Rachid Ababou,
R Ababou
John Wiley & Sons
e druk, 2018
9781848215283
Capillary Flows in Heterogeneous and Random Porous Media
Specificaties
Gebonden, 402 blz.
|
Engels
John Wiley & Sons |
e druk, 2018
ISBN13: 9781848215283
Rubricering
Verwachte levertijd ongeveer 9 werkdagen
Samenvatting
This book focuses on statistical approaches to air/water flow in heterogeneous media, particularly for applications in soil hydrology where the unsaturated flow model of Darcy–Richards can be used. Beyond the assumptions of unsaturated flow, we present also a more general description of immiscible two–phase flow, with a wetting phase (water) and a non–wetting phase (air or oil), each with its own viscosity and density. Thus, we describe quasi–analytically 2–phase flow dynamics for axial flow in tubes/joints, possibly with axially variable diameter/aperture.
Specificaties
Inhoudsopgave
<p>1 Introduction and outline</p>
<p>2 Pore scale capillary air/water systems at equilibrium, steady flow, and dynamic flow regimes in tubes and joints</p>
<p>2.1 Quasi–static equilibrium and the macroscopic ?á(?é) moisture retention curve: a simple analytical example (random bundle of tubes, uniformly distributed radii)</p>
<p>2.1.1 Static equilibrium in a single vertical tube ("pore")</p>
<p>2.1.2 Static equilibrium in a statistical system of "pores" represented by a bundle of vertical tubes: construction of macroscopic moisture retention curve ?á(pC) or ?á(?é)</p>
<p>2.2 Steady–state Poiseuille flow in a bundle of tubes filled with water (no air): simplified analyzis, leading to Darcy′s law and Kozeny–Carman permeability</p>
<p>2.2.1 Specific area (general concept + application to bundle of tubes)</p>
<p>2.2.2 Poiseuille flow</p>
<p>2.2.3 From Poiseuille flow to Kozeny–Carman</p>
<p>(the various forms of K–C + discussion of dimensionless constant)</p>
<p>2.3 Steady–state Poiseuille / capillary flow of water in an unsaturated set of planar joints (air/water system): scale analyses leading to relations between porosity (?Ö), permeability (k), and capillary length scale (?Üc)</p>
<p>2.4 Steady water flow in statistical sets of tubes/joints with variable apertures or constrictions: macroscopic ?á(pc) and K(pc) relations for parallel or series systems</p>
<p>2.5 Pore scale dynamics in 1D: immiscible 2 phase visco–capillary flows in tubes and joints with uniform or variable radii/apertures (geometrically simplified quasi–1D approach)</p>
<p>2.6 Pore scale dynamics in a planar joint with randomly variable 2D aperture field a(x,y): transient drainage under the action of capillary forces & viscous dissipation (2 phase wetting/non wetting flow system)</p>
<p>3 Darcy scale and macroscale capillary flows with Richards/Muskat models (in heterogeneous media and statistical continua)</p>
<p>3.1 Introduction and summary (scales, REV concept, etc )</p>
<p>3.2 Continuum equations for unsaturated Darcy–Richards flow and 2 phase Darcy–Muskat flow in spatially variable porous media</p>
<p>3.2.1 Darcy s law for single–phase flows (including a slide "from N–S to Darcy")</p>
<p>3.2.2 Generalized Darcy s law for two–phase flows: Darcy–Muskat</p>
<p>3.2.3 From Darcy–Muskat to Darcy–Richards(–Buckingham)</p>
<p>3.3 Observations on capillary effects in heterogeneous unsaturated media (statistical continua) and macro–scale flow behavior: review+analyses</p>
<p>3.3.1 Introduction and overview ( )</p>
<p>3.3.2 Applied context of the study, literature review (and acknowledgments)</p>
<p>3.3.3 Review of macro–scale behavior of unsaturated flow (moisture migration) in randomly heterogeneous/stratified geologic media (rocks, soils): theoretical findings (macro–permeability Kii(?é)) and experimental evidence on nonlinear anisotropy</p>
<p>3.3.4 Macro–scale analyzis of unsaturated flow in randomly heterogeneous/stratified geologic media: parametrization of heterogeneity relation between saturated hydraulic conductivity Ks(x) and scale factor ?Ò(x) of local permeability curves Kii(pC,x)</p>
<p>3.3.4.1 Spatial distribution of conductivity–suction curves, cross–correlations, and consequences on flow paths at low vs. high suction (capillary barrier effect at high suction)</p>
<p>3.3.4.2 Anisotropy of macro–scale flow: anisotropy of the nonlinear macro–permeability Kii(?É) in randomly heterogeneous and/or randomly stratified soils ?» this to be moved in the next section</p>
<p>3.4 Upscaling unsaturated flow equations in randomly heterogeneous or stratified media: effective macroscale relations (?á(pC), K(pC)), and emergence of a capillary number for statistical continua</p>
<p>3.4.1 Review of some upscaling models for (?á(pC), K(pC)), and their applications to unsaturated flow in randomly heterogeneous/stratified geologic media</p>
<p>3.4.2 The Power Average Model of Ababou et al. (1993), and the resulting nonlinear anisotropic macro–scale Kii(pC) or Kii(?É) curve for randomly heterogeneous/stratified media</p>
<p>3.4.3 Behavior of upscaled permeability Kii(?É): the role of capillary length scale, geometric fluctuation scale, and dimensionless "capillary number </p>
<p>3.5 Capillarity, sorptivity, and localized ponding over a heterogeneous soil surface during infiltration: a simplified stochastic analysis of the genesis of ponding with randomly variable scaling parameter</p>
<p>3.5.1 Introduction and summary (case of stochastic infiltration on a randomly permeable soil surface)</p>
<p>3.5.2 Internal ponding at a material interface (between two layers)</p>
<p>3.5.3 Localized surface ponding under point or line source flux</p>
<p>3.5.4 A simplified model of ponding time under fixed rainfall rate</p>
<p>3.5.5 A simplified scaling model of soil heterogeneity in (x,y)</p>
<p>3.5.6 Stochastic analysis of space–time distributed ponding on a heterogeneous soil surface (analytical results on the evolution of excess rainfall, wet area, and wet patches)</p>
<p>3.6 Immiscible 2–phase capillary flows in stratified and/or randomly heterogeneous media: Darcy–Muskat upscaling / statistical continuum approach</p>
<p>3.6.1 Introduction, summary, and brief literature review </p>
<p>3.6.2 Steady state 2 phase flow in statistically heterogeneous 1D and 3D porous media under zero–mean capillary gradient: effective macro–scale ?á(pc) & K(pc) curves</p>
<p>3.6.3 Transient 2 phase flow in statistically heterogeneous 1D (stratified) porous medium: macro–scale hysteresis and kinetic effects on ?á(pc) and K(pc) curves due to heterogeneity </p>
<p>4 Recapitulation, conclusions, and outlook</p>
<p>5 Appendices</p>
<p>5.1 Appendix A1: Summary of governing flow equations (PDE′s) at various scales (pore systems, planar joints, continuous porous media)</p>
<p>5.2 Appendix A2: Random numbers, spatial point processes (Poisson point processes), and spatially correlated random fields (covariance functions, spectral densities, Wiener–Khinchine theory)</p>
<p>6 Reference</p>
<p>2 Pore scale capillary air/water systems at equilibrium, steady flow, and dynamic flow regimes in tubes and joints</p>
<p>2.1 Quasi–static equilibrium and the macroscopic ?á(?é) moisture retention curve: a simple analytical example (random bundle of tubes, uniformly distributed radii)</p>
<p>2.1.1 Static equilibrium in a single vertical tube ("pore")</p>
<p>2.1.2 Static equilibrium in a statistical system of "pores" represented by a bundle of vertical tubes: construction of macroscopic moisture retention curve ?á(pC) or ?á(?é)</p>
<p>2.2 Steady–state Poiseuille flow in a bundle of tubes filled with water (no air): simplified analyzis, leading to Darcy′s law and Kozeny–Carman permeability</p>
<p>2.2.1 Specific area (general concept + application to bundle of tubes)</p>
<p>2.2.2 Poiseuille flow</p>
<p>2.2.3 From Poiseuille flow to Kozeny–Carman</p>
<p>(the various forms of K–C + discussion of dimensionless constant)</p>
<p>2.3 Steady–state Poiseuille / capillary flow of water in an unsaturated set of planar joints (air/water system): scale analyses leading to relations between porosity (?Ö), permeability (k), and capillary length scale (?Üc)</p>
<p>2.4 Steady water flow in statistical sets of tubes/joints with variable apertures or constrictions: macroscopic ?á(pc) and K(pc) relations for parallel or series systems</p>
<p>2.5 Pore scale dynamics in 1D: immiscible 2 phase visco–capillary flows in tubes and joints with uniform or variable radii/apertures (geometrically simplified quasi–1D approach)</p>
<p>2.6 Pore scale dynamics in a planar joint with randomly variable 2D aperture field a(x,y): transient drainage under the action of capillary forces & viscous dissipation (2 phase wetting/non wetting flow system)</p>
<p>3 Darcy scale and macroscale capillary flows with Richards/Muskat models (in heterogeneous media and statistical continua)</p>
<p>3.1 Introduction and summary (scales, REV concept, etc )</p>
<p>3.2 Continuum equations for unsaturated Darcy–Richards flow and 2 phase Darcy–Muskat flow in spatially variable porous media</p>
<p>3.2.1 Darcy s law for single–phase flows (including a slide "from N–S to Darcy")</p>
<p>3.2.2 Generalized Darcy s law for two–phase flows: Darcy–Muskat</p>
<p>3.2.3 From Darcy–Muskat to Darcy–Richards(–Buckingham)</p>
<p>3.3 Observations on capillary effects in heterogeneous unsaturated media (statistical continua) and macro–scale flow behavior: review+analyses</p>
<p>3.3.1 Introduction and overview ( )</p>
<p>3.3.2 Applied context of the study, literature review (and acknowledgments)</p>
<p>3.3.3 Review of macro–scale behavior of unsaturated flow (moisture migration) in randomly heterogeneous/stratified geologic media (rocks, soils): theoretical findings (macro–permeability Kii(?é)) and experimental evidence on nonlinear anisotropy</p>
<p>3.3.4 Macro–scale analyzis of unsaturated flow in randomly heterogeneous/stratified geologic media: parametrization of heterogeneity relation between saturated hydraulic conductivity Ks(x) and scale factor ?Ò(x) of local permeability curves Kii(pC,x)</p>
<p>3.3.4.1 Spatial distribution of conductivity–suction curves, cross–correlations, and consequences on flow paths at low vs. high suction (capillary barrier effect at high suction)</p>
<p>3.3.4.2 Anisotropy of macro–scale flow: anisotropy of the nonlinear macro–permeability Kii(?É) in randomly heterogeneous and/or randomly stratified soils ?» this to be moved in the next section</p>
<p>3.4 Upscaling unsaturated flow equations in randomly heterogeneous or stratified media: effective macroscale relations (?á(pC), K(pC)), and emergence of a capillary number for statistical continua</p>
<p>3.4.1 Review of some upscaling models for (?á(pC), K(pC)), and their applications to unsaturated flow in randomly heterogeneous/stratified geologic media</p>
<p>3.4.2 The Power Average Model of Ababou et al. (1993), and the resulting nonlinear anisotropic macro–scale Kii(pC) or Kii(?É) curve for randomly heterogeneous/stratified media</p>
<p>3.4.3 Behavior of upscaled permeability Kii(?É): the role of capillary length scale, geometric fluctuation scale, and dimensionless "capillary number </p>
<p>3.5 Capillarity, sorptivity, and localized ponding over a heterogeneous soil surface during infiltration: a simplified stochastic analysis of the genesis of ponding with randomly variable scaling parameter</p>
<p>3.5.1 Introduction and summary (case of stochastic infiltration on a randomly permeable soil surface)</p>
<p>3.5.2 Internal ponding at a material interface (between two layers)</p>
<p>3.5.3 Localized surface ponding under point or line source flux</p>
<p>3.5.4 A simplified model of ponding time under fixed rainfall rate</p>
<p>3.5.5 A simplified scaling model of soil heterogeneity in (x,y)</p>
<p>3.5.6 Stochastic analysis of space–time distributed ponding on a heterogeneous soil surface (analytical results on the evolution of excess rainfall, wet area, and wet patches)</p>
<p>3.6 Immiscible 2–phase capillary flows in stratified and/or randomly heterogeneous media: Darcy–Muskat upscaling / statistical continuum approach</p>
<p>3.6.1 Introduction, summary, and brief literature review </p>
<p>3.6.2 Steady state 2 phase flow in statistically heterogeneous 1D and 3D porous media under zero–mean capillary gradient: effective macro–scale ?á(pc) & K(pc) curves</p>
<p>3.6.3 Transient 2 phase flow in statistically heterogeneous 1D (stratified) porous medium: macro–scale hysteresis and kinetic effects on ?á(pc) and K(pc) curves due to heterogeneity </p>
<p>4 Recapitulation, conclusions, and outlook</p>
<p>5 Appendices</p>
<p>5.1 Appendix A1: Summary of governing flow equations (PDE′s) at various scales (pore systems, planar joints, continuous porous media)</p>
<p>5.2 Appendix A2: Random numbers, spatial point processes (Poisson point processes), and spatially correlated random fields (covariance functions, spectral densities, Wiener–Khinchine theory)</p>
<p>6 Reference</p>