels. They tively reliableresults. Figure 28 shows an examplefound that the setting rate in foamedcrosslinked of the wellbore downhole closure tools they used forgel was almost two orders of magnitudehigher than testing. 6y pumping small vclumes (e.g., 1-2 bbLs)in foamed Linear (uncrossLinked)gel. They also and seatint!tbe CRC mandrel* in the GRC nippLe*withfound that foamed crosslinkedgels were less the HP pressuregauge* (* - patentedequipmentaffected by changes in foam quality. names) below the mandrel, it is possible to shut-in

the welL downhoLe to minimize wellbore voLumeFoam has developeda definite pLace in frac- effects and improve the potentialfor definitive

turing applications. It is particularlyadvanta- measurements. Another method tested by Amoco as angeous in low-pressureformationswhere there is alternateto downhol.eshut-inequipmentuses a con-limited reservoirenergy available t~ clean up a stant rate flow-backcontrol device at the surfacewell after fracturing. One disadvar.tagethat to improve in-situ stress measurementsfrom theremainswith foams is the limitationon achieving pump-in/flow-backmethod. Daneshy,et al.jl10

.

427

AN OVERVIEWOF RECENT ADVANCES IN HYDRAULIC FRACTURING .8 TECHNOLOGY 14085

reportedon a techniquefor conductingin-situ Their study demonstratedgood agreementbetweenstressmeasurementsduring drilling operation. field techniquesand theoreticalcalculationsus~dThis method employs a packer in the openhole section in vertical fracturegrowth analysis.very near the bottom of the hole. In addition tostresedata, orientedcores from the formation imme- FRACTURENAPPINGdiatelybelow the fracturedopenhoLe eection alsoprovideinformationabout the azimuthaltendencies A number of relativelysignificantinvestiga-of a fracture. tions have enhancedthe work of previoue investiga-

tors117-123 for mapping the azimuthal trends ofIt has become apparentthat in-situ stresses hydraulicallyinduced fractures. These included:

can vary significantlybetween adjacent formations. (1) the De artment of Energy lfultiwellExperimentData by Warpinski,at al., depicted in Fig. 29, show (~)124,1~S in the Piceance Baein near Rifle,in-situstress differencesof more than 2000 psi Colorado; (2) the experim~~tprimarilyfunded by theoccurringover relativelysmall vertxcal intervals Gas Research Institute(GRI) and jointl(e.g., less than 100 ft). Large stress differences

~ conductedwith Dowell/Schlumbergerand Amoco12617 at AMOCOS

have also been observedby Amoco in the Eaat Texas Mounds Test Site near Tulsa Oklahoma;1*8 from multiple wells inCottonValley (ETCV),Wyoming Hoxa Arch, and (3) investigationsby Lacy

ColoradoWattenbergtight formationgas plays. In several fields in East Texas and Alaska; andview of the major effect that in-situ stress pro- (4) studies by Griffin12g in the Kuparuk River For-files have on fracturepropagationgexnetry, it is mation on the Alaskan North Slope. The large numbervery importantto have methods to r~liablydetermine of tests have provided the opportunityto compare athem. There have been some successf~lefforts using wide variety of azimuth mapping methods.acousticalwavetrain (i.e., shear and compreasionalvelocity)measuremanteto profile in-situ stresses. The resultsof the methods used in the NWX azi-Laborat~~~work by Lin,lllMao, et ll.,112 Newbarry, muth study lre eurmmarizedin Table 6. The analysiset al., and field data from Johnson and of the borehole seismic in the Paludal zone areAlbright114have verifiedthat these type methods shown in Figs, 32 and 33 which depict the azimuthhave a relativelygood potentialfor use in in-situ trends and vertical growth tendencies,respectively.atreesprofiLing. In-situstr=ssesare estimated The relativelyclose agreementbetween the boreholefrom observationsof acousticalvelocity changes seismicand the oriented core strain recoverydataresultingfrom stressthan es on cores.

fsome in Table 6 are encouragingfor the potentialof

resultsobtained by Aaocol 5 using long-spaced these two methods.digital sonic (LSDS) logs (i.e., acousticalwave-train data) corroboratedwith pump-in stress tests The tests at Hounds consistedof employingshoweda good correlationbetween these two methods. aeven fracturemapping methods in a 1000-ft (320-m)Figure 30 shows l comparisonof stressescalculated deep sandstoneformation. The results of thesefrcm acousticalwavetraindata obtainedwith a testa are suzszarizedin Table 7.127 Here thelong-spaceddigital sonic (LSDS) log versus those luthora concludedthat the true fractureazimuthmeasuredby pump-in stress tests. These data was W95E as suggestedby borehole televisioncameraincluderesults from both sanda lnd shales in the observations,surface tiltmeters,and strain relaxa-Hoxa Arch formations,and the Blocker,Carthage,and tion measurements. The differingresults from theWoodlawnfields in the ETCV play. The excellent DifferentialStrain Curve Analysis (DSCA) and Dif-correlat.ioneobservedhere may partiallyresult from ferentialWave Velocity Analysis (tHiVA)data weresome inherentgeologicalsimilaritybetween these attributed to paleostresaregimes combinedwith cur-particulartight gag formation. Uarpinaki,et al., rent strese regimaa. Caliper logs and remotedid not observe aa close an agreement in studies of eeismic sensingdid not yield definitiveresults.the ColoradoMesaverdeGroup formationswhich areshown in Fig. 31. Here frac gradientsmeaaured from Lacy:a work includedactive seismicmeasure-pump-inteets were compared to chose calculatedfrom mants from tiltmeteraand l triaxialboreholeLSDS logs. However, it still appears that acous- seismic (TABS) tool plus predictivemethods ofticalwavetrainmeasuremantahave l high potential stress relief, thermal expansion,and sonic velocityas a useful method for inferringin-situ stress pro- maasurementson oriented sandstonecores. Testfiles for many applications. For reliableuse, they depths ranged from 8500 ft (2590 m) to 12,000 ftwill probablyhave to be developed for each partic- (3660 m). The results indicatedgood comparisonsofular field or geologicalhorizons in a given area. azimuth trends between the tiltmeters,TABS, and

stress relaxationdata. Figure,34shows an exampleA relativelycomprehensiveinvestigationof the of tiltmeterdata and Fig. 35 the TABS results on

effect of the in-situatress profile on vertical the same well. Note in Fig. 34 how much thefracture growth in the Mission Canyon Ratcliffe for- interpretationimprovedby increasingthe number ofmationa in North Dakotawas conducted by Begnaud, tiltmatersfrom 8 to 18 in an array.et al.116 Their paper discusses several teetingtechnique used to determinethat vertical fractures Griffin investigatedazimuth measurementsfromare not confinedwithin the pay zone during both welLbore ellipticity,on site core strain relaxa-Hission Canyon and Ratcliffefracture treatments. tion, differentialstrain curve anaLysis,differea-They presentedseveralmethods of determininghori- tial wave velocityanalysis,TABS, impressionzontal stress differencesbetween the pay zones and packers,and borehole televiewerstudiee. Thetheir bounding formations. These included in-situ results indicatedthat all of the methods yieldedmaasurementa(usinglcid treatments,mini-frac,and azimuth information;however, in theee tests thepump-in/flowbacks),differentialstrain curve anal- TABS method waa preferred from botha definitive andyees, conventionalcore analyses,and LSDS logs. economical standpoint.

.

.14085 RALPH U. VEATCH, JR. AND ZISSIS A. HOSCHOVIDIS 9

Other investigatorshave reportedthe resultsof azimuth studiesusifimentations tiltmeter!ll~On?~~ky ne type Of itl~t.rll-and borehole seismicte~hniques.134$13sAll have obtaineddefinitivesignal responsesfrom their instrumentationwhichyielded azimuth interpretations. From all of thework to date, it appears that techniquesare nowavailablewhich can provide azimuth information.However, in view of the uncertaintyinvolvedwithany single given method, one should employ a suffi-cient number of differentmethods to corroborateresults.

for the general case over a wide range ofdimensionlesstimes (tD) and dimensionlesstime ref-erence values (t*) where type curves are given forthe dimensionlesspressuredifferencefunction,c(tD,qp.

The functionG correspondsto the pressuredif-ference function,Ap(tD,tfi)which is computedby

Ap(tD,t~)= p(t~) - p(tD) ................(17)

FRACTURINGTREATMENTDIAGNOSTICSAND DESIGN I Dimensionlesstime, tD, is computedbyThere have been several significantadvances in

fracturingtreatmentdiagnosticand desi~..tech-nolog t~ extend the work of previous investiga-~or8.~3s 144 ~uch of this work relates to theinterpretationof downhole fracturingpressures(DFPs)while pumpingand the analysisof shut-indecline pressuresafter pumping is stopped. Itincludesmethods applied both to minifrac calibra-tion treatmentsand to stimulationtreatments.

Inl~~ area of treatingpressures,Conway,et al., suggestedthat five basic types of frac-ture behaviorcould be identifiedfrom downholefracturingpressures(DFPs)during pumping. Alarge number of treatmentpressurecharts were eval-uated, grouped by similarbehavior,and correlatedwith various design models or propagationmodes.The five types were designatedls follows:(I) Khristianovich- Geertsma - de Klerk (KGD),(II) Perkins-Kern-Nordgren(pKN),(III) Penny-Shaped,(IV) Medlin and Fitch, and(V) liolteand Smith. Ty es II and V have been docu-mented in previouswork.~3642s144 The others aredescribedon the basis of net DFP (i.e., DFP qinusclosure stress) versus pumping time plots on Logar-ithmic scale. Type I exhibits a constantnet DFP ordeclineswith a SLOPS of 0.05. Type 111 declinessteadilyand then increasesrather rapidlywith a2:1 slope. Type IV behavior,investigatedby Medlinand Fitch,14s is characts ized by large pressureincreases early in the treatmentand usuallyapproachesa screenoutmode by tha time viscousslurry reaches the formationresultingin veryLittle proppantentering the fracture. Conse-quently,well performanceis relativelypoor.Figure 36 depicts typical behaviorof plots for logof net DFP versus log of time. The Type I, II, 111,and IV curves are arranged in order of screenouttendencies,with Type I being the lowest and Type IVthe highest. Conway, et al., suggest the importanceof identifyingcharacteristicDFP behaviorpatternsearly in the life of a fracturingtreatmentprogramto improvedesign lnd execution of future treat-ments. tlethodshave been investigatedfor esti-mating DFP from surfacepre$sure data.

In the area of post-treatmentpressuredeclinefor determiningfracturingtreatmentdesign parame-ters, Nolte147 extendedhis original type curve

37 for general application*pressuredecline analysisThis covers a wide range of conditionsfrom highleakoff formations,as addressedby Smith,140to thevery low leakoff tight gz..sformations. The analysiswas also developed fe .de with either the PKN, KCD,or Penny fracturingmodels. Figure 37 can be used

t - toD=~ l **.******.*.l ..***...*.*.....(18)

where t is the time after shut-in,to is the pumpingtime, and tfiranges from 0.05 CO 2.0.

By plottingt versus the decline pressurefunctionjAp (tD,t~),on the same logarithmicscaleas the type curve scale, and findingthe type curvedecline match pressure,p*, one can use Eq. (19) forany of the three models (i.e.,PKN, KCD, or Radial)to calculatethe desired fracturedesign parameters(i.e., C, rp, E, orhf,L,R)

IIfPKN

c = rp< E p 32L CD. **(19)

@ dlaL

where C is fluid loss coefficient;p* is the typecurve match decline; r is the ratio of permeabLe tofractureareas; E is ?ha plane-strainelasticmodulus: B is the ratio of average to wellborenetpressure;h is the vertical fractureheight (PKN);

iL is the fr cture length, tip to tip (KCD): R is thefracture radius (Radisl);and Ap(tD,t#) is thedecline pressurefunction.

Martins and Harper 14s developeda type curveapproach for a fracture in l long perforatedintervalwhere it ia assumed that the fractureevolves as a family of confocalellipsesand thecreated fracturelength is on the same order of mag-nitude as the perforatedinterval. Leeig alsodeveloped type curves specificallyfor the KGD andRadial geometry models. These conform closelywiththose presentedby Nolte.

Using conceptssimilar to those presentedpre-:~:~1~~ Barrington,et aL.,150 and Harrin~tonfind

l method was developedby NoLtels forusing pressuredecline data to design proppantandfluid schedules for fracturing treatments usingfluid volume efficiencies,as expressed in Eq. (20):

429

AW UVEKVIBWUF ltlZGfiN1AuVANbna lm nxunAuLIAb rmnu~uumu .10 TECHNOLOGY 14G85

f= fq l *..****.,**. . . . . 0.0....0. ,.00 (20)

k

where f is the fracturevolume, V2 iS the 10ssvolume, and ef is fluid efficiencyfor the slurry.

Figure 38 is used to estimate ef frOM dimen-sionless closure time (i.e., the closure timefpumping time ratio, tc/ti). Then, Eq. (21) is usedto compute the requiredpad pumping time/treatmentpumping time ratio

tf 2=:= (1 - e )f= fi2...................21)i

for a selected treatment,where t is the padpumping time, t. is the total tre~tmentpumpingtime, and g2 islche loss ratio. Uith this methodcurves such as those shown in Fig. 39 can be con-structedwnich optimize proppantconcentration.Here dimensionlessslurry concentration,C , is theratio of the pumping slurry concentration~othe ~slurry concentrationin the fracture,Cs/C , and iq

irelated to dimensionlessslurry pumping t~ e, ~,.~y

J?CD (E) =& l . . . . ..0.0 . . . . . . . ..0...0 . . . . ..(22)

tlt.-fwhere: 6= ~-; ,...OO. eooooO(Z 3)oooo0(Z3)

and t =time(t>ft,) .

An example of the results for applying thismethod is shown in Fig. 40 where we eee very closelgreement between optimizingproppant schaduleswiththis techniqueas compared to those derived fromcomputer simulatormodels for three types of geom-etry (i.e., constantheight, growing height, andradial growth), This approach enables one to designproppant schedulesfrom field qinifrac pressuredecline data with very little a priori knowledge ofthe fracturegeometry. Note that a better lgreementwith computer simulatedresults may be obtained byincreasingf by 0.05. This paper also proposesamethod for estimatingexposure time to reservoirtemperature,and this can provide guidance in sched-ulingfluid gellin~agents and additives. Previouswork by Crawfordls also discusses the impact offluid efficiencyon proppantschedulingfor treat-ment deeign.

A very comprehensiveand compLete set of diag-nostic tests is being conductedac the DepartmentofEnergy MultiwellExperiment(IIUK)Site near RifLe,Colorado. The experimentis still in progress.Findings to date are discussed in recent docume~~~-tion by Northrop,et al.,1S4 Warpinski,et al.?

1S6 AS stated by Northrop~and Sattler,et al.et al., one of the purpoeesof the work is to inves-tigate the effectivenessof stimulationtechnologywith diagnosticinstrumentationand productionper-)

for-mce testing. Features of the MNX incLude:(1) three closely-spacedwells (115-215ft, 35-66 m)for reservoircharacterization,interferencetesting,well-to-wellgeophysicalprofiling,andplacementof diagnosticinstrumentationadjacent tothe fracturetreatment;(2) completecore takenthrough the formationsof interest;(3) a comprehen-sive core analysis program; (4) an extensive loggingprogramwith conventionaland experimentalLogs;(5) determinationof,in-situ stresses in sands andbounding shales; (6) use of various seismic surveysand sedimentologicalanalyses to determine Lens mor-phology and extent; (7) use of seismic,electricalpotential,and tilt diagnostictechniquesforhydraulic fracturecharacterization;and (8) aseries of stimulationexperimentsto address keyquestions. Many of the techniquesdeveloped fromthis experimentare being incorporatedinto practicethroughoutthe industry.

In the area of fracturedesign, several inves-tigatorshave presentedres~~~eof specialdesignapplications. Kim, at al., concluded it may bepossible to use fracturingpressure,pressuredecline data, and poet-fracturingtemperaturesur-veys to speculateinferencesof fractureorientationrelativeto the azimuth of a deviatedwellbore incertain areas. Other investigation have discussedspecialdesignsl:~rgeothermalreservoirs,1.58frac-ture acidizing, soft unf~f~~~2formations,180 andmultiple zone stimulation.

REAL-TINEMONITORINGAND CONTROL EQUIP14ENT

One of thf~more significantrecent advancementsin fracturingtechnologyhaa been the developmentofon-site data gatheringand monitoringequipment,andtreatingequipmentwhich is designed for computercontrol.

Coo er, et al.,163 Hannah, et ai.?164 and Har-ringtonlisdeecribe some of the on-site computerizedpLottinglnd analysiscapabilities,lnd monitoringsystems. These capabilitiesincludean on-site,field durable, transportablecomputer system; soft-ware for real-timeanalysis and graphi.aldisplay ofboth fracturing~pumping and post-shut-indeclinepressuredata; lnd an on-site rheologytest systeminterfacedwith the computer for determiningtheolo-gical flow data pertinent to the treatment.Figure 41 shows one example of the type of real-time, on-site data displayswhich are now availableindustrywidefrom the fracturingservice companies,and treatmentmonitoringservicecompanies.

There has been even more significantprogressenhancingthese capabilitiessince the presentationsby the above authors were published. Enhancementsand advancementsin computer hardware,software,microprocessor,servo-controLof blending equipment,proppantdensitometers,and on-site theologicaltestequipmenthave significantlyimprovedthe design andexecution of fracturingtreatments. The computerage has truly come for fracturing!

FRACTURE PROPAGATIONSItlULATIONMODELS

There have been some vety significantadvance-ments in the area of hydraulic fracturepropagationmodeling. Recent developmentsof working three-

430

14085 RALPH U. VEATCH, JR. AND ZISSIS A. MOSCHOVIDIS LA

0=* 9

dimensionalcomputercodes have4%WM?d:: he

et al.187 However,FE methods are generallywork of previousinvestigators. computationallydemandingas compared to BIEthis section,the theory behind 3D simulationis methods.summarizedand some examplesof actual fieLd casestudiesusing a 3D model are presented. Some The BIE method is based on the influencefunc-emphasis is given to the assumptionsfor the tion (Greensfunction)approachand reduces thegoverningequationsand to the numericaltechniques problem to singularintegralequationson the ptane

of the fracture.lgOlgl These equationscan beused in the models.solvednumericallyby discretizationo~9:h~9jomain

The hydraulicfracturingmodels presentedin of the fractureby FE,173 collocation, orthe literatureare numerousand of diverse com- finitedifference(FD) methods. The BIE method canplexity. They may be classified,accrrdingto their be practicallyapplied for homo eneous formationstrtltmentof the general fracturingequationsand tfor which the Greens functionl3 is wellkfiown. Itfracturegeometrycapabilities,into the following has been employed for the majority of the fracturingcategories: (a) simple geometrygeneral models, models both two-dimensional[simple1g4and tom-(b) lumped parametermodels, (c) two-dimensional plex:88) and 3DO;73S191S192 The foLlowin(2D) models, (d) pseudo three-dimensional(P3D) ?9Mlr:;equation (derivedfrom dislocationtheorymodels, and (e) three-dimensional(3D) planar frac- elastic potentialtheorylgO1g7lgsis commonlyture models. Detaileddescriptionof these models used:lies beyond the scope of this paper. However,anexcellenttreatmentof theirmain featuresis givenb~ Hendelsohn.1811s2 p(Xi*X~) = J{+ (xl-xi) ~

The basic elementsof fracturingmodels are(1) a crack openingmodel, (2) a fluid flow model,(3) a crack propagationcriterion,and (4) (when

aw+ (X2 Xfi) ~ 1 dxl dx2 *.*....(24)

numericalsoLutionsare performed)a fracturingpro- 1pagationalgorithm. It is the fracturepropagationalgorithmthat combines the fluid flow and fractureopening interactioninto a highly nonlinearcoupled whereproblemwhich satisfiesthe fracturepropagationcriterionwhile furnishinga numerical solution. IAll models treat the fractureprocese in aquasi-staticsense,meaning that inertialtermsare neglectedboth in the fractureopening and fluidmomentum equations. The formationis assumed to belinearlyelasticand the fracturingcriterionis andformulatedusing Giffiths183184lpproach in termsof the formationfracturetoughness(i.e., criticalstrese intensityfactor,K )~ For meet eiodels,flow R2 x (xl-~i)2+ (x2-x;)2 ,ineide the fractureis app~oximetedwith equationeior laminar flow of l Newtonianor Power Law fluidbetween parallelplates. Leak-off is usually and where S is the domain of the crack on th: X1-X2consideredas ona-dimeneionaland perpendicularto coordinateplane; p(x ,X2) ia the excess fluLd pres-the surfaceof the fracture. Leak-offvelo;~gy,VL, sure; (x,x~) ie ln 0&servationpoint on S; w isis assumed to be given by Cartersformula. iRecently,temperatureeffects and pore pressure

the frac ure width; and p and V l re the shearmodulus and Poissonsratio of the formation,

effects on closure streae have aleo been estimated respactivety. A differentBIE formulationhas alsousing simple one-dimensionalmodels, such as those been used by Mastrojannis,et al.;lgl199however,suggestedby Keck, et al.86 The great majority of this model does not have fluid flow and uses hydro-models lssume that the fractureie planar and static pressureto calculatecrack opening.remains planar during propagation. The generalproblemof a curved hydraulicfracture in a layeredformation( full 3D model) is computationally

Efforts to model crack opening behavior in l.ay-

intractableat the present time. However, someered inhomogeneousformationsusing EXE methodologyhave also been undertaken. A combinationof the BIE

models with curved fracturesin the sense oftwo-dimensionaLelasticityhave been presentedl~{

and FE methods, refarredto as the surface integral

Ingraffea,et al.1a7finite element hybrid (SIFEH)200method, is being

and Narendranand Cleary. investigated. Recently,the Greens function for

Crack Opening: Formulationand solutionof thetwo jointedhalf spaces of differentelastic proper-ties has been derivedby J. C. Lee and L. N. Keer

general crack opening problemcan be done usingfinite element (FE) or boundaryintegralequation

(Studyof a Three-DimensionalCrack Terminatingat

(BIE) techniques. The FE method can be applied toan Interface,to be publishedin the Journal ofAppliedt4echanics).This functioncan be applied to

determinefracturewidth for any shape of fracture(planaror curved)and for both homogeneousor inho-

obtain a first-orderapproximationfor the elasticfieldsof a crack in a Layered formation. Such an

mogeneous (layered)formations. It has been suc- approachhas been presentedby Clifton,201 where acessfullyapplied in a 3D plar,arfra;$~remodel numericalevaluationof the above Creene functionwithout fluid flow by Morita, et al. and in a was used. SimilarLy,the two jointedhalf spacemodel for curved 2D hydraulicfractureswithbranches (in the 2D elasticitysense) by Ingraffea,

Greens functionscan be used in the SIFEH method.A simpler,Less rigorousapproach to obtain crackopenings,by superpositionof the deformationsof a

r... . . . . . . -- -. --... . . . . . . . . . ..- --- . ---------- -------------

12 TECHNOLOGY 14085

half space due to a point load perpendicularto itssurface,has been presentedby Barree.202 ~e K(p~SftRf,elastic propertiesof the various formation layers

...)~K ~ ,..*.*.*.*........t..(26)were introduceddirectly in this fundamentalsolu-tion which is integratedover the fracturearea toobtain the crack opening due to a given excess for a stable crack. The notation here en,phasizespressuredistribution. that the stress intensityfactor depends on excess

pre:sure p, fracture shape S , positionon the crackFluid Flow: The consnonapproach to fluid flow front R , and ... idenotes ny other dependenceon

as related to hydraulic fracturingis to integrate meteriaf properties,inhomogeneityboundaries,etc.the continuityand momentum equationsacross the Although the above criterion(when violated)deter-width of the fractureand derive two-dimensional mines the Locationsof the crack front that propa-equationsin the plane of the fracture. This gate, it does not provide informationabout theapproachis necessary to make the problem tractable. velouity of crack propagationv (definedas theSuch an approach is valid because fracturewidth is craf,kfront displacementnormaleto the crack frontsmell relative to the fracturearea dimensions. during a time step). The functionalrelationshipFluid pressureand density do not vary appreciably betw?en K, Kc and VC cannot be obtained from analyt-across the fracturewidth. Fluid velocity vertical ical ~onsiderations,but must be determinedexpezi-to the fracturefaces is small and has a zero mentally. However, since mass balance dominates theaverage value over the fracturewidth. The velocity fracturingprocess,most reasonableassumptions199componentsin the plane of the fractureare assum~d can be made without significantlyaffecting thehave a known dist.:ibutionover the fracturewidth. final results.This can be approximatedby the velocity profile forLaminarflow of a Newtonianor Power Law fluid A simple, yet effectiveway, to enforce a crit-between parallelplates. Using such an integration icaL stress intensityfactor at the crack front isprocedure,203and neglectinginertialterms and to estimatea critical crack opening w at a giventerms involvingveLocity2~~adients,the following distance behind the crack front. The ~ctual crackequationcan be derived: opening for a stabLe crack should not exceed this

estimate [relationanalogousto Eq. (26)]. Valuesfor w can be estimated in terms of K from two-

P,a + rl(v/w)n-lva/w2 = p fa , a= 1,2 ...(25) dimensionalcrack displacements,20sb$ Eq. (27),

w =4(1-v)(Kc/@~~\ .................(27)where c

q = 2K(4+2/n)n ? where r is a specificdistance behind the crackfront and V,U are the Shear modulus and the Pois-sons ratio of the medium.

and tensorialnotation is employed. Here v is thefluid velocity;v is the fluid velocitymeg~itude; Applicationof 3D Model to Field Cases: Thef is the acceleration due to body forces; p is the applicationof 3D simulatorsis primarily importantf~uid pressure;p is the fluid density;w is the for complex reservoir conditions,i.e., where therefractureopening; and K and n are the consistency are multiple zones with varying elastic propertiesindex and flow behavior index of the fracturingfluid.

and leak-offcharacteristicsand where closurestress profilesdictate complicatedfracturegeome-tries. For such in-situ conditions,the fraccure

Eq. (25) is the momentum equationused in shape is unknown l priori and, dependingon in-situhydraulicfracturing. This form or simplifiedformsfor one-dimensionalflow are used in all fracturing

parameters,can be drasticallydifferent than2;~eshape the P3D simulators(Settariand Clear

models. Numerical solutionof Eq. (25) can be Palmer an{ Craig, 286zoa pal~r and Luiskutty9 ~210 212 Advani,etal,,obtainedeither with FE or FD methods. The FE Ueyer, 213 Thiercelin,

~E~~3:$f6;f!ii~$4b0th f?r 3D simula-et al., .215) can predict.214 and Settarl For these

and stmplerones in which one- complex types of simulations,a 3D fracturingmodeldimensionalflow (sireLe geometry,lumped and P3D is required. Abou-Sayedand Sinah218and Abou-

20E The FD method is more com-models) is assumed.

~~~~s~!g~ied for one-

Sayed, et al.217 presenteda case study using such adimensionalfluid flow 3D model (the Terra Tek, Inc. TerraFracmodel) that

quantifiedthe influenceof various in-situ condi-tions on fracturegeometry. In the remainderof

Fracture PropagationAlgorithm: Virtually all this section,two examples of unconfinedfracturecrack propagationalgorithmsare iterativein nature growth, simuLatedwith a version of the same 3Demployingan implicitor explicit FD approximation model.,are discuesed.of time derivatives. Time step and crack advance-ment are usually related by a crack propagationcri- The two examples are from an actual field caseterionexpressed from Linear fracturemechanics as study. Figure 42 shows the two closure stress pro-

files and the other field parametersused in thestudy. They were derived from our best estimatesof the in-situconditions. Case A representsthebase case; Case B has a 200 psi lower cloeure stressin the T-zone relative ts Case A (attributedto a

432

14085 RALPH U. VEATCH, JR. AND 21SS1S A. ?lOSCHOVIDIS 13

pressuredraw down scenarioafter production)and a the perforations(i.e. at 0.0 ft) are plottedversus50 psi higher closure stress in the dense streak the total injectedvolume. In case A we see no sig-(Dense-zone)at the upper portion of the U zone. nificantdifferencebetween these two values. TheyThe elaaticpropertiesare the same for all zones both increasewith the treatmentvolume, In case B(E = 1.26 x 106 psi, and v = 0.4), The perforations the maximum width occurs in T-zoneand increasesare locateddirectly below the Dense-zone. A con- with the volume injectedl s lxpected. However,thestant pumpingrate of 15 bbl/minwas maintained width at the perforationsinitiallyincreases(whileduring the treatment. Other data used are: fluid the fractureis still a penny) and subsequentlyviscosity90 cp (18.8 x 10-4 lb s/ft2): fluid den- decreasesat about 200 bbls, to remain constantatsity 1.3 g/cm3 (81*4 lb/ft3= 0.563 psi/ft);reser- approximately0.10 in. for the remainingof thevoir pressure 6275 psi at the perforat~ons:and treatment. For Case 8 in-situ conditions,anformation toughness 100C psi~in. increasedpad volume does not diminish the danger of

screen-out. A higher viscosity fluid and smallCompletionexperiencein the field had estab- proppantmay be required to pump the fracturing

lished that the target zone (T-zone)should not be treatmentsuccessfullywithout experiencingan unde-directlyperforatedbecause of severe solids produc- sirablescreenout. Note that the width at perfora-tion problems. The U-zonelocateddirectly below tions can actuallydecrease during pumping of thethe T-zoneis perforatedinstead. Treatments ini- treatment,especiallywhen unconfined,unsynszatrictiated in the U-zonehave the dual purpose of sti- fracturegrowth occurs. This was in fact observedmulatingthe U-zoneand also consnunicatingwith in simulatedcases with no closure stress discontin-the T-zone. Fractureheight growth was not uities but which had a steeperclosure stressgra-expectedto be confinedto the U-zone,and complex clientof 0.85 psi/ft,and a fluid density offractureshapes were expectedto evolve because of 0.84 g/cm3 (52.5 lb/ft3 = 0.364 psi/ft) with thethe in-situconditions. In the past, it had been remainingconditionsbeing the same. An intuitivethe practice to design such fracture treatments explanationfor constant or decreasingwidth at theueing a Radial (penny-shaped)model for lack of a perforationswith increasingpumped volume is thatbetter alternative. However,with the advent of a the fracture becomes locally stifferat the perfo-3D model, it was possibleto determine fracture rationsand pushes the fluid towards more flexibleshape and study the effectsof closure stress pro- vocationsnear the center of the fracture. Suchfile, actualclosure stressgradient, leak-off behaviorcan be quantifiedonly througha 3D frac-variation,and positionof perforations. It is this ture simulation.capabilitythat makes a 3!)model so useful forfieldswhere no significantconfiningbarriers exist The width history plot may be used to estimateor where special fracturingtreatmentslt interfaces the pad volume and the total treatmentvolume soneed to be designed. that proppant is introducedwhen the fracturehas

attained sufficientwidth. The maximum proppantFigure43 shows the fractureshape evolution size may also be estimated. For example, case B

for Case A for injectedvolumes ranging from allowa at most l 20/40 proppantwith a maximum prop-113-1338bbls. The fracturewas initiatedas a pant diameter of 0.0331 in. to be pumped.small pennyof 10 ft radius Locatedat the centerof the perforationa(i.e.,8366 ft), which is the The character of the downhole pressurebehaviororigin of the verticalY-axis. Note that the frac- for the two casea is lleo different as shown inture lssentiallyremainsapproximatelya penny, Fig. 47. The maximum pressure in the fractureandalthoughsome confinementcan be observedat the the pressureat the perforationsare plotted versusS-zone/T-zoneinterface. the total injectedvolume. Note that the pressure

values plottadare in excess of a referencepressureFigure44 shows the fractureshape evolution of 7084 psi. Due to hydrostaticpressure the max-

for case B where injectedvolumes ranged from 87 to imum pressureoccurs below the perforations. Case A1424 bbls. The fracturewas initiatedas a 10-ft demonstratesa typical pressure decrease duringradial crack at the center of the perforations. The pumpingwhich is characteristicof unconfinedfrac-resultingshape is drasticallydifferent than that ture growth of a penny shaped fracture. Case Bof Case A. The fracture grows mainly in the shows a more complicatedpressure behevior lt theT-zonewhere closure stress is low. This type of early pumping stages.This ia due to the presenceofbehaviorcan only be quantifiedby numerical simula- the pressurebarrier in the Dense-zone. Thetion and representsa delicatebalance between in- pctentialtouse the pressure plot as a closuresitu valuesof closure stress,closure gradients, stress diagnostictool (by comparingthe simulatedleak-off,locationof the perforations,and fluid pressurewith the actual pumping pressureduring arheology. mini-fractest) exists but has not been utilized in

this study. In many simulatedcases the pressureFigure45 comparesthe fracturewidth profiles profilemay not be smooth, as in these cases, but

along the well-bore for both cases A and B. In case may have severalspuriousspikes. Such spuriousA, the wximum fracturewidth occurs close to the pressurespikes can be correlatedto relativelybigperforations. In case B the fracturegrows unaymme- volume balanceerrors, and thus are easily identifi-tricallywith respect to the perforationsand a able.point of reducedwidth develops there, referred toas a width pinch point. Width pinchingnear the Figure 48 showe the evolutionof the fractureperforationsmay cause an undesirablescreen-out dimanaions,i.e., maximum fracture Length, fractureduring the earLy stages of the treatment. Figure 46 height above the perforations,fracturedepth belowshows the fracturewidth history for both cases. the perforations,and maximum fractureheight areThe maximum fracturewidth and the fracturewidth at plottedversus the total volume injected. In Case A

433

AN OVERVIEWOF RECENT ADVANCES IN HYDRAULICFWCTURING14 TECHNOLOGY 14085

the fracturepropagatesin both che horizontaland 8a. Cooke, C. E. Jr.: Effectsof FracturingFluidverticaldirections. In case B the fracture is on FractureConductivity,~. ~. ~.essentiallyconfinedheight-wiseand grows length- (Ott. 1975) 1273-82.wise in the T-zone. An estimate of the totalfracturetreatmentvolume may be made from this 8b. Cooke, C. E, Jr.: Fracturingwith a Highplot, based on the desired dimensionsof the frac- StrengthProppant,~. Pet. Tech. (Oct. 1977)

ture. ~, 1222-26.

In conclusion,3D simulatorsare very valuable 9. Neal? E.,.A.,Parmley,J. L., and Colpays,P.for many aspects of hydraulicfracturinganalysis J.: Ox~de Ceramic Proppantsfor Treatmentofand design. They can be used to: (a) determinethe Deep Well Fractures,paper SPE 6316 presentedfractureshape for given in-situand pumping condi- at the 1977 SPE Annual TechnicalConferenceandtions; (b) estimate proppantsize, pad volume, and Exhibition,Denver,Oct. 9-12.treatmentvolume from the fracturewidth and frac-ture dimensionhistories;(c) study the effect of 10. Sinclair,A. R. and Graham, J. U.: A Newthe locationof the perforationsand the associated Proppant for HydraulicFracturing,paper pre-problemsof width pinching;and (d) diagnose in-situ sented at the 1978 ASME Energy TechnologyCon-closure stress featuresby comparingthe actual ference,Houston,Nov. 5-9.mini-fracpressurewith simulatedpressure.

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14085 RALPH W. VEATCH, JR. AND 21SS1S A. MOSCHOVIDIS 17

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-

77. Clark, P. E. and Guler, N.: ProppantTrane-port in Vertical Fractures: SettlingVelocityCorrelations,*paper SPE 11636 presentedat the1983 SPE/DOE Sympoeiumon Low-Permeability,Denver,Harch 14-16.

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Foamed FracturingFluids

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89. Harrie, P. C.: Effectsof Texture on Rheologyof Foam FracturingFluids,paper SPE 14257

I

AN OVERVIEW OF RECENT ADVANCES IN HYDRAULIC FRACTURING18 TECHNOLOGY 14085

presentedat the 1985 SPE Annual Technical In-SituStress Contrasts,paper SPE 8937Conferenceand Exhibition,Las Vegas, presentedat the 1980 SPE/DOE UnconventionalSept. 22-25. G.ssRecoverySymposium,Pittsburgh,Hay 18-20.

90. Harris, P. C.: DynamicFluid-LossCharacter- 101. Koerperich,E. A.: Shear-WaveVelocitiesDet-isticsof COZ Foam FracturingFluids, paper ermined from Long- and Short-SpacedBoreholeSPE 13180 presentedat the 1984 SPE Annual Fall AcousticalDevices,SPE. J. (Oct. 1980)TechnicalConferenceand Exhibition,Houston, 317-26.

Sept. 16-19.102. Teufel, L. U.: Determinationof In-Situ

91. Harris, P. C. and Reidenbach,V. C.: High- Stress from Anelastic Strain RecoveryHeasure-TernperatureTheologicalStudy of Foam Frac- ments of Oriented Cores, paper SPE 11649 pre-turing Fluids,paper SPE 13177 presentedat sented at the 1983 SPE/DOE Symposiumon Lowthe 1984 SPE Annual Technical Conferenceand Permeability,Denver, March 14-16.Exhibition,Houston,Sept. 16-19.

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