Accurate Simulation of Non-Darcy Flow in Stimulate

SPE132093AccurateSimulationofNon-DarcyFlowinStimulatedFracturedShaleReservoirsBarryRubin,SPE,ComputerModellingGroupLtd.Copyright2010,SocietyofPetroleumEngineersThispaperwaspreparedforpresentationattheSPEWesternRegionalMeetingheldinAnaheim,California,USA,27–29May2010.ThispaperwasselectedforpresentationbyanSPEprogramcommitteefollowingreviewofinformationcontainedinanabstractsubmittedbytheauthor(s).ContentsofthepaperhavenotbeenreviewedbytheSocietyofPetroleumEngineersandaresubjecttocorrectionbytheauthor(s).ThematerialdoesnotnecessarilyreflectanypositionoftheSocietyofPetroleumEngineers,itsofficers,ormembers.Electronicreproduction,distribution,orstorageofanypartofthispaperwithoutthewrittenconsentoftheSocietyofPetroleumEngineersisprohibited.Permissiontoreproduceinprintisrestrictedtoanabstractofnotmorethan300words;illustrationsmaynotbecopied.TheabstractmustcontainconspicuousacknowledgmentofSPEcopyright.AbstractUnconventionalshalegasreservoirsrequirestimulationviahydraulicfracturingofpre-existingfracturenetworksforpracticalexploitation,creatingastimulatedreservoirvolume(SRV).WithintheSRV,gasflowfromthenano-Darcyshaletothecomplexstimulatedfracturenetworkhasbeenmodeledinreservoirsimulatorsusingavarietyoftechniqueswhichupscale/simplifythefracturenetwork.Thesimulationtechniquesusedinthepastwerenormallynotcomparedwithreferencesolutions.Thisworkinvestigatesusingfinely-griddedsinglewellreferencesolutions(approximately6-14millioncells)forsimulatingDarcyandnon-DarcyflowwithinanexplicitlymodeledSRVcomplexfracturenetwork,in2-D,withandwithoutprimaryhydraulicfractures,aswellasscenarioswhichmodelstresssensitivepermeabilityandlaterre-stimulationofahorizontalwell.Thenetworkfracturesusecellswhichareonly0.001ft.wide.ThereferencesolutionsarecomparedwithstandarddualpermeabilityandMINC(multipleinteractingcontinua)dualcontinuamodelsaswellasnovelmodelswhichsimulateflowinsideoftheSRVusingcoarse,logarithmicallyspaced,locallyrefined,dualpermeabilitygrids,andsimulateflowoutsideoftheSRVusingunrefineddualpermeabilitygrids.Thesecoarsemodelscanberuninminutesonstandardhardware,whereasthereferencemodelscantakedaystorunonthesamehardware.WewillshowthatexcellentmatchestothereferencesolutionsarepossibleusingamodestnumberofrefinementstosimulatetheflowwithintheSRVwhenthefracturepermeabilityandthefractureForchheimernumber(fornon-Darcyflow)arescaledasdescribedinthepaper.Thesetechniquesallowtheuseof2.0ft.widefractureconduitstomimicnon-Darcyflowin0.001ft.widefractures.Goodagreementbetweenthereferenceandcoarsemodelsareobservedevenduringtheearlyflowperiodofthereservoir.IntroductionTherehavebeenmanyrecentpapersdiscussingthemodelingofgasproductionfromunconventionalshalegasreservoirs.WorkbyMayerhofferetal.1andCipolla2aretwoexcellentexamples.Theydiscussusingnumericalsimulationofexplicitfracturenetworkscreatedinastimulatedreservoirvolume(SRV)tomodelthephysicsofflowwithinafracturedshalereservoir.Thesepapersdiscussedthesimplificationsmadeinordertoproducereasonableresultsandnoted(1)theneedtomodelfracturesexplicitlyattheirtruewidth(ontheorderof0.001ft.)whenaccountingfornon-Darcyflow.Itisthislastrequirementwhichcanmakethesimulationofsuchsystemsadauntingtask.Thesesimulations,withexplicitfracturerepresentation,uselargedetailedgridsandrequiresignificantexecutiontimesduetoboththelargenumberofcellsusedandthesmallsizeoffracturecellsused.Theultimategoalofthisworkistoproducepredictivefracturedshalegassimulationmodelswhichareeasytosetupandthatruninminutesratherthanhoursordays.Thesepredictivemodelswouldbesmallenoughtobequicklyrunwhileactuallystimulatingthereservoirand/orbeusedinhistorymatching/optimizationsoftware.Itiseasytoproposepotentialmodels,butinordertoensuretheaccuracyofthesimplifiedmodels,itisnecessarytocomparethemwithextremelyfinegridreferencesolutionswhicharecapableofmodelingfractureflowusingcellswhicharenolargerthanthewidthofactualfractures,andflowintothefracturefromthematrixusingcellssmallenoughtoproperlycapturetheverylargepressuredropsinvolved.Thesimplifiedmodelsmustbeabletoreproducethefracturedshalegasreferencesolutionsortheywouldnotbepredictive.Thereforethefirstgoalofthisworkistoproducerealisticreferencesolutions.Thisstudyconsidersonly2-Darealmodelsduetomodelsizeconstraintsandassumesonlygasismobile.Thereferencesolutionsneedtomodeltheflowintothefracturesandthroughthefracturesveryaccurately.Theyrepresentthefracturenetworkusingagridwhichmodelsthefracturesexplicitly2SPE132093using0.001ft.widegridcellsandtheshaleusingalargenumberofcellswhosesizeincreaseslogarithmicallyaswemoveawayfromthefracturetoproperlysimulatethelargepressuredropbetweenmatrixandfracture.Obtainingthissortofaccuracycomesatthecostofusingalargenumberofsimulationcells(5-14millionorsoin2-D).Inthisworkwecomparetheresultsofthereferencesolutions(whichtakemanyhoursofsimulationtime)toanumberofdifferentsimplifiedgrids(whichtakeminutesofsimulationtime).WecomparedualpermeabilitymodelsandMINC(multipleinteractingcontinua)modelswiththereferencesolutions.Weinvestigatetheuseofanewdualpermeabilitybasedtechniquewhich,with