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SPE-28608-PA

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SPE 28608 PA
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ImprovedReservoirCharacterizationinLow-PermeabilityReservoirsWithGeostatisticalModelsD.N.Meehan,SPE,UnionPacificResourcesCo.,andS.K.Verma,SPE,StanfordU.SummaryThispaperisafieldapplicationofmodemgeostatisticalreservoircharacterizationtoacomplex,low-permeabilitygasreservoir.Multiwellhistorymatchingwiththisapproachisshowntobesignificantlybetterthanthosedonewithhistoricalapproaches.Importantopportunitiesforadditionaldrillingwereidentified;however,theseadditionalinfilllocationsrequiredsignificantlylowerwellcoststobecommercial.IntroductionInfi!!drillinghasbeencommerciallysuccessfulinmanylowpermeability,heterogeneousgasreservoirs.Reservoirdiscontinuitieshaveoftenbeensuspectedasafactorinpoorgasrecoveriesonwidespacing.Largeverticalandlateralvariationsinpermeabilitymakeitdifficulttoaccountforpartialdrainageatinfilllocations.Determinationofthenumberofwellsthatmustbedrilledtorecoverthegasandtheeffectsofheterogeneitiesonoptimalwellspacingandfracturelengthisnecessary.Inthispaper,acasehistoryillustratesthepowerofincorporatinghigh-resolution,fine-gridgeostatisticalmodelsinsimulatingreservoirbehavior.Previousreservoir-simulationstudiesprovidedacceptablematchesofflowratesandpressuresbyfairlyarbitraryreductionsinthelog-derivednetpayfortheentirereservoirorawayfromthewell.However,thesemodelsfailedtomatchextendedpressurebuildups.Thebuildupsindicatesignificantlyhighergasin-placeinthereservoirthanisindicatedbysimulationmatchesbasedonsimplerreservoirdescriptions.Thegeostatisticalmodelpresentedhereresultedinexcellentmultiple-wellhistorymatchesandmatchedthelong-termbuildup.Thetechniquesforgeneratingthereservoirdescriptionandreservoir-simulationresultsaresummarized.Predictionsofinfill-drillingsuccesswiththismodelarebetterthanthoseofpriormodels.Predictionsofincrementalgasrecoveriesfrominfilldrillingfromthismodelareconsistentwithobservedresults.Reservoirheterogeneities(specifically,thelateralcontinuityofpermeability)appeartobethemostimportantfactorsincontrollinginadequatedrainageoftheuppermostintervalsinthisreservoir.Theselateralheterogeneitiesappeartobediageneticpermeabilityalterationsthatresultinpartialcompartmentalizationofthemanyindividualsands.Optimalwellspacinginvery-low-permeabilityreservoirshasbeenaddressedbynumerousauthors.WellswithpermeabilitiesintheCottonValleyrange(~0.01md)generallyindicateextremelylong"optimal"fracturelengths(ofteninexcessofI,OOO-ftfracturehalf-lengths).Itisdoubtfulthatsuchfracturescanbecreatedwithoutvastlylargerjobsthanpredictedbyconventionalhydraulic-fracturemodels.Economicapproachesusedinconventionalfractureoptimizationmodelsmaybeinappropriateinthickintervalswithfewstressbarriers.Inadequatebarrierstofracture-heightgrowthandreservoirheterogeneitiesindicatetheneedforcloserspacingandmoderatefracturelengths.Continuedinfilldrillingaccomplishestwothings:namely,increasedaccesstopoorlydrainedportionsofthereservoirwithbetterstimulationsandaccelerationofrecoveriesfromthemostcontinuousportionsofthereservoir.Currentwellcostscanjustifyincrementalrecoveriesatthecurrentspacinglevels;however,significantCopyright1995SOCietyofPetroleumEngineersOriginalSPEmanuscriptreceivedforreviewOct.10,1994.RevisedmanuscriptreceivedApril27,1995.PaperpeerapprovedMay1.1995.Paper(SPE28608)firstpresentedatthe1994AnnualTechnicalConferenceandExhibition.Sept.25-28.SPEReservoirEngineering,August1995gaswillremainunrecovered.Theimportanceofloweringwellcostsisdescribed.GeologyTheCarthage(CottonValley)fieldisinPanolaCountyinEastTexas.TheCottonValleysandstonesoftheCarthagefieldconsistofaseriesofmarineandlagoonaldepositsoverlyingthegentleregionalstructureassociatedwiththeSabineuplift.AtitscresttheCottonValleysectionis1,200ftthick,expandingto1,500ftdowndip.TheCottonValleyintervalincludesvery-fine-grainedsandstones,siltstones,shales,andlimestones.Sedimentsweredepositedbylongshorecurrentsthatdepositedcontinuouscleansandsinashallowmarineenvironment.Shalelaminationsareextensive,resultinginsmallsandmembersranginginthicknessfromafewinchesto10toISft.Boundingshalelaminaearelenticularanddiscontinuous.Diagenesisintheformofcalcitecementationandquartzovergrowth,combinedwithoverburdenpressure,hasdramaticallyreducedporosityandpermeability.Sandporositiesrangefrom2%to12%withmicrodarcy-Ievelpermeabilities.Massivehydraulic-fracturestimulationsarerequiredforcommercialcompletions.PreviousStudiesModemhydraulic-fracturingtechniquesandimprovednaturalgaspricesresultedinrapiddevelopmentoftheCarthage(CottonValley)gasfieldduring1976-79.Attemptstomodelwellperformancefollowedquickly,withwell-testandsimulationstudiesindicatinghydraulic-fracturelengthsmuchshorterthanpredictedbyconventional2Dfracturemodels.In1992,anin-houseteamcompletedonereservoir-simulationstudyontheCarthageGasUnit21(CGU-21)toevaluateSO-acredrillingpotential.Cartesiangrids,withoneofthedirectionsorientedintheexpectedfracturedirection,wereusedwithuniformreservoirproperties.Thereservoirwasdividedintothreenoncommunicatinglayersandonecommunicatinglayer.Ahistorymatchwithwellhead-pressurecontrolswasperformed.Theonlywaythatagoodmatchcouldbeobtainedwasbycompartmentalizingtheupperlayers.MeehanandPennington1andSchell2tookasimilarapproach.Individualflowing-pressuredeclineswerematched;however,themodelpressurecouldnotincreasetotheobservedvalueinWellCGU-21-2whenitwasshutinforanIS-monthpressurebuildup.Simplesingle-layermodelswerealsomadebutrequiredlargedecreasesinnetpayandadecreaseinreservoirpermeabilitywithtime(oranincreaseinskineffect)tomatchproduction.ThisStudyThestudywasdividedintofourstages:(1)analyzingdata,(2)characterizingthereservoironthebasisofgeostatisticalmethods,(3)creatingareservoirmodelfornumericalsimulation,and(4)matchingreservoirandwellperformanceandmakingreservoirperformancepredictions.DataAnalysis.Twotypesofdatawereusedinthestudy:datatoarriveatthegeologicalmodelofthereservoirandproduction/pressuredataforeachwell.Thefirststageoftheprojectconsistedofgatheringalllog,core,productionandpressuredata.Logswererecalibratedandinterpretedonaconsistentbasis,matchingcoredataforporositiesandshalecontent.Flowmeterlogswereavailableatseveraltimesformostwells;individuallayerflowrateswereusedashistorymatchparameters.Flowingtubingpressures,welltests,pressurebuildups,pressuregradientchecks,andproductiondata157werealsointegrated.Wellflowratesandflowingtubingpressureswereusedtocalculatebottomholeflowingpressures.Incorporatingflowinggradientdataimprovedthepressuredropcalculations.GeologicalData.Exhaustivepetrophysicalstudiesofallwellsincorporatingthefullrangeofavailableopenholelogsandcoreanalyseswereconducted.Foot-by-footestimatesofporosity,;shalevolume,Vsh;andwatersaturation,s'v,weremadeandintegratedwithformationtopsandbottom.Analyticalplots(includinghistogram,probability,andscatter)for,Vsh,andSwweremadeforeachgroupandsub-groupofsands.Thisanalysisisusefulforunderstandingfrequencydistributions,detectingcorrelationsbetweenproperties,identifyingoutliers,andprovidingregionalstatistics.Onlyamodestcorrelationexistsbetweenporosityandwatersaturationformostgroupsofsands.Theseplotswerealsousefulinpreparinggeostatisticalsimulationstobeundertakenandinunderstandingthenumerousrealizations.ProductionandPressureData.ThesectiontakenforstudywasaroundCGU-21.Theareacoveredbythestudyis9,000ftinthexdirectionand7,000ftintheydirection(1,446acres).Theareacontains10wellsthathaveproducedfromtheLowerCottonValleysands.Thesurrounding24wellswerenotincludedinthereservoirsimulationmatchbutwereanalyzedforvariogramdevelopmentandgeostatisticalmodeling.Thefirstwell(WellCGU-21-2)inthesimulationareabeganproductioninJan.1979.Thiswellproducedintermittentlyowingtogasdemand.Earlybottomholepressure(BHP)buildupmeasurementsfailedtostabilize.However,wellheadflowingpressureswereavailablefortheentirewellhistoryinadditiontonumerousmeasuredBHP's.MeasuredandmodeledBHP'swereinexcellentagreement,providingconfidenceintheuseofflowingtubingpressureinthesimulationruns.GeostatisticalSimulations.ThegeologicalmodelwasgeneratedwithageostatisticalapproachprovidedbyagroupatStanfordU.basedonthe"Amocodataset."3Thisapproachissummarizedherewithoutextensivediscussionofthegeostatisticalprinciplesinvolved.Thefirststepistogetfaciesdistributions,followedbydeterminationof,Vsh,andSw'Thisinformationisusedtoprovideinitialestimatesofpermeability.Formationtopsforeachintervalaredeterminedbykriging.Vshasafunctionofareallocationanddepthisthefirstattributeaddressed.Followingourstatisticalstudy,weexaminedthespatialcontinuityofeachreservoirpropertyasmeasuredbythevariogram.Variogramsareafirst-ordermeasureofanattribute'sspatialvariability.ComputingtheVariogram.Spatialvariabilityiscommonlymeasuredbythesemivariogram,definedastheaveragesquareddifferencebetweentwoattributevaluesapproximatelyseparatedbyvector:n(h)y(~=(itlL(Xi-y),..........................(I)nh)i=lwheren(h)isthenumberofpairs,XiisthevalueatthestartortailofPairi,andYiisthecorrespondingendorheadvalue.hcanbespecifiedwithdirectionalanddistancetolerances.AsemivariogramisIlormallyusedforthesamevariable(e.g.,twovaluesseparatedbyh).Anotherusefulmeasureofspatialvariabilityistheindicatorsemivariogram.Thisvariogramiscomputedonaninternallyconstructedvariableandrequiresthespecificationofacontinuousvariableandcutofftocreateanindicatortransform.Foraspecificcutoffanddatumvaluetheindicatortransformisdefinedas{IifXi~kcIi=0otherwise'..............................(2)HorizontalandverticalindicatorsemivariogramsofVshforeachgroupofsandswascomputed.Cutoffswerebasedonthecumulativeprobabilitydistributionofthevariable.WidelyavailableGSLIBprograms4wereusedtocomputethevariogramsaswellastoperformallthegeostatisticalmodelingusedinthisstudy.158ModelingtheVariogram.Standardvariogrammodelseasilyfitthedata;examplecomputedandmodeledhorizontalindicatorvariogramsshowtheverticalvariogramofVshforonegroupofsands(Fig.1).Allthewellsinthesimulationstudyareawereusedtodevelopthevariogrammodelsaswellastheoffsetwellswithin3,000ftofthesimulationarea.Formosthorizontalvariograms,asphericalmodelwassufficienttomodelhorizontalvariability,whileacombinationofexponentialandsphericalvariogramswasusedtomodelverticalvariability.Notallcutofflevelsshowgoodhorizontalcorrelation;verticalvariogramsarebettercorrelatedbecauseofthepresenceofshort-scaledata.Datainthex-Yplanearesparselylocatedwiththeminimumdistancebetweentwowellsbeing=900ft.Atsomecutofflevelsamodelwithrange>900ftwasobserved.Forlevelswherethecorrelationrangefromtheavailabledatawasnotobserved,avalueandthatagoodcrossvariogramexisted(atleastintheverticaldirection)forallthegroupsofsands.PorosityrealizationswereinitiallymodeledindependentoftheVshrealizations.ThisapproachdidnotresultinanacceptablecorrelationbetweentheVshand¢>realizations.FollowingtheapproachoutlinedinRef.5,wefoundthatmakingthe¢>realizationsdependentontheVshrealizationswasnecessary.Markov-Bayes6simulationswereusedfor¢>toaccountfortherelationshipbetweenVshand¢>byuseofVshdataassoftindicatordata.Thisapproximatesindicatorcokriging,wherethesoftindicatorcovariancesandcross-covariancesarecalibratedfromthehardindicatorcovariancemodels.ModelingSw,Permeability,andFormationTops.SwvaluesateachgridlocationwereoriginallygeneratedbyuseofMarkovBayessimulationswiththeVshand¢>valuesassoftdatapoints;however,wefoundthatlinearcorrelationsofSwwith¢>andVshreducedcomputationaltimeandgeneratedverysimilarresults.Vsh'¢>'andSwvalueswereusedtodetermineaninitialpermeabilityvalueforeachgridpointwitharelationshipoftheform0900800700.600.50DAD0.300.200.100900800700600.500.400.300.200.10Fig.2-ThreeVshrealizationsofonegroupofsands.SPEReservoirEngineering,August1995k=a2(¢>6/S~Vsh)'...............................(5)whereaisaconstantobtainedbyhistorymatching.Permeabilityvaluesweremodifiedduringthehistorymatch;Fig.4givesatypicalrealizationforpermeability.Formationtopsforindividuallayerswereobtainedwithordinarykriging.NumericalReservoirModelingFine-scalerealizationsofVsh,Sw,¢>'andkwerecomputedatgridnodeswithdimensionsof200x200x5ft(385,875gridpoints).Flowsimulationgridpointlocationshadtobereducedtosolvetheproblemonaworkstationinareasonableamountoftime.ScalingUp.Inthehorizbntalplane,wedecidedtostaywiththe200x200-ftblockdimensions(thescaleatwhichgeostatisticalsimulationwasdone)tokeepenoughblocksbetweeninfillwells.Wedeterminedthatsimulatorperformancewasacceptablewithupto40,000gridblocks(afewhoursperrun),dictatingthelevelofverticalscaleup.LayersweregroupedtolumphighVshcontent(shaly)intervals,reducingthemodelto24layerswith37,800gridblocks.Weusedsimplescaling-uptechniquestocomputeeffectivepermeabilityofthecoarseblocksbecausethereductionfactorwasonly=0.10andadjacentfinelayersofsimilarVshpropertiesweregroupedtogether.Verticalpermeabilitywascomputedbyharmonicaveraging,andhorizontalpermeabilitywascomputedwitharithmeticaveraging.Effectiveporosityofthecoarseblockswasalsocomputedbyarithmeticaveraging.OtherInputParameters.TenCottonValleywellsareinthesimulatedarea.Hydraulicfractureswithincreasedpermeabilitynearthewellblocksweremodeledconventionallywithlocalrefinedgrids.Experimentswithlocalgridsconfirmedthenecessarylevelofrefinementbymatchinganalyticsolutions.Fracturelengthswereobtainedbymatchingthenetpressuresobservedduringthehydraulicfracturetreatments.Severaldifferenthydraulic-fracturemodelswereusedtoestimatexI;eachofthesegavereasonablysimilarresultswhenthenetpressureswerematched.HistoryMatch.Gasproductiondatabywellwasthecontrolparameter,withtubingheadpressure,Ptf,usedasthematchingparameter.Averagemonthlyproductionwasused.WellCGU-21-2hasthelongestproductionhistoryandhasanextendedpressurebuildup.Westartedtomatchthisdrawdownandbuildupperformancetoobtainreasonablepermeabilitymultiplicationfactorsforthewholereservoir.Twotypesofpermeabilitymodifierswereusedinthehis-0.80(J)Ql0.60:l(ij>"0Qln;"30.40Ei:i50.20O.OO~""':!':""'-'-"'-.....-T"""--'-""""--r-'-"'--~""""""-""-0.000.200.400.600.80ActualdataFig.3-ExampleQ-QplotofVshindicatorsimulationusedtoselectrealizations.15927·621·321·621·422·420.618·9Fig.4-Permeabilityrealizationforentirearea.torymatch,global,a,andlocal.Localpermeabilityintherefinedgridnearthewellaccountedforhydraulicfracturing.Afactorof0.13fortheoverallpermeabilityvalues(a,derivedbycorrelation)gaveaverygoodmatchforthepressuredataofWellCGU-21-2.Fracturepermeabilityhadtobereducedwithtime,indicatingpossiblefracturepluggingand/orproppantcrushing.Theclosematchofeachofthetransientdrawdownperiods(followingtheshut-ins)confirmedthedecreasingfracturepermeability/widthproduct.Fig.5illustratesthehistorymatchofWellCGU-21-2.TheupperportionofFig.5comparestheflowingtubingpressurescalculatedfromalltestpointsandtheextendedpressurebuildupwiththesimulatedvaluesofBHP.ThemeasuredBHPvalueshavebeenconvertedtosurfacevaluesforcomparisonwiththesimulatedvaluesinFig.5.Thelowerportionofthefigurecomparestheactualflowrates(basedprimarilyonaveragemonthlyproduction)enteredintothemodelandeachreportedwelltest.Virtuallyallthediscrepanciesinthepressurematchcanbeunderstoodbycomparingthetestdataandmonthlyproduction.Onseveraloccasionsfollowingashortshut-inperiod,thetestproductiondataaresignificantlyhigherthanthemonthlyaverageproductionusedtocontrolthemodel.Intheseinstances,modelpressurese
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