Topical Report Hydraulic Fracture Model Comparison Study: Complete Results " Prepared by: N. R. Warpinski, Sandia National Laboratories I. S. Abou-Sayed, Mobil Exploration and Production Services Z. Moschovidis, AMOCO Production Company C. Parker, CONOCO GasResearchInstHute Tight Sands and Gas Processing Research Department Febnm_ 1993 @STIRIBUTION OF THIS DOCUMENT IS UNLIMITED , II TI , ii ,- , i i ,t i i i i, ,i , ,, , i , lr
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Prepared by:N. R. Warpinski, Sandia National LaboratoriesI. S. Abou-Sayed, Mobil Exploration and Production ServicesZ. Moschovidis, AMOCO Production CompanyC. Parker, CONOCO
GasResearchInstHute
Tight Sands and GasProcessing Research DepartmentFebnm_ 1993 @STIRIBUTION OF THIS DOCUMENT IS UNLIMITED
, II TI , ii ,- , i i ,t i i i i, ,i , ,, , i , lr
GRi9310109 SAND93-7042
HYDRAULIC FRACTURE MODEL COMPARISON STUDY:COMPLETE RESULTS
TOPICAL REPORT(February, 1993)
Prepared byN. R. Warpinski Sandia NationalLaboratories
I.S. Abou-Sayed Mobil Explorationand ProductionServicesZ. Moschovidis AMOCO ProductionCompany
C. Parker CONOCO
PreparedatSandia NationalLaboratories
Division6114P.O. Box5800
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LEGAL NOTICE This reportwas preparedby SandiaNationalLaboratoriesasan accountof work sponsoredby the Gas Research Institute(GRI). NeitherGRI, membersof GRI, norany personactingon behalfof either:
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"-R-D=ORTIX)(_UIdENTATION '" .[Pmrr .o. z S. r._. k=c.,,.k,_No.PAGE GRI-93/0109
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4. Title a_l Sul_Hle S. ReLmsctOete
2/17/93 Preparatiol
Hydraulic Fracture Model Comparison Study" Complete Results Li,
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Topical report on the •results of the Fracture Propagation Modeling Forum
i
This study is a comparison of hydraulic fracture models run using test data from the GRI
height versions; (2) 3-1ayer pseudo-3-D models; and (3) 5-1ayer 3-D or pseud.o-3D models.Model calculations were provided by several consulting companies, oll producing
companies, service companies, and academia. Modelers were given the measured stress and
material property data obtained at SFE-3 and fluid properties approximating those used
during SFE-3 stimulations. Companies were allowed to run any or all of the three cases
(constant height, 3 layer, or 5 layer) using their own models or commercial models they
had purchased, Included with the results are brief discussions of each model. Thispaper documents the differences in length, height, width, pressure, and efficiency
predicted by the various models for each of the three cases. Well-known differences in
length between 2-D PKN and GDK models are shown, but so are differences between thepseudo-3-D and fully-3-D models. For example, two of the models yield much shorter
lengths than other 3-D models. Overall, efflciencies varied between 40% and 97%, and
net pressures ranged from about 700 to 1600 psi for the 3-1ayer and 5-1ayer cases.
Heights varied from 300-700 ft. These comparisons clearly show that fracture design
models give widely varying results. These results provide the petroleum engineer a
practical comparison of the various available design models for an actual field test.
17. _ Aaal_Is e. Oev_
Tight gas sands, hydraulic fracturing, fracture modeling
(See ANSI--Z311.111) See Ilnelesm:lNe_s en Reveesbe _--'CIONAL Irl_ Z?2 (4-77_(For_merty INTIS..-$ 5)Oe@e_men! _ Commerce
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Title HydraulicFracture Model ComparisonStudy:CompleteResults
Contractor Sandia NationalLaboratories
GRI ContractNumber: 5089-211-2059
Principal N.R. WarpinskiInvestigator
Report February 1991-February, 1993Period Topical Report
Objective To developa comparativestudyof hydraulic-fracturesimulatorsin orderto providestimulationengineerswiththe necessaryinformationto make rationaldecisionson the type of modelsmostsuitedfor theirneeds.
Characteristicsof these reservoirs,however,makeproductiondifficultand often economicand stimulationis required. Hydraulicfra¢;_uringis one of the mostimportantstimulationtechniquesavailableto thepetroleumengineer,being used extensivelyintightgas sandstones,coalbed methane,highpermeabilitysandstonesinAlaska,very weak sandstonesoff theUS. gulfcoast, in horizontalwells in chalks,and inmanyotherapplicationsfromwastedisposaltogeothermalreservoirs. Because of thisdiversityofapplication,hydraulicfracturedesignmodelsmustbeable to accountfor widelyvaryingrockproperties,reservoirproperties,in situstresses,fracturingfluids,and proppantloads. As a result, fracturesimulationhas emergedas a highlycomplexendeavorthat mustbe able to describemanydifferentphysicalprocesses.
In addition,manymodelershave addedad-hocfeaturesto theirmodelsto simulatemechanismsthatare notwell understoodat thistime. Such mechanismsincludetipeffects,wall roughness,complexfracturing,andsomeaspectsof heightgrowth. As a result,fracturemodelshave becomeheteromorphicwith nostandardof comparison.Engineersare thusfacedwith
a difficultchoice in selectinga model that isappropriatefor their needs.
Technical The technical approach was to collectand integrateApproach the resultsof the Fracture Model PropagationForum
intoa comparativestudyof the similarityanddifferencesof hydraulic-fracturemodeloutputrunonthe same inputdata. Participatingmodelersweregiven twotreatmentdata sets (one Newtonianfluid,one power-lawfluid) and four differentgeometries(constant-heightPKN, constant-heightGDK, 3-layer, 5-layer) and asked to providelength,height,maximumwidthat the wellbore,average widthat the wellbore,averagewidth in the wholefracture, net pressure,andefficiencyat 25 minuteintervalsthroughoutthe fracturetreatment(totaltime of 200 minutes). These resultswere assembledby a four membercommittee intoplotsand tablesof comparativedata.
Results This report is a comparisonof the fracture modelingresultsof twelve differentsimulators,someof them runin differentmodesforeight separatedesigncases.Comparisonsof length,width,height,net pressure,maximumwidthat thewellbore,average widthat thewellbore,and averagewidth in the fracturehave beenmade, bothfor the final geometryand as a functionoftime. For the modelsin thisstudy,differencesinfracturelength,heightandwidthare often greaterthana factor of two. In addition,severalcomparisonsof thesame modelwithdifferentoptionsshow a largevariabilityin modeloutputdependingupon the optionschosen. Two comparisonswere madeof the samemodel runby differentcompanies; in bothcases theagreementwas good.
Figure I Lengthcomparisonfor cases 1-4Figure2 Net pressurecomparisonfor cases 1-4Figure 3 Efficiencycomparisonfor cases 1-4Figure4 Comparisonof maximumwidthat wellbore for cases 1-4Figure 5 Comparisonof average widthat wellbore for cases 1-4Figure 6 Comparisonof average width in fracture for cases 1-4Figure 7 Lengthhistoryfor case 1Figure 8 Net pressurehistoryfor case 1Figure 9 Historyof widthat wellborefor case 1Figure 10 Lengthhistoryfor case 2Figure 11 Net pressurehistoryfor case 2Figure 12 Historyof widthat wellborefor case 2Figure 13 Lengthhistoryfor case 3Figure 14 Net pressurehistory for case 3Figure 15 Historyof widthat wellborefor case 3Figure 16 Lengthhistory for case 4Figure 17 Net pressurehistory for case 4Figure 18 Historyof widthat wellborefor case 4Figure 19 Lengthhistory for otherconstantheight-models- 200 cpFigure 20 Net pressurehistoryfor other constantheight-models- 200 cpFigure 21 Historyof widthat wellborefor other constant-heightmodels- 200 cpFigure22 Lengthhistoryfor otherconstantheight-models- n', k'Figure 23 Net pressurehistoryfor otherconstantheight-models- n', k'Figure24 Historyof widthat wellborefor other constant-heightmodels- n', k'Figure25 Lengthcomparisonfor cases5 and 6Figure26 Heightcomparisonfor cases5 and 6Figure27 Net pressurecomparisonfor cases 5 and6Figure28 Efficiencycomparisonfor cases 5 and6Figure29 Comparisonof maximumwidthat wellborefor cases 5 and 6Figure30 Comparisonof average widthatwellborefor cases 5 and6Figure31 Comparisonof average widthin fracturefor cases 5 and 6Figure 32 Lengthhistoryfor case 5Figure 33 Heighthistoryfor case 5Figure 34 Net pressurehistoryfor case 5Figure 35 History of widthat wellborefor case 5Figure 36 Lengthhistoryfor case 6Figure 37 Heighthistoryfor case 6Figure 38 Net pressurehistoryfor case6Figure 39 Historyof widthat wellborefor case 6Figure40 Lengthcomparisonfor cases 7 and 8Figure41 Heightcomparisonfor cases 7 and8Figure42 Net pressurecomparisonfor cases7 and8Figure43 Efficiencycomparisonfor cases 7 and 8
Figure44 Comparisonof maximumwidthat wellborefor cuses 7 and 8Figure45 Comparisonof average widthat wellborefor cases 7 and 8Figure 46 Comparisonof average width in fracturefor cases 7 and 8Figure47 Lengthhistoryfor case 7Figure.48 Heighthistoryfor case 7Figure49 Net pressurehistoryfor case 7Figure 50 Historyof widthat wellbore for case 7Figure51 Lengthhistoryfor case 8Figure52 Heighthistoryfor case 8Figure53 Net pressurehistoryfor case 8Figure54 Historyof widthat wellbore forcase 8
AppendixAFigureA1 Heightprofile- case 5FigureA2 Width profile- case 5FigureA3 Heightprofile- case 6FigureA4 Width profile- case 6FigureA5 Heightprofile- case 7FigureA6 Width profile- case 7FigureA7 Heightprofile- case 8FigureA8 Width profile- case 8
AppendixBFigureB1 Heightprofile- case 5FigureB2 Width profile- case 5FigureB3 Heightprofile- case 6Figure B4 Width profile- case 6Figure B5 Heightprofile- case 7Figure B6 Width profile- case 7Figure B7 Heightprofile- case 8Figure B8 Width profile- case 8
AppendixCFigureC1 Heightprofile- case 5FigureC2 Width profile- case 5FigureC3 Heightprofile- case 6FigureC4 Width profile- case 6FigureC5 Heightprofile- case 7FigureC6 Width profile- case 7FigureC7 Heightprofile- case 8FigureC8 Width profile- case 8
AppendixDFigureD1 Heightprofiles- cases 5-8
AppendixEFigure E1 Height profile- case 5Figure E2 Width profile -case 5Figure E3 Height profile- case 6Figure E4 Width profile- case 6Figure E5 Height profile- case 7Figure E6 Width profile- case 7Figure E7 Height profile- case 8Figure E8 Width profile..case 8
AppendixFFigure F1 Height profile(Stimplan)-case 5Figure F2 Width profile(Stimplan)-case 5Figure F3 Height profile(Stimplan)- case 6Figure F4 Width profile(Stimplan)-case 6FigureF5 Height profile(Stimplan)- case 7FigureF6 Width profile(Stimplan)- case 7FigureF7 Height profile(Stimplan)- case 8Figure F8 Width profile(Stimplan)- case 8FigureF9 Height profile(TerraFrac) - case 8
AppendixGFigureG1 Height profile-case 5FigureG2 Width profile-case 5FigureG3 Height profile- case 6FigureG4 Width profile- case 6FigureG5 Height profile- case 7FigureG6 Width profile- case 7FigureG7 Heightprofile- case 8Figure G8 Width profile- case 8
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1.0 RESEARCH OBJECTIVES
The objectiveof the GRI FracturePropagationModelingForumand the associatedpublicationof the results inthis report is to assemblea comparativestudyof availablehydraulicfracture models. Hydraulicfracturingis one of the mostimportantstimulationtechniquesavailable to the petroleumengineer,being used extensivelyin tightgassandstones,l-5 coalbedmethane,6 highpermeabilitysandstonesinAlaska,7 veryweak sandstonesoffthe US. gulfcoast,8 inhorizontalwells in chalks,9,10 and in manyother applicationsfromwaste disposalto geothermalreservoirs. Becauseof thisdiversityof application,hydraulicfracturedesignmodelsmustbe able to accountforwidelyvaryingrockproperties,reservoirproperties,insitustresses,fracturingfluids,and proppantloads. As a result,fracturesimulationhasemerged as a highlycomplexendeavor_hatmustbe able to describemanydifferentphysicalprocesses.
As the complexityof hydraulicfracturinghas increased,manymodelershave usedad-hoc features intheir modelsto simulatemechanismsthat are notwell understoodatthis time. Suchmechanismsincludetip effects,wall roughness,complexfracturing,and someaspectsof heightgrowth. As a result,fracturemodelshave becomeheteromorphicwith no standardof comparison. Engineersare thus facedwith adifficultchoice inselectinga model that is appropriatefor their needs.
In order to comparemodelsin a reasonablesense,ali modelsmustbe runwiththesame input. The purposeof the Forumwas to bringconcernedmodelerstogethertoshare resultsof theirmodelsand to agree ona setof rigid inputdata that ali couldrunfor a comparativestudy. Participatingmodelerswere given twotreatmentdata sets(one Newtonianfluid,one power-lawfluid) and four differentgeometries(constant-heightPKN, constant-heightGDK, 3-layer, 5-layer) and asked to providelength,height,maximumwidthat the we,bore, averagewidthat the we,bore, average widthinthewhole fracture,net pressure,and efficiencyat 25 minuteintervalsthroughoutthefracturetreatment(totaltimeof 200 minutes). This reportdocumentsali of the resultssuppliedby the modelersand tabulatesand plotsthoseresults.
Im
2.0 RATIONALE
The petroleumengineer, who mustdesignthe fracture treatment, is often confrontedwith a difficultchoice of selectinga suitablehydraulic-fracturemodel for his/her needs,yet there is very littlecomparative informationavailable to help in making that choice,particularlywith respect to the newer 3-D and pseudo-3-D models. Many experiencedengineers will also have their own biasesabout hydraulicfracture performance andwouldprefer to find a code whoseoutputis mostconsistentwiththe engineersexperience. The purposeof this report is to help providesome guidanceby comparingmanyof the available simulators.
This reporthad itsorigins in the Fracture PropagationModelingForum held February26-27, 1991, near Houston,TX. Thisforum,whichwas sponsoredby the GasResearch Institute,was open to ali knownhydraulicfracturing modelers. Participantswere asked to providefracturedesignsbased on the SFE No. 3 fracture experiment,aswell as a history match of the actual pressure data fromthe treatment. AftercomparisonOfthe fracture designsand historymatchespresentedat this meeting,afinal, reviseddesigndata setwas given to ali participants. Most of the reviseddatasetswere returnedby September1991, althougha couplewere returned or modifiedaslateas November 1993. The resultsin this report are derivedfrom the modelcalculationsof the reviseddesigndata set. Bece3seof the difficultyin tryingtoestablishany consistencyin the use of the actual treatmentdata (e.g., effects of thebreaker, temperature, rate changes,etc.), itwas decidedthat any further attempttocompare history matcheswouldneed to be deferred. Thus, publicationof forum resultsis limitedto the design phaseonly.
To publishthe results,a four-membercommittee(the authors)was chosenfromforumparticipants. In assemblingthiscomparison,the membersof the committeehavepurposelyattemptedto avoidmakinganyjudgmentsaboutthe relative value of differentmodelsso as not to injectour biases intothiscomparison. Only the resultsandquantifiablecomparisonsare given.
Since hydraulicfracturingis performedin a large percentageof gas completions(andin recompletions),the benefitto the gas consumercomesfrom the optimizationof thistechniquewhen an appropriatemodel is used. Optimizationresultsin morecost-effectivecompletions,enhancedgas production,lowerwellheadcosts,andadditionalsupply.
The modelerswho participatedinthe forum and prepared data for thispaper deservespecialthanksfor their efforts. Most importantly,Dr. Steve Holditch of S.A. Holditch&Associatesshouldbe singledoutfor specialmentionas the prime moverof the forum,afollow-upSPE paper, and this report.
3.0 BACKGROUND - BASIC MODELING DISCUSSION
In recentyears, there has been a proliferationof fracturingsimulatorsused in the oilindustry. This proliferationwas intensifiedby the availabilityof personalcomputersandthe need for fast runningdesign simulatorsfor use in the field. Applyingthese modelsas "black boxes",withoutknowingthe underlyingassumptionsmay lead to erroneousconclusions,especiallyfor unconfinedfracture growth. While specificdescriptionsofthe individualmodelsare given in section4.0, thissection providesa general overviewof hydraulic-fracturemodelsand cataloguesthe variousmodelsintosimilargroupings.
Hydraulicfracturingis a complex non-linearmathematicalproblem,that involvesthemechanicalinteractionof the propagatingfracturewiththe fluiddynamicsof theinjectedslurry. Severalassumptionsare commonlymade to render the problemtractable:plane fractures,symmetricwithrespectto the wellbore;elasticformation;linearfracturemechanics for fracturepropagationprediction;powerlaw behavioroffracturingfluidsand slurries;simplificationof fracture geometry, and its representationbyfew geometricparameters;etc. The reader isreferred to the SPE MonographVolume 1211 for a detaileddescriptionof the governingequations. Althoughthemodelspredict"trends"of treating pressurebehavior;they may notalwaysreliablypredict the observedbehaviorfor a giventreatment. This discrepancyhas beenattributedto manycomplex interactionsof the injectedfluidswiththe formationthat arenotwell understood.
An attemptto phenomenologicallycharacterizesomeof these complexprocessesoccurringwithinthe fracture(e.g., multiplefractures,increasedfrictionallosses)andnear the fracture tip(e.g. non-linearformationbehavior,microcracking,formationplasticity,dilatancy,plugging,etc.) was made invarioussimulatorsby the introductionof additionalad hocparameters("knobs"). The choiceof values forthese parametersis onlybasedon the experienceof the modeler,possiblywithsomeguidancefromthelaboratory,fieldobservations,or fromothercomputationalresources(e.g., finiteelementcodes). These knobsare usedto matchmodel predictionswithfield observedbehavior,and result in the lackof a standardmodel responsefor a givenphysicalproblem. This issuewas addressedinthe forumby havingdifferentparticipants(severaldifferentmodels)simulatecommontestcases derived fromthe actual SFE No.3 well fracturingtreatment. These modelscan be categorizedinthe orderofdecreasingcomplexityas follows:
(1) Planarthree-dimensional(3D) models
* TerraFrac of TerraTek, Inc.12-16 runbyARCO* HYFRAC3D by Dr. Advaniof LehighUniversity17
(2) UniqueFinite DifferenceSimulatorGOHFER of MarathonOil Co.18,19
(3) Planar Pseudothree-dimensionalmodels
A-"Cell" Approach
STIMPLAN of NSI, Inc.ENERFRAC of Shell20,21TRIFRAC of Holditch& Assoc.
B- Overall Fracture GeometryParameterization
FRACPRO of RES, Inc.22-25MFRAC-II of Meyer and Assoc.26-29
(4) Classic PKN and GDK Models30-35
PROP of Halliburton34-36Chevron2-D model37Conoco2-D model38,39Shell2-D modelPseudo-3-Dmodelsrun in constant-heightmode
A discussionof the basicsof these modelsis givento providesomeinsightson themodel assumptionsand howthey are expectedto affectthe results.
3.1 ..planar3-D Models
The TerraFrac12-16 and the HYFF<AC3D17 modelsemploysimilarassumptionsandformulatethe physicsrigorously,assumingplanarfractures of arbitraryshape inalinearlyelasticformation,two dimensionalflow inthe fracture, power lawfluids,andlinearfracture mechanicsfor fracture propagation.Their differenceis inthe numericaltechniqueto calculatefractureopening.TerraFrac usesan integralequationrepresentation,while the HYFRAC3D modeluses the finiteelement method. Bothmodelsuse finiteelementsfor two-dimensionalfluidflow withinthe fractureandemploya fracture tip advancementproportionalto the stressintensityfactor on the fracture tipcontour.
3.2 planar 3-D Finite-Difference.ModeI_,GOHFER
Besidesthe numericaltechniqueused, thismodel18,19 is differentfromthe previousmodelsin twofundamentalways: (a) fracture opening is calculated by superpositionusingthe surfacedisplacementof a half space undernormalload (BoussinesqSolution);(b) the fracture propagateswhen the tensile stressnormalto the fracturingplane exceeds the tensilestrengthof the formationat somedistanceoutsidethefracture by enforcingthe tensilecriterionat the centroidof the cells "outside"the
fracturingcontour. This model predictshigher treatingpressuresand shorterandwiderfractures as comparedwith the ones of the previous3D models.
3.3 Pseudo-3-D Models
These modelswere developedfrom the PKN modelby removingthe requirementofconstantfracture height. They use equationsbased onsimple geometries(radial, twodimensional,elliptical)to calculate fracture widthas a functionof positionand pressureand applya fracturepropagationcriterionto both lengthand height. Furthermore,theyassumeone dimensionalflow alongthe lengthof the fracture.
These modelscan be dividedintotwo categories:(A) modelsthat dividethe fra_urealong its lengthinto"cells", anduse localcell geometry(two-dimensionalcrackorpennycrack) to relatefracture openingwith fluidpressure;(B) modeQsthat use aparametricrepresentationof the total fracture geometry. As a resultof theseassumptions,it is expectedthat each classwill havedifferentfracture geometry, evenfor the simplecase of a confinedfracture.
The pseudo..3Dsimulatorsare extensivelyusedfor fracturedesignbecause of theirefficiencyand their availabilityon personalcomputers. However,they are directlyapplicableonlyfor the geometriesthat are notsignificantlydifferentfrom the basicassumptionsof the model(e.g., modelsbasedon a PKNgeometryshouldhave largelength/heightratiosto be appropriate). For relativelyunconfinedfracture growthin acomplexin situstressprofile,a 3D model is thusmoreaccurate in predicting"trends"offracture geometry. To avoid thisproblem,somepseudo-3-Dmodelsattemptto includetruly3D fracture behaviorintermsof "history" matchingor "lumped"parametersdeterminedfromfully3D-solutionsof simplerproblemsor determinedfrom simulationsusing3D models.
3.4 Classic PKN and GDK Models
The difference in treatingpressurebehaviorand fracturegeometryof the PKN andGDK modelsis well documentedin the literature11,40 and need not be repeatedhere.
4.0 FRA(_TURE MODELS
This sectiondescribesthe individualfracture modelsthat were used inthis comparison.Shortdescriptionsof the modelswere providedby the modelersor by the companieswho ran commerciallyavailable models.
4.1 S.A. Holditch& Assoc. (TRIFRAC)
SAH's hydraulicfracturing modelTRIFRAC is a pseudo-3-D fracture propagationandproppanttransport modelthat computescreated and proppedfracture dimensionsusinga finite-differencenumericalapproach, lt has the capabilityto handle multiplenon-symmetricstress layerswith uniquevalues for Young'smodulus,Poisson'sratio,fracture toughness,permeability,porosity,and fluid leakoffcoefficientsfor each layer.Properties for a maximumof twenty-twolayerscan be inputcurrently.
The apparentviscosityof the fracturingfluid is computedbased upon the shear rateinsidethe fracture and changes in n' and k' due to variationsof temperatureand time.A temperaturecalculation modelis thuspart of TRIFRAC. Choice of initiatingthehydraulicfracture fromten differentlayerssimultaneouslyis available. Special optionsare available to inputpumpschedulefor nitrogenfoamtreatments.
The created geometrycomputationmoduleis coupledwitha rigorousfinite differenceproppanttransportsimulatorthat solvessimultaneouslyfor proppantdistribution,transport,and settlingalongwiththe growthof the fracture. Dependinguponthe fluid "velocityalong the heightof the fracture andthe rate of settlingof the proppant,themodelcomputesthe proppantprofileat each time stepduringthe job.
TRIFRAC also has the simplertwo-dimensionalgeometrycomputationalfinite-differencemodelsof Geertsma and DeKlerk,and Perkins,Kern,and Nordgren.Horizontalfracturegeometrycalculationusingthe GDK methodis also available. Alithese modelsare coupledwith proppanttransportcalculationmodules.
4.2 Meyer & Associates(MFRAC-II)
MFRAC-I126-29is a pseudo-3-Dhydraulicfracturingsimulator. MFRAC-II alsoincludesoptionsfor the penny,Geertsma-deKlerkand Perkins-Kem/Nordgrentype2-Dfracturingmodels. Version7.0, written in C++ anddevelopedunderMicrosoftWindows3.x, offersa user interfacewhich takesfull advantageof the facilitiesexistingunderthisoperatingsystem. The program'sfeatures includeintelligentmenus, a complete fluiddatabase,flexibleunitsand usercustomizedhelp screens.Thisstudywas run usingMFRAC-II, Version 6.1.
MFRAC-II accountsfor the coupledparametersaffectingfracturepropagationandproppanttransport. The majorfracture, rockandfluidmechanicsphenomenainclude:(1) multi-layer,unsymmetricalconfiningstresscontrast,(2) fracturetoughnessand
tiploverpressureeffects, (3) rockdeformation,(4) variable injectionrate and timedependentfluid rheologyproperties,(5) multi-layerleak-offwith spurt lossand (6) 2-Dproppanttransport. The fracture propagationmodelcalculatesfracture length,upperand lower heights,width,net pressure,efficiency,and geometryparametersas afunctionof time. The widthvariationas a functionof heightand confinings_ressis alsocalculated.
In orderto provideapplicabilityover the broadestrange of circumstances,MFRAC-IIoffersnumerousoptionswhich can be employedby the user. These optionsand otherfree parameters("knobs")allowscustomizationin the modelingapproachadopted.MFRAC-II was run in twodifferentmodesto demonstratethe effectsof someof theseparameters. In one case, the base modelusingthe systemdefaultswas run(designatedMEYER-1); in a secondcase (MEYER-2) additionalparameters(suchasgreater friction dropin the fracture)were applied. In bothcases, as a default,theviscousthinningassumptionwas made. Withoutviscousthinning,the effectivefrictionfactor wouldhave increased,resultingin highernet pressures,greaterwidthsand ashorter length. In addition,the fully implicitcoupledmodelfor heightgrowth(Vet. 7.0)
. resultsin increaseddevelopmentof fractureheightand net pressurefor certain multi-layerformations.
4.3 Advani (Lehiah HYFRAC3D)
The 3 layer and 5 layermodel results(Cases5 through8) are obtainedfromtheHYFRAC3D code.17 This finiteelementcode is based on a set of coupledmassconservation,fluidmomentum,constitutiveelasticityand fracture mechanicsequationsgoverningplanarhydraulicfracturepropagationin a multilayeredreservoir. A mappingtechniqueof the baseline mesh(88 triangularelementsrepresentinghalfof thefracture)definedin a unitcircleto arbitraryshapedfracturegeometriesis utilized inthenumericalschemefor trackingthe movingfracturefront.
The PKN modelresults(Cases I and2) are also based on a two-dimensionalfiniteelementmodelsimulatorwith standardPKN modelequationsincludingvertical stiffnessand one-dimensionalfluidflow. These simulationresultsare obtainedusing20 lineelementsfor the normalized,time-dependentfracture half-length.
4.4 Shell (ENERFRAC)
ENERFRAC20,21 is a hydraulicfracture modelthat predictsfracturedimensionsforuncontained(circular)and contained(rectangular)fractures. ENERFRAC incorporatesfracturetipeffects in additionto the other interactingprocessesof viscousfluidflow,elastic rockdeformation,and fluid loss. Fracturetip effectsare accountedfor throughadirect inputof the rock'sapparentfracturetoughnessor the fracturetip net pressure(overpressure). This overpressureis definedas the instantaneousshut-in-pressureminusthe closurepressureand can be determinedinthe field froma micro&acormini&actest.
Shell also provided2-D PKN and GDK model results. The ENERFRAC resultsprovideda usefulcomparisonof the effect of free modelparameters(the "knobs"discussedearlier) on the results. Shell providedresultsfor typicalfracture toughnessvalues measured in lab tests (the base case, designatedENERFRAC-1) and also for aseveral tip overpressures. The particularcase of a tip overpressureof 1000 psi(ENERFRAC-2) is shownin several plotsfor comparisonwiththe base case. Thiscomparisonallowsus to see the effect of fracture tip overpressureon fracture geometryand net pressure.
4.5 Halliburton(PROP)
The PROP program34-36 is a 2-D fracture designmodelbased on Daneshy'snumericalsolution. Its numericalnaturemakesthe modelmuchmore flexiblethanmostanalytical models. For example,the programhas recentlybeen modifiedfor useof multiplefluidsand rateswithina singletreatment,each fluidwith itsown set of time-and temperature-dependentrheologicalparameters. In additionto the power-lawmodelnormallyusedto characterize gelledfracturingfluids,PROP uses the three-parameterHerscheI-Bulkleymodelfor fluidscontaininga nitrogenor carbondioxidephase. The program'sproppanttransportcalculationsare of similarcapability.
Althoughthe modeloriginallypresentedby Daneshywas basedon the Khristianovic-Zheltovwidthequation(designatedGDK inthispaper), the PROP programhas sincebeen expandedto includea similarnumericalsolutionof PKN-type geometrywith awidthprofilebased on calculated localpressures. The resultspresentedhere are forthe GDK-typesolutiononly.
4.6 (_hevron
Chevron's2-D fracturingsimulatoris capableof predictingthe propagationof constantheighthydraulicallyinducedverticalfractures for a power-lawfluid. The simulatoralsoincludesa proppanttransportmodelwith proppantsettlingand a productionmodel.The simulatoris capable of predictingthe createdfracture geometrybased on eitherPerkins-Kem-Nordgren(PKN) or the Geertsma-deKlerk(GDK) models, lt is mostsuitableto designfractureswhere the geologicconditionsrestrictheightgrowth. Infracture propagationmodels,the equationsdescribingconservationof mass,conservation of momentum,continuityof fluid flow,and linear elasticdeformationof therock in plane strainare usedto calculatemassflux,fracturewidth, pressure,and lengthas functionof time. The proppanttransportmodelcalculates thefinal proppedconcentration,width,andbank heightgivena settlementvelocity,and can predictpossibleproblemscaused by proppantbridgingor screenout.
The fracturedwell productionmodelis based on an analyticsolutiondevelopedby Leeand Brockenbrough37 to studythe transientbehaviorof a well interceptedby a finiteconductivityfracture in an infinitereservoir. Thisproductionmodelprovidesthe short
time productionresults. Combiningthissolutionwiththe well knownsemi-logasymptoticsolutionfor longertime periodsprovidesa reliable tool for predictingthepotentialproductivityof the fracturedweil.
4.7 Conoco
Conoco'sfracture designprogramis a constant-heightmode/_.2-D)where either PKNor GDK geometrycan be selected,as describedby McLeod.,au lt has single inputsforn', k' and leakoffcoefficient. However,the model is capable of calculatingthe positionsand concentrationsof progressivefluidlproppantstages. Fracturearea can becalculated by either the Howardand Fast Modelor an extremelyaccuratesimplificationby Crawford.39
4.8 Marathon (GOHFER)
MarathonOil Company'sGrid OrientedHydraulicFractureExtensionReplicator(GOHFER)18,19 is a planar3-D fracture geometry simulatorwithcoupledmulti-dimensionalfluid flowand particletransport. As indicatedby the name, the model isbasedon a regulargrid structurewhich is usedfor boththe elastic rockdisplacementcalculationsand as a planar 2-D finitedifferencegridfor the fluidflow solutions. Theareal pressuredistributionobtainedfromthe fluidflow equations,includingproppanttransport,is iterativelycoupledto the elasticdeformationsolution. Using thefinitedifferencescheme for fluidflowallowsmodelingof multiplediscretefluidentry pointsrepresentingperforationsat variouslocations.
Eachgrid nodecan be assignedan individualvalueof net stress,pore pressure,permeability,porosity,wall-buildingcoefficient,rock strength,Young'sModulus,andPoisson'sRatio, as well as variablesdescribingfracturewall roughnessand tortuosity.The displacementof the fracture face at each node is determinedby integrationof thepressuredistributionoverali nodes, includingthe computedtensile stressdistributionin the unbrokenrock surroundingthe fracture. The fracturewidthequationused is thegeneral formula for displacementof a semi-infinitehalf-spaceacted upon byadistributedload, given by Boussinesq.The solutionis generalenoughto allowmodelingof multiplefracture initiaticnsitessimultaneously,and is applicableto anyplanar 3-D geometryfromperfect containmentto uncontrolledheightgrowth.
4.9 ARCO (usingTerraFr.ac)
TerraFracTM Code12-16 isa fullythree-dimensionalhydraulicfracturesimulator, ltwas initiatedat Terra Tek in 1978 and itscommercialavailabilitywas announcedinDecember,1983. The overall approachused inthe modelis to subdividethe fractureintodiscreteelementsand to solvethe governingequationsfor these elements. Thesegoverningequationsconsistof (1) 3-D elasticityequationsthat relate pressureonthecrack faces to the crack opening,(2) 2-D fluidflowequationsthat relate the flow inthefracture to the pressuregradientsin the fluid,and (3) a fracturecriterionthatrelatesthe
lO
intensityof stressstate ahead of the crackfront to the critical intensityfor Mode Ifracture growth. TerraFrac providesmanydistinctivefeatures including(1) 2-D fluidflowfor both proppantand temperaturedistribution,(2) multiplestages havingdifferentfluids,proppants,rates, withfluidand proppantpropertiesbeing functionsoftemperature if desired, (3) multiplelayers,each havingdifferentin situstress, Young'smodulus,fracture toughness,Poisson'sratio,and leakoff,(4) poroelasticandthermoelasticcapabilitiesfor waterfloodingand other applications,(5) a robustmeshgeneratorto handle a wide variety of fracture geometriesand a quasi-Newtonmethodto solvethe nonlinearsystemof equationsfor the fluidpressures(thisapproachprovidesfor fast convergenceand highaccuracy),and (6) a post-shut-incalculationcapabilityfor which noadditionalassumptionsare made (onlythe injectionratechanges).
4.10 NSI (STIMPLAN)
STIMPLAN is a state-of-the-art 3-D hydraulic-fracturesimulatorfor fracture designandanalysis incomplexsituationsinvolvingheightgrowth,proppantsettling,foamfluids,tipscreen out, etc. The modelhas completefluid/proppanttrackingthat allows foroptimumfluidselectionand schedulingbasedon time andtemperaturehistory.Fractureheightgrowth is calculatedthroughmultiplelayers,and includesproppantsettlingand bridgingcalculations. A FractureAnalysis/HistoryMatchingmoduleprovidesfor historymatchingof measurednet treatingpressuresto yield the mostaccuratepossibleestimationof actual fracturegeometry and behavior. Also,simulationsduring the fractureclosure(pressuredecline)periodaid in pressuredeclineanalysisforfluid lossin complexgeologicsituations.
4.11 ResourcesEnaineerinqSystems(FRACPRO)
FRACPRO22-25 usesmeasuredvaluesof flowrate,proppantconcentration,and fluidrheologyparametersto calculate the pressuredropdowna wellboreof variabledeviationand diameter,and the time historiesof the fracturegrowthand the netfracture pressureare calculated. The wellbore modelhandlesnon-Newtonianfluidsand correctsfor the effects of nitrogenfoam, carbondioxide,and proppantphases.The modelalso accountsfor frictionvariationfromentrainedproppant.
The fracture model is 3-D, inthat spatialvariationsin reservoirstress,modulus,pressure,and flow distributionare taken intoaccount. However,it does not need tocalculate the variationsat specificpointswithinthe fracture. Instead,the effects areintegratedinto functionalcoefficientsof governingdifferentialequations,greatlysimplifyingthe calculation of the fracturedimensions. The modulecan therefore runmanytimesfaster than real time,as requiredfor historymatchingon-site. Thecoefficientsnecessary to calculate the spatialvariationsare calculatedfrom a fullthreedimensionalmodeland checkedagainstexperimentaland fieldtestdata.
11
FRACPRO handlesup to three moduluszones, up to fiftystresszones,and up to fiftypermeable (leakoff) zones. Fluid lossis modeledas one-dimensionalflowperpendicularto the fractureface, followingDarcy-lawbehavior, includingspurt loss,filtercakebuildupon the fracture face, and a compressiblereservoir-fluidregion. Therise in confiningstressdue to poroelasticeffects (backstress)is included. Heattransfermodelingassumesthat there is a cubic-fittemperaturedistributionbetween thefractureand the end of the heat transferregion.
FRACPRO modelsthe convectionandsettling of proppantina fracture.Proppantconvectionis a processwherebyheaviertreatmentstages (e.g., proppantstages)displace rapidlydownwardfrom the perforationsto the bottomof the fracture. Thosestages are thenreplacedby the pad, or by low-concentrationproppantstages. Initiallaboratoryand computersimulationsindicatethat proppantconvection may be thedominantmechanismin propped-fracturestimulations.As weil, FRACPRO can beused to model proppantsettling. The proppantis carriedwith the fracturingfluid, andsettles. The model takesinto accountthe effectsof non-Newtonianfluids,hinderedsettling rates, and settledbank buildup.
4.12 .Texaco(usinaFRACPRO)
FRACPRO was also runby TEXACO for sixdifferentcases. These includesingle-layerPKN and GDK modes,a 3-layer case withconstantfrac fluidviscosity,and 5-layercases for constantfluidviscosity,power-law-fluidbehavior,and power-law-fluidbehaviorwiththe tip dominatedrheologybehaviornotoperating. The 5-layer runsprovidea goodcomparisonof tip-dominatedvs. conventionalrheologyresultsusingFRACPRO. The 3--layerand the tip-dominated5-layer cases providea goodcomparisonof the resultsfor two differentcompaniesusingthe same model.
4.13 ARCO (usingSTIMPLAN)
STIMPLAN was also run by ARCO for fourdifferentcases. These includeboth3--layerand 5-layer cases. These resultsprovidea good comparisonof the resultsfor twodifferentcompaniesusingthe same model.
12
5.0 $FE-3 FORMATION AND TREATMENT DATA
The input data for the fracturemodelingcomp&:isonis based upon the resultsobtainedat the GRI-sponsoredSFE-3 experiment.3,41 SFE-3 was drilled as the MobilCargillUnit No. 15 well in the Waskom Field, HarrisonCounty,Texas. The well was spuddedin September, 1988, and drilledto a totaldepthof 9700 ft (2957 m). Of particularinterestwas the CottonValley Taylor sand whichwas perforatedbetween 9225-9250 ft(2812-2819 m) and 9285-9330 ft (2830-2844 m). An extensivelog programwas runonthiswell and detailedcoreanalyses performed. Both prefracwell-testingand post-fracproductiontestingwere performed. Two minifracsand one full-scale treatmentwereconducted as partof the stimulationprogram.
The SFE-3 data setwas specificallychosentc insurethat the modelcomparisonwouldbe performedwith actual field data and notfor a contriveddata set that mightfavoronetype of modeloverothers. In addition,the SFE-3 data set is one of the mostcompletesets of well informationavailable, and includesstress,rockand reservoirandwell-performance results.
For this initialstudy,the relevantrockand reservoirinformationare showninTable 1.As will be describedinthe nextsection,three differentphysicalconfigurationswereconsidered:a singlelayer, three layers, andfive layers. Stressand rock propertymeasurementswere averagedover the appropriatedepthsfor each interval to yieldthephysicaldata given inTable 1. Most importantly,the stresscontrastsrangefrom 1450-1650 psi (10-11.4 MPa), althoughthe lowerbarrier is only40 ft (12 m) thickfor the fivelayer configuration. Young'smodulusand Poisson'sratiowere obtainedfrom sonicmeasurements,thusaccountingfor the elevatedvaluesof Young'smodulus.
The actual SFE-3 treatmentwas a thirteen-stageprocedureusing primarilya40 lbl1000 gal (4.8 kg/m3) crosslinkedgelwith sandstagesvarying from 1-8 ppg(120 kglm3). For the purposeof thiscomparison,the treatmentwas simplifiedto asingle, constant-property,fluidwith no proppant,primarilybecause changes in fluidpropertiesdue to temperatureor the additionof proppantcan notbe easilyquantifiedand any resultingcomparisonswouldbe of questionablevalue.
13
6.0 TEST CASES
As noted inthe descriptionsection,mostof the models are capable of accommodatingand processinga much broader range of complex data thanpresented in thisdata set(i.e., multiplerockproperties, leak-offcoefficients,n',k', etc.). Refer to Tables 1 and 2for the complete set of data input. However, the data setwas arbitrarilyrestrictedtolimitas many discretionaryinputsas possibleto allowa moredirect comparisonofmodelperformance. The treatment inputis also not to be construedas optimumdesignparameters, but rather an approximationof thatfrom SFE No. 3.
There were a totalof eight possiblecaseseach participantcould model if they sochose. These were GDK, PKN, 3-layer, and 5-layer caseswithseparate runs for aconstantNewtonianviscosityand a constantn' and k'power-lawfluidas follows:
The PKN and GDK cases were runwith a constant height(2-D) setat 170 ft (52 m).The 3-layer and 5-layer caseswere run usinga 3-D or a Pseudo-3-Dmodelallowingfractureheightto be determinedby the model. Of particularinterestwas if the fracturebrokethroughzone 4 in the 5-layer case.
The importantrockpropertydata for the 3-layer case are showngraphicallyin Figure1,and the data for the 5-layer case are shownin Figure2. These stressand modulusprofilesare simplificationsof the actual stressand modulusprofilesmeasuredat theSFE No. 3 site.
14
_ 7.0 MODEL RESULTS
A shortsummaryof the final geometryat the end of pumpingis given in Tables 3-5 forthe 2-D, 3-layer, and 5-layer cases respectively. A summaryof the time tobreakthroughfor the 5-layer calculationsis given in Table 6. Ali of the submitteddatafromthe modelersare given inTables 7-83, in the followingorder:
The graphsof the data shown inthissectionwere derivedfromthis tabular data set. Inaddition,somemodelersprovidedadditionalgraphicalinformationon the width andheightprofilesalong the lengthof the crack. These are given inthe followingappendices:
Consideringfirst the 2-D summaryresultsgiven in Table 1, the final half lengthfor aliofthe 2-D modelsare shownin Figure3. The well-knowndifferencein lengthestimatesbetweenthe PKN and GDK modelsis evident inthese results,butsomedifferencesbetween differentmodelsin each groupbecomeapparent. Presumably,thisdifferenceisbecause of otheroptionsincludedin somemodels. The effectof the differentrheologiesis generallysmall. Besidesthe PKN and GDK models,GOHFER andENERFRAC-1 and -2 are also shown.
' II , , ii I =, , , , .... lP _.... m_ _111
15
The reductionin lengthbetweenENERFRAC-1 and ENERFRAC-2 is due tL,increasedtipoverpressur,-,.Likewise, the reduction in lengthbetweenMEYER-1 and MEYER-2 isdue to optionsthatwere includedin MEYER-2 w_ich reflectthe designers'incorporationof morecompley_hysicsintothe fracturingprocess.
The net pressuresfor the 2-D models, shownin Figure4, followa similarpatterntolength,withthe GDK modelsgivinglow pressuresand the PKN modelsprovidinghighnet.pressures. GOHFER is differentinthat it predictsshortlengths,like the GDKmodels,but highpressureslike the PKN models.
The efficienciesfor the 2-D calculationsare shown in Figure 5. Values ranged from 70-95%.
The fracture maximumwidthis shownin Figure6, while the average widthat thewellboreis given in Figure7, and the averagewidththroughoutthe whole fracture is_:,hownin Figure8. As expected, the GDK models;providemuchgreaterwidththan thePKN models. GOHFER's width is moresimilarto the GDK modelswhile ENERFRAC'swidth is closerto the PKN models.
The time-historyresultsfor Case I (GDK with200=cpfluid) are shownin Figures9-11for length, net pressureand widthat the wellbore,respectively, lt is interestingto notethat even for thissimpledata set there is a significantdifferencebetween the variousGDK ,_oclels.
Time-historyresultsfor Case 2 (GDK withpower-lawfluid) are shown in Figures12-14for I_ngth,net pressureandwidthat the wellbore,respectively.Aswith the Case 1results,there is also a significantdifferenceinthe calculationsof the variousmodels.
Time history,resultsfor Case 3 (PKN with200-cp fluid) are shownin Figures15-17 forlength,net pressureand maximumwidthat the welllbore,respectively. DifferentPKNmodelsalso have considerabl_variationin theircalculatedoutput.
Time history resultsfor Case 4 (PKN withpower-lawfluid) are showninFigures18-20for length,net pressureand maximumwidthat the wellbore,respectively.
Time history resultsfor other2-D modelsusinga 200-cp fluid (these do notfit exactlyintothe Ca_e I or 3 categories)are shown in Figures21-23 for length,net pressureand maximumwidthat the wellbore,respectively. The effectof tip overpressureis seenbycomparingthe two ENERFRAC cases.f
Time historyresultsfor other2-D modelsusinga power-lawfluidare shown inFigures24-26 for length,net pressureand maximumwidthat the wellbore,respectively. Tip-overpressureeffectscan be again seen for a power-lawfluid.
II I ! ......
16
7.2 3-Layer Results
The 3-layer summaryresults(Table 4) showconsiderablymore variabilitythan the 2-Dcases. A comparisonof ali 3-Layer lengthcalculations(Cases 5 and 6) is showninFigure27. The fracture half lengthvariesfrom less than 1000 ft for FRACPRO togreater than 3000 ft for the conventionalpseudo-3-D models. An interestingandillustrativecomparisonis seen in the differencesbetween MEYER-1 and -2. MEYER-2,usingsomefeatures that the modelerbelievesare moreappropriatephysics,resultsina fracture lengththat is nearly 1000 ft less than the base case with no options. Manysuchoptionshave probablybeen employedon the other models,butwere notidentifiedas suchfor thiscomparison
The favorablecomparisonbetween ARCO and NSI runningStimplan,and a similarfavorablecomparisonbetween TEXACO and RES runningFRACPRO, showthatconsistentresultscan be obtainedfroma given modeleven if run by differentorganizations.
The fracture heightcomparison,given in Figure 28, showsthat muchgreater heightgrowthis obtained by FRACPRO than by other models. Net pressures,showninFigure29, are particularlyhigh in FRACPRO and GOHFER. Efficienciesvary from40% to greater than 95%, as given in Figure 30.
Fracture maximumwidths(at the wellbore) are given in Figure31, the maximumaverage widthat the wellboreis shownin Figure32, and the averagewidth in the entirefracture is shown in Figure33. In ali three cases, Fracproand GOHFER calculatemuchgreaterwidthsthan the other models.
Time historiesfor Case 5 (3-layerwith200-cp fluid) are given in Figures34-37 forlength,height,net pressureand maximumwidthat the wellbore,respectively. Thesegraphsclearly showthatthere is an amazingrange of outputfrom the differentmodels,even for this relativelysimplecase.
Time historiesfor Case 6 (3-layer with power-lawfluid) are given in Figures38-41 forlength,height,net pressureand maximumwidthat the wellbore,respectively. Heightgrowthis extremelyfast in FRACPRO, but much bettercontainedin mostof the othermodels.
7.3 5-Layer Results
The 5-layer (Cases 7 and 8) summaryresults(Table 5) are similarto the 3-layercomparison,except thatthe lengthin somemodelsis shorterbecause the heightbreaksthroughthe lowerbarrier. The half lengthsare shownin Figure42 andthefractureheightsare given in Figure43. Net pressuresrangefromnearly700 psi(4.8 MPa) to almost 1400 psi (9.7 MPa), as shownin Figure44. Efficienciesrange_rom;=bout60% to 97%, as shownin Figure45. Again, there is relativelygood
17
agreement betweenthe same model runby two differentcompanies(Stimplanby NSIand ARCO and Fracproby RES and Texaco).
The maximumfracturewidth at the wellboreis shown inFigure 46, the fracture averagewidthat the wellbore isgiven in Figure47, and the average widththroughoutthe entirefracture is shownin Figure 48. As in the 3-layer case, Fracproand GOHFER providethe mostwidthdevelopment.
Time historiesfor Case 7 (5-layer with 200-cp fluid) are shown in Figures49-52 forlength,height,net pressure,and maximumwidthat the wellbore, respectively. Thelengthdevelopmentin thiscase is notuniformbecause heightbreakthroughintothelowerbarrier limitsgrowthin someof the models. Bycomparingali these resultswiththe 3-layer calculations,the effect of breakthroughintothe lower low-stressregioncanbe seen.
Time historiesfor Case 8 (5-layer withpower-lawfluid) are shown in Figures53-56 forlength,height,net pressure,and maximumwidthat the weUbore,respectively. One ofthe interestingresultsof thisstudyis the behaviorof the pressureresponseas thefracture breaks intothe lowerbarrier. Somemodelshave pressuredecreasing,othershave pressureremainingfiat,while otherscontinueto have pressureincrease.
8.0 DISCUSSION
The completionengineer nowhas a widearray of hydraulicmodelsavailable for bothdesignand analysisof hydraulic-fracturetreatments. However,these modelscalculatewidelydifferentfracturegeometriesfor the same inputparameters,and itbecomesimportantto choosea modelthat meetsthe needsof that particularengineer. Thepurposeof thiscomparisonstudyisto evaluatethe size of the differenceand to providesufficientinformationfor the engineerto make a studiedchoice.
lt is clear that thereare somemodelsthat predictresultsthat are significantlydifferentfromthe majority. Consideringthe 5-layer cases shownin Figures42-44, FRACPROcalculates veryshort fracture lengthsandhighnet pressuresand largeheight.GOHFER also predictsshortfracture lengthsand highnet pressures,butthe heightgrowthis notas severe. TRIFRAC, STIMPLAN,TERRAFRAC, and MFRAC-II are aliin generalagreement,with longerfractures,lessheight,and somewhatlowernetpressures. HYFRAC3D is midwaybetweenthe two endcases.
MFRAC-II (in 2-D, 3-layer and5-layer geometries),ENERFRAC (in2-D geometry),andTexaco'sFRACPRO cases (5-layergeometry)were run in twodifferentmodesand thusprovidea usefulassessmentof the importanceof the optionsthat are availableto thefracturedesigner. In the originalformulationof thisstudy,the modelerswere asked torun their modelsin botha base mode(no options)and thenwith a best-optionmode,that is,a modethat reflectedtheir expectationsof the optionsneededto providetheclosestsimulationof true fracturebehavior. Such optionsmay have includedtip
18
effects, higherfrictionalpressuredrops in the fracture, multiplefracture strands,enhanced toughness,or others.
In the three cases mentionedabove, the modelersprovidedsuch a comparison,andthese resultscan be used to estimate howsignificantlythe engineer can modifythefracture designby tryingto incorporatehisestimateof the "best physics"possiblefor agiven reservoir. Presumably,such an estimatewouldbe guided by experiencewiththereservoir. For the 5-layer case with non-Newtonianviscosity,"best physics"resultsforfracture lengthdifferedby about 22% for MFRAC-I! and 57% for FRACPRO run byTexaco. For the 2-D case with non-Newtonianrheology,ENERFRAC resultsdifferedby about7%. Since manymodelshave such options,these resultsshouldbe a usefulguidelinefor estimatingthe differences in modeldesignsthat can be obtained.
The 2-D models,both PKN and GDK, generallyprovideself-consistentresultsand thedifferencesbetweenthese typesof models has been discussedin priorpublications.11,40 Chevron's2-D model,however,yields considerablyshorterlengthsthan the other PKN and GDK models. GOHFER is also of notebecause ityieldsalengthtypical of the GDK models withthe net pressureof the PKN models. Otherdifferences inthese 2-D modelsare minor.
This particularcase was chosen because itwas a realisticfield situationforwhichdetaileddata were available. The committeeandthe modelersali recognize that otherformations,with differentstressand lithologydata, may providea considerablydifferentcomparisonof the models. Goodexampleswouldbe caseswhere there are minimalstresscontrastsandwhere the stresscontrastsare extremelylarge, ltwouldbebeneficial if futuremodel comparisonstudiesinvestigatedthose cases as weil.
lt is also interestingto note thatthere was generalagreementamongthe modelersatthe forumthat pressure-historymatching(not includedinthis report)wouldalwaysresult in similarfracturegeometries,regardlessof the model. This is because a matchof the pressurewillconstrainthe widthof the fracture, and hence lengthand heightwillvary by relativelysmallamounts. Such an agreementis notthe case, however,fordesign modeling(the resultsof this report)where the pressureis determinedby themodel.
Finally, in assemblingthiscomparison,the membersof the committee(the authors)havepurposelyattemptedto avoid makingany value comparisonsbetweenthe variousmodels. Only the resultsand quantifiablecomparisons(e.g., modelA frac lengthisgreater than modelB frac length)are given,as itwouldtake a committeewith greaterpowers than thisone has to trulyknowhowthe fracture is evolvinginthe subsurfaceand, thus,to decidewhich model is better.
19
9.0 CONCLUSIONS
A comparisonstudyof manyof the available hydraulicfracturemodelshas beencompleted. This studyprovidesinformationon the relative differencesinthe modelsforthisone particularcase.
These comparisonsshow that differencesin calculatedfracture lengthscan be large,as much as a factor of threedifference. Fracture heights,for the multi-layercases, candifferby more than 50%. Net pressuresalso differby a factor of two.
Calculationsfromthe same modelwith differentoptionsgive a useful comparisonof theimportanceof ali of the additionalphysicalmechanismsthat are continuouslybeingaddedto the modelsto explainthe wide varietyof pressureresponsesobserved indifferentreservoirs. Such optionsgive the completionsengineer considerableflexibility,butalso difficultchoicesof when variousoptionsshouldbe used.
, ,, _ i, II ' ,, , , ,, m, If' '' ' ' ' ' ' .....
20
10.0 REGOMMENDATIONS
Two primary recommendationsresultfrom thisstudy.• ltwould be beneficial to performthis same type of studyfor different input
conditions. This particularcase was chosen because itwas a realisticfield situationfor which detaileddata were available. Other warrantedcases are those wherethere are minimalstresscontrastsand where the stresscontrastsare extremelylarge
• The pressure-historymatches thatwere performed at the Fracture PropagationModelingForumprovidedmany interestingresults,butwere notsuitable fordocumentationbecausethere was no simpleway to compare the variousmodels.However,a comparisonof pressure-historymatcheswouldbe of value.
2. Robinson,B.M., S.A. Holditch& R.E. Peterson,"The Gas Research Institute's2ndStaged Field Exp.:A Studyof HydraulicFracturing,"SPE 21495, Gas Tech. Symp.,Houston,TX, Jan. 1991.
3. Robinson,B.M., S.A. Holditch,W.S. Whitehead & R.E. Peterson,"HydraulicFracturingResearch in EastTexas: Third GRI Staged Field Experiment",JPT, Vol.44, 78.87, Jan. 1992.
4. Saunders, B.F., B.M. Robinson,S.A. Holditch& R.E. Peterson,"HydraulicFracturingResearch in the FrontierFormationthroughthe Gas Research Institute'sFourthStaged Field Experiment,"SPE 24854, 67th Ann.Tech. Conf.,Washington,D.C., 909-922, Oct. 1992.
5. Northrop,D.A. & K-H. Frohne, ''The MultiwellExperiment- A Field LaboratoryinTight Gas SandstoneReservoirs,"JPT, Vol. 42, 772-779, June 1990.
6. Cramer, D.D., "The UniqueAspectsof FracturingWestern U.S. Coalbeds,"JPT,Vol. 44, 1134-1140, Oct. 1992.
7. Martins, P.J., J.C. Abel, C.G. Dyke, C.M. Michel & G. Stewart,"Deviated WellFracturingand ProppantProductionControlin the PrudhoeBay Field,"SPE 24858,67th Ann. Tech. Conf., Washington,D.C., 955-970, Oct. 1992.
17. Advani, S.H., T.S. Lee & J.K. Lee, "Three-DimensionalModelingof HydraulicFractures in LayeredMedia: Part I -Finite ElementFormulations,"ASM.E J. Ener.qyRes. Tech., Vol. 112, 1-9, 1990.
26. Meyer, B.R., "Design Formulaefor 2-D and 3-D Vertical HydraulicFractures:ModelComparisonand ParametricStudies,"SPE 15240, Unconv.Gas Tech. Symp.,Louisville,KY, 391-401, May 1986.\
27. Meyer, B.R., "Three-DimensionalHydraulicFracturingSimulationon PersonalComputers:Theory and ComparisonStudies,"SPE 19329, Eastern Reg. Mtg.,Morgantown,WV, p. 213, Oct. 1989.
28. Meyer, B.R., G.D. Cooper& S.G. Nelson,"Real-Time 3-D HydraulicFracturingSimulation:Theory and Field Case Studies,"SPE 20658, 65th Ann. Tech. Conf.,New Orleans, LA,417-431, Sept. 1990.
29. Hagel, M. & Meyer, B., "UtilizingMini-Frac Data to ImproveDesign andProduction,"CIM 92-40, Pet. Soc. of CIM Ann. Tech. Conf., Calgary,Alberta, June1992.
32. Geertsma,J. & F. deKlerk, "A RapidMethodof PredictingWidth and ExtentofHydraulicInducedFractures,"JPT, Vol. 21, 1571-1581, Dec. 1969.
33. Nordgren,R.P., "Propagationof Vertical HydraulicFractures,"SPE_.___JJ,Vol. 12, 306-314, Aug. 1972.
34. Daneshy,A.A., "On the Designof Vertical HydraulicFractures,"JPT,83-93, Jan.1973.
35. Daneshy,A.A., "NumericalSolutionof Sand Transport in HydraulicFracturing,"P.J.._!.,132-140, Jan. 1978.
36. Poulsen,D.K. & W.S. Lee, "FractureDesignwithTime- and Temperature-DependentFluid Properties,"SPE 12483, 1984 FormationDamage ControlSyrup.,Bakersfield,CA., Feb 13-14, 1984.
24
37. Lee, S.T. & J.R. Brockenbrough,"A New Analytical Solutionfor Finite-ConductivityVertical Fractureswith Real Time and LaPlace Space :ParameterEstimation,"SPE 12013, 58th AnnualTech. Conf., San Francisco,CA, October 5-8, 1983.
38. McLeeod, H. O., "A SimplifiedApproachto Designof FracturingTreatments UsingHighViscosity Cross-LinkedFluids,"SPE 11614, Low Perm.Symp., Denver, CO,121-136., March 1983.
39. Crawford,H.R., "Proppant Schedulingand Calculationof Fluid Lost DuringFracturing,"SPE 12064, 58thAnn. Tech Conf., San Francisco,CA, Oct. 1983..
40. Geertsma, J. & R. Haafkens, "A Comparisonof the Theories for PredictingWidthand Extentof Vertical HydraulicallyInducedFractures,"ASME J. Enerqv Res.Tech., Vol. 101, 8-19, March 1979.
41. -"Staged Field ExperimentNo. 3," GRI-9110048, GRI Final Report, Feb. 1991.
25
Tables and Figures
26
Table I Rock and Reservoir DataI
Interval Depth Zone In Situ Poisson's Young's Fracture(ft) Thickness (ft) Stress Ratio Modulus Toughness
Appendix A Width and height profiles for SAH Trifrac
Figure Al-A8 give the height profiles and width profiles calculated by Trifrac as afunction of length for cases 5-8. These profiles were provided by S.A. Holditch &Assoc. and have not been changed for publication.
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116
Appendix B Width and height profiles for Meyer-1
FigureBl-B8 give the heightprofilesandwidthprofilescalculated by MFRAC-II (no"knobs")as a function of lengthfor cases 5-8. These profileswere providedby Meyer&Assoc.and have not been changedfor publication.
117
118
119
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120
121
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122
123
124
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125
Appendix C Width and height profiles for Meyer-2
Figure C1-C8 give the height profiles and width profilescalculated by MFRAC-II("knobs" on) as a function of length for cases 5-8. These profiles were provided byMeyer & Assoc. and have not been changed for publication.
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126
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131
132
133
t34
Appendix D Width and height profiles for Advani model
Figure D1 givesthe heightprofilescalculatedby HYFRAC3D for cases 5-8. Theseprofileswereprovidedby S.Advaniof Lehigh Universityand have not been changedfor publication.
135
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136
Appendix E Width and height profiles for GOHFER
Figure El-E8 give the height profilesandwidthprofilescalculatedby GOHFER as afunction of lengthfor cases 5-8. These profileswere providedbyMarathon.and havenotbeen changedfor publication.
137
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145
Appendix F Width and height profiles for ARCO (Stimplan & TerraFrac)
Figure F1-F8 give the height profiles and width profiles as a function of length for cases5-8 using Stimplan. Figure F9 gives the height profile as a function of length for case 8using TerraFrac. These profiles were provided by ARCO and have not been changedfor publication.
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155
Appendix G Width and height profiles for RES Fracpro
Figure G1-G8 give the height profiles and width profiles calculated by Fracpro as afunction of length for cases 5-8. These profiles were provided by RES and have notbeen changed for publication.
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