油气藏数值模拟

油藏流体及其与岩石作用的复杂性岩石非均质性及孔隙结构（孔道大小、孔隙之间关系）油、气和水的组分各不相同，各组分间存在相间传质，流体性质随温度、压力的变化很大油层中的流体与岩石相互作用产生物理化学现象如扩散、吸附等各种提高采收率方法的使用，如热力采油、化学驱、混相驱以及各种增产措施如酸化等油藏研究方法直接观察法如钻观察井、井下测试、井下电视、岩心实验、开辟生产实验区等)模拟法模拟法

模拟法

物模数模

数学模拟数学模型求解方法

解析法数值方法

数值模拟利用计算机模型模拟仿真油气复杂开发过程，动态重现开发历史，预测未来开发动态，可在计算机上“多次”模拟开发过程，进行油田开发方案优选、产量和地层压力动态预报、寻找开发中后期剩余油分布和采收率预测、经济效益预测以及对整个油田开发的重大问题进行决策的一门有效的工具。实际上就是通过渗流微分方程方程，借用大型计算机，计算数学的求解，结合油藏地质、油藏描述、油藏工程、试井等学科再现油田开发的过程，由此来解决油田实际问题。油气藏数值模拟—科学开发油气田的关键技术WhySimulation?EvaluatingReservoirManagementStrategiesSimulation:

WhyOilCompaniesBuy70%ofoilinthereservoirleftbehindReservoirSimulation“see”insidereservoirsLowriskfindtrappedoil/gaslearnwheretodrilldecidebestexploitationHelpsproducemoreoil/gasHighreturnandyield数值模拟的基本过程

建立数学模型建立数值模型建立计算机模型建立一套描述油藏流体渗流的偏微分方程组。完整的数学模型包括定解条件（初始条件和边界条件）。偏微分方程组非线性有限差分方程组线性代数方程组离散化线性化将各种数学模型的计算方法编制成计算机程序，用计算机计算各种结果。渗流数学模型的建立单相流体基本渗流微分方程三维空间单相渗流的达西定律多相多组分渗流基本微分方程

基本流动方程—多相流

两相非混相流体油相基本流动方程：水相基本流动方程：辅助方程数值模型的建立：微分方程的离散化时间与空间离散考察函数u(x),其自变量的一阶导数可定义为下面的各种极限：前差商中心差商后差商一阶导数的差商逼近

导数的差商逼近混合二阶差商逼近二阶偏导数的差商逼近网格系统油藏ab油藏有效网格无效网格。(i,j)。。(i,j)有限差分方程的建立考虑二维椭圆型微分方程：空间离散AerialViewofaReservoirwithSuperimposedGrid空间离散i-1,ji,ji+1,ji,j-1i,j+1五点差分格式Applymaterialbalanceequationforoilandwaterforeachgridblock计算传导率（

Transmissibility）ConsistsoftwopartsGeometricpart(flowarea)Saturationandpressuredependentpart(mobility)Useharmonicaverageforpermeabilityinseries计算传导率（Transmissibility）SolveforPi+1/2矩阵AP=fwiaijbijcijdijeij二维自然排列时五对角矩阵结构示意图BenefitsofSimulationFieldmanagementstrategiesSupportgeological&engineeringanalysisAddreservesIdentifyremedialmeasures&opportunitiesBenefitsofSimulationIncreaseproductionImproveoperationalefficiencyPreventmistakesCorrectmistakesNegotiations&assettradesPreventMistakesDesignofprocessesTransferofoflaboratoryprocesstothefieldDesignoffieldpilotsDesign&optimizationofnewfieldoperationsCorrectMistakesNewwelldrilledwithoutsimulation-producesonlywaterSimulationdetermineswhatcanbedone-successorabandonSavesfield,savesoperatorSupportGeological&EngineeringAnalysisLargeIndonesianfield4kmx8kmEightsands,faulted,severalhundredfeetthick60yearsofhistorySeverelossofproductionSupportGeological&EngineeringAnalysisWaterfloodimplemented-littleresponseEngineerbelieveswellsaredamaged,modelsfield,getswaterfloodforecastSupportGeological&EngineeringAnalysisOnlywaythatsimulationwillmatchperformanceofprimary&waterfloodistousewelldamagefactorinthesimulatorSupportGeological&EngineeringAnalysisRecommendsworkoverforwellsEachwellgoesfrom4BOPDto400BOPDFieldnowmatchessimulatorforecastCutAwayofReservoir-SeeInsideProductiondecisionsaremoreeffectivewithsimulationOilisRedWaterisBlueHistoryMatchforWell,2-14(WaterCut&GOR)InitialSwYear12InitialSwWaterfloodYear123DVisualizationofSteamChamberGrowth-ElementofSymmetry-3YearsAdditionalConceptsItislessexpensivetoaddhydrocarbonsfromexistingreservoirsthantofindnewones.Simulationcanincreaserecoverybyatleast5%overtheshorttermandevenmoreoverthelongerterm.Simulationprovidesatooltoevaluatefieldmanagementstrategies.Example

CasesLightOil-EcuadorWaterfloodoperationIdentifypoorlysweptareasValueofadditionaloil$30-40MMUSCostofstudy$250MUSProfitabilityratio140:1GasFieldDevelopmentWellcost$3MMUSIndonesia,junglelocation,paddevelopment,deviatedwellsModellingpredicteddevelopmentwith3fewerwells,saved$9MMCostofstudy-US$60,000Profitabilityratio150:1MatureWaterfloodOOIP15.0MillionTonnes,16degreeAPI,

Por=32%,Perm=2500md.,AquiferSupportProductionsince1938=36%OOIP

Currentlyat99%H2Ocut,~100Toil/dayEvaluatetertiarysteamfloodwithcurrentstatus:

1.Highwatercut

2.StrongaquifersupportStudydividedintotwophases:

1.Mechanisticfeasibilitystudy

2.Comprehensive3DfullfieldmodelMatureWaterfloodStructureTop,WellLocationsMatureWaterflood/TertiaryEORMatureWaterfloodSensitivity,screeningrunssuggested:

1.Aquiferintercept

2.CrestalsteaminjectionFieldscalemodelverified;aquiferintercept,crestalinjection,steamquality,steam-oilratio,steamoverride,welllocations,recovery,sensitivityrunsModelprediction:

1.Additional20%OOIPrecovery

2.ReduceH2Oproduction

3.DowndipsteamdrivewithgravityeffectContinueusingmodelduringproduction/drillingoperationsMatureWaterflood/TertiaryEORMatureWaterflood/TertiaryEORMatureWaterflood/TertiaryEORMatureWaterfloodHistoryMatchPredictionOver95%watercutOilincreaseinresponsetoSteaminjectionWatercutdecrease/AssessingWaterfloodPerformanceAssessingWaterfloodPerformanceAssessingWaterfloodPerformanceAssessingWaterfloodPerformanceAssessingWaterfloodPerformanceConclusionsAdvanced,modernsimulatorsareimportanttoolsforstrategyevaluationReservoirsimulationisakeycomponentofreservoirmanagementAdditionalvaluecanbefoundin“depleted”reservoirsIncrementaloilproductioncanbeprofitablyachievedusingtherightIORmethodsBOPDHowintegratedstudiesleadtoincreasedproductionReservoirManagementProcessMulti-disciplinaryTeamsINTEGRATEDRESERVOIRMODELGEOLOGYPETROPHYSICSGEOSTATISTICSENGINEERINGGEOPHYSICSIntegratedStudiesApproachGeophysicsReservoirVisualizationReservoirSimulation3-DModelCorePetrophysicsFeedbackLoopStratigraphyW6LAGUNILLASINFERIOR:MATUREHEAVYOILLAB.RESERVOIRMANAGEMENTIntegratedStudiesApproach由谁来做油藏数值模拟

油藏数值模拟是一门综合性很强的科学技术，它涉及的知识领域很广，包括油田地质学、油层物理学、油藏工程学、采油工程学、数学、计算机系统和油藏数值模拟程序。要做好一个模拟，需要上述方面专家配合，尤其需要一个能熟练掌握上述领域的有丰富经验的油藏工程专家完成油藏模拟工作。什么时候开始做模拟

在编制油田开发方案、寻找剩余油分布、研究油田开采机理、油气田开发重大问题决策需要答案和结果及一般的常规计算解决不了问题的时侯，开始做油藏数值模拟油藏数值模拟应用--黑油模型的应用模拟初期开发方案

实施方案的可行性评价选择井网、开发层系、井数和井位选择注水方式对比不同的产量效果油藏和流体性质的敏感性研究

油藏数值模拟应用--黑油模型的应用对已开发油田历史模拟

证明地质储量，确定基本的驱替机理确定产液量和生产周期确定油藏和流体特性指出问题、潜力所在区域

油藏数值模拟应用--黑油模型的应用动态预测

评价提高采收率的方法一次采油注水、注气注聚合物、注胶束、注表面活性剂注CO2和其它混相驱注蒸汽、火烧油藏数值模拟应用--黑油模型的应用研究剩余油饱和度分布

研究剩余油饱和度分布范围和类型单井进行调整，改变液流方向、改变注采井别、改变注水层位扩大水驱油效率和波及系数回答油田开发中所遇到的问题及解决问题的方法

油藏数值模拟应用--黑油模型的应用评价潜力和提高采收率的方法

确定井位、加密井的位置确定产量、开采方式确定地面和井的设备油藏数值模拟应用--黑油模型的应用专题和机理问题的研究

对比注水、注气和天然枯竭开采动态研究各种注水方式的效果研究井距、井网对油藏动态的影响研究不同开发层系对油藏动态的影响研究在各种不同开发方案的各种指标研究单井产量对采收率的影响

油藏数值模拟应用--黑油模型的应用

研究注水速度对产油量和采收率的影响研究油藏平面性质和层间非均质性对油藏动态的影响验证油藏的面积和地质储量检验油藏数据为谈判和开发提供必要的数据

BenefitsofIntegratedStudiesPreventmisapplications processfeasibilityanddesign labscale-up pilotdesign designandoptimizenewfieldoperationsImproveimplementation

minimizesurprises simulationallows“whatif” incorporateresultsdynamically identifyandquantifylatelifeoptionsSupportgeological&engineeringanalysisIdentifyremedialmeasures&opportunitiesSTEAMZONEOIL+WATERSTEAM+HOTWATERSTEAMPRODUCERINJECTORBASEROCKGRAVITYCONDENSATEDSTEAMHOTOILCOLDOILPRODUCINGZONEHEATLOSSESW6LAGUNILLASINFERIPOMATUREHEAVYOILLAB.THEPROCESSProcessConceptualizationandVisualizationW6LAGUNILLASINFERIOR:MATUREHEAVYOILLAB.OTHERAPPLICATIONSProcessConceptualizationandVisualizationHexagonpatternat133mTOTALWells/block=108133m231m72additionalplus36existingDrainageOptimizationProposedspacingConceptualBlockDiagramLenticularDevelopmentFORGAS/IMEXGas

Deliverability

Forecasting

WellboreGatheringSystemContractsSandfacePlantReservoirAdditionalConceptsItisgenerallylessexpensivetoimproverecoveryofhydrocarbonsfromexistingreservoirsthantofindnewones.Simulationcanincreaserecoverybyatleast5%overtheshorttermandevenmoreoverthelongerterm.Simulationprovidesatooltoevaluatefieldmanagementstrategies.ReservoirModellingforAdvancedProcessesAdvancedRecoveryProcessesConventionOilWaterInjectionMosteffective,applicabletomostofthereservoir.Recoveryfactorbasedondisplacementefficiency,volumetricsweepefficiencyApplicablewithhorizontal,multi-lateralwellsAdvancedRecoveryProcessesGasInjectionImmiscibleorMisciblegasdisplacementDisplacementefficiencyaffectedbydegreeofmiscibilityIfmiscible,highdisplacement,ifimmiscible,moderatedisplacementefficientSweepefficiencycouldbepoorduetogaschannellingandgascuspingMoreextensiveuseofmulti-lateralandhorizontalwellstoincreasesweepefficiencyAdvancedRecoveryProcessesPolymerInjectionIncreasesweepefficiencyEffectivewithhighviscositycontrast,improvemobilityratioHighconsumptionofpolymerifreservoirconditionisunfavorable(ie,highsaltcontent,hightemperature)AdvancedRecoveryProcessesTertiaryRecoverySchemeMiscibleflood-FirstcontactorMultiplecontactMultiplecontactdividedintovaporizationandcondensationtypeSolventused,CO2,LPGPhasebehaviourofmixtureplaysimportantroleinmisciblefloodHighdisplacementefficiency>80percentUsehorizontal/multi-lateralwellstoimprovesweepefficiencyAdvancedRecoveryProcessesChemicalfloodUseofgel,polymertoimprovesweepefficiencyUseofalkali,surfactanttoreducesurfacetensionandincreasedisplacementefficiencyin-situchemicalreactiontakesplacetogenerategelorsurfactantMasstransfer,dispersionofcomponentsindifferentphases(oleicoraqueous)AdvancedRecoveryProcessesHeavyOilRecoveryProcessesSteamInjectiontolowerresidualoilsaturationReductionofviscosityduetotemperaturechangesGeneratinggasphaseindistillationprocessandhelpsweepefficiencyFlowlargelydependsonmaintainingsteam,hotwaterfrontAdvancedRecoveryProcessesCombustionprocessMostlyinjectionofairorenriched(Oxygen)airBurningofhydrocarbonin-situgeneratesfluegas,CO2,steam,lightdistillatetoreduceviscosityofoilCombinationofgasdrive,steamdrive,waterdriveSolid(coke)depositionisfrequentHardtocontrolfirefrontprogressionAdvancedRecoveryProcessesChemicalInjectionPolymer,Alkaline,Surfactantreducesurfacetensionandlowerresidualoil,increasemobilityratiocontrolDecreaseoilviscosity,enhanceswellingofoiltoincreaseoilmovementSignificantincreaseoilrecoverywheresteaminjectionisnotfeasible(ieHighpressureheavyoilreservoir)AdvancedRecoveryProcessesSAGDDualorSinglewellSteamAssistedGravityDrainageProcessSteamchamberformation,keytosuccessinSAGDprocessSteammustbeinjectedathightemperatureandqualityOilviscosityreducedandflowalongsteam/oilinterfaceCountercurrentfluidflow,highrecovery>70%AdvancedRecoveryProcessesVAPEXProcessInjectionofvaporizedfluid(LPGorCO2)intoheavyoilreservoirSolventChamberformanddiffuseintoheavyoilOilviscosityreduceandflowalonginterfacebetweenoil/solventHighrecovery>70percentAdvancedRecoveryProcessesColdProductionCoproductionofsandandoiltogetherSandcutrangefrom3to50percentWormholeformation,dilationofformationrockSuspectedfoamyoil,gassuspendedinoilasdisperseddropletenhancefluidflowwithsmalldropletsoffoamybubbleinoilAdvancedRecoveryProcessesElectricalheatingElectricalenergyistransmittedtoreservoirviaelectricprobeReservoirfluid(formationwater)isbeingheatedupbyelectricalcurrentflowHeatedwatertransmitenergytooilandreduceviscosityOil/waterflowonacyclicprocess,similartosteamcyclingprocessAdvancedRecoveryProcessesMicrobesprocessInjectionofMicrobesandnutrientsintoreservoirBio-surfactantsarebeinggeneratedbymicrobesin-situSurfactantsreducedoil/waterinterfacialtensionandreduceviscosityOilflowwitheachbatchinjectionofMicrobeshardtocontrolmicrobesgrowthAdvancedRecoveryProcessesAdvancedrecoveryprocessesincludingsecondary/tertiaryprocessescanbesimulatedmathematicallyResultsofsimulationcanbevisualizedusingadvancedgraphicfeaturessuchas3-D,crosssectiondisplaytounderstandtheprocessmechanismSimulationofrecoveryprocesshelpsprofessionalstodesigndifferentoperatingconditionsbasedontheactualreservoirconditions.Avoidexpensivefieldtestandlaboratoryexperimentby“simulating”differentrecoveryscenarioAdvancedRecoveryProcessesAdvancedsimulatorswithpreandpostprocessorshelpengineerstounderstandandresolvealotoftechnicalquestionsRigidformulationinsimulatorsandflexibleuserdefinedreactionkineticshelpstocreatedifferenttypesofprocessescombinationSuperior3-Dgraphicshelpsengineersreviewdifferentproductionscenariowithoutactualfieldoperation.AdvancedRecoveryProcessesTypesofSimulatorsavailableBlackOil(IMEX)Compositional(GEM)Advancedprocessincludingthermal/Chemical(STARS)GridBuilder/ModelBuilder-PreprocessingResults3-D,Graphs,Reportwriter-PostProcessingWhoaretheplayerstoday?113AllTypesofReservoirModels

WithAdvancedWindowsSystemsSuperiorTechnologyHeavyOilThermal

Non-Thermal

STARSSTARSIMEXWaterFlood

ConventionalOil/GasChemical

Volatile