MATRIX-FRACTURE INTERACTION ANALYSIS IN FRACTURED UNCONVENTI

MATRIX-FRACTUREINTERACTIONANALYSIS

INFRACTUREDUNCONVENTIONALGAS

RESERVOIR

by

LongCai

cCopyrightbyLongCai,2014

AllRightsReserved

AthesissubmittedtotheFacultyandtheBoardofTrusteesoftheColoradoSchoolofMinesinpartialful llmentoftherequirementsforthedegreeofMasterofScience(PetroleumEngineering).

Golden,ColoradoDateGolden,ColoradoDateSigned:LongCaiSigned:Dr.Yu-ShuWuThesisAdvisor

Signed:

Dr.WilliamFleckenstein

ProfessorandHead

DepartmentofPetroleumEngineering

ABSTRACT

Handling owthroughfracturedmediaiscriticalinshalegasreservoirsimulation,asgasproductionfromsuchlow-permeabilityformationsreliesonfractures,fromhydraulicfractures/networktovariousscalednaturalfractures,toprovide owchannelsforgas owtoproductionwells.Currenttechnologiesandmodelingapproachesusedforunconventionalfracturedreservoirsimulationareborroweddirectlyfromthoseusedinconventionalreser-voirsimulation,whichweredevelopedinthepasthalfcentury.Sincethe1960s,signi cantprogresshasbeenmadeinmathematicalmodelingof owandtransportprocessesinfrac-turedrock,suchasexplicitdiscrete-fractureandmatrixmodel,thedual-continuummethod,includingdouble-porosityandmulti-porosityandthemultipleinteractingcontinuamethod(MINC).

Theexplicitdiscrete-fractureandmatrixmodelislimitedforapplication,duetothecomputationalintensityinvolved.Thedoubleporositymodeliswidelyusedinconventionalreservoirsimulation,butitmaybenotapplicableforunconventionalshalegasreservoirsimulation,asaresultoftheundesiredreservoircondition.TheMINCmethodtreatsinter-porosity owinafullytransientwaybyfurthersubpidinginpidualmatrixblockswithanumberof1-Dnestedmeshes.TheMINCconcept,however,assumesthatfracture-matrix owiscontrolledonlybythedistancetothenearestfracturesurroundingthematrixblock,whichisshowntobenolongerapplicableaftertheearlyrapidtransientperiodof ow..Thisresearchanalyzesthelimitationsofthedoubleporositymodel,withseveralshapefactors,andtheMINCmodel.AnewmethodcalledtheSchwarz-Christo elconformalmappingisintroduced.Thismethodimprovesthematrix-fractureinteractionmodelingforthesquare,orcubic,system.AconceptcombinestheMINCandtheSchwarz-Christo elmappingconceptbytheanalyticalsolutioncanaccuratelysimulatethematrix-fracturein-teraction.

TABLEOFCONTENTS

ABSTRACT.........................................iiiLISTOFFIGURES......................................xLISTOFTABLES......................................xivLISTOFSYMBOLS.....................................xvLISTOFABBREVIATIONS...............................xviiiACKNOWLEDGMENTS..................................xixDEDICATION........................................xx

CHAPTER1INTRODUCTION...............................1

1.1CurrentandForecastStatusofUnconventionalGasProductioninthe

UnitedStates.....................................2

CharacteristicsofGasShale.............................2

FractureSystemsinGasShale............................4

GasTransportPhysicsinDi erentPorosity....................5

CurrentModelProblemStatement.........................5

1.5.1

1.5.2

1.5.3

1.6

1.7TheDoublePorosityModel.........................6TheMultipleInteractingContinua(MINC)Model.............7FineGridSimulation.............................71.21.31.41.5Objectives.......................................8ThesisOrganization..................................8

CHAPTER2LITERATUREREVIEW..........................10

2.1MathematicalModelsandNumericalApproach.................10

2.1.1

2.1.2

2.1.3GoverningEquationinaREV(RepresentativeElementaryVolume)..10MassConservationinaREV.......................11FlowAcrossanInterface..........................11

2.1.3.1

2.1.3.2SpatialDiscretization......................12TransmissibilityCalculation...................12

2.2GasTransportMechanismIntroductionandMathematicalDescription....13

2.2.1DarcyFlow.................................13

2.2.1.1

2.2.2Darcy’sLaw............................14KnudsenDi usion.............................14

2.2.2.1

2.2.2.2KnudsenDi usionMathematicalDescription.........15SlippageFactorDetermination.................15

2.2.3GasAdsorptionandDesorption......................17

2.2.3.1

2.2.3.2LangmuirIsothermalEquation.................17GasAdsorptionandDesorptionParameterDetermination..18

2.2.4

2.2.5Non-DarcyFlow..............................19Geomechanics................................20

2.2.5.1

2.2.5.2GeomechanicsDataAcquisition.................21Remark..............................22

2.3PrimaryModelDataAcquisition.........................22CHAPTER3DOUBLEPOROSITYMODELINTRODUCTIONAND

EVALUATION................................23

3.1DoublePorosityModelIntroduction........................24

3.2Pseudo-Steady-StatesBasedDoublePorosityModel...............25

3.2.1

3.2.2

3.2.3WarrenandRootShapeFactor......................26Kazemietal.ShapeFactor........................26Coats’ShapeFactor............................27

3.3NumericalVeri cationoftheDoublePorosityModelwithDi erentShape

Factors........................................27

3.3.1

3.3.2

3.3.3SystemGeometry,FracturetreatmentandInitialConditions......27PostedResultsIntroduction........................28NumericalSimulationResultsandDiscussion..............29

3.4LimandAzizShapeFactor............................32

3.4.1

3.4.2TheIntroductionofLimandAzizShapeFactor.............32LimandAzizShapeFactorNumericalEvaluation............33

3.5Conclusion......................................36CHAPTER4TRANSIENTFLOWBASEDMODEL-NESTEDSUB-BLOCKS

DESIGN...................................37

4.1MINCConceptIntroduction............................37

4.1.1

4.1.2

4.1.3

4.2MINCConceptExplanation........................38MINCModelEvaluation..........................39MINCConcep …… 此处隐藏：14878字，全部文档内容请下载后查看。喜欢就下载吧 ……