DeutschesFachbuch.de : Transport Modelling in Hydrogeochemical Systems Von David J. Logan

INHALTSVERZEICHNIS | öffnen

Contents
Prefacevii
1 The Diffusion Equation 1
1.1 The Diffusion Equation. 1
1.2 Semi-Infinite Domains. 8
1.2.1 Boundary Value Problems. 8
1.2.2 An Inverse Problem. 12
1.3 Sources and Duhamel's Principle. 13
1.4 Bounded Domains. 16
1.5 The Maximum Principle. 19
1.5.1 Maximum and Minimum Principles. 19
1.5.2 Comparison and Uniqueness. 25
1.6 Reference Notes. 27
2 Reaction-Advection-Dispersion Equation 29
2.1 Mass Balance. 30
2.2 Several Dimensions. 35
2.3 Adsorption Kinetics. 37
2.3.1 Instantaneous Kinetics. 38
2.3.2 Noninstantaneous Kinetics. 40
2.3.3 Mulitple-Site Kinetics. 41
2.4 Dimensionless Equations. 43
2.5 Nonlinear Equations. 44
2.5.1 A Comparison Principle. 45
2.5.2 Similarity Solutions. 48
2.5.3 Blowup of Solutions. 50
2.5.4 Stability of the Zero Solution. 52
2.6 The Reaction-Advection Equation. 54
2.6.1 Semilinear Equations. 54
2.6.2 Quasilinear Equations. 56
2.7 Examples. 58
2.7.1 Advection-Dispersion Equation. 58
2.7.2 Boundary Conditions. 60
2.7.3 A Perturbation Problem. 62
2.7.4 Radial Dispersion. 65
2.7.5 Fractured Media. 68
2.8 Reference Notes. 73
3 Traveling Wave Solutions 75
3.1 Examples of Traveling Waves. 75
3.2 Hydrogeological Models. 83
3.2.1 The Equilibrium Model. 83
3.2.2 The Nonequilibrium Model. 86
3.2.3 A Nonlinear Advection Model. 87
3.3 Discontinuous Wave Fronts. 89
3.3.1 Smooth Wave Fronts. 91
3.3.2 Supercritical Waves. 93
3.3.3 Langmuir Kinetics. 95
3.3.4 Convergence to Traveling Waves. 97
3.4 Stability of Traveling waves. 98
3.4.1 General Ideas. 98
3.4.2 L 2-Stability of Traveling Waves. 103
3.5 A Bioremediation Model. 107
3.6 Reference Notes. 111
4 Filtration Models 113
4.1 Models for Colloid Transport. 114
4.1.1 The Herzig-Leclerc-LeGoff Model. 114
4.1.2 Small Dispersion. 116
4.1.3 Variable Rate Law. 118
4.1.4 Classical Filtration Theory. 120
4.2 An Attachment-Detachment Model. 121
4.2.1 The Model. 121
4.2.2 Traveling Waves. 122
4.2.3 Contamination and Remediation Waves. 124
4.2.4 Bounded Domains. 129
4.3 Reference Notes. 133
5 Subsurface Flow Dynamics 135
5.1 Darcy's Law. 135
5.1.1 Kinematical Flow Relations. 136
5.1.2 Darcy's Law in One Dimension. 138
5.1.3 Darcy's Law in Higher Dimensions. 139
5.2 Models of Groundwater Flow. 144
5.2.1 The Governing Equations. 144
5.2.2 Boundary Conditions and Free Surfaces. 145
5.2.3 The Dupuis Hypothesis. 148
5.3 Transient Flows. 152
5.3.1 The Diffusion Equation. 152
5.3.2 Unsaturated Media. 155
5.3.3 The Presence of Solutes. 158
5.3.4 Thermal Changes. 159
5.4 Reference Notes. 161
6 Transport and Reactions in Rocks 163
6.1 Reaction Fronts. 164
6.1.1 A Redox Front. 164
6.1.2 Upstream Fronts. 165
6.2 Porosity-Mineralogy Changes, I. 169
6.2.1 Dispersive Reaction Fronts. 171
6.2.2 Pure Advection Fronts. 173
6.3 Porosity-Mineralogy Changes, II. 174
6.3.1 The Model Equations. 175
6.3.2 Dimensionless Equations. 179
6.3.3 Pressure-driven flow. 181
6.3.4 Velocity-Driven Flow. 181
6.3.5 Numerical Results. 183
6.4 General Equations of Reaction and Flow. 184
6.4.1 Mineral-Porosity Changes. 186
6.4.2 Solute Changes. 187
6.4.3 Reaction Kinetics. 187
6.5 Reference Notes. 189
A The Finite-Difference Method 193
B The Method of Lines 201
C Numerical Inversion of Transforms 205
D Notation and Symbols 209
References 211
Index 221
[weiter lesen]

REGISTER | öffnen

Index
A
adsorption, 37
advection, 32
advection equation, 34
Airy's equation, 66
aquifer, 136
average velocity, 31
B
Barenblatt solution, 143
bioremediation, 107
blowup, 51
Boussinesq equation, 152
Buckingham-Darcy law, 156
Burgers' equation, 79
C
Cauchy problem, 4
Cauchy-Dirichlet problem, 8
Cauchy-Neumann problem, 9
cementation, 163
Clausius-Duhem inequality, 6
closed operator, 102
colloid, 41, 113
compaction factor, 114
comparison principle, 25, 45, 46
compression wave, 77
confined domain, 145
consolidation theory, 144
contamination wave, 77, 123
continuity equation, 137
convolution, 5
Crank-Nicolson method, 199
D
Darcy velocity, 31, 138
Darcy's law, 138, 140
- unsaturated flow, 156
decay, 34
degenerate, 8, 45
diffusion ball, 22
diffusion constant, 1
diffusion equation, 1, 152
Dirichlet boundary condition, 8, 17
dispersion coefficient, 33
- hydrodynamic, 33
dispersion equation, 34
dissolution, 163
distribution constant, 39
dolomitization, 183
drawdown, 154
Duhamel's principle, 13
Dupuis hypothesis, 148
Dupuis-Forchheimer equation, 150
E
effective region of influence, 25
eigenfunction, 18
eigenvalue, 18, 101
elliptic, 45
- uniformly, 45
energy method, 53
equilibrium model, 43, 83
erfc function, 65
error function, 5
exponential integral, 154
F
fabric, 30
Fick's law, 2, 20, 32
filter coefficient, 115
filtration, 113
- deep bed, 116
filtration velocity, 138
finite difference method, 193
Fisher's equation, 79
flux, 31
- advective, 32
- bounded, 90
- molecular diffusion, 32
Fourier boundary condition, 10, 18, 60
Fourier's method, 16
Fourier-Kelvin problem, 10
fracture, 68
free surface condition, 145
fundamental solution, 3
G
Green's function, 4
H
head, 138, 139
- elevation, 139
- pressure, 139
- suction, 156
Henry's theorem, 103
Herzig-Leclerc-LeGoff model, 114
heteroclinic orbit, 80
Hubert space, 17
hydraulic conductivity, 138
I
impermeable boundary, 146
incompressibility, 137
inverse problem, 12
isotherm
- adsorption, 39
- Freundlich, 40
- Langmuir, 39
- linear adsorption, 39
J
Jacob's approximation, 155
K
kinematic dispersion, 32
kinetics
- attachment-detachment, 121
- instantaneous, 38
- multiple site, 41
- noninstantaneous, 40
Korteweg-deVries equation, 83
Koseny-Carman formula, 130
Kozeny-Carman formula, 180
L
linearization, 100
linearized perturbation equation, 100
longitudinal dispersivity, 33
M
mass action, 188
mass balance, 31, 35, 69, 137, 186
mean value property, 23
method of lines, 201
Monod kinetics, 108
N
Navier-Stokes equations, 138, 141
Neumann boundary condition, 9, 17
nonequilibrium model, 43, 86
nonlocal equation, 131
nullclines, 86
P
parabolic, 1, 7, 45
- uniformly, 7, 45
Peclet number, 43
periodic boundary conditions, 9
permeability, 139
plane wave, 2, 58
Poiseuille flow, 143
Poisson representation, 5
porosity, 30
porous media equation, 49
pulse, 77
Q
quasi-steady state hypothesis, 189
quasilinear, 56
R
radial dispersion, 65
rarefaction wave, 77
reaction kinetics, 187
redox front, 164
remediation wave, 77, 123
replacement reaction, 163, 175
reservoir boundary, 146
resolvent set, 101
retardation constant, 39
Richard's equation, 157
S
saturated, 30, 136
seepage face, 146
similarity solution, 48
singular perturbation, 62
specific storage coefficient, 155
specific yield, 152
spectrum
- continuous, 101
- essential, 101
- point, 101
- residual, 101
square integrable functions, 17
stability
- traveling waves, 98
- zero solution, 52
Stehfest algorithm, 66, 207
storativity, 155
strong maximum principle, 24
Sturm-Liouville problem, 18
T
Talbot algorithm, 205
Theis' approximation, 155
thermal energy balance, 160
tortuosity, 32
transmissivity, 152
traveling wave, 34, 75
U
unconfined domain, 145
uniqueness, 26
unsaturated media, 155
upstream front, 165
V
variation of parameters, 15
volume balance equation, 114
volumetric water content, 155
W
water table, 136
wave front, 75, 122
- discontinuous, 89
weak maximum principle, 20
[weiter lesen]