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lifArticlehistory:Received24October2016Receivedinrevisedform6January2017Accepted10February2017Availableonline21February2017abstractproductionrateisapursuedgoalwhichcouldbeachievedonlythroughwellpatternandwellperformanceoptimization.Yangetal.(2016)statedthatwellplacementoptimizationhaslessef-fectonhomogenousandsimplestructureoilreservoir.However,considerabledifferenceonthefinalprofitswouldbeobservedinheterogeneousandanisotropicreservoirafterwellpatternandwell16).Delalatandmediahasinheteroge-chforincor-ityinproductionevaluations,eachetal.,2013;petroleumengi-neering,earlyoptimizationstudiesoninflowperformancerela-tionship(IPR)featuredsimplereservoirmodelsandlinearprogrammingtechniques(GharbiandMansoori,2005).Guo(2001)proposedpayzonethickness,reservoirrockpermeability,fluidviscosity,wellboreradius,drainageareaandskinfactoraseffectualparametersinIPRpredicationmodel,whenbottomholepressuredataarenotavailable.Hagoort(2007)studiedverticalarrayofperforationsforIPRpredictioninproductionwells.ThismodelwaslatermodifiedbyLuandTiab(2008),whichpresentedsteadystateContentslistsavailableScienceJournalofNaturalGasScienceandEngineering40(2017)277e287E-mailaddress:msoleimani@shahroodut.ac.ir.1.IntroductionTotaloilproductionfromhydrocarbonreservoirgreatlydependsonwelllocations,petrophysicalpropertiesofthereservoirrock,geologicalpropertiesofthereservoir,wellperformanceconditionandotheroperationalparameters.Amongtheseparameters,wellgeometryandwell-patterndesignhavecriticalimportanceonhy-drocarbonfielddevelopment(OnwunaluandDurlofsky,2011).ShadizadehandZoveidavianpoor(2009)statedthatoptimizedperformanceoptimization(Soleimanietal.,20Kharrat(2013)statedthathomogeneityofporoushighestefficiencyinproduction(namely40%),whileneousmediaitdecreasesto37%.Thepracticalapproaporatingimpactofthereservoirheterogenescenarioentailsnumerous(objective)functionrequiringafullsetofreservoirsimulationrun(BalouchiNozohour-leilabadyandFazelabdolabad,2015).DuringapplicationofadvancedmethodsinKeywords:InflowperformancerelationshipMaximumefficientrateHeterogeneousreservoirWellperformanceProductionoptimizationhttp://dx.doi.org/10.1016/j.jngse.2017.02.0171875-5100/©2017ElsevierB.V.Allrightsreserved.Inthisstudy,anintegratedoptimizationprocedurewasproposedforwellperformanceanalysisinaheterogeneousoilfieldfromsouthwestIran.Proposedintegratedstrategyoptimizeswellperformanceinaniterativemanner,whilefluidproperties,geologicalandpetrophysicaldatawereanalyzedseparatelybynewadvancedmethods.Subsequently,integratedsolutionwasintroducedbyintegratingvariouswelltypesgeometryandfinezonationofthetargetformation.Combinationbetweeneachzoneandeachwelltypewasbasedonthreepotentialoilbearingzonespredefinedbywelllogdataanalysis.Targetfor-mation,theSarvakformationlimestone,wasdividedinto10differentzonesandmuchmoresubzonesaccordingtothegeologicalandpetrophysicaldata.Afterwards,17wellswithvariousgeometriesweremodeledintheupscaledreservoirmodel.Fluidpropertiesandreservoircharacteristicswerealsoob-tainedandanalyzedfromdifferentsamplestakenfromtargetformation.Resultsofapplyingthepro-posedintegrationstrategydefinedthatthemaximumproductionrateoccurswhilewatercutdoesnotexceed10%.Performedanalysisalsosuggest15MPaastheoptimalvalueofthesurfacegasliftpressureandstatethatthegasoilratioshouldnotexceedthisratioattheflowingwellsbottomcondition.Sensitivityanalysisontubesizeexpresses4.67-inchestubeastheoptimumvalue.Meanwhile,sensitivityanalysisonflowraterepresentsthatoptimalvalueofthisparametershowshighsensitivitytochangesinproductionindex.Resultsshowedthat7%changeinproductionindexwillmake4%changesinoptimalgasflowratevalue.©2017ElsevierB.V.Allrightsreserved.articleinfoWellperformanceoptimizationforgasheterogeneousreservoirbyfinezonationintegrationM.SoleimaniFacultyofMining,PetroleumandGeophysics,ShahroodUniversityofTechnology,IranJournalofNaturalGasjournalhomepage:www.elsevier.comtoperationinaanddifferentwelltypeatScienceDirectandEngineering/locate/jngsecurvewerealsoevaluatedwithproposingseparateproductivityequationfordifferentwelltypes.Subsequently,performancepre-dictionforthestudyreservoirwasaccomplishedsucceededbyfinalandpseudo-steadystateproductivityequationsforanoff-centerpartiallypenetratingverticalwellinananisotropicreservoir.LuandTiab(2011)alsopresentedpseudo-steady-stateproductivityformulaforapartiallypenetratingverticalwellinabox-shapedreservoir.Bahadorietal.(2013)developedasimple-to-useequa-tionfortheoilflowratepredictionasafunctionofdimensionlesslengthandratioofhorizontaldisplacementwelllengthoverdrainageareasideforvariousdrainageareas.Ahmadietal.(2015)developedaleastsquaresupportvectormachine(LSSVM)modelforpredictingpseudoskinfactorofhorizontalwellsintherect-angulardrainageareausingartificialneuralnetwork(ANN)withlinkedtotheparticleswarmoptimization(PSO).TabatabaeiandZhu(2010)consideredthreedifferentboundaryconditionsforanalyticalIPRpredictioninhorizontalwells.Theseboundarycon-ditionswereconstantboundarypressure(steady-stateflowcon-dition),no-flowboundary(pseudo-steady-stateflow)conditionandinfiniteactingreservoir(transientflow)condition.ThestudyofTabatabaeiandZhu(2010)wascompleteincaseofusingvarioustypesofequationofstatesandboundaryconditions.Duetothesimilarityofthereservoirinthisstudy(thissimilarityreferstothefluidproperty,reservoirrockpropertyandreservoirpetrophysicalcharacteristics)withtheconditionsofwhatwerepresentedbyTabatabaeiandZhu(2010),theirstrategywasusedhereforIPRprediction.However,productionoptimizationprocessrequiresunder-standingoftheactualcharacteristicsofthereservoir(SoleimaniandJodeiri-Shokri,2015).Thesecharacteristicsconsistofreser-voirpetrophysicalproperties,averagereservoirpressure,drainagedata,skinfactor,bottomholeflowpressureandwellheadpressure.Severalmethodswereintroducedtousethesedataforwellper-formanceoptimizationwhichevolutionarystrategiesarecurrentlythemostpopularmethods.SarmaandChen(2008)listedvariousmethodsforwellsystemanalysiswithdifferentalgorithmslikeasstochasticdirections,patternsearches,directsearchesaswellasderivativemethodslikeasfinitedifferencesoradjointgradientestimationmethods.Nozohour-leilabadyandFazelabdolabad(2015)havedrawnacceptableresultbyapplicationtheArtificialBeeColony(ABC)algorithmintheirstudy.DuetothesimilarityofthestudyreservoirinthisresearchwithwhatwasstudiedbyNozohour-leilabadyandFazelabdolabad(2015),thereforetheABCalgorithmwasselectedhereforoptimizingproduction.Toperformnaturalflowanalysisandoptimization,porosityandpermeabilityvaluesmustbeupscaledfromthemeasurementscaletothegrid-blockscale.Thereexistnumerousmethodsforupscal-ingporosityandpermeabilityvalues(Wuetal.,2002;Rekdal,2009;Chen,2009;SharifiandKelkar,2013;Noorbakhshetal.,2014).IlievandRybak(2008)introducedasimplenumericalupscalingapproachbysolvingmultiscaleellipticproblems.Themaincom-ponentsoftheirmethodare:i)localsolutionofauxiliaryproblemsingridblocksandformalupscalingofobtainedresultsforbuildingacoarsescaleequation;ii)globalsolutionoftheupscaledcoarsescaleequation;andiii)reconstructionofafinescalesolutionbysolvinglocalblockproblemsonadualcoarsegrid.Inthisstudy,weusedthenumericalmethodofIlievandRybak(2008)forporosityandpermeabilityupscaling.Afterwardsnaturalfluidflowanalysiscouldbeperformedbydifferentgeometryofproductionwells.However,itshouldbenotedthatvariousbottomholeconditionsanddifferenttubingsizeofeachproductionwellinagasliftedoilfieldwouldcausethegasliftperformancedifferforeachindividualwell.Inotherwords,theproductivityindex(PI)foreachtubingsizemaydifferwhileeachsizemayproducedifferentamountofoilforequalamountofgasinjectedintothem.Therefore,itisrequiredtoperformasensitivityanalysisfordifferenttubingsize.DuetohighaccuracyofnonlineardynamicmodelpresentedM.Soleimani/JournalofNaturalGasScience278bySharmaandGlemmestad(2013),thismethodwasusedfornaturalflowanalysis.ItshouldbeagainemphasizedthatduemanyadvantagesoftheequationintroducedbyLuandTiab(2008),theirequationwasselectedforthisstudy.Theyhavederivedanequationforboxshapedreservoirmodel,whichisappropriatemodelforfinezonationofthestudyreservoir.Theyhavealsoshowedthattheoff-centeroftheproductionwellcouldbeignoredandalsotheequa-tioncouldbeappliedperfectlyforpartiallypenetratedwell,whichisthecasethatwewouldhaveinfinezonationapproach.ThestudyofTabatabaeiandZhu(2010)wascompleteincaseofusingvarioustypesofequationofstatesandboundaryconditions.TheyhaveconsideredthreedifferentboundaryconditionsforanalyticalIPRpredictioninhorizontalwells.Theseboundarycon-ditionswereconstantboundarypressure(steady-stateflowcon-dition),no-flowboundary(pseudo-steady-stateflow)conditionandinfiniteactingreservoir(transientflow)condition.Besidesthat,duetothesimilarityofourwellgeometryandwellconditions,wedecidedtousetheirequationforhorizontalwellsIPRanalysis.Thissimilarityreferstothefluidproperty,reservoirrockpropertyandreservoirpetrophysicalcharacteristics.TheconditionsofTabatabaeiandZhu(2010)forhorizontalwellsareinaccordancewiththeconditionsofLuandTiab(2008)forverticalwells,whichmakeseaseuseoftheintegrationprocedure.2.IntegratedstrategyproposedinthisstudyTabatabaeiandZhu(2010)derivedvariousproductivityequa-tionswithdifferentboundaryconditionsforpartiallypenetratingverticalwell.Sincevarioustypesofproductionwellsaregoingtobecombinedwithfinezonationinthisstudy,equationsderivedbyLuandTiab(2008);TabatabaeiandZhu(2010)andBahadorietal.(2013)wereusedforwellsshowninFig.1.Forbilateralwelltype,weusedequationofBahadorietal.(2013):Jh¼q0PRC0Pwf¼kh141:2b0m00@1lnC18r0erwC19C0A0þSfþSmþSCA;hC0C0þDq01A;(1)sensitivityanalysishereinthisstudy.Yet,alltherequiredstepsandinformationwereperformedandpreparedtopavethewayforwellperformanceanalysisbyanintegrationapproach.Inthisstudy,weproposedanintegratedstrategytoresolveambiguitiesandwellperformanceanalysisofaheterogeneousreservoirfromsouthwestIran.Hence,sincethemainconcernwastostudyoptimizationofthewellperformanceinaheterogeneousreservoir,andweshouldseektomethodologiesthatcouldhandleheterogeneityofthemedia,weproposedanin-tegratedsolutionbycombiningtwostrategiesofusingdifferentwelltypesinboxshapedreservoirmodelcombinedbythinreser-voirzonation.Thusspecificmethodofwellperformanceanalysisinheterogeneousreservoirwasperformedinthefirststep,followedbywellsystemanalysis.Thisintegrationprocedurewasusedtodevelopinflowandtubingperformancecurvesfromresultsofamultiphaseflowsimulator.Pressuredrop,fluidpropertiesandrelatedchangesinwellcolumn,inflowandtubingperformanceandEngineering40(2017)277e287typesFig.1.ProductionwellM.Soleimani/JournalofNaturalGasSciencer0e¼ffiffiffiApr;(2a)Sf¼C0lnC20L4rwC21;(2b)Parametersintheequationsaredescribedinthenomenclaturesection.Byconsideringthepseudo-steady-stateflowforhorizontalwell,thefollowingequationwasused(TabatabaeiandZhu,2010):q0¼ffiffiffiffiffiffiffikkzpbC16PC0PwfC17141:2m0B0"lnffiffiffiAprw!þlnCHC00:75þSþSR#;(3)lnCH¼6:28aIanihC2013C0x0aþC16x0aC172C21C0lnC16sinpz0hC17C012lnC18aIanihC19C01:088;(4)Parametersintheequationsaredescribedinthenomenclaturesection.Forverticalwelltypes,byconsideringthepseudo-steady-stateflow,weusedtheequationintroducedbyLuandTiab(2008):q0¼FDC16kxk1=2yC17LprðPaC0PwÞðmBÞC0QþSpsC1;(5)usedinthisstudy.andEngineering40(2017)277e287279Q¼C182XeYeC1916C0Xw2XeþX2w2X2e!C0C1812pC19lnf4jsin½pð2YwþRwÞC2=ð2YeÞC138jC2sin½pRw=ð2YeÞC138g;(6)Parametersintheequationsaredescribedinthenomenclaturesection.Itshouldbenotedthatalltheaboveequationsarecalcu-latedinaboxshapedreservoirmodel.Fig.2showstheboxshapereservoirmodelforvertical,horizontalanddeviatedwellconsid-eredinthisstudy.Inallthemodels,wellwithlengthL,drainsabox-shapedreservoirwithheighth,lengthXe(xdirection),andwidthYe(ydirection).Intheverticalwells,thewellisparalleltothezdi-rectionwithproductionlengthofLprC20handhorizontalwellsareparalleltothexdirection.Inallthepartofthereservoirbeforeproduction,pressureisuniformlydistributedinthereservoir,equaltotheinitialpressure,Pi.Pressureassumedtobeequaltotheinitialvalueatreservoirconstantpressureboundaries(bottomwaterinthisreservoir)duringproduction.ProductionoccursthroughawellofradiusRw,representedinthemodelbyauniformlinesink.Itisalsoassumedthatthroughtheentirereservoir,asinglephasefluidofsmallandconstantcompressibilityCf,constantviscositym,withformationvolumefactorofbo,flowsfromthereservoirtothewell.Otherminorfluidpropertieswhichareindependentofpressureandgravityforcesareneglectedinperformanceanalysis.Anyadditionalpressuredropscausedbyformationdamage,stimulationorperforationarealsoignored.Itisassumedinthemodelthatalltheboundariesofthebox-shapeddrainagevolumearesealed.Afterdefiningthewellperformanceanalysisequationsandconditions,anoptimizationalgorithmshouldbeselectedforwellsystemper-formanceoptimization.Asitwaspreviouslymentioned,theABCalgorithmwasselectedforthispartofthestudy.Assumingthenumberofoptimizationparametersandxiasasolution,wewouldFig.2.(a)Geometryofwelltypesinaboxshapedmodelandshowingtheparametersofwells.(b)Flowlinestowellandgeometryofsequenceofwellsinthereservoir.Relatedparametersareexplainedinnomenclatures.M.Soleimani/JournalofNaturalGasScience280have:xij¼xmin;jþrand½0;1C138C0xmax;jC0xmin;jC1xi¼ð1;2;3;/;SNÞ;(7)Wherexminandxmaxarerespectivelythelowerandupper-boundariesofparametersforspecificsolution,xi,indimensionj(j¼1,2…D)andrand[0,1]isascalingfactorrepresentingarandomnumberbetween[0,1].TheD-dimensionalsolutionsgeneratedintheinitializationstep(C¼0)aresubjecttorepeatedcycles(C¼1,2…,MCN),(whereMCNstandsformaximumcyclenumber)untilaterminationcriterionissatisfied.Bothglobalaswellaslocalprobabilisticsearch/selectionisimplementedinasingleABCcycle.Thealgorithmisperformingasthefollowing(Nozohour-leilabadyandFazelabdolabad,2015):1.Generatearandomly-distributedpopulationofsolutions(xi)inthesearchspaceXi{1,2.,..,SN}2.Evaluatethenetpresentvalue(NPV)objectivefunctionofsolutionsinstep1.3.Cycle¼14.Producenewsolutions(ni)foremployedbeesandevaluatetheirNPVvalues.5.Foremployedbees,applythegreedyselectionscheme(be-tweenniandxi).6.CalculatetheprobabilityvaluePiforthesolutionxi.7.Assignonlookerbeestothesolutionswithprobabilisticselection.8.Producenewsolutions(ni)foronlookerbeesandevaluatetheirNPVvalues.9.Applythegreedyselectionprocesstoonlookerbees.10.Determinetheabandonedsolutionforthescout,replaceitwitharandomlyproducedsolution(xi).11.Producenewsolutions(xi)forscoutbees,ifnosolutionwasabandoned.12.Memorizethebestsolution,sofar13.Cycle¼cycleþ114.Untilcycle¼MaximumnumberofcyclesTheNPVfunctionthatisusedherecomesasthefollowing:NPV¼Xr0q0C0rpwqpwC0riwqiwð1þbÞtC0ðNoCoþNiCwÞ;(8)Withboundaryconditions:XNiNi¼0qiw¼Qw;XN0N0¼0qpw¼Qo(9)Parametersintheequationsaredescribedinthenomenclaturesection.Afterdefiningthewellperformanceanalysisequationandoptimizationalgorithm,structureoftheintegratedstrategycouldbedefined.Anintegrationofgeologicalandpetrophysicalandwelldatawithfluidpropertieswouldbeusedinreservoircharacter-ization.Subsequently,reservoircharacteristicscombinedwithfinezonationanddifferentwelldatawouldbeusedforwelltypese-lectionforeachzone.Thiscombinationcouldbegovernedbyanyartificialintelligenceorneuralnetworktools.Inthisstudy,anexpertsystemwasusedfortheproposedstrategy.However,duetothefewwellswehadinthisstudy,wecouldnotaffordalargeknowledgebasefortrainingstep.Asmallscaleknowledgebasewaspreparedfordifferen
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