Groundwater pollution : theory, methodology, modelling, and practical rules

CONTENTS ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . vii KEYS TO THIS BOOK . . . . . . . . . . . . . . . . . . . . . ix INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . xi CHAPTER 1 . GENERAL DESCRIPTION OF GROUNDWATER POLLUTION . . . 1 1.1. Definition of groundwater pollution . . . . . . . . . . . . . . . 1 1.2. Origins of groundwater pollution . . . . . . . . . . . . . . . . 1 1.3. Physical characteristics of groundwater pollution . . . . . . . . . . . 2 CHAPTER 2 . THE THEORY OF DISPERSION IN POROUS MEDIA . . 2.1. Description of dispersion . . . . . . . . . . . . . . 2.1.1. A simple example . . . . . . . . . . . . . . 2.1.2. Defiaition of dispersion . . . . . . . . . . . . 2.1.3. Mechanisms of dispersion . . . . . . . . . . . . 2.1.4. Characteristic parameters of dispersion . . . . . . . . . . . . . . . . . 2.3.1. Experimental results . . . . . . . . . . . . . 2.3.2. Critiques of the concept of continuous medium . . . . 2.3.3. Influence of the boundary . . . . . . . . . . . 2.3.5. Conclusion . . . . . . . . . . . . . . . . 2.2. Conceptual representations of dispersion 2.3. Critiques of the classical foundations of the dispersion equation . 2.3.4. Critiques of the concept of spatial averaging . . . . . . (homogeneous media) . . . . . . . . . . . . . . 2.4. Laboratory investigations of the foundations of dispersion 2.4.1. Dimensional analysis . . . . . . . . . . . . . 2.4.2. Tracer case: longitudinal dispersion . . . . . . . . 2.4.3. Tracer case: lateral dispersion . . . . . . . . . . 2.4.4. General case: longitudinal dispersion (unconsolidated media) 2.4.5. General case: lateral dispersion . . . . . . . . . . . . . . . . 2.5.1. A stratified medium . . . . . . . . . . . . . 2.5.2. A heterogeneous non-stratified medium 2.5.3. Conclusion . . . . . . . . . . . . . . . . 2.5. Laboratory investigations in heterogeneous media . . . . . . . . . . . 5 . . . . 5 . . . . 5 . . . . 6 . . . . 6 . . . . 8 . . . 1 3 . . . 17 . . . 18 . . . 21 . . . 23 . . . 25 . . . 26 . . . 27 . . . 28 . . . 29 . . . 32 . . . 34 . . . 36 . . . 37 . . . 38 . . . 44 . . . 46 CHAPTER 3 . THE METHODOLOGY OF TECHNICAL STUDIES OF GROUNDWATER POLLUTION . . . . . . . . . . . . . . . . . . . 47 3.1. The scale problem . . . . . . . . . . . . . . . . . . . . 47 3.2. The methodology . . . . . . . . . . . . . . . . . . . . 48 3.2.1. Decision criteria . . . . . . . . . . . . . . . . . . 48 3.2.2. The dispersion scheme . . . . . . . . . . . . . . . . 49 3.2.3. Practical use of the dispersion scheme . . . . . . . . . . . 50 3.2.4. The general methodology . . . . . . . . . . . . . . . 53 3.3. Examples: Type projects . . . . . . . . . . . . . . . . . . 54 3.3.1. A study of pollution hazards in a large aquifer feeding an urban community . . . . . . . . . . . . . . . . . . . . 54 XIV CONTENTS 3.3.2. The setting of sanitary landfills near an urban community . . . . 56 CHAPTER 4 . THE EXPERIMENTAL DETERMINATION OF GROUNDWATER POLLUTION PARAMETERS . . . . . . . . . . . . . . . 59 59 4.1.1. The longitudinal dispersion coefficient . . . . . . . . . . 60 4.1.2. The lateral dispersion coefficient . . . . . . . . . . . . 65 4.1.3. Radial flow . . . . . . . . . . . . . . . . . . . 66 4.1.4. Remarks about heterogeneous media . . . . . . . . . . . 68 . . . . . 68 4.2.1. Local scale: a single-well pulse technique . . . . . . . . . . 68 4.2.2. Global scale 1 : multiple-well methods . . . . . . . . . . . 78 4.2.3. Global scale 2: a single-well method . . . . . . . . . . . 83 4.2.4. Regional scale: use of environmental tracers . . . . . . . . . 100 . . . . . . 102 4.3.1. Indirect estimates of the velocities through Darcy's law . . . . . 103 4.3.2. Direct estimates of velocities . . . . . . . . . . . . . . 106 4.3.3. The single-well possibilities . . . . . . . . . . . . . . 110 4.3.4. A note on porosity measurements in the saturated zone . . . . . 111 CHAPTER 5 . CLASSICAL MATHEMATICAL MODELS AND THEIR NUMERICAL FORMULATION . . . . . . . . . . . . . . . . . . 115 5.1. Canonical rectangular coordinate models . . . . . . . . . . . . 115 5.1.1. Bidimensional monolayer model . . . . . . . . . . . . 115 5.1.2. Bidimensional multilayer model . . . . . . . . . . . . . 118 5.2. Curvilinear coordinate models . . . . . . . . . . . . . . . . 120 5.2.1. Curvilinear coordinates: some definitions . . . . . . . . . 120 5.2.2. Single-well model . . . . . . . . . . . . . . . . . 123 5.2.3. Multiple-well model . . . . . . . . . . . . . . . . . 127 5.3. Analytical models . . . . . . . . . . . . . . . . . . . . 130 5.3.1. A monodimensional model . . . . . . . . . . . . . . 13 0 5.3.2. A bidimensional horizontal model . . . . . . . . . . . . 1 31 5.4. A black-box model . . . . . . . . . . . . . . . . . . . 133 5.4.1. Classical deconvolution methods . . . . . . . . . . . . 135 5.4.2. Emsellem's deconvolution method . . . . . . . . . . . . 136 CHAPTER 6 . CASE HISTORIES . . . . . . . . . . . . . . . . . 1 41 6.1. Description and evolution of an existing case of pollution: pollution of the Rhine aquifer by mining wastes . . . . . . . . . . . . . . . 1 41 6.1.1. General description of the problem . . . . . . . . . . . 142 6.1.2. The operations . . . . . . . . . . . . . . . . . . 142 6.1.3. The models . . . . . . . . . . . . . . . . . . . 148 6.1.4. Conclusions . . . . . . . . . . . . . . . . . . . 15 4 6.2. The protection of an aquifer against possible pollution . . . . . . . . 155 6.2.1. Preliminary study of existing data . . . . . . . . . . . . 155 6.2.2. The working assumption . . . . . . . . . . . . . . . 15 6 6.2.3. The determination of the dispersion parameters . . . . . . . 157 6.2.4. The models . . . . . . . . . . . . . . . . . . . 161 6.3. Salt-water intrusion into a coastal aquifer . . . . . . . . . . . . 161 6.3.1. Preliminary studies . . . . . . . . . . . . . . . . . 161 6.3.2. The working assumption . . . . . . . . . . . . . . . 1 65 6.3.3. Use of the dispersion scheme . . . . . . . . . . . . . . 16 5 6.3.4. Difficulties of the study . . . . . . . . . . . . . . . 16 6 4.1. Explicit formulas for the estimate of dispersion coefficients . . . . . . 4.2. Field methods for the determination of dispersion coefficients 4.3. Field methods for the determination of pollution velocities CONTENTS xv 6.4. A radioactive pollution by liquid wastes . . . . . . . . . . . . . 167 6.4.1. Preliminary studies . . . . . . . . . . . . . . . . . . 168 6.4.2. Decision criteria . . . . . . . . . . . . . . . . . . 171 6.4.3. The dispersion scheme . . . . . . . . . . . . . . . . 171 6.4.4. The determination of the dispersion coefficients . . . . . . . 173 6.4.5. A forecasting model of pollution . . . . . . . . . . . . 175 CHAPTER 7 . POLLUTION AND THE MANAGEMENT OF WATER RESOURCES - A GENERAL METHODOLOGY . . . . . . . . . . . . . . 1 77 7.1. Technical methodology . . . . . . . . . . . . . . . . . . 178 7.2. Preparation and treatment of the information . . . . . . . . . . . 1 80 7.2.2. Screening of numerical information . . . . . . . . . . . 181 7.2.3. Structuration of non-numerical information . . . . . . . . . 185 7.2.4. Optimization of the investigation and control nets . . . . . . 186 7.3. The models . . . . . . . . . . . . . . . . . . . . . . 187 7.3.1. The hydraulic models . . . . . . . . . . . . . . . . 187 7.3.2. The pollution models . . . . . . . . . . . . . . . . 189 7.4. Management concepts . . . . . . . . . . . . . . . . . . 190 7.4.1. Place of groundwater-pollution management . . . . . . . . 191 7.4.2. Elements of water-resources management . . . . . . . . . 193 7.4.3. Basic principles of an approach to water-resources management . . 195 7.2.1. System identification . . . . . . . . . . . . . . . . 180 CHAPTER 8 . AN INVERSE DISPERSION PROBLEM: THE POINT-DILUTION THEORY . . . . . . . . . . . . . . . . . . . 199 8.1. Preliminary definitions . . . . . . . . . . . . . . . . . . 199 8.2. The determination of the diffusion coefficient of an isotropic diffusion operator with constant coefficients . . . . . . . . . . . . . . . . . 201 8.3. The determination of the coefficients of the diffusion operator with varying coefficients . . . . . . . . . . . . . . . . . . . . . . 205 8.3.1. The isotropic diffusion operator . . . . . . . . . . . . 205 8.3.2. The anisotropic diffusion operator . . . . . . . . . . . . 214 8.4. The mathematical model and the experience . . . . . . . . . . . 215 8.4.1. Consistency between the model and the experience . . . . . . 215 8.4.2. Elements for an error calculus on the dispersion coefficients . . . 216 8.4.3. Stability of the point-dilution theory . . . . . . . . . . . 220 CHAPTER 9 . NUMERICAL ANALYSIS OF GROUNDWATER POLLUTION PROBLEMS . . . . . . . . . . . . . . . . . . . . . 223 9.1. Iterative procedures: Principles and theorems . . . . . . . . . . . 224 9.1.1. Principle . . . . . . . . . . . . . . . . . . . . 224 9.1.2. Convergence . . . . . . . . . . . . . . . . . . . 22 6 9.1.3. Construction of an iterative process . . . . . . . . . . . 228 9.1.4. Application to linear systems of equations . . . . . . . . . 229 9.1.5. Linear systems: basic theorems . . . . . . . . . . . . . 231 9.2. Iterative procedures for linear systems: Methods . . . . . . . . . . 235 9.2.1. Jacobi’s method on a simple example . . . . . . . . . . . 235 9.2.2. Gauss-Seidel method on a simple example . . . . . . . . . 23 6 9.2.3. Successive overrelaxation method on a simple example . . . . . 237 9.2.4. General formulas . . . . . . . . . . . . . . . . . 23 8 9.2.5. Convergence of the methods . . . . . . . . . . . . . . 239 9.2.6. Block iterative methods . . . . . . . . . . . . . . . 241 9.3. Direct procedures . . . . . . . . . . . . . . . . . . . . 243 XVI CONTENTS 9.3.1. General Gauss elimination method . . . . . . . . . . . . 243 9.3.2. Tridiagonal Gauss elimination method . . . . . . . . . . 244 . . . . . . . 2 46 9.4.1. Approximation of derivatives . . . . . . . . . . . . . 246 9.4.2. Approximation of the equation . . . . . . . . . . . . . 247 9.4.3. Stability and convergence of the approximations . . . . . . . 250 9.4.4. Alternating Direction Implicit Procedure (ADIP) . . . . . . . 253 9.4.5. Some difficulties of the finite-difference approximations . . . . 254 9.4.6. The method of characteristics . . . . . . . . . . . . . 256 9.4.7. A finite-element approximation: Galerkin’s method . . . . . . 2 58 9.5. The balance-of-fluxes theory of the hydrologic equation . . . . . . . 262 9.5.1. Balance of elementary blocks . . . . . . . . . . . . . 26 2 9.5.2. Boundary conditions . . . . . . . . . . . . . . . . 265 9.5.3. A simple example . . . . . . . . . . . . . . . . . 265 9.5.4. Some properties of the transmissivity matrix . . . . . . . . 267 9.6. Practical use of modelling techniques and programming . . . . . . . 268 Appendix I . BASIC FACTS OF GROUNDWATER MOVEMENT . . . . . . . 275 A.l.l. Cause of groundwater movement . . . . . . . . . . . . 275 A.1.2. Confined and unconfined aquifers . . . . . . . . . . . . 276 A.1.3. Hydraulic gradient and velocities . . . . . . . . . . . . 27 7 A.1.4. Darcy’s law . . . . . . . . . . . . . . . . . . . 279 A.1.5. Filtration rate of flow . . . . . . . . . . . . . . . . 279 A.1.6. Darcy’s porosity . . . . . . . . . . . . . . . . . . 2 80 A.1.7. Transmissivity . . . . . . . . . . . . . . . . . . 281 A.1.8. The storage coefficient . . . . . . . . . . . . . . . 281 A.1.9. Generalization of Darcy’s law . . . . . . . . . . . . . 283 A.l.lO. Some considerations about the flow regimes . . . . . . . . 28 6 Appendix I1 . ELEMENTS OF GEOPHYSICS: SURFACE ELECTRICAL METHODS . 289 A.2.1. Potential Method (P.M.) . . . . . . . . . . . . . . . 28 9 A.2.2. Resistivity measurements . . . . . . . . . . . . . . . 2 90 A.2.3. Resistivity profiles . . . . . . . . . . . . . . . . . 29 1 A.2.4. Rectangle measurements . . . . . . . . . . . . . . . 2 91 A.2.5. Electrical soundings . . . . . . . . . . . . . . . . 292 Appendix I11 . SOME ELEMENTS OF MATRIX ALGEBRA . . . . . . . . 297 A.3.1. The vector space R” . . . . . . . . . . . . . . . . 2 97 A.3.2. Matrices . . . . . . . . . . . . . . . . . . . . 298 A.3.3. Determinants . . . . . . . . . . . . . . . . . . . 30 4 A.3.4. Eigenvalues and eigenvectors of a matrix of order n . . . . . . 306 A.3.5. Norms of vectors and matrices . . . . . . . . . . . . . 30 8 Appendix IV . WATER QUALITY: NORMS AND CRITERIA . . . . . . . . 311 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . 313 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . 327