Multiphase Flow in Permeable Media - A Pore-Scale Perspective

519 Pages·2017·38.879 MB·English

by  Blunt, Martin J.

MULTIPHASE FLOW IN PERMEABLE MEDIA
A Pore-Scale Perspective
Hydrocarbonproduction,gasrecoveryfromshale,CO storageandwatermanage-
2
ment have a common scientific underpinning: multiphase flow in porous media.
This book provides a fundamental description of multiphase flow through porous
rock, with emphasis on the understanding of displacement processes at the pore,
ormicron, scale.Fundamentalequationsandthe principal conceptsusingenergy,
momentumandmassbalancearedeveloped.Thelatestadvancesinhigh-resolution
three-dimensional imaging and associated modelling are explored. The treatment
ispedagogical,developingsoundphysicalprinciplestopredictflowandrecovery
through complex rock structures while providing a review of the recent litera-
ture. This systematic approach makes it an excellent reference for those who are
newtothe field. It providesthe scientific backgroundnecessaryfor a quantitative
assessmentofmultiphasesubsurfaceflowprocesses,andisidealforhydrologyand
environmental engineering students, as well as professionals in the hydrocarbon,
waterandcarbonstorageindustries.
MARTIN J. BLUNT is professor of Petroleum Engineering at Imperial College
London,visitingprofessoratPolitecnicodiMilanoandeditor-in-chiefofthejour-
nalTransportinPorousMedia.Hepublisheswidelyonmultiphaseflowinporous
media applied to oil recovery, groundwater flows and carbon dioxide storage. He
is a distinguished member of the Society of Petroleum Engineers (SPE), having
won the 2011 SPE Lester C. Uren Award, and the 2012 Darcy Medal for lifetime
achievement from the Society of Core Analysts. The book is inspired by recent
research and based on courses taught to thousands of students and professionals
fromaroundtheworld.

MULTIPHASE FLOW IN
PERMEABLE MEDIA
A Pore-Scale Perspective
MARTIN J. BLUNT
ImperialCollegeLondon
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Informationonthistitle:www.cambridge.org/9781107093461
DOI:10.1017/9781316145098
(cid:2)c MartinJ.Blunt2017
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Firstpublished2017
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LibraryofCongressCataloging-in-PublicationData
Names:Blunt,MartinJ.
Title:Multiphaseflowinpermeablemedia:apore-scaleperspective/MartinJ.Blunt,
ImperialCollegeLondon
Description:Cambridge:CambridgeUniversityPress,2017.
Identifiers:LCCN2016026616 | ISBN9781316145098
Subjects:LCSH:Multiphaseflow. | Fluiddynamics. | Porousmaterials.
Classification:LCCTA357.5.M84B582017 | DDC532/.56–dc23
LCrecordavailableathttps://lccn.loc.gov/2016026616
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Thisworkisdedicatedtomyfamily,andparticularlytoCatherine,whois
nolongerheretoreadit.Iamsorrythatthisisfarlessthanyoucouldhave
achieved,butitisthebestIcanmanage.

Contents
Preface pagexiii
Acknowledgements xvi
ListofSymbols xvii
1 InterfacialCurvatureandContactAngle 1
1.1 InterfacialTension 1
1.2 Young-LaplaceEquation 4
1.3 TheYoungEquationandContactAngle 7
1.3.1 TheYoungEquationasanEnergyBalance 10
1.3.2 InterfacialTension,RoughnessandWettability 11
1.3.3 CapillaryRise 14
1.3.4 HistoricalInterlude:ThomasYoungandtheMarquis
deLaplace 16
2 PorousMediaandFluidDisplacement 17
2.1 Pore-SpaceImages 17
2.1.1 StatisticalandProcess-BasedPore-SpaceReconstruction 22
2.1.2 Definition of a Porous Medium, Representative
Volumes,PorosityandSaturation 29
2.2 Pore-ScaleNetworksandTopologicalDescription 32
2.2.1 TransportNetworks 33
2.2.2 NetworkConstruction 35
2.2.3 GeneralizedNetworkModels 45
2.2.4 TopologicalDescriptorsofthePoreSpace 50
2.3 WettabilityandDisplacement 56
2.3.1 ThermodynamicDescriptionofDisplacementProcesses 56
2.3.2 DisplacementSequences 59
2.3.3 WettabilityandWettabilityChange 60
2.3.4 SurfaceRoughnessandContactAngleHysteresis 65
2.3.5 EffectiveContactAngleandCurvature 69
vii
viii Contents
3 PrimaryDrainage 73
3.1 EntryPressuresandFluidConfigurations 74
3.1.1 WettingLayers 79
3.1.2 EntryPressuresforIrregularThroats 82
3.2 MacroscopicCapillaryPressureinDrainage 85
3.3 BundleofTubesModelandtheThroatSizeDistribution 89
3.3.1 PredictionofCapillaryPressurefromImages 92
3.4 InvasionPercolation 95
3.4.1 ScalingRelationsinInvasionPercolation 99
3.4.2 DisplacementunderGravityandGradientPercolation 105
3.4.3 InvasionPercolation,NormalPercolationandFlow 109
3.5 FinalSaturationandMaximumCapillaryPressure 110
4 ImbibitionandTrapping 115
4.1 LayerFlow,SwellingandSnap-Off 116
4.1.1 RoofSnap-OffduringDrainage 122
4.2 Piston-LikeAdvanceandPoreFilling 126
4.2.1 Piston-LikeThroatFilling 126
4.2.2 CooperativePoreFilling 128
4.2.3 CompetitionbetweenSnap-OffandCooperativePore
Filling 132
4.2.4 FrequencyofDifferentFillingEvents 135
4.2.5 DynamicsofFilling 141
4.2.6 DisplacementasaSeriesofMetastableStates 144
4.3 DisplacementPatternsinImbibition 145
4.3.1 PercolationwithTrapping 145
4.3.2 InvasionPercolationwithTrapping 147
4.3.3 FrontalAdvance 148
4.3.4 ClusterGrowth 149
4.3.5 PhaseDiagramsforCapillary-ControlledDisplacement 149
4.3.6 InfiltrationorUnstableImbibitionunderGravity 157
4.4 MacroscopicCapillaryPressure 161
4.5 InterfacialArea 165
4.6 CapillaryTrappingandResidualSaturation 168
4.6.1 DirectImagingofTrappedClustersand
PercolationTheory 168
4.6.2 EffectofInitialSaturation 176
5 WettabilityandDisplacementPaths 188
5.1 DefinitionsandCapillaryPressureCycles 188
Contents ix
5.2 OilandWaterLayers 194
5.2.1 PinnedWaterLayersandForcedSnap-Off 194
5.2.2 ForcedWaterInjectionandOilLayerFormation 196
5.2.3 RecapofDisplacementProcesses 200
5.3 CapillaryPressuresandWettabilityIndices 201
5.3.1 WettabilityTrendsandRelationshipsbetweenIndices 204
5.3.2 DisplacementStatisticsinMixed-WetSystems 208
5.4 TrappinginMixed-WetandOil-WetMedia 211
5.4.1 Layer Connectivity as a Function of Initial Water
Saturation 213
5.4.2 Pore-Scale Observation of Trapping in
Mixed-WetSystems 216
6 Navier-StokesEquations,Darcy’sLawandMultiphaseFlow 219
6.1 Navier-StokesEquationsandConservationofMass 219
6.1.1 FlowinaPipe 221
6.1.2 TheWashburnEquation 225
6.1.3 FlowinWettingLayers 228
6.1.4 ReynoldsNumberandtheStokesEquation 233
6.2 Darcy’sLawandPermeability 236
6.2.1 PermeabilityofaBundleofCapillaryTubes 238
6.2.2 TypicalPermeabilityValues 239
6.2.3 TheLeverettJFunction 243
6.2.4 ComputingFlowFieldsonPore-SpaceImages 247
6.3 TheMultiphaseDarcyLawandRelativePermeability 254
6.3.1 HistoricalInterlude:Muskat,LeverettandBuckingham 254
6.3.2 AssumptionsInherentintheMultiphaseDarcyLaw 255
6.4 CapillaryNumberandPore-ScaleDynamics 257
6.4.1 MacroscopicFlowPatternsforImbibition 257
6.4.2 Capillary Number and the Perturbative Effect of
FlowRate 263
6.4.3 LayerConductanceandViscousEffects 265
6.4.4 CorrelationLengthsforPercolation-LikeDisplacement 270
6.4.5 CorrelationLengthandResidualSaturation 273
6.4.6 MobilizationofTrappedGanglia 275
6.4.7 GanglionDynamics,ConnectivityandFlowRegimes 279
6.4.8 ViscousandCapillaryForcesasanEnergyBalance 285
6.4.9 DirectComputationofMultiphaseFlow 288
6.5 ExtensionstotheMultiphaseDarcyLaw 298
6.5.1 InfiltrationandPhaseFieldModels 298