Learn the fundamental concepts that underlie the physics of multiphase flow and transport in porous media with the information in Essentials of Multiphase Flow in Porous Media, which demonstrates the mathematical-physical ways to express and address multiphase flow problems. Find a logical, step-by-step introduction to everything from the simple concepts to the advanced equations useful for addressing real-world problems like infiltration, groundwater contamination, and movement of non-aqueous phase liquids. Discover and apply the governing equations for application to these and other problems in light of the physics that influence system behavior.
1. Setting the Stage. 1.1 Introduction. 1.2 Phases and Porousmedia. 1.3
Grain and Pore Size Distributions. 1.4 The Concept of Saturation. 1.5 The
Concept of Pressure. 1.6 Surface Tension Considerations. 1.7 Concept of
Concentration. 1.8 Summary. 1.9 Exercises.
2. Mass Conservation Equations.
2.1 Introduction. 2.2 Microscalemass Conservation. 2.3 Integral Forms Ofmass
Conservation. 2.4 Integral Theorems. 2.4.1 Divergence Theorem. 2.4.2
Transport Theorem. 2.5 Point Forms Ofmass Conservation. 2.6 Themacroscale
Perspective. 2.6.1 The Representative Elementary Volume. 2.6.2 Global and
Local Coordinate Systems. 2.6.3 Macroscopic Variables. 2.6.4 Definitions Of
Macroscale Quantities. 2.6.5 Summary Of Macroscale Quantities. 2.7 The
Averaging Theorems. 2.7.1 Spatial Averaging Theorem. 2.7.2 Temporal Averaging
Theorem. 2.8 Macroscalemass Conservation. 2.8.1 Macroscale Point Forms. 2.8.2
Integral Forms. 2.9 Applications. 2.9.1 Integral Analysis. 2.9.2 Point
Analysis. 2.10 Summary. 2.11 Exercises.
3. Flow Equations. 3.1
Introduction. 3.2 Darcy'S Experiments. 3.3 Fluid Properties. 3.4 Equations of
State for Fluids. 3.4.1 Mass Fraction. 3.4.2 Mass Density and Pressure. 3.4.3
Fluid Viscosity. 3.5 Hydraulic Potential. 3.5.1 Hydrostatic Force and
Hydraulic Head. 3.5.2 Derivatives of Hydraulic Head. 3.6 Single Phase Fluid
Flow. 3.6.1 Darcy'S Law. 3.6.2 Hydraulic Conductivity and Permeability. 3.6.3
Derivation of Groundwater Flow Equation. 3.6.4 Recapitulation of the
Derivation. 3.6.5 Initial and Boundary Conditions. 3.6.6 Two-Dimensional
Flow. 3.7 Two-Phase Immiscible Flow. 3.7.1 Derivation of Flowequations. 3.7.2
Observations on the Pc - Sw Relationship. 3.7.3 Formulas for The Pc - Sw
Relationship. 3.7.4 Observations of the Ka Rel - Sw Relationship. 3.7.5
Formulas for the Ka Rel - Sw Relation. 3.7.6 Special Cases of Multiphase
Flow. 3.8 The Buckley-Leverett Analysis. 3.8.1 Fractional Flow. 3.8.2
Derivation of the Buckley-Leverett Equation. 3.8.3 Solution of the
Buckley-Leverett Equation. 3.9 Summary. 3.10 Exercises.
4. Mass Transport
Equations. 4.1 Introduction. 4.2 Velocity in the Species Transport
Equations. 4.2.1 Direct Approach. 4.2.2 Rigorous Approach. 4.2.3 Distribution
Approach. 4.2.4 Summary. 4.3 Closure Relations for the Dispersion Vector. 4.4
Chemical Reaction Rates. 4.5 Interphase Transfer Terms. 4.5.1 Kinetic
Formulation. 4.5.2 Equilibriumformulation. 4.5.3 Summary: Kinetic Vs.
Equilibrium Formulations. 4.6 Initial and Boundary Conditions. 4.7
Conclusion. 4.8 Exercises.
5. Simulation. 5.1 1-D Simulation of Air-Water
Flow. 5.1.1 Drainage in a Homogeneous Soil. 5.1.2 Drainage in a Heterogeneous
Soil. 5.1.3 Imbibition in Homogeneous Soil. 5.2 1-D Simulation of Dnapl-Water
Flow. 5.2.1 Primary Dnapl Imbibition In Homogeneous Soil. 5.2.2 Density
Effect. 5.2.3 Dnapl Drainage in Homogeneous Soil. 5.2.4 Secondary Imbibition
of Dnapl in Homogeneous Soil. 5.2.5 Secondary Drainage in Homogeneous Soil.
5.2.6 Primary Imbibition in Heterogeneous Soil. 5.3 2-D Simulation of
Dnapl-Water Flow. 5.3.1 Dnapl Descent into a Water-Saturated Reservoir. 5.4
Simulation Of Multiphase Flow And Transport. 5.4.1 1-D Two-Phase Flow and
Transport. 5.4.2 2-D Two-Phase Flow and Transport. 5.5 2-D Single-Phase Flow
and Transport. 5.5.1 Base-Case. 5.5.2 Effect of Inflow. 5.5.3 Impactofwell
Discharge. 5.5.4 Effect of Adsorption. 5.5.5 Effect of a Low Transmissivity
Region. 5.5.6 Effect of a High Transmissivity Region. 5.5.7 Effect of Rate of
Reaction. 5.6 3-D Single-Phase Flow and Transport. 5.7 2-D Three-Phase Flow.
5.8 Summary.
6. Select Symbols.
George F. Pinder, PHD, is the Director of the Research Center for Groundwater Remediation Design and also a Professor of Civil and Environmental Engineering, Mathematics and Statistics, and Computer Science at the University of Vermont. He has served on the editorial board of numerous journals including the International Journal for Numerical Methods in Fluids. He has published extensively in the fields of groundwater flow and transport modeling and has written on the use of such models in combination with optimization methods in addressing problems of environmental optimal design. William G. Gray, PHD, is a Professor of Environmental Sciences and Engineering at the University of North Carolina at Chapel Hill. He has over thirty years of research and teaching experience in environmental modeling and the physics of flow in porous media. He has published widely on various aspects of environmental modeling and simulation and has served as editor and on the editorial boards of leading journals in his field. He is a Fellow of the American Geophysical Union.
