Modeling Groundwater Flow and Contaminant Transport / Edition 1

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Overview

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.

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Editorial Reviews

From the Publisher
From the reviews:

“This book is a comprehensive and authoritative treatise of groundwater flow and transport modeling. It provides easy-to-follow descriptions of basic concepts, governing equations, relevant parameters, methods of measurement and observation, numerical solution methods, and interpretation of results, for real-world situations. It is a "must have" for students, teachers, researchers, engineers, and managers in subsurface hydrology and management." S.M. Hassanizadeh, Professor of Hydrogeology, Utrecht University, The Netherlands

“A very comprehensive and well written textbook that addresses the formulation of both conceptual and mathematical models to predict flow and transport through porous media and to make decisions for a sustainable development of the subsurface resources and remediation of contaminated groundwater based on optimal management under uncertainty. The readers who are potentially interested include practitioners, modelers, managers and researchers as well as students at the graduate and upper undergraduate level in civil and environmental engineering." Giuseppe Gambolati, Universita degli Studi di Padova, Italy

“This book is a must for researchers as well as practitioners who are interested in understanding the fundamentals and the state-of-the-art of groundwater modeling issues." Prabhakar Clement, Arthur H. Feagin Chair of Civil Engineering, Auburn University, USA

“I teach three graduate courses, “Introduction to Modeling Transport Phenomena for Aquifer Remediation”, “Modeling Flow and Transport through Heterogeneous Media”, and “Numerical Approximation by the Finite Element Method”, to students coming from Natural Sciences and Engineering Sciences areas at my university, and also at several world-wide institutes. This book comprehensively covers a spectrum of theoretical and practical topics addressing quantitative modeling and environmental issues of groundwater flow and transport. I will definitely recommend the book as a valuable reference to my students and colleagues. " Shaul Sorek, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Israel

“This is an excellent reference book for postgraduate students and researchers in the discipline of groundwater. This book provides detailed information regarding modelling of contaminant transport in porous medium that is particular important for environmental scientists and numerical modellers." Dong-Sheng Jeng, NRP Chair in Civil Engineering, University of Dundee, Scotland, UK

“Bear and Cheng have provided a unified and systematic approach in this reference book for engineers and scientists interested in modelling subsurface flow. They presented each chapter with clarity explaining why the topics discussed are of importance. In addition to covering traditional areas of groundwater flow and contaminant transport, the authors provide a good introduction to topics such as uncertainty, optimization and inverse problems which gained importance in recent years." Yavuz Corapcioglu, Department of Civil Engineering, Texas A&M University, USA

“This book presents the methodology and procedures for constructing complete mathematical models of two problems: first, groundwater flow, and second, groundwater contaminant transport, both in saturated and unsaturated zones. … The book could be of interest to researchers, scientists and professionals who face the need to build and solve models of flow and contaminant transport in the subsurface.” (Valeriu Al. Sava, Zentralblatt MATH, Vol. 1195, 2010)

“This new textbook by Jacob Bear … and Alexander H.-D. Cheng provides a comprehensive reference on this subject. … The topics covered in this textbook are comprehensive, and the treatment is extremely thorough; thus … Modeling Groundwater Flow and Contaminant Transport provides an excellent, up-to-date reference for researchers and professionals interested in modeling groundwater flow.” (Sujit S. Datta, Pure and Applied Geophysics, August, 2012)

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Product Details

Table of Contents

Preface

List 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 retention curve

6.1.6 Matric and other potentials

6.1.6 Hysteresis

6.1.8 Saturation distribution along the vertical

6.1.9 Specific yield and field capacity

6.2 Motion Equations

6.2.1 Coupling between the phases

6.2.2 Darcy’s law for unsaturated flow

6.2.3 Effective permeability

6.3 Mass Balance Equation and Complete Model

6.3.1 Mass balance equations

6.3.2 Initial and boundary conditions

6.3.3 Complete flow model

6.4 Methods of Solution

6.4.1 Analytical solutions

6.4.2 Numerical solutions

6.5 Some Comments on Three Fluid Phases

6.5.1 Statics

6.5.2 Motion equations for three fluids

6.5.3 Mass balance equation and complete model

7 MODELING CONTAMINANT TRANSPORT

7.1 Contaminant Fluxes

7.1.1 Measures of phase composition

7.1.2 Advective flux

7.1.3 Diffusive flux

7.1.4 Hydrodynamic dispersion

7.1.5 Dispersive flux

7.1.6 Dispersion coefficient and dispersivity

7.1.7 Total flux

7.1.8 Field-scale heterogeneity

7.2 Balance Equation for Single Species

7.2.1 Single cell model

7.2.2 Fundamental balance equation

7.2.3 Pumping and injection

7.3 Sources and Sinks

7.3.1 Conditions for chemical equilibrium

7.3.2 Equilibrium chemical reactions

7.3.3 Equilibrium adsorption

7.3.4 Ion exchange

7.3.5 Volatilization and dissolution

7.3.6 Nonequilibrium reactions

7.3.7 Biotransformations

7.4 Complete Mathematical Model with Sources

7.4.1 Balance equations with sources

7.4.2 Retardation

7.4.3 Initial condition and boundary conditions

7.4.4 Complete model for single component

7.4.5 Some analytical solutions

7.5 Immobile Water and Double Porosity Models

7.5.1 Immobile water

7.5.2 Double porosity medium

7.6 Eulerian-Lagrangian Formulation

7.7 Evaluating Dominance of effects

7.8 Transport Without Dispersion

7.8.1 Transport by advection only

7.8.2 Velocity field

7.8.3 Travel time

7.9 Multiple Components and Reactive Transport

7.9.1 Radionuclide decay chain

7.9.2 Chemically reacting species

7.9.3 Three multicomponent phases

7.9.4 Primary variables

7.9.5 Methods of solution for reactive transport models

7.10 Remediation Techniques

7.10.1 General considerations

7.10.2 Caps and cutoff walls

7.10.3 Pump-and-treat

7.10.4 Soil vapor extraction

7.10.5 Air sparging

7.10.6 Permeable reactive barrier

8 NUMERICAL MODELS AND COMPUTER CODES

8.1 Finite Difference Methods

8.1.1 Laplace equation

8.1.2 Diffusion equation

8.1.3 Cell-centered approach

8.1.4 Boundary and boundary conditions

8.2 Finite Volume Methods

8.3 Finite Element Methods

8.3.1 Weighted residual methods

8.3.2 Galerkin finite element methods

8.3.3 Meshless finite element methods

8.3.4 Control volume finite element methods

8.4 Boundary Element Methods

8.5 Radial Basis Function Collocation Methods

8.6 Eulerian-Lagrangian Methods

8.6.1 Lagrangian method

8.6.2 Method of characteristics

8.6.3 Random walk method

8.6.4 Modified Eulerian-Lagrangian method

8.7 Matrix Solution

8.7.1 Conjugate gradient method

8.7.2 Preconditioning

8.8 Computer Codes

9 SEA WATER INTRUSION

9.1 Occurrence and Exploration

9.1.1 Occurrence of seawater intrusion

9.1.2 Exploration of saltwater intrusion

9.2 Sharp Interface Models

9.2.1 Sharp interface

9.2.2 Ghyben-Herzberg approximation

9.2.3 Upconing

9.2.4 Essentially horizontal flow model

9.2.5 Some analytical solutions for stationary interface

9.2.6 Multilayered Aquifers

9.3 Transition Zone Modeling

9.3.1 Variable density model

9.3.2 Examples

9.4 Management of Coastal Aquifer

10 MODELING UNDER UNCERTAINTY

10.1 Shastic Processes

10.1.1 Random process

10.1.2 Quantifying uncertainty as shastic process

10.1.3 Ensemble statistics

10.1.4 Spatial (or temporal) statistics

10.1.5 Ergodicity hypothesis

10.2 Tools for Uncertainty Analysis

10.2.1 Kriging

10.2.2 Sensitivity analysis

10.2.3 Monte Carlo simulation

10.2.4 Generation of random field

10.3 Examples of Uncertainty Problems

10.3.1 Random boundary conditions

10.3.2 Uncertain parameters

11. OPTIMIZATION, INVERSE, AND MANAGEMENT TOOLS

11.1 Groundwater Management

11.2 Optimization

11.2.1 Optimization problem

11.2.2 Linear programming

11.2.3 Nonlinear problems and unconstrained optimization

11.2.4 Gradient search method

11.2.5 Genetic algorithm and simulated annealing

11.2.6 Chance constrained optimization

11.2.7 Multiobjective optimization

11.3 Inverse Problem

11.3.1 Pumping test

11.2.2 Regional scale parameter estimation

References

Index

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