TopicalReport

HydraulicFractureModelComparisonStudy:CompleteResults "

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

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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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Topical report on the •results of the Fracture Propagation Modeling Forum

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This study is a comparison of hydraulic fracture models run using test data from the GRI

Staged-Field Experiment #3 (SFE-3). Models compared include" (i) PKN and GDK constant-

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.

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Tight gas sands, hydraulic fracturing, fracture modeling

b. |deeRIfm_/Ol_n.(_ed Terms

SFE No. 3, fracture height, Fracpro, Trifrac, Stimplan, MFRAC-II, GOHFER, HYFRAC3D,TerraFrac, Enerfrac

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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.

Technical Largequantitiesof naturalgas existin lowPerspective permeabilityreservoirsthroughoutthe US.

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.

Table of Contents

1.0 RESEARCH OBJECTIVES 12.0 RATIONALE 23.0 BACKGROUND - BASIC MODELING DISCUSSION 3

3.1 Planar 3-D Models 43.2 Planar 3-D FiniteDifferenceModel - GOHFER 43.3 Pseudo-3-D Models 53.4 Classic PKN and GDK Models 5

4.0 FRACTURE MODELS 64.1 S.A. Holditch& Assoc. (TRIFRAC) 64.2 Meyer & Associates(MFRAC-II) 64.3 Advani (Lehigh HYFRAC3D) 74.4 Shell (ENERFRAC) 74.5 Halliburtion(PROP) 84.6 Chevron 84.7 Conoco 94.8 Marathon (GOHFER) 94.9 ARCO (usingTerraFrac) 94.10 NSI (STIMPLAN) 104.11 ResourcesEngineeringSystems(FRAPRO) 104.12 Texaco (usingFRACPRO) 11

5.0 SFE-3 FORMATION AND TREATMENT DATA 126.0 TEST CASES 137.0 MODEL RESULTS 14

7.1 2-D Results(Cases 1-4) 147.2 3-Layer Results 167.3 5-Layer Results 16

8.0 DISCUSSION 179.0 CONCLUSIONS 1910.0 RECOMMENDATIONS 2011.0 REFERENCES 21

APPENDIX A 107APPENDIX B 116APPENDIX C 125APPENDIX D 134APPENDIX E 136APPENDIX F 145APPENDIX G 155

Listof Tables

Table I Rockand ReservoirDataTable 2 Treatment DataTable 3 2-D Resultsat End of PumpTable 4 3-Layer Resultsat End of PumpTable 5 5-layer Resultsat End of PumpTable 6 Time to breakthroughintolower layerTable 7 S.A Holditch& Assoc.- GDK Constantheight 14=200cpTable 8 S.A Holditch& Assoc.- GDK Constantheight n'=0.5, k, =o. o6Table 9 S.A Holditch& Assoc.- PKNConstantheight 14=200cpTable 10 S.A Holditch& Assoc.- PKN Constantheight n'-0.5, k'=0.06Table 11 S.A. Holditch& Assoc.- 3-layer 14=200cpTable 12 S.A. Holditch& Assoc.- 3-layer n'=0.05, k'=0.06Table 13 S.A. Holditch& Assoc.- 5-layer 14=200cpTable 14 S.A. Holditch& Assoc.- 5-layer n'=0.05, k'=0.06Table 15 Meyer & Assoc. - GDK Constantheight 14=200cp Base CaseTable 16 Meyer & Assoc. - GDK Constantheight n'=0.5, k'=0.06 Base CaseTable 17 Meyer & Assoc. - PKN Constantheight 14=200cp Base CaseTable 18 Meyer & Assoc. - PKN Constantheight n'=0.5, k'=0.06BaseCaseTable 19 Meyer & Assoc.- 3-layer 14=200cp Base CaseTable 20 Meyer & Assoc.- 3-layer n'=0.5, k'=0.06 Base CaseTable _1 Meyer & Assoc.- 5-layer 14=200cp Base CaseTable 22 Meyer & Assoc. - 5-layer n'=0.5, k'=0.06 Base CaseTable 23 Meyer & Assoc. - GDK Constantheight 14=200cp KnobsonTable 24 Meyer & Assoc.- GDK Constantheight n'-0.5, k'=0.06 KnobsonTable 25 Meyer & Assoc. - PKN Constantheight 14=200cp Knobs onTable 26 Meyer & Assoc. - PKN Constantheight n'-0.5, k'=0.06 Knobs onTable 27 Meyer & Assoc.- 3-layer 14=200cp Knobs onTable 28 Meyer & Assoc.- 3-layer n'=0.5, k'=0.06 KnobsonTable 29 Meyer & Assoc.- 5-layer 14=200cp KnobsonTable 30 Meyer & Assoc.- 5-layer n'=0.5, k'=0.06 KnobsonTable 31 Advani - PKN ConstantHeight 14=200cpTable 32 Advani- PKN ConstantHeight n'=0.50k'=0.06Table 33 Advani- 3-Layer 14=200cpTable 34 Advani- 3-Layer n'=0.5, k'=0.06Table 35 Advani- 5-Layer 14=200cpTable 36 Advani- 5-Layer n'=0.5, k'=0.06Table 37 Shell - GDK ConstantHeight 14=200cpTable 38 Shell - GDK ConstantHeight n'=0.5, k'=0.06Table 39 Shell - PKN ConstantHeight 14=200cpTable 40 Shell - PKN ConstantHeight n'=0.5, k'=0.06Table 41 Shell ENERFRAC 14=200cp Base CaseTable 42 Shell ENERFRAC n'=0.5, k'=0.06 Base CaseTable 43 Shell ENERFRAC 14=200cp Overpressure=500psi

I "

Table 44 Shell ENERFRAC n'=0.5, k'=0.06 Overpressure=500 psiTable 45 Shell ENERFRAC 1_=200cp Overpressure=1000 psiTable46 Shell ENERFRAC n'=0.5, k'=0.06 Overpressure=1000 psiTable 47 Shell ENERFRAC 1_=200cp Overpressure=1500 psiTable 48 Shell ENERFRAC n'=0.5, k'=0.06 Overpressure=1500 psiTable 49 Shell ENERFRAC 1_=200cp Overpressure=2000psiTable 50 Shell ENERFRAC n'=0.5, k'=0.06 Overpressure=2000 psiTable 51 Halliburton GDK ConstantHeight !_=200cpTable 52 Halliburton GDK ConstantHeight n'=0.5, k'=0.06Table 53 Chevron GDK ConstantHeight !_=200cpTable 54 Chevron PKN ConstantHeight 1_=200cpTable 55 Conoco GDK ConstantHeight !_=200cpTable 56 Conoco GDK ConstantHeight n'=0.5, k'=0.06Table 57 Conoco PKN ConstantHeight p=200 cpTable 58 Conoco PKN ConstantHeight n'=0.5, k'=0.06Table 59 MarathonGOHFER ConstantHeight 1_=200cpTable 60 MarathonGOHFER ConstantHeight n'=0.5, k'=0.06Table 61 MarathonGOHFER 3-Layer 1_=200cpTable 62 MarathonGOHFER 3-Layer n'=0.5, k'=0.06Table 63 MarathonGOHFER 5-Layer !_=200cpTable 64 MarathonGOHFER 5-Layer n'=0.5, k'=0.06Table 65 ARCO Stimplan 3-Layer 1_=200cpTable 66ARCO Stimplan 3-Layer n'=0.5, k'=0.06Table 67ARCO Stirnplan 5-Layer 1_=200cpTable 68 ARCO Stimplan 5-Layer n'=0.5, k'=0.06Table 69 ARCO TerraFrac 5-Layer n'=0.5, k'=0.06Table 70 NSI Tech. Stimplan 3-Layer p=200 cpTable 71 NSI Tech. Stimplan 3-Layer n'=0.5, k'=0.06Table 72 NSI Tech. Stimplan 5-Layer 1_=200cpTable 73 NSI Tech. Stimplan 5-Layer n'=0.5, k'=0.06Table 74 RES Fracpro 3-Layer 1_=200cpTable 75 RES Fracpro 3-Layer n'=0.5, k'=0.06Table 76 RES Fracpro 5-Layer p=200 cpTable 77 RES Fracpro 5-Layer n'=0.5, k'=0.06Table 78 Texaco Fracpro GDK ConstantHeight !_=200cpTable 79 Texaco Fracpro PKN ConstantHeight _=200 cpTable 80 Texaco Fracpro 3-Layer p=200 cpTable 81 Texaco Fracpro 5-Layer !_=200cpTable 82 Texaco Fracpro 5-Layer n'=0.5, k'=0.06Table 83 Texaco Fracpro 5-Layer n'=0.5, k'=0.06 No tip effects

I

Listof Figures

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

ir _,ll

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.

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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.

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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.

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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:

Case 1 GDK Constantheight- 200 cp fluidCase 2 GDK Constantheight- Power-lawfluid (n', k')Case 3 PKN Constantheight- 200 cp fluidCase 4 PKN Constantheight- Power-lawfluid (n', k')Case 5 3-Layer - 200 cp fluidCase 6 3-Layer - Power-lawfluid (n', k_)Case 7 5-Layer - 200 cp fluidCase 8 5-Layer- Power-lawfluid (n', k')

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.

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_ 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:

S.A. Holditch&Assoc. Trifrac Tables 7-14Meyer & Assoc.M-FRAC-II base case (Meyer-I) Tables 15-22Meyer & Assoc.M-FRAC-II "knobs" (Meyer-2) Tables 23-30Advani HYFRAC3D Tables 31-36Shell 2-D Models Tables 37-40Shell Enerfrac. Tables 41-50Halliburton2-D Prop Tables 51-52Chevron2-D models Tables 53-54Conoco2-D models Tables 55-58Marathon GOHFER Tables 59-64ARCO (Stimplan) Tables 65-68ARCO (TerraFrac) Table 69NSI Stimplan Tables 70-73RES Fracpro Tables 74-77Texaco (Fracpro) Tables 78-83

The graphsof the data shown inthissectionwere derivedfromthis tabular data set. Inaddition,somemodelersprovidedadditionalgraphicalinformationon the width andheightprofilesalong the lengthof the crack. These are given inthe followingappendices:

S.A. Holditch& Assoc.Trifrac AppsndixAMeyer & Assoc.M-FRAC-II basecase (Meyer-I) AppendixBMeyer & Assoc.M-FRAC-I! "knobs"(Meyer-2) AppendixCAdvaniHYFRAC3D AppendixDMarathon GOHFER AppendixEARCO (StimplanandTerraFrac) AppendixFRES Fracpro AppendixG

7.1 2-D Results,(Cases 1-4)

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

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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 ! ......

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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

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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.

21

11.0 REFERENCES

1. Holditch, S.A., B.M. Robinson, W.S. Whitehead & J.W. Ely, 'The GRI Staged FieldExperiment,".SPEForm. Eval., 519-533, Sept. 1988.

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.

8. Monus, F.L., F.W. Broussard,J.A. Ayoub,& W.D. Norman, "FracturingUnconsolidatedSand FormationsOffshoreGulf of Mexico," SPE 24844, 67th Ann.Tech. Conf., Washington,D.C., 817.831, Oct. 1992.

9. Owens, K.A., S.A.Andersen& M.J. Economides,"Fracturing PressuresforHorizontalWells," SPE 24822, 67th Ann. Tech. Conf., Washington,D.C., 581-588,Oct. 1992.

10. Meehan, D.N., "StimulationResultsin the Giddings(AustinChalk) Field," SPE24783, 67th Ann.Tech. Conf.,Washington,D.C., 195-205, Oct. 1992.

11. Gidley,S.A. Holditch,D.E. Nierode,& R.W. Veatch, Editors,"Recent AdvancesinHydraulicFracturing,"SPE MonographVolume12, Richardson,TX, June 1989.

12. Clifton,R.J. & A.S. Abou-Sayed,"On the Computationof the Three-DimensionalGeometryof HydraulicFractures,"SPE 7943, SPE/DOE Low Perm.Gas Res.Syrup.,Denver,CO, May 1979.

..... ' "rl'' , , ,, ,, , ,, , ,, ,, _l ..... 1LI ' ,r_ ........

22

13. Clifton, R.J. & A.S. Abou-Sayed, "A VariationalApproachto the Predictionof theThree DimensionalGeometry of HydraulicFractures," SPE 9879, SPE/DOE LowPerm. Res. Symp.,Denver, CO, May 1981.

14. Clifton, R.J. & J.J. Wang, "Multiple Fluids,ProppantTransport, and Thermal Effectsin 3-DimensionalSimulationof HydraulicFracturing,"SPE 18198, 63rd Ann. Tech.Conf., Houston,TX, Oct. 1988.

15. Clifton, R.J. & J.J. Wang, "Modeling of PoroelasticEffectsin HydraulicFracturing,"SPE 21871, JointRocky Mt. Regional/LowPerm. Res. Symp.,Denver, CO, April1991.

16. Clifton, R.J. & J.J. Wang, "AdaptiveOptimalMesh Generatorfor HydraulicFracturingModeling,"32nd U.S. RockMech. Symp.,1991.

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.

18. Barree, R.D. "A Practical NumericalSirP,ulatorforThree DimensionalFracturePropagationin HeterogeneousMedia," SPE 12273, ReservoirSimulationSymp.,San Francisco,CA, 403-411 Nov. 1983.

19. Barree, R.D. "A New Lookat Fracture-TipScreenoutBehavior,"JPT, Vol. 43, 138-143, Feb. 1991.

20. Shlyapobersky,J., "Energy Analysisof HydraulicFracturing,"Proc.26th U.S.Symp.on Rock Mechanics,Rapid City, SD, June 1985.

21. Shlyapobersky,J., G.K. Wong & W.W. Walhaug, "OverpressureCalibratedDesignof HydraulicFractureSimulations,"SPE 18194, 63rd Ann. Tech. Conf., Houston,TX, October 1988.

22. Cleary, M.P., "Analysisof the Mechanismsand Proceduresfor ProducingFavorable Shapesof HydraulicFracturing,"SPE 9260, SPE Ann.Tech. Conf.,Dallas, TX, Sept. 1980.

23. Cleary, M.P., "ComprehensiveDesignFormulaefor HydraulicFracturing,"SPE9259, SPE Ann.Tech. Conf., Dallas,TX, Sept. 1980.

24. Cleary, M.P., C.A. Wright & T.B. Wright, "Experimentaland ModelingEvidenceforMajor Changes inHydraulicFracturingDesignand Field Procedures,"SPE 21494,SPE Gas Tech. Symp.,Houston,TX, Jan. 1991.

23

25. Cleary, M.P. & Amaury Fonseca,"Proppant Convectionand Encapsulation inHydraulicFracturing: Practical Implicationsof ComputerLaboratorySimulations,"SPE 67th Ann. Tech. Conf., Washington,D.C., Oct. 1992.

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.

30. Kristianovich,S.A. & Y.P. Zheltov,"Formationof Vertical Fracturesby MeansofHighlyViscousLiquid," Proc.FourthWorld Pet. Cong.,Rome,Volume II, 579-586,1955.

31. Perkins,T.K. & L.R. Kern, "Widths of HydraulicFractures,"JPT, Vol. 13, 937-949,Sept. 1961.

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

,,, (psi) (psi _/in), Single-Layer (2-D Case

[ 1 9170-9340 170 5700 0.21 8.5xl 0" 2000 ilill I

, 3-Layer (3-0) Case,

1 8990-9170 !80 7150 0.30 6.5x10 u " 20002 9170-9340 170 5700 0.21 8.5xl 0t_ 2000 |3 9340-9650 310 7350 0.29 5.5x10 _ 2000 |

S-Layer (3-0) Case1 8990-9170 180 7150 0.30 6.5x10t_ 200,02 9170-9340 170 5700 0.21 8.5xl 0_ 20003 9340-9380 40 7350 0.26 5.4xl 0t_ 2000

4 9380-9455 75 5800 0.20 7.9xl 0_ 200,05 9455-9650 195 8200 0.30 4.0x10 _ 2000m i

Table 2 Treatment Data

Bottom-holetemperature 246° F |Reservoirpressure 3600 psi !Spurt loss 0.0

I Fluid leakoffheight entirefractureheight IFluidleakoff coefficient 0.00025ft/_/min I

Viscosity- Case A 200 cp IViscosity- Case B n' : 0.5; k' : 0.06

I

Fluidvolume IOTO00bblsInjectionrate 50 bpm

Proppant i none

27

Table 3 2-D Results at End of Pump

2OOCP

MODEL LENGTH HEIGHT PRESSURE WMAX WAVG W WAVG F EFFICSAH (GDK) ..2542 170 62 0.848 0.849 0.605 85.5

_ SAH (P.KN) 4855 170 1094 0.502 0.394 0.289 72.3_ MARATHON 2584 294 1685 0.91 0.76 0.73 93• MEYER1(GDK) 2659 170 70 0.79 0.79 0.62 83.1

MEYER1(PKN) 4507 170 1188 0.55 0.43 0.32 72.2MEYER2(GDK) 2288 170 97 0,94 0.94 0.74 85.4MEYER2(PKN) 3803 170 1474 0.68 0.'53 0.4 76.6

_ SHELL(GDK) 2724 170 53 0.78 0.78 0.61 84SHELL(PKN) 4039 170 1377 0.59 0.46 0.37 75TEXACO-FP 1898 200 131.9 1.06 94.4TEXACO-FP 3587 200 _ 1377 0.72 90

_ CHEV(GDK) 1347 170 81.9 0.77" 0.77 0.6 81.9CHEV(PKN) 2029 170 1380 0.63 0.36 73

_ ADVANI 4595 170 1182 0.54 0.43 0.32 73.8_ HALLIB 2212 170 82 0.98 0.98 0.77 85.9

CONOCO(GDK) 2716 170 0.767 ' 0.6 82.5CONOCO,(PKN) 3986 170 0.554 0.37 74.4

ENERFRC-1 38,36 170 1595 0.627 0.492 0.387 75ENERFRC-2 3556 170 1684 0.704 0.553 0.434 78

n', k'

MODEL LENGTH HEIGHT PRESSURE WMAX WAVGW WAVG F EFFICSAH (GDK) 2542 170 61.8 0.85 0.85 0.6 61.8SAH (PKN) 4629 170 1167.5 0.54 0.42 0.28 73.6

MARATHON 2516 204 1824 0.98 0.82 0.75 93MEYER1(GDK) 2098 170 117 1.04 1.04 0.82 86.4MEYERI(PKN) 4118 170 1397 0.64 0.5 0.36 74.3MEYER2(GDK) 1808 170 161 1.24 1.24 0.97 88.3MEYER2(pKN_) 3395 170 1774 0.81 0.64 0.46 79SHELL(GDK) 2142 170 89 1.03 1.03 0.81 89SHELL(PKN) 3347 170 1754 0.75 0.59 0.47 79

ADVANI 4046 170 1474 0.68 0.53 0.38 76.9HALLIB 2031 170 97 1.07 1.07 0.84 86

_ CONOCO(GDK) 2304 170 0.933 0.933 0.733 85.2CONOCO(PKN) 3656 170 0.6:):) 0.415 76.5

ENERFRC-1 3396 170 1880 0.738 0.58 0.456 78ENERFRC-2 3155 170 1986 0.817 0.641 0.504 81.7

iIII r I ,, i '1 II ,,I I ,i rl I li ii '1 ,,, I

28

Table 4 3-Layer Results at End of Pump

200 3-LAYERCP

MODEL LENGTH HEIGHT PRESSURE W MAX W AVG W W AVG F EFFICSAH 3408 318 1009 0.65 0.35 0.3 77,,,

NSI 3750 903 283 0.56 0.32 0.25 66,,,

RES 1744 544 1227 0.9 0.54 0.36 80

MARATHON 1360 442 1387 1.04 0.68 0.64 96MEYER-1 3549 291 987 0.58 0.35 0.29 70.3MEYER-2 2692 ' 361)' 1109 0.72 0.41 0.34 74.3

,

ARCO-STIM 3598 306 992.. 0.57 0.31 0.25 67TEXACO-FP 836 740 1561 1.333 89,

ADVANI 2089 357 1113 0.66 0.33 0.25 43

I I

n', k' 3-LAYERMODEL ' LENGTH HEIGHT PRESSURE WMAX WAVGW WAVG F EFFICi I II I I

SAH 3259 371 109.3. . 0.75 0.38 0.31 77.6NSf 3289 329 1005. 0.67 0.35 0.26 68RES 902 596 1428 1.1 0.74 0.49 62

MARATHON 1326 442 1433 1.08 0.71 0.66 " 96, i,

MEYER-1 2915 337 1094 0.69 0.4 0.32 72.7,,! i

MEYER-2 2120 413 1212 _ 0.86 0.48 0.4 76.9ARCO-STIM 3235 353 1083 0.65 0.33 0.26 69

, , ,,, ,,,,

ADVANI 2424 435 1171 0.74 0.34 0.21 47i

29

Table 5 54ayer Resurm at End of Pumpi

2C0 5-1_YERCF'

MODEL LENGTH HEIGHT PRESSURE WMAX WAVG W WAVG F EFFICI III I I I

SAH 2905 394 960 0.72 0.42 0.31 80.1NSI 3709 361 852 0.63 0.38 0.25 66RES 1754 501 1119 0.83 0.8 0.4 82

MARATHON 1224 476 1250 'I .03 0.7 0.65 97i

MEYER-1 2962 328 669 0.5 0.36 0.28 70.5i

MEYER-2 2407 327 768 0.6 0.46 0.35 74.8ARCO-STIM 3399 394 944 0.64 0.36 0.24 68

,, ,,

TEXACO-FP 934 605 934 1.32 89.6,,

ADVAN I 1594 438 1129 0.61 0.45 0.36 58.1

n',k' 3-LAYERMODEL LENGTH HEIGHT PRESSURE W MAX W AVG W W AVG F EFFIC

I

SAH 2642 430 1035.5 0.82 0.46 0.31 81.8NSI 27_5 388 935 0.71 0.42 0.25 70RES 1042 500 1358 1.18 0.9 0.6 87

MARATHON 11'36 476 1262 1.04 0.71 0.66 93, i ,, . i,i

MEYER-1 2535 330 766 0.6 0.46 0.37 73.7MEYER-2 1980 349 891 0.75 0.57 0.42 77.8

ARCO-STiM 2926 405 968 0.7 70ARCO-T;= 3124 449 1160 (:1.74 62

, i

TEX-FP 1089 578 1365 1.19 88.5TX-FPTIP 1168 614 1285 1.077 87.7ADVANI 1870 458 11L_1 0.$5 0.47 0.34 64m ,,

Table 6 Time to breakthrough into lower layer

MODEL Newtonian n', k'ARCO TerraFrac 60

ARCO STIMPLAN 63 50i

SAH TRIFRAC 70 50NSI STIMPLAN 140 75

TEXACO FRACPRO 8 6TEXACO FRACPRO-TIP i

J

RES FRACPRO 10 7MARATHON GHOFER <25 <25MEYER MFRAC-II - 1 113 69MEYER MFRAC-II-2 44 30......

AE'VANI 55 40

30

Table7 S.AHoklitch&Assoc..GDKConstaf_height ps200cp

ii

Time Height H_ Lenglh NetPressure Efficiency Max. Width' Avg.Width Avg. Wldlh(rain) (It) (lt) (ps_) (%) (in) in Fmc at Wellbore

(in) (in)0 170 10 721 99 0.039 0.032 0.03925 170 661 119 89 0.426 0.284 0.425

i

50 170 1036 96 88 0.537 0.370 0.537i

75 170 1348 84 87 0.614 0.429 0.614100 170 1624 77 87 0.676 0.475 0.676125 170 1876 72 86 0.727 0.514 0.727

i

150 170 2110 68 68 0.772 0.547 0.772i i i

175 170 2332 65 86 0.812 0.578 0.812,,

200 170 2542 62 68 0.848 0.605 0.848i

Table 8 8.A Hokiitch & Assoc. - GDl( Constant height n',,0.6, k',,0.U

i i i i

I Tta, Height Half _ NetPressure Efficiency Max.Width Avg.Width Avg. WidthI (m) (lt) (lt) Lo,_) (%) (in) In Fmc at Wellbore

0 170 10 682 99 0.037 0.033 0.037,,

25 170 626 134 90 0.452 0.267 0.45250 170 942 118 68 0.567 0.365 0.56775 170 1195 I09 68 0.704 0.436 0.704100 170 1415 103 89 0.789 0.484 0.789125 t70 1613 gg 68 0.863 0.543 0.863150 170 1796 96 88 0.929 0.587 0.929175 170 1967 93 68 0.988 0.626 0.968,,

200 170 2128 91 88 1.04 0.662 1.04dm i i

Table| 8.AHolditch&Assoc..PKNConstantheight p_L'00cp

Time Height Half length NetPnmsure Efficiency Max.Width Avg.Width Avg.Width(mM) (It) (It) (.rod) (%) (in) In Fmc at Wellbore

(in) (in)0 170 10 42 98 0.079 0.13 0.01525 170 1067 712 83 0.327 0.157 0.25650 170 1771 827 80 0.379 0.203 0.29675 170 2379 901 78 0.413 0.229 0.325100 170 2934 955 76 0.438 0.247 0.344125 170 3452 996 75 0.458 0.260 0.360150 I70 3941 1035 74 0.475 0.271 0.373175 170 4406 1086 73 0.489 0.281 0.382200 170 4855 1094 72 0.502 0.290 0.394

Table 10 8.A Hoklitch & Assoc.. PKNConstant height n'a0J, k'e0.Ni

Time Height HalfLengl_ NetPressure Efficiency Max. Width Avg.Width Avg.Width(rain) (It) (ft) _ (%) (in) In Fmc at Welll_m

(in) (in)i

0 170 10 42 98 0.019 0.013 0.01525 170 1084 6gg 82 0.321 0.167 0.25250 170 1764 831 80 0.382 0.192 0.30075 170 2342 919 78 0.422 0.217 0.331

i

100 170 2862 gsg 77 0.452 0.235 0.356

125 170 3341 1042 76 0.478 0.250 0.376150 170 3793 I089 75 0.500 0.263 0.393175 170 4220 1131 74 0.519 0.273 0.408,200 170 4629 1168 74 0.536 0.263 0.421

I

!

31

Table 11 S.A. Holditch & Assoc.. 3.layer p,,200 cp

I II I

Time Height Upper Lower Half NetPressure Efficiency Max.Width Avg.Width Avg. Width(rain) (It) Height Height Length (psi) (%) (in) inFmc at Wellbore

(ft) (ft) (ft) (in) (in)0 172 86 86 15 164 95 0.076 0.059_ 0.__r_g25 z._ 121 112 76g 768 84 0.423 0 _ 0.27350 _ 133 120 1288 846 82 0.486 0.248 0.30175 268 142 126 1720 894 61 0.529 0.264 0.319100 281 150 131 2105 928 80 0.561 0.275 0.330125 291 156 135 2458 953 79 0,588 0.___3 O3_'__150 301 162 13g :_/_2 975 78 0.610 0.290 0.343175 310 167 142 3107 993 77 0.R"_ 0.__296 0.348200 318 172 145 3408 1009 77 0.647 0.301 0.3_r,3

Table 12 8.A. Holditch & Assoc.. 3.kiyer n',,0.01S,k',,0.0iS

Time Height Upper Lower Half Net Pressure Efficiency Max. Width Avg. Width _,vg.Width(min) (It) Height Height Length (psi) (%) (in) InFmc at Wellborn

(It) (It) (It) (in) (in)0 172 86 86 16 164 95 0.076 0.__n_ 0.0625 238 124 114 610 787 64 0.438 0.216 0.28050 266 141 125 1319 886 62 0.5_') 0.241 0.31675 289 155 134 172g 947 61 0.581 0__259 0.3___100 306 168 142 2056 991 80 .... 0.627 0.273 0.347125 326 177 148 2415 1024 79 0.664 0.__:____ 0.359150 342 187 155 2717 105t 76 O__a96 0.291 0.368175 357 197 161 2995 1073 78 0.724 0.299 0.377200 371 206 165 ,, 3259 1093 77 0.751 0.__ 0.384

Table 13 8.A. Holditch• Assoc. - 6.Myer lA-200 cp

Time Height Upper Lower Half Net Pressure Efficiency MAx.Width AVg.Width AVg.Width(rain) (ft) Height Height Length (Ix,I) (%) (In) In Fmc at We, bore

(ft) (It) (It) On) On)0 173 87 68 12 209 96 0.097 0.075 0.07525 231 120 111 781 750 65 0.420 0.224 0.27350 250 132 119 1318 836 82 0.480 0.244 0._975 2_ 141 128 1767 883 80 0.Sw 0._9___ 0.316100 328 155 173 2124 912 79 0.604 0.271 0.='_'_'_'_'_'_'_'_'____125 3_ 165 204 2338 930 80 0.660 0.283 0.394150 ;._/ 171 216 2525 943 80 0.__R__ 0.292 0.410t75 391 174 217 2710 953 80 0.705 0.299 0.417200 394 177 217 2906 960 80 0.716 0.__ 0.423

Table 14 S.A. Holditch & Assoc.. IS.layer n',,0.0$, k',,6.06

Time Height Upper Lower Haft NetPrmmum Efficiency Max. Width Avg.Width Avg.Width(min) (It) Height Height Lenglh (IXd) (%) (In) In Fmc litWeUbore

(ft) (ft) (It) (in) (in)0 173 87 68 12 209 96 0.097 0.075 0.07525 235 123 113 u22 ,, 777 84 0.434 0.213 0.27950 263 13g 124 1356 874 81 0.512 0.236 0.31275 364 164 200 1706 929 81 0.__53 0.255 0.391100 396 178 217 1886 964 61 0.722 0.273 0.425125 405 186 219 2071 ...985 82 0.754 0.286 0.z_150 414 194 _ 2264 1006 82 0.781 0.295 0.447175 422 201 221 2442 1021 82 0.501 0.3___'J 0.4542_ 430 207 _: 2642 1036 82 0.818 0.309__ 0.461

32

Tablo 18 Meyer&Aswc..GDKConstmtheight p,,200cp BaseCase

i ,.

Height HIIIf Length I_t_' Elticl_ Max. Width Avg.Width Avg.Width(rain) (It) (n) (psi) (_) On) _ Fmc atWe,bore

, (in) (in)0 170 0 0 100 0 0 025 170 _ 138 88 0.402 0.315 0.40250 170 1062 110 86 0.504 0.395 0.50475 170 1406 g6 85 0.575 0.451 0.575100 170 1607 88 85 0.631 0.4g5 0.631125 170 1961 82 84 0,679 0.532 0.679150 170 2207 77 84 0.720 0.564 0.720175 170 2430 73 83 0.757 0.593 0.757200 170 2650 70 83 0.790 0.619 0.790

Table 18 Meyer & Assoc.. GDl( Constant height n',,0.8, k',,O.N BaN Case

I 1 i

Time Height Half Lenglh Net Pressure ElticMnoy Max. Width Avg.Width Avg.Width(rain) (It) (lt) (psi) (%) (in) InFmc atWellbore

. , (in) _}

. 0 170 0 0 100 0 0 025 170 611 178 89 0.45e 0.380 0.450

50 170 g22 154 88 0.603 , 0.473 0.60375 170 1173 142 88 0.708 0,555 0.7081O0 170 1391 134 87 0.793 0.621 0.793125 170 t ,588 129 87 0.865 0.678 0.86515X) 170 178g 124 87 0.930 0.729 0.930"'/5 170 1939 120 87 0.988 0.774 0.988

!1 200 170 2_6 117 86 1.041 0.816 1.041i m

Table 17 Meyer&Ast, x..PKNConstm_height p,,200cp BaseCase.li

Time Height Half _ Net Prmure EIl_enoy Max. Width Avg.Width Avg.(mln) (lt) (lt) (psi) (%) (in) In Fmc at Wellborn

_n) (_)0 170 0 0 100 0 0 025 170 948 813 84 0.373 0.21g 0.29250 170 1605 924 80 0.424 0.248 0.332H ,,,,

75 170 2178 995 78 0.457 0.287 0.358100 170 2700 1048 77 0,481 0.281 0.377125 170 3187 1002 78 0,501 0.292 0.393, m

150 170 3647 1128 74 0.518 0.302 0.406175 170 4086 11ISO 73 0.532 0.310 0.417200 170 4507 1188 72 0.545 0.318 0.427

Table 1| Meyer • Assoc.. PKN Constant height n',,0.6, k',,,0.NBue Cuei i

Time Height HalfLength Nat Pmmum Efficiency Max. Width Avg.Width Avg.Width(rain) (It) (lt) _ (%) (in) in Fmc atWellborn

(in) (in)0 170 0 0 100 0 0 025 t70 g34 862 84 0.305 0.222 0.31050 170 t 530 1013 81 0,465 0.260 0.36475 170 2057 1114 79 0.511 0.286 0.401100 170 2524 11go 78 0.546 0.305 0.428125 170 2957 1253 77 0.575 0.321 0.451150 170 3363 1307 76 0.600 0.335 0.470i

t 75 170 374g 1354 75 0.621 0.347 0.487,i

200 170 4118 1397 74 0.641 0.358 0.502i ||l ii

33

Table 19 Meyer & Assoc. - 3.1ayer p,,200 cp Bile Case

Time Height Upper Lower" Half Net Pressure Efficiency Max. Width Avg.Width Avg.Width(rain) (It) HeigM Height Length (1_) (%) (in) in Fmc atWe, bore

(ft) (ft) (ft) (in) (in)0 170 85 85 0 0 100 0 0 025 214 110 104 872 740 83 0.385 0.208 0._268__--i

50 234 122 112 1421 826 80 0.445 0.232 0._5_75 249 131 118 1867 876 77 0.482 0.247 0.311100 260 138 122 2281 910 75 0.510 0.257 0.3____125 zlu 144 126 2620 935 74 0.532 0.266 0.331150 zlu 149 129 2950 956 72 0.550 0.273 0.__'_B_175 284 153 131 32r'_ 973 71 0.566 0.279 0.345200 291 157 134 3549 987 70 0.580 0.285 O,__r,q_

TaMe 20 Meyer & Assoc. - 3-layer n',,0.6, k',,0.04 BaseCise

Time Height Upper Lower ' Half NetPressure Efrx:tency Max.Width Avg.Width Avg. Width(rain) (It) Height Height Length (psi) (%) (in) in Fmc atWelllxxe

(It) (it) (ft) (in) (in)0 170 85 85 0 0 100 0 0 025 217 112 105 845 784 84 0.414 0.214 0o__'_650 247 130 117 1307 8_4 80 0.496 0.248 03____75 269 143 126 1868 957 78 0.549 0.267 0.345

,100 287 154 133 1975 1000' 77 0.Sg0 0.282 0.361125 301 153 138 2244 1032 76 0.622 0.295 ' 0.374

.150 315 172 143 2487 1057 75 0.650 0.305 0._quB-_5175 326 179 147 ,.. 2708 1077 74 0.673 0.314 0.394200 337 186 151 2915 10_4 73 0.694 0,_ 0.402

Table 21 Meyer & Assoc.. I.iayer lA-200 cp Base Case

Time Height Upper Lower Haft NetPressure Efficiency Max.Width Avg. Width Avg.Width(min) (it) Height Height Length (psi) (%) (in) in Fmc at Wellbore

(it) (It) (n) , _n) (in)0 170 es es 0 0 too 0 0 025 193 111 104 872 743 83 0.387 0.20e 0.26850 , 205 124 113 1414 829 80 0.446 0.231 0.29475 212 132, 119 1863 879 77 0.483 0.246 0.310100 219 139 123 2257 913 75 0.511 0.257 0.321125 232 144 138 2554 933 73 0.538 0.260 0.321150 25g 143 16g 2626 79g 72 0.520 0.268 0.336175 21_ 132 206 2716 674 71 0.487 0.267 0.341200 284 123 205 2962 669 71 0.497 Oo_'_B2_ 0.364

Table 22 Meyer & Assoc.- iS.layer n',,0.6, k',,0.M Base Cise

i

"nrne He,ht Upper Lower H,df NetPressureEfrr..W_-yMax.Wk_ Avg.wm_ Avg.Wk:th(rain) (It) Height Height Length (1:_) (%) (in) inFmc atWelObore

(n) (It) (It) (in) (in)o 17o es es o , o lOO o o o25 219 113 106 842 786 84 0.415 0.214 O__L_50 249 131 118 1303 898 80 0.497 0.246 O,X:_75 278 144 134 1643 952 78 0.552 0.263 0.338100 322 146 176 1725 823 77 0.558 0.262 0.367125 343 134 209 1844 723 76 0.544 0.296 0.395150 330 123 207 2099 734 75 0.566 0.316 0.425175 329 122 207 2327 751 75 0.583 0.327 0.441200 330 122 208 2535 766 74 0.599 0.336 0.455

34

Tablen Meyor&Assoc..GDKConstanthMght p,,200cp Knobson

i I

Tlme Height Half Length Net Pressure Efficiency Max.Width Avg. Width Avg. Width(min) (ft) (ft) (psi) (%) (In) In Fmc at WeUbore

(in) (in)0 170 0 0 100 0 0 025 170 589 192 89 0.479 0.376 0.47950 170 927 153 88 0.601 0.471 0.601

75 170 1208 134 88 0.686 0.538 0.686100 170 1457 122 87 0.754 0.501 0.754125 170 1685 114 86 0.811 0.635 0.811150 170 1896 107 86 0.860 0.674 0.860175 170 20_ 102 86 0.904 0.709 0.904200 170 2288 97 85 0.944 0.740 0.944

ii i i i i i

Table 24 Moyer & Assoc. - GDK Consbmt height n',,031,k',,O.N Knobs on

i

Tkne Height Half l.onglh Net Pressure Efficiency Max.Width Avg.Width Avg.Width(._n) (ft) (ft) C._) (%) (In) InFmc _ wo,boro

(In) (In)0 170 0 0 100 0 0 025 170 515 255 91 0.556 0.436 0.55650 170 784 218 go 0.724 0.568 0.72475 170 1002 Ig0 89 0.846 0.663 0.846100 170 1192 187 89 0.945 0.741 0.945125 170 1363 178 89 1.030 0.807 1.030150 170 1521 171 8g 1.105 0.866 1.105175 170 161_ 166 88 1.173 0.919 1.173200 170 1808 161 88 1.235 0.968 1.235

i

Table26 Meyer&Assoc.-PKNConstantheigM p,,200cp Knobsoni

Time Height Hill' Length Net Prlmm_ Efficiency Mix. Width Avg.Width Avg.Width(rain) (lt) (lt) (psi) (%) (in) In Fmc at Welroom

_ _) on)0 170 0 0 100 0 0 025 170 785 1002 87 0.460 0.273 0.36050 170 1337 1141 84 0.524 0.310 0.41175 170 1820 1231 82 0.565 0.334 0.443100 170 2262 1298 go 0.596 0.352 0.467,,,,, |

125 170 2676 1353 79 0.621 0.367 0.486150 170 3068 13g9 78 0.642 0.379 0.503i,,|

175 170 3443 1438 77 0.660 0.350 0.517200 170 3803 1474 77 0.676 0.35g 0.530

TaMe 2t; Meyer & Assoc.. PKN Constant height n',,0A, k',,0.M Knobs on

Time Height Half l.lmgth NetPressure Efficiency Max. Width Avg. Width Avg. Width(rain) (lt) (lt) (pml) (%) On) In Fmc at WeUbore

. _) . (_)0 170 0 0 100 0 0 025 170 741 1110 87 0.50g 0.291 0.3gg50 170 1238 1298 85 0.505 0.339 0.46775 170 1667 1422 83 0.652 0.371 0.5i I100 170 2056 1517 82 0.696 0.395 0.546125 170 2417 1596 81 0.732 0.415 0.574150 170 2759 1662 80 0.763 0.433 0.598175 170 3083 1721 80 0.790 0.448 0.619200 170 3395 1774 79 0.614 0.461 0.638i i

i

35

Tablo 27 Meyer & Assoc.. 3.1myer p=200 cp Knobs on

Time Height Upper Lower Half Net Pressure" Efficiency MaX.Width Avg.Width Avg. Width(mln) (It) HeigM HelgM Length (IXd) (%) (in) inFmc at Wellbore

(ft) (lt) (ft) (in) (in)o 17o es es o o 1oo o o o

, •

25 235 122 113 696 870 es 0.477 0.255 0.31950 268 142 126 110g 960 83 0.553 0.283 0.349,,,

75 290 156 134 1446 1008 81 0.59g 0.301 0.365100 307 167 140 1740 1040 79 0.632 0.313 0.377125 321 176 145 2005 1064 77 0.659 0.323 0.387150 332 183 149 2250 1082 76 0.680 0.331 0.395

175 343 190 153 2478 . 1067 75 0.699 0.338 0.401200 360 195 156 2592 110g 74 0.715 0.344 0.407

i i i, a

Table 211Meyer & Assoc.. 341yet n',,Q.6,k",,,O.OSKnobs on

Time Height Upper Lowm' Half Net Pressure Efficiency Max.Width Avg.Width Avg.Width(rain) (ft) HelgM HetgM Length (Psi) (%) (in) in Fmc at Wellborn

(ft) (It) (ft) (in) (in)0 170 es es 0 0 100 0 0 0, ,,

25 246 129 117 637 944 87 0.534 0.276 0.35250 291 156 135 g68 1048 84 0.634 0.313 0.39275 322 175 147 1225 1102 82 0.697 0.335 0.415,,,

100 347 191 156 1444 1138 81 0.743 0.352 0.433125 367 204 163 1636 1163 80 0.780 0.366 0.447150 385 216 16g 1811 1163 79 0.811 0.378 0.459175 400 226 174 1971 1199 78 0.637 0.388 0.46g200 413 235 178 2120 1212 77 0.861 0.397 0.478

Table 2t Meyer • Assoc.. 6-Myer p=200 cp Knobs on

Time Height Upper Lower Half NatPressure Efficiency Max. Width Avg.Width Avg. Width(mln) (ft) Height Height Length (l::ml) (%) (In) InFmc atWellbore

(ft) (ft) (ft) (in) (_)0 170 es es 0 0 100 0 0 025 237 124 113 6es 874 86 0.479 0.255 0.31850 282 144 138 1085 94g 63 0.556 0.276 0.33775 346 136 210 1162 687 81 0.5t 7 0.296 0.373,,

I00 325 119 206 1484 708 79 0.537 0.316 0.404126 325 118 207 1743 727 78 0.556 0.328 0.420150 325 118 207 1977 743 77 0.572 0.338 0.435175 326 118 208 21gg 757 76 0.586 0.346 0.447200 327 t 19 208 2407 748 75 0.596 0.353 0.457

Table 30 Meyer & Assoc. - 6.layer n',,0.6, k'=0.H Knobs on

Time Height Upper Lower Haft Nat Pressure Efficiency Max.Width Avg. Width Avg. Width(mln) (ft) Height Height Length (IO_i) (%) (in) in Fmc lit Well)ore

(ft) (ft) (ft) (in) (in)0 170 85 85 0 0 100 0 0 025 241g 131 118 633 ' 94,9 87 0.535 0.276 0.35050 341 144 197 801 797 84 0.580 0.313 0.39975 337 128 20g 1029 770 83 0.607 0.346 0.455100 336 127 20g 1255 805 81 0.643 0.367 0.487125 338 t27 211 1454 632 80 0.673 0.383 0.513150 341 129 212 1638 854 79 0.699 0.398 0.533175 345 132 213 1814 874 79 0.724 0.411 0.551,

200 349 135 214 1980 891 78 0.746 0.423 0.567i

,,

36

Table 31 Advani. PKN Constant Height _,,200 cpiiii i i

I - i i i i

Time Height Half Length Net Pressure Eff_.,ienoy Max. Width Avg.Width Avg.Width(rain) (it) (it) (p_) (%) (in) inFrc e W_lbom

(in) (in)0 170 0 0 100 0 0 0

25 170 968 804 84 0.369 0.216 0.__9_950 170 1638 915 81 0.420 0.246 0,_75 170 5550 987 79 0.453 0.265 0.3_r,6100 170 2752 1041 78 0.476 0.280 ' 0.375125 170 . 3246 1065 77 0.496 0.292 0.391150 170 3718 1121 76 0.515 0.302 0.404175 170 4165 1153 75 0.529 0.310 0.415200 170 4595 1182 74 0.542 0.318 0.426

i i i

Table 32 Advani. PKN Constant Height n',,0.6, k',,0.04

Time Height Half_ N= Pressure E_ Max.WkRh Avg.Width Avg.(rain) (It) (It) (psi) (%) (in) in Fmc atWeUbore

(in) (in)o 17o o" o lOO o o o25 17o m9 _0 65 o.413 o.:m 0.32450 170 1513 1062 83 0.467 0.271 0.-__'1_L375 170 2020 1170 81 0.537 0.298 0.421100 170 2479 1252 80 0.575 0.319 0.461125 170 2904 ....1320 79 0.606 0.337 0.475150 170 3303 1378 76 0.632 0.352 0,._a__175 170 3683 1429 78 0.656 0.365 0.5152gO 170 4046 1474 77 0.676 0.377 0.531

Table 33 Advanl. 3.Layer p,,_ ep

T_e He,ht Upper Lower H_ NetPrm._ Errr._ Mx.W_h Avg.W_ Avg.W_h(rain) (It) Height Height Leflglh (j_d) (%) On) in Fmc atWe,bore

(It) (It) (It) (I,1) On)0 170 65 85 0 0 100 0 0 025 ' 240 124 116 654 885 67 0.434 0.218 0.26750 274 143 131 1069 972 58 0.513 0.220 0.29875 298 158 141 1303 1040 58 0.571 0.245 0.316100 316 169 147 1501 1048 52 0.598 0.248 0.326125 328 177 151 1635 1077 51 0.624 0.265 0.3_'_150 340 165 155 1778 1090 46 0.634 0.265 0.326175 352 193 159 1983 1112 44 0.649 0.238 0.327200 357 195 162 2089 1113 43 0.658 0.250 0.331

Table 34 Advani - 3.Layer n',,O.6,k',,O.06" le

(rain) (It) Height He=jht Length (psi) (%) in Fmc at WeUbore(ft) (It) (It) . (in) (in)

0 170 65 85 0 0 100 0 0 025 249 131 117 905 865 71 0.422 0.165 0.25150 296 157 139 1323. 995 64 0.530 0.191 0.28675 315 169 146 1313 1017 59 0.568 0.198 0.303100 329 179 151 1790 1048 58 0.598 0.218 0.309125 361 198 165 2018 1106 54 0.646 0.206 0.318150 372 202 171 2188 1104 52 0.659 0.213 0.319175 406 226 180 2381 1142 52 0.706 0.216 0.334200 435 244 191 2424 1171 47 0.743 0.211 0.339

iii !

37

Table 36 Advan! - 6.Layer p_00 cp

Time Height Upper Lower Half Net Pre.urn Efficiency Max. Wklth Avg.Width Avg.Width(rain) (11) Height HelgM Length (PSi) (%) (in) in Fmc atWellborn

(ft) (It) (It) (in) (in)o 17o 85 es o o 1oo o o o25 240 124 116 654 885 67 0.434 0.218 0.26750 276 144 132 1073 965 58 0.513 0.220 0.29975 3eo 151 229 1194 I065 e2 o.e67 o.2_ o.386100 392 161 231 1227 1051 es 0.702 0.340 0.408125 403 159 234 1273 1048 63 0.727 0.359 0.421150 413 177 237 1363 1047 58 0.720 0.337 0.402.,175 430 190 241 1506 1076 57 0.749 0.336 0.406200 438 195 243 1594 1129 58 0.805 0.364 0.445

i

Ti_ X Advani. 6.Layer n'=0.6, k'-0.04

Time HetgM Upper Lower Half NetPrmure Efficiency Max.Width Avg.Width Avg. Width(mln) (It) HetgM Height Length (psi) (%) (in) InFmc at Wellborn

(lt) (lt) (lt) _n) (_)0 170 es es 0 0 100 0 0 025 248 131 117 905 865 71 0.422 0.165 0.25150 378 147 231 1150 992 72 0.597 0.244 0.34075 388 157 231 1159 1021 76 0.662 0.29g 0.377100 3_ 166 232 1206 1044 70 0.695 0.308 0.3516125 422 187 •235 1502 1027 es 0.697 0.278 0.373150 430 193 237 1751 1035 62 0.704 0.267 0.370175 44,9 205 244 1853 1095 61 0.770 0.289 0.410200 458 210 248 1870 1151 64 0.848 0.337 0.465

i ,,

38

Table 31' Shell. GDl( Constant Height F,,,,200cp

a i t

Time Height Half Length Net Pressure Efficiency Max. Width Avg. Width Avg. Width(rain) (lt) (11) (Psi) (%) (in) in Fmc at Wellbore

(in) (in)0 170 0 0 100 0 0 025 170 704 104 88 0.396 0.311 0.39650 170 1107 83 67 0.486 0.3g0 0.49675 170 1441 73 86 0.566 0.445 0.566i

100 170 1738 66 86 0.622 0.489 0.622125 170 2007 62 85 0.669 0.525 0.669 - :.150 170 2261 58 85 0.710 0.557 0.710175 170 24,99 55 84 0.746 0.586 0.746p,

200 170 2725 53 84 0.779 0.612 0.779I li

Table 38 Shell - GDl( Comitant Height n'-0.6, k',,0.04

"' Time Height Half_ Net Pressure Efltclency Max.W_lth 'Avg.'Width ' ' Avg.(m_) (n) (it) (psi) (_) (kn) inFmc it Week,re

_) ph)0 170 0 0 100 0 0 025 170 624 134 90 0.453 0.356 0.45350 170 g42 117 89 0.596 0.466 0.59875 170 1196 106 89 0.ego 0.549 0.699100 170 1421 102 88 0.784 0.615 0.784125 170 1622 98 88 0.856 0.672 0.856150 170 1807 g4 88 0.920 0.722 0.920175 170 1979 91 88 0.977 0.768 0.977200 170 2142 89 67 1.030 0.809 1.030

Table 39 Shell. PKNConstant Height p"20O cp',lm,

Time Height Half Length I _Pressure Efficiency Max.Width AVg.Width AVg.Width(min) (It) (lt) (l:xd) (%) (in) in Fmc atWellbore

_) _)0 170 0 0 100 0 0 025 170 948 848 84 0.358 0.225 0.28i50 170 1540 993 81 0.423 0.266 0.33275 170 2044 1092 79 0.466 0.293 0.366100 170 24,96 1168 78 0.,499 0.314 0.392i

125 170 2917 1232 77 0.526 0.331 0.413150 170 3310 1286 76 0.550 0.345 0.432175 170 3683 1334 76 0.570 0.358 0.448200 170 403g 1376 75 0.589 0.370 0.463

Table40 Shell - PKNConmnt Height n',,0.6, k',,0.N

Time Heght Half Length NetPressure Efficiency Max.Width Avg. Width Avg. Width(rain) (lt) (lt) (pid) (%) (in) in Fmc atWellbore

(in) (in)0 170 0 0 100 0 0 025 170 863 g50 85 0.400 0.251 0.31450 170 1356 1160 83 0.4,93 0.310 0.38775 170 1767 1307 82 0.567 0.350 0.437100 170 2132 1424 81 0.607 0.382 0.477125 170 2465 1522 80 0.650 0.406 0.511150 170 2776 1608 80 0.687 0.432 0.540175 170 306g 1685 79 0.720 0.452 0.565200 170 3347 1754 79 0.750 0.471 0.58g

39

Table 41 Shell ENERFRAC p,,200 cp Base Case

li I I I

Time Height Half Length Net Pressure Efficiency Max. Width Avg.Width Avg.Width(min) (it) (ft) (psi) (%) (in) in Fmc at Wellbore

(in) (in)0 170 0 0 100 0 0 025 170 611 1093 85 0.423 0.261 0.33250 . 170 1373 1237 83 0.483 0.296 0.38075 170 1863 1332 81 0.522 0.322 0.410100 170 2311 1405 79 0.551 0.340 0.433125 170 2729 1464 78 0.575 0.354 0.451150 170 3125 1513 77 0.594 0.367 0.467175 170 3503 1557 76 0.612 0.377 0.480200 170 3866 1595 75 0.627 0.387 0.492

i i i i

Table 42 Shell ENERFRAC n',,,O.8,k'V,O.M Base CoM

. ii i

Time Height Half Length Net Pressure Efficiency Max. Width Avg.Width Avg. Width(min) (ft) (ft) (psi) (%) (in) inFmc st Wellbore

.. (in) (in)0 170 0 0 100 0 0 025 170 770 1160 86 0.448 0.276 0.35250 170 1267 135g 84 0.530 0.327 0.41775 170 1693 1494 82 0.585 0.381 0.459100 170 2079 1598 81 0626 0.386 0.492125 170 2436 1684 80 0.661 0.408 0.519150 170 2772 1757 79 0.680 0.426 0.542

175 170 3092 1821 79 0.715 0.441 0.562200 170 3396 1880 78 0.738 0.456 0.580

Table 43 Shell ENERFRAC p=200 cp Ovetpreuure,,Ir_O psi

i i

Time Height Half Length Net Pressure Efficiency Max.Width Avg.Width Avg.Width(mln) (n) (ft) (o_) (_) (in) inFmc atW_Ibore

, (in) (in)0 170 0 0 100 0 0 025 170 772 1120 86 0.448 0.277 0.352,,.

50 170 1322 1259 83 0.506 0.312 0.39675 170 1806 1353 81 0.543 0.335 0.427100 170 2249 1424 80 0.571 0.352 0.449125 170 2663 1462 79 0.594 0.366 0.467150 170 3054 1531 78 0.613 0.378 0.482175 170 3429 1574 77 0.630 0.389 0.4,95200 170 378g 1612 76 0.645 0.396 0.506

Table 44 Shell ENERFRAC n'-0.6, k',,0.N Overprossure-600 psi

i

Time Height Half Length NetPressure Efficiency Max. Width AVg.Wk:lth Avg.Width(mln) (ft) (ft) (psi) (%) (in) in Fmc at Wellbore

(in) (in)0 170 0 0 100 0 0 025 170 730 1200 87 0.477 0.294 0.37550 170 1220 1392 84 0.556 0.343 0.437,,,

75 170 1642 1524 83 0.608 0.375 0.478100 170 2024 1626 82 0.64_ 0.400 0.509125 170 2379 1710 81 0.682 0.420 0.535150 170 2714 t782 80 0.710 0.438 0.558175 170 3031 1846 79 0.735 0.453 0.577200 170 3336 1903 79 0.757 0.467 0.595i

4O

Table 48 8hatl ENERFRAC IA_0 cp _10_) psi

Time Height HalfLength N'atP'ml_e Efficiency Max. Width Avg.Width Avg.Width(rain) (It) (lt) (psi) (%) (in) inFmc at We, bore

(in) (in)0 170 0 0 100 0 0 025 170 660 1262 88 0.536 0.332 0.42250 170 1174 1372 86 0.585 0.361 0.429,

75 170 1634 1451 84 0.616 0.380 0.484100 170 2060 1513 82 0.640 0.395 0.502125 170 2460 1565 81 0.65g 0.407 0.518150 170 2840 1610 80 0.676 0.417 0.531175 170 3205 1649 79 0.691 0.425 0.543200 170 3556 1684 79 0.704 0.434 0.553

• i i i

TaMe 48 Shell ENERFRAC n',,0.6, k',,0.N Ovsq:remmml000 psi

i i

Time Height Hs,' Length Net Pressure Efficiency Max. Width Avg.Width Avg.Width(mln) (ft) (lt) (psi) (%) (in) In Fmc at We,bore

(,in} (in)0 170 0 0 100 0 0 025 170 626 1359 89 0.570 0.352 0.44850 170 1069 1519 86 0.637 0.393 0.50075 170 14,96 1635 85 0.682 0.421 0.536100 170 1868 1727 84 0.718 0.443 0.564125 170 2215 1805 82 0.748 0.461 0.587150 170 2543 1872 82 0.773 0.477 0.607,,,, ,,

175 170 2855 1932 81 0.796 0.491 0._25200 170 3155 1966 80 0.817 0.504 0.641

i ii 1 --- i

Table 47 Shell ENERFRAC 1_,,2_ cp Overpressure-llr_) psi

m,

Time Height Half Length Net Pressure Efficiency Max.Width AVg.Width Avg.Wk:Ith(mln) (lt) (lt) (Psi) (%) (in) In Fmc at Wedlbom

(in) _n)0 170 0 0 100 0 0 025 170 524 1591 91 0.695 0.429 0.54650 170 970 1648 88 0.730 0.450 0.57375 170 1384 1696 86 0.751 0.463 0.580100 170 1776 1737 85 0.767 0.473 0.603....125 170 2148 1774 84 0.781 0.462 0.614150 170 2506 1806 83 0.794 0.490 0.623175 i70 2850 1836 82 0.805 0.496 0.632.200 170 3184 1863 81 0.814 0.502 0.640

i i

TaMe 48 Shell ENERFRAC n',,0.6, k'-0.N Overpressurm,1600 psii|111

Time _:_;_i HalfLength NetPressure Efr_mcy Max. Width AVg.Width Avg.Width(min) (ft) (It) (psi) (%) (in) In Fmc atWellbore

(in) (in)0 170 0 0 100 0 0 025 170 507 1672 91 0.721 0.445 0.56650 170 920 1776 8g 0.774 0.477 0.60875 170 1297 1862 87 0.805 0.4_ 0.635 "I00 170 1647 1934 86 0.837 0.516 0.657125 170 1977 1998 85 0.861 0.531 0.676150 170 2291 2054 84 0.882 0.544 0.693i175 170 2591 2105 83 0.901 0.558 0.707200 170 2881 2152 82 0.918 0.566 0.721i

41

Table O Shell ENERFRAC pt_200cp Overprenum2000 psi

i |

Time Height Half Length NetPressure Efficiency Max.Width Avg.Width Avg.Width(min) (It) (ft) (psi) (%) (in) in Fmc atWe, bore

(in) (*n)0 170 0 0 100 0 0 025 170 420 2035 93 0.884 0.545 0.69450 170 878 2059 90 0.921 0.568 0.72375 170 1141 2061 89 0.937 0.578 0.736100 170 1482 2102 87 0.947 0.584 0.744125 170 1813 2122 86 0.956 0.580 0.751150 170 2133 2141 85 0.963 0.594 0.757175 170 2446 2159 84 0.970 0.598 0.762200 170 2750 2175 84 0.976 0.602 0.767

Table 60 Shell ENERFRAC n',,0.6, k',,0.X Overprusure,,2000 psi

i I i i i

Time Height Half Length Net Pressure Efficiency Max.Width Avg.Width Avg.Width(n'dn) (ft) (It) (l:Nd) (%) (in) inFmc at We, bore

(in) . (in)0 170 0 0 100 0 0 025 170 413 2088 93 0.900 0.555 0.70750 170 765 2148 91 0.951 0.586 0.74775 170 1098 2203 89 0.978 0.603 0.768100 170 1414 2252 68 0.999 0.616 0.784.125 170 1717 2297 87 1.016 0.627 0.798150 170 2008 2339 86 1.032 0.637 0.811175 170 2290 2378 85 1.047 0.646 0.822200 170 2583 2414 85 1.060 0.654 0.833

i

42

Tablo 61 I_lllbuNon GDl( Constant Height _,,200 cp

Time Height HalfLength Net Prmum Efficiency Max. Width Avg. V_/idth Avg. Width(min) (It) (It) (psi) (%) (in) in Fmc atWellbore

(in) (in)0 170 0 0 100 0 0 025 170 535 186 91 0.53 0.42 0.5350 170 858 141 _ 0.86 0.52 0.6675 170 1132 120 88 0.74 0.58 0.74100 170 1378 108 88 0.80 0.63 0.80125 170 1605 98 87 0.85 0.67 0.85150 170 1818 92 87 0.90 0.71 0.90175 170 2020 86 86 0.94 0.74 0.94200 170 2212 82 86 0.98 0.77 0.98

II

Table 12 Hilibwton (_DI( Constant Height n',,O.6,k',,0.N

Time Height HalfLength Net Prm_ Eff'K_ency Max.Width Avg. Width Avg.Width(rain) (It) (It) (Ix_i) (%) (in) in Fmc at We, bore

(in) (in)0 170 0 0 100 0 0 025 170 560 168 91 0.51 0.40 0.5150 170 861 140 89 0.65 0.51 0.6575 170 1106 126 68 0.75 0.5_ 0.75100 170 1322 117 68 0.84 0.68 0.84125 170 1518 110 87 0.90 0.71 0.90150 170 1699 105 87 0.97 0.76 0.97175 170 1870 101 68 1.02 Q_RO_ 1.02200 170 2031 97 86 1.07 0.84 1.07

43

T_leli,1 Chevron GDK_llelght ll-200q:)

Time Height I 'Half Length Net'l:h'enum Efflct_ Max. Width Avg.Width Avg.Width(rain) (ft) I (ft) (Imi) (%) (in) in Fmc at We, bom

I (in) (in)0 170 0 0 100 0 0 0

2=3 1ro 386 116 85 0.333 0.262 0.33350 170 581 102 84 0.438 0.343 0.43875 170 774 94 83 0.530 0.416 0.530100 170 906 90 83 0.589 0.462 0.589125 170 1026 87 83 0.640 0.502 0,640150 170 1137 84 82 0.585 0.538 0.585175 170 1241 82 82 0.726 0.570 0.726200 170 1347 80 82 0.767 0.602 0.767

i n IINNI INI I

TM_IeIM Chevron PKN Constant HelgM IA=200cp

Height Half f.ength Net Pm' EffK:_kmcy Max. Width 'Avg.Width Avg. Width(min) (ft) (ft) (pail) (%) (in) in Fmc t Wellborn

(in) (in)0 170 0 0 100 0 0 -25 17(! 454 837 82 0.384 0.216 -50 170 744 968 80 0.453 0.254 -75 170 1049 1108 77 0.506 0.285 ---

t00 170 1267 1179 76 0.541 0.304 -125 170 1470 1239 75 0.569 0.319 -150 170 1660 1291 74 0.5_2 0.332 -175 170 1841 1336 73 0.613 0.344 -200 170 2029 1380 73 0.633 0.355 -

plJa

44

TableM Conoco GDKConstant Height p._mCl)

Time Height HaftLength NetPrmure Efr_ Max.Width Avg.Width Avg.(rain) (ft) (ft) (Psi) (%) (in) inFmc at Wellbore

(in) (in)0 170 0 - 100 0 0 025 170 704 - 87 0.391 0.307 0.39150 170 1106 - 86 0.48Q 0.384 0.488

75 170 1438 - 85 0.550 0.438 0.558100 170 1734 - 84 0.613 0.481 0.613125 170 2004 - 84 0.650 0.517 0.650,H

150 170 2255 - 83 0.699 0.540 0.699175 170 2492 - 83 0.735 0.577 0.735200 170 2716 - 83 0.767 0.602 0.767ii li

,

Table U Conoco GDK Constant Height n',,0.6, k',,0.M

Time Height' Half Length Net _ Efficiency _ _'k_h Avg._ Avg.Width(rain) (It) (lt) (psi) (%) (in) inFmc mtWelllxxe

pn) On)0 170 0 - 100 0 0 __.025 170 674 - 88 0.411 0.323 0.41150 170 1015 - 87 0.541 0.424 0.54175 170 1290 - 86 0.634 0.496 0.634100 170 1530 - 86 0.711 0.558 0.711125 170 1745 - 86 0.776 0.800 0.776,i

150 170 1944 - 86 0.833 0.854 0.833i , ,,iq ,li

175 170 212g - 85 0.886 0.6Q5 0.886200 170 2304 - 85 0.933 0.733 0.933

li

Treblei7 Conoco PKN Constant Height lA,,200cp

Time Height HaftL_ NetPressure Efficiency Max.Width Avg.Width Avg. Width(min) (It) (lt) (.rod) (%) (in) in Fmc mtWetlbore

on) on)0 170 0 - 100 - 0 0i i i i

25 170 830 - 85 - 0.250 0.37550 170 1418 - 82 - 0.286 0.428

75 170 1925 - 80 - 0.308 0.462.100 170 2386 - 78 - 0.325 0.488125 170 2817 - 77 - 0.339 0.508150 170 3225 - 76 - 0.351 0.526175 170 3614 - 75 - 0.351 0.541200 170 3086 - 74 - 0.370 0.554

li

Table 88 Conoco PKN Conmnt Height n',,0.6, k'-0.N

Time Height HuffLength NetPressure Efrx_'_/ Max.Width Avg.Width Avg.Width(mM) (ft) (ft) (iii) (%) {in) in Fmc mtWellborn

(_) (_)0 t70 0 - 100 - 0 025 170 831 - 85 - 0.253 '0.38050 170 1367 - 82 - 0.29Q 0.448.75 170 1826 - 81 - 0.329 0.483i

100 170 2240 - 80 - 0.352 0.528125 170 2624 ° 79 - 0.371 0.557150 170 2985 - 78 - 0.388 0.581175 170 3328 - 77 - 0.402 0.603200 170 3656 m 77 " 0.415 0.622

i

45

Table _ Mlrattm_ GHOFER Constant Height p,,298 cpii

Time Height Half Leng_ Net Prelmum Effick_ Max. Wia_ Avg. Width Avg.Width(mln) (It) (lt) (1_) (%) (in) in Fmc at We,bore

(in) (in)0 204 0 0 100 0 0 0.7525 204 374 1819 97 0.91 0.68 0.7550 204 714 1742 96 0.91 0.71 0.75

,75 204 1054 1668 95 0.88 0.6g 0.75100 204 1360 1694 95 0.93 0.72 0.75125 204 1666 1683 94 0.g0 0.72 0.75150 204 1972 1684 94 0.91 0.72 0.75175 204 2312 1678 94 0.g0 0.72 0.76200 204 2584 1685 93 0.gl 0.73 0.76

i....

Table SO MirMhon GHOFER Constant HetgM n',:O.5,k'uO.08

, li'IIII i i l i

Time Height HalfLength NetPressure Effk_kmcy Max. Width Avg.Width Avg.Width(rain) (ft) (It) (psi) (%) (in) in Fmc at We, bore

(in) (in)0 2O4 0 0 100 0 0 025 204 374 1832 97 0.91 0.68 0.7650 204 714 1767 95 0.92 0.71 0.7675 204 1020 1764 95 0.93 0.72 0.77100 204 1360 1754 95 0.93 0.72 0.77125 204 1632 1776 94 0.g5 0.74 0.78,,

1_ 204 1938 1786 g4 0.96 0.73 0.79

175 204 2244 1805 g4 0.97 . 0.74 0.80200 204 2516 1825 g3 0.98 0.75 0.82

Table 11 Marathon GHOFER 3.Layer p,,200 cp

Time Height Upper Lower Half Net Pressure EtTr_-y Max.Width Avg.Width Avg. Width(mln) (It) Height Height Length (psl) (%) (in) in Fmc atWellbore

(ft) (it) (ft) (in) (in)0 - - - 0 0 100 0 0 025 374 204 170 306 1423 98 0.84 0.51 0.5550 374 238 170 476 1435 97 0.95 0.59 0.6675 408 238 170 612 1426 97 1.00 0.61 0.67100 408 238 170 782 1413 97 1.0I 0.63 0.68125 442 238 204 918 1391 97 1.02 0.62 0.67150 442 238 204 1054 13_4 97 1.03 0.63 0.68175 442 238 i 204 1190 1396 97 1.04 0.65 0.6g

203 442 238 I 204 1360 '138g g6 1.04 0.64 0.68

Table 12 Marathon GHOFER 3-I.ayer n',,0.6, k',,0.04

Time Height Upper Lower Haft Net Pressure Efr_._q_cy Max. Width Avg.Width Avg. Width(mln) (it) Height Height Length (psi) (%) (in) in Fmc at Wellbore

(It) (It) (It) (in) (in)0 - - 0 0 100 0 0 025 374 204 170 306 1434 98 0.84 0.51 ' 0.55"50 374 204 170 476 1450 98 0.98 0.5g 0.6675 408 204 170 612 1441 97 1.04 0.61 0.68100 442 204 204 782 1414 97 1.02 0.61 0.67

125 442 238 204 884 1434 97 1.06 0.64 0.70150 442 238 204 1020 1434 97 1.07 0.65 0.71175 442 238 204 1190 1431 97 1.07 0.65 0.72

200 442 238 204 1326 1433 96 1.08 0.66 0.71

46

TaMe a Marathon GHOFER 6.Layer p,,200 cp

Time Height Upper '_ Half Net Pressure Efficiency Max. Width Avg.Width Avg. Width(rain) (ft) Height Height Length (psi) (%) (in) inFmc at We, bore

(It) (It) (It) (in) (in)0 - . . 0 0 100 0 0 0

25 340 204 170 306 1447 9e 0.84 0.53 0.5850 442 204 _ 406 1323 96 0.96 0.50 0.6475 442 204 238 544 1303 97 1.00 0.63 0.71100 442 204 _ 714 1266 97 0.99 0.63 0.70125 476 238 236 850 1251 97 1.00 0.63 0.67150 476 238 238 952 1257 97 1.02 0.64 0.69175 47_ .238 z._ 1068 1254 97 1.03 0.65 0.70

4r_ 238 _ 1224 1250 97 1.03 0.65 0.70

Table (14Marathon GHOFER |4.ayer n'n0.6, k',,0.M

Time He,ht Upper Loww H_f ' NetPressureEmc_mcyMax.Width Avg.Wm_ Avg.Width(mln) (it) Height Height _ _ (%) (in) in Fmc at WeUbom

(it) (it) (It) (_) (_)0 - - - 0 0 100 0 0 025 30_ ,170 136 306 1455 96 0.64 0.54 0.6250 442 204 238 408 1316 95 0.95 0.50 0.6675 442 204 238 544 1268 95 0.98 0.61 0.68100 442 204 238 680 1285 94 1.01 0.64 0.71125 442 204 238 816 1268 94 1.01 0.65 0.74t50 476 238 238 918 1265 94 1.03 0.64 0.70175 4rt_ 238 238 1054 1257 93 1.03 0.65 0.70

476 238 238 1156 1263 93 1.04 0.66 0.71

47

TaMe 66 ARCO $Umpian 3.Layer p:_00 cp

Time Height Upper Lower HaW Net Pressure Efficiency Max. Width Avg.Width Avg.Width(min) (lt) Height Height Length (1_i) (%) (in) in Fmc atWe"bore

. (It) (lt) (It) (in) (in)0 170 85 85 0 0 100 0 0 025 249 t 54 96 920 824 80 - 0.19 -50 259 159 100 1422 868 76 0.21 -75 269 164 105 1850 902 74 - 0.23 -100 280 171 110 2248 927 73 0.23, , ,,

125 288 175 113 2616 955 71 - 0.24 -150 295 180 116 2960 963 70 0.24 -175 300 182 118 3286 976 68 0.25 -

,,,

200 306 186 121 3598 992 67 0.57 0.25 0.31, ,, , ,, ,,, , , , ,

Table lM.ARCOStimpian 3.Layer n',,0.6, k',,0.04

Time Height Upper Lower Half NetPressure Efficiency Max.Wlcllh Avg.Width Avg.Width(rain) (lt) Height Height length (psi) (%) On) in Fmc atWe"bore

(lt) (a) (lt) (_) (in)0 170 85 es 0 0 too 0 0 025 252 155 97 900 845 81 - 0.19 -i

50 271 155 105 1356 911 77 - 0.22 -75 289 176 113 1748 956 75 - 0.23 -100 305 185 120 2094 9g0 73 - 0.24 -,, ,

125 315 191 124 2409 1016 71 - 0.25 -150 328 196 130 2703 1043 71 - 0.25175 340 205 135 2976 1061 69 - 0.26 -200 353 213 141 3235 1083 68 0.65 0.26 0.33

Table |/ARCO Stknplan 6.Layer F,,20Ocp

Time Height Upper bower Half Net Pressure Efficiency Max.Width Avg.Width Avg.Width(rain) (lt) Height Height Length (psl) (%) On) in Fmc atWe,bore

(lt) (a) (a) on) _n)0 170 85 85 0 0 100 0 0 025 251 157 95 926 816 80 - 0.19 -50 268 168 100 1425 860 77 - 0.21 -75 354 175 180 1863 881 74 - 0.22 -100 369 176 194 2225 885 72 - 0.22

i

125 369 176 194 2540 891 70 - 0.24150 380 176 205 2846 900 6g - 0.24175 380 176 205 3118 906 68 - 0.25200 394 180 215 3399 944 68 0.64 0.24 0.36

Table611ARCO Stimpian 64Jyer n'uO.6,k',,0.N

Time H_ht Upper Lower Haft Net Pressure Efficiency Max. Width Avg. Width Avg.Width(rain) (lt) Height Height Length (psi) (%) On) in Fmc at We"bore

(lt) (ft) (ft) (in) (in)0 170 65 65 0 0 100 0 0 025 250 156 94 889 822 80 0.19 -50 328 174 154 1358 890 77 - 0.20 -75 379 175 204 1718 920 75 0.22 -100 390 178 212 200g 930 74 - 0.24 -125 396 182 215 226g 932 73 0.25 -150 402 187 216 2497 931 71 0.26 -175 403 188 216 2717 967 71 0.26 -200 405 190 216 2926 968 70 0.70 0.27 0.40' ,, ,,, ,,,, ,, ,, , ,, _r -, _i

48

Table M ARCO T_aFmc 6.Lnyor n',,O.6,k'wO.N

i i - i i 1

Height Upper _ Half Nat Prusum Eff'_ienoy Max.Width Avg.Width Avg. Width(mln) (It) Height Height Length (p_) (%) (in) in Fmc atWellborn

(It) (lt) (it) (in) (in)o 17o e5 es o o too o o o25 226 142 84 921 864 81 0.37 - -50 246 150 g6 1371 981 71 0.45 - .75 358 170 188 1802 g97 73 0.47

,,,,,

100 370 182 188 2133 1030 67 0.52 - -..125 3gg 211 188 2378 1080 67 0.63 -.,150 408 220 188 2651 1120 65 0.67 -175 423 234 188 2923 1150 64 .07 - -200 449 239 210 3124 1160 62 0.74 - -

,

49

Table 70 NSl Tech. 8timpian 34.ayer p_O0 cp

Time Height Upper Lower Half Net Pressure Efficiency Max. Width Avg.width Avg.Width(min) (ft) Height Height Length (psi) (%) (in) inFrac atWe, bore

(It) (lt) (ft) (in) (in)0 170 85 68 0 0 100 0 0 025 237 119 ' 118 906 684 81 0.38 0.19 0.23

,,,

50 246 122 124 1447 746 75 0.43 0.20 0.2575 252 124 127 1914 787 73 0.46 0.21 0.28

100 256 126, 130 2336 818 71 0.49 0.22 0.29125 259 127 132 2725 840 69 0.50 0.22 0.30150 267 131 136 308g 865 68 0.52 0.23 0.31175 275 135 141 3428 884 67 0.54 0.24 0.31

[-200 283 138 144 3750 903 66 0.56 0.25 0.32i

Til)li 71 NSI Tech. Stimplln 34.ayer n_0.S, k_0.06

Time Height Upper Lower Half Net Pressure Efficiency MaxlWidth Avg. Width Avg. Width(rain) (ft) Height Height Length (psi) (%) (in) inFmc at We, bore

(It) (lt) (lt) (in) (in)0 170 85 85 0 0 100 0 0 025 240 120 120 851 696 80 0.40 0.17 0.25i

50 253 125 128 1340 796 76 0.47 0.20 0.28,,,

75 265 130 135 1758 862 74 0.52 0.22 0.31100 284 139 145 2123 910 72 0.56 .. 0.23 0.32125 296 146 142 2450 945 71 0.60 0.24 0.33150 308 151 158 2749 970 70 0.63 0.25 0.34,,,

175 322 157 165 3032 1003 69 0.65 0.25 0.34200 329 160 168 3289 1005 68 0.67 0.26 0.35

ii, , i

Tib_ 72 NS1Tech. Stimpian 64.ayer pm200 cp

Time Height Upper Lower Half Net Pressure Effk_y Max.Width Avg.Width Avg.Width(rain) (lt) Height Height Length (psi) (%) (in) in Fmc atWellborn

(n) (lt) (lt) (in) (_n)0 170 85 85 0 0 100 0 0 025 172 124 105 911 582 78 0.38 0.17 0.2450 238 125 112 1468 757 76 0.43 0.21 0.27,,

75 242 126 117 1945 ...... 799 74 ...0.46 .. 0.22 0.29I00 246 126 120 2373 828 72 0.49 0.23 0.31125 342 149 '193 2739 " 828 70 0.56 0.23 ' 0.33150 _ 153 203 3079 848 68 0.60 0.23 0.35175 364 157 206 3424 871 67 0.63 0.24 0.38200 361 155 206 3709 852 68 0.63 0.25 0.38

Table 73 NSI Tech. Stimplan 64.ayer n_0.6, k_0.04

Time Height upper Lower Half Net Pressure Efficiency Max.Wi_ Avg. Width Avg. Width(rain) (ft) Height Height Length (psi) (%) (in) in Frac atWellbore

(ft) (ft) (ft) (in) (in)0 170 85, 85 0 0 100 0 .,. 0 025 233 125 106 866 708 80 0.40 0.18 0.2550 244 126 118 1362 810 77 0.47 0.21 0.3075 354 152 203 1757 848 74 0.61 0.22 0.37100 385 157 20g 2069 878 73 0.65 0.23 0.3g,,,

125 375 162 213 2333 904 72 0.66 0.24 0.3g150 381 165 215 2555 850 71 0.66 0.24 0.38175 384 167 216 2749 924 70 0.70 0.25 0.41

. _ ] 3_ t_ 2,0 ] _6s _5 70 0.7_ 0.2s " 0.42

50

Table 7'4 RES FmclXO 34.ayer p,,200 cp

Time Height Upper Lower _ Net Press_ EfficMflcy I_. Wi_h Avg.Width Avg. Width(rain) (lt) Height Height Length (psi) (%) (in) in Fmc at Wellb_

(lt) (lt) (lt) (in) ..... (in)0 170 85 85 0 0 100 0 0 025, 347 218 129 446 1130 92 0.62 0.32 0.4850 400 262 138 711 1162 89 0.W 0.34 0.5175 439 294 145 932 1185 87 0.73 0.34 0.51

100 469 319 150 1124 1202 85 0.76 0.35 0.53125 495 340 155 1300 1215 84 0.78 0.35 0.53150 516 359 157 1481 1222 82 0.87 0.35 0.53175 531 373 158 1608 1223 81 0.88 0.36 0.54200 544 385 159 1744 1227 80 0.90 0.36 0.54

Table 76 RES Fracpro S-Layer n_,0J, k',,O.0e

Time Height Upper Lower Half Net Prlmmre Efflctenoy 'Max._ A_. Width AVg.Width(mifi) (lt) Height Height Length (psi) (%) (in) in Fmc letWellbore

(lt) (lt) (lt) _) (in).o 17o es es o o 1oo o o o25 337 189 145 325 1334 80 0.72 0.39 0.5950 4o4 331 173 ,ms 1363 75 0.04 o.43 o.4375 452 261 191 571 1381 71 0.91 0.44 0.44100 498 2es 2o4 e56 1_ em 0.96 0.48 0.48125 521 305 216 729 1405 67 1.01 0.47 0.47

150 549 323 226 793 1413 65 1.04 0.48 0.48175 574 340 234 850 1421 63 1.08 0.48 0.48200 596 354 242 902 1428 62 1.10 0.49 0.49

, , ,, , i

Table 71 RES Frm li4.ayer p,,200 cp

Time Height Upper Lower Half Net Pressure Effk:iency _ Width AVg.Width AVg.(mM) (It) Height Height Length (j_) (%) On) InFmc at Welllxxe

(lt) (lt) (lt) (_) (_)0 17o,, 85 85 0 0 100 0 0 025 396 200 196 406 979 91 0.57 0.30 0.4550 420 222 196 665 1013 89 0.67 0.34 0.5175 430 239 200 887 1042 87 0.71 0.36 0.54100 456 253 203 1086 1064 86 0.75 0.37 0.56125 469 265 204 1269 1081 es 0.77 0.38 0.57i i

150 480 275 205 143_ 1096 84 0.80 0.39 0.59i

175 491 285 206 1600 1109 63 0.81 0.40 0.60200 501 294 207 1754 1119 62 0.83 0.40 0.80

Table 77 RES Frm:pro 6.Layer n',,0.6, k',,O.04

Time Height Upper Lower Half NetPmssixe Efficiency Max.Width AVg.Width Avg. Width(mln) (ft) Height Height Length (pld) (%) (in) inFmc st WeUbore

(It) (ft) (It) (in) (in)o 17o es es o o IOO o o o25 406 202 .204 293 1263 ...... 93 0.74 0.42 0.6350 475 252 223 424 1317 92 0.91 0.49 0.7475 516 286 230 535 1343 90 1.01 0.52 0.78100 545 312 233 632 1360 90 1.08 0.56 0.84125 569 333 236 719 1375 89 1.14 0.58 0.87150 583 347 2"36 846 1355 88 1.14 0.57 0.86175 592 357 235 952 1352 87 1.16 0.58 0.87, ,,

II 200 _ _ 2",_ 1042 1358 87 1.18 0.60 0._ I

-

51

Table 78 Texaco Fracpro GDK Constant Height p,,200 cp

I t t t t t

Time Height Haft Length Net Pressure Efficiency Max. Width Avg.Width Avg.Width(min) (ft) (lt) (psi) (%) (in) in Fmc at Wellborn

(in) (in)0 170 0 0 lO0 0 0 025 170 636 144 91 0.39 0.39 -50 170 1002 113 89 0.48 0.48 .75 170 1307 99 88 0.55 0.55 -

100 170 1577 . 89 88 0.60 0.60 -125 170 1824 83 87 0.64 0.64 .150 170 2055 78 87 0.68 0.68 -175 170 2273 74 86 0.71 0.71 -200 170 2480 71 86 0.74 0.74 -

ii i t t t

Tat_ 19 Texaco Fmcl_rO PKN Constant HelgM p,,300 cp

Time Height HalfLength Net Pmuum Efficiency Max. Width Avg.Width Avg.Width-(mln) (It) (It) (psi) (%) (in) in Fmc at Wellborn

_n) On)0 170 0 0 100 0 0 025 170 849 653 88 0.33 - -50 170 1449 732 85 0.3g - .75 170 1976 783 83 0.42 - -100 170 2460 823 81 0.44 - -125 170 2915 854 80 0.46 - . -150 170 3346 881 79 0.48 - .175 170 375g g04 78 0.49 - -,,

200 170 4157 925 77 0.50 - -

Table60 Texaco Fracpro 34Jyer p"200 cp

Time Height Upper Loww Half NetPressure Efficiency Max. Wk_ Avg.Width Avg.WidthL(mln) (It) Height Height _ (psi) (%) On) inFmc atWellborn

(ft) (ft) (n) , (in) (in)0 170 85 es 0 0 too 0 0 025 315 203 112 521 1024 85 0.55 -50 355 236 119 836 1065 80 0.61 - .75 3_' 254 123 1065 1083 76 0.64 - .100 ,392 267 125 129g 1098 74 0.66 - ,,

125 404 2_ 127 14,90 1100 72 0.68 -150 315 286 129 1666 1119 71 0.70 - -175 426 295 131 1830 1125 69 0.71 - .200 435 302 133 1983 1132 68 0.72 - -

Table II1Texaco Frac_o 6-Layer iz-200 cp

Time Height Upper Lower Haft NetPressure Eff_,_mcy Max.Width Avg. Width Avg.Width(min) (lt) Height Height Length (1_) (%) On) in Fmc lt Wellborn

(a) (a) (a) _) _n)0 170 85 85 0 0 100 0 0 025 367 176 191 463 872 84 0.50 -50 383 190 193 751 915 80 0.57 -75 398 201 195 1000 944 77 0.61 -100 404 206 195 1233 962 75 0.63 " -125 411 214 197 144,9 976 73 0.64 -150 ,416 220 196 164,9 988 72 0.66 - .175 422 224 198 1835 999 70 0.67 . -

52

T_le 82 Texaco Fracpro 8.Layer n',,O.ii, k',,O.04

ii

Time Height Upper Lower Haft Net Pressure Efficiency Max.Width Avg.Wio_ Avg.Width '(rain) (It) Height Height Length (psi) (%) (in) inFmc at We,bore

(rf) (lt) (ft) (in) (in)0 170 o5 a5 0 0 100 0 0 025 414 207 207 283 1251 88 0.72 - -50 473 255 218 442 1234 85 0.8475 505 285 220 580 1235 82 0.91 - -

100 ,5,30 3! 0 220 704 1240 81 0.96 - .125 552 330 222 818 1250 79 1.01 - .150 571 348 223 926 1257 78 1.05 - .175 588 364 224 1028 1263 77 1.08 - -200 602 378 224 1125 1270 76 I .I I - -

Table 83 Texaco Fracpro 6.Laye_rn',,0.6, k',,0.06 No tlp effects

'Time Height upper Low_ ' _ 'NM Pressure Efficiency Max. Wio_ Avg.Width Avg.Width(min) (ft) Height Height Length (psi) (%) (in) in Fmc at We,bore

(n) (n) (n) (_) (_)0 170 85 85 0 0 100 0 0 025 250 164 92 8,_ e,_ eo 0.35 - .50 286 186 100 1308 930 74 0.40 - -75 348 161 187 1603 796 70 0.35 - .100 360 171 189 1802 845 67 0.42 - -125 370 t79 191 2020 876 65 0.44 - -150 378 186 192 2234 900 64 0.46 - -175 385 192 193 2440 919 63 0.46 - .200 391 197 194 2636 934 62 0.4g - -

" Iii

53

54,

55

58

57

,, , ,, pl , 4,, " lr ,,i_ , ,

58

,i n i,i

59

60

@1

B2

63

i , , , ,, i ii rl ' i ,,,

84

65

66

67

68

@g

7O

,, iii

71

72

.... III

73

74

75

lr 'Til III

76

77

?8

79

80

d. 0

o _.,i,o m' •o:

-=

81

82

83

d. o

o _,

II Q.

84

85

@7

88

8g

90

91

0

92

0

o _._,o _.,o_

II

93

1 i i' i, II GJ' ...... pilr , _r ,,

94

95

C)

o:il

-=:

96

97

!II

98

0

II

I, 1F, r

gg

100

101

102

103

104

105

106

I07

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.

108 c_F--- oI.Q

I!II 12z

,,,o_1 ! _ (2)• _ 0

m ! 1221.12: 0ZOO fr)klJ

klJ._CI "_ ' I "--/

• , ' iC) "_ I I 0

!0 I '_ I,--_ ('r) _ i I Od13_'.I-- : t I

4-J(1) I _

.,...._._ F.... 1 1_ "_ I J

I0 ,-"-_ I _

C

•._ c.) i I __!.1_ I ! I i

-_0 I z I

l ,I 0 -r

f_. m r..

m 121 _

u_ I I oU_

_ ! ! '

! I o"

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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

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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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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.

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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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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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