Dynamics of Fluids in Porous Media

This is the definitive work on the subject by one of the world's foremost hydrologists, designed primarily for advanced undergraduate and graduate students of ground water hydrology, soil mechanics, soil physics, drainage and irrigation engineering, and sanitary, petroleum, and chemical enginee...

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Bibliographic Details
Main Author: Bear, Jacob
Format: eBook Book
Language:English
Published: New York Dover Publications 1972
Dover
Dover Publications, Incorporated
Edition:1
Subjects:
Fluid dynamics
General Engineering & Project Administration
General References
Groundwater flow
ISBN:9780486656755, 0486656756
Online Access:Get full text
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Table of Contents:
  • Title Page Preface Table of Contents 1. Introduction 2. Fluid and Porous Matrix Properties 3. Pressure and Piezometric Head 4. The Fundamental Fluid Transport Equations in Porous Media 5. The Equation of Motion of a Homogeneous Fluid 6. Continuity and Conservation Equations for a Homogeneous Fluid 7. Solving Boundary and Initial Value Problems 8. Unconfined Flow and the Dupuit Approximation 9. Flow of Immiscible Fluids 10. Hydrodynamic Dispersion 11. Models and Analogs Answers to Exercises Bibliography Index
  • 4.3 Equations of Mass, Momentum and Energy Conservation in a Fluid Continuum -- 4.3.1 Mass Conservation of a Species -- 4.3.2 Mass Conservation of a Fluid System -- 4.3.3 Conservation of Linear Momentum of a Species α -- 4.3.4 Conservation of Linear Momentum of a Fluid System -- 4.4 Constitutive Assumptions and Coupled Processes -- 4.4.1 General Considerations -- 4.4.2 Principles to be Used in Forming Constitutive Equations -- 4.4.3 Coupled Processes -- 4.5 A Porous Medium Model -- 4.5.1 The Conceptual Model Approach -- 4.5.2 A Model of Flow Through a Porous Medium -- 4.5.3 Frames of Reference -- 4.5.4 An Averaging Procedure -- 4.6 Equations of Volume and Mass Conservation -- 4.6.1 Equation of Volume Conservation -- 4.6.2 Equation of Mass Conservation of a Species in Solution -- 4.6.3 Equation of Mass Conservation -- 4.7 Equation of Motion -- 4.8 Tortuosity and Permeability -- 4.8.1 Relationship Between Tortuosity and Permeability -- 4.8.2 Tortuosity and Other Transport Coefficients -- 4.8.3 Formation Factor and Resistivity Index (Amyx 1960) in Reservoir Engineering -- CHAPTER 5 The Equation of Motion of a Homogeneous Fluid -- 5.1 The Experimental Law of Darcy -- 5.2 Generalization of Darcy's Law -- 5.2.1 Isotropic Medium -- 5.2.2 Anisotropic Medium -- 5.3 Deviations from Darcy's Law -- 5.3.1 The Upper Limit -- 5.3.2 The Lower Limit -- 5.3.3 The Slip Phenomenon -- 5.4 Rotational and Irrotational Motion -- 5.4.1 The Potential and Pseudopotential -- 5.4.2 Irrotational Flow -- 5.5 Hydraulic Conductivity of Isotropic Media -- 5.5.1 Hydraulic Conductivity and Permeability -- 5.5.2 Units and Examples -- 5.6 Anisotropic Permeability -- 5.6.1 The Principal Directions -- 5.6.2 Directional Permeability -- 5.7 Measurement of Hydraulic Conductivity -- 5.7.1 General -- 5.7.2 The Constant Head Permeameter -- 5.7.3 The Falling Head Permeameter
  • Cover -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- CHAPTER 1 Introduction -- 1.1 Aquifers, Ground Water and Oil Reservoirs -- 1.1.1 Definitions -- 1.1.2 The Moisture Distribution in a Vertical Profile -- 1.1.3 Classification of Aquifers -- 1.1.4 Properties of Aquifers -- 1.1.5 The Oil Reservoir -- 1.2 The Porous Medium -- 1.3 The Continuum Approach to Porous Media -- 1.3.1 The Molecular and Microscopic Levels -- 1.3.2 Porosity and Representative Elementary Volume -- 1.3.3 Areal and Linear Porosities -- 1.3.4 Velocity and Specific Discharge -- 1.3.5 Concluding Remarks -- CHAPTER 2 Fluids and Porous Matrix Properties -- 2.1 Fluid Density -- 2.1.1 Definitions -- 2.1.2 Mixture of Fluids -- 2.1.3 Measurement of Density -- 2.2 Fluid Viscosity -- 2.2.1 Definition -- 2.2.2 Non-Newtonian Fluids -- 2.2.3 Units -- 2.2.4 Effect of Pressure and Temperature -- 2.2.5 Measurement of Viscosity -- 2.3 Fluid Compressibility -- 2.4 Statistical Description of Porous Media -- 2.4.1 Particle-Size Distribution -- 2.4.2 Pore-Size Distribution -- 2.4.3 Other Statistical Descriptions -- 2.5 Porosity -- 2.5.1 Porosity and Effective Porosity -- 2.5.2 Porosity, Structure and Packing -- 2.5.3 Porosity Measurement -- 2.6 Specific Surface -- 2.6.1 Definitions -- 2.6.2 Measurement of Specific Surface -- 2.7 Matrix and Medium Compressibility -- CHAPTER 3 Pressure and Piezometric Head -- 3.1 Stress at a Point -- 3.2 Hydrostatic Pressure Distribution -- 3.3 Piezometric Head -- CHAPTER 4 The Fundamental Fluid Transport Equations in Porous Media -- 4.1 Particles, Velocities and Fluxes in a Fluid Continuum -- 4.1.1 Definitions of Particles and Velocities -- 4.1.2 Diffusive Velocities and Fluxes -- 4.1.3 The Eulerian and Lagrangian Points of View -- 4.1.4 The Substantial Derivative -- 4.2 The General Conservation Principle
  • 5.7.4 Determining Anisotropic Hydraulic Conductivity -- 5.8 Layered Porous Media -- 5.8.1 Flow Normal and Parallel to the Medium Layers -- 5.8.2 Equivalent Hydraulic Conductivity of Arbitrarily Directed Flow -- 5.8.3 A Layered Medium as an Equivalent Anisotropic Medium -- 5.8.4 Girinskii's Potential -- 5.9 Compressible Fluids -- 5.10 Derivations of Darcy's Law -- 5.10.1 Capillary Tube Models -- 5.10.2 Fissure Models -- 5.10.3 Hydraulic Radius Models -- 5.10.4 Resistance to Flow Models -- 5.10.5 Statistical Models -- 5.10.6 Averaging the Navier-Stokes Equations -- 5.10.7 Ferrandon's Model -- 5.11 Flow At Large Reynolds Numbers -- 5.11.1 The Phenomenon -- 5.11.2 Turbulence, Inertial Forces and Separation -- 5.11.3 Some Examples of Proposed Nonlinear Motion Equations -- 5.12.1 The Forces -- 5.12.2 Piping and Quicksand -- 5.12 Seepage Forces and Stresses -- CHAPTER 6 Continuity and Conservation Equations for a Homogeneous Fluid -- 6.1 The Control Volume -- 6.2 Mass Conservation in a Nondeformable Porous Matrix -- 6.2.1 The Basic Continuity Equation -- 6.2.2 Continuity Equation for an Incompressible Fluid -- 6.2.3 Continuity Equation for a Compressible Fluid -- 6.3 Mass Conservation in a Consolidating Medium -- 6.3.1 Vertical Compressibility Only -- 6.3.2 Extension to Three Phases and to Three-Dimensional Consolidation -- 6.3.3 Barometric Efficiency of Aquifers -- 6.4 Continuity Equations for Flow in Confined and Leaky Aquifers -- 6.4.1 The Horizontal Flow Approximation -- 6.4.2 Flow in a Confined Aquifer -- 6.4.3 Flow in a Leaky Aquifer -- 6.4.4 Averaging the Exact Equations over a Vertical Line -- 6.4.5 The Boltzmann Transformation -- 6.5 Stream Functions -- 6.5.1 Pathlines, Streamlines, Streaklines and Fronts -- 6.5.2 The Stream Function in Two-Dimensional Flow -- 6.5.3 The Stream Functions in Three-Dimensional Flow
  • 8.4.5 The Method of Small Perturbations
  • 6.5.4 The Partial Differential Equations for the Lagrange and Stokes Stream Functions -- 6.5.5 The Relationships between the Potential and the Stream Functions 233 -- 6.5.6 Solving Problems in the ϕ-ψ Plane -- 6.6 Flow Nets and Ground Water Contour Maps -- 6.6.1 The ϕ-ψ Flow Net -- 6.6.2 The Ground Water Contour Map -- 6.7 The Partial Differential Equations Describing Flow of an Inhomogeneous Incompressible Fluid in Terms of Ψ -- 6.7.1 Two-Dimensional Flow -- 6.7.2 Axisymmetric Flow -- CHAPTER 7 Solving Boundary and Initial Value Problems -- 7.1 Initial and Boundary Conditions -- 7.1.1 Boundary of Prescribed Potential -- 7.1.2 Boundary of Prescribed Flux -- 7.1.3 The Steady Free (or Phreatic) Surface without Accretion -- 7.1.4 The Unsteady Free (or Phreatic) Surface without Accretion -- 7.1.5 The Steady Free (or Phreatic) Surface with Accretion 256 -- 7.1.6 The Unsteady Free (or Phreatic) Surface with Accretion -- 7.1.7 Boundary of Saturated Zone (or of Capillary Fringe) -- 7.1.9 Capillary Exposed Faces -- 7.1.10 Discontinuity in Permeability -- 7.1.11 A Note on Anisotropic Media -- 7.1.12 Boundary Conditions in Terms of Pressure or Density -- 7.2 A Well Posed Problem -- 7.3 Description of Boundaries in the Hodograph Plane -- 7.3.1 The Hodograph Plane -- 7.3.2 Boundaries in the Hodograph Plane -- 7.3.3 Examples of Hodograph Representation of Boundaries -- 7.3.4 Intersection of Boundaries of Different Types -- 7.4 The Relations between Solutions of Flow Problems in Isotropic and Anisotropic Media -- 7.4.1 The Flow Equations -- 7.4.2 Relationships among Parameters in the Two Systems -- 7.4.3 Examples -- 7.5 Superposition and Duhamel's Principles -- 7.5.1 Superposition -- 7.5.2 Unsteady Flow with Boundary Conditions Independent of Time -- 7.5.3 Unsteady Flow with Time-Dependent Boundary Conditions -- 7.6 Direct Integration in One-Dimensional Problems
  • 7.6.1 Solution of the One-Dimensional Continuity Equation -- 7.6.2 Advance of a Wetting Front -- 7.7 The Method of Images -- 7.7.1 Principles -- 7.7.2 Examples -- 7.8 Methods Based on the Theory of Functions -- 7.8.1 Complex Variables and Analytic Functions -- 7.8.2 The Complex Potential and the Complex Specific Discharge -- 7.8.3 Sources and Sinks -- 7.8.4 Conformal Mapping -- 7.8.5 The Schwarz-Christoffel Transformation -- 7.8.6 Fictitious Flow in the -- 7.9 Numerical Methods -- 7.9.1 Method of Finite Differences -- 7.9.2 The Method of Finite Elements -- 7.9.3 Relaxation Methods -- 7.9.4 Schmidt's Graphic Method -- 7.10 Flow Nets by Graphic Methods -- 7.1.8 The Seepage Face -- CHAPTER 8 Unconfined Flow and the Dupuit Approximation -- 8.1 The Dupuit Approximation -- 8.1.1 The Dupuit Assumptions -- 8.1.2 Examples of Application to Hydraulic Steady Flows in Homogeneous Media -- 8.1.3 Unconfined Flow in an Aquifer with Horizontal Stratification -- 8.1.4 Unconfined Flow in an Aquifer with Vertical Strata -- 8.1.5 Unconfined Flow in a Two-Dimensional Inhomogeneous Medium -- 8.2 Continuity Equations Based on the Dupuit Approximation -- 8.2.1 The Continuity Equation -- 8.2.2 Boundary and Initial Conditions -- 8.2.3 Some Solutions of Forchheimer's Equation -- 8.2.4 Some Solutions of Boussinesq's Equation -- 8.3 The Hodograph Method -- 8.3.1 The Functions ω and -- 8.3.2 The Hodograph Method -- 8.3.4 Hamel's Mapping Function -- 8.3.5 Zhukovski's and Other Mapping Functions -- 8.3.6 A Graphic Solution of the Hodograph Plane -- 8.4 Linearization Techniques and Solutions -- 8.4.1 First Method of Linearization of the Boussinesq Equation -- 8.4.2 The Second Method of Linearization of the Boussinesq Equation -- 8.4.3 The Third Method of Linearization of the Boussinesq Equation -- 8.4.4 The Method of Successive Steady States