Conclusion

It is clear that the material considered in this monograph does not exhaust the widediversity of hydrogeological problems whose solution requires the use of the appa-ratus of groundwater migration theory. The priority in the choice of the problemswas primarily determined by the experience of the author in processing the actual(both field and laboratory) materials collected during studies at real hydrogeolog-ical sites. The author believes that this experience has clearly demonstrated that,methodologically, the integrated approach to studying phenomena of mass transferaccompanied by chemical reactions in the subsurface basing on the combination ofanalytical, numerical, and numerical–analytical methods of studies is most produc-tive in both the solution of applied hydrogeological problems and conceptual modelconstruction aimed at the development of basic knowledge about solute migrationin the subsurface hydrosphere.

The author also hopes that this book will help the reader to see that to find effec-tive solutions of some hydrogeological problems does not always require one to useextremely complex calculation algorithms involving the entire spectrum of possiblemigration mechanisms and hydrochemical interactions. Although the state-of-the-art in numerical modeling methods in hydrogeology allows the researcher to copewith problems of practically any complexity, the obtained results are commonlynot convincing because it is difficult to properly evaluate all parameters of suchnumerical models. Therefore, the use of reasonably simplified analytical models,which were the main focus of this study, and, sometimes, expert estimates mayyield more tangible and practically significant results. The solution of practical(engineering) problems is impossible without the involvement of diverse geologicaland experimental material and requires the results to be checked against alternativemodels. The hope to awake hydrogeologists’ interest in the search for new, alterna-tive solutions of the problems considered in this book was among the incentives forthe author to write it.

Unfortunately, the prescribed, and thus limited, volume of this monograph failedto allow the author to consider some processes accompanying the multiphase flowof immiscible fluids denoted by the well-known abbreviation NAPLs and knownmost often to be hazardous groundwater pollutants often not less toxic than ra-dionuclides. This range of multiphase flow problems also includes the descriptionof motion in geological beds of liquefied greenhouse gases – a problem currently

V.G. Rumynin, Subsurface Solute Transport Models and Case Histories, 801Theory and Applications of Transport in Porous Media 25,DOI 10.1007/978-94-007-1306-2, c© Springer Science+Business Media B.V. 2011

802 Conclusion

efficient nature-conservative measures, namely, the sequestration of carbon dioxidein geological media in response to climate change, using, in particular, the capacityof deep saline aquifers to sequester this gas. The author’s experience in such studiescould serve as a basis for a special publication.

very popular. Its solution is associated with the substantiation of one of the most

Index

AAbel’s integral, 271Accumulation rate, 144, 148, 149, 413, 718,

723Actinides, 167, 502–505, 560, 615, 681, 700,

704, 713, 717, 728, 730–734, 739,753, 754, 784, 786, 791, 792, 795,797

migration of, 730, 731, 733Adsorption. See SorptionAdsorption-desorption. See Sorption-

desorptionAdvection. See also Convection

–dispersion equation, 18, 19, 45, 46, 67,115, 116, 203, 207, 208, 239, 292,296, 329, 332, 333, 796

transport equation, 29, 114, 237, 289velocity, 7, 199, 208, 209, 768vertical, 173, 199, 208–217, 473

Advection–dispersion model, 18, 38, 70, 238,244, 453

Advective-diffusive transfer, transverse,199–217

Advection–dispersion transport, 121, 249, 612Advective fluid velocity. See also Advection

velocity, 7, 208exchange, 4, 174, 200, 212solute transport, 5, 200, 482, 590–607

Age of a water parcel, 149tracers, 143, 149, 150

Agglomeration (coagulation/flocculation),720, 721

of colloids, 721, 723Aggregation, 718, 719, 722Airy equation/function, 292–294, 304, 307Anion exclusion effects, 677Anisotropic diffusion properties, 13

porous medium, 14, 674Anisotropy coefficient/ratio

factor, 7, 445–447, 678in hydraulic conductivity, 7, 318, 326, 433,

464in permeability, 5, 7, 653in the physical properties/anisotropy of

rock properties, 7, 13, 649planar, 7profile, 7, 464

Apparent diffusion coefficient, 11, 207, 235,668, 671, 672, 674, 675, 677–679,709

Aquifer anisotropy, 289, 420, 447anisotropic, 433, 445–447, 474equivalent homogeneous, 242, 249, 296,

321, 439heterogeneity, 15, 466, 495, 512, 535, 623heterogeneous, 123, 186, 243, 245, 287,

508, 545leaky, 199, 339–351multi-layer, 199salinization, 215, 531, 535sloping, 545, 551, 552stratified, 473, 480system, leaky, 208–217

leaky, stratified, 342two-aquifer, 342, 344–346two-layer, 346–351

two-layer, 346–351Atmospheric pressure, 78, 79, 97, 98, 687, 693Averjanov and Gardner model, 85, 105, 113Averjanov equation, 82, 85, 96, 103Avogadro number, 147, 773, 776

BBalance equation, 33, 45, 104, 133, 141, 200,

230, 246, 272, 340–342, 359, 379,407, 575, 594, 604, 745, 758

isotopic, 139, 140estimation, 201–202

V.G. Rumynin, Subsurface Solute Transport Models and Case Histories, 803Theory and Applications of Transport in Porous Media 25,DOI 10.1007/978-94-007-1306-2, c© Springer Science+Business Media B.V. 2011

804 Index

Base flow, 369, 372–375Basic/fundamental solution, 35–38, 41, 42, 49,

132, 155, 235, 239, 295, 607–610,782, 784

Batch experiments, 570, 573–580sorption experiments, 566–568, 571,

573–580, 624, 629, 633, 636, 637,639, 658, 660, 679, 693

Bernoulli equation, 593Bessel function, 53, 206, 232, 248, 293, 298,

342, 608Boltzmann factor, 773

particle, 776, 779transformation, 91, 93, 94variable, 91, 112

Boltzmann’s constant, 773Boundary condition

Cauchy, 19, 21, 23, 43, 64, 66, 126concentration, 10, 18–20Dirichlet, 18, 36, 43, 69, 484Neuman, 18third-type (see Boundary condition,

Cauchy)Breakthrough concentration functions, 44, 320,

343, 668curve, 44, 67, 220, 227, 287, 297, 303

time lag for, 311–316Brine–freshwater interface. See Interface

freshwater–salt waterBrine migration, 468–489, 495–517

transport, 453–460well-disposal, 545–556

Brook–Corey function/model, 80, 83, 85, 94,103, 268

Bruce and Klute equation, 91, 92Buckley–Leverett function, 455

CCapacitance densities, 774, 777Capacity coefficient, 222Capillary-adsorption, 79, 85, 97, 103

forces, 79, 85, 87, 97, 103, 387, 389, 393Capillary equilibrium, 87

forces, 92, 95, 103, 276, 387, 389, 393fringe, 264head, 79, 98, 261, 262, 269pressure, 77, 79, 80, 81, 87, 259, 266, 389

entry, 80, 81, 87, 268saturation curve, 81

zone, 90Capture zones, 29, 363Catchment flow path, 128, 129, 180, 181Catchment-scale models, 367, 369

Cauchy condition. See Boundary condition,Cauchy

problem, 20–23solution of, 20–23, 62, 64, 66, 126

Cauchy–Riemann equations, 26, 175Chain decay, 135–146

two-member/two-stagemember decay, 64, 68–70, 135–149,

249–252rule, 35, 54, 220

Channeling, 9Characteristic equation, 125, 175, 183, 281,

325solution, 23, 24, 28, 29, 96, 99, 107–111,

125–128, 185, 280–282, 318, 453,755

Charge balance, 776planes of, 773surface, 719, 720, 771, 775–777

density, 773, 776, 777Charge of colloids, 720, 771Chemical heterogeneity of an aquifer, 623,

634–636reactions and transformations, 60–70, 353,

357, 496, 545, 559, 569, 623, 719,743, 744, 771

weathering, 8, 351, 353–355, 715, 727Chemistry of plutonium, 784–787Chlorofluorocarbon, 149–151Clay

Aalenian Opalinus, 13, 648–650Callovo-Oxfordian, 13, 648–650Rupelian Boom, 13, 648–650, 657, 677

Colloidformation, 718, 720, 750mixture, 755. 766, 767organic, 716–718, 727, 729, 732–734particles, 718, 721, 722, 728, 732, 739,

755, 762, 778precipitation of, 723, 725, 728, 766

populations, 715, 716, 718, 719, 755, 757stability, 715, 719–722, 734stabilization of, 734system, 716, 717, 720, 731, 734, 743

stability of, 715, 719–722, 734transport, 713, 733, 734, 771

Colloidal. See ColloidColloid-facilitated solute transport/colloid-

facilitated transport, 566, 713–715,733, 739, 755–769, 771–797

Index 805

Colloids, artificial (anthropogenic), 718intrinsic (real), 713, 739, 741, 743–746,

749, 750, 753, 788, 792pseudocolloids, 713, 739, 743, 744, 753,

789Complexation reactions, 559, 772, 775,

784–797Complex formation reactions, 744, 772, 776,

788, 793potential function, 20, 421

Compressibility, 553rock, 553

Compression tests, triaxial, 652–656Compression tests, uniaxial, 652, 653Concentration asymptotic distribution of, 54

atomic, 139, 141, 147, 683field, three-dimensional, 54fronts, 11, 17, 24, 29, 45, 64, 114, 173, 513,

597, 600, 604, 633, 759, 766–768,785, 795

function, 10, 19, 20, 28, 36, 43, 44, 46, 59,62, 66, 127, 128, 130, 133, 151,181, 182, 211, 252, 304, 305, 314,319–321, 328–332, 364, 384, 385,394, 401, 402, 696, 784

gradients, 145, 173input, 24, 34, 182, 211, 239, 265, 290, 294,

298, 303, 304, 307, 320, 331, 360,633

peak, 9, 151, 266, 307, 310, 609, 613profile, initial, 21, 62, 63, 66, 143, 144,

340, 383, 576, 629, 666, 683, 699,747, 762, 779, 780, 794, 795

resident, 19, 20source, point source, 47–52, 56, 478, 479,

673wave, stationary, 127, 212, 248, 251–254,

395, 590, 594–596Conductivity heterogeneity. See Hydraulic

conductivityContaminant transport, 1, 208, 369, 495, 510,

585, 588, 716, 766Contamination plume, 285, 500–508Continuity condition, 9, 459, 473

equation, 459Continuum assumption/concept, 3, 78, 261

macroscale, 78, 261Convection cell, 413, 473

flow, 413, 423, 473vertical, 209, 473

Convex sorption isotherm. See Isotherm,convex

Convolution integral, 133, 181, 223, 232, 239,248, 272, 312, 609

Coordinate system/coordinates, curvilinear,24–33, 45, 318

Cartesian, 5, 26, 27, 30, 45cylindrical (axisymmetric), 27, 45

Correlation scale, 16, 130, 244, 644Coulombic forces, 559, 775Critical pumping rate, 430–436, 483, 489

rise, 431–436

DDamkohler number, 234Darcy–Buckingham equation, 82Darcy/Darcy’s law, 3–7, 14, 28, 82–84, 86, 95,

262, 267, 343, 388, 417, 424, 426,453, 467

Darcy velocity, 4, 82, 90, 145, 166, 167, 175,176, 188, 191, 192, 209, 216, 217,221, 237, 244, 262, 289, 317, 329,418, 419, 431, 441, 453–457, 467,599, 722, 723, 756, 762, 779, 793

Dating, helium-4 method, 143–148, 162–168tritium-helium-3 method, 138–139, 146tritium method, 138, 146

Daughter isotope, 136, 138products, 138

Dead-end microfractures, 14zones, 7, 14

Decay (see also chain decay), 60, 64–70, 131,135, 180, 182, 185, 204, 245–255,380, 594–598

constant, 51, 56, 58, 131, 138, 142, 204,249, 279, 380, 594, 615, 730

first-order, 64–68, 131products, 145, 149, 152–157, 167, 251, 615

Deformation parameters, 649, 652–657modulus of, 654, 655, 658

Delay (mixing) factor, 312, 313, 315, 316Delta function, 15, 34, 36, 41, 47, 50, 211, 229,

239, 291, 306, 315, 674Density charges, 777

contrast, 323, 447, 453, 455, 488convection/advection, 7, 423, 453, 457,

473, 475, 478difference, 416–418, 420, 423, 430, 439,

457, 463, 464, 501gradient, 6, 329, 441, 453, 455, 470, 474,

478, 479, 541vertical, 6, 441, 453, 455, 470, 471,

474, 478, 479, 489, 542variations, 464, 488, 547

Density-dependent transport, 464, 482, 488Density-induced advection, 442, 464, 475

transport, 463, 464, 471

806 Index

Depression cone, 344, 351, 352, 357, 539curve, 344

Deprotonation, 772, 773, 775, 779Desorption, 561, 565–580, 598–603, 627–637,

643, 644, 658, 681–701, 709–710,725, 728–730, 757–767

isotherms, 578, 579, 630, 631, 638, 661,683, 689–693, 695, 707

Desorptionkinetics/kinetics of desorption, 566–568,

571–573, 602, 615, 616, 630, 687,694, 713, 729, 765, 768, 792

multistep, 571, 578, 580, 685, 689–694,697, 707, 709

Diffusion (molecular diffusion), 6, 11–18,38, 145, 200–213, 219–225, 259,264, 266, 269, 354, 357, 362, 499,662–679

anisotropyapparent, 11, 13, 668, 670, 672, 674,

675, 677–679coefficient, 6, 12–17, 85, 220, 225, 236,

290, 295, 354, 662, 668, 669, 672,677, 675, 678

effective, 11, 12, 13, 38, 145, 677, 678coefficient, 13, 38, 145, 358, 677, 678

equation, 35, 36, 46, 55, 203, 223–225, 230exchange, 212, 217, 243, 252, 264, 266,

293, 311, 678experiments, 663–665, 670, 679flux, 11, 362model, asymptotic, 207, 244, 292

geometry-based, 223–225, 227, 267pore, coefficient, 11, 14, 15, 38, 202,

221–223, 236, 269, 591, 666, 667,670, 674

reverse, 666surface, 12

Diffusion-accessible porosity, 6, 12, 677Diffusive layer, 199, 776Diffusivity, 85, 91, 92, 94, 113, 219, 268, 269,

274, 277, 305, 342, 343, 550, 553of moisture flux, 85, 91, 94

Dipole system, 31, 332, 333Dirac delta function (impulse function)/Dirac

pulse, 34, 41, 47, 50, 69, 211, 229,239, 291, 303, 306, 315, 331, 674

Dirichlet condition. See Boundary condition,Dirichlet

Discrete approach, 221Dispersion, 11–18, 33–60, 238–242, 755–758,

762and advection fluxes, 14, 49, 200, 291

coefficient, 11, 14, 15, 45, 46, 112, 114,116, 444

hydrodynamic, 14–17longitudinal, 15, 16, 33, 46, 53, 203,

204, 756transverse, 15–17, 53, 199

longitudinal, 57, 106, 114, 200, 228, 244,295, 298, 301, 479, 594, 612

mechanical (see Dispersion, hydrody-namic)

problem, three-dimensional, 16, 54, 56, 58,60, 242, 243

radial, 298scale-dependent, 199, 288, 292solute, 3, 15, 17, 36, 37, 43, 106, 114, 115,

235, 236, 244, 246, 482, 636total, coefficient of, 14, 15transverse, 55, 58, 200, 245, 636two-dimensional, 54, 60zone, 37, 114, 420, 473, 531, 587, 636

Dispersive mixing, 129Dispersivity, 15, 16, 38, 199, 229, 303, 313,

316, 479, 591longitudinal, 15, 16, 56, 303transverse, 15

Displacement, piston-like. See also Piston-likedisplacement, 38, 95, 96, 97, 115,116, 201, 205, 207, 229, 231, 242,289, 299, 318, 320, 325, 448, 585,601, 608, 766

radial, 447–452unconfined, 451–452

Disproportionation reactions, 785, 788Dissolution, 163, 523, 559, 574–580, 602, 624,

684, 687, 688, 693, 694, 696–698,719, 722, 785

Dissolution products, 574, 698Distributed-parameter model, 367Distribution coefficients, 246, 506, 562, 563,

567, 568, 571, 588, 589, 601,622–626, 658–662, 679, 694, 704,707, 743, 746, 749, 753, 760, 765

histograms, 623–625, 640of moisture (see Moisture capacity,

distribution)of transit time (see Transit flow, time

distribution)DLVO theory, 719, 720Domenico’s formula/solution, 56, 58Double electric layer, 720, 721Doublet test. See Tracer test, doubletDrainage front, 281, 282

water, 281

Index 807

Drying front, 96, 97process, 96

Dual domain approach (dual porosity concept),243

permeability models, 259porosity aquifer/formation, 292, 299

concept, 259models, 299, 627, 679

porosity–dual permeability modeling, 259,261

concept (see Dual porosity concept)structure, 84, 238

Dual porosity concept, 219, 220, 259Dual-site model, 569–571, 643Duhamel integral, 222Dupuit-Forchheimer assumption, 120,

175–177, 183, 187, 290, 304, 360,408, 417, 447, 451

Dupuit formula, 290, 304, 360Dynamic effects, 14, 33, 87

EEnergy barrier, 720, 722Effective hydraulic conductivity coefficient,

261single porosity model, 228, 234–236

Effective-porosity, 27–29, 236, 511, 513,585–588, 664, 667, 668, 759–761,768

Electrical capacitance, 776, 777conductivity, 12, 523–525, 531resistivity, 524, 526

Electrostatic interactions, 559, 570, 720, 771,778, 779

particles, 771potential, 771, 778, 783repulsion, 719, 721

Elementary representative volume, 3, 9, 236Empirical semivariograms, 640, 642Energy barrier, 720–722Engineering barriers, 734Equation of continuity, 85, 86, 176, 388, 464Equations of isotopic balance, 139–141Equations of state (EOS), 468Equilibrium state, 418, 572, 605, 630, 685, 728

concentration, 572, 605, 686dynamic, 417–436, 630, 707local, 253, 573

Equipotential lines, 29, 30, 32, 551Eulerian analytical method, 245Evapotranspiration, 77, 88, 161, 371, 387, 398,

399

Exchange capacity, 564, 575, 603, 604, 635,651

cation, 564, 575, 576, 603, 606–607, 635,651

kinetics, 597total, 575, 603, 604

Exclusion effect, 622, 677Exponentially decaying input, 41, 42Exponential model, 93, 129, 179, 642

FFaraday’s number, 773Fickian advection–dispersion model, 38, 70,

244process, 38, 266transport equation, 37

Fickian-type equation, 287Fick’s law, 14, 18, 223

first, 14, 223–225second, 18

Filtration coefficient, 723Fingering, 453, 468, 476, 477Fission products, 136, 615, 681Fissure density. See Fracture densityFlow-dividing line, 29, 31Flow field, unidirectional, 15, 46–60, 174, 285,

724axial-symmetric, 288, 289, 295, 297, 305,

307, 309convergent, 302–311divergent, 288–302film, 261function, 24–27, 237, 318line, 178, 179, 184, 192, 216, 317–319,

321, 325, 330, 334microstructure of, 7miscible-fluid, 406, 466, 478model, 89, 90, 369, 464, 510, 545, 552, 554

multiphase, 77, 453, 801nonequilibrium, 266–282one-dimensional, 27overland, 369, 385path, 78, 128, 129–131, 174, 177, 180, 261,

287, 509, 512focused, 78preferential, 78, 261, 511, 512, 615

pathway (see Flow path)radial, 27, 178, 231, 287–302, 305, 344structure, 24, 27, 45, 237, 289, 305two-phase, 439, 453–460, 468, 470, 475,

476, 481unconfined, 175, 188, 194, 372, 380, 465variable-density, 465, 467, 468

808 Index

Flow field, unidirectional (cont.)velocity potential, 174, 237

real, 20, 24, 30, 46, 96, 724vertical component of, 173, 186, 329

Flow-focusing in individual fractures, 8phenomena, 8, 10

Flux concentration, 19, 20, 42Fokker-Planck equation, 306–307Fourier number, 298Fractionation of infiltration, 385Fracture aperture/width, 8, 290

density, 8, 17, 301intersections, 9network, 78, 220, 221, 228, 243, 245, 261,

266, 278, 279, 649, 650discrete, 78, 261

porosity, 5–7, 159, 221, 499, 500, 511, 517Fractured-porous aquifer/reservoir, 222, 239,

243, 253, 309–311, 313–316, 322,323, 333, 335, 713

Fractured rocks, 3–5, 7–9, 11, 13, 15, 17, 78,221, 231, 261, 313, 511, 537, 562,634

space, discrete, 8, 17, 220Fracture-filling materials, 567Fracture-matrix exchange kinetics, 231, 235,

246Free water surface, 304Frequency distribution, 128, 181, 624Fresh–saltwater interface. See Interface

freshwater–saltwaterFreshwater lens, 427–429, 431

pressure, 429, 431, 432Freundlich isotherm/Freundlich sorption

isotherm, 562, 563, 569, 573, 587,593, 611, 626, 627, 636, 639–642,660, 692

Front of piston-type displacement. SeePiston-type displacement

Full-miscibility approach, 516Function of influence of the well, 314Fundamental solution, 35–38, 41, 42, 49, 69,

99, 235, 607–610, 782, 784

GGardner formula, 80Geochemical conditions, 339, 496, 588, 791Geological boundaries, 47, 58–60Geostatistical analysis, 510, 643Ghyben-Herzberg rela-

tion/relationship/approximation,419, 421, 430, 431

Girinski potential, 188

Global isotopes, 149–152isotopic tracers, 151, 250tracers (see Global isotopes)

Goldstein function, 232, 248, 608Gouy–Chapman theory, 777Gravitational effects, 723

instabilities, 500potential, 721

Gravity effects. See Gravitational effectsfactor, 727forces, 723, 724movement, 473

Green–Ampt model/solution, 97–102Green functions, 48–51, 58Groundwater age, 144, 148, 149, 163, 167,

177, 250dating, 143–146flow balance

fully miscible, 464natural, 144net, 176regional, 157, 162, 167velocity, 18, 34

quality, 199, 325, 339–365, 421, 519,523–526, 538, 539, 552, 566, 601,620–622, 731, 733

deterioration of, 77recharge, 18, 123, 131, 149, 173, 191, 259,

372, 373, 385–390, 498table, 77, 78, 183, 259, 260, 262, 263, 266,

339, 357, 358, 523, 526, 624, 682,684

vulnerability, 131, 149assessment, 131, 149

withdrawal, 522

HHead drawdown, 330Heaviside function/step function, 34, 36, 274Henry isotherm, 586

problem, 471–473Henry’s equilibrium constant, 357Hydraulic-conductivity anisotropy, 318Hydraulic/piezometric head, 5, 6, 79, 97, 98,

290, 339, 420, 421, 423, 432, 465,473, 547–550, 552–554, 648

anisotropy, 7conductivity, 5–9, 24, 81, 82–84, 103, 131,

187, 189, 213, 243, 261, 278, 303,326, 374, 392, 417, 431, 446, 635,653

unsaturated soil, 82diffusivity, 305, 342, 343, 550, 553

effective, 342, 343

Index 809

head, 4–6, 79, 82, 86, 97–99, 290, 339, 423,430, 432, 435, 465, 473, 547–554,648, 649

properties, 84, 386, 390, 652–653Hydrochemical barrier. See Hydrogeochemical

barrierinteractions, 623inversion, 214transformations, 353zonality, 173, 216, 286, 537–539, 542, 547,

551Hydrogeochemical barrier, 508, 720

stratification, 287, 538, 539, 547, 549zonality, 173, 216, 286, 537–539, 542, 547,

551Hydrograph separation, 369Hydrolysis reactions, 787, 788Hydrostatic conditions, 420

model, 430pressure, 79

Hydrous ferric oxides, 772Hydroxyl groups, 779, 789, 790Hysteresis in adsorption (sorption), 566, 569,

612, 627–634of adsorption process (see Hysteresis in

adsorption)phenomena, 566, 709of retention functions (see Hysteresis in the

water retention functions)in sorption, 566, 627–634, 709–710in the water retention functions, 84, 89, 90

IIdeal mixing model, 125, 131Imbibition, water imbibitions, 103, 111–113,

259, 266, 267, 269, 272–274, 278,279, 387, 389, 391, 392

Immiscible fluids, 420, 439–452Implicit error function, 305Impulse concentration source, input. See Input

concentration signal, impulseInfiltration, 77–116, 123, 124, 133, 136,

173, 180–191, 253, 259, 262, 272,278–282, 353, 358, 363, 371–380,384, 385–390, 426, 474

capacity, 92, 100–102front, 78function, 100, 101, 388, 390model, 79–106, 388–390

process, unsteady, 92, 375rate, 92, 104, 111, 157, 159, 187, 264, 358,

383, 411–415, 417, 427potential, 388–390, 392–393

Infiltration recharge, 110, 139, 155, 158, 160,183, 188, 196, 202, 205, 209, 211,281, 383, 395, 397, 399, 407, 416,418, 419, 422, 449, 538, 545, 552,725, 743

accumulated, 92, 100–102cumulative, 92, 102, 104

Initial abstraction, 414, 426, 427condition, 18, 21, 36, 47, 62, 64, 66, 88,

126, 136, 380, 409, 410, 574discontinuous, 391

Input concentration, 41, 55, 239, 307, 587function, 34, 66, 154, 182, 265, 304, 331,

360, 598signal, impulse/ pulse, 34, 41, 47, 55, 154,

182, 211, 265, 304, 307square-pulse, 587, 598step/step-wise, 239

Interface, sharp, approach, 420, 429, 430, 464,469, 511–513

brine-freshwater, 447, 453displacement, 439–452, 470–471equilibrium of, 246freshwater–saltwater, 15, 438, 440, 441,

443, 445, 447, 449, 451, 452, 453,455, 457, 459, 486, 489, 553

stability, 477, 789, 790solid-liquid, 671, 683, 772tilted, 443, 445, 447

Interflow/throughflow, 372Interlayer exchange, 146, 165, 200–208, 212,

231factor, 146

Intrusion of salt seawater. See Seawaterintrusion

Iodine deposit, 213, 215, 217Ion exchange, 507–508, 559, 568, 574, 575,

589, 602–604, 698, 704, 705, 779Ion-exchange equilibrium, 575Ionic strength, 564, 668, 692, 718, 720–722,

727, 729, 730, 771, 777, 788, 789Iron hydroxides, 508, 626, 722Irreversibility in adsorption. See Adsorption,

irreversibleIrreversible process, 568, 600, 723, 728

reaction, 559, 730Isothermal relationship, 572, 626, 630, 640,

660Isotherm, 60–64, 245–246, 561–566, 585–598,

622–633, 658–660, 681–698,724–727, 758–760

concave, 60, 61, 588convex, 60, 246, 585, 588, 606linear (see Henry isotherm)

810 Index

Isotherm (cont.)nonlinear, 60, 61, 562, 565single-component, 561, 588

KKinematic wave approach, 301, 304, 305

equation, 269, 279, 386theory, 125, 267

Kinetic coefficient, 296, 378, 410constant, 374, 378, 379, 384, 410, 568,

572, 573, 575, 579, 696, 733, 755,765, 767, 768, 792

dissolution constant, 576equation, 87, 131, 356, 387, 576, 612, 723first-order, 64–68, 231–234, 563, 612theory, 125, 563

Kinetics of desorption. See Desorption kineticsKronecker’s delta function, 15

LLambert W-function, 100, 101Land ponding, 389Langmuir isotherms, 561–563, 586, 587, 726,

768Laplace equation, 25, 26, 432

inverse, numerical methods for, 39, 40,206, 266, 273–275, 299, 307, 310

laplace integral transform, 38–45, 67, 132,134, 140, 203, 209, 228–229, 232,238–243, 247, 250, 253, 265, 272,275, 292, 294, 298, 306–309, 312,608

Laplacian, 25Lauverier formula/solution, 205, 299Law of mass action, 575, 774Leakage, 10, 18, 51, 139, 208, 212, 213, 216,

217, 339, 340, 342, 344, 346, 372,374, 376, 378, 384, 423, 424, 426,435, 453, 463, 468, 476, 495, 500,510, 512, 517, 618, 620, 681, 731

velocities, 212, 344Leaky stratified system. See Aquifer system,

leaky, stratifiedLeaky system. See Aquifer system, leakyLeibnitz rule, 440Linear accumulation model, 144

distribution coefficient, 144Liquid/solid/liquid-to-solid ratio, 565Lumped capacitance model, 206, 207, 225,

229, 231, 234, 237, 240, 241, 247,265, 323

Lumped-parameter approach/model, 369–402,410

MMacrodispersion coefficient, 107, 207, 228,

235, 236, 244, 245, 254asymptotic, coefficient of, 52–54, 207, 235

Macrodispersivity, 199, 610Mass balance

approach, integral, 272–273conservation equation/law, 63, 467equation, 33, 45, 136, 145, 200, 230, 246,

311, 340–342, 359, 379, 380, 449,467, 575, 752, 758, 761

exchange, 10, 201, 202, 234, 238, 246, 247,300

coefficient, 165, 225, 231, 250, 287,323

kinetic, 219, 231, 235, 238, 243, 246,289

parameters, 234, 301, 302, 310, 314first-order, coefficient model, 243multi-rate, 227, 228, 234rate function, 222–223transfer coefficient, 227, 234, 243, 314,

316, 323Mass-fraction. See Soil organic carbon, mass

fraction ofMatrix diffusion, 9, 219, 220, 225–231, 247,

293, 299, 301, 309, 713kinetics, 301, 302porosity, 220, 499potential, 78, 79retardation factor, 11, 245, 246rock, 139, 147, 204, 499, 501, 513, 560,

627, 698, 757unlimited, 225, 229–231, 234, 237, 240,

241, 247, 250, 299, 309, 322, 334Mechanical parameters, 652Memory function, 222, 223, 225–228, 234,

238, 292Metal oxides, 623, 719Microdispersion, 11, 45–58, 114, 207, 290,

293–298, 306–309, 312, 321, 587axial-symmetric, 297longitudinal, 244, 290, 295

Migration velocities, 217, 262, 505, 508, 604,768

Model calibration, 509, 512, 515, 545, 552,553

Moistening front. See Moisture frontMoisture-based, 86Moisture capacity, 102, 104, 107, 108, 118,

286content, 80–83, 87, 88, 91–95, 97, 98, 104,

110, 111, 113, 655, 672diffusivity equation, 91

Index 811

distribution, 90, 94, 95, 111, 116, 280evapotranspiration, 77, 88, 387, 398, 399front, 91, 105, 114, 766imbibition, 111, 279, 387, 392migration, 212, 261, 264, 276partitioning, 371potential, 79profile, 95, 97, 111, 113, 259specific function, 82, 86transfer coefficient, 106, 110, 125, 282,

283, 284effective, 260, 262equation, 85, 87, 104, 105, 108, 114steady-state, 111, 264–266

transport, 264–266wave, 93, 105, 281

Molar concentration, 147, 563, 778, 794volume, 147

Molecular-diffusion. See Diffusion, molecularMonitoring, 130, 139, 161, 162, 164, 173, 186,

250, 287, 311, 353, 370, 394, 501,502, 505, 508, 517, 524, 543, 545,550, 554, 566, 618, 621, 627, 684,701, 731

Multicomponent approach, 509, 561multi-site reactive transport models, 589

NNatural attenuation, 123, 245, 572, 588, 616,

622, 627, 634, 682, 705groundwater salinity stratification, 325, 705

Neumann condition. See Boundary condition,Neumann

Nonequilibrium model, 260, 572–573Nonideal phenomena, 566Nonpoint-source pollution, 123Nuclear tests/nuclear weapon tests, 149, 151,

152Numerical dispersion, 332, 470, 472, 474, 479,

482, 483, 513, 531, 762Numerical simulators

DENSFLOW, 452, 464, 466, 470, 471,476, 477, 511, 512, 515

GEON-3DM, 478, 480LEHGC, 778, 779, 782METROPOL-3, 466MIG2, 466, 468, 475, 4762PHFLOW, 468, 475–478, 481SEAWAT, 466, 478, 480SUTRA, 466, 482, 485TOUGH2, 451, 452, 466, 468, 470,

472–482, 485, 511, 513, 514, 516,529, 552

T2VOC, 451, 452, 468, 470, 475–478, 481

OOne-dimensional model, 33–46, 107, 305Organic carbon, 586, 603, 604, 812

dissolved, 789matter, 563natural, 569

Oxidation, 351–365, 718kinetics, 355–356potential, 506, 786rate of, 354, 361state, 785–787

Oxygen migration/transport, 357–358, 364

PParent isotope, 137, 147Pareto’s law, 716Particle agglomeration, 720

motion trajectories, 14, 21, 26, 32, 45, 184,185, 192, 225, 318, 722

size distribution, 628, 637, 741travel time, 24, 33

Partitioning coefficient, 563of flows, 369, 399of precipitation, 371, 375, 386, 394, 402

Peak deviatoric stress, 655Peclet number, 20, 113, 217, 292, 295, 302,

305, 307, 309, 310, 321, 473Percolation threshold, 8Permeability, 4, 5, 7–12, 214, 260, 325, 441,

454, 467discontinuity in, 459distribution, 666, 668effect of variations in, 245relative, 454

Phase continuity equations, 454Physically based model, 388Physical properties, 3, 10, 388, 439, 451, 548,

637, 640, 648–652, 719Piezometric head, 79, 421, 423, 430, 432, 547,

550Piston flow, 129Piston-like displacement motion, 38, 115, 116,

185, 201, 207, 242, 252, 289, 295,299–300, 309, 322, 323, 325, 448,470, 586, 591, 592, 596, 609, 766,768

Piston-type displacement/replacement, 37, 38,55, 57

Plasticity index, 652, 654, 657, 658Point source. See Concentration source, pointPoisson’s ratio, 653, 657, 658Polymerization, 787–789Pore-size distribution index, 80

812 Index

Pore water (capillary) pressure head, 79squeezing of, 340

Porosity, 4–8, 219–222effective, 5–7, 236, 511, 585–588, 667,

668, 759–761, 768(capacity) ratio, 222total, 6, 79, 244, 658, 702

Potential function, 20, 24, 26, 31, 32, 188, 237,373, 421, 427

of mass transport, 759, 763, 766–768Precipitation, 106, 124, 129, 150, 151, 153,

162, 260, 370–375, 378, 386–390,392–399, 402, 405, 412, 508, 522,722, 723, 725, 773, 787, 797

Preferential pathways. See Flow pathpreferential

Pressure gradient, 431, 439, 454head-based equation, 86

Probability integral (error function integral),35

Profile heterogeneity, 475, 535Protonation, 772–774, 779Pseudocolloids. See Colloids, pseudocolloidsPulse injection, 46, 227, 316Pyrite, 352–356, 362–365, 567

oxidation, 352, 354–357, 362, 364, 365Pyrrhotine, 353, 354

QQuasi-one-dimensional, 29, 45–46, 123, 199,

237, 317, 321, 386, 442Quasi-steady conditions, 111, 225

pollution plumes, 247Quasi-steady-state assumption, 341, 350Quickflow, 369

RRadioactive carbon, 151

pollution, 152, 502, 731waste, 13, 17, 161, 162, 168, 495, 681

intermediate-level, 162, 495low-level, 162, 495, 681, 702, 750

Radioactive waste (RW) disposal sites,159–163, 566, 647, 682, 683, 698,731, 750–754

Radionuclide adsorption, 567, 643, 684,701–706

migration monitoring, 618mobility of, 517, 682, 699

Radionuclidesamericium 241Am(III), 724cesium (Cs)-137, 627, 697chlorine (Cl)-36, 663, 672, 673, 677, 679

cobalt (Co)-60, 501curium (Cm)-244, 503krypton (Kr)-85, 149, 151neptunium (Np(IV))-237, 729plumbum (Pb)-210, 730plutonium-238, 239, 240, 504, 785plutonium 240Pu/239Pu, 731, 732polonium (Po)-210, 730ruthenium (Ru)-106, 501strontium (Sr)-90, 602, 696technetium (Tc)-99, 502tritium (H-3), 501, 620uranium (U), 701, 728

Rainfall-runoff model, 388, 390Random walk method, 468, 477Rate coefficient of reaction. See Reaction rateReaction rate, 355, 356, 572

of deprotonation (see Deprotonation)reaction(s) of protonation (see Protonation)

Reactive sites, 569, 573, 599, 612, 613Recharge rate, 175, 372–374, 387, 426

areal, 175rate, areal, 10, 175, 447, 499

Remediation, 219, 288, 324, 566, 572, 588,622

Replacement front, 35, 38, 609, 701Representative elementary volume (REV), 3,

9, 236Reservoir models, 128–131, 179–181, 387

theory, 128, 129Residence time, 131, 134, 149, 154, 156, 167,

181, 193, 226, 234, 331, 728Residence time, mean, 131Residual volumetric water content, 80

water content (see Residual volumetricwater content)

Resistivity survey, 524Response functions, 39, 153–157Retardation factor. See Retention factorRetention curve, 80–82

factor, 62, 167potential maximum, 391, 392of radionuclides, 506, 658

REV. See Representative elementary volumeRock capacity factor, 586Runoff curve number, 391

overland, 385potential, 391surface, 369, 371, 387, 391, 393, 395–397,

401, 402

SSaltwater cone, 430, 432, 433

pressure, 432

Index 813

upconing, 432wedge, 465, 473, 519, 533

Saltwater-freshwater interface. See Interfacefreshwater–saltwater

Saturation (saturation function), 77, 78, 80, 81,87, 261, 263, 453

effective, 453–456, 458jumps, 458, 468profile, 262–264

Scale-dependent behavior, 199, 288, 292phenomenon, 199

Schematization of natural conditions, 38Seawater intrusion, 421–427, 519–530

wedge, 421, 422, 426, 427Selective sorption method, 565Selectivity coefficient, 575Self-similar front, 93, 105

solution, 93Semi pervious bed/layer, 160, 165, 208, 209,

212, 340, 350, 374Shape factor, 12, 226, 268Sharp-interface approach/concept/

assumption/model. See Interface,sharp, approach

Shearing resistance, 653angle of, 653

Shear strength, 655Shift transformation, 93Size distribution, 80, 83, 628, 637, 640, 650,

716, 729, 732, 740, 741Skin effect, 291, 306, 311Soil active layer, 387

conservation service curve number method,390

macroporous, 260moisture capacity, 80

characteristic, 80organic carbon mass fraction of, 563water diffusivity, 84, 85, 94, 268

diffusivity effective, 84–85sorptivity, 92

Solute balance, 124, 206, 209, 457exchange, 116front of, 37transport components, 38, 43

multicomponent, 778–784multi-rate, 234parameters, effective, 771, 773radial, 27

two-dimensional, 25Solution of the traveling-wave. See Wave,

traveling, solutionSorption, 60–64, 245, 561–613, 617–709,

724–733, 755–767

barrier, 504capacity, 61, 563, 565, 587, 607, 632, 634,

647, 690, 699, 700, 706, 766, 767,772, 791

distribution (partition) coefficientscoefficients of, 562

equilibria, 630, 724, 758equilibrium approach, 246experiments, 566–568, 571, 573–580hysteresis, 598–602interaction, 636irreversibility, 613, 634, 755, 761irreversible, 600, 601, 633, 692, 760, 761,

767isotherm (model), 60–62, 561–563, 571,

572, 586, 587, 593, 630, 689,690–695

concave, 588convex, 588linear, 588

kinetic-controlled, 248kinetics, 571–573, 575, 588, 609–611, 671,

687, 694, 697, 727–730, 767, 768nonequilibrium, 242, 572, 573, 607–613nonlinear, 24, 64, 586–588, 590–598, 610,

611, 636, 637onto colloids, 739of radionuclides, 562, 565retardation (see Sorption retention)retention, 167, 506, 620reversible, 585, 600, 613, 633, 634,

758–760site, 561, 564, 569–574, 612–613, 629,

683, 692, 724, 760, 775density, 776, 778, 794

(reactive) sites, 569specific, 570surface, coefficient, 61, 246, 589, 660, 677,

692, 710Sorption-desorption kinetics, 694, 765Sorptive capacity, 724, 747

number, 724Sorptivity, 92, 103, 113, 269Space-time scale, 223Spatial correlation scale, 667

moment, 223, 277, 280, 667variability, 615, 627, 634–636, 640variability of sorption parameters, 634–644variations, 643–644variations in mechanical properties,

653–656variations in physical properties, 653–656variations in the physicochemical

characteristics, 634–649

814 Index

Specific discharge, 4, 5, 24, 25, 28, 30, 123,183, 187, 267, 289, 422, 440, 453

flux, 82, 96, 112, 319function, 20–24potential, 24, 25storage, 5, 341, 466surface, 61, 221, 223, 355, 562, 715, 773,

778area, 236, 355, 564, 715, 724

velocities, 612Square-wave pulse. See Input, square pulseStatistical (temporal) moments. See Temporal

momentsdispersion, 44

Steady-state asymptotics, 52–54pollution, 56

Step function. See Heaviside functionStern layer, 570Stochastic continuum approach, 261

fracture-continuum, 261model, 6, 130, 635process, 130, 245

Storage capacity, 222, 231, 275, 300, 312, 379,401, 406, 509, 516, 542, 587, 606,609, 722

coefficient, 222Stratified sediments, 84

system, 10, 90, 145, 193, 200, 244, 674multi-layer, 188–192, 199

Stream function, 20, 25, 26, 32, 174hydrographic record, 369

Streamline, 20, 25, 26, 29, 30–33, 45, 177,237, 238, 321, 322

equation, 177neutral, 30, 31

Streamline-based approach, 237, 238, 321, 322Strength parameters, 654Suction height, 260, 262

pressure, 87–90, 260, 267dynamic, 260, 262

Sulfate-ion, 352Sulfate pollution, 353Sulfide minerals, 351Sulfur hexafluoride, 149, 150Sulphide leaching, 362–365

oxidation, 362Superposition, 26, 30, 32, 42, 48, 58, 132, 155,

320, 331, 376, 377, 599method, 58, 156, 376, 377principle, 26, 48

Surface complex formation, 565, 566, 701,773, 776, 777, 779, 793

complexation models, 771–778theory, 772, 777

functional groups, 772, 773of porous blocks, 226, 245potential, 773, 774, 777, 778reactions, 772–777site density, 776

TTemporal moment, first, 44

moments, 45Time characteristic, 177–179, 318, 326

lag effect, 312–314Time-shift function, 94Tortuosity, 12, 13, 279Toth isotherm, 563Tracer dilution, 311–316

input function, 315, 316mode, non-recirculating, 319, 320recirculating, 320

test, 287–335doublet, 325, 330, 334

Trajectory(ies) of particle(s), 184, 185Transfer function, 130, 181, 222–228, 307

layer-by-layer, 201, 202parameter, 216, 217rate function, 222

Transit flow, 315time distribution, 128–131, 174, 181

mean, 129relative cumulative frequency

distribution of, 128, 181Transitional (dispersion) zone, 531Transition zone size, 38Transport front, 37, 110, 608, 766

fast, 698radionuclide, 759regime, 127, 207, 221, 610, 611two-dimensional, 53

Travel time, 9, 24, 33, 44, 143, 177, 178, 236,316, 317, 330

variance of, 44Triaxial test. See Compression tests, triaxialTriple-layer model, 773Tritium distribution, 182Tritium-helium-3 method, 157Turn-over time, 128, 129, 155, 159, 181Two-dimensional problem, 50

profile models, 439–447, 515Two-layer

stratum, 202, 216system, 199, 205, 207, 209, 212, 231, 240,

343, 346–351Two-phase model, 453, 481

Index 815

UUltrafiltration, 505, 732, 739–745, 750, 752,

753Uniaxial compression strength, 653Unlimited diffusion capacity model, 252

matrix diffusion mode (see Unlimiteddiffusion capacity model)

Unsaturated fractured-porous systems, 259,267

zone, 266Unstable (radioactive) component, 136Upconing process, 329, 433, 535

VVadose zone, 77, 79, 387, 394Van der Waals attraction/forces, 721Van Genuchten formula, 81Variogram-analysis, 641Velocity potential, 26, 174, 237, 431

variations, 237Vertical component of velocity. See Flow

velocity, vertical component ofdipole tests, 329–333electrical sounding, 526, 527geochemical zonality, 538head distribution, 549migration, 585, 587stratification, 538

Viscous resistance forces, 451Volumetric density of fractures, 8

water content, 77, 80, 82, 392

WWaste disposal site, 159, 164, 548, 698, 729,

740, 750Wastewater injection, 545–556Water absorption model, 91–94

balance, 367, 374, 377, 408basin’s, 374

discharge, 386exchange, 128, 130, 137, 156, 278

active, zone of, 4, 149rate of, 128

hardness, 351, 352quality, 505, 520, 524, 525retention curve/function, 80, 81, 84withdrawal, 364, 365, 421, 486, 487, 519,

522, 523, 529Wave velocity, 93, 279

leaching, 506rarefaction, 62, 64shock, 64travelling, 93, 105, 611

solution, 590Wellhead (sanitary) protection zones, 29Well, injection, time lag of, 315

observation, 311–314penetrating, 162, 164, 173, 193, 739, 740pumping, 123, 302, 316, 328, 339, 349,

417, 421, 430, 432, 481, 482, 523,535

recharge wells, 161, 288, 289, 291, 316,318, 321, 546, 551, 552, 681, 739,740, 750

Wetted contact area, 268, 269, 278Wetting front, 78, 94–97, 104, 269–272, 278,

281instability of, 82process, 82