Comparison of theory and experiment for solute transport in highly heterogeneous porous medium

Advances in Water Resources

Volumn 30, Issue 11, 2007, Pages 2235-2261

  Golfier, Fabrice ^a   Quintard, Michel ^b   Cherblanc, Fabien ^c   Zinn, Brendan A ^d   Wood, Brian D ^e  

^a CRPG CNRS   (France)

^b IMFT   (France)

^c UNIV MONTPELLIER   (France)

^d Massachusetts Institute of Technology Cambridge   (United States)

^e Oregon State University   (United States)

Author keywords

Mass transfer; Mobile immobile; Solute transport; Upscaling; Volume averaging

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FLOW VISUALIZATION; GREEN'S FUNCTION; HYDRAULIC CONDUCTIVITY; MASS TRANSFER; POROUS MATERIALS;

MACROSCALE TRANSPORT EQUATION; STEADY-STATE CLOSURE;

SOLUTE TRANSPORT;

EIGENVALUES AND EIGENFUNCTIONS; FLOW VISUALIZATION; GREEN'S FUNCTION; HYDRAULIC CONDUCTIVITY; MASS TRANSFER; POROUS MATERIALS; SOLUTE TRANSPORT;

BREAKTHROUGH CURVE; CONDUCTIVITY; GREEN FUNCTION; MASS TRANSFER; POROUS MEDIUM; SOLUTE TRANSPORT; STEADY-STATE EQUILIBRIUM; VISUALIZATION;

EID: 34548324803     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2007.05.004     Document Type: Article

References (89)

1. Berkowitz B., Scher H., and Silliman S.E. Anomalous transport in laboratory-scale, heterogeneous porous media. Water Resour Res 36 (2000) 149-158
2. Benson D.A., Wheatcraft S.W., and Meerschaert M.M. Application of a fractional advection-dispersion equation. Water Resour Res 36 (2000) 1403-1412
3. Haggerty R., McKenna S.A., and Meigs L.C. On the late-time behavior of tracer breakthrough curves. Water Resour Res 36 (2000) 3467-3479
4. Meerschaert M.M., Benson D.A., and Bäumer B. Multidimensional advection and fractional dispersion. Phys Rev E 59 (1999) 5026-5028
5. Margolin G., and Berkowitz B. Application of continuous time random walks to transport in porous media. J Phys Chem B 104 (2000) 3942-3947
6. Schumer R., Benson D.A., Meerschaert M.M., and Baeumer B. Fractal mobile/immobile solute transport. Water Resour Res 39 (2003) 1296 10.1029/2003WR003141
7. Cushman J.H., and Ginn T.R. Fractional advection-dispersion equation: a classical mass balance with convolution-Fickian flux. Water Resour Res 36 (2000) 3763-3766
8. Deng F.-W., and Cushman J.H. Comparison of moments for classical-, quasi-, and convolution-Fickian dispersion of a conservative tracer. Water Resour Res 31 (1995) 1147-1149
9. Wood B.D., and Kavvas M.L. Correction to "Stochastic solute transport under unsteady flow conditions: comparison of theory, Monte Carlo simulations, and field data" by Brian D. Wood and M. Levent Kavvas. Water Resour Res 35 (1999) 2889
10. Wood B.D., and Kavvas M.L. Stochastic solute transport under unsteady flow conditions: comparison of theory, Monte Carlo simulations, and field data. Water Resour Res 35 (1999) 2889
11. Wood B.D., and Kavvas M.L. Correction to "Ensemble-averaged equations for reactive transport in porous media under unsteady flow conditions" by Brian D. Wood and M. Levent Kavvas. Water Resour Res 35 (1999) 2887
12. Wood B.D., and Kavvas M.L. Ensemble-averaged equations for reactive transport in porous media under unsteady flow conditions. Water Resour Res 35 (1999) 2887
13. Wood B.D. A connection between the Lagrangian stochastic-convective and cumulant expansion approaches for describing solute transport in heterogeneous porous media. Adv Water Resour 22 (1998) 319-332
14. Simmons C.S., and Kincaid C.T. Scale-dependent effective dispersion coefficients for one-dimensional solute transport. Proceedings of the seventh annual AGU front range branch hydrology days, 21-23 April, 1987 (1987), Colorado State University, Fort Collins
15. Zhang Q. The asymptotic scaling behavior of mixing induced by random velocity field. Adv Appl Math 16 (1995) 23-58
16. Zhang Q. Multi-length-scale theories for scale-up problem and renormalized perturbation expansion. Adv Water Resour 20 (1997) 317-333
17. Panfilov M. Macroscale models of flow through highly heterogeneous porous media (2000), Kluwer, Dordrecht
18. Auriault J.L., and Lewandowska J. Non-Gaussian diffusion modeling in composite porous-media by homogenization - tail effect. Transp Porous Med 21 (1995) 47-70
19. Quintard M., Cherblanc F., and Whitaker S. Dispersion in heterogeneous porous media: one-equation non-equilibrium model. Trans Porous Med 44 (2001) 181-203
20. Ahmadi A., Quintard M., and Whitaker S. Transport in chemically and mechanically heterogeneous porous media, V., two-equation model for solute transport with adsorption. Adv Water Resour 22 (1998) 59-86
21. Dagan G., Fiori A., and Jankovic I. Flow and transport in highly heterogeneous formations: 1. Conceptual framework and validity of first-order approximations. Water Resour Res 39 (2003) 1268
22. Haggerty R., and Gorelick S.M. Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity. Water Resour Res 31 (1995) 2383-2400
23. Jankovic I., Fiori A., and Dagan G. Flow and transport through two-dimensional isotropic media of binary conductivity distribution. Part 2: NUMERICAL simulations and comparison with theoretical results. Stoch Environ Res Risk Assess 17 (2003) 384-393
24. Jankovic I., Fiori A., and Dagan G. Flow and transport in highly heterogeneous formations: 3. Numerical simulations and comparison with theoretical results. Water Resour Res 39 (2003) 1270
25. Brown C.J., Coates J.D., and Schoonen M.A.A. Localized sulfate-reducing zones in a coastal plain aquifer. Ground Water 37 (1999) 505-516
26. Murphy E.M., Schramke J.A., Fredrickson J.K., Bledsoe H.W., Francis A.J., Sklarew D.S., et al. The influence of microbial activity and sedimentary organic carbon on the isotope geochemistry of the Middendorf aquifer. Water Resour Res 28 (1992) 723-740
27. de Smedt F., and Wierenga P.J. Mass transfer in porous media with immobile water. J Hydrol 41 (1979) 59-67
28. Parker J.C., and Valocchi A.J. Constraints on the validity of equilibrium and first-order kinetic transport models in structured soils. Water Resour Res 22 (1986) 399-407
29. Glueckauf E. Theory of chromatography, part 10, Formulae for diffusion into spheres and their application to chromatography. Trans Faraday Soc 51 (1955) 1540-1551
30. Harvey C.F., and Gorelick S.M. Temporal moment-generating equations: modeling transport and mass transfer in heterogeneous aquifers. Water Resour Res 31 (1995) 1895-1911
31. Nkedi-Kizza P., et al. On the equivalence of two conceptual models for describing ion exchange during transport through an aggregated oxisol. Water Resour Res 20 (1984) 1123-1130
32. Young D.F., and Ball W.P. Estimating diffusion coefficients in low-permeability porous media using a macropore column. Environ Sci Technol 32 (1998) 2578-2584
33. Rabideau A.J., and Miller C.T. Two-dimensional modeling of aquifer remediation influenced by sorption nonequilibrium and hydraulic conductivity heterogeneity. Water Resour Res 30 (1994) 1457-1470
34. Raats P.A.C. Transport in structured porous media. Proc Euromech 143 (1981) 221-226
35. Raats P.A.C. Tracing parcels of water and solutes in unsaturated zones. In: Yaron B., and Dagan G. (Eds). Pollutants in porous media: the unsaturated zone between soil surface and groundwater (1984), Springer-Verlag, New York
36. Griffioen J. Suitability of the first-order mass transfer concept for describing cyclic diffusive mass transfer in stagnant zones. J Contam Hydrol 34 (1998) 155-165
37. Cunningham J.A., and Roberts P.V. Use of temporal moments to investigate the effects of nonuniform grain-size distribution on the transport of sorbing solutes. Water Resour Res 34 (1998) 1415-1425
38. Carrera J., et al. Solution methods and qualitative effects. Hydrogeol J 6 (1998) 178-190
39. Bertin H., Panfilov M., and Quintard M. Two types of transient phenomena and full relaxation macroscale model for single phase flow through double porosity media. Transp Porous Med 39 (2000) 73-96
40. Cherblanc F., Ahmadi A., and Quintard M. Two-medium description of dispersion in heterogeneous porous media: calculation of macroscopic properties. Water Resour Res 39 (2003) 1154 10.1029/2002WR001559
41. Cherblanc F., Ahmadi A., and Quintard M. Two-domain description of solute transport in heterogeneous porous media: Comparison between theoretical predictions and numerical experiments. Adv Water Resour 30 (2007) 1127-1143
42. Moyne C. Two-equation model for a diffusive process in porous media using the volume averaging method with an unsteady state closure. Adv Water Resour 20 (1996) 63-76
43. Chastanet J, Wood BD. The mass transfer process in a two-region medium. Water Resour Res, in review.
44. Zinn B., Meigs L.C., Harvey C.F., Haggerty R., Peplinski W.J., and von Schwerin C.F. Experimental visualization of solute transport and mass transfer processes in two-dimensional conductivity fields with connected regions of high conductivity. Environ Sci Technol 38 (2004) 3916-3926
45. Dykhuizen R.C. A new coupling term for dual-porosity models. Water Resour Res 26 (1990) 351-356
46. Gerke H.H., and Van Genuchten M.T. A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resour Res 29 (1993) 305-319
47. Gerke H.H., and Van Genuchten M.T. Macroscopic representation of structural geometry for simulating water and solute movement in dual-porosity media. Adv Water Resour 19 (1996) 343-357
48. Gwo J., Jardine P., Wilson G., and Yeh G. Using a multiregion model to study the effects of advective and diffusive mass transfer on local physical non-equilibrium and solute mobility in a structured soil. Water Resour Res 32 (1996) 561-570
49. Skopp J., Gardner W.R., and Tyler E.J. Solute movement in structured soils: two-region model with small interaction. Soil Sci Am J 45 (1981) 837-842
50. Vogel T., Gerke H., Zhang R., and Genuchten M.V. Modelling flow and transport in a two-dimensional dual-permeability system with spatially variable hydraulic properties. J Hydrol 238 (2000) 78-89
51. Barenblatt G.E., Sheltov I.P., and Kochina I.N. Basic concept of the theory of seepage of homogeneous liquids in fissured rocks. J Appl Math Mech 24 (1960) 1286-1303
52. Goltz M.N., and Roberts P.V. Three-dimensional solutions for solute transport in an infinite medium with mobile and immobile zones. Water Resour Res 22 (1986) 1139-1148
53. van Genuchten M.T., and Wierenga P.J. Mass transfer studies in sorbing porous media: I. Analytical solutions. Soil Sci Am J 40 (1976) 473-480
54. Zurmühl T., and Durner W. Modeling transient water and solute transport in a biporous soil. Water Resour Res 32 (1996) 819-829
55. Quintard M., and Whitaker S. Transport in chemically and mechanically heterogeneous porous media IV: large-scale mass equilibrium for solute transport with adsorption. Adv Water Resour 22 (1998) 59-86
56. Whitaker S. The method of volume averaging. In: Bear J. (Ed). Theory and applications of transport in porous media (1999), Kluwer, Dordrecht
57. Bear J. Hydraulics of groundwater. In: Chow V.T., and Linsley R.K. (Eds). McGraw-Hill Series inf Water Resources and Environmental Engineering (1979), McGraw-Hill, New York 569
58. Takacs L. A two-step scheme for the advection equation with minimised dissipation and dispersion errors. Mon Weather Rev 113 (1985) 1050-1065
59. Bruneau C.H., Fabrie P., and Rasetarinera P. An accurate finite difference scheme for solving convection-dominated diffusion equations. Int J Numer Meth Fluids 24 (1997) 169-183
60. Edwards M.G., and Rogers C.F. Finite volume discretization with imposed flux continuity for the general tensor pressure equation. Comput Geosci 2 (1998) 259-290
61. Bear J. On the tensor form of dispersion in porous media. J Geophys Res 66 (1961) 1185-1197
62. Flury M., and Wai N.N. Dyes as tracers for vadose zone hydrology. Rev Geophys 41 (2003) 1002 10.1029/2001RG000109
63. Gray W.G., et al. Mathematical tools for changing spatial scales in the analysis of physical systems (1993), CRC Press, Boca Raton, FL
64. Anderson T.B., and Jackson R. A fluid mechanical description of fluidized beds. Ind Eng Chem Fundam 6 (1967) 527-538
65. Cushman J.H. Volume averaging, probabilistic averaging, and ergodicity. Adv Water Res 6 (1983) 182-184
66. Howes F.A., and Whitaker S. The spatial averaging theorem revisited. Chem Eng Sci 40 (1985) 1387-1392
67. Slattery J.C. Flow of viscoelastic fluids through porous media. AIChE J 13 (1967) 1066-1071
68. Whitaker S. Diffusion and dispersion in porous media. AIChE J 13 (1967) 420-427
69. Gwo J.-P., O'Brien R., and Jardine P. Mass transfer in structured porous media: embedding mesoscale structure and microscale hydrodynamics in a two-region model. J Hydrol 208 (1998) 204-222
70. Kitanidis P.K. The concept of the dilution index. Water Resour Res 30 (1994) 2011-2026
71. van Genuchten M.T., and Dalton F.N. Models for simulating salt movement in aggregated field soils. Geoderma 38 (1986) 165-183
72. Landerau P., Noetinger B., and Quintard M. Quasi-steady two-equation models for diffusive transport in fractured porous media: large-scale properties for densely fractured systems. Adv Water Resour 24 (2001) 863-876
73. Chen Z.-X. Transient flow of slightly compressible fluids through double-porosity, double-permeability systems - a state-of-the-art review. Transport Porous Med 4 (1989) 147-184
74. Rao P.S.C., et al. Solute transport in aggregated porous media: theoretical and experimental evaluation. Soil Sci Am J 44 (1980) 1139-1146
75. Bibby R. Mass transport of solutes in dual-porosity media. Water Resour Res 17 (1981) 1075-1081
76. Pruess K., and Narasimhan T.N. A practical method for modeling fluid and heat flow in fractured porous media. Soc Petrol Eng J 25 (1985) 14-26
77. Gilman J.R. An efficient finite-difference method for simulating phase segregation in the matrix blocks in double-porosity reservoirs. SPE Reservoir Eng (1996) 403-413
78. Rao P.S.C., Rolston D., Jessup R., and Davidson J. Experimental and mathematical description of nonadsorbed solute transfer by diffusion in spherical aggregates. Soil Sci Am J 44 (1980) 684-688
79. Kfoury M., Ababou R., Nœtinger B., and Quintard M. Matrix-fracture exchange in a fractured porous medium: stochastic upscaling. Comptes Rendus Mec 332 (2004) 679-686
80. Rayleigh L.J.W.S. On the influence of obstacles arranged in rectangular order upon the properties of the medium. Philos Mag 34 (1892) 481-489
81. Quintard M. Diffusion in isotropic and anisotropic porous systems. Transport Porous Med 11 (1993) 187-199
82. Quintard M., Kaviany M., and Whitaker S. Two-medium treatment of heat transfer in porous media: numerical results for effective properties. Adv Water Resour 20 (1997) 77-94
83. Shonnard D.R., and Whitaker S. The effective thermal conductivity for a point-contact porous medium: an experimental study. Int J Heat Mass Transfer 37 (1989) 2817-2834
84. Fabrie P., Quintard M., and Whitaker S. Calculation of porous media effective properties: computational problems and required unit cell features. Proceedings of the conference on mathematical modelling of flow through porous media (1995), World Scientific Publishing Company, London
85. Landerau P. Modèles macroscopiques pour les écoulements monophasiques en milieux poreux fracturés: application au tests de puits. pH.D. thesis, University of Bordeaux I, 2000.
86. Wood B.D., et al. Volume averaging for determining the effective dispersion tensor: closure using periodic unit cells and comparison with ensemble averaging. Water Resour Res 38 8 (2003) 1210 10.1029/2002WR001723
87. Myint-U T., and Debnath L. Partial differential equations for scientists and engineers. 3rd ed. (1987), Prentice-Hall, Englewood Cliffs (NJ)
88. Coddington E.A., and Levinson N. Theory of ordinary differential equations (1955), McGraw-Hill, New York
89. Carslaw H.S., and Jaeger J.C. Conduction of heat in solids. 2nd ed. (1959), Oxford University (Clarendon) Press, Oxford