Geological fluid dynamics : sub-surface flow and reactions

This book is the long-awaited successor to Owen M. Phillips's classic textbook, Flow and Reactions in Permeable Rocks, published in 1991. In the intervening eighteen years between the two, significant advances have been made to our understanding of subterranean flow, especially through the vast amount of research into underground storage of nuclear waste and aquifer pollution. This new book integrates and extends these modern ideas and techniques and applies them to the physics and chemistry of sub-surface flows in water-saturated, sandy and rocky media. It describes essential scientific concepts and tools for hydrologists and public health ecologists concerned with present day flow and transport, and also for geologists who interpret present day patterns of mineralization in terms of fluid flow in the distant past. The book is ideal for graduate students and professionals in hydrology, water resources, and aqueous geochemistry.

Preface	p. xi
1 Introduction	p. 1
2 The basic principles	p. 6
2.1 Pores and fractures	p. 6
2.2 Geometrical characteristics	p. 8
2.2.1 Porosity	p. 8
2.2.2 Double porosity in a fracture-matrix medium	p. 11
2.3 The transport velocity and mass conservation	p. 12
2.3.1 Mass Conservation	p. 13
2.3.2 The incompressibility condition	p. 14
2.3.3 The stream function	p. 16
2.4 Darcy's law	p. 18
2.4.1 Hydrostatics	p. 18
2.4.2 Interstitial flow through a uniform matrix	p. 19
2.4.3 Permeability	p. 21
2.4.4 Reduced pressure and buoyancy	p. 23
2.4.5 Boundary conditions	p. 24
2.5 Mechanical energy balances	p. 27
2.5.1 Flow tubes and flow resistance	p. 27
2.5.2 Energy balances	p. 29
2.6 Two theorems	p. 31
2.6.1 The uniqueness theorem	p. 31
2.6.2 The minimum dissipation theorem	p. 32
2.7 The thermal energy balance	p. 33
2.8 Dissolved species balance	p. 35
2.8.1 Rate-limiting steps and the solute source term	p. 37
2.8.2 First-order reactions	p. 40
2.9 Equations of state	p. 41
2.10 Dispersion	p. 43
2.10.1 Kinematics of dispersion	p. 44
2.10.2 Dispersion in a steady plume	p. 48
3 Patterns of flow	p. 51
3.1 Flow in uniform permeable media	p. 51
3.1.1 Flow constraints	p. 52
3.1.2 Laplace's equation	p. 56
3.1.3 Some local flow patterns	p. 59
3.1.4 Two-dimensional surface aquifers	p. 61
3.2 Three-dimensional surface aquifer flow	p. 63
3.2.1 How do surface aquifers work?	p. 63
3.2.2 Regional scale aquifer flow	p. 67
3.2.3 An example: the aquifer in Kent County, Maryland	p. 70
3.2.4 Scales of water table elevation; relaxation, emergence and recharge times	p. 73
3.2.5 Groundwater age distribution in an aquifer	p. 77
3.3 Dispersion and transport of marked fluid	p. 78
3.3.1 Measurements of permeability variations in sandy aquifers	p. 78
3.3.2 Measured dispersion of injected tracers over sub-kilometer scales	p. 83
3.3.3 Flow through a spatially random permeability field	p. 85
3.4 Layered media	p. 93
3.4.1 Anisotropy produced by fine-scale layering	p. 93
3.4.2 Flow across layering with scattered fracture bands or gaps	p. 96
3.4.3 Confining layers in a surface aquifer	p. 100
3.4.4 Mixing in more permeable lenses	p. 105
3.5 Fracture-matrix or "crack and block" media	p. 106
3.5.1 Reservoirs and conduits	p. 109
3.5.2 Transport of passive solute in co-existing fracture and matrix block flows	p. 111
3.5.3 A passive contaminant front in a fracture-matrix aquifer	p. 113
3.5.4 Distributed solute entering across the water table	p. 116
3.6 Flow transients	p. 118
3.6.1 Diffusion of pressure	p. 118
3.6.2 Pressure diffusion and de-gassing following seismic release	p. 120
3.6.3 Diffusion of pressure in a fracture-matrix medium	p. 121
4 Flows with buoyancy variations	p. 125
4.1 The occurrence of thermally driven flows	p. 125
4.2 Buoyancy and the rotation vector	p. 127
4.3 General properties of buoyancy-driven flows	p. 130
4.3.1 Heat advection versus matrix diffusion: the Peclet number	p. 131
4.3.2 Thermally driven flows: the Rayleigh number	p. 133
4.4 Steady low Rayleigh number circulations	p. 135
4.4.1 Slope convection with large aspect ratio l/h	p. 135
4.4.2 Circulation in isolated, sloping permeable strata	p. 137
4.4.3 Compact layered platforms and reefs at low Rayleigh numbers	p. 140
4.4.4 Two-dimensional reefs or banks	p. 143
4.5 Intermediate and high Rayleigh number plumes	p. 146
4.5.1 Two-dimensional numerical solutions	p. 146
4.5.2 How do these flows work?	p. 153
4.5.3 Scaling analysis for two-dimensional flows	p. 155
4.5.4 Circular platforms	p. 158
4.5.5 Similarity solutions-two-dimensional plumes	p. 159
4.5.6 The axi-symmetrical plume in a semi-infinite region	p. 162
4.6 Salinity-driven flows	p. 164
4.6.1 Freshwater lenses	p. 165
4.6.2 Gravity currents in porous media	p. 168
4.7 Thermal instabilities	p. 170
4.7.1 Rayleigh-Darcy instability	p. 171
4.7.2 A physical discussion	p. 176
4.7.3 Related configurations	p. 178
4.8 Thermo-haline circulations	p. 180
4.8.1 Temperature destabilizing, salinity stabilizing	p. 183
4.8.2 Both temperature and salinity stabilizing	p. 185
4.8.3 Both temperature and salinity destabilizing	p. 185
4.8.4 Temperature stabilizing, salinity destabilizing	p. 185
4.8.5 Brine invasion beneath hypersaline lagoons	p. 187
4.9 Instability of fronts	p. 189
5 Patterns of reaction with flow	p. 194
5.1 Simple reaction types	p. 194
5.1.1 Dissolution	p. 195
5.1.2 Combination	p. 197
5.1.3 Replacement	p. 199
5.2 An outline of flow-controlled reaction scenarious	p. 202
5.2.1 The equilibration or reaction length	p. 203
5.2.2 The reaction front scenario	p. 204
5.2.3 The gradient reaction scenario	p. 206
5.2.4 Mixing zones	p. 208
5.3 Leaching or deposition of a mineral constituent	p. 208
5.3.1 Dissolution in a uniform flow	p. 208
5.3.2 Leaching in aquifer flow with infiltration across the water table	p. 211
5.3.3 Dissolution in a fracture-matrix medium	p. 215
5.3.4 The depletion time	p. 217
5.4 The isothermal reaction front scenario	p. 218
5.4.1 The front propagation speed and the fluid-rock ratio	p. 219
5.4.2 Profiles in the reaction front	p. 223
5.4.3 Reaction fronts in fracture-matrix media	p. 225
5.4.4 Sorbing contaminant plumes	p. 228
5.5 The gradient reaction scenario	p. 235
5.5.1 Dissolution and deposition rates in gradient reactions	p. 239
5.5.2 The rock alteration index	p. 242
5.5.3 Enhancement and destruction of porosity	p. 243
5.6 The mixing zone scenario	p. 247
5.7 Isotherm-following reactions	p. 249
5.7.1 The reaction zone	p. 251
5.7.2 Dehydration	p. 253
5.8 Paleo-convection and dolomite formation in the Latemar Massif	p. 255
5.9 Distributions of mineral alteration in Mississippi Valley-type deposits	p. 260
6 Extensions and examples	p. 264
6.1 Extensions	p. 264
6.2 Examples	p. 265
6.2.1 Coastal salt wedges	p. 265
6.2.2 Permeability variations and the rotation vector	p. 265
6.2.3 Confined aquifers	p. 266
6.2.4 An unconfined or surface aquifer with a locally fractured confining layer	p. 267
6.2.5 The Hole-Shaw cell	p. 267
Bibliography	p. 269
Index	p. 279

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