Geological Fluid Dynamics: Sub-surface Flow and Reactions

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Preface......Page 13
Contents......Page 9
1 Introduction......Page 15
2.1 Pores and fractures......Page 20
2.2.1 Porosity......Page 22
2.2.2 Double porosity in a fracture–matrix medium......Page 25
2.3 The transport velocity and mass conservation......Page 26
2.3.1 Mass conservation......Page 27
2.3.2 The incompressibility condition......Page 28
2.3.3 The stream function......Page 30
2.4.1 Hydrostatics......Page 32
2.4.2 Interstitial flow through a uniform matrix......Page 33
2.4.3 Permeability......Page 35
2.4.4 Reduced pressure and buoyancy......Page 37
2.4.5 Boundary conditions......Page 38
2.5.1 Flow tubes and flow resistance......Page 41
2.5.2 Energy balances......Page 43
2.6.1 The uniqueness theorem......Page 45
2.6.2 The minimum dissipation theorem......Page 46
2.7 The thermal energy balance......Page 47
2.8 Dissolved species balance......Page 49
2.8.1 Rate-limiting steps and the solute source term......Page 51
2.8.2 First-order reactions......Page 54
2.9 Equations of state......Page 55
2.10 Dispersion......Page 57
2.10.1 Kinematics of dispersion......Page 58
2.10.2 Dispersion in a steady plume......Page 62
3.1 Flow in uniform permeable media......Page 65
3.1.1 Flow constraints......Page 66
3.1.2 Laplace’s equation......Page 70
3.1.3 Some local flow patterns......Page 73
3.1.4 Two-dimensional surface aquifers......Page 75
3.2.1 How do surface aquifers work?......Page 77
3.2.2 Regional scale aquifer flow......Page 81
3.2.3 An example: the aquifer in Kent County, Maryland......Page 84
3.2.4 Scales of water table elevation; relaxation, emergence and recharge times......Page 87
3.2.5 Groundwater age distribution in an aquifer......Page 91
3.3.1 Measurements of permeability variations in sandy aquifers......Page 92
3.3.2 Measured dispersion of injected tracers over sub-kilometer scales......Page 97
3.3.3 Flow through a spatially random permeability field......Page 99
3.4.1 Anisotropy produced by fine-scale layering......Page 107
3.4.2 Flow across layering with scattered fracture bands or gaps......Page 110
3.4.3 Confining layers in a surface aquifer......Page 114
3.4.4 Mixing in more permeable lenses......Page 119
3.5 Fracture–matrix or “crack and block” media......Page 120
3.5.1 Reservoirs and conduits......Page 123
3.5.2 Transport of passive solute in co-existing fracture and matrix block flows......Page 125
3.5.3 A passive contaminant front in a fracture–matrix aquifer......Page 127
3.5.4 Distributed solute entering across the water table......Page 130
3.6.1 Diffusion of pressure......Page 132
3.6.2 Pressure diffusion and de-gassing following seismic release......Page 134
3.6.3 Diffusion of pressure in a fracture–matrix medium......Page 135
4.1 The occurrence of thermally driven flows......Page 139
4.2 Buoyancy and the rotation vector......Page 141
4.3 General properties of buoyancy-driven flows......Page 144
4.3.1 Heat advection versus matrix diffusion: the Peclet number......Page 145
4.3.2 Thermally driven flows: the Rayleigh number......Page 147
4.4.1 Slope convection with large aspect ratio l/h......Page 149
4.4.2 Circulation in isolated, sloping permeable strata......Page 151
4.4.3 Compact layered platforms and reefs at low Rayleigh numbers......Page 154
4.4.4 Two-dimensional reefs or banks......Page 157
4.5.1 Two-dimensional numerical solutions......Page 160
4.5.2 How do these flows work?......Page 167
4.5.3 Scaling analysis for two-dimemsional flows......Page 169
4.5.4 Circular platforms......Page 172
4.5.5 Similarity solutions – two-dimensional plumes......Page 173
4.5.6 The axi-symmetrical plume in a semi-infinite region......Page 176
4.6 Salinity-driven flows......Page 178
4.6.1 Freshwater lenses......Page 179
4.6.2 Gravity currents in porous media......Page 182
4.7 Thermal instabilities......Page 184
4.7.1 Rayleigh–Darcy instability......Page 185
4.7.2 A physical discussion......Page 190
4.7.3 Related configurations......Page 192
4.8 Thermo-haline circulations......Page 194
4.8.1 Temperature destabilizing, salinity stabilizing,…......Page 197
4.8.4 Temperature stabilizing, salinity destabilizing,…......Page 199
4.8.5 Brine invasion beneath hypersaline lagoons......Page 201
4.9 Instability of fronts......Page 203
5.1 Simple reaction types......Page 208
5.1.1 Dissolution......Page 209
5.1.2 Combination......Page 211
5.1.3 Replacement......Page 213
5.2 An outline of flow-controlled reaction scenarios......Page 216
5.2.1 The equilibration or reaction length......Page 217
5.2.2 The reaction front scenario......Page 218
5.2.3 The gradient reaction scenario......Page 220
5.3.1 Dissolution in a uniform flow......Page 222
5.3.2 Leaching in aquifer flow with infiltration across the water table......Page 225
5.3.3 Dissolution in a fracture–matrix medium......Page 229
5.3.4 The depletion time......Page 231
5.4 The isothermal reaction front scenario......Page 232
5.4.1 The front propagation speed and the fluid–rock ratio......Page 233
5.4.2 Profiles in the reaction front......Page 237
5.4.3 Reaction fronts in fracture–matrix media......Page 239
5.4.4 Sorbing contaminant plumes......Page 242
5.5 The gradient reaction scenario......Page 249
5.5.1 Dissolution and deposition rates in gradient reactions......Page 253
5.5.2 The rock alteration index......Page 256
5.5.3 Enhancement and destruction of porosity......Page 257
5.6 The mixing zone scenario......Page 261
5.7 Isotherm-following reactions......Page 263
5.7.1 The reaction zone......Page 265
5.7.2 Dehydration......Page 267
5.8 Paleo-convection and dolomite formation in the Latemar Massif......Page 269
5.9 Distributions of mineral alteration in Mississippi Valley-type deposits......Page 274
6.1 Extensions......Page 278
6.2.2 Permeability variations and the rotation vector......Page 279
6.2.3 Confined aquifers......Page 280
6.2.5 The Hele-Shaw cell......Page 281
Bibliography......Page 283
Index......Page 293