Physicochemical fluid dynamics in porous media: applications in geosciences and petroleum engineering

396 Pages·2019·12.853 MB·English

by  Panfilov, Mikhail Borisovich

PhysicochemicalFluidDynamics
inPorousMedia

Physicochemical Fluid Dynamics
in Porous Media
ApplicationsinGeosciencesandPetroleumEngineering
MikhailPanfilov
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10 9 8 7 6 5 4 3 2 1
v
Contents
Preface xv
Introduction xvii
1 ThermodynamicsofPureFluids 1
1.1 EquilibriumofSingle-phaseFluids–EquationofState 2
1.1.1 AdmissibleClassesofEOS 2
1.1.2 vanderWaalsEOS 3
1.1.3 Soave-Redlish-KwongEOS 3
1.1.4 Peng–RobinsonEOS 5
1.1.5 MixingRulesforMulticomponentFluids 5
1.2 Two-phaseEquilibriumofPureFluids 5
1.2.1 Pseudo-liquid/Pseudo-gasandTrueLiquid/Gas 6
1.2.2 EquilibriumConditionsinTermsofChemicalPotentials 6
1.2.3 ExplicitRelationshipforChemicalPotential 7
1.2.4 EquilibriumConditionsinTermsofPressureandVolumes 8
1.2.5 SolvabilityoftheEquilibriumEquation–Maxwell’sRule 9
1.2.6 CalculationofGas–LiquidCoexistence 10
1.2.7 LogarithmicRepresentationforChemicalPotential–Fugacity 11
2 ThermodynamicsofMixtures 13
2.1 ChemicalPotentialofanIdealGasMixture 13
2.1.1 Notations 13
2.1.2 DefinitionandPropertiesofanIdealGasMixture 14
2.1.3 EntropyandEnthalpyofIdealMixing 15
2.1.4 ChemicalPotentialofIdealGasMixtures 16
2.2 ChemicalPotentialofNonidealMixtures 17
2.2.1 GeneralModelforChemicalPotentialofMixtures 17
2.2.2 ChemicalPotentialofMixturesThroughIntensiveParameters 19
2.3 Two-phaseEquilibriumEquationsforaMulticomponentMixture 20
2.3.1 GeneralFormofTwo-phaseEquilibriumEquations 20
2.3.2 EquilibriumEquationsintheCaseofPeng–RobinsonEOS 21
2.3.3 K-values 23
2.3.4 CalculationofthePhaseComposition(“flash”) 24
2.3.5 ExpectedPhaseDiagramsforBinaryMixtures 24
vi Contents
2.4 EquilibriuminDiluteMixtures 26
2.4.1 IdealSolution 26
2.4.2 ChemicalPotentialforanIdealSolution 27
2.4.3 EquilibriumofIdealGasandIdealSolution:Raoult’sLaw 27
2.4.4 EquilibriumofDiluteSolutions:Henry’sLaw 28
2.4.5 K-valuesforIdealMixtures 28
2.4.6 CalculationofthePhaseComposition 29
3 ChemistryofMixtures 31
3.1 Adsorption 31
3.1.1 MechanismsofAdsorption 31
3.1.2 Langmuir’sModelofAdsorption 32
3.1.3 TypesofAdsorptionIsotherms 34
3.1.4 MulticomponentAdsorption 35
3.2 ChemicalReactions:MathematicalDescription 36
3.2.1 ElementaryStoichiometricSystem 36
3.2.2 ReactionRate 37
3.2.3 ParticleBalanceThroughtheReactionRateinaHomogeneous
Reaction 37
3.2.4 ParticleBalanceinaHeterogeneousReaction 38
3.2.5 Example 39
3.3 ChemicalReaction:Kinetics 39
3.3.1 KineticLawofMassAction:Guldberg–WaageLaw 39
3.3.2 KineticsofHeterogeneousReactions 40
3.3.3 ReactionConstant 41
3.4 OtherNonconservativeEffectswithParticles 42
3.4.1 DegradationofParticles 42
3.4.2 TrappingofParticles 42
3.5 Diffusion 42
3.5.1 Fick’sLaw 43
3.5.2 PropertiesoftheDiffusionParameter 44
3.5.3 CalculationoftheDiffusionCoefficientinGasesandLiquids 45
3.5.3.1 DiffusioninGases 45
3.5.3.2 DiffusioninLiquids 46
3.5.4 CharacteristicValuesoftheDiffusionParameter 46
3.5.5 AboutaMisuseofDiffusionParameters 47
3.5.5.1 AMisuseofNondimensionlessConcentrations 47
3.5.5.2 DiffusionastheEffectofMoleFractionAnomalybutnottheNumber
ofMoles 47
3.5.6 Stefan–MaxwellEquationsforDiffusionFluxes 48
4 ReactiveTransportwithaSingleReaction 51
4.1 EquationsofMulticomponentSingle-PhaseTransport 51
4.1.1 MaterialBalanceofEachComponent 51
4.1.2 ClosureRelationships 52
4.1.2.1 ChemicalTerms 52
4.1.2.2 TotalFlowVelocity–Darcy’sLaw 53
Contents vii
4.1.2.3 DiffusionFlux–Fick’sLaw 53
4.1.3 TransportEquation 53
4.1.4 TransportEquationforDiluteSolutions 55
4.1.5 ExampleofTransportEquationforaBinaryMixture 55
4.1.6 SeparationofFlowandTransport 56
4.2 ElementaryFundamentalSolutionsof1DTransportProblems 56
4.2.1 ConvectiveTransport–TravelingWaves 57
4.2.2 TransportwithDiffusion 58
4.2.3 LengthoftheDiffusionZone 59
4.2.4 PecletNumber 59
4.2.5 TransportwithLinearAdsorption–DelayEffect 60
4.2.6 TransportwithNonlinearAdsorption:DiffusiveTravelingWaves 60
4.2.7 OriginofDiffusiveTravelingWaves 62
4.2.8 TransportwithaSimplestReaction(orDegradation/Trapping) 62
4.2.9 MacrokineticEffect:ReactiveAccelerationoftheTransport 63
4.3 ReactiveTransportinUndergroundStorageofCO 64
2
4.3.1 ProblemFormulationandSolution 65
4.3.2 EvolutionofCO Concentration 66
2
4.3.3 EvolutionoftheConcentrationofSolidReactant 67
4.3.4 EvolutionoftheConcentrationoftheReactionProduct 67
4.3.5 MassofCarbonTransformedtoSolid 68
5 ReactiveTransportwithMultipleReactions(ApplicationtoIn
SituLeaching) 71
ISLTechnology 71
5.1 CoarseMonoreactionModelofISL 73
5.1.1 FormulationoftheProblem 73
5.1.2 AnalyticalSolution 74
5.2 MultireactionModelofISL 75
5.2.1 MainChemicalReactionsintheLeachingZone 75
5.2.2 TransportEquations 77
5.2.3 KineticsofGypsumPrecipitation 78
5.2.4 DefiniteFormoftheMathematicalModel 79
5.3 MethodofSplittingHydrodynamicsandChemistry 80
5.3.1 PrincipleoftheMethod 80
5.3.2 ModelProblemofInSituLeaching 81
5.3.3 AnalyticalAsymptoticExpansion:Zero-OrderTerms 82
5.3.4 First-OrderTerms 83
5.3.5 SolutioninDefiniteForm 84
5.3.6 CaseWithoutGypsumDeposition 84
5.3.7 AnalysisoftheProcess:ComparisonwithNumericalData 85
5.3.8 ExperimentalResults:ComparisonwithTheory 86
5.3.9 RecoveryFactor 88
6 SurfaceandCapillaryPhenomena 91
6.1 PropertiesofanInterface 91
6.1.1 CurvatureofaSurface 91
viii Contents
6.1.2 SignedCurvature 92
6.1.3 SurfaceTension 94
6.1.4 TangentialElasticityofanInterface 95
6.2 CapillaryPressureandInterfaceCurvature 96
6.2.1 Laplace’sCapillaryPressure 96
6.2.2 Young–LaplaceEquationforStaticInterface 97
6.2.3 SoapFilmsandMinimalSurfaces 99
6.2.4 CatenoidasaMinimalSurfaceofRevolution 101
6.2.5 Plateau’sConfigurationsforIntercrossedSoapFilms 102
6.3 Wetting 103
6.3.1 Fluid–SolidInteraction:CompleteandPartialWetting 103
6.3.2 NecessaryConditionofYoungforPartialWetting 104
6.3.3 HysteresisoftheContactAngle 106
6.3.4 CompleteWetting–ImpossibilityofMeniscusExistence 106
6.3.5 ShapeofLiquidDropsonSolidSurface 107
6.3.6 Surfactants–SignificanceofWettingforOilRecovery 109
6.4 CapillaryPhenomenainaPore 110
6.4.1 CapillaryPressureinaPore 110
6.4.2 CapillaryRise 112
6.4.3 CapillaryMovement–SpontaneousImbibition 113
6.4.4 MenisciinNonuniformPores–PrincipleofPoreOccupancy 114
6.4.5 CapillaryTrapping–PrincipleofPhaseImmobilization 115
6.4.6 EffectiveCapillaryPressure 116
6.5 AugmentedMeniscusandDisjoiningPressure 118
6.5.1 MultiscaleStructureofMeniscus 118
6.5.2 DisjoiningPressureinLiquidFilms 119
6.5.3 AugmentedYoung–LaplaceEquation 120
7 MeniscusMovementinaSinglePore 123
7.1 AsymptoticModelforMeniscusneartheTripleLine 123
7.1.1 ParadoxoftheTripleLine 123
7.1.2 FlowModelintheIntermediateZone(Lubrication
Approximation) 124
7.1.3 Tanner’sDifferentialEquationforMeniscus 125
7.1.4 ShapeoftheMeniscusintheIntermediateZone 127
7.1.5 ParticularCaseofSmall𝜃:Cox–VoinovLaw 128
7.1.6 ScenariosofMeniscusSpreading 128
7.2 MovementoftheAugmentedMeniscus 130
7.2.1 LubricationApproximationforAugmentedMeniscus 130
7.2.2 AdiabaticPrecursorFilms 132
7.2.3 DiffusiveFilm 132
7.3 MethodofDiffuseInterface 133
7.3.1 PrincipleIdeaoftheMethod 133
7.3.2 CapillaryForce 134
7.3.3 FreeEnergyandChemicalPotential 135
7.3.4 ReductiontoCahn–HilliardEquation 137