Hydraulic Fracture Models

April 4, 2018 | Author: Adi Victor | Category: 3 D Modeling, Flow Measurement, Fluid Dynamics, Continuum Mechanics, Applied And Interdisciplinary Physics
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Topical ReportHydraulic Fracture Model Comparison Study: Complete Results " Prepared by: N. R. Warpinski, Sandia National Laboratories I. S. Abou-Sayed, Mobil Exploration and Production Services Z. Moschovidis, AMOCO Production Company C. Parker, CONOCO GasResearchInstHute Febnm_ 1993 @STIRIBUTION Tight Sands and Gas Processing Research Department , II TI , ii ,, i i ,t i i i i, ,i , ,, , i , lr OF THIS DOCUMENT IS UNLIMITED GRi9310109 SAND93-7042 HYDRAULIC FRACTURE MODEL COMPARISON STUDY: COMPLETE RESULTS TOPICAL REPORT (February, 1993) Prepared by N. R. Warpinski Sandia NationalLaboratories I.S. Abou-Sayed Mobil Explorationand ProductionServices Z. Moschovidis AMOCO ProductionCompany C. Parker CONOCO Preparedat Sandia National Laboratories Division6114 P.O. Box 5800 =3 _ _ _ _ _ E_ _ ,. ':'c: d_N =°">"*-'I _ = E ",_= ,-, == =oy. Albuquerque,New Mexico87185 °..¢j ,J:= ._o_ ""6 *",_ G For GAS RESEARCH INSTITUTE ContractNo. 5089-211-2059 m =O m I= _,.. _->.=_ =_ _ _ _ _= _= " _ >" = = I= ¢= _ _ ,,=, _d I= ,.,., = _ O >, u_oo i::'.' =s>, .= _a = === o _."E ¢; _==-- =_^_o °._ '__= = _ ii--. E _ _=o _= .- _ - = =,_ > = o w o_ =_ GRI Project Manager Steve Wolhart Tight Gas SandsField Evaluation -== =..=. _= 8 a .¢= _ _, "- ,= February 1993 =o ,_"-._ .-= = -_=" "" ° DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED GRI DISCLAIMER LEGAL NOTICE This reportwas prepared by Sandia National Laboratoriesas an accountof work sponsoredby the Gas Research Institute(GRI). Neither GRI, members of GRI, nor any personacting on behalf of either: a. Makes any warrantyor representation,expressor implied,with respect to the accuracy,completeness,or usefulnessof the informationcontained in this report,or that the use of any apparatus,method,or processdisclosed in this report maynot infringeprivatelyownedrights;or b. Assumesany liabilitywithrespect to the use of, orfor damagesresulting from the use of, any information,apparatus,method,or process disclosed in this report. _No. . 3 layer.k. HYFRAC3D.sw_.[Pmrr . but so are differences between the pseudo-3-D and fully-3-D models. New Mexico Nem . r. Oev_ Tight gas sands. Report ]iS. This paper documents the differences in length."-R-D=ORT IX)(_UIdENTATION '" .. width.. Fro. Stimplan. and efficiency predicted by the various models for each of the three cases.. 4. oll producing companies. . _ Aaal_Is e. Sandia National Division 6253 P.-$ Z?2 (4-77_ (For_merty Irl_ 5) Oe@e_men! _ Commerce ii . efflciencies varied between 40% and 97%.-. Illinois 60631 |. Models compared include" (i) PKN and GDK constantheight versions. Overall.. GOHFER. i| C. . These comparisons clearly show that fracture design models give widely varying results. Box 5800 _ Albuquerque..r q . two of the models yield much shorter lengths than other 3-D models.-. COSATI |L Avelleblllty F'_ld/Gnm@ _sternont height. _. Trifrac.._.n4 _. These results provide the petroleum engineer a practical comparison of the various available design models for an actual field test.. c.(_ed Terms SFE No. h.. Moschovidis ii 111 S___-_ |O.t. |deeRIfm_/Ol_n... height. For example. Modelers were given the measured stress and material property data obtained at SFE-3 and fluid properties approximating those used during SFE-3 stimulations.. Included with the results are brief discussions of each model.. (_ |L TJ_N of . service companies. (2) 3-1ayer pseudo-3-D models. Warpinski. _ p.o-3D models. Parker.R.. Companies were allowed to run any or all of the three cases (constant height.. _--'CIONAL INTIS. Pmiect/Tesk/Work Unit "_"°" . Supl_mmntary Nate_ Topical report on the •results of the Fracture i Propagation Modeling Forum This study is a comparison of hydraulic fracture models run using test data from the GRI Staged-Field Experiment #3 (SFE-3).. g. and net pressures ranged from about 700 to 1600 psi for the 3-1ayer and 5-1ayer cases._m4 Covered |_ Sl_msoflnl f_lpmixetkm Gas Research Institute 8600 Bryn Mawr Avenue Chicago.S. Pe_4om_ql Oqenlzotton Neme I. 2/17/93 Hydraulic i._) _. PAGE GRI-93/0109 . MFRAC-II. Topical |_.. 17. Enerfrac c. Title a_l Sul_Hle z S. .O. I1_ 144::ul14tlr loeql (Thll C IqeiXl_) 1_1._ L _. Preparatiol Fracture Model Comparison Study" Complete Results L L -- "_"_"_')N.111) unlimited unclass if led . and (3) 5-1ayer 3-D or pseud.0. Z. Heights varied from 300-700 ft. Model calculations were provided by several consulting companies. S. c__ e. ReLmsct Oete k=c. Abou-Sayed. . Fracpro. hydraulic fracturing.. fracture modeling b. of Peles Release (See ANSI--Z311. (a 5089-211-2059 87185 .... fracture TerraFrac. 3.. P_c.o. and academia. . Laboratories ._ See Ilnelesm:lNe_s en Reveesbe zz.. Well-known differences in length between 2-D PKN and GDK models are shown. or 5 layer) using their own models or commercial models they had purchased.111 and Address No. pressure.. Hydraulicfra¢.R._uring one of the most is importantstimulation techniquesavailable to the petroleumengineer. 1993 Topical Report To develop a comparativestudyof hydraulic-fracture simulatorsin order to providestimulationengineers withthe necessaryinformationto make rational decisionson the type of modelsmost suitedfor their needs. however. fracturesimulation has emergedas a highlycomplexendeavorthat must be able to describemanydifferent physicalprocesses. and proppantloads.hydraulicfracturedesign modelsmustbe able to accountfor widely varyingrockproperties. and in many otherapplicationsfromwaste disposalto geothermalreservoirs. highpermeability sandstonesin Alaska.Engineersare thusfaced with Technical Perspective .being used extensivelyin tight gas sandstones.in situstresses.make productiondifficultand often economicand stimulation is required. wall roughness.coalbed methane.complexfracturing.Title Contractor HydraulicFracture Model ComparisonStudy: Complete Results Sandia National Laboratories GRI Contract Number: 5089-211-2059 Principal Investigator Report Period Objective N.manymodelershave added ad-hoc features to theirmodelsto simulatemechanismsthat are not well understood thistime. in horizontalwells in chalks. Warpinski February 1991-February. As a result. In addition. Such mechanisms at includetip effects. reservoirproperties. Because of this diversityof application. Large quantitiesof natural gas existin low permeabilityreservoirsthroughoutthe US.fracturingfluids. fracture modelshave becomeheteromorphic with no standardof comparison. Characteristicsof these reservoirs. gulfcoast.very weak sandstonesoff the US. and some aspectsof heightgrowth. As a result. Participatingmodelerswere given two treatmentdata sets (one Newtonianfluid. one power-lawfluid) and four differentgeometries (constant-heightPKN.heightand width are often greater than a factor of two. In addition. Results This report is a comparisonof the fracture modeling resultsof twelve differentsimulators. maximumwidthat thewellbore.and efficiencyat 25 minuteintervalsthroughoutthe fracture treatment (totaltime of 200 minutes). height. For the modelsin this study. maximum width at the wellbore.average width at the wellbore.and averagewidth in the fracture have been made. height. Technical Approach The technical approach was to collectand integrate the resultsof the Fracture Model PropagationForum intoa comparative studyof the similarityand differences of hydraulic-fracturemodel outputrun on the same inputdata.a difficultchoice in selectinga model that is appropriatefor their needs. Two comparisons were made of the same model run by differentcompanies. net pressure. These results were assembledby a four member committee intoplots and tables of comparativedata. . average width in the wholefracture.differencesin fracture length. bothfor the final geometryand as a functionof time.width. in bothcases the agreementwas good. Comparisonsof length. constant-heightGDK. 5layer) and asked to providelength.some of them run in differentmodesforeight separate design cases.net pressure.several comparisonsof the same modelwithdifferentoptionsshow a large variabilityin modeloutputdependingupon the options chosen. 3-layer.average widthat the wellbore. 3 Advani (Lehigh HYFRAC3D) 4.0 TEST CASES 7.GOHFER 3.2 3-Layer Results 7. (TRIFRAC) 4.1 Planar 3-D Models 3.0 RATIONALE 3.12 Texaco (usingFRACPRO) 5.0 MODEL RESULTS 7.Table of Contents 1.1 2-D Results(Cases 1-4) 7.0 REFERENCES APPENDIX A APPENDIX B APPENDIX C APPENDIX D APPENDIX E APPENDIX F APPENDIX G 1 2 3 4 4 5 5 6 6 6 7 7 8 8 9 9 9 10 10 11 12 13 14 14 16 16 17 19 20 21 107 116 125 134 136 145 155 .7 Conoco 4.0 RESEARCH OBJECTIVES 2.6 Chevron 4.9 ARCO (usingTerraFrac) 4. Holditch& Assoc.0 DISCUSSION 9.8 Marathon (GOHFER) 4.5 Halliburtion(PROP) 4.3 Pseudo-3-D Models 3.4 Shell (ENERFRAC) 4.11 Resources EngineeringSystems(FRAPRO) 4.2 Meyer & Associates(MFRAC-II) 4.0 SFE-3 FORMATION AND TREATMENT DATA 6.BASIC MODELING DISCUSSION 3.10 NSI (STIMPLAN) 4.0 FRACTURE MODELS 4.0 CONCLUSIONS 10.0 BACKGROUND .2 Planar 3-D FiniteDifference Model .4 Classic PKN and GDK Models 4.3 5-Layer Results 8.0 RECOMMENDATIONS 11.A.1 S. PKN Constantheight 14=200cp Knobs on Table 26 Meyer & Assoc. .5.06 Table 35 Advani.3-Layer n'=0.06 Base Case Table 17 Meyer & Assoc. k'=0. .5. .5-layer 14=200cp Knobson Table 30 Meyer & Assoc.PKN Constantheight n'-0.5.PKNConstantheight 14=200cp Table 10 S.06 Table 15 Meyer & Assoc.PKN Constantheight n'=0.5..PKN ConstantHeight n'=0..GDK Constantheight n'-0.3-Layer 14=200 cp Table 34 Advani.. k'=0. k'=0.5-Layer 14=200 cp Table 36 Advani.A Holditch& Assoc. k'=0.5. .5-layer 14=200cp Base Case Table 22 Meyer & Assoc. k'=0.5-layer n'=0.. o6 Table 9 S.06 Table 11 S.. k'=0..5.5.Listof Tables Table I Rock and Reservoir Data Table 2 Treatment Data Table 3 2-D Results at End of Pump Table 4 3-Layer Results at End of Pump Table 5 5-layer Results at End of Pump Table 6 Time to breakthroughintolower layer Table 7 S.5.A.06 Knobson Table 25 Meyer & Assoc. k'=0. ..GDK Constantheight 14=200cp Table 8 S.3-layer n'=0. k'=0.5.PKN ConstantHeight n'=0. k'=0.PKN ConstantHeight 14=200cp Table 32 Advani. .06 Table 41 Shell ENERFRAC 14=200cp Base Case Table 42 Shell ENERFRAC n'=0. k'=0. . k'=0.5-layer n'=0.5.GDK Constantheight 14=200cp Knobson Table 24 Meyer & Assoc. Holditch& Assoc.06 Table 37 Shell ...06 Base Case Table 43 Shell ENERFRAC 14=200cp Overpressure=500psi I " ..3-layer 14=200cp Table 12 S..GDK ConstantHeight 14=200cp Table 38 Shell .06 Knobson Table 31 Advani ..3-layer 14=200cp Knobs on Table 28 Meyer & Assoc..PKN Constantheight n'-0.3-layer 14=200cp Base Case Table 20 Meyer & Assoc.05.GDK Constantheight n'=0.A Holditch& Assoc.5. k'=0.5-layer n'=0.5.06 Table 13 S.06 Knobs on Table 27 Meyer & Assoc.5-Layer n'=0.5.PKN ConstantHeight 14=200 cp Table 40 Shell . k'=0.3-layer n'=0.06Base Case Table 19 Meyer & Assoc.A Holditch& Assoc. .06 Base Case Table 23 Meyer & Assoc. k.A..A Holditch& Assoc.PKN Constantheight 14=200cp Base Case Table 18 Meyer & Assoc. Holditch& Assoc. k'=0.GDK Constantheight n'=0. k'=0.05. Holditch& Assoc.5.. k'=0.A.06 Table 33 Advani.50k'=0.3-layer n'=0..A.GDK ConstantHeight n'=0. Holditch& Assoc. =o.GDK Constantheight 14=200cp Base Case Table 16 Meyer & Assoc.5.06 Base Case Table _1 Meyer & Assoc.06 Knobson Table 29 Meyer & Assoc.06 Table 39 Shell .5-layer 14=200cp Table 14 S. 5. k'=0. k'=0. Stimplan 5-Layer n'=0. k'=0. k'=0.06 Table 76 RES Fracpro 5-Layer p=200 cp Table 77 RES Fracpro 5-Layer n'=0.06 Table 57 Conoco PKN ConstantHeight p=200 cp Table 58 Conoco PKN ConstantHeight n'=0.06 Table 59 Marathon GOHFER ConstantHeight 1_=200 cp Table 60 MarathonGOHFER ConstantHeight n'=0.06 Table 67ARCO Stirnplan 5-Layer 1_=200 cp Table 68 ARCO Stimplan 5-Layer n'=0.5. k'=0.5.5.06 Table 78 Texaco Fracpro GDK ConstantHeight !_=200cp Table 79 Texaco Fracpro PKN ConstantHeight _=200 cp Table 80 Texaco Fracpro 3-Layer p=200 cp Table 81 Texaco Fracpro 5-Layer !_=200cp Table 82 Texaco Fracpro 5-Layer n'=0.Table 44 Shell ENERFRAC n'=0.06 Table 53 Chevron GDK ConstantHeight !_=200cp Table 54 Chevron PKN ConstantHeight 1_=200 cp Table 55 Conoco GDK ConstantHeight !_=200cp Table 56 Conoco GDK ConstantHeight n'=0.06 Table 69 ARCO TerraFrac 5-Layer n'=0. k'=0. Stimplan 5-Layer 1_=200 cp Table 73 NSI Tech.5.06 Overpressure=1500 psi Table 49 Shell ENERFRAC 1_=200cp Overpressure=2000 psi Table 50 Shell ENERFRAC n'=0.5.06 Overpressure=500 psi Table 45 Shell ENERFRAC 1_=200cp Overpressure=1000 psi Table46 Shell ENERFRAC n'=0.5. k'=0. k'=0.06 Table 72 NSI Tech.06 Table 70 NSI Tech. k'=0.5. k'=0.06 Table 63 MarathonGOHFER 5-Layer !_=200cp Table 64 MarathonGOHFER 5-Layer n'=0.5.06 Table 61 MarathonGOHFER 3-Layer 1_=200cp Table 62 MarathonGOHFER 3-Layer n'=0.5. k'=0.5.5. k'=0. k'=0.5.5.06 Overpressure=2000 psi Table 51 Halliburton GDK ConstantHeight !_=200cp Table 52 Halliburton GDK ConstantHeight n'=0.06 Overpressure=1000 psi Table 47 Shell ENERFRAC 1_=200cp Overpressure=1500 psi Table 48 Shell ENERFRAC n'=0. k'=0.5. k'=0. k'=0.06 Table 74 RES Fracpro 3-Layer 1_=200 cp Table 75 RES Fracpro 3-Layer n'=0.06 Table 65 ARCO Stimplan 3-Layer 1_=200cp Table 66ARCO Stimplan 3-Layer n'=0. k'=0.5. Stimplan 3-Layer p=200 cp Table 71 NSI Tech.5.06 Table 83 Texaco Fracpro 5-Layer n'=0. k'=0.5. k'=0.5.06 No tip effects I . Stimplan 3-Layer n'=0. 200 cp Figure 21 Historyof width at wellborefor other constant-heightmodels.n'. k' Figure 25 Length comparisonfor cases 5 and 6 Figure 26 Height comparisonfor cases 5 and 6 Figure 27 Net pressurecomparisonfor cases 5 and 6 Figure 28 Efficiency comparisonfor cases 5 and 6 Figure 29 Comparisonof maximumwidthat wellborefor cases 5 and 6 Figure 30 Comparisonof average widthat wellborefor cases 5 and 6 Figure 31 Comparisonof average widthin fracturefor cases 5 and 6 Figure 32 Lengthhistoryfor case 5 Figure 33 Heighthistoryfor case 5 Figure 34 Net pressurehistoryfor case 5 Figure 35 History of widthat wellborefor case 5 Figure 36 Length historyfor case 6 Figure 37 Height historyfor case 6 Figure 38 Net pressurehistoryfor case 6 Figure 39 Historyof width at wellborefor case 6 Figure 40 Lengthcomparisonfor cases 7 and 8 Figure 41 Heightcomparisonfor cases 7 and 8 Figure 42 Net pressurecomparisonfor cases7 and 8 Figure 43 Efficiencycomparisonfor cases 7 and 8 .200 cp Figure 20 Net pressurehistoryfor other constantheight-models.200 cp Figure 22 Lengthhistoryfor otherconstantheight-models.n'.List of Figures Figure I Lengthcomparisonfor cases 1-4 Figure 2 Net pressure comparisonfor cases 1-4 Figure 3 Efficiencycomparison for cases 1-4 Figure 4 Comparisonof maximumwidthat wellbore for cases 1-4 Figure 5 Comparisonof average width at wellbore for cases 1-4 Figure 6 Comparisonof average width in fracture for cases 1-4 Figure 7 Length historyfor case 1 Figure 8 Net pressure historyfor case 1 Figure 9 Historyof width at wellborefor case 1 Figure 10 Length historyfor case 2 Figure 11 Net pressure historyfor case 2 Figure 12 Historyof widthat wellborefor case 2 Figure 13 Lengthhistoryfor case 3 Figure 14 Net pressurehistory for case 3 Figure 15 Historyof width at wellborefor case 3 Figure 16 Lengthhistory for case 4 Figure 17 Net pressurehistory for case 4 Figure 18 Historyof width at wellborefor case 4 Figure 19 Lengthhistory for otherconstantheight-models. k' Figure 24 Historyof widthat wellborefor other constant-heightmodels.n'. k' Figure 23 Net pressurehistoryfor otherconstant height-models. case 5 Width profile.case 6 Width profile.case 6 Width profile.cases 5-8 .case 7 Width profile.48 Figure 49 Figure 50 Figure 51 Figure 52 Figure 53 Figure 54 AppendixA FigureA1 FigureA2 Figure A3 Figure A4 Figure A5 Figure A6 FigureA7 FigureA8 AppendixB Figure B1 Figure B2 Figure B3 Figure B4 Figure B5 Figure B6 Figure B7 Figure B8 AppendixC Figure C1 Figure C2 Figure C3 Figure C4 Figure C5 Figure C6 Figure C7 Figure C8 Comparisonof maximumwidth at wellborefor cuses 7 and 8 Comparisonof average width at wellbore for cases 7 and 8 Comparisonof average width in fracturefor cases 7 and 8 Lengthhistoryfor case 7 Height historyfor case 7 Net pressurehistoryfor case 7 Historyof widthat wellbore for case 7 Lengthhistoryfor case 8 Heighthistoryfor case 8 Net pressurehistoryfor case 8 Historyof widthat wellbore for case 8 Heightprofile.case 7 Heightprofile.case 7 Heightprofile.Figure 44 Figure 45 Figure 46 Figure 47 Figure.case 7 Heightprofile.case 5 Heightprofile.case 8 AppendixD Figure D1 Heightprofiles.case 8 Width profile.case 8 Width profile.case 5 Width profile.case 8 Width profile.case 6 Heightprofile.case 6 Heightprofile.case 7 Width profile.case 7 Width profile.case 6 Width profile.case 5 Heightprofile.case 6 Heightprofile.case 8 Heightprofile.case 8 Heightprofile.case 5 Width profile.case 5 Heightprofile. case 8 Height profile(Stimplan)-case 5 Width profile (Stimplan)-case 5 Height profile(Stimplan).case 6 Height profile.case 8 Height profile-case 5 Width profile-case 5 Height profile.case 6 Width profile.case 8 i r _.case 7 Width profile.case 6 Width profile .case 6 Height profile.case 8 Width profile.case 7 Height profile .case 8 Width profile.case 8 Height profile(TerraFrac) .case 7 Width profile (Stimplan).Appendix E Figure E1 Figure E2 Figure E3 Figure E4 Figure E5 Figure E6 Figure E7 Figure E8 AppendixF Figure F1 Figure F2 Figure F3 Figure F4 Figure F5 Figure F6 Figure F7 Figure F8 Figure F9 AppendixG Figure G1 Figure G2 Figure G3 Figure G4 Figure G5 Figure G6 Figure G7 Figure G8 Height profile.case 7 Width profile..case 7 Height profile(Stimplan).ll .case 8 Width profile (Stimplan).case 6 Width profile (Stimplan)-case 6 Height profile(Stimplan).case 7 Height profile.case 5 Width profile -case 5 Height profile . G maximumwidth at the we.1. average widthat the we. This reportdocumentsali of the results suppliedby the modelersand tabulatesand plotsthoseresults.many modelershave usedadhoc features in their modelsto simulatemechanismsthat are not well understoodat this time. high permeabilitysandstonesin Alaska. and proppantloads. net pressure.hydraulicfracture design modelsmust be able to accountfor widely varying rock properties. one power-lawfluid) and four differentgeometries(constantheightPKN. As the complexityof hydraulicfracturinghas increased. average widthin the whole fracture.fracturingfluids.in situ stresses.bore. As a result.bore. reservoirproperties.complexfracturing. Such mechanismsincludetip effects. ali modelsmustbe run withthe same input. gulf coast.wall roughness.-5 coalbed methane. being used extensivelyin tightgas sandstones. I m . 5-layer) and asked to providelength.fracture simulationhas emerged as a highlycomplex endeavor _hatmust be able to describemany differentphysicalprocesses.and efficiencyat 25 minuteintervalsthroughoutthe fracturetreatment (totaltime of 200 minutes). Engineersare thus faced with a difficultchoice in selectinga model that is appropriatefor their needs. Because of this diversityof application. constant-height DK. The purposeof the Forumwas to bringconcernedmodelerstogetherto share resultsof theirmodelsand to agree on a set of rigid inputdata that ali couldrun for a comparativestudy. Participatingmodelerswere given two treatmentdata sets (one Newtonianfluid. As a result.7 very l 6 weak sandstonesoffthe US. 3-layer. In order to comparemodelsin a reasonablesense. Hydraulicfracturingis one of the most importantstimulation techniquesavailable to the petroleumengineer.8 in horizontalwells in chalks.0 RESEARCH OBJECTIVES The objectiveof the GRI FracturePropagationModelingForum and the associated publicationof the results in this report is to assemble a comparativestudyof available hydraulicfracture models.fracture modelshave become heteromorphic with no standardof comparison.9. and someaspects of heightgrowth.10 and in many other applicationsfromwaste disposalto geothermalreservoirs.height. Many experienced engineers will also have their own biases about hydraulicfracture performance and would prefer to find a code whose outputis mostconsistentwiththe engineers experience. Most of the reviseddata setswere returnedby September 1991. .etc.the membersof the committeehave purposelyattemptedto avoid makingany judgmentsabout the relative value of different modelsso as not to injectour biases intothis comparison.a four-membercommittee(the authors)was chosenfromforum participants.Dr. publicationof forum results is limitedto the design phase only. althougha couple were returned or modifiedas late as November 1993. Holditch& Associatesshouldbe singledout for special mentionas the prime mover of the forum.the benefitto the gas consumercomes from the optimizationof this techniquewhen an appropriate model is used. The purpose of this report is to help providesome guidance by comparing many of the available simulators. 3 fracture experiment. who mustdesign the fracture treatment. effects of the breaker. Participants were asked to providefracture designsbased on the SFE No.A. and additional supply. This forum.TX. rate changes.was open to ali knownhydraulicfracturing modelers. The results in this report are derivedfrom the model calculationsof the revised design data set. reviseddesign data set was given to ali participants. Bece3se of the difficultyin trying to establishany consistencyin the use of the actual treatmentdata (e. Steve Holditch of S.). near Houston.enhancedgas production.as well as a history match of the actual pressure data fromthe treatment. After comparisonOfthe fracture designsand historymatches presented at this meeting. and this report. The modelerswho participatedin the forum and prepared data for this paper deserve specialthanksfor their efforts.a final. Since hydraulicfracturingis performedin a large percentageof gas completions(and in recompletions). Most importantly. it was decidedthat any further attemptto compare history matcheswould need to be deferred. Thus.0 RATIONALE The petroleumengineer.2. To publishthe results.a follow-upSPE paper.lowerwellhead costs. In assemblingthis comparison. This report had itsorigins in the Fracture PropagationModelingForum held February 26-27.g. particularlywith respect to the newer 3-D and pseudo-3-D models. is often confronted with a difficultchoice of selecting a suitable hydraulic-fracturemodel for his/her needs. 1991.. Only the resultsand quantifiablecomparisonsare given. whichwas sponsoredby the Gas Research Institute. yet there is very little comparative informationavailable to help in making that choice. temperature. Optimizationresults in more costeffective completions. linearfracturemechanics for fracturepropagationprediction. This discrepancyhas been attributedto manycomplex interactionsof the injectedfluidswiththe formationthat are not well understood.and result in the lackof a standardmodel responsefor a givenphysical problem. there has been a proliferationof fracturingsimulatorsused in the oil industry.0 BACKGROUND . The choice of values forthese parameters is only based on the experienceof the modeler.elasticformation. The reader isreferred to the SPE Monograph Volume 1211 for a detailed descriptionof the governingequations.ormation f plasticity.microcracking.plugging.g.field observations.. and its representation of byfew geometricparameters. Several assumptionsare commonlymade to render the problem tractable:plane fractures.especiallyfor unconfinedfracture growth.g. Advani of LehighUniversity 17 (2) Unique Finite DifferenceSimulatorGOHFER of MarathonOil Co.symmetricwithrespectto the wellbore.withoutknowingthe underlyingassumptionsmay lead to erroneous conclusions.19 . An attemptto phenomenologically characterizesome of these complexprocesses occurringwithinthe fracture (e. While specificdescriptionsof the individualmodelsare given in section 4.etc. non-linearformationbehavior.possiblywithsome guidancefromthe laboratory.BASIC MODELING DISCUSSION In recentyears..increasedfrictionallosses)and near the fracture tip (e.simplification fracture geometry.etc.dilatancy. Inc.powerlaw behaviorof fracturingfluidsand slurries.g.they may not alwaysreliably predict the observedbehaviorfor a giventreatment. Althoughthe modelspredict "trends"of treating pressurebehavior. 3 well fracturingtreatment.) was made in varioussimulatorsby the introduction of additionalad hocparameters("knobs"). this section providesa general overview of hydraulic-fracture modelsand cataloguesthe various modelsintosimilargroupings. This issuewas addressedin the forumby having differentparticipants (several differentmodels)simulatecommontest cases derived from the actual SFE No. Applyingthese models for as "black boxes".12-16 run byARCO * HYFRAC3D by Dr.or from othercomputationalresources(e.18.that involvesthe mechanicalinteractionof the propagatingfracturewiththe fluid dynamicsof the injectedslurry. multiplefractures. These knobsare usedto matchmodel predictionswithfield observed behavior. Hydraulicfracturingis a complex non-linearmathematicalproblem. This proliferationwas intensifiedby the availabilityof personalcomputersand the need for fast runningdesign simulators use in the field. These modelscan be categorized in the order of decreasingcomplexityas follows: (1) Planar three-dimensional(3D) models * TerraFrac of TerraTek.3.0. finite element codes). ENERFRAC of Shell20. power lawfluids.two dimensionalflow in the fracture. and linearfracture mechanicsfor fracture propagation.GOHFER Besidesthe numericaltechniqueused.planar -D Models 3 The TerraFrac12-16 and the HYFF<AC3D models employsimilarassumptionsand 17 formulatethe physicsrigorously. B.26-29 (4) Classic PKN and GDK Models30-35 PROP of Halliburton 34-36 Chevron 2-D model37 Conoco2-D model38.TerraFrac uses an integralequation representation.21 TRIFRAC of Holditch& Assoc.22-25 MFRAC-II of Meyer and Assoc. Their difference is in the numerical technique to calculatefracture opening. Inc.assumingplanarfractures of arbitraryshape in a linearlyelasticformation.while the HYFRAC3D modeluses the finite element method.Overall Fracture GeometryParameterization FRACPRO of RES.(3) Planar Pseudo three-dimensionalmodels A-"Cell" Approach STIMPLAN of NSI.39 Shell 2-D model Pseudo-3-D modelsrun in constant-height ode m A discussionof the basicsof these modelsis givento provide some insightson the model assumptionsand howthey are expected to affectthe results.19 is differentfromthe previous modelsin two fundamentalways: (a) fracture opening is calculated by superposition usingthe surfacedisplacementof a half space undernormalload (Boussinesq Solution).2 planar 3-D Finite-Difference.(b) the fracture propagateswhen the tensile stressnormal to the fracturing plane exceeds the tensilestrengthof the formationat some distanceoutsidethe fracture by enforcingthe tensilecriterionat the centroidof the cells "outside"the . Inc. this model18. 3. ModeI_.1 . Both modelsuse finite elementsfor two-dimensionalluidflow withinthe fracture and employ f a fracture tip advancementproportionalto the stressintensityfactor on the fracture tip contour.. 3. 4 Classic PKN and GDK Models The difference in treatingpressurebehaviorand fracturegeometry of the PKN and GDK modelsis well documentedin the literature 11..fracturingcontour.elliptical)to calculate fracture width as a functionof positionand pressure and apply a fracture propagationcriterionto both lengthand height. two dimensional.some pseudo-3-Dmodelsattempt to include truly3D fracture behaviorin termsof "history" matchingor "lumped"parameters determinedfromfully 3D-solutionsof simplerproblemsor determinedfrom simulations using3D models. They use equations based on simple geometries(radial. These modelscan be dividedintotwo categories:(A) modelsthat divide the fra_ure along its lengthinto"cells". The pseudo. . and use local cell geometry(two-dimensionalcrack or penny crack) to relatefracture openingwith fluid pressure.it is expected that each classwill have differentfracture geometry. Furthermore.a 3D model is thus moreaccurate in predicting"trends"of fracture geometry.3 Pseudo-3-D Models These modelswere developedfrom the PKN model by removingthe requirementof constantfracture height. 3..g.they assume one dimensionalflow alongthe lengthof the fracture.3Dsimulatorsare extensivelyusedfor fracture design because of their efficiencyand their availabilityon personalcomputers. 3.they are directly applicableonly for the geometriesthat are not significantly differentfrom the basic assumptionsof the model(e. This model predicts higher treatingpressuresand shorter and wider fractures as comparedwith the ones of the previous3D models.(B) modeQshat use a t parametricrepresentationof the total fracture geometry. To avoid thisproblem.40 and need not be repeatedhere. However. modelsbased on a PKN geometry should have large length/heightratios to be appropriate). As a resultof these assumptions. even for the simplecase of a confinedfracture. For relativelyunconfinedfracture growthin a complexin situ stressprofile. fracture toughness. MFRAC-II accountsfor the coupledparametersaffectingfracture propagationand proppanttransport.1.and fluid leakoffcoefficientsfor each layer. Geertsma-deKlerkand Perkins-Kem/Nordgrentype 2-D fracturing models.2 Meyer & Associates(MFRAC-II) MFRAC-I126-29is a pseudo-3-Dhydraulicfracturingsimulator. Horizontalfracture geometry calculationusingthe GDK methodis also available. offersa user interfacewhich takes full advantage of the facilitiesexistingunderthis operatingsystem. Ali these modelsare coupledwith proppanttransportcalculationmodules. and Nordgren. A temperature calculation modelis thus part of TRIFRAC. Properties for a maximumof twenty-twolayers can be inputcurrently. Version 6.and settlingalongwiththe growthof the fracture.flexible units and usercustomizedhelp screens.A. Holditch& Assoc.x.the model computesthe proppantprofileat each time step duringthe job. The majorfracture. The created geometrycomputationmoduleis coupledwitha rigorousfinite difference proppanttransport simulatorthat solves simultaneously proppantdistribution. rockand fluid mechanicsphenomenainclude: (1) multi-layer. 4. The apparent viscosityof the fracturingfluid is computedbased upon the shear rate insidethe fracture and changes in n' and k' due to variationsof temperature and time. Choice of initiatingthe hydraulicfracture from ten differentlayers simultaneouslyis available. Special options are available to inputpump schedule for nitrogenfoam treatments. Dependinguponthe fluid " velocityalong the heightof the fracture and the rate of settlingof the proppant.porosity.4. The program'sfeatures includeintelligentmenus.(2) fracturetoughnessand u c .Poisson'sratio. Shortdescriptionsof the modelswere providedby the modelersor by the companies who ran commerciallyavailable models.1 S. nsymmetrical onfiningstresscontrast.permeability. lt has the capabilityto handle multiple non-symmetricstress layerswith uniquevalues for Young'smodulus. Version7.0 FRA(_TURE MODELS This sectiondescribesthe individualfracture modelsthat were used in this comparison.Thisstudywas run using MFRAC-II. written in C++ and developedunder MicrosoftWindows 3. MFRAC-II also includesoptionsfor the penny.0. TRIFRAC also has the simplertwo-dimensionalgeometry computational initef differencemodelsof Geertsma and DeKlerk. 4. a complete fluid database.Kern. (TRIFRAC) SAH's hydraulicfracturing modelTRIFRAC is a pseudo-3-D fracture propagationand proppanttransport modelthat computescreated and proppedfracture dimensions usinga finite-differencenumericalapproach. for transport. and Perkins. elastic rockdeformation.3 Advani (Lehiah HYFRAC3D) The 3 layer and 5 layermodel results(Cases 5 through8) are obtainedfromthe HYFRAC3D code.the effectivefriction factor would have increased. 7.upper and lower heights.(4) variable injectionrate and time dependent fluid rheologyproperties. In one case. Fracture tip effectsare accountedfor througha direct inputof the rock's apparentfracturetoughnessor the fracturetip net pressure (overpressure). The PKN modelresults(Cases I and 2) are also based on a two-dimensionalfinite element model simulatorwith standardPKN modelequationsincludingvertical stiffness and one-dimensionalfluidflow. These optionsand other free parameters ("knobs")allows customization the modelingapproachadopted. A mapping technique of the baseline mesh(88 triangularelementsrepresentinghalfof the fracture) definedin a unitcircleto arbitraryshapedfracturegeometriesis utilized in the numericalschemefor trackingthe movingfracturefront. 4.resultingin highernet pressures.tiploverpressureeffects.(5) multi-layerleak-offwith spurt lossand (6) 2-D proppanttransport.constitutive elasticityand fracture mechanicsequations governingplanarhydraulicfracturepropagationin a multilayeredreservoir.and geometryparameters as a functionof time.efficiency. This overpressureis definedas the instantaneousshut-in-pressure minusthe closurepressureand can be determinedin the field froma micro&acor mini&actest.MFRAC-II offers numerousoptionswhich can be employedby the user. (3) rockdeformation. in a secondcase (MEYER-2) additionalparameters(suchas greater friction drop in the fracture) were applied. In order to provideapplicabilityover the broadestrange of circumstances. .greater widthsand a shorter length.time-dependentfracture half-length.0) resultsin increased developmentof fracture heightand net pressurefor certain multilayerformations. These simulationresultsare obtainedusing20 line elementsfor the normalized. in MFRAC-II was run in two differentmodesto demonstratethe effectsof some of these parameters. Without viscousthinning. 4.width. net pressure.17 This finite elementcode is based on a set of coupledmass conservation.and fluid loss.21 is a hydraulicfracture modelthat predictsfracturedimensionsfor uncontained(circular)and contained(rectangular)fractures.4 Shell (ENERFRAC) ENERFRAC20. The width variationas a functionof heightand confinings_ressis also calculated. as a default. ENERFRAC incorporates fracture tip effects in additionto the other interactingprocessesof viscousfluidflow.fluid momentum.the fully implicitcoupledmodelfor heightgrowth(Vet. In addition. The fracture propagationmodel calculatesfracture length. In bothcases. . the base model usingthe systemdefaults was run (designatedMEYER-1).the viscousthinningassumptionwas made. the PROP programhas since been expandedto includea similarnumericalsolutionof PKN-type geometrywith a widthprofile based on calculated local pressures. lt is most suitableto designfractureswhere the geologicconditionsrestrictheightgrowth. In additionto the power-law model normallyusedto characterize gelled fracturingfluids. Its numericalnature makesthe model muchmore flexiblethan most analytical models.Shell also provided2-D PKN and GDK model results. 4.each fluid with itsown set of timeand temperature-dependentrheologicalparameters.5 Halliburton(PROP) The PROP program 34-36 is a 2-D fracture designmodel based on Daneshy's numericalsolution. The proppanttransportmodelcalculates thefinal propped concentration. The simulatoris capable of predictingthe createdfracture geometrybased on either Perkins-Kem-Nordgren(PKN) or the Geertsma-deKlerk(GDK) models. The program'sproppanttransportcalculationsare of similarcapability.and linear elastic deformationof the rock in plane strainare usedto calculate mass flux. pressure.fracture width. This comparison allows us to see the effect of fracture tip overpressureon fracture geometry and net pressure. and bank heightgiven a settlementvelocity. designated ENERFRAC-1) and also for a several tip overpressures. For example.6 (_hevron Chevron's2-D fracturingsimulatoris capable of predictingthe propagationof constant heighthydraulicallyinducedverticalfractures for a power-lawfluid. This productionmodel providesthe short . Althoughthe modeloriginallypresented by Daneshywas based on the KhristianovicZheltov widthequation(designatedGDK in this paper). The particularcase of a tip overpressureof 1000 psi (ENERFRAC-2) is shownin several plotsfor comparisonwiththe base case.the equationsdescribingconservationof mass. PROP uses the threeparameterHerscheI-Bulkleymodelfor fluidscontaininga nitrogenor carbondioxide phase.and length as function of time. The simulatoralso includesa proppanttransportmodelwith proppantsettlingand a productionmodel. 4.continuityof fluid flow. Shell providedresultsfor typicalfracture toughness values measured in lab tests (the base case.and can predict possibleproblemscaused by proppantbridgingor screen out. The ENERFRAC results provided a useful comparisonof the effect of free model parameters (the "knobs" discussedearlier) on the results. The fractured well productionmodelis based on an analyticsolutiondevelopedby Lee and Brockenbrough37 to studythe transientbehaviorof a well interceptedby a finite conductivityfracture in an infinitereservoir. The resultspresentedhere are for the GDK-type solutiononly.the programhas recentlybeen modifiedfor use of multiplefluidsand rates within a single treatment.width. In fracture propagationmodels. conservation of momentum. Combiningthis solutionwiththe well knownsemi-log asymptoticsolutionfor longertime periods providesa reliable toolfor predictingthe potentialproductivityof the fracturedweil. However.(2) 2-D fluidflowequationsthat relate the flow in the fracture to the pressuregradientsin the fluid. as describedby McLeod. as well as variablesdescribingfracture wall roughnessand tortuosity. the model is based on a regular grid structurewhich is usedfor boththe elastic rockdisplacement calculationsand as a planar 2-D finite difference gridfor the fluidflow solutions.19 is a planar3-D fracture geometry simulatorwithcoupledmultidimensionalfluid flowand particletransport. given by Boussinesq. Each grid node can be assignedan individualvalue of net stress. The fracture widthequationused is the the general formula for displacementof a semi-infinitehalf-spaceacted upon bya distributedload.39 4.The solutionis general enoughto allow modelingof multiplefracture initiaticnsitessimultaneously..includingproppant transport.9 ARCO (usingTerraFr.wall-buildingcoefficient. The overall approach used in the modelis to subdividethe fracture intodiscreteelementsand to solvethe governingequationsfor these elements.is iterativelycoupledto the elasticdeformationsolution.time productionresults.au lt has single inputsfor n'. 4. permeability.and Poisson'sRatio. includingthe computedtensile stressdistribution in the unbrokenrock surrounding fracture.Young'sModulus. The displacementof the fracture face at each node is determinedby integrationof the pressuredistribution over ali nodes.8 Marathon (GOHFER) MarathonOil Company'sGrid Oriented HydraulicFractureExtensionReplicator (GOHFER)18. and (3) a fracturecriterion thatrelates the . 4. lt was initiatedat Terra Tek in 1978 and itscommercialavailabilitywas announcedin December.ac) TerraFracTM Code12-16 isa fullythree-dimensionalhydraulicfracturesimulator. Using thefinite differencescheme for fluidflowallows modelingof multiplediscretefluid entry points representingperforationsat variouslocations. nd is applicableto any a planar 3-D geometryfrom perfect containmentto uncontrolledheightgrowth.7 Conoco Conoco'sfracture design programis a constant-heightmode/_.the model is capable of calculatingthe positions and concentrationsof progressivefluidlproppantstages.rock strength. 1983. These governingequationsconsistof (1) 3-D elasticityequationsthat relate pressureon the crack faces to the crack opening. pore pressure. Fracturearea can be calculated by either the Howardand Fast Model or an extremelyaccurate simplification by Crawford.2-D)where either PKN or GDK geometrycan be selected. The areal pressuredistribution obtainedfrom the fluidflow equations. k' and leakoff coefficient.porosity. As indicatedby the name. and flow distribution taken intoaccount. The modelalso accountsfor frictionvariationfrom entrainedproppant. Young's modulus. withfluid and proppantpropertiesbeing functionsof temperature if desired.foam fluids.(5) a robustmesh generatorto handle a wide variety of fracture geometriesand a quasi-Newtonmethod to solve the nonlinearsystemof equationsfor the fluid pressures(this approach providesfor fast convergenceand high accuracy).and (6) a post-shut-incalculation capabilityfor which no additionalassumptionsare made (only the injectionrate changes). (3) multiplelayers.proppantsettling.as requiredfor history matchingon-site. A FractureAnalysis/HistoryMatching module providesfor historymatchingof measured net treatingpressuresto yield the most accurate possibleestimationof actual fracturegeometry and behavior. TerraFrac providesmany distinctivefeatures including(1) 2-D fluid flowfor both proppantand temperature distribution. The modulecan therefore run many timesfaster than real time. The fracture model is 3-D.and proppantphases.greatly simplifyingthe calculation of the fracturedimensions.and includesproppant settlingand bridgingcalculations. The model has completefluid/proppanttrackingthat allows for optimumfluid selection and schedulingbased on time and temperaturehistory.rates.lO intensityof stress state ahead of the crackfront to the critical intensityfor Mode I fracture growth.it does not need to are calculate the variationsat specificpointswithinthe fracture. However. The coefficientsnecessary to calculate the spatialvariationsare calculatedfrom a fullthree dimensionalmodel and checked againstexperimentaland field test data.tip screen out. carbon dioxide.Poisson'sratio.11 ResourcesEnaineerinqSystems(FRACPRO) FRACPRO22-25 uses measuredvalues of flowrate. in that spatialvariationsin reservoirstress. Also.modulus.(4) poroelastic and thermoelasticcapabilitiesfor waterfloodingand other applications.and fluid rheologyparametersto calculate the pressuredrop downa wellboreof variable deviationand diameter.each having differentin situ stress. The wellbore modelhandles non-Newtonianfluids and corrects for the effects of nitrogenfoam. Fractureheightgrowth is calculatedthroughmultiplelayers. proppants.the effects are integratedintofunctional coefficientsof governingdifferentialequations.and the time historiesof the fracturegrowth and the net fracture pressureare calculated. 4. pressure. 4. and leakoff.proppantconcentration. Instead. etc. simulations during the fractureclosure(pressuredecline) period aid in pressure decline analysisforfluid lossin complex geologicsituations. .10 NSI (STIMPLAN) STIMPLAN is a state-of-the-art 3-D hydraulic-fracturesimulatorfor fracture design and analysis in complex situationsinvolvingheightgrowth.fracture toughness.(2) multiplestages having different fluids. or by low-concentration proppantstages. The 3--layerand the tip-dominated5-layer cases providea good comparisonof the resultsfor two differentcompaniesusingthe same model. includingspurt loss. .and power-law-fluid behaviorwiththe tip dominatedrheologybehaviornot operating. hindered settling rates. 4.13 ARCO (usingSTIMPLAN) STIMPLAN was also run by ARCO for fourdifferentcases. followingDarcy-law behavior. These resultsprovidea good comparisonof the resultsfor two differentcompaniesusingthe same model. The rise in confiningstress due to poroelasticeffects (backstress)is included.g.power-law-fluid behavior. Initial laboratoryand computersimulationsindicatethat proppantconvection may be the dominantmechanismin propped-fracture stimulations.. and settledbank buildup. conventionalrheologyresultsusing FRACPRO. The 5-layer runs provide a goodcomparisonof tip-dominatedvs. These includeboth3--layer and 5-layer cases. filtercake buildupon the fracture face. up to fiftystress zones.and 5-layer cases for constant fluidviscosity.As weil. Heat transfer modelingassumesthat there is a cubic-fittemperaturedistributionbetween the fracture and the end of the heat transfer region. Proppant convectionis a processwhereby heaviertreatmentstages (e.a 3-layer case withconstantfrac fluid viscosity.12 . 4. These includesingle-layer PKN and GDK modes. and up to fifty permeable (leakoff) zones. FRACPRO can be used to model proppantsettling. and settles. proppantstages) displace rapidlydownwardfrom the perforationsto the bottomof the fracture. Fluid lossis modeled as one-dimensionalflow perpendicularto the fractureface.11 FRACPRO handles up to three moduluszones. Those stages are then replaced by the pad. The proppantis carriedwith the fracturingfluid. FRACPRO modelsthe convectionand settling of proppantina fracture. The model takes into accountthe effects of non-Newtonianfluids.Texaco(usina FRACPRO) FRACPRO was also run by TEXACO for six differentcases. and a compressiblereservoir-fluidregion. Most importantly. 15 well in the Waskom Field.thusaccountingfor the elevatedvalues of Young'smodulus. and drilledto a total depth of 9700 ft (2957 m). 1 SFE-3 was drilled as the Mobil Cargill 4 Unit No.the relevantrockand reservoirinformationare shownin Table 1. andfive layers.8 kg/m3) crosslinkedgel with sandstagesvarying from 1-8 ppg (120 kglm3). three layers. For this initialstudy.Texas. Harrison County.the treatmentwas simplifiedto a single. As will be describedin the next section. In addition. .12 5. luidwith no proppant. Both prefracwell-testingand post-frac productiontestingwere performed.0 $FE-3 FORMATION AND TREATMENT DATA The input data for the fracture modeling comp&:isonis based upon the resultsobtained at the GRI-sponsored SFE-3 experiment. The actual SFE-3 treatmentwas a thirteen-stageprocedureusing primarilya 40 lbl1000 gal (4.the SFE-3 data set is one of the mostcomplete sets of well informationavailable. constant-property. The SFE-3 data set was specificallychosentc insurethat the model comparisonwould be performed with actual field data and notfor a contrived data set that mightfavor one type of model over others. and includesstress. Stress and rock property measurementswere averaged over the appropriatedepthsfor each interval to yieldthe physicaldata given in Table 1. For the purposeof thiscomparison. Young'smodulusand Poisson'sratiowere obtainedfrom sonic measurements. Two minifracsand one full-scale treatmentwere conducted as part of the stimulationprogram.4 MPa).3.rock and reservoirand wellperformance results. althoughthe lowerbarrier is only 40 ft (12 m) thick for the five layer configuration. The well was spudded in September. Of particular interestwas the CottonValley Taylor sand whichwas perforated between 9225-9250 ft (2812-2819 m) and 9285-9330 ft (2830-2844 m).three differentphysicalconfigurations were considered: a single layer. he stresscontrastsrange from 1450t 1650 psi (10-11. An extensive log programwas run on this well and detailed core analyses performed. 1988.primarilybecause changes in fluid f propertiesdue to temperatureor the additionof proppantcan not be easily quantified and any resultingcomparisonswould be of questionablevalue. 13 6.0 TEST CASES As noted in the descriptionsection, mostof the models are capable of accommodating and processinga much broader range of complex data than presented in this data set (i.e., multiplerock properties, leak-offcoefficients,n', k', etc.). Refer to Tables 1 and 2 for the complete set of data input. However, the data set was arbitrarilyrestricted to limitas many discretionaryinputsas possibleto allowa more direct comparisonof modelperformance. The treatment inputis also not to be construedas optimumdesign parameters, but rather an approximationof thatfrom SFE No. 3. There were a total of eight possiblecases each participantcould model if they so chose. These were GDK, PKN, 3-layer, and 5-layer cases withseparate runs for a constantNewtonianviscosityand a constant n' and k' power-lawfluid as follows: Case 1 GDK Constantheight- 200 cp fluid Case 2 GDK Constantheight- Power-lawfluid (n', k') Case 3 PKN Constantheight- 200 cp fluid Case 4 PKN Constantheight- Power-lawfluid (n', k') Case 5 3-Layer - 200 cp fluid Case 6 3-Layer - Power-lawfluid (n', k_) Case 7 5-Layer - 200 cp fluid Case 8 5-Layer- Power-lawfluid (n', k') The PKN and GDK cases were runwith a constant height(2-D) set at 170 ft (52 m). The 3-layer and 5-layer cases were run usinga 3-D or a Pseudo-3-D modelallowing fracture heightto be determinedby the model. Of particularinterestwas if the fracture broke throughzone 4 in the 5-layer case. The importantrockproperty data for the 3-layer case are showngraphicallyin Figure 1, and the data for the 5-layer case are shownin Figure2. These stressand modulus profilesare simplifications the actual stressand modulusprofilesmeasured at the of SFE No. 3 site. 14 _ 7.0 MODEL RESULTS A shortsummaryof the final geometryat the end of pumpingis given in Tables 3-5 for the 2-D, 3-layer, and 5-layer cases respectively. A summaryof the time to breakthroughfor the 5-layer calculationsis given in Table 6. Ali of the submitteddata from the modelersare given in Tables 7-83, in the followingorder: S.A. Holditch&Assoc. Trifrac Tables 7-14 Meyer & Assoc. M-FRAC-II base case (Meyer-I) Tables 15-22 Meyer & Assoc. M-FRAC-II "knobs" (Meyer-2) Tables 23-30 Advani HYFRAC3D Tables 31-36 Shell 2-D Models Tables 37-40 Shell Enerfrac. Tables 41-50 Halliburton2-D Prop Tables 51-52 Chevron 2-D models Tables 53-54 Conoco2-D models Tables 55-58 Marathon GOHFER Tables 59-64 ARCO (Stimplan) Tables 65-68 ARCO (TerraFrac) Table 69 NSI Stimplan Tables 70-73 RES Fracpro Tables 74-77 Texaco (Fracpro) Tables 78-83 The graphsof the data shown in this section were derivedfrom this tabular data set. In addition,some modelersprovidedadditionalgraphicalinformationon the width and heightprofilesalong the lengthof the crack. These are given in the following appendices: S.A. Holditch& Assoc. Trifrac AppsndixA Meyer & Assoc. M-FRAC-II base case (Meyer-I) AppendixB Meyer & Assoc. M-FRAC-I! "knobs"(Meyer-2) AppendixC AdvaniHYFRAC3D AppendixD Marathon GOHFER AppendixE ARCO (Stimplan and TerraFrac) AppendixF RES Fracpro AppendixG 7.1 2-D Results,(Cases 1-4) Consideringfirst the 2-D summaryresultsgiven in Table 1, the final half lengthfor ali of the 2-D modelsare shownin Figure3. The well-knowndifferencein lengthestimates betweenthe PKN and GDK modelsis evident in these results,but some differences between differentmodelsin each groupbecomeapparent. Presumably,this difference isbecause of otheroptionsincludedin somemodels. The effectof the different rheologiesis generally small. Besidesthe PKN and GDK models,GOHFER and ENERFRAC-1 and -2 are also shown. ' II , , ii I =, , , , .... lP _ .... m_ _111 15 The reductionin length betweenENERFRAC-1 and ENERFRAC-2 is due tL,increased tip overpressur,-,.Likewise, the reduction in lengthbetweenMEYER-1 and MEYER-2 is due to optionsthatwere includedin MEYER-2 w_ich reflectthe designers' incorporationof more compley_hysicsintothe fracturingprocess. The net pressuresfor the 2-D models, shown in Figure 4, followa similarpattern to length, withthe GDK modelsgivinglow pressuresand the PKN modelsprovidinghigh net.pressures. GOHFER is differentin that it predictsshortlengths,like the GDK models,but high pressureslike the PKN models. The efficienciesfor the 2-D calculationsare shown in Figure 5. Values ranged from 7095%. The fracture maximumwidthis shownin Figure6, while the average widthat the wellbore is given in Figure 7, and the average widththroughoutthe whole fracture is _:,hown Figure 8. As expected, the GDK models; rovidemuchgreater widththan the in p PKN models. GOHFER's width is more similarto the GDK modelswhile ENERFRAC's width is closerto the PKN models. The time-historyresultsfor Case I (GDK with 200=cpfluid) are shown in Figures 9-11 for length, net pressureand widthat the wellbore,respectively, lt is interestingto note that even for this simpledata set there is a significantdifferencebetween the various GDK ,_oclels. Time-history resultsfor Case 2 (GDK withpower-lawfluid) are shown in Figures 12-14 for I_ngth, net pressureand widthat the wellbore,respectively. As with the Case 1 results,there is also a significantdifferencein the calculationsof the variousmodels. Time history, esultsfor Case 3 (PKN with200-cp fluid) are shownin Figures 15-17 for r length,net pressureand maximumwidthat the welllbore,respectively. DifferentPKN modelsalso have considerabl_variationin theircalculated output. Time history resultsfor Case 4 (PKN with power-lawfluid) are shownin Figures 18-20 for length, net pressureand maximumwidthat the wellbore,respectively. Time history resultsfor other2-D models usinga 200-cp fluid (these do not fit exactly intothe Ca_e I or 3 categories)are shown in Figures21-23 for length,net pressure and maximumwidthat the wellbore,respectively. The effectof tip overpressureis seen bycomparingthe two ENERFRAC cases. Time historyresultsfor other2-D models usinga power-lawfluidare shown in Figures24-26 for length,net pressureand maximum widthat the wellbore, respectively. Tip-overpressure effects can be again seen for a power-lawfluid. f II I ! ...... given in Figure 28.2 3-Layer Results The 3-layer summaryresults(Table 4) show considerablymore variabilitythan the 2-D cases. Many suchoptionshave probably been employedon the other models.=bout 0% to 97%.except thatthe lengthin some modelsis shorterbecause the height breaksthroughthe lowerbarrier. The fracture heightcomparison. Efficienciesrange _rom. MEYER-2.8 MPa) to almost 1400 psi (9. as shownin Figure45. Height growth is extremelyfast in FRACPRO. showthat consistent resultscan be obtainedfrom a given modeleven if run by different organizations. height.7 MPa). but much bettercontainedin most of the other models. even for this relativelysimplecase.and a similar favorable comparisonbetween TEXACO and RES runningFRACPRO. and the average width in the entire fracture is shown in Figure 33. Net pressuresrange from nearly 700 psi (4. Efficienciesvary from 40% to greater than 95%. net pressureand maximumwidth at the wellbore. as shownin Figure 44. 7. the maximum average widthat the wellbore is shownin Figure 32. The half lengthsare shownin Figure 42 and the fracture heightsare given in Figure 43. height. there is relativelygood 6 . Again. showsthat muchgreater height growthis obtained by FRACPRO than by other models. These graphsclearly show thatthere is an amazingrange of outputfrom the differentmodels. net pressureand maximumwidthat the wellbore. A comparison of ali 3-Layer lengthcalculations(Cases 5 and 6) is shownin Figure 27. Fracproand GOHFER calculate muchgreater widthsthan the other models. Time historiesfor Case 6 (3-layer with power-lawfluid) are given in Figures 38-41 for length. Time historiesfor Case 5 (3-layer with200-cp fluid) are given in Figures 34-37 for length. but were not identifiedas suchfor thiscomparison The favorable comparisonbetween ARCO and NSI runningStimplan. The fracture half lengthvaries from less than 1000 ft for FRACPRO to greater than 3000 ft for the conventionalpseudo-3-D models. Net pressures. as given in Figure 30.3 5-Layer Results The 5-layer (Cases 7 and 8) summaryresults(Table 5) are similarto the 3-layer comparison.respectively. Fracture maximumwidths(at the wellbore) are given in Figure 31.shownin Figure 29.16 7. An interestingand illustrativecomparison is seen in the differencesbetween MEYER-1 and -2.respectively. are particularlyhigh in FRACPRO and GOHFER. In ali three cases.resultsin a fracture lengththat is nearly 1000 ft less than the base case with no options. usingsome features that the modeler believes are more appropriatephysics. Some modelshave pressuredecreasing.17 agreement betweenthe same model run by two differentcompanies (Stimplanby NSI and ARCO and Fracpro by RES and Texaco). The purposeof thiscomparisonstudyisto evaluatethe size of the differenceand to provide sufficientinformationfor the engineerto make a studiedchoice.respectively. STIMPLAN. TRIFRAC.0 DISCUSSION The completionengineer nowhas a wide array of hydraulicmodelsavailable for both design and analysisof hydraulic-fracture treatments.the effect of breakthroughintothe lower low-stressregion can be seen. that is. GOHFER also predictsshortfracture lengthsand high net pressures.and somewhatlower net pressures. and the average widththroughoutthe entire fracture is shownin Figure 48.the modelerswere asked to of run their modelsin botha base mode(no options)and then with a best-optionmode. However. a modethat reflectedtheir expectations the optionsneededto providethe of closestsimulationof true fracturebehavior. while otherscontinueto have pressureincrease.ENERFRAC (in 2-D geometry).net pressure.and it becomes importantto choosea modelthat meetsthe needs of that particular engineer. height. As in the 3-layer case.and maximumwidth at the wellbore. FRACPRO calculates very short fracture lengthsand high net pressuresand large height.height. TERRAFRAC. Time historiesfor Case 8 (5-layer withpower-lawfluid) are shown in Figures 53-56 for length. net pressure.butthe height growthis not as severe. and MFRAC-II are ali in general agreement. Consideringthe 5-layer cases shownin Figures42-44. the fracture average width at the wellbore isgiven in Figure 47. with longerfractures.and maximumwidth at the weUbore. HYFRAC3D is midwaybetweenthe two end cases.less height. The maximumfracturewidth at the wellbore is shown in Figure 46. respectively. Fracpro and GOHFER provide the mostwidth development. lt is clear that there are some modelsthat predict resultsthat are significantlydifferent from the majority. 8. By comparingali these resultswith the 3-layer calculations. One of the interestingresultsof this studyis the behaviorof the pressureresponseas the fracture breaks intothe lower barrier. MFRAC-II (in 2-D. In the originalformulation this study.and Texaco'sFRACPRO cases (5-layer geometry)were run in two differentmodesand thus providea usefulassessmentof the importanceof the optionsthat are available to the fracture designer. The lengthdevelopmentin this case is not uniformbecause heightbreakthroughintothe lowerbarrier limitsgrowthin some of the models. 3-layer and 5-layer geometries). Time historiesfor Case 7 (5-layer with 200-cp fluid) are shown in Figures49-52 for length.others have pressureremainingfiat.these modelscalculate widely differentfracturegeometriesfor the same inputparameters. Such optionsmay have includedtip . The 2-D models.g. Only the resultsand quantifiablecomparisons(e.or others. the modelersprovided such a comparison."best physics"resultsfor fracture lengthdifferedby about 22% for MFRAC-I! and 57% for FRACPRO run by Texaco.yields considerablyshorterlengths than the other PKN and GDK models.for design modeling(the resultsof this report)where the pressureis determinedby the model. The committeeand the modelersali recognize that other formations. may providea considerablydifferent comparisonof the models.18 effects.these resultsshouldbe a useful guidelinefor estimatingthe differences in modeldesignsthat can be obtained.both PKN and GDK. and hence lengthand heightwill vary by relativelysmall amounts. For the 2-D case with non-Newtonianrheology. however. higher frictional pressure drops in the fracture.and these resultscan be used to estimate howsignificantlythe engineer can modifythe fracture design by tryingto incorporate his estimate of the "best physics"possiblefor a given reservoir. generally provideself-consistentresultsand the differencesbetween these types of models has been discussedin prior publications. Such an agreement is not the case. as it wouldtake a committeewith greater powers than thisone has to trulyknow howthe fracture is evolving in the subsurface and. enhanced toughness. however. Presumably. For the 5-layer case with non-Newtonianviscosity. GOHFER is also of note because it yieldsa lengthtypical of the GDK models withthe net pressureof the PKN models. This particular case was chosen because it was a realisticfield situationforwhich detailed data were available..11. to decidewhich model is better. Finally. Other differences in these 2-D modelsare minor.with differentstressand lithologydata. This is because a match of the pressurewill constrainthe width of the fracture.40 Chevron's2-D model. lt is also interestingto note thatthere was general agreement amongthe modelersat the forumthat pressure-historymatching(not includedin this report) would always result in similarfracture geometries. modelA frac lengthis greater than modelB frac length)are given.regardlessof the model. Good exampleswould be cases where there are minimal stress contrastsand where the stresscontrastsare extremelylarge. Since many modelshave such options. in assemblingthis comparison. thus.such an estimatewould be guided by experience withthe reservoir. multiplefracture strands.the membersof the committee(the authors) have purposelyattemptedto avoid makingany value comparisonsbetween the various models. lt would be beneficial if futuremodel comparisonstudiesinvestigatedthose cases as weil.ENERFRAC resultsdiffered by about 7%. In the three cases mentionedabove. . _ i. II ' . .19 9... Fracture heights.. If' '' ' ' ' ' ' . can differby more than 50%. These comparisonsshow that differencesin calculatedfracture lengthscan be large. Net pressuresalso differby a factor of two. m. . Such optionsgive the completionsengineer considerable flexibility..for the multi-layercases. as much as a factor of three difference.. This studyprovidesinformationon the relative differencesin the modelsfor this one particularcase.0 CONCLUSIONS A comparisonstudyof many of the available hydraulicfracture modelshas been completed... . Calculationsfrom the same modelwith differentoptionsgive a useful comparisonof the importance of ali of the additionalphysicalmechanismsthat are continuouslybeing added to the modelsto explainthe wide varietyof pressureresponsesobserved in differentreservoirs.but also difficultchoices of when variousoptionsshouldbe used. . . . but were not suitable for documentationbecausethere was no simpleway to compare the various models.0 REGOMMENDATIONS Two primary recommendationsresultfrom this study. This particularcase was chosen because it was a realisticfield situation for which detailed data were available. .20 10. Other warranted cases are those where there are minimalstress contrastsand where the stress contrastsare extremely large • The pressure-historymatches thatwere performed at the Fracture Propagation Modeling Forum providedmany interestingresults. • lt would be beneficial to performthis same type of studyfor different input conditions. a comparisonof pressure-historymatches would be of value. However. A.M. Holditch. Sept.. Oct. Tech.. D.831. Washington. Gas Res. Northrop..S.. Veatch.Washington.W.. 67th Ann.. K. 1992.D. "Fracturing UnconsolidatedSand FormationsOffshoreGulf of Mexico.C. Conf. .A Field Laboratoryin Tight Gas SandstoneReservoirs.J. Peterson.M. Oct. B. & K-H. Houston. Owens. Oct."Recent Advancesin HydraulicFracturing..W. June 1990. 581-588.D. Norman. D. Tech. S. Oct. 1992....R...A. 6. Denver. D.W. 67th Ann.E. 1991. 11. . 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Meehan. 44.C. Jan. C." SPE 24858.TX. 1992. 519-533. Peterson. 8. SPE/DOE Low Perm.r_ ." SPE 24822. Cramer.A.: A Studyof HydraulicFracturing.S. & A. J. Ely. May 1979.A.S. ... 772-779.."SPE 24854.. 1992.. .F."JPT.S... "The Unique Aspectsof FracturingWestern U. 67th Ann..S. Tech.D.."On the Computationof the Three-Dimensional Geometryof HydraulicFractures." SPE 24844. P.. Whitehead & R.A.. Washington.0 REFERENCES 1. Holditch& R.D. . F. 1992. 44.SPEForm. 42.JPT." SPE 24783.A. Coalbeds. Conf. . Peterson. Syrup. 78. 67th Ann.. "StimulationResultsin the Giddings(AustinChalk) Field. C. Martins.M. Conf. 909-922..21 11.W."SPE MonographVolume 12. Whitehead & J. Stewart. B. F. Conf. Economides. June 1985. Rapid City. CO. Advani.K. TX.. 19.S. 16.W.K. & J.J. M.J.. C. SPE Ann. Ener.. Tech. Joint Rocky Mt. Houston.P. and Thermal Effects in 3-DimensionalSimulationof Hydraulic Fracturing. 20. G. Conf. ulatorfor Three DimensionalFracture Propagationin HeterogeneousMedia.S. May 1981. 1-9. Oct.P. 1991.J. 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"OverpressureCalibrated Design of Hydraulic FractureSimulations. Barree.. 1990. Lee & J. CO. Sept. R. 17.H. Cleary. Cleary. Regional/LowPerm. Feb. J. Wright.. "Energy Analysisof HydraulicFracturing..D.A. R.P. Jan. Clifton. Tech. Abou-Sayed. Conf. Symp. 63rd Ann.J.. Wang. 23. Shlyapobersky. 1988. & J. Denver. "AdaptiveOptimalMesh Generatorfor Hydraulic FracturingModeling.. & A. SD. April 1991. Symp."ASM. Conf.J. Houston. Wang."SPE 9259. 1980.on Rock Mechanics.. 21.TX. Wang. Lee.S. Reservoir SimulationSymp.. "Multiple Fluids. Dallas. Clifton. "Experimentaland ModelingEvidencefor Major Changes in HydraulicFracturingDesignand Field Procedures. 18. TX. Symp. 63rd Ann. Symp. 403-411 Nov. "On the Designof Vertical HydraulicFractures. . 132-140. 1955.FourthWorld Pet.83-93. Tech. Perkins.and TemperatureDependentFluid Properties. Rome.A. M. Tech. B. & Amaury Fonseca."SPE_. "NumericalSolutionof Sand Transport in HydraulicFracturing. 21. Conf. Kristianovich. 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Proc. \ 27.Gas Tech.KY. B. Calgary. Aug._!.S. 1961.R.T. Tech. 12. G.S. Volume II. 31. 314.D. "A Rapid Methodof PredictingWidth and Extentof HydraulicInducedFractures. Cong.. Louisville.D."Proppant Convectionand Encapsulation in HydraulicFracturing: Practical Implicationsof ComputerLaboratory Simulations. "Widths of HydraulicFractures."SPE 15240. Cleary. 32."SPE 19329."JPT.R..WV.. Mtg. M.. deKlerk. Unconv. Feb 13-14.. Oct. 417-431.P.. Dec.. B. "Design Formulaefor 2-D and 3-D Vertical HydraulicFractures:Model Comparisonand ParametricStudies...J. 1969. "A SimplifiedApproachto Designof FracturingTreatments Using High Viscosity Cross-LinkedFluids. San Francisco.. Brockenbrough.."A New Analytical Solutionfor Finite-Conductivity Vertical Fractureswith Real Time and LaPlace Space :ParameterEstimation. March 1983. "A Comparisonof the Theories for PredictingWidth and Extentof Vertical HydraulicallyInduced Fractures. 101. O. -"Staged Field ExperimentNo." SPE 12013. GRI Final Report. McLeeod. Symp. H.. & R. March 1979. Conf. 58th Ann..CA.R. San Francisco." GRI-9110048. 40."SPE 11614.T. 1991. "Proppant Schedulingand Calculationof Fluid Lost During Fracturing. J. 121-136. S. Tech Conf.R. . Denver. Feb. CO. Haafkens."ASME J. 3. Oct. 39.. 41. Low Perm.24 37. & J. 1983. Crawford. Lee.. Enerqv Res. Tech. Geertsma. Vol. H. 38.CA. October 5-8... 1983. 58th Annual Tech. 8-19."SPE 12064. 25 Tables and Figures . Case B n' : 0.5x10 _ 6.21 7350 0.30 5700 0.29 S-Layer (3-0) Case 7150 0.20 8200 0.5xl 0_ 5.5x10 u " 8. [ .0x10 _ !80 170 310 180 170 40 75 195 i m 3-Layer (3-0) Case.4xl 0t_ 7.0 | ! I I Fluid leakoff coefficient entirefractureheight I Fluid leakoffheight 0..5x10t_ 8.21 lill I Young's Modulus Fracture Toughness (psi _/in) 2000 2000 2000 2000 200.9xl 0_ 4.30 5700 0.0 2000 i 8.00025ft/_/min Viscosity.30 | | Table 2 Treatment Data Bottom-holetemperature Reservoirpressure Spurt loss 246° F 3600 psi 0.26 Table I Rock and Reservoir Data I Interval Depth (ft) . 7150 0. 1 2 3 1 2 3 4 5 1 In Situ Poisson's Stress Ratio (psi) Single-Layer (2-D Case 170 5700 0.Case A 200 cp I Viscosity.5xl 0" 6.21 7350 0.26 5800 0.06 Fluid volume IOTO00bbls Injectionrate 50 bpm Proppant i none . 9170-9340 8990-9170 9170-9340 9340-9650 8990-9170 9170-9340 9340-9380 9380-9455 9455-9650 Zone Thickness (ft) ..5. k' : 0.5xl 0t_ 5.0 2000 2000 200. 641 WAVG F 0.84 0.58 0.434 WAVG F 0.81 0.1 72.81 89 1.07 0.492 0.502 0..627 0.38 0.24 0.59 WAVG W 0.46 1.27 Table 3 2-D Results at End of Pump 2OO CP MODEL SAH (GDK) SAH (P.36 3556 LENGTH 2542 4629 2516 2098 4118 1808 3395 2142 3347 4046 2031 2304 3656 3396 3155 HEIGHT 170 170 294 170 170 170 170 170 170 200 200 170 170 170 170 170 170 170 170 HEIGHT 170 170 204 170 170 170 170 170 170 170 170 170 170 170 170 PRESSURE 62 1094 1685 70 1188 97 1474 53 1377 131.2 85.738 0.79 0.47 0.817 iIII r I .63 0.2 76.933 1880 1986 0.59 0.68 97 1.82 0.289 0.98 ' n'.i rl I li ii '1 .24 1774 0.704 0.4 0.06 0.9 73 73.07 0.82 1.4 75 78 EFFIC 61.415 0.504 _ PRESSURE WMAX 61.46 0.62 0.43 0.2542 4855 2584 2659 4507 2288 3803 2724 4039 1898 3587 1347 2029 4595 2212 2716 3986 38.767 0.43 0.98 117 1. I .37 0..03 0.36 0.75 0.72 0.61 0.I I .9 _ 1377 81.32 0.8 0.3 93 83.04 1397 0.6 93 86.4 74.03 1754 0.78 0.94 0.6 0.9 1380 1182 82 WMAX 0.36 0.933 0.64 1.6 84 75 94.94 0.6 0.8 73.77" 0.9 86 85.55 0.394 0.456 0.7 _ _ • _ _ _ _ 0.5 74..54 0.74 0.77 0.76 0. i '1 II .28 0.91 0.79 0.98 0.5 72.75 1474 0.37 EFFIC 85.9 82.85 0.3 88.53 1.6 0.'53 0..5 78 81.42 0.64 161 1.78 0.8 85.605 0.97 0.848 0.5 1.(PKN) ENERFRC-1 ENERFRC-2 MODEL SAH (GDK) SAH (PKN) MARATHON MEYER1(GDK) MEYERI(PKN) MEYER2(GDK) MEYER2(pKN_) SHELL(GDK) SHELL(PKN) ADVANI HALLIB CONOCO(GDK) CONOCO(PKN) ENERFRC-1 ENERFRC-2 LENGTH .32 0..5 0.4 76.387 0. k' 1595 1684 0.77 0.849 0.KN) MARATHON MEYER1(GDK) MEYER1(PKN) MEYER2(GDK) MEYER2(PKN) SHELL(GDK) SHELL(PKN) TEXACO-FP TEXACO-FP CHEV(GDK) CHEV(PKN) ADVANI HALLI B CONOCO(GDK) CONOCO.73 0.3 79 89 79 76.85 1167.54 1824 0.733 0.553 WAVGW 0.68 0.554 0.6:):) 0.4 90 81.04 0. 28 Table 4 3-Layer Results at End of Pump 200 CP 3-LAYER MODEL SAH NSI RES MARATHON MEYER-1 MEYER-2 ARCO-STIM TEXACO-FP ADVANI n', k' 3-LAYER MODEL ' SAH NSf RES MARATHON MEYER-1 MEYER-2 ARCO-STIM ADVANI i I , LENGTH 3408 3750 1744 1360 3549 2692 3598 836 2089 HEIGHT 318 903 544 442 291 ' 361)' 306 740 357 I PRESSURE W MAX W AVG W 1009 0.65 0.35 283 0.56 0.32 1227 0.9 0.54 1387 1.04 0.68 987 0.58 0.35 1109 0.72 0.41 ,,, ,,, , W AVG F 0.3 0.25 0.36 0.64 0.29 0.34 0.25 0.25 I EFFIC 77 66 80 96 70.3 74.3 67 89 43 992.. 1561 1113 0.57 , 0.66 0.31 1.333 0.33 LENGTH 3259 3289 902 1326 2915 2120 3235 2424 HEIGHT 371 329 596 442 337 413 353 435 II , ,,! PRESSURE WMAX 109.3. . 0.75 1005. 0.67 1428 1.1 1433 1.08 1094 0.69 1212 _ 0.86 1083 0.65 1171 0.74 i, i , i WAVGW 0.38 0.35 0.74 0.71 0.4 0.48 0.33 0.34 WAVG F 0.31 0.26 0.49 0.66 " 0.32 0.4 0.26 0.21 I I ,,, ,,,, EFFIC 77.6 68 62 96 72.7 76.9 69 47 29 Table 5 54ayer Resurm at End of Pump i 2C0 CF' 5-1_YER MODEL SAH NSI RES MARATHON MEYER-1 MEYER-2 ARCO-STIM TEXACO-FP ADVAN I I III i i LENGTH 2905 3709 1754 1224 2962 2407 3399 934 1594 HEIGHT 394 361 501 476 328 327 394 605 438 PRESSURE WMAX 960 0.72 852 0.63 1119 0.83 1250 'I .03 669 0.5 768 0.6 944 0.64 934 1129 0.61 ,, ,, WAVG W 0.42 0.38 0.8 0.7 0.36 0.46 0.36 1.32 0.45 II I ,, WAVG F 0.31 0.25 0.4 0.65 0.28 0.35 0.24 0.36 EFFIC 80.1 66 82 97 70.5 74.8 68 89.6 58.1 n', k' m 3-LAYER MODEL SAH NSI RES MARATHON MEYER-1 MEYER-2 ARCO-STiM ARCO-T;= TEX-FP TX-FPTIP ADVANI , LENGTH 2642 27_5 1042 11'36 2535 1980 2926 3124 1089 1168 1870 i ,, . i,i HEIGHT 430 388 500 476 330 349 405 449 578 614 458 PRESSURE W MAX W AVG W 1035.5 0.82 0.46 935 0.71 0.42 1358 1.18 0.9 1262 1.04 0.71 766 0.6 0.46 891 0.75 0.57 968 0.7 1160 (:1.74 1365 1.19 1285 1.077 11L_1 0.$5 0.47 I , i ,, W AVG F 0.31 0.25 0.6 0.66 0.37 0.42 0.34 EFFIC 81.8 70 87 93 73.7 77.8 70 62 88.5 87.7 64 Table 6 Time to breakthrough into lower layer MODEL ARCO TerraFrac ARCO STIMPLAN SAH TRIFRAC NSI STIMPLAN TEXACO FRACPRO TEXACO FRACPRO-TIP RES FRACPRO MARATHON GHOFER MEYER MFRAC-II - 1 MEYER MFRAC-II-2 AE'VANI i J Newtonian 63 70 140 8 10 <25 113 44 55 ...... n', k' 60 50 50 75 6 i 7 <25 69 30 40 30 Table7 Time (rain) 0 25 50 75 100 125 150 175 200 Height (It) 170 170 170 170 170 170 170 170 170 S.AHoklitch&Assoc..GDKConstaf_height Net Pressure (ps_) 721 119 96 84 77 72 68 65 62 Efficiency (%) 99 89 88 87 87 86 68 86 68 ps200cp ii H_ Lenglh (lt) 10 661 1036 1348 1624 1876 2110 2332 2542 Max. Width' (in) 0.039 0.426 0.537 0.614 0.676 0.727 0.772 0.812 ,, 0.848 i i i i i i Avg.Width in Fmc (in) 0.032 0.284 0.370 0.429 0.475 0.514 0.547 0.578 0.605 i Avg. Wldlh at Wellbore (in) 0.039 0.425 0.537 0.614 0.676 0.727 0.772 0.812 0.848 Table 8 8.A Hokiitch & Assoc. - GDl( Constant height n',,0.6, k',,0.U I I i i i i Tta, (m) 0 25 50 75 100 125 150 175 200 Height (lt) 170 170 170 170 170 t70 170 170 170 Half _ (lt) 10 626 942 1195 1415 1613 1796 1967 2128 Net Pressure Lo,_) 682 134 118 I09 103 gg 96 93 91 Efficiency (%) 99 ,, 90 68 68 89 68 88 68 ,, 88 i Max.Width (in) 0.037 0.452 0.567 0.704 0.789 0.863 0.929 0.988 1.04 i Avg.Width In Fmc 0.033 0.267 0.365 0.436 0.484 0.543 0.587 0.626 0.662 Avg. Width at Wellbore 0.037 0.452 0.567 0.704 0.789 0.863 0.929 0.968 1.04 dm Table| Time (mM) 0 25 50 75 100 125 150 175 200 Height (It) 170 170 170 170 170 170 I70 170 170 8.AHolditch&Assoc..PKNConstantheight Net Pnmsure (.rod) 42 712 827 901 955 996 1035 1086 1094 Efficiency (%) 98 83 80 78 76 75 74 73 72 p_L'00cp Avg.Width In Fmc (in) 0.13 0.157 0.203 0.229 0.247 0.260 0.271 0.281 0.290 Avg.Width at Wellbore (in) 0.015 0.256 0.296 0.325 0.344 0.360 0.373 0.382 0.394 Half length (It) 10 1067 1771 2379 2934 3452 3941 4406 4855 Max.Width (in) 0.079 0.327 0.379 0.413 0.438 0.458 0.475 0.489 0.502 Table 10 8.A Hoklitch & Assoc.. PKN Constant height n'a0J, k'e0.N i Time (rain) 0 25 50 75 100 125 150 175 200 I Height (It) 170 170 170 170 i 170 170 170 170 170 Half Lengl_ (ft) 10 1084 1764 2342 2862 3341 3793 4220 4629 Net Pressure _ i Efficiency (%) 98 82 80 78 77 76 75 74 74 Max. Width (in) 0.019 0.321 0.382 0.422 0.452 0.478 0.500 0.519 0.536 42 6gg 831 919 gsg 1042 I089 1131 1168 Avg.Width In Fmc (in) 0.013 0.167 0.192 0.217 0.235 0.250 0.263 0.273 0.263 Avg.Width at Welll_m (in) 0.015 0.252 0.300 0.331 0.356 0.376 0.393 0.408, 0.421 ! 273 0.561 0.075 0.291 0. 3.410 0.724 0.501 0.06 Time (min) 0 25 50 75 100 125 150 175 2_ Height (It) 173 235 263 364 396 405 414 422 430 Upper Height (ft) 87 123 13g 164 178 186 194 201 207 Lower Height (ft) 68 113 124 200 217 219 _ 221 _: Haft Net Prmmum Lenglh (IXd) (It) 12 209 u22 .434 0.0.286 0. Holditch & Assoc.280 0.3___ 0.___3 0.0iS Time (min) 0 25 50 75 100 125 150 175 200 Height (It) 172 238 266 289 306 326 342 357 371 Upper Height (It) 86 124 141 155 168 177 187 197 206 Lower Height (It) 86 114 125 134 142 148 155 161 165 Half Length (It) 16 610 1319 172g 2056 2415 2717 2995 ..059_ 0_ 0.664 O__a96 0..512 0.417 0. 3259 Net Pressure (psi) 164 787 886 947 991 1024 105t 1073 1093 Efficiency (%) 95 64 62 61 80 .0._/ 391 394 Upper Height Lower Height Half Length Net Pressure (Ix.604 0.__ _.__n_ 0.__296 0.751 Avg.__53 0. Holditch & Assoc.__:____ 0.0$..Width (in) 0. 85 9 2264 1006 2442 1021 2642 1036 Efficiency (%) 96 84 81 81 61 82 82 82 82 Max.097 0...716 AVg.216 0. Width In Fmc (in) 0.447 0. Holditch & Assoc.273 0.3___'J 0.__R__ 0.Width In Fmc AVg. 3.264 0._9 0..384 Table 13 8...273 0.309__ Avg.075 0.layer n'..236 0.754 0.647 Avg.610 0.075 0.076 0.377 0.A...301 0.31 Table 11 S.Width In Fmc (in) 0.kiyer n'.Width in Fmc (in) 0.581 0.241 0__259 0.A.. 777 1356 874 1706 929 1886 964 2071 . Holditch • Assoc. k'.3 Table 12 8.271 0.Myer lA-200 cp Time (rain) 0 25 50 75 100 125 150 t75 200 Height (ft) 173 231 250 2_ 328 3_ .__ 0.368 0.vg.627 0.279 0.529 0.Sw 0.299 0.316 0.425 0. .283 0.076 0..301 Avg.295 0.I) 209 750 836 883 912 930 943 953 960 Efficiency (%) 96 65 82 80 79 80 80 80 80 MAx.316 0. Width at Wellbore (in) 0.423 0.292 0.01S.660 0. k'.Width (In) 0.255 0.z_ 0.06 0.Width lit WeUbore (in) 0.Width at We.454 0.781 0.275 0.A. bore (ft) (It) (It) On) On) 87 120 132 141 155 165 171 174 177 68 111 119 128 173 204 216 217 217 12 781 1318 1767 2124 2338 2525 2710 2906 0.486 0..330 O3_'__ 0.705 0.312 0.588 0. Width (in) 0._9___ 0.438 0.461 .299 0.722 0.248 0.3_r.213 0.layer p. IS.5_') 0.348 0.244 0.6.075 0..6.224 0.='_'_'_'_'_'_'_'_'___ _ 0.394 0.Width at Wellborn (in) 0..__r_g 0.097 0.420 0.273 0.343 0.347 0.0._ _ 268 281 291 301 310 318 Upper Height (ft) 86 121 133 142 150 156 162 167 172 Lower Height (ft) 86 112 120 126 131 135 13g 142 145 Half Length (ft) 15 76g 1288 1720 2105 2458 :_/_2 3107 3408 Net Pressure (psi) 164 768 846 894 928 953 975 993 1009 Efficiency (%) 95 84 82 61 80 79 78 77 77 Max.818 Avg.423 Table 14 S.319 0.A.R"_ 0.200 cp I II I Time (rain) 0 25 50 75 100 125 150 175 200 Height (It) 172 z.480 0.391 0.290 0. Width (In) 0. 79 76 78 77 Max.359 0. 790 Table 18 Meyer & Assoc.774 0.. 0 25 50 75 1O0 125 15X) "'/5 200 ..302 0.li Max.0..545 Avg.465 0.Width in Fmc 0 0.708 0.21g 0... x..401 0.588 178g 1939 2_6 Net Pressure (psi) 0 178 154 142 134 129 124 120 117 ElticMnoy (%) 100 89 88 88 87 87 87 87 86 Max.248 0.757 0.603 0.bore (in) 0 0. (in) 0 0.511 0.222 0.502 (in) (in) i ...790 Avg..NBue Cue i i Time (rain) 0 25 50 75 100 125 150 t 75 200 Height (It) 170 t70 170 170 170 170 170 170 170 Half Length (lt) 0 g34 t 530 2057 2524 2957 3363 374g 4118 Nat Pmmum _ 0 862 1013 1114 11go 1253 1307 1354 1397 Efficiency (%) 100 84 81 79 78 77 76 75 74 Max.621 0.6.564 0.720 0.451 0.45e 0.377 0.428 0.631 0.200cp BaseCase .473 0.504 0.358 0.451 0..575 0.32 Tablo 18 Meyer&Aswc.i i ||l ii .N BaN Case I 1 i Time (rain) Height (It) Half Lenglh (lt) 0 611 g22 1173 1391 t .Width In Fmc 0 0.450 0.501 0. at Wellborn 0 0.Width _ Fmc (in) 0 0.260 0. GDl( Constant height n'.200cp BaseCase .315 0.041 Avg.335 0. .621 0.603 0.O.930 0.708 0.373 0.041 !1 i m Table 17 Meyer&Ast.424 0.518 0. (rain) 0 25 50 75 100 125 150 175 200 Height (It) HIIIf Length (n) 0 I_t_' (psi) 0 138 110 g6 88 82 77 73 70 Elticl_ (_) 100 88 86 85 85 84 84 83 83 Max.292 0.321 0.631 0.Width In Fmc Avg.793 0..988 1.457 0.406 0.347 0.292 0.729 0.380 0.555 0.793 0.470 0.988 1.Width .504 0.417 0..305 0.816 _} 0 0.865 0.619 atWe. m Table 1| Meyer • Assoc.393 0. 170 170 170 170 170 170 170 170 170 .546 0.0.286 0.402 0. .Width at Wellborn 0 0.310 0.487 0.427 _n) (_) H .8.358 Avg.Width at Wellbore .679 0.. PKN Constant height n'.720 0.865 0.575 0..318 Avg.575 0.GDKConstmtheight i p. 170 170 170 170 170 170 170 170 170 _ 1062 1406 1607 1961 2207 2430 2650 0 0.593 0.532 0.679 0.310 0. Width (in) 0 0.757 0. Width (in) 0 0.930 0.4g5 0.0.281 0.364 0. k'.402 0.600 0.287 0.305 0.678 0.PKNConstm_height Time (mln) 0 25 50 75 100 125 150 175 200 Height (lt) 170 170 170 170 170 170 170 170 170 Half _ (lt) 0 948 1605 2178 2700 3187 3647 4086 4507 Net Prmure (psi) 0 813 924 995 1048 1002 1128 11ISO 1188 EIl_enoy (%) 100 84 80 78 77 78 74 73 72 p.481 0. k'.641 Avg.532 0.395 0.. Width On) Avg. Width (in) 0 0.332 0. .268 0.549 0.1ayer p.__r._5_ 0.510 0.layer n'. (1:_) (%) (in) Avg.ht (rain) (It) Height Upper Lower H. 151 845 1307 1868 1975 2244 2487 2708 2915 0.295 0.566 0.402 Table 21 Meyer & Assoc.231 0.544 0.q_ TaMe 20 Meyer & Assoc.20e 0.262 0..341 0.650 0. I.257 0.X:_ 0.267 Oo_'_B2_ 0.566 0..336 (in) o O__L_ O.310 0.Width at Wellbore 0 25 50 75 100 170 193 .6._ 0o__'_6 03____ 0.246 0.338 0.232 0..257 (in) 0 0.M Base Cise i "nrne He.483 0._268__ -0.552 0.200 cp Bile Case Time (rain) 0 25 50 75 100 125 150 175 200 Height (It) 170 214 234 249 260 zlu zlu 284 291 Upper HeigM (ft) 85 110 122 131 138 144 149 153 157 Lower" Height (ft) 85 104 112 118 122 126 129 131 134 Half Length (ft) 0 i 872 1421 1867 2281 2620 2950 32r'_ 3549 Net Pressure (1_) 0 740 826 876 910 935 956 973 987 Efficiency (%) 100 83 80 77 75 74 72 71 70 Max.311 0.Width (in) Avg. Wk:th at WelObore o 25 50 75 100 125 150 175 200 17o 219 249 278 322 343 330 329 330 (n) es 113 131 144 146 134 123 122 122 (It) es 106 118 134 176 209 207 207 208 (It) o 842 1303 1643 1725 1844 2099 2327 2535 .367 0.345 O. k'.622 0.273 0.364 Table 22 Meyer & Assoc.214 0.268 0.445 0. .694 0 0 112 130 143 154 153 172 179 186 105 117 126 133 138 143 147 . wm_ in Fmc Avg.100 125 .W_-y Wk_ Max.496 0.6.0.214 0.285 Avg.3-layer n'.33 Table 19 Meyer & Assoc..520 0.314 0..580 Avg.Width (in) Avg.316 0._quB-_5 0.414 0.305 0.673 0.497 0.0.599 (in) o 0.260 0.321 0.558 0.532 0.150 175 200 170 217 247 269 287 301 315 326 337 85 85 0 0 784 8_4 957 1000' 1032 1057 1077 10_4 100 84 80 78 77 76 75 74 73 0 0.336 0.iayer lA-200 cp Base Case Time (min) Height (it) Upper Height Lower Height Haft Length Net Pressure (psi) Efficiency (%) Max.550 0.441 0.df Height Length Net ressure P Efrr.455 . 139 (It) es 104 113 119 123 (n) 0 872 1414 1863 2257 . Width (in) 0 0.296 0.Width at We.482 0.487 0.327 0.248 0.415 0.446 0.279 0.247 0.425 0. 0 743 829 879 913 too 83 80 77 75 0 0.263 0. Width at Welllxxe (in) 0 25 50 75 ..395 0.497 0.04 Base Cise Time (rain) Height (It) Upper Height (It) Lower Height (it) ' Half Length (ft) Net Pressure (psi) Efrx:tency (%) Max.345 0.246 0.0.282 0. bore (in) 0 0.Sg0 0.iS.321 125 150 175 200 232 25g 21_ 284 144 143 132 123 138 16g 206 205 2554 2626 2716 2962 933 79g 674 669 73 72 71 71 0. 205 212 219 (it) es 111 124 132.374 0.. k'.394 0..294 0.583 0.331 0.385 0.0.Width in Fmc (in) Avg.387 0.3. o 786 898 952 823 723 734 751 766 lOO 84 80 78 77 76 75 75 74 o 0.Width in Fmc (in) 0 0. .511 _n) 0 0.3____ 0. Width in Fmc Avg..266 0.208 0.361 ' 0.267 0.538 0.__'_B_ 0. 350 0.846 0.601 0.635 0. 0 741 1238 1667 2056 2417 2759 3083 3395 _) 0 0.Width In Fmc _) Avg. PKN Constant height n'.740 i Avg.105 1.621 0.030 1.968 _ wo..467 0.724 0.846 0..200cp Max..501 0..5i I 0.944 Knobson I Half Length (ft) 0 589 927 1208 1457 1685 1896 20_ 2288 Net Pressure (psi) 0 192 153 134 122 114 107 102 97 i i Efficiency (%) 100 89 88 88 87 86 86 86 85 i i Avg. k'.860 0.686 0.371 0.031.Width 170 170 170 170 170 170 170 170 170 0 515 784 1002 1192 1363 1521 161_ 1808 i 0 0.GDKConstanthMght i p..556 0.0A. (_) 0 0.lmgth (lt) Net Pressure (pml) 0 1110 1298 1422 1517 1596 1662 1721 1774 i Efficiency (%) 100 87 85 83 82 81 80 80 79 Max.479 0.O.030 1.486 0.944 i i Table 24 Moyer & Assoc.596 0.732 0. oro b (In) 0 0.860 0.k'.663 0.754 0.642 0.741 0.Width Table26 Time (rain) 0 25 50 75 100 .517 0.505 0.173 1.471 0.Width (In) 0 0.811 0.568 0.GDK Consbmt height n'.904 0.686 0.| 175 200 Height (lt) 170 170 170 170 170 170 170 170 170 Meyer&Assoc.503 0.448 0.676 Avg.360 0.614 i Avg.273 0.310 0.660 0.235 InFmc (In) 0 0.173 1.. Width On) 0 0.638 ..105 1.367 0.754 0.._) 0 255 218 Ig0 187 178 171 166 161 Efficiency (%) 100 91 go 89 89 89 8g 88 88 Max.395 0.Width at Welroom on) 0 0.334 0.724 0.N Knobs on i Tkne (.530 TaMe 2t.436 0.411 0.34 Tablen Tlme (min) 0 25 50 75 100 125 150 175 200 Height (ft) 170 170 170 170 170 170 170 170 170 Meyor&Assoc.3gg 0. Meyer & Assoc. Width at WeUbore (in) 0 0.598 0.M Knobs on Time (rain) 0 25 50 75 100 125 150 175 200 i Height (lt) 170 170 170 170 170 170 170 170 170 Half l.415 0. | 125 150 i.376 0.807 0.546 0.461 .460 0.379 0.35g 0 0..352 0.790 0.945 1.50g 0.652 0.467 0...709 0.235 Avg.291 0.945 1.811 0. Width at WeUbore . . Width In Fmc (in) 0 0.339 0.Width (In) Avg..538 0.904 0.onglh (ft) Net Pressure C.556 0.200cp Knobson i _ Hill' Length (lt) 0 785 1337 1820 2262 2676 3068 3443 3803 Mix.601 0.-PKNConstantheigM Net Prlmm_ (psi) 0 1002 1141 1231 1298 1353 13g9 1438 1474 Efficiency (%) 100 87 84 82 go 79 78 77 77 p.919 0.565 0.763 0.0.443 0.619 0. Width In Fmc Avg.674 0.. Width (in) 0 0.479 0._n) 0 25 50 75 100 125 150 175 200 Height (ft) Half l.866 0.574 0.433 0.524 0.696 0. ..349 0.350 0.layer n'.401 0.387 0.479 0.447 0.632 0.383 0.352 0.551 0.Width (in) o o 870 960 1008 1040 1064 1082 1067 110g .556 0..Width (in) 0 0.313 0.9 797 770 805 632 854 874 891 Efficiency (%) 100 87 84 83 81 80 79 79 78 Max. 341yet n'.338 0.398 0.OS Knobs on Time (rain) 0 25 50 75 100 125 150 175 200 Height (ft) 170 246 291 322 347 367 385 400 413 Upper HelgM (ft) es 129 156 175 191 204 216 226 235 Lowm' HetgM (It) es 117 135 147 156 163 16g 174 178 Half Length (ft) 0 . Width at Wellbore (ft) es 124 144 136 119 118 118 118 t 19 (ft) es 113 138 210 206 207 207 208 208 (ft) 0 6es 1085 1162 1484 1743 1977 21gg 2407 (in) 0 0.607 0. a 1oo es 83 81 79 77 76 75 74 o 0. Width lit Well)ore (in) 0 0.337 0.567 . 637 g68 1225 1444 1636 1811 1971 2120 Net Pressure (Psi) 0 944 1048 1102 1138 1163 1163 1199 1212 Efficiency (%) 100 87 84 82 81 80 79 78 77 Max.316 0.415 0.344 0..255 0..861 .353 (_) 0 0.580 0.634 0.407 Table 211Meyer & Assoc.556 0.378 0.395 0.596 Avg.k".. k'=0..746 Avg.276 0.586 0.365 0.477 0.346 0.301 0.743 0..420 0.296 0.811 0.455 0.534 0.423 Avg.447 0.346 0.Width at Wellborn (in) 0 0.659 0. 3.313 0..Width In Fmc Avg.323 0.Q.673 0.319 0..388 0.780 0.283 0.35 Tablo 27 Meyer & Assoc. 213 214 Haft Length (ft) 0 633 ' 801 1029 1255 1454 1638 1814 1980 Nat Pressure (IO_i) 0 94.643 0..5t 7 0.637 0.335 0.399 0.352 0.331 0. .699 0.328 0..411 0.. 6-Myer p=200 cp Knobs on Time (mln) 0 25 50 75 I00 126 150 175 200 Height (ft) 170 237 282 346 325 325 325 326 327 Upper Height Lower Height Half Length Nat Pressure (l::ml) 0 874 94g 687 708 727 743 757 748 Efficiency (%) 100 86 63 81 79 78 77 76 75 Max..0. Table 30 Meyer & Assoc.O.392 0.6.255 0.724 0.276 0. Width (In) 0 0.433 0.H Knobs on Time (mln) 0 25 50 75 100 125 150 175 200 Height (ft) 170 241g 341 337 336 338 341 345 349 i Upper Height (ft) 85 131 144 128 127 t27 129 132 135 Lower Height (ft) 85 118 197 20g 20g 211 212 .680 0.478 Table 2t Meyer • Assoc.553 0.537 0.338 0.404 0.715 Avg.397 Avg.487 0.6.Width in Fmc (in) 0 0. o 25 50 75 100 125 150 175 200 17o 235 268 290 307 321 332 343 360 i es Lower HelgM (lt) es Half Length (ft) Net Pressure" Efficiency (IXd) (%) • MaX. Width in Fmc (in) 0 0.46g 0.318 0.1myer p=200 cp Knobs on Time (mln) Height (It) Upper HeigM (ft) .373 0. 2592 i i 0.535 0. Avg.697 0.572 0.367 0.435 0.457 .366 0. 1446 1740 2005 2250 2478 .6..276 0.459 0.59g 0. .377 0.513 0.699 0.Width (in) 0 0.533 0. Width at Wellbore (in) o 122 142 156 167 176 183 190 195 113 126 134 140 145 149 153 156 696 110g .Width in Fmc (in) o Avg.313 0. 298 0.496 0.1320 1378 1429 1474 lOO 65 83 81 80 79 76 78 77 o o.634 0.:m o 0._ 0.316 0.319 0. 3..Width in Fmc (in) Avg. W_h at We.298 0.267 0.537 0.676 o o.571 0.06 " le (rain) 0 25 50 75 100 125 150 175 200 (It) 170 249 296 315 329 361 372 406 435 Height (ft) 65 131 157 169 179 198 202 226 244 He=jht (It) 85 117 139 146 151 165 171 180 191 iii Length (It) 0 905 1323.339 .515 0.327 0.310 0.O.3_r.420 0.531 Table 33 Advanl. W_ in Fmc 0 0.36 Table 31 Advani. k'.515 0.542 i Table 32 Advani...Width 0 0.245 0.265 0.W_h On) 0 0.318 0.598 0..632 0.218 0.656 0.326 0.WkRh (in) Avg.365 0.467 0.302 0.0.6.649 0.659 0.216 0.ht (It) 170 240 274 298 316 328 340 352 357 Upper Lower Height 65 124 143 158 169 177 165 193 195 Height 85 116 131 141 147 151 155 159 162 H_ Leflglh 0 654 1069 1303 1501 1635 1778 1983 2089 Net rm.377 0..191 0.216 0.624 0.0.413 0.6.319 0.271 0.3.426 e W_lbom (in) 170 170 170 170 170 170 170 170 170 0 968 1638 5550 2752 .568 0.213 0.326 0.475 0.O. at WeUbore (in) o 25 50 75 100 125 150 175 2gO 17o 17o 170 170 170 170 170 170 170 o" m9 1513 2020 2479 2904 3303 3683 4046 o _0 1062 1170 1252 .529 0._a__ 0.k'.238 0.337 0.434 0.165 0.658 Avg.286 0.303 0.324 0..200 cp iiii i I i i i i i Time 0 25 50 75 100 125 150 175 200 (rain) Height (it) Half Length (it) Net Pressure (p_) Eff_.598 0..248 0.251 0.422 0.318 Avg.334 0. Width (in) Avg.352 0.220 0.ienoy (%) 100 84 81 79 78 77 76 75 74 Max.646 0.421 0.280 0.246 0.309 0.530 0.6 ' 0.Layer n'. PKN Constant Height n'.3_'_ 0.265 0..198 0.476 0. 3246 3718 4165 4595 i i 0 804 915 987 1041 1065 1121 1153 1182 0 0.369 0...404 0._ P (j_d) 0 885 972 1040 1048 1077 1090 1112 1113 Errr.265 0.292 0.415 0._ ep T_e (rain) 0 25 ' 50 75 100 125 150 175 200 He.391 0.04 Time (rain) Height (It) Half _ (It) N= Pressure (psi) E_ (%) Max.606 0.211 at WeUbore (in) 0 0.206 0.453 0.706 0._ (%) 100 67 58 58 52 51 46 44 43 Mx.-__'1_L3 0.575 0..461 0.513 0.375 0.Width inFrc (in) 0 0.__9_9 0.bore 0 0.1) On) Table 34 Advani . PKN Constant Height _.250 Avg.218 0. 100 71 64 59 58 54 52 52 47 0 0.Layer p.743 ! in Fmc (in) 0 0.331 (It) (It) (It) (I. 1313 1790 2018 2188 2381 2424 (psi) 0 865 995 1017 1048 1106 1104 1142 1171 (%) . 727 0.04 Net Prmure (psi) 0 865 992 1021 1044 1027 1035 1095 1151 .337 0.299 25 50 o 17o 240 276 392 403 413 430 438 85 es o 885 965 o 1oo 67 58 0.267 0.Width (in) 0 0.251 0.220 Avg.402 0.749 0.9 458 Upper HetgM es 131 147 157 166 187 193 205 210 Lower Height es 117 231 231 232 •235 237 244 248 X Advani. 0.445 Ti_ Time (mln) 0 25 50 75 100 125 150 175 200 HetgM (It) 170 248 378 388 3_ 422 430 44.422 0. Wklth (in) Avg. Half Length 0 905 1150 1159 1206 1502 1751 1853 1870i Efficiency (%) 100 71 72 76 70 es 62 61 64 Max.421 0.3516 0.289 0.704 0.410 0.29g 0.770 0.267 0.6.165 0..340 0.2_ 0.e67 0.513 o o o 75 100 125 150 175 200 3eo 151 161 159 177 190 195 229 1194 1227 1273 1363 1506 1594 I065 1051 1048 1047 1076 1129 e2 es 63 58 57 58 o.465 (lt) (lt) (lt) _n) (_) .597 0.Width in Fmc (in) 0.406 0. 6.Layer p_00 Time (rain) Height (11) Upper Height (ft) 124 144 Lower HelgM (It) 116 132 231 234 237 241 243 Half Length (It) 654 1073 Net Pre.244 0.377 0.359 .218 0.Width at Wellborn (in) 0.805 o.408 0.364 i o.Layer n'=0. k'-0.434 0.697 0.695 0.337 Avg.308 0.386 0.662 0.848 Avg.340 0.37 Table 36 Advan! .urn (PSi) Efficiency (%) cp Max.278 0..6.370 0.373 0.702 0.Width In Fmc 0 0.336 0. Width at Wellborn 0 0.720 0. 413 0.589 AVg.96 2917 3310 3683 403g I _Pressure (l:xd) 0 848 993 1092 1168 1232 1286 1334 1376 Efficiency (%) 100 84 81 79 78 77 76 76 75 Max.650 0.669 0.04 "' Time 0 25 50 75 100 125 150 175 200 Height Half _ Net Pressure Efltclency Max.463 _) _) i Table 40 Shell .746 0.437 0.856 0.511 0.496 0.6.557 0.W_lth 'Avg.0.920 0.525 0.358 0.58g .28i 0.lm.382 0.856 0.720 0. GDl( Constant Height F.99 2725 Net Pressure (Psi) 0 104 83 73 66 62 58 55 53 Efficiency (%) 100 88 67 86 86 85 85 84 84 Max.477 0.re ph) 0 0.432 0.612 (in) 0 0. (m_) (n) (it) (psi) 0 134 117 106 102 98 g4 91 89 (_) 100 90 89 89 88 88 88 88 67 (kn) 170 170 170 170 170 170 170 170 170 0 624 g42 1196 1421 1622 1807 1979 2142 0 0. k'.710 0..370 AVg.920 0. Table 38 Shell .350 0.622 0.293 0. Width at Wellbore (in) 0 0.750 Avg.471 Avg.310 0. Width (in) 0 0.266 0.489 0.392 0..453 0.809 it Week.387 0.779 I li i .GDl( Comitant Height n'-0.453 0.566 0.768 0.0.332 0..452 0.396 0.93 0.3g0 0.251 0..314 0.ego 0.38 Table 31' Shell.977 1.710 0.Width at Wellbore 0 0..445 0.Width in Fmc 0 0. Width in Fmc (in) 0 0.400 0.PKN Conmnt Height n'.977 1.687 0.784 0. Width at Wellbore (in) 0 0.225 0.565 0.Width (in) 0 0. k'.615 0.N Time (rain) 0 25 50 75 100 125 150 175 200 Heght (lt) 170 170 170 170 170 170 170 170 170 Half Length (lt) 0 863 1356 1767 2132 2465 2776 306g 3347 Net Pressure (pid) 0 g50 1160 1307 1424 1522 1608 1685 1754 Efficiency (%) 100 85 83 82 81 80 80 79 79 Max.746 0.331 0. p.549 0.699 0.432 0.486 0.672 0.466 0..'Width ' ' Avg.358 0.0..6.669 0.598 0.466 0. PKN Constant Height p"20O cp '.314 0.540 0.396 0.779 Avg.030 Table 39 Shell.550 0.030 inFmc _) 0 0.345 0.Width (in) 0 0.200cp a i t Time (rain) 0 25 50 75 100 125 150 175 200 Height (lt) 170 170 170 170 170 170 170 170 170 Half Length (11) 0 704 1107 1441 1738 2007 2261 24.499 0.526 0.607 0.406 0.586 0.423 0. Time (min) 0 25 50 75 100 125 150 175 200 Height (It) 170 170 170 170 170 170 170 170 170 Half Length (lt) 0 948 1540 2044 24.622 0.448 0.366 0.570 0.566 0.596 0.4.784 0.:.722 0. Width in Fmc Avg.567 0.311 0.356 0. Width Avg.562 0.381 0.612 0.509 0.482 0.39 Table 41 Shell ENERFRAC p.433 0.8.95 0.575 0.451 0.389 0..710 0.577 0.530 0..396 atW_Ibore (in) 0 0.757 .506 0.M Base CoM . Width st Wellbore (in) 0 0.4.375 0.k'V.483 0.423 0.630 0.410 0.448 0.335 0.366 0.352 0. 75 100 125 150 175 200 Height (it) 170 170 170 170 170 170 170 170 170 Half Length (ft) 0 611 1373 1863 2311 2729 3125 3503 3866 Net Pressure (psi) 0 1093 1237 1332 1405 1464 1513 1557 1595 Efficiency (%) 100 85 83 81 79 78 77 76 75 i Max.738 Avg.64_ 0.6.277 0.492 i Table 42 Shell ENERFRAC n'.427 0. 0 25 50 75 100 125 150 175 200 Height (ft) 170 170 170 170 170 170 170 170 170 Half Length (ft) 0 770 1267 1693 2079 2436 2772 3092 3396 Net Pressure (psi) 0 1160 135g 1494 1598 1684 1757 1821 1880 Efficiency (%) 100 86 84 82 81 80 79 79 78 Max.467 Avg.453 0.377 0..682 0.613 0.420 0.354 0.594 0.680 0.O. Table 44 Shell ENERFRAC n'-0.608 0.715 0.327 0.551 0.340 0.200 cp Base Case li I I I Time (min) 0 25 50 .519 0.396 0.441 0.456 Avg.352 0. 0 1120 1259 1353 1424 1462 1531 1574 1612 (_) 100 86 83 81 80 79 78 77 76 (in) 0 0.594 0.627 i Avg.478 0.Width Avg.367 0..Wk:lth in Fmc (in) 0 0.Width in Fmc (in) 0 0.378 0.477 0. Width (in) 0 0.343 0.400 0.522 0.276 0.0.352 0.543 0..O.448 0.294 0.467 0.Ir_O psi i i Time Height Half Length Net Pressure Efficiency Max.387 i Avg.595 ..380 0.661 0.438 0. i AVg. ii i Time (min) .332 0. Width (in) 0 0.Width at Wellbore (in) 0 0.Width at Wellbore (in) 0 0..426 0.375 0.585 0626 0.542 0. k'.459 0..N Overprossure-600 psi i Time (mln) 0 25 50 75 100 125 150 175 200 Height (ft) 170 170 170 170 170 170 170 170 170 Half Length (ft) 0 730 1220 1642 2024 2379 2714 3031 3336 Net Pressure (psi) 0 1200 1392 1524 1626 1710 t782 1846 1903 Efficiency (%) 100 87 84 83 82 81 80 79 79 Max.480 0.735 0.Width (mln) 0 25 50 75 100 125 150 175 200 (n) 170 170 170 170 170 170 170 170 170 (ft) 0 772 1322 1806 2249 2663 3054 3429 378g (o_) . Width (in) 0 0.322 0..558 0.556 0.296 0.467 0..417 0.386 0.261 0.408 0.580 Table 43 Shell ENERFRAC p=200 cp Ovetpreuure. Width in Fmc (in) 0 0.571 0.506 .492 0.437 0.645 inFmc (in) 0 0.312 0.449 0.535 0. 632 0.566i 0 0.Width at We.805 0.691 0.614 0.704 • psi Avg.543 0.422 0.603 0.682 0.585 0.570 0.623 0.695 0.443 0.462 0.564 0. .6.640 0.773 0.558 0.445 0..516 0.490 0.805 0.' Length (lt) 0 626 1069 14.640 i i TaMe 48 Shell ENERFRAC n'.796 0.4O Table 48 8hatl ENERFRAC IA_0 Time (rain) 0 25 50 75 100 125 150 175 200 Height (It) 170 170 170 170 170 170 170 170 170 Half Length (lt) 0 660 1174 1634 2060 2460 2840 3205 3556 N'atP'ml_e (psi) 0 1262 1372 1451 1513 1565 1610 1649 1684 cp _10_) Max.721 0.693 0.332 0. Width (in) 0 0.502 0.Width at Wellbore Time (min) 0 25 50 75 I00 125 i 150 175 200 _:_.Width (in) 0 0.Width in Fmc (in) 0 0.882 0..814 AVg.781 0. bore (in) 0 0. Width (in) 0 0.484 0.0.1600 psi Max.531 0.504 Table 47 Shell ENERFRAC 1_.0.553 i i TaMe 48 Shell ENERFRAC n'.817 Avg..837 0.518 0.901 0..861 0. Avg.536 0.491 0.429 0.407 0.544 0.2_ cp Overpressure-llr_) psi m.608 0.N i|111 Overpressurm.718 0.Width at We.730 0..463 0..496 0.580 0.434 i Efficiency (%) 100 88 86 84 82 81 80 79 79 .607 0. k'.bore (in) 0 0.531 0.751 0. Time (mln) 0 25 50 75 100 125 150 175 200 Height (lt) 170 170 170 170 170 170 170 i70 .4_ 0.0..536 0.Width In Fmc (.546 0.918 AVg.477 0.Width In Fmc Avg.566 0.417 0.657 0. 170 Half Length (lt) 0 524 970 1384 1776 2148 2506 2850 3184 Net Pressure (Psi) 0 1591 1648 1696 1737 .425 0.774 0.641 ii 1 --i Time (mln) 0 25 50 75 100 125 150 175 200 i Height (ft) 170 170 170 170 170 170 170 170 170 Hs.767 0. 0.450 0.477.500 0.65g 0.473 0.393 0.721 .461 0.676 0.in} 0 0.Wk:Ith at Wedlbom (in) 0 0.637 0.421 0.395 0._25 0.707 0. 1774 1806 1836 1863 Efficiency (%) 100 91 88 86 85 84 83 82 81 Max..352 0.. k'-0.Width In Fmc Avg.573 0.429 0.96 1868 2215 2543 2855 3155 Net Pressure (psi) 0 1359 1519 1635 1727 1805 1872 1932 1966 Efficiency (%) 100 89 86 85 84 82 82 81 80 Max.794 0.616 0.748 0.380 0.361 0.587 0.N Ovsq:remmml000 i i psi Avg._i (ft) 170 170 170 170 170 170 170 170 170 Half Length (It) 0 507 920 1297 1647 1977 2291 2591 2881 Net Pressure (psi) 0 1672 1776 1862 1934 1998 2054 2105 2152 Efr_mcy (%) 100 91 8g 87 86 85 84 83 82 (in) (in) 0 0.635 " 0. Width (in) 0 0.6..502 _n) 0 0.676 0..448 0. 41 Table O Shell ENERFRAC pt_200cp Overprenum2000 Time (min) 0 25 50 75 100 125 150 175 200 Height (It) 170 170 170 170 170 170 170 170 170 Half Length (ft) 0 420 878 1141 1482 1813 2133 2446 2750 Net Pressure (psi) 0 2035 2059 2061 2102 2122 2141 2159 2175 Efficiency (%) 100 93 90 89 87 86 85 84 84 Max.Width (in) 0 0.884 0.921 0.937 0.947 0.956 0.963 0.970 0.976 psi i | Avg.Width in Fmc 0 0.545 0.568 0.578 0.584 0.580 0.594 0.598 0.602 Avg.Width at We, bore 0 0.694 0.723 0.736 0.744 0.751 0.757 0.762 0.767 (in) (*n) Table 60 Shell ENERFRAC n',,0.6, k',,0.X Overprusure,,2000 psi i I i i i Time (n'dn) 0 25 50 75 100 125 150 175 200 Height (ft) 170 170 170 170 170 170 170 170 170 Half Length (It) 0 413 765 1098 1414 1717 2008 2290 2583 Net Pressure (l:Nd) 0 2088 2148 2203 2252 2297 2339 2378 2414 Efficiency (%) 100 93 91 89 68 87 86 85 85 Max.Width (in) 0 0.900 0.951 0.978 0.999 1.016 1.032 1.047 1.060 Avg.Width Avg.Width in Fmc at We, bore (in) . (in) 0 0 0.555 0.707 0.586 0.747 0.603 0.768 0.616 0.784 . 0.627 0.798 0.637 0.811 0.646 0.822 0.654 0.833 i 42 Tablo 61 I_lllbuNon GDl( Constant Height _,,200 cp Time (min) 0 25 50 75 100 125 150 175 200 Height (It) 170 170 170 170 170 170 170 170 170 Half Length (It) 0 535 858 1132 1378 1605 1818 2020 2212 Net Prmum (psi) 0 186 141 120 108 98 92 86 82 Efficiency (%) 100 91 _ 88 88 87 87 86 86 Max. Width (in) 0 0.53 0.86 0.74 0.80 0.85 0.90 0.94 0.98 Avg. V_/idth in Fmc (in) 0 0.42 0.52 0.58 0.63 0.67 0.71 0.74 0.77 II Avg. Width at Wellbore (in) 0 0.53 0.66 0.74 0.80 0.85 0.90 0.94 0.98 Table 12 Hilibwton Time (rain) 0 25 50 75 100 125 150 175 200 Height (It) 170 170 170 170 170 170 170 170 170 Half Length (It) 0 560 861 1106 1322 1518 1699 1870 2031 Net Prm_ (Ix_i) 0 168 140 126 117 110 105 101 97 (_DI( Constant Height n',,O.6,k',,0.N Eff'K_ency (%) 100 91 89 68 68 87 87 68 86 Max.Width (in) 0 0.51 0.65 0.75 0.84 0.90 0.97 1.02 1.07 Avg. Width in Fmc (in) 0 0.40 0.51 0.5_ 0.68 0.71 0.76 Q_RO_ 0.84 Avg.Width at We, bore (in) 0 0.51 0.65 0.75 0.84 0.90 0.97 1.02 1.07 43 T_leli,1 Time (rain) 0 2=3 50 75 100 125 150 175 200 i n IINNI Chevron GDK_llelght Efflct_ (%) 100 85 84 83 83 83 82 82 82 ll-200q:) Max. Width (in) 0 0.333 0.438 0.530 0.589 0.640 0.585 0.726 0.767 Avg.Width in Fmc 0 0.262 0.343 0.416 0.462 0.502 0.538 0.570 0.602 INI Height (ft) 170 1ro 170 170 170 170 170 170 170 I 'Half Length I (ft) Net'l:h'enum (Imi) 0 116 102 94 90 87 84 82 80 Avg.Width at We, bom 0 0.333 0.438 0.530 0.589 0,640 0.585 0.726 0.767 I I 0 386 581 774 906 1026 1137 1241 1347 (in) (in) TM_IeIM Chevron PKN Constant HelgM IA=200cp Height (ft) 170 17(! 170 170 170 170 170 170 170 Half f.ength (ft) 0 454 744 1049 1267 1470 1660 1841 2029 Net Pm' (pail) 0 837 968 1108 1179 1239 1291 1336 1380 EffK:_kmcy Max. Width (%) (in) 100 82 80 77 76 75 74 73 73 0 0.384 0.453 0.506 0.541 0.569 0.5_2 0.613 0.633 'Avg.Width in Fmc 0 0.216 0.254 0.285 0.304 0.319 0.332 0.344 0.355 Avg. Width t Wellborn (min) 0 25 50 75 t00 125 150 175 200 (in) (in) - -- plJa 711 0.622 (_) (_) i i .371 0.438 0.557 0.iq .711 0.415 Avg.650 0.428 0.776 0.496 0.424 0.0.H li .M Time (rain) 0 25 50 75 100 125 150 175 200 Height' (It) 170 170 170 170 170 170 170 170 170 Half Length (lt) 0 674 1015 1290 1530 1745 1944 212g 2304 Net _ (psi) Efficiency (%) 100 88 87 86 86 86 86 85 85 _ _'k_h (in) 0 0. .933 Avg.Width (in) 0 0.6Q5 0.29Q 0.339 0.Width mtWelllxxe pn) 0 0.0.613 0.528 0.rod) Efficiency (%) 100 i 85 82 80 78 77 76 75 74 Max.650 0.6.602 Avg.0.411 0.933 li .0.448 0.375 0. 0.581 0.699 0.526 0.558 0.253 0.767 Avg.554 on) Table 88 Conoco PKN Conmnt Height n'. at Wellbore (in) 0 0.48Q 0.776 0. Width mtWetlbore i i li on) 0 0.380 .Width in Fmc 0 0. k'-0.Width in Fmc 0 0.508 0.854 0.Width in Fmc (in) 0 0.411 0.541 0.603 0.800 0. Width mtWellborn 0 '0._ in Fmc Avg.541 0.6.402 0.488 0.44 TableM Time (rain) 0 25 50 75 100 125 150 175 ii 200 Height (ft) 170 170 170 170 170 170 170 170 170 HaftLength (ft) 0 704 1106 1438 1734 2004 2255 2492 2716 Conoco GDKConstant Efr_ (%) 100 87 86 85 84 84 83 83 83 Height p.886 0.735 0..481 0.329 0.351 0.699 0.391 0.488 0.833 0.351 0.325 0.308 0.200cp Time (min) 0 25 50 75 100 125 150 175 200 Height (It) 170 170 170 170 170 170 170 170 170 HaftL_ (lt) 0 830 1418 1925 2386 2817 3225 3614 3086 Net Pressure (.462.733 On) __.540 0.384 0..634 0.286 0.577 0._mCl) Max.517 0.323 0.352 0.833 0.388 0. Table U Conoco GDK Constant Height n'.250 0.886 0..391 0.613 0.307 0.735 0.767 Net Prmure (Psi) - .Width (in) i Avg.0 0..370 Avg.Width {in) " Avg.550 0.558 0.i i . k'.541 0.li Treblei7 Conoco PKN Constant Height lA.N Time (mM) 0 25 50 75 100 125 150 175 200 Height (ft) t70 170 170 170 170 170 170 170 170 HuffLength (ft) 0 831 1367 1826 2240 2624 2985 3328 3656 Net Pressure (iii) ° m Efrx_'_/ (%) 100 85 82 81 80 79 78 77 77 Max.483 0..634 0. 06 1. k'.Width in Fmc (in) 0 0.77 0.75 0.77 0.68 Table 12 Marathon GHOFER 3-I.68 0.65 0..72 0.65 0....75 (in) 0 0.07 1.76 0.66 Avg..72 0.66 0.03 1. li'IIII i il i Time (rain) 0 25 50 75 100 125 1_ 175 200 Height (ft) 2O4 204 204 204 204 204 204 204 204 Half Length (It) 0 374 714 1020 1360 1632 1938 2244 2516 Net Pressure (psi) 0 1832 1767 1764 1754 1776 1786 1805 1825 Effk_kmcy (%) 100 97 95 95 95 94 g4 g4 g3 Max..g5 .74 0. Wia_ (in) 0 0.64 Avg.63 0.Width in Fmc (in) 0 0.68 0. Width (%) (in) 100 98 98 97 97 97 97 97 96 0 0.04 Time (mln) 0 25 50 75 100 125 150 175 200 Height (it) 374 374 408 442 442 442 442 442 Upper Height (It) 204 204 204 204 238 238 238 238 Lower Height (It) 170 170 170 204 204 204 204 204 Haft Length (It) 0 306 476 612 782 884 1020 1190 1326 Net Pressure (psi) 0 1434 1450 1441 1414 1434 1434 1431 1433 Efr_.68 0.97 .75 0.82 Table 11 Marathon GHOFER 3.98 1.gl Avg.75 0.bore (in) 0.:O.75 100 125 150 175 200 .91 0._q_cy Max. Width in Fmc (in) 0 0.68 0.76 0.g0 0. 0.0.91 0.72 0.59 0.67 0.68 0.200 cp Time (mln) 0 25 50 75 100 125 150 175 203 Height (It) 374 374 408 408 442 442 442 442 Upper Lower Height Height (ft) (it) 204 170 238 170 238 170 238 170 238 204 238 204 238 i 204 238 I 204 Half Length (ft) 0 306 476 612 782 918 1054 1190 1360 Net Pressure (psl) 0 1423 1435 1426 1413 1391 13_4 1396 '138g EtTr_-y (%) 100 98 97 97 97 97 97 97 g6 Max.00 1.Width (in) 0 0. 0.79 0.80 0.73 0.63 0. Height (It) 204 204 204 204 204 204 204 204 204 i Half Leng_ (lt) 0 374 714 1054 1360 1666 1972 2312 2584 Table SO MirMhon GHOFER Constant HetgM n'.71 0. Width at Wellbore (in) 0 0.96 0.07 1.75 0.62 0. Width at Wellbore (in) 0 ' 0.08 Avg.72 0.76 0.84 0. Width (in) 0 0.5g 0. bore (in) 0 0..02 1.04 1.98 Avg.75 0.02 1.72 0.91 0.71 0.88 0.65 0.08 .Width in Fmc Avg.61 0.64 0.75 0.93 0.0.45 Table _ ii Mlrattm_ GHOFER Constant Height p.k'uO.61 0.95 1.5.70 0.72 0.04 Avg.76 Time (mln) 0 25 50 .84 0.74 0.78 0.91 0.75 0.67 0.71 .ayer n'.72 0.73 Avg.Width at We..67 0.93 0.66 0.71 0.93 0.51 0.6g 0.51 0.04 1.55 0.6g 0.0I 1.298 cp Net Prelmum (1_) 0 1819 1742 1668 1694 1683 1684 1678 1685 Effick_ (%) 100 97 96 95 95 94 94 94 93 Max.92 0.Width at We.55" 0.6.61 0.g0 0.Layer p. 74 0. Wm_ Avg.70 0.6.63 0. Width at We.96 1.98 1.200 cp Net Pressure (psi) 0 1447 1323 1303 1266 1251 1257 1254 1250 Efficiency (%) 100 9e 96 97 97 97 97 97 97 Max.64 0.71 0.63 0._ _ Marathon GHOFER 6.238 238 '_ Height (It) .53 0.00 0.95 0.65 0.70 0.65 Avg.03 1.64 0.02 1.67 0.50 0.03 1.170 204 204 204 204 238 238 238 (it) 136 238 238 238 238 238 238 238 (It) 0 306 408 544 680 816 918 1054 1156 0 1455 1316 1268 1285 1268 1265 1257 1263 100 96 95 95 94 94 94 93 93 0 0.71 0.99 1. 170 _ 238 _ 236 238 z.66 (_) 0 0.64 0.66 0.01 1.01 1.Layer p.65 0.84 0.68 0.03 1. Max.70 0.64 0..62 0. bore (in) 0 0.ht Upper Loww (mln) 0 25 50 75 100 125 t50 175 (it) Height Height _ H_f ' Net ressure P Emc_mcy Width Avg..46 TaMe a Time (rain) 0 25 50 75 100 125 150 175 Height (ft) 340 442 442 442 476 476 47_ 4r_ Upper Height (It) .58 0.50 0.03 Avg.69 0. Width _ (%) (in) in Fmc at WeUbom (it) 30_ 442 442 442 442 476 4rt_ 476 .Width in Fmc (in) 0 0.00 1.63 0.ayer n'n0. k'.64 0. 204 204 204 204 238 238 .70 Half Length (It) 0 306 406 544 714 850 952 1068 1224 Table (14Marathon GHOFER |4.61 0. Width (in) 0 0.65 0.70 0.M Time He.54 0.0.04 (_) 0 0.71 . Width (in) 0 .19 0.26 (in) 0 0.47 TaMe 66 ARCO $Umpian 3.64 Avg.20Ocp Time (rain) 0 25 50 75 100 125 150 175 200 Height (lt) 170 251 268 354 369 369 380 380 394 Upper Height bower Height Half Length Net Pressure (psl) 0 816 860 881 885 891 900 906 944 Efficiency (%) 100 80 77 74 72 70 6g 68 68 Max.6. .Width at We"bore (in) 0 ...25 0.24 0..Width in Fmc (in) 0 0.19 0.k'.Layer F.26 0..33 .36 Table 611 ARCO Stimpian 64Jyer n'uO.27 . 0.21 0..31 Table lM.20 0. - . _i ..23 0.22 0.26 0.N Time (rain) 0 25 50 75 100 125 150 175 200 ' H_ht (lt) 170 250 328 379 390 396 402 403 405 Upper Height (lt) 65 156 174 175 178 182 187 188 190 Lower Height (ft) 65 94 154 204 212 215 216 216 216 Haft Length (ft) 0 889 1358 1718 200g 226g 2497 2717 2926 Net Pressure (psi) 0 822 890 920 930 932 931 967 968 Efficiency (%) 100 80 77 75 74 73 71 71 70 Max.25 0. k'.19 0. Avg.19 0.Width at We"bore (in) 0 0..22 0. Avg..25 . Net Pressure (1_i) 0 824 868 902 927 955 963 976 992 Efficiency (%) 100 80 76 74 73 71 70 68 67 Max.21 0. . .22 0.Width at We..26 0.25 0..24 0.bore (lt) (a) (a) on) _n) 0 - 85 157 168 175 176 176 176 176 180 i 85 95 100 180 194 194 205 205 215 0 926 1425 1863 2225 2540 2846 3118 3399 0 0.. ... Avg. 0. Table |/ARCO Stknplan 6.0. 3598 .24 0. . .23 0.Wlcllh On) Avg.0.Width in Fmc Avg.23 0.6.. .22 0..Width at We"bore 0 25 50 75 100 125 150 175 200 170 252 271 289 305 315 328 340 353 (lt) 85 155 155 176 185 191 196 205 213 (a) es 97 105 113 120 124 130 135 141 (lt) 0 900 1356 1748 2094 2409 2703 2976 3235 i 0 845 911 956 9g0 1016 1043 1061 1083 too 81 77 75 73 71 71 69 68 0 0.. .25 0.40 .Layer p:_00 cp Time (min) .Width in Fmc Avg.. .24 0.0.24 0.. Width in Fmc (in) 0 0.Width On) 0 0.25 0.65 (_) 0 0.70 Avg.24 0. 0 25 50 75 100 125 150 175 200 170 249 259 269 280 288 295 300 306 Height (lt) Upper Height (It) 85 t 54 159 164 171 175 180 182 186 Lower Height (lt) 85 96 100 105 110 113 116 118 121 HaW Length (It) 0 920 1422 1850 2248 2616 2960 3286 . . ..57 . _r -..Layer n'.. Width On) 0 - 0.04 Time (rain) Height (lt) Upper Height Lower Height Half length Net Pressure (psi) Efficiency (%) Max.24 0. .ARCOStimpian 3. 52 . 0. - - - .. o .k'wO.07 0.47 0.6. Width at Wellborn (in) o 25 50 75 100 125 150 175 200 17o 226 246 358 370 3gg 408 423 449 e5 142 150 170 182 211 220 234 239 es 84 g6 188 188 188 188 188 210 .63 0.48 Table M ARCO T_aFmc i i - 6.Width (in) Avg..45 0. 67 65 64 62 o 0.. o 921 1371 1802 2133 2378 2651 2923 3124 o 864 981 g97 1030 1080 1120 1150 1160 too 81 71 73 67 .Lnyor n'..Width in Fmc (in) Avg.67 .O..N i i 1 (mln) Height (It) Upper Height (It) _ Height (lt) Half Length (it) Nat Prusum (p_) Eff'_ienoy (%) Max.37 0..74 o .. 21 0.65 0. bore (in) 0 25 50 75 100 125 150 175 [-200 170 237 246 252 256 259 267 275 283 85 68 0 0 684 746 787 818 840 865 884 903 100 81 75 73 71 69 68 67 66 0 0.25 .40 0..25 0. _ ] 3_ t_ 2.34 0.25 0. 0 0.21 0.24 0.63 .25 0.22 0.32 Til)li 71 NSI Tech..21 0. 0. Stimplan 64..ayer n_0.30 0.. 0.33 0..22 0. 8timpian 34.60 0. bore (in) 85 120 125 130 139 146 151 157 160 i 85 120 128 135 145 142 158 165 168 0 851 1340 1758 2123 2450 2749 3032 3289 ii.32 0.3g 0.22 0. 0.Wi_ (in) 0 .43 0.23 0. 127 131 135 138 118 124 127 130 132 136 141 144 906 1447 1914 2336 2725 308g 3428 3750 i 0.23 0.. 125 126 152 157 162 165 167 Lower Height (ft) 85 106 118 203 20g 213 215 216 Half Length (ft) 0 866 1362 1757 2069 2333 2555 2749 Net Pressure (psi) 0 708 810 848 878 904 850 924 Efficiency (%) 100 80 77 74 73 72 71 70 Max.31 0.54 0.63 0.Width (in) 0 0.23 0.66 0.3g 0.40 0.65 0.25 0.24 0.38 0..31 0.56 0.56 0 0 119 ' 122 124 126. Stimpian 64.70 Avg..S.33 0.38 0.42 .38 0.49 0.63 Avg. (It) (lt) (lt) MaxlWidth (in) 0 0.24 0.28 0.Width in Fmc 0 0.46 0.22 0.43 .06 Time (rain) 0 25 50 75 100 125 150 175 200 Height (ft) 170 240 253 265 284 296 308 322 329 Upper Height Lower Height Half Length Net Pressure (psi) 0 696 796 862 910 945 970 1003 1005 Efficiency (%) 100 80 76 74 72 71 70 69 68 .37 0.. Width in Fmc (in) Avg.27 0.29 0..38 (n) (lt) 0 911 1468 1945 .23 0..35 i Tib_ 72 NS1Tech.23 .24 0.56 .ayer n_0. Width (%) (in) Avg.31 0.22 0. Width in Frac (in) 0 0.23 0.52 0..25 Avg.35 0.52 0.25 0.ayer p_O0 cp Time (min) Height (ft) Upper Height (It) Lower Height (lt) Half Length (ft) Net Pressure (psi) Efficiency Max. Width at Wellbore (in) 0 0. 0.04 Time (rain) 0 25 50 75 100 125 150 175 Height (ft) 170 233 244 354 385 375 381 384 upper Height (ft) 85..46 ..23 0. 0.66 0.7_ 0.25 Avg.41 .0 ] _6s _5 70 0. 0 0.17 0. k_0.17 0...67 Avg.49 0.18 0. .24 0. Width at We.width in Frac (in) Avg.61 0.ayer pm200 cp Time (rain) 0 25 50 75 I00 125 150 175 200 Height (lt) 170 172 238 242 246 342 _ 364 361 Upper Height 85 124 125 126 126 149 153 157 155 Lower Height 85 105 112 117 120 '193 203 206 206 Half Length Net Pressure (psi) 0 582 757 799 828 828 848 871 852 Effk_y (%) 100 78 76 74 72 70 68 67 68 Max. k_0.34 0.6.47 0.Width at Wellborn 0 0.29 0.38 0.28 0.24 0. 2373 2739 " 3079 3424 3709 (lt) (in) (_n) ' Table 73 NSI Tech.. Stimplln 34.20 0..47 0.49 Table 70 NSl Tech.2s " 0.19 0. 0.31 0.Width at We.50 0.0..60 0.26 .30 0..20 0. 34 0.78 0. 50 75 100 125 150 175 200 Height (lt) 170 347 400 439 469 495 516 531 544 Upper Height (lt) 85 218 262 294 319 340 359 373 385 Lower Height (lt) 85 129 138 145 150 155 157 158 159 _ Length (lt) 0 446 711 932 1124 1300 1481 1608 1744 Net Press_ (psi) 0 1130 1162 1185 1202 1215 1222 1223 1227 EfficMflcy (%) 100 92 89 87 85 84 82 81 80 I_.Width in Fmc (in) Avg.80 0.32 0. .35 0.34 0.08 1.91 o.76 0.59 50 75 4o4 452 331 261 173 191 .0J.01 1.56 0.83 AVg.04 0.87 0.04 Time (mln) Height (ft) Upper Height (It) Lower Height (ft) Half Length (It) Net Pmssixe (pld) Efficiency (%) Max.14 1.48 0.54 0.34 0.53 0.57 0.96 1.57 0..90 Avg.36 Avg.77 0.87 0.35 0.80 i i i Table 77 RES Frm:pro 6.O.Layer n'.35 0. k'..60 0. Wi_h (in) 0 0.56 0.14 1. 1317 1343 1360 1375 1355 1352 ..._ (in) A_. o 0.42 0.36 0.6.48 0.60 0.48 0.40 (_) 0 0.39 0.04 1.84 0.88 0.0e Time (mifi) Height (lt) Upper Height Lower Height Half Length Net Prlmmre (psi) Efflctenoy (%) 'Max.40 0.ms 571 1363 1381 75 71 0.0.59 0.74 0.W 0. 396 420 430 456 469 480 491 501 Upper Height Lower Height Half Length Net Pressure (j_) 0 979 1013 1042 1064 1081 1096 1109 1119 li4...54 0..48 0..Width (in) AVg.91 1. 202 252 286 312 333 347 357 _ .48 0. (in) 0 0..01 1.50 Table 7'4 RES FmclXO 34. 1358 IOO 93 92 90 90 89 88 87 87 o 0.52 0..O. k'.ayer p..49 0.62 0.87 0.36 0.200 cp Effk:iency (%) 100 91 89 87 86 es 84 63 62 _ Width On) 0 0.74 0. 498 521 549 574 596 2es 305 323 340 354 2o4 216 226 234 242 e56 729 793 850 902 .39 (in). Width in Fmc AVg.81 0.38 0..49 Table 71 RES Frm Time (mM) 0 25 50 75 100 125 150 175 200 Height (It) 17o.Width In Fmc AVg.47 0.44 100 125 150 175 200 .48 0.. Width st WeUbore (in) o 25 50 75 100 125 150 175 II 200 17o 406 475 516 545 569 583 592 _ es es o o 1263 . at Welllxxe (lt) 85 200 222 239 253 265 275 285 294 (lt) 85 196 196 200 203 204 205 206 207 (lt) 0 406 665 887 1086 1269 143_ 1600 1754 (_) 0 0.200 cp Time (rain) 0 25.58 0.45 0._ I - .78 0.30 0.47 0.48 0.Width in Fmc (in) 0 0.49 0.86 0. Width at Wellb_ .43 0.53 0.57 0.63 0.16 1.51 0.43 0.10 0.37 0.71 0.54 Table 76 RES Fracpro S-Layer n_.67 0.ayer p.._ 293 424 535 632 719 846 952 1042 0.51 0.75 0.08 1.204 223 230 233 236 2"36 235 2".58 0.Width letWellbore o 25 17o 337 (lt) es 189 (lt) es 145 (lt) o 325 o 1334 1oo 80 o 0.72 _) o 0.44 o...53 0.. em 67 65 63 62 i 0.51 0. 1_ 1405 1413 1421 1428 .18 o o .73 0. 57 0. Table 60 Texaco Fracpro 34Jyer p"200 cp Time (mln) Height (It) Upper Height Loww Height Half _ Net Pressure (psi) Efficiency (%) Max.66 0.90 1666 1830 1983 0 1024 1065 1083 1098 1100 1119 1125 1132 ._mcy (%) 100 84 80 77 75 73 72 70 Max.64 0.55 0.Width at Wellborn (in) 0 . _n) 0 " . .61 0.300 cp Time (mln) 0 25 50 75 100 125 150 175 200 Height (It) 170 170 170 170 170 170 170 170 170 Half Length (It) 0 849 1449 1976 2460 2915 3346 375g 4157 Net Pmuum (psi) 0 653 732 783 823 854 881 g04 925 Efficiency (%) 100 88 85 83 81 80 79 78 77 Max.50 Avg.48 0.60 0.44 0.64 0. - Table II1 Texaco Frac_o 6-Layer iz-200 cp Time (min) 0 25 50 75 100 125 150 175 Height (lt) 170 367 383 398 404 411 .33 0.55 0.68 0.51 Table 78 Texaco Fracpro GDK Constant Height p.Width lt Wellborn (a) (a) (a) _) 0 .63 0.WidthL at Wellborn 0 25 50 75 100 125 150 175 200 170 315 355 3_' . 1824 2055 2273 2480 Net Pressure (psi) 0 144 113 99 89 83 78 74 71 i t Efficiency (%) lO0 91 89 88 88 87 87 86 86 t Max.Width in Fmc Avg. .Widthat Wellborn _n) 0 - On) 0 .49 0. - Tat_ 19 Texaco Fmcl_rO PKN Constant HelgM p.64 0.71 0.74 t Avg.66 0.Width On) 0 0. - - . Width in Fmc Avg.48 0.67 Avg. too 85 80 76 74 72 71 69 68 0 0.61 0. Wk_ On) Avg.9 164.71 0..39 0. Width (in) 0 0.416 422 Upper Height 85 176 190 201 206 214 220 224 Lower Height 85 191 193 195 195 197 196 198 Haft Length 0 463 751 1000 1233 144.68 0.50 0.71 0.46 0.. Width (in) 0 0.200 cp I t t t t t Time (min) 0 25 50 75 100 125 150 175 200 Height (ft) 170 170 170 170 170 170 170 170 170 ii Haft Length (lt) 0 636 1002 1307 1577 .72 (in) 0 - (in) 0 .68 0.42 0. .60 0.74 Avg.Width in Fmc Avg. .9 1835 Net Pressure (1_) 0 872 915 944 962 976 988 999 Eff_. .55 0.70 0.39 0...3g 0.Width in Fmc (in) 0 0.48 0. . - .392 404 315 426 435 (ft) 85 203 236 254 267 2_ 286 295 302 (ft) es 112 119 123 125 127 129 131 133 (n) 0 521 836 1065 129g 14.64 0. 01 1.6.52 T_le 82 Texaco Fracpro 8.46 0.06 No tlp effects 'Time (min) 0 Height (ft) 170 upper Height Low_ Height ' _ Length 'NM Pressure (psi) 0 Efficiency (%) 100 Max. .42 0... .72 0..96 1.04 ii Time (rain) Height (It) Upper Height (rf) Lower Height (lt) Haft Length (ft) Net Pressure (psi) Efficiency (%) Max.ii.Layer n'.0.4g - .Laye_rn'. k'. .44 0. k'.0.Width at We.35 0.30 552 571 588 602 o5 207 255 285 3! 0 330 348 364 378 a5 207 218 220 220 222 223 224 224 0 283 442 580 704 818 926 1028 1125 0 1251 1234 1235 1240 1250 1257 1263 1270 100 88 85 82 81 79 78 77 76 0 0.Width (in) Avg.40 0. ._ 1308 1603 1802 2020 2234 2440 2636 e.Wio_ in Fmc (in) Avg.Width ' at We.91 0.08 I .bore (n) 85 (n) 85 (n) 0 (_) 0 (_) 0 25 50 75 100 125 150 175 200 250 286 348 360 370 378 385 391 164 186 161 171 t79 186 192 197 92 100 187 189 191 192 193 194 8.O.Width in Fmc Avg._ 930 796 845 876 900 919 934 eo 74 70 67 65 64 63 62 0.bore (in) 0 25 50 75 100 125 150 175 200 170 414 473 505 .I I 0 - 0 .O.05 1.46 0.84 0. - Table 83 Texaco Fracpro 6.5. Wio_ (in) 0 Avg. - " Iii .35 0.. 53 . 54. . 55 . 58 . " lr .. pl . . _ . 4.. .i ...57 . . 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 . .i. o m' o: -= • .80 d. 0 o _. 81 . 82 . 83 d. II Q. . o o _. 84 . 85 . . @7 . 88 . 8g . 90 . 91 0 . o _. o_ II .._.92 0 o _. . II GJ ' . _r .93 1 i i' i. pilr .... ... 94 . 95 C) o: il -=: . 96 . 97 ! II . 98 0 II I . r . 1F. 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 a function of length for cases 5-8. and have not been changed for publication. Holditch & Assoc.A. These profiles were provided by S. + 0 LO 0 0 I.._ "--/ (2) 0 0 fr) ..._aH adn_.12: ZOO klJ klJ.1_ I -_0 I I ! z l I I .+._ejj .....I 0 __! i -r r._ c.._ F..Q I 0 0 _ I 0 Lr). "_ I 0 C) 0 CU 1 LI..I-: (1) .--_ ('r) _ 13_'. _ "_ 0 . f_.) _q6.-"-_ • .) i ._ .108 F--- c_ o I. m m 121 _ u_ _ I ! I ! oU_ ' ! ! I I o" " ._ _ 0 C) . (:1..__ 0 0 CU 0 I..:1. ! ! • CI "_ C) "_ 0 I '_ ..Q I ! I I o_1 m 12z _ _ 1221. I I i t I 1 I I ' I I ! I I ' i 0 Od 4-J _ 1 J I _ C •.. . . n-3 :>. W C::) II _ i . LQ CU_r] C_]_.. • ._. . .-! . LL I-_ 0 . _ _ I I I 0 0 . I 0 0 ' ' 0 J 0 0 i -o 0 0_-_ 0 1 I .L_ I_ "_"CO.. (_) . t_l J : ! I I " I i C) L_4-J _ ' i . __ I. __ ___ (I. . ' _ II ' Illl ' t_li _H6_._ C.._-_ _ ! I I J P Q.lp . _ ..oeJ..c_J 01 I_.111 i I I °.]-1 _.. ..aH 8Jr13.__ u. 0 0 . "_. t i C... • • OJ C> r'-. r _" .._ C'UOJ OJO'J ._-.U o > -re ITJ _ &__ 5_s- __! z e _ N-L_ I_ I . I : _ _ • " . . . . . These profileswere providedby Meyer & Assoc.and have not been changedfor publication.116 Appendix B Width and height profiles for Meyer-1 Figure Bl-B8 give the heightprofilesand width profilescalculated by MFRAC-II (no "knobs")as a function of lengthfor cases 5-8. . 117 . 118 . I . ..119 I I I ' I _1_11 "''' ''m_ a ' . . i _ . . 120 . _ U] 0013 I ! O01 N o oO_ (D -_ rr) __ oZ I I o o OOBOOf:- 8 2 ix . I I 0 0 c_ca ¢G 00 (/_ (I) .) I I I ¢.. cD o_ 0 O0! - .' OOg- Y (I) ._ CII -r " _ >. .121 o ° r'-I I I_ .. . ..I I .. _ ° I ! I I. p-----I q. . 0 0 0 CO ' 'I | ' ' ' |' I ' .---i -4-) ooa ' #.q_ . 122 . 123 . 124 . . i i IJ i 125 Appendix C Width and height profiles for Meyer-2 Figure C1-C8 give the height profiles and width profiles calculated by MFRAC-II ("knobs" on) as a function of length for cases 5-8. ' " " '""_......... i i.. 'M. '. li"" . and have not been changed for publication. _ .. These profiles were provided by Meyer & Assoc.... l__l _-_ I 0 I d I I 00 - o l ..126 L i | j i 0 _--_ I I • r. 127 . 128 . 129 t I . " I I I - ooc- CD I ..--I _.130 0 I ! I . 131 . 132 . 133 . t34 Appendix D Width and height profiles for Advani model Figure D1 givesthe heightprofilescalculated by HYFRAC3D for cases 5-8. Advani of Lehigh Universityand have not been changed for publication. . These profileswere providedby S. 135 0 o 0 . 136 Appendix E Width and height profiles for GOHFER Figure El-E8 give the height profilesand widthprofiles calculatedby GOHFER as a function of lengthfor cases 5-8. These profileswere providedbyMarathon. and have not been changedfor publication. . _.137 0 .¢0 . d 138 . 139 . • 140 0 " " [ 0 . 141 0_ . ._- _ o u • o 0j oI • c. i . I .__ II ___ "un'LIIp!M _I_H 'TI ' ' .a CO C o _-- -0 o o (D -o n __ o OO"" (_ "O j:::: _ _ _ oo :E 'u_ 0 o I 0 CO 2 a W LIo o co d d ..4._ co o" I o! _0_.. .__ u.143 d > • .J T" CD _i "__- _ • 0 o 0 .._.__ O) e- • 0 0 " 0 0 0 ' 0 _ b.._..c::" +" C)1 E .i cu . (1) >" --J ...H6!eH eJnloeJ-. _CD 0 u_ [12 ' . _ 3 . w c_ }.Q qL o 0 0 C_i . . 144 _ -0 o . 145 Appendix F Width and height profiles for ARCO (Stimplan & TerraFrac) Figure F1-F8 give the height profiles and width profiles as a function of length for cases 5-8 using Stimplan. Figure F9 gives the height profile as a function of length for case 8 using TerraFrac. These profiles were provided by ARCO and have not been changed for publication. viii ' . ..r...... t.......* :........ ' ...... b.. ° I ..t. z ' .-*............ 5500 St.....-" ... _. lD e- ........_....o../ .....*lh*...** .... ....... ' _ " _.. ? ..... :_ *H..... = ..146 SIT[ _3 t (3-1age_... .. ess(psi) 758_ -05_J l_iat. ... ".......) Cot.. .. .... !. q.......... \ 6 .-. ii...._.... st. ..... • I ' '...._" ¢ '.. "! i i ! _......- o.... : ' : .l. : . : .llo..* ..." _ _ | . .....-. i .. .. ....i. %... t **..-. i b 0 a a o i * * 0.i-_t ' i s | : _. Uisc...... ' ' ......0 57 in I 0 IU (/) ! 0....... | : e 9488 i • 'i I } • : * - ' i JJ " i......h (in) • ...... ill i ii ... _ ..... i..... 4.. J _ • L_ ' Max _idth.._ '.. ** ........ ' . •..... % % .... ..... 9300 .. • i i.. i 92@0 .__ LL Li..50 7 i 9180 .. _.'r o ! _ e-m t I0 0 I • ' ° o Q. 0 0 ' 0 0 :> . _ + _ ° o') " ! ! -I × W ff'j ' o o .147 T° t' J o o !o o ° o o / . eu E w ! 1 0 0 0 0 ' 0 0 I 0 0 0 0 ! 0 0 . t / 7 . ....... . "! ' ... :' ...........' .. ......_...... .......... " :...... " ..... l ........ i ' ' ' • ' ' ! I . . ...I .....s. .......th (in) ....... " ": '. _ ............ ." ' ' '.. . ... 0...> 9380 .. 'mm _ ___ | .. ... i... != :i ' i l"*_ A............. ... .. .....Uar.. ' • L_... : ° !......... . ............" \. ' ]__.......... '.. " . _.' ..... ' ' ........ .. ' ' :... ' . $2OO I | i ...... =q_ ......................... " . _ .. .... • i i i t..Sg ] | ! | ..: • ' _ ! I . i... ......148 559=0 _Stress(psi) | i= I • J lH ii SFEtt3(3-lager...i.......... ......._.......... • ! ....Visc) 7500 -O50 Hi. o • | ....... le .._ IL If I ...... ..... ! 9108 ...... i ... ..........: t_ Ha× _iathO 65lr........ = I / \ -_ • .. = a f" . "i ! I ... "s.. ' " i .. .... .. ... = ' . .'" '.._i ".... "................ ...... • CD 4) c_ ! l- m_ o t0 "1" LI... ._:.... ..I . o o . • i I . . = r o o . o .149 o o "'ll_ .'- . N ' W i l u_ m L i I i "- 1 o o II) i 9 I o .- 2 e- o o 0 • . o m i / ! i m 0 I io 0 I u °m : ' nu ' mm l ! I I° 0 0 0 _" © > } ni.. | o o I_.L. o '_ O_ o (. Q.. _ o o N o o ¢0 o o _ o 0 It) I o a .0 3 . . .151 _ 8 - 0 • - C} 0 IX) c-I ° _" _J ! _ l r " g 0 ° W " ff'j V-- o lD l i t l __o e. I I I : | I _ o o 0 O_ 00 o 0 0 O_ o C) .'O_ o 0 t'_ 0") o 0 _ O) o 0 _r 01 o C) lc) O_ o 0 _ID O_ o 0 I_. • t . O_ C7_ .- _ ! E l • -_ co LI. ...i . .._.. . i rl . .*oel.o el eee.4.Ilo e e eeeee t . eo eel o e • I • • " o • " at • • o . oe oee .... _. n.....q. e.50 • . e Ploeleleea. ea. . ii i i • • • • • • • • ilo6eee•et • • • • • • • e • • e • • • • e • • • • J • • • o o • • • • e i .pl ' . Ipllelll ip$ eiip el oi le leeoliol 93_ Illllleel eli lpci el lille I oi ii oi ii oil ell ilo oi el el l le $1lip oi I.. L_ tD ..oee eeeoe J eeoo • ooo. • e • i o le lee.lleolee$lll o... • .eeesel eeleeeoe eco el I • • ...l. ef.. ... _ el.. o ..im "rb.78 { e I t ei E e.... • ..li : • • .}. IJee leQeee le • • o e • o 91013 9288 . j. Ii 11. e. I • el Ill.. eo. oa.. .la.. .: i 'i "i"i ..ess (psi) 8500 -0.....152 $F£ #3(5-1age_.l. Uisc) Uar.. . ... Hax 14iat]1 in -. $ I . leela | iii OIIIP i iii"'--"''"--''' ' ii " O' •':i. iiiieloloeleleooeel.. e o o J e . 5588 St_.._ ..• • .i. • e • • el .lP el Oi loeb • eeOlell eoolo$ooe OOOIOOIQI leqJo.iml] .50 Hiclth (in) 0. • _.... ..be .i. .Je collie tOOlo leOee liege lie lie le IqJle$ di eel e e • • • ii oil elolne_ lie li lille til..e L o I : e e e • l • • $ • ' - " • o e • I ii • 1 ! • 9500 ' $ $ i . q .e e• al.e I._eo le. 153 . . 155 Appendix G Width and height profiles for RES Fracpro Figure G1-G8 give the height profiles and width profiles calculated by Fracpro as a function of length for cases 5-8. . These profiles were provided by RES and have not been changed for publication. o o o . 4 .... i 1 i 0 _ 0 .-I I i i i i I I I i i I I ii I i I I -cT) cO --- I 0 IL ¢_I _ .. .. i I I I I I . . I I ..... t. ' i i i 0 _ ID .. 0 0 0 0 (_l) qld_3 . tl e. I I r . . I I-.. -. .. i ..... ....-" .. p.. I i I .. i I T . ' ...157 LLJ o 0 0 (D CO I d /d o 0 0 i I I I I I (_ o_ . ... ........ 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