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IFACPapersOnLine50-1(2017)11275–11280ScienceDirectAvailableonlineatwww.sciencedirect.com2405-8963©2017,IFAC(InternationalFederationofAutomaticControl)nullnullinnullnullnullnullnullernulldnullAllrinulltnullrenullrnulldnullnullerrenullenullunderrenullonnullnulllitnullofInternationalFederationofAutomaticControlnull10null016nullnullfacolnull017null8null632©2017,IFAC(InternationalFederationofAutomaticControl)nullnullinnullnullnullnullnullnullernulldnullAllrinulltnullrenullrnulldnull10null016nullnullfacolnull017null8null6322405-8963Anadaptiverobustoptimizationschemeforwater-floodingoptimizationinoilreservoirsusingresidualanalysisstarM.MohsinSiraj∗,PaulM.J.VandenHof∗andJanDirkJansen∗∗∗ElectricalEngineering,ControlSystemsgroup,EindhovenUniversityofTechnology,TheNetherlands.(e-mails:m.m.siraj,p.m.j.vandenhof@tue.nl).∗∗DepartmentofGeoscienceandEngineering,DelftUniversityofTechnology,TheNetherlands.(e-mail:j.d.Jansen@tudelft.nl)Abstract:Model-baseddynamicoptimizationofthewater-floodingprocessinoilreservoirsisacomputationallycomplexproblemandsuffersfromhighlevelsofuncertainty.Atraditionalwayofquantifyinguncertaintyinrobustwater-floodingoptimizationisbyconsideringanensembleofuncertainmodelrealizations.Thesemodelsaregenerallynotvalidatedwithdataandtheresultingrobustoptimizationstrategiesaremostlyofflineoropen-loop.Themainfocusofthisworkistodevelopanadaptiveoronlinerobustoptimizationschemeusingresidualanalysisasamajoringredient.Themodelsinanensembleareconfrontedwithdataandanadaptedensembleisformedwithonlythosemodelsthatarenotinvalidated.Asanextstep,therobustoptimizationisagainperformed(i.e.,updated/adjusted)withthisadaptedensemble.Theadaptedensemblegivesalessconservativedescriptionofuncertaintyandalsoreducesthehighcomputationalcostinvolvedinrobustoptimization.Simulationexampleshowsthatanincreaseintheobjectivefunctionvaluewithareductionofuncertaintyonthesevaluesisobtainedwiththedevelopedadaptiverobustschemecomparedtoanopen-loopofflinerobuststrategywiththefullensembleandanadaptiveschemeusingEnsembleKalmanFilter(EnKF),whichisoneofthemostcommonparameterestimationmethodsinreservoirsimulations.Keywords:Uncertaintyhandling,water-floodingoptimization,residualanalysis,onlinerobustoptimization1.INTRODUCTIONDynamicoptimizationofthewater-floodingprocesshasshownsignificantscopeforimprovementoftheeconomiclife-cycleperformanceofoilfieldscomparedtoamorecon-ventionalreactivestrategy,seee.g.,BrouwerandJansen(2004);Jansenetal.(2008);Foss(2012);VandenHofetal.(2012).Besidescomputationalcomplexity,inducedduetocomplexnon-lineardynamicsandhencenon-convexity,oneofthekeychallengesinthismodel-baseddynamicoptimizationisthehighlevelsofuncertaintyarisingfromthemodelingprocessofwaterfloodingandfromstronglyvaryingeconomicconditions.Variousapproachestodecisionmakingunderuncertaintycanbeimplementedintwodifferentways,seee.g.,Bert-simasandThiele(2006).Inopen-looporofflineschemes,robustoptimizationisperformedonlyonceunderagivendescriptionofuncertainty.Robustoptimizationcanalsobeusedinanadaptiveoronlinefashionwheretheun-certaintyisreducedwiththeinformationthatisrevealedovertime.Ageneralpracticeofquantifyinguncertaintyinwater-floodingoptimizationisascenario-basedapproachwhereanensembleofuncertainparameters(e.g.,reser-starTheauthorsacknowledgefinancialsupportfromtheRecoveryFactoryprogramsponsoredbyShellGlobalSolutionsInternational.voirmodels),seee.g.,VanEssenetal.(2009);Capoleietal.(2013)isconsidered.Thesemodelsaremostlyeithergeneratedbyusinggeostatisticaltools,seee.g.,MariethozandCaers(2014)orhanddrawn,andaretypicallynot(in)validatedbytheproductiondata.Hencetheymayprovidea(very)conservativedescriptionofuncertainty.Anadaptivescheme,i.e.,Closed-LoopReservoirManage-ment(CRLM)hasbeenintroducedinJansenetal.(2005),wherethereservoirmodelvariables(statesand/orparam-eters)areupdatedusingdataassimilationorComputerAssistedHistoryMatching(CAHM)techniques,suchasEnsembleKalmanFilter(EnKF),variationalapproaches,etc.,seee.g.,Evensen(2009);Aanonsenetal.(2009);OliverandChen(2011)andtheoptimizationisadaptedwithupdatedmodel(s).Intherobustsettings,asrobustoptimizationusesanensembleofmodelrealizations,pos-teriorensemble,e.g.,estimatedbyEnKF,canbedirectlyusedinanadaptivefashionresultinginarobustCLRM,seee.g.,Chenetal.(2009),Chenetal.(2010),Capoleietal.(2013).Thepurposeofthisworkistodeviseanadaptiverobustschemethatcanbeupdatedwiththegivenproductiondata.Themainfocusistoaddressthequestion:howtheavailableinformation(data)withtimecanbeusedtoshrinktheuncertaintyspacebyselectingfewernumberofProceedingsofthe20thWorldCongressTheInternationalFederationofAutomaticControlToulouse,France,July9-14,2017Copyright©2017IFAC11767Anadaptiverobustoptimizationschemeforwater-floodingoptimizationinoilreservoirsusingresidualanalysisstarM.MohsinSiraj∗,PaulM.J.VandenHof∗andJanDirkJansen∗∗∗ElectricalEngineering,ControlSystemsgroup,EindhovenUniversityofTechnology,TheNetherlands.(e-mails:m.m.siraj,p.m.j.vandenhof@tue.nl).∗∗DepartmentofGeoscienceandEngineering,DelftUniversityofTechnology,TheNetherlands.(e-mail:j.d.Jansen@tudelft.nl)Abstract:Model-baseddynamicoptimizationofthewater-floodingprocessinoilreservoirsisacomputationallycomplexproblemandsuffersfromhighlevelsfuncertainty.Atraditionalwayofquantifyinguncertaintyinrobustwater-floodingoptimizationisbyconsideringanensemblefuncertainmodelrealizations.Thesemodelsaregenerallynotvalidatedwithdataandtheresultingrobustoptimizationstrategiesaremostlyofflineoropen-loop.Themainfocusofthisworkistodevelopanadaptiveoronlinerobustoptimizationschemeusingresidualanalysisasamajoringredient.Themodelsinanensembleareconfrontedwithdataandanadaptedensembleisformedwithonlythosemodelsthatarenotinvalidated.Asanextstep,therobustoptimizationagainperformed(i.e.,updated/adjusted)withthisadaptedensemble.Theadaptedensemblegivesalessconservativedescriptionofuncertaintyandalsoreducesthehigcomputationalcostinvolvedinrobustoptimization.Simulationexampleshowsthatanincreaseintheobjectivefunctionvaluewithareducnofuncertaintyonthesevaluesisobtainedwiththedevelopedadaptiverobustschemecomparedtoanopen-lopofflinerobuststrategywiththefullensemblendanadaptiveschemeusingEnsembleKalmanFilter(EnKF),whichisoneoftheostcommonparameterestimationmethodsinreservoirsimulations.Keywords:Uncertaintyhandling,water-floodingoptimization,residualanalysis,onlinerobustoptimization1.INTRODUCTIONDynamicoptimizationofthewater-floodingprocesshasshownsignificantscopeforimprovementoftheeconomiclife-cycleperformanceofoilfieldscomparedtoamorecon-ventionalreactivestrategy,seee.g.,BrouwerandJansen(2004);Jansenetal.(2008);Foss(2012);VandenHofetal.2012).Besidescomputationalcomplexity,inducedduetocomplexnon-lineardynamicsandhencenon-convexity,oneofthekeychallengesinthismodel-baseddynamicptimizationisthehighlevelsofuncertaintyarisingfromthemodelingprocessofwaterfloodingandfromstronglyvaryingeconomicconditions.Variousapproachestodecisionmakingunderuncertaintycanbeimplementedintwodifferentways,seee.g.,Bert-simasandThiele(2006).Inopen-looporofflineschemes,robustoptimizationisperformedonlyonceunderagivendescriptionofuncertainty.Robustoptimizationcanalsobeusedinanadaptiveoronlinefashionwheretheun-crtaintyisreducedwiththeinformationthatisrevealedovertime.Ageneralpracticeofquantifyinguncertaintyinwater-floodinoptimizationisascenario-basedapproachwhereanensembleofuncertainparameters(e.g.,eser-starTheauthorsacknowledgefinancialsupportfromtheRecoveryFactoryprogramsponsoredbyShellGlobalSolutionsInternational.voirmodels),seee.g.,VanEssenetal.(2009);Capoleietal.(2013)isconsidered.Thesemodelsaremostlyeithergeneratedbyusinggeostatisticaltools,seee.g.,MarietozandCaers(2014)orhanddrawn,andaretypicallynot(in)validatedbytheproductiondata.Hencetheymayprovidea(very)conservativedescriptionofuncertainty.Anadaptivescheme,i.e.,Closed-LoopReservoirManage-ment(CRLM)asbeenintroducedinJansenetal.(2005),wherethereservoirmodelvariables(statesand/orparam-eters)arupdatedusingdataassimilationorComputerAssistedHistoryMatching(CAHM)techniques,suchasEnsembleKalmanFilter(EnKF),variationalapproaches,etc.,seee.g.,Evensen(2009);Aanonsenetal.(2009);OliverandChen(2011)andtheoptimizationisadaptedwithupdatedmodel(s).Intherobustsettings,asrobustoptimizationusesanensembleofmodelrealizations,pos-teriorensemble,e.g.,estimatedbyEnKF,canbedirectlyusedinanadaptivefashionresultinginarobustCLRM,seee.g.,Chenetal.(2009),Chenetal.(2010),Capoleietal.(2013).Thepurposeofthisworkistodeviseanadaptiverobustscmethatcanbeupdatedwiththegivenproductiondata.Themainfocusistoaddressthequestion:howtheavailableinformation(data)withtimecanbeusedtoshrinktheuncertaintyspacebyselectingfewernumberofProceedingsofthe20thWorldCongressTheInternationalFederationofAutomaticControlToulouse,France,July9-14,2017Copyright©2017IFAC11767nadaptiverobustoptiizationscheeforater-floodingoptiizationinoilreservoirsusingresidualanalysisstarM.MohsinSiraj∗,Paul.J.VandenHof∗andJanDirkJansen∗∗∗ElectricalEngineering,ControlSystemsgroup,EindhovenUniversityofTechnology,TheNetherlands.(e-mails:m.m.siraj,p.m.j.vandenhof@tue.nl).∗∗DepartmentofGeoscienceandEngineering,DelftUniversityofTechnology,TheNetherlands.(e-mail:j.d.Jansen@tudelft.nl)Abstract:Model-baseddynamicoptimizationofthewater-floodingprocessinoilreservoirsisacomputationallycomplexproblemandsuffersfromhighlevelsofuncertainty.Atraditionalwayofquantifyinguncertaintyinrobustwater-floodingoptimizationisbyconsideringanensembleofuncertainmodelrealizations.Thesemodelsaregenerallynotvalidatedwithdataandtheresultingrobustoptimizationstrategiesaremostlyofflineoropen-loop.Themainfocusofthisworkistodevelopanadaptiveoronlinerobustoptimizationschemeusingresidualanalysisasamajoringredient.Themodelsinanensembleareconfrontedwithdataandanadaptedensembleisformedwithonlythosemodelsthatarenotinvalidated.Asanextstep,therobustoptimizationisagainperformed(i.e.,updated/adjusted)withthisadaptedensemble.Theadaptedensemblegivesalessconservativedescriptionofuncertaintyandalsoreducesthehighcomputationalcostinvolvedinrobustoptimization.Simulationexampleshowsthatanincreaseintheobjectivefunctionvaluewithareductionofuncertaintyonthesevaluesisobtainedwiththedevelopedadaptiverobustschemecomparedtoanopen-loopofflinerobuststrategywiththefullensembleandanadaptiveschemeusingEnsembleKalmanFilter(EnKF),whichisoneofthemostcommonparameterestimationmethodsinreservoirsimulations.Keywords:Uncertaintyhandling,water-floodingoptimization,residualanalysis,onlinerobustoptimization1.INTRODUCTIONDynamicoptimizationofthewater-floodingprocesshasshownsignificantscopeforimprovementoftheeconomiclife-cycleperformanceofoilfieldscomparedtoamorecon-ventionalreactivestrategy,seee.g.,BrouwerandJansen(2004);Jansenetal.(2008);Foss(2012);VandenHofetal.(2012).Besidescomputationalcomplexity,inducedduetocomplexnon-lineardynamicsandhencenon-convexity,oneofthekeychallengesinthismodel-baseddynamicoptimizationisthehighlevelsofuncertaintyarisingfromthemodelingprocessofwaterfloodingandfromstronglyvaryingeconomicconditions.Variousapproachestodecisionmakingunderuncertaintycanbeimplementedintwodifferentways,seee.g.,Bert-simasandThiele(2006).Inopen-looporofflineschemes,robustoptimizationisperformedonlyonceunderagivendescriptionofuncertainty.Robustoptimizationcanalsobeusedinanadaptiveoronlinefashionwheretheun-certaintyisreducedwiththeinformationthatisrevealedovertime.Ageneralpracticeofquantifyinguncertaintyinwater-floodingoptimizationisascenario-basedapproachwhereanensembleofuncertainparameters(e.g.,reser-starTheauthorsacknowledgefinancialsupportfromtheRecoveryFactoryprogramsponsoredbyShellGlobalSolutionsInternational.voirmodels),seee.g.,VanEssenetal.(2009);Capoleietal.(2013)isconsidered.Thesemodelsaremostlyeithergeneratedbyusinggeostatisticaltools,seee.g.,MariethozandCaers(2014)orhanddrawn,andaretypicallynot(in)validatedbytheproductiondata.Hencetheymayprovidea(very)conservativedescriptionofuncertainty.Anadaptivescheme,i.e.,Closed-LoopReservoirManage-ment(CRLM)hasbeenintroducedinJansenetal.(2005),wherethereservoirmodelvariables(statesand/orparam-eters)areupdatedusingdataassimilationorComputerAssistedHistoryMatching(CAHM)techniques,suchasEnsembleKalmanFilter(EnKF),variationalapproaches,etc.,seee.g.,Evensen(2009);Aanonsenetal.(2009);OliverandChen(2011)andtheoptimizationisadaptedwithupdatedmodel(s).Intherobustsettings,asrobustoptimizationusesanensembleofmodelrealizations,pos-teriorensemble,e.g.,estimatedbyEnKF,canbedirectlyusedinanadaptivefashionresultinginarobustCLRM,seee.g.,Chenetal.(2009),Chenetal.(2010),Capoleietal.(2013).Thepurposeofthisworkistodeviseanadaptiverobustschemethatcanbeupdatedwiththegivenproductiondata.Themainfocusistoaddressthequestion:howtheavailableinformation(data)withtimecanbeusedtoshrinktheuncertaintyspacebyselectingfewernumberofProceedingsofthe20thWorldCongressTheInternationalFederationofAutomaticControlToulouse,France,July9-14,2017Copyright©2017IFAC11767starj∗,l.J.∗ir∗∗∗ctrialiolssp,sityof,l.(e-ails:..siraj,p..j.e.nl).∗∗ofciiftsityof,erl.(e-ail:j.d.delft.nl)l-siciztiofter-flossinilreserirsistiollypleblesuffrsfrolelsfint.ditioltifyingintinstter-floiztioisidelefinlreliztio.slsrellytlidateithresultingtiztiosteiesrestlyinerlo.ifofthisislornlinetiztiosresllysissjorrediet.lsinlereteithleisfoithslstretinlidated.sstep,stiztioisinrfo(i.e.,teteiththisble.leivslesstivscriptiofintlsrestiolstinlvintiztion.tioplesstincresinjetivtiolueithretiofintsluesisineithlotsreloinetsteithfullblesbleFilterhicisfsterestiisireseroirsilis.:rtaint,ter-floiztion,residllysis,nlintiztio1.iciztiofter-flossssiifitfirtoftlifclerfofoilfielst-tialristr,seee.g.,er(;etal.(;(;etal.(.estialplit,itl-licsit,fllesinthisl-siciztioislelsfrtaintrisfrolingessfterflofrostrolyicnditio.riosdeisiokingunderrtaintiltitifferts,seee.g.,t-siiel(.-lsctiztioisrforivescritiofcertait.sttiialinrnlinefasrertaintisreithinfotiotisrelerti.lpraticftifrtaintiner-fliiiisirerlofcertaiers(e.g.,reser-starauthorsacwledgefinancialortftheeryactorysponsoredShellGlobalSolutionsIternational.oirels),see.g.,etal.(;oleietal.(issier.elsleiterersiisticaltols,e.g.,iets(r,ticalllidatetio.tivsriptiofint.tisci..,oirt()itrietal.(,rereseirlriables(stesr-eters)siassiliterssisteistctes,ssbleFilterriatiols,etc.,e.g.,(;etal.(;r)iztioisithtel(s).Itsttings,sttiiseslofelrealiis,os-teriorble,.g.,estediretlyinfasresultinginte.g.,etal.(,etal.(,oleietal.(.sefthisisviststteithivtio.infoisssstion:ilableinfotio)ithsintssleferrfProceedingsofthe20thWorldCongressTheInternationalFederationofAutomaticControloulouse,France,July9-14,2017Copyright©2017IF11276M.MohsinSirajetal./IFACPapersOnLine50-1(2017)11275–11280representativemodelsinanensemble(reducetheensemblesize)orinotherwordshowuncertaintyispropagatedandcanbereducedinanadaptiveonlinesetting?Theconceptofresidualanalysisisused,wherethemodelsinanensembleareconfrontedwithdataandareinvalidatediftheydonotsufficientlyagreewiththeobserveddata.Anadaptedensembleisformedwithonlythosemodelsthatarenotinvalidatedthusprovidingalessconservativede-scriptionofuncertaintywithareducednumberofmodelsinanensemble.Theadaptedensembleisusedinarobustoptimizationinanonlinefashion.Residualanalysisfollowsan’exclusionapproach’touncertainty
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