I
Index
Abstract
VII
1. Pollutants propagation: mathematical modeling
1
1.1. Propagation mechanisms of pollutants in groundwater 2
1.1.1. Advection 2 1.1.2. Molecular diffusion 2 1.1.3. Kinematic dispersion 3 1.1.4. Hydrodynamic dispersion 5 1.1.4.1. Peclet number 6 1.1.5. Reaction models 7 1.1.6. Biodegradation 9 1.1.7. Adsorption/Desorption 10
1.2. Differential equation fundamentals for mass transport 13
1.2.1. Mass balance for the contaminant 13
1.2.2. Conservative and non-conservative solutes 14
1.3. Theoretical models for one-dimensional problems 17
1.3.1. Conservative solutes 17
1.3.1.1. Continuous inlet distribution 17
1.3.1.2. Impulsive inlet distribution 18
1.3.2. Non-conservative solutes 18
1.3.2.1. Solutes subject to chemical degradation 19
II
1.3.2.3. Solutes subject to chemical degradation and adsorption 20
1.4. Comparison of the one-dimensional models 29
1.4.1. Limit conditions of the Williams & Tomasko one-dimensional solution 29
1.4.2. Validity of the Williams & Tomasko one dimensional solution 32
1.5. Theoretical models for three-dimensional problems 34
1.5.1. Conservative solutes 34
1.5.1.1. Instantaneous inlet distribution, point source 34
1.5.1.2. Continuous inlet distribution, areal source 35
1.5.2. Non conservative solutes 36
1.5.2.1. Instantaneous point source 37
1.5.2.2. Continuous volumetric source 39
1.5.2.3. Plane source 40
1.5.2.4. Continuous volumetric source with exponential source decay 43
1.5.2.5. Continuous plane source with exponential source decay 44
1.6. Comparison between plane source and volumetric source: numerical
simulations 45
Bibliography 48
List of Tables 50
III
2. Analytical solutions of one-dimensional contaminant
transport with source production-decay in a semi-finite
domain
51
2.1. Governing equations 54
2.2. Analytical solutions for one-dimensional problems 55
2.2.1. Constant inlet distribution subject to first-type boundary conditions and
semi-finite domain 56
2.2.2. Constant inlet distribution subject to third-type boundary conditions
and semi-finite domain 56
2.2.3. Exponential inlet distribution subject to first-type boundary conditions
and semi-finite domain 57
2.2.4. Exponential inlet distribution subject to third-type boundary conditions
and semi-finite domain 58
2.3. The proposed analytical solution with simultaneous source production
and decay 58
2.3.1. General inlet distribution subject to third-type boundary conditions and
semi-finite domain 59
2.3.2. Models comparison 63
2.4. Some possible solutions 65
2.4.1. Linear combination of exponential inlet distribution subject to third-type boundary conditions and semi-finite domain 65
2.4.1.1. Limit cases 67
2.4.2. Linear combination of exponential inlet distribution subject to first-type boundary conditions and semi-finite domain 69
IV
2.4.3. Consecutive reactions at the source subject to third-type boundary
conditions in semi-finite domain 74
2.4.4. Consecutive reactions at the source subject to first-type boundary
conditions in semi-finite domain 76
2.4.5. Finite release at the source subject to third-type boundary conditions in
semi-finite domain 77
2.5. Some simulations and discussion 78
2.5.1. Linear combination of exponential inlet distribution subject to third-type boundary conditions and semi-finite domain 80
2.5.1.1. Limit cases 83
2.5.2. Linear combination of exponential inlet distribution subject to first-type boundary conditions and semi-finite domain 88
2.5.2.1. Limit cases 91
2.5.3. Finite release at the source subject to third-type boundary conditions in
semi-finite domain 94 2.6. Example of application 96 Appendix A 100 Bibliography 104 List of Tables 108 List of Figures 108
3. Analytical solutions and approximation errors of new
3D contaminant transport models
110
V
3.2. Three-dimensional solution for a plane source with exponential decay 121 3.3. Approximation Errors 123 3.3.1. Concentration fields 127 3.3.2. Relative errors 131 3.3.2.1. Time dependence 135 3.3.3. Centerline profiles 138 3.3.4. Transverse profiles 140
3.4. Three-dimensional solutions for a plane source with exponential decay
and production at the source 143
3.5. Approximation Errors for 3D solutions for a plane source with
exponential decay and production at the source 147
3.5.1. Concentration fields 149 3.5.2. Relative errors 154 3.5.2.1. Time dependence 156 3.5.3. Centerline profiles 160 3.5.4. Trasverse profiles 163 Bibliography 165 List of Tables 169 List of Figures 169
