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9781402066825

PDF

834

Jacob Bear

Theory and Applications of Transport in Porous Media

PDF

PDF

Adobe DRM [Hard-DRM]

Englisch

In many parts of the world, groundwater resources are under increasing threat from growing demands, wasteful use, and contamination. To face the challenge, good planning and management practices are needed. A key to the management of groundwater is the ability to model the movement of fluids and contaminants in the subsurface. The purpose of this book is to construct conceptual and mathematical models that can provide the information required for making decisions associated with the management of groundwater resources, and the remediation of contaminated aquifers.The basic approach of this book is to accurately describe the underlying physics of groundwater flow and solute transport in heterogeneous porous media, starting at the microscopic level, and to rigorously derive their mathematical representation at the macroscopic levels. The well-posed, macroscopic mathematical models are formulated for saturated, single phase flow, as well as for unsaturated and multiphase flow, and for the transport of single and multiple chemical species. Numerical models are presented and computer codes are reviewed, as tools for solving the models. The problem of seawater intrusion into coastal aquifers is examined and modeled. The issues of uncertainty in model input data and output are addressed. The book concludes with a chapter on the management of groundwater resources. Although one of the main objectives of this book is to construct mathematical models, the amount of mathematics required is kept minimal.

In many parts of the world, groundwater resources are under increasing threat from growing demands, wasteful use, and contamination. To face the challenge, good planning and management practices are needed. A key to the management of groundwater is the ability to model the movement of fluids and contaminants in the subsurface. The purpose of this book is to construct conceptual and mathematical models that can provide the information required for making decisions associated with the management of groundwater resources, and the remediation of contaminated aquifers.The basic approach of this book is to accurately describe the underlying physics of groundwater flow and solute transport in heterogeneous porous media, starting at the microscopic level, and to rigorously derive their mathematical representation at the macroscopic levels. The well-posed, macroscopic mathematical models are formulated for saturated, single phase flow, as well as for unsaturated and multiphase flow, and for the transport of single and multiple chemical species. Numerical models are presented and computer codes are reviewed, as tools for solving the models. The problem of seawater intrusion into coastal aquifers is examined and modeled. The issues of uncertainty in model input data and output are addressed. The book concludes with a chapter on the management of groundwater resources. Although one of the main objectives of this book is to construct mathematical models, the amount of mathematics required is kept minimal.

PrefaceList of Main Symbols

1 INTRODUCTION

1.1 Role of Groundwater in Water Resources

Systems

1.1.1 The hydrological cycle

1.1.2 Surface water versus groundwater

1.1.3 Characteristics of groundwater

1.1.4 Functions of aquifers

1.1.5 Subsurface contamination

1.1.6 Sustainable yield

1.2 Modeling

1.2.1 Modeling concepts

1.2.2 Modeling process

1.2.3. Model use

1.3 Continuum Approach to Transport in Porous Media

1.3.1 Phases, chemical species and components

1.3.2 Need for a continuum approach

1.3.3 Representative elementary volume and averages

1.3.4 Scale of heterogeneity in continuum models

1.3.5 Homogenization

1.4 Scope and Organization

2 GROUNDWATER AND AQUIFERS

2.1 Definitions of Aquifers

2.2 Moisture Distribution in a Vertical Soil Profile

2.3 Classification of Aquifers

2.4 Solid Matrix Properties

2.4.1 Soil classification based on grain size distribution

2.4.2 Porosity and void ratio

2.4.3 Specific surface

2.5 Inhomogeneity and Anisotropy

2.6 Hydraulic Approach to Flow in Aquifers

3 REGIONAL GROUNDWATER BALANCE

3.1 Groundwater Flow and Leakage

3.1.1 Inflow and outflow through aquifer boundaries

3.1.2 Leakage

3.2 Natural Replenishment from Precipitation

3.3 Return Flow from Irrigation and Sewage

3.4 Artificial Recharge

3.4.1 Objectives

3.4.2 Methods

3.5 River-Aquifer Interrelationships

3.6 Springs

3.7 Evapotranspiration

3.8 Pumping and Drainage

3.9 Change in Storage

3.10 Regional Groundwater Balance

4 GROUNDWATER MOTION

4.1 Darcy's Law

4.1.1 The empirical law

4.1.2 Extension to a three-dimensional space

4.1.3 Hydraulic conductivity

4.1.4 Extension to anisotropic porous media

4.2 Darcy's Law as Momentum Balance Equation

4.2.1 Darcy's law by volume averaging

4.2.2 Darcy's law by homogenization

4.2.3 Effective hydraulic conductivity by homogenization

4.3 Non-Darcy Laws

4.3.1 Range of validity of Darcy's law

4.3.2 Non-Darcian motion equations

4.4 Aquifer Transmissivity

4.5 Dupuit Assumption for a Phreatic Aquifer

5 WATER BALANCES AND COMPLETE FLOW MODEL

5.1 Mass Balance Equations

5.1.1 Fundamental mass balance equation

5.1.2 Deformable porous medium

5.1.3 Specific storativity

5.1.4 Flow equations

5.2 Initial and Boundary Conditions

5.2.1 Boundary surface

5.2.2 Initial and general boundary conditions

5.2.3 Particular boundary conditions

5.3 Complete 3-D Mathematical Flow Model

5.3.1 Well-posed problem

5.3.2 Conceptual model

5.3.3 Standard content of a flow model

5.4 Modeling 2-D Flow in Aquifers

5.4.1 Deriving the 2-D balance equations by integration

5.4.2 Another derivation of the 2-D balance equations

5.4.3 Complete aquifer flow models

5.4.4 Effect of storage changes in an aquitard

5.4.5 Multilayered aquifer-aquitard system

5.4.6 Groundwater maps and streamlines

5.5 Land Subsidence

5.5.1 Integrated water mass balance equation

5.5.2 Integrated equilibrium equation

5.5.3 Terzaghi-Jacob vs. Biot approaches

5.5.4 Land subsidence produced by pumping

6 MODELING FLOW IN THE UNSATURATED ZONE

6.1 Statics of Fluids in the Unsaturated Zone

6.1.1 Water content

6.1.2 Surface tension

6.1.3 Capillary pressure

6.1.4 Retention curve

6.1.5 Experimental determination of

1 INTRODUCTION

1.1 Role of Groundwater in Water Resources

Systems

1.1.1 The hydrological cycle

1.1.2 Surface water versus groundwater

1.1.3 Characteristics of groundwater

1.1.4 Functions of aquifers

1.1.5 Subsurface contamination

1.1.6 Sustainable yield

1.2 Modeling

1.2.1 Modeling concepts

1.2.2 Modeling process

1.2.3. Model use

1.3 Continuum Approach to Transport in Porous Media

1.3.1 Phases, chemical species and components

1.3.2 Need for a continuum approach

1.3.3 Representative elementary volume and averages

1.3.4 Scale of heterogeneity in continuum models

1.3.5 Homogenization

1.4 Scope and Organization

2 GROUNDWATER AND AQUIFERS

2.1 Definitions of Aquifers

2.2 Moisture Distribution in a Vertical Soil Profile

2.3 Classification of Aquifers

2.4 Solid Matrix Properties

2.4.1 Soil classification based on grain size distribution

2.4.2 Porosity and void ratio

2.4.3 Specific surface

2.5 Inhomogeneity and Anisotropy

2.6 Hydraulic Approach to Flow in Aquifers

3 REGIONAL GROUNDWATER BALANCE

3.1 Groundwater Flow and Leakage

3.1.1 Inflow and outflow through aquifer boundaries

3.1.2 Leakage

3.2 Natural Replenishment from Precipitation

3.3 Return Flow from Irrigation and Sewage

3.4 Artificial Recharge

3.4.1 Objectives

3.4.2 Methods

3.5 River-Aquifer Interrelationships

3.6 Springs

3.7 Evapotranspiration

3.8 Pumping and Drainage

3.9 Change in Storage

3.10 Regional Groundwater Balance

4 GROUNDWATER MOTION

4.1 Darcy's Law

4.1.1 The empirical law

4.1.2 Extension to a three-dimensional space

4.1.3 Hydraulic conductivity

4.1.4 Extension to anisotropic porous media

4.2 Darcy's Law as Momentum Balance Equation

4.2.1 Darcy's law by volume averaging

4.2.2 Darcy's law by homogenization

4.2.3 Effective hydraulic conductivity by homogenization

4.3 Non-Darcy Laws

4.3.1 Range of validity of Darcy's law

4.3.2 Non-Darcian motion equations

4.4 Aquifer Transmissivity

4.5 Dupuit Assumption for a Phreatic Aquifer

5 WATER BALANCES AND COMPLETE FLOW MODEL

5.1 Mass Balance Equations

5.1.1 Fundamental mass balance equation

5.1.2 Deformable porous medium

5.1.3 Specific storativity

5.1.4 Flow equations

5.2 Initial and Boundary Conditions

5.2.1 Boundary surface

5.2.2 Initial and general boundary conditions

5.2.3 Particular boundary conditions

5.3 Complete 3-D Mathematical Flow Model

5.3.1 Well-posed problem

5.3.2 Conceptual model

5.3.3 Standard content of a flow model

5.4 Modeling 2-D Flow in Aquifers

5.4.1 Deriving the 2-D balance equations by integration

5.4.2 Another derivation of the 2-D balance equations

5.4.3 Complete aquifer flow models

5.4.4 Effect of storage changes in an aquitard

5.4.5 Multilayered aquifer-aquitard system

5.4.6 Groundwater maps and streamlines

5.5 Land Subsidence

5.5.1 Integrated water mass balance equation

5.5.2 Integrated equilibrium equation

5.5.3 Terzaghi-Jacob vs. Biot approaches

5.5.4 Land subsidence produced by pumping

6 MODELING FLOW IN THE UNSATURATED ZONE

6.1 Statics of Fluids in the Unsaturated Zone

6.1.1 Water content

6.1.2 Surface tension

6.1.3 Capillary pressure

6.1.4 Retention curve

6.1.5 Experimental determination of

In many parts of the world, groundwater resources are under increasing threat from growing demands, wasteful use, and contamination. To face the challenge, good planning and management practices are needed. A key to the management of groundwater is the ability to model the movement of fluids and contaminants in the subsurface. The purpose of this book is to construct conceptual and mathematical models that can provide the information required for making decisions associated with the management of groundwater resources, and the remediation of contaminated aquifers.