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lityPetrEcoleNationaleSupC19erieuredesIndustriesChimiques,UniversitC19edeLorraine,LaboratoireRC19eactionsetGC19eniedesProcC19edC19eseUPR3349,1rueGrandville,articleinfoArticlehistory:Received2November2016Receivedinrevisedform2June2017Accepted16June2017Keywords:PSO-SVMrecoveryfactor,ervoir.Generallycanbeobtainedapproachescandisplacement[2e6]andoilfieldonrecoveryfactorestimationforthelow-permeabilityreservoirisahotanddifficultissuebecauseofthecomplexnon-linearfluidflowthroughporousmedium,suchasnon-Darcyflow,startingpressuregradient,stresssensitivityandfluid-solidcoupling,whichindicatethattheconventionalmethodsarenotsuitablefordeterminationoftherecoveryfactorinlow-permeabilityreservoirs.Asearlyas1997,Wangetal.[9]proposedfivedifferentmethodsforcalculatingtherecoveryfactoroflow-permeabilityreservoir,butdifferentmethodswereonly*Correspondingauthor.StateKeyLaboratoryofOilandGasReservoirGeologyandExploitation,SouthwestPetroleumUniversity,Chengdu610500,China.E-mailaddress:bxqiang3210_88@163.com(X.Bian).PeerreviewunderresponsibilityofSouthwestPetroleumUniversity.ProductionandHostingbyElsevieronbehalfofKeAiContentslistsavailablePetroleumjournalhomepage:www.keaipublishing.coPetroleumxxx(2017)1e71.IntroductionItiswellacknowledgedthattheoilrecoveryfactorhasbeenseenasoneofthemostimportantparametersintheprocessofreservoirdevelopment.Theassessmentofwhethertheoilfieldisfullyexploitedoreconomicrecoveryismaximizedheavilydependsontheaccuracyofestimatingoilespeciallyforthelow-permeabilityresspeaking,thedeterminationofrecoveryfactoreitherexperimentallyornumerically,andthesebedividedintothreemajorgroups:water/oilmechanism[1],mathematicalstatisticstheorydevelopmentdynamics[7,8].However,thestudyRecoveryfactorLowpermeabilityReservoirOutlierdetectionhttp://dx.doi.org/10.1016/j.petlm.2017.06.0012405-6561/Copyright©2017,SouthwestPetroleumUaccessarticleundertheCCBY-NC-NDlicense(http://creatiPleasecitethisarticleinpressas:B.Han,X.permeabilityreservoir,Petroleum(2017),http://dx.doi.oabstractOilrecoveryfactorisoneofthemostimportantparametersinthedevelopmentprocessofoilreservoir,especiallyinthelow-permeabilityreservoir.Ingeneral,thedeterminationofrecoveryfactorcanbeobtainedeitherexperimentallyornumerically.Experimentalmethodisoftentime-consumingandexpensive,whilenumericalmethodhasbeenalwaysconfinedtonarrowrangeofapplicationorrelativelylargeerror.Recently,anintelligentmethodhasbeenprovenasanefficienttooltomodelthecomplexandnonlinearphenomena.Inthiswork,anintelligentmodelbasedonsupportvectormachineincombinationwiththeparticleswarmoptimization(PSO-SVM)techniquewasestablishedtopredictoilrecoveryfactorinthelow-permeabilityreservoir.InputvariablesoftheproposedPSO-SVMmodelwiththeaidofagreycorrelationanalysismethodarepermeability,wellspacingdensity,production-injectionwellratio,porosity,effectivethickness,crudeoilviscosityandoutputparameterisoilrecoveryfactoroflow-permeabilityreservoir.Theaccuracyandreliabilityoftheproposedmodelwereevaluatedthrough34datasetscollectedintheopenliteratureandcomparedwithPSO-BPneuralnetwork,empiricalmethodfromOilandGasCompany.TheresultsindicatedthatthePSO-SVMmodelgivesthebestresultswithaverageab-soluterelativedeviation(AARD)of3.79%,whileAARDsforthePSO-BPneuralnetworkandempiricalmethodare9.18%and10.0%,respectively.Furthermore,outlierdetectionwasusedonthebasisofwholedatasetstodefinitethevaliddomainsofPSO-SVMandPSO-BPmodelsbydetectingtheprobabledoubtfulrecoveryfactordatainthelow-permeabilityreservoir.Copyright©2017,SouthwestPetroleumUniversity.ProductionandhostingbyElsevierB.V.onbehalfofKeAiCommunicationsCo.,Ltd.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).BP20451,NancyCedex9,FranceAhybridPSO-SVM-basedmodelfordetrecoveryfactorinthelow-permeabiBingHana,XiaoqiangBiana,b,*aStateKeyLaboratoryofOilandGasReservoirGeologyandExploitation,SouthwestbC19niversity.Productionandhostingvecommons.org/licenses/bBian,AhybridPSO-SVM-basedrg/10.1016/j.petlmerminationofoilreservoiroleumUniversity,Chengdu610500,ChinaatScienceDirectm/en/journals/petlmbyElsevierB.V.onbehalfofKeAiCommunicationsCo.,Ltd.Thisisanopeny-nc-nd/4.0/).modelfordeterminationofoilrecoveryfactorinthelow-.2017.06.001>>>:i;j¼1yiC03C0Xmi;j¼1C0aiC0aC3iC14C0xi;xjC1aC3i2ð0;CÞ(4)wheremisthenumberofsupportvectors.Anewhyperplanefwasgeneratedthroughtheoptimizationtraining:networkmodelwasalsopresentedtoestimatetherecoveryfactor.TheaccuracyoftheproposedhybridPSO-SVM-basedmodelwascomparedwithPSO-BPneuralnetworkandempir-icalmethodfromOilandGasCompanytodemonstratetheval-idityofthepresentedPSO-SVM-basedmethod.Inaddition,outlierdiagnosiswasperformedfordetectionoftheprobabledoubtfulrecoveryfactorinlow-permeabilityreservoir.2.Methodology2.1.SupportvectormachineregressionSupportvectormachine(SVM)basedonstatistical-learningtheoryisaninnovativemachinelearningalgorithmemployedbyVapniketal.[40]in1995andwidelyusedforclassificationandregression[41e43].TheSVMalgorithmfollowsthestructural-risk-minimizationprinciple,whichhastheadvan-tagesofstrongtheoryandgoodgeneralizationability.Thisnewalgorithmcanwellsolvethepracticalproblemofsmallsampleswiththehighdimensionandnonlinearity,effectivelyavoidlocaloptimum,poorgeneralizationabilityandthedifficultyofselectingstructuralparameters,andalsoovercomethedisad-vantagesofconventionalBPneuralnetwork.WhenitcomestothenonlinearSVMregression,thebasicideaistotransformthenonlinearregressionproblemoflowdimensionalspaceintolinearregressionofhighdimensionalfeaturespacebyanonlinearmapping(particularlyradialbasisfunction).ThespecificalgorithmofSVM'sdualoptimizationproblemisasfollows:max24C012Xni¼1Xnj¼1C0aiC0aC3iC1C16ajC0aC3jC174C0xi;xjC1þXni¼1aið3C0yiÞþXni¼1aC3ið3þyiÞ35(1)s:t:80Þ(3)Calculationb:8Xmmodelfordeterminationofoilrecoveryfactorinthelow-017.06.001studies[12,13,48e50]andtheavailabledata[51],agreyrela-tionalanalysis[52,53]isadoptedtoscreenoutthemajorfactorswhosecorrelationdegreesaremorethan0.65,asshowninFig.1.Thecorrelationdegreeslessthan0.65arenotshowninFig.1.AscanbeseeninFig.1,thefactorsofthefirstthreecorrelationdegreesarepermeability(K),wellspacingdensity(S)andproduction-injectionwellratio(g).Theorderofthelatterthreeisporosity(4),effectivethickness(H)andviscosityofcrudeoil(m),respectively.K,namedthegeologicalfactor,isthemostimpor-tantfactoraffectingrecoveryfactoroflow-permeabilityreser-voir.Sandgareengineeringfactorsandthepracticaldevelopmentoperationcanbeavailablefromtheengineeringfactor,whichcaneffectivelyimprovetherecoveryoflow-permeabilityreservoir.Certainly,4,Handmareallgeologicalfactors.ItwassurprisingthatAARDandR2ofthePSO-SVMmodelis9.3%and0.843ifthefirstfivefactorswereusedasinputpa-3.2.Selectionoflearningsamplesleumxxx(2017)1e73fðxÞ¼Xni;j¼1C0aiC0aC3iC14C0xi;xjC1þb(5)Withxi;xj2Rn;b2R(6)2.2.ParticleswarmoptimizationtechniqueTheparticleswarmoptimization(PSO)algorithm,firstlyproposedbyEberhartandKennedy[44]inthe1995,isanopti-mizationalgorithminspiredbythesocialbehaviorofbirdsandusedtosolveallkindsofoptimizationproblems.Themostfundamentalideaisthateachbirdintheflocksisconsideredasoneoftheparticles,theneachparticlerepresentsapotentialsolutiontotheoptimizationproblemandalsocorrespondstoanadaptivefunctiontodeterminethedegreeofparticlemovement.Thespeedofparticlesdeterminesthedirectionanddistanceofparticlemovement,whilethevelocityoftheparticleisadjusteddynamicallywiththemovementofitsownandotherparticlessoastorealizeoptimizationoftheindividualinthesolutionspaceofoptimization.Ingeneral,thePSOisencodedwithsimplereal-valueencryptionandlessadjustmentparameters,whichisabletoshowgoodperformanceinsolvingnonlinearmulti-objectiveconstrainedoptimizationproblems.Someresearchers[45e47]foundthatPSO-basedANNhasabettertrainingperformance,fasterconvergencerate,aswellasabetterpredictingabilitythanBP-basedANN.AsforthePSOalgorithm,eachindividualparticleoftheswarmisconsideredasavectorxithatcontainstherequiredparametersinordertooptimizetheobjectivefunction.Theparticledimensionisthenumberofparametersandtheparticlelengthisseenasthedimensionofthisfunction.TheirpositionXikandvelocityVikarerandomlyinitializedinaspaceofpossiblesolutions.Theobjectivefunctionvalueisthencalculatedforeachparticle.Meanwhile,thevelocitiesandpositionsareupdatedbasedonthesevalues.Thealgorithmupdatesthepositionsandvelocitiesoftheparticlesbyfollowingtheequations:Vkþ1i¼uVkiþ41C16gkC0XkiC17þ42C16IkiC0XkiC17(7)Xkþ1i¼XkiþVkþ1i(8)whereuistheconstantinertiaweight,41and42aredeterminedbyc1r1andc2r2,respectively.3.Design,developmentandtestofSVMmodelingInthispart,threepracticalstepswouldbeconsideredwiththeaimtofindtheoptimalSVMmodelforpredictionofoilre-coveryfactorinlow-permeabilityreservoirs.Moreover,theac-curacyandreliabilityoftheproposedmodelwereevaluatedthrough34datasetscollectedintheopenliterature.3.1.InputandoutputvariablesTheestimationofoilrecoveryfactoroflow-permeabilityreservoirsisarelativelycomplexprocesswhichisinfluencedbymanyfactors,mainlyincludingreservoirphysicalproperties,fluidpropertiesanddevelopmentdynamics.Nevertheless,itisextremelydifficulttotakeintoaccountallthefactorssimulta-B.Han,X.Bian/Petroneously.Therefore,itisnecessarytofindoutmajoraffectingfactorconsideredasahighpriority.AccordingtopreviousPleasecitethisarticleinpressas:B.Han,X.Bian,AhybridPSO-SVM-basedpermeabilityreservoir,Petroleum(2017),http://dx.doi.org/10.1016/j.petlmDataselectionofthePSO-SVMmodelisoneofthemostimportantstagesinordertoincreasetheaccuracyofmodelpredictionbyobtainingagoodtrainingset.Duetothefewnumberofreportedrecoveryfactorsinlow-permeabilityreser-voirsfromopenliterature,thedatainthisworkwerecollectedfromref.50andref.51.34differentdataseriesbelongingto12differentgeographicandoilregionsfromJilinOilfieldwereusedtomakethesamplesrepresentativeanddiverse.TherangeofthesampledatashouldbewideandthespecificdataareshowninTable1.Thesedatawererandomlydividedintotwosetsincludingtrainingset(25ofalldata)andtestingset(9ofalldata).rameters,whilethoseforthesixfactorsare3.79%and0.997.Thereasonmaybethattheinfluenceoffluidviscosityonrecoveryfactoroflow-permeabilityreservoircannotbeneglected.How-ever,whenwatercontentratiowasaddedtoinputparametersconsideredastheseventhfactorwithcorrelationdegree0.483,theperformanceoftheproposedPSO-SVMmodelbecomesverypoorandtheerror(AARD¼15.6%)isalsorelativelylargerthanthatwithonlysixfactors.Basedontheaboveanalysis,wechoosethefirstsixfactors(K,S,g,4,Handm)asinputparameters.Therecoveryfactor(ER)wassetasoutputparameter.Therefore,amodelonthebasisofPSOandSVMwasestablishedtopredicttherecoveryfactoroflow-permeabilityreservoir.Fig.1.Greycorrelationdegreeofeachparameter.modelfordeterminationofoilrecoveryfactorinthelow-.2017.06.001Sampledatawerenormalizedandanti-normalizedbyemploying“mapminmax”functiontoimprovetheaccuracyofprediction.Themappingusedbythe“mapminmax”functionisgivenasfollows:~x¼2xC0xminxmaxC0xminC01;ð~x2½C01;1C138Þ(9)3.3.ModelestablishmentandparametersoptimizationInthiswork,theMATLABsoftwareandLIBSVM-3.1-FarutoUltimate3.1Modetoolbox(byfaruto)[54]wereusedtoestab-lishthePSO-SVMmodelandthentrainit.The3-SVRregressionmodelduringtrainingwaschosenasthekernelfunction(UsuallyRBFkernelfunction)toobtainthegoodperformance.Theper-formanceof3-SVRregressionmodelstronglydependsontheselectionof3-SVRregressionparameters,mainlyincluding:penaltyfactorCandkernelfunctionparametergandtheallowableerror3.Therefore,thekeyprocessofmodelestab-lishmentistheoptimizationofparameter(C,gand3)[55].Currently,themethodscommonlyusedtooptimizeparametersbutthegeneralizationabilityoftheregressionmodelisverypoor,namedtoolearningphenomenon;iftheCvalueistoosmall,seekingoptimalprocesstakesalongtimeandthesearchisnotcomplete,sothefittingresultsoftrainingsamplesarealsoverypoorandtheabilityofthemodelgeneralizationisverylow.Inotherwords,thereisaseriousphenomenonoflearning.ItwasfoundthattheCvalueshouldbechosenassmallaspossible(usuallybetween0and100)toensurethegoodgeneralizationandaccuracyof3-SVRregressionmodel.Thus,forPSO-SVMmodel,theglobaloptimalpenaltyfactorC¼11.01,g¼0.01,c1¼1.5,c2¼1.7,maxgen¼100,pop¼20.TheprocessofsearchingparameterisgiveninFig.3.ItcanbeseenfromFig.3thattheoptimalerrorissetto0.05andtheoveralltrainingerrordecreaseswithalgebraofevolutionfrom0.28to0.1,indicatingthegoodstabilityofrange.3.4.ComparisonwithBPneuralnetworkBPneuralnetworkisthecorepartofforwardneuralnetworkaswellastheessenceoftheartificialneuralnetwork.UsingtheTable1TherangeoftrainingandlearningsamplesfortheproposedSVMmodel.VariableK/mDF/%m/mPasH/mr/wellkmC02gER/%Range0.5e3910.5e23.33.9e12.72.8e23.56.2e35.31.5e1015e40.5B.Han,X.Bian/Petroleumxxx(2017)1e74of3-SVRregressionmodelareasfollows:empiricalmethod,gridsearchmethod,Bayesianframeworkmethod,geneticalgorithmandsoon.Butinthepresentwork,anovelintelligentoptimi-zationalgorithm-ParticleSwarmOptimization(PSO)algorithmwasemployedintheprocessofparameteroptimization.TheflowchartofthePSOalgorithmisshowninFig.2.Intheprocessofparameteroptimization,thepenaltyfactorCisthemostimportantparameterwhichgreatlyaf-fectstheaccuracyof3-SVRregressionmodel.IfCvalueistoolarge,trainingsampleshavetheveryhighfittingaccuracy,Fig.2.FlowchartofparameteroptimizationPleasecitethisarticleinpressas:B.Han,X.Bian,AhybridPSO-SVM-basedpermeabilityreservoir,Petroleum(2017),http://dx.doi.org/10.1016/j.petlm.2samesampledata,a3layerBPneuralnetworkbasedonPSOisestablishedandtheoptimalweightsandthresholdsaredeter-minedbyPSOalgorithm.Afterrepeatedcalculation,thebasicstructureofthenetworkis6-10-1.Thedataarenormalizedandant-normalizedbyusingmapminmaxfunction.Inparticular,trainingperiodis100,thelearningrateis0.1andthetrainingtargetis10C05.Inordertoevaluatetheperformanceanddemonstrateac-curacyofpredictionsbetweenSVMandBPneuralnetwork,thestatisticalerroranalysesarechosenasfollows:forthePSOalgorithm.modelfordeterminationofoilrecoveryfactorinthelow-017.06.001AscanbeseenfromtheTables2and3andFig.4,theaccuracyofPSO-SVMmodel(AARD¼3.79%,Emax¼2.75%,RMS¼1.22%)ismuchbetterthanthatofthePSO-BPmodel(AARD¼9.18%,Emax¼5.44%,RMS¼2.52%).Thecorrelationcoefficient(R2¼0.997)ofthePSO-SVMmodelismuchcloserto1.More-over,themaximumabsolutedeviationandtherootmeansquareerrorarelessthanthoseofthePSO-BPmodel.Nevertheless,theaccuracyofempiricalmethodfromOilandGasCompanyistheworstamongthemethodsconsideredinthisworkwithAARD¼10%[9].B.Han,X.Bian/Petroleumxxx(2017)1e75-Emax(Maximumabsolutedeviation):Thatisthemaximumvalueamongthedifferencebetweenexperimentalvalueandforecastvalue.Emax¼MaxC12C12C12ycalC0yexpC12C12C12(12)-RMS(RootMeanSquared):thisparameterisacriterionofdatadistributionaroundzerodeviationline.RMS¼264PC16ycalC0yexpC172N37512(13)-R2(CorrelationCoefficient):Thecorrelationcoefficientisaquantitythatgivesthequalityofaleastsquaresfittingtooriginaldata.R2¼1C0"PC12C12C12ycalC0yexpC12C12C122Py2cal#(11)AARD¼1NXNi¼1C12C12C12C12ycalC0yexpycalC12C12C12C12iC2100%(10)-AARD(averageabsoluterelativedeviation):Fig.3.Fitnesscurveintheprocessofoptimization.whereycalandyexparethecalculatedandexperimentalrecoveryfactor,respectively.TheresultsofbothPSO-BPandPSO-SVMmodelsarelistedinTable2andFig.4.TheevaluationparametersofbothmodelsareshowninTable3.Table2Comparisonofpredictedrecoveryfactorsbydifferentmodels.K/mD4/
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