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HowmuchstimulatedresepermeabilitycouldenhanceSalamAl-Rbeawi*METU-NorthernCyprusCampus,CyprusarticleinfoArticlehistory:Received13February2017Receivedinrevisedform13August2017Accepted15August2017Availableonline1September2017Keywords:UnconventionalreservoirsStimulatedreservoirvolumeUnderstandingtheimpactofasymmetricalstimulatedreservoirvolumesonreservoirperformance.3)theentirelifeofreservoirinterestingpointsinSRVscomparedtoer,atearlypro-ofassymmetricitytheassymmetricity.Allrightsreserved.1.IntroductionTheconceptofstimulatedreservoirvolume(SRV)hasbeenrecentlyreportedintheliteratureasacrucialparameterfor*Correspondingauthor.ContentslistsavailableJournalofNaturalGasScienceJournalofNaturalGasScienceandEngineering46(2017)764e781E-mailaddress:salam@metu.edu.tr.Developinganalyticalmodelsfordifferentlinearflowregimesthatcoulddevelopduringreservoir.4)Comparingtheproductivityindexfordifferentstimulatedandun-stimulatedvolumesassumingbothsymmetricalandasymmetricalreservoirvolume.Themostthisstudyare:1)ProductivityindexdropssignificantlyforthecaseofasymmetricalsymmetricalSRVs.2)TheSRVenhancesproductivityindexmorethanUSRV,howevductiontime,thereisnoimpactforbothofthemonproductivityindex.3)Theimpactisseenatallproductiontime.4)Flowregimetypesarenotchangedwithrespectto©2017ElsevierB.V.pressurebehaviorinunconventionalreservoirsandconsidersvariableSRVsandUSRVs.Thismodelin-cludesstimulatedmatrixpermeability,non-Darcyflowimpact,andhydraulicfractureconductivity.2)StimulatedmatrixpermeabilityFracturedformationsReservoirmodelingReservoirperformancehttp://dx.doi.org/10.1016/j.jngse.2017.08.0171875-5100/©2017ElsevierB.V.Allrightsreserved.rvoirvolumeandinducedmatrixunconventionalreservoirperformanceabstractThispaperinvestigatestheimpactsofstimulatedreservoirvolume(SRV)onreservoirperformanceforunconventionalhydraulicallyfracturedformations.ItfocusesalsoontheeffectsofdifferentpetrophysicalpropertiesofSRVaswellasdifferentvolumeandpetrophysicalpropertiesofunstimulatedpartofporousmedia(USRV).Theinfluencesofhydraulicfractureconductivity,fractureassymmetricity,andnon-Darcyflowpermeabilityinreservoirpressureprofilehavebeensubstantiallystudiedinthispaper.Stimulatedreservoirvolumerepresentsthevolumeofporousmediawherecomplexnetworkstructuresformedfromnaturallyinducedfractures,multiplehydraulicfractures,andoriginalmatrix.SRVischaracterizedbyaninducedorastimulatedmatrixpermeabilitywhichistypicallygreaterthantheoriginalmatrixpermeability.Theformationsofinterest,inthisstudy,areconsideredhavingeitherstimulatedreservoirvolumeonlyorbothstimulatedandun-stimulatedreservoirvolumesanddepletedbymultiplehydraulicfracturescontrolledbynon-Darcyflow.TheimpactsofSRVandUSRVonpressuredistributions,flowregimes,andproductivityindiceshavebeenstudiedusingmulti-linearflowregimesapproach.Anewanalyticalmodelhasbeenproposedinthispaperforpressurebehaviorofahorizontalwellintersectedbymultiplehydraulicfracturesassumingsymmetricalandasymmetricalstimulatedreservoirvolumes.Thismodelwasdevelopedusingmulti-linearflowregimesapproachwithanadjustmentforvariableSRVsandUSRVs.Thevolumeofstimu-latedpartinthereservoirisdeterminedbyhydraulicfracturehalflength,numberoffracturesandspacingbetweenthem,andfractureheight.Theimpactofinducedorstimulatedmatrixpermeabilityinthestimulatedreservoirvolumeandfractureconductivityaswellasnon-Darcyflowimpactonpressurebehaviorshavealsobeeninvestigated.Severalanalyticalmodelsforflowregimes,expectedtodevelopduringtheentireproductionlifeofreservoir,werealsoproposedinthisstudy.Asetoftype-curveswasdesignedforpseudo-pressurenormalizedrateandpseudo-pressurenormalizedcumulativeratewithproductiontime.Theoutcomesofthisstudycanbesummarizedas:1)Generatingananalyticalmodelthatdescribesjournalhomepage:www.elsevier.com/locate/jngseatScienceDirectandEngineering½kðyDÞ¼kiatyD¼wD=2C138,thenEq.(1)canbere-written:maximizingreservoirperformance.ItwasintroducedforthefirsttimebyFisheretal.,(2004)andpresentedasatechniquetocorrelatemicroseismicimagestowellperformanceintheBarnettshale.Themainreasonforintroducingthisconceptisthefailuresinreservoircharacterizationprocessresultedbyapplyingthebi-wingplanefracturewhichwasusedbyseveralresearchesattheearlydaysofhydraulicfrackingstimulation.AccordingtoCipollaandWallace(2014),theconceptwasdevelopedtoprovidesomequantitativemeasureofstimulationeffectivenessintheBarnettshalebasedonthesizeofmicroseismicimage.SRVisdefinedasthepartoftheporousmediawherefracturenetworksarecreatedbystimulationprocess.Thesenetworksconsistofhydraulicfracturesaswellasnaturallyinducedfracturesimbeddedinsidetheoriginalmatrixtexture.Inshalereservoirs,stimulatedreservoirvolumeisdeterminedtheoreticallybythefracturelength,fractureheight,andthespacingbetweenfractures.Practically,itisdeterminedasthesizeofcreatedfracturenetworkwhichcanbeapproximatedasthe3Dvolumeofmicroseismic-eventcloud(Mayerhoferetal.,2010).Unfortunately,therelationshipbetweenSRVandhydraulicfracturegeometrybasedonthesizeofmicroseismicimagesisnotverywellestab-lishedsincetheseimagesmaycaptureonlysmallportionofoveralldeformationcausedbyfrackingprocess(MaxwellandCipolla,2011;Warpinskietal.,2013).Microseismicimagesmayprovidegoodestimationsforfractureheight,fracturehalflength,andfracturelocation(GauravandKashikar,2015),buttheycan'tpro-videgoodinsightsforfracturestructure.Theseimagescan'tdetermine,forexample,thedistributionofproppantinsidehy-draulicfracturesandthusthevariationofconductivityalongfrac-turehalf-length(FungandDu,2016)aswellashowmuchthematrixpermeabilityhasbeenstimulated.Stimulatedreservoirvolumeischaracterizedbyinducedorstimulatedmatrixpermeabilityresultingfromhydraulicfrackingprocess.Thispermeabilityis,ingeneral,greaterthantheintrinsicpermeabilityoftheoriginaltextureofporousmediabetweenfractures.Itisnotconstantalloverthestimulatedreservoirvolume,butitchangeswiththedistancefromhydraulicfractures.ItmovesfromthemaximumvalueðkiÞclosetothefracturefacetotheminimumvalueðkmÞ,originalmatrixpermeabilitybeforestimu-lation,attheinterfacebetweentwofractures.Fuentes-Cruzetal.,2014andFuentes-CruzandValko2015,suggestedexponentialandlinearrelationshipsbetweenthetwovaluesofmatrixstimu-latedpermeability.Notonlythevolumeofbothstimulatedandun-stimulatedporousmediaandhowmuchtheoriginalmatrixhasbeenstimu-latedcouldinfluenceunconventionalreservoirperformance,butalsohydraulicfracturefeaturesaswellastheflowpatterninsidethesefracturescouldalsohaveconsiderableeffectsonperfor-mance.Fractureconductivityisoneofthesefeatureswhichhasimportantroleindeterminingpressuredropalonghydraulicfrac-tures.Itisthemeasurefortheeasinessofflowthatthefluidcouldundergoinsidefractures.Itisnotconstantalongthefracture,butithasavariablevaluechangesfromthemaximumoneclosetothewellboretotheminimumoneclosetothefracturetip(LuoandTang,2015).Fracturedimensionsarealsokeyparametersinpres-surebehaviorinsidehydraulicfractureandinthestimulatedporousmedia.Needlesstosaythatfracturehalf-lengthandthegrowingheightduringstimulationdeterminethestimulatedreservoirvolume.Severalresearcheshaveindicatedtherelationshipbetweenfractureconductivityandflowpatterninsidehydraulicfracture(Martinsetal.,1990;Vincentetal.,1999;Settarietal.,2000;ZengandZhao,2008;ZhangandYang,2014).Accordingtotheirstudiesandlaboratoryexperiments,non-DarcyflowhasbeenrecognizedS.Al-Rbeawi/JournalofNaturalGasScienceasthedominantflowpatterninsidefracturesduetobothnarrowkðyDÞ¼kmþðkiC0kmÞC0eC0bwD=2C0eC0byeDC1eC0byD(2)Forananalyticalsolutionofpressuredistributionintheporousmedia,theaveragestimulatedmatrixpermeabilitycanbeusedwhichiscalculatedatthemid-pointofanindividualfracturecrosssectionareaofflowandhighfractureconductivity.Thesetwoparametersworktogethertoincreasethevelocityoffluidinsidehydraulicfractureswhichinturnleadstosignificantincreaseintheinertialforces.Increasingtheinertialforcesmaysetuptheenvi-ronmentfordevelopingnon-Darcyflow.2.StimulatedmatrixpermeabilityReservoirmatrixinunconventionalreservoirsrespondsforstimulatingprocessbyinitiatinghydraulicfracturesanddevelopingcomplexfracturenetworkinthevicinityofthefractures.Thesenetworksarerepresentedbythestimulatedreservoirvolumeandcharacterizedbytheexistenceofstimulatedmatrixpermeability.Fig.1showsthemicroseismicsurveyforsevenhydraulictreat-mentsinthelowerBarnettshale(Fisheretal.,2005).ItcanbeseenclearlyfromthismicroseismicmapviewsevenSRVshavingdifferentcharacteristicssuchasdifferentvolumesanddifferentstimulationimpactsintheporousmedia.Geomechanicalconditionsmayhavesignificantimpactonstimulatedreservoirvolumecharacteristics.Thedensityofnaturalfracturesthatcouldbeintersectedbythepropagatedhydraulicfractureineachvolume,andtheangelofintersectionbetweennaturalandhydraulicfracturesaswellasthedifferencebetweentheminimumandmaximumstressmagnitudesandthemaximumstressorientationimpactthegrowthofthehydraulicfractureineachfrackingstage(SuppachoknirunandTutuncu,2016a;Suppachoknirunetal.,2016b)andhencethevolumeofstimu-latedporousmedia.However,inthisstudy,theimpactofthegeomechanicalconditionsisconsideredbythechangesinthematrixpermeabilityofstimulatedreservoirvolumewiththedis-tancetotheno-flowboundary.Additionally,thepermeabilityofSRVsisassumedtobegreaterthanthepermeabilityofUSRVsduetotheeffectofinducedmicrofracturesintheSRVsresultedfromthechangesinthestressdistributioncausedbyfrackingprocess.Therefore,theconceptofstimulatedreservoirvolumeanditspet-rophysicalpropertiesmayeliminatethenegativeimpactoftheassumptionofplannergeometryofhydraulicfractures.Fig.2illustratesthechangeinthematrixpermeabilitycausedbyfrackingprocess.ThemaximumvalueofthestimulatedmatrixpermeabilityisobservedclosetothefracturefaceðyD¼wD=2Þandtheminimumstimulatedmatrixpermeabilitycanbeassumedequalstotheoriginalmatrixpermeabilityattheno-flowboundarybetweenadjacentfracturesðyD¼yeDÞ.Usingtheexponentialapproximation,thestimulatedmatrixpermeabilityatanypointinthestimulatedreservoirvolumecanbeformulatedasfollows:kðyDÞ¼kmþaeC0byD(1)whereðkmÞistheoriginalmatrixpermeability,ðaÞandðbÞareconstantsdependonreservoirtypeanditsgeomechanicalprop-erties.Assumingthatthestimulatedmatrixpermeabilityequalstheoriginalmatrixpermeabilityattheno-flowboundarybetweenadjacentfracturesi.e½kðyDÞ¼kmatyD¼yeDC138andequalsthemaximumstimulatedmatrixpermeabilityatthefracturefaceandEngineering46(2017)764e781765spacingi.e.ðyD¼yeD=2Þ:S.Al-Rbeawi/JournalofNaturalGasScience766kavg¼kmþðkiC0kmÞC0eC0bwD=2C0eC0byeDC1eC0byeD=2(3)yeD¼yexfr(4)yD¼yfxfr(5)wD¼wfxfr(6)Fig.1.MicroseismicsurveyforsevenhydraulicfracturingtreatmentsFig.2.StimulatedorinducedreservandEngineering46(2017)764e781where:ðyeÞisthedistancetoreservoirouterboundaryintheY-direction,ðyfÞisthespacingbetweentwoadjacentfractures,ðwfÞisthehydraulicfracturewidth,ðxfrÞisthereferencehydraulicfracturehalf-lengthandisconsideredasthelongestfracturehalf-lengthinthisstudy.3.Non-DarcyflowimpactItiswellknownthatthedeliverabilityofhydraulicfracturesisveryhighduetothebigsurfaceareaprovidedbyfracturesforreservoirfluidtomovefromporousmediaintothefractures.Therefore,thevelocityoffluidinsidehydraulicfracturesisgrowinggraduallyasthefluidmovestowardshorizontalwellbore.IncreasingthevelocityleadstoincreasetheinertialforceswhichininlowerBarnettshale(Fisheretal.,2005).oirmatrixpermeability.turncausessharpincreaseinthepressuredrop.Thisenvironmentismostsuitablefornon-DarcyflowtodevelopwhereinDarcylawmaynolongerbeapplicable.Severalsolutionshaveaddressedtheimpactofnon-Darcyflowinsidehydraulicfractureonpressurebehaviorofunconventionalreservoirs.OneofthesesolutionshasbeensuggestedbyBarreeandConway(2004),2009andfocusedonintroducinganewmodelforthepressuredropinsidehydraulicfractures.ThismodelincludestheconceptofminimumfracturerelativepermeabilityðkmrÞwhichisdefinedastheratioofmini-mumfracturepermeabilityðkfmÞduringnon-DarcyflowtotheDarcyflowfracturepermeabilityðkfÞ.Mathematically,itis:kmr¼kfmkf(7)Thepressuredrop,accordingtoBarreeandConwayapproach,insidehydraulicfracturescanbeformulatedas:vPvx¼mqf2wfhfkfd(8)where:ðqfÞishydraulicfractureflowrate,ðwfÞisthefracturehalfwidth,ðhfÞisfractureheight,ðmÞisreservoirfluidviscosity,andðdÞisnon-DarcyflowpermeabilitycoefficientwhichwasproposedbyBarreeandConwayas:d¼kmrþð1þkmrÞC181þrvmtC19(9)where:ðrÞisreservoirfluiddensity,ðvÞisfluidvelocity,andðtÞischaracteristiclengthcanbedeterminedbynon-linearregressionanalysisofactuallabapparentpermeabilitydata(BarreeandConway,2004).Indimensionlessunits,non-DarcyflowpermeabilitycoefficientðdÞiswrittenas:d¼kmrþð1þkmrÞð1þFNDÞ(10)where:ðFNDÞisnon-Darcyflownumberandmathematicallydefined:FND¼rQscBg2mtwfhf(11)where:ðQscÞisthetotalsurfacegasproduction,andðBgÞisthegasformationvolumefactor.Totalwellborepressuredropinfracturedreservoirsisaffectedalsobyhydraulicfractureconductivity.Physically,fracturecon-ductivityisameasureoftheeasinessofflowinsidefractures,therefore,thehighertheconductivity,thelowerthepressuresdropis.Mathematically,itisdefinedas:FCD¼kfwfksrvxf(12)where:ðksrvÞisthestimulatedreservoirvolumepermeabilitywhichcanbeconsideredequaltoðkavgÞcalculatedbyEq.(3),ðxfÞisthefracturehalf-length.ForDarcyflow,fractureconductivityisnotconstantalonghy-draulicfractures.Itchangesfromthemaximumvalueclosetothewellboretotheminimumvalueatthefracturetip(LuoandTang,2015).However,non-DarcyflowcouldreducetheconductivityS.Al-Rbeawi/JournalofNaturalGasScienceespeciallythemaximumvaluewhenthisflowreachesitsmaximumimpactclosetothewellbore.Therefore,thereissmalldifferencebetweenfractureconductivityatthefracturetipandclosetothewellbore.Guppyetal.,1982statedthatthisdifferencedoesnothavesignificantimpactonpressurebehaviorsandflowregimesforfracturedformationandsuggestedusingequivalentconductivityintheflowequations.4.MathematicalmodelingConsiderarectangularunconventionalreservoirwithtwosideboundariesð2xe&2yeÞheightisðhÞasshowninFig.3.Theforma-tionisstimulatedbymultiplehydraulicfracturespropagatingtoacertaindistancefromahorizontalwellbore.Thedrainageareawherethefracturespropagateiscalledstimulatedreservoirvol-ume(SRV).Theouterdrainageareaofthereservoirdoesnotun-dergothestimulationprocess;therefore,itiscalledun-stimulatedreservoirvolume(USRV).TheintrinsicpropertiesofUSRVareðkm;∅mÞðpermeabilityandporosityrespectivelyÞ;whiletheintrinsicpropertiesofSRVareðksrv;∅srvÞ.Thedimensionsofhy-draulicfracturesareðxf;hf;wfÞwhereðxfÞisfracturehalf-length,ðhfÞisthefractureheight,andðwfÞisthefracturehalf-width.Thefracturesareassumedfullypenetratingtheformationinthever-ticaldirectioni.e.formationthicknessisequaltofractureheightðh¼hfÞ.TheSRVshavedifferentvolumes,differentfracture-halflengthðxfÞandfracturespacingðyfÞ,andtheyasymmetricallypropagateintheporousmedia.Accordingly,theflowratesofhy-draulicfracturesarenotequal.Wellborepressurebehaviorforthissystemcanbecalculatedusingthefollowingmodel:PwfD¼Xi¼ni¼1qDiPDFi(13)where:ðnÞisthenumberofhydraulicfractureinthesystem,ðqDÞisthedimensionlessflowrateofindividualhydraulicfractureanddefinedbytheindividualfractureflowrateðqf;Mft3=DayÞ,totalsurfaceflowrateðQsc;MSCF=DayÞ,andgasformationvolumefactoredðBg;ft3=SCFÞ.Mathematically,itis:qD¼qfQscBg(14)ThepressuredropineachhydraulicfractureðPDFÞ,mentionedinEq.(13),shouldbeestimatedforeachfractureconsideringthevolumeofstimulatedpartofreservoirinthevicinityofthisfrac-ture,itsfractur
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