Basic transport properties in natural porous media

Complexity

Volumn 10, Issue 3, 2005, Pages 22-37

  Hunt, A G ^a  

^a WRIGHT STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14844286437     PISSN: 10762787     EISSN: None     Source Type: Journal    
DOI: 10.1002/cplx.20067     Document Type: Review

References (58)

1. de Gennes, P.G. Physics of Disordered Materials; Adler, D.; Fritzsche, H.; Ovshinsky, S.R., Eds.; Plenum Press: New York, 1985.
2. Katz, A.J.; Thompson, A.H. Fractal sandstone pores: Implications for conductivity and pore formation. Phys Rev Lett 1985, 54, 1325-1328.
3. Turcotte, D.L. Fractals and fragmentation. J Geophys Res 1986, 91, 1921-1926.
4. Rieu, M.; Sposito, G. Fractal fragmentation, soil porosity, and soil water properties I. Theory. Soil Sci Soc Am J 1991, 55, 1231.
5. Tyler, S.W.; Wheatcraft, S.W. 1990, Fractal processes in soil water retention. Water Resour Res 1990, 26, 1045-1054.
6. Broadbent, S.R.; Hammersley, J.M. Percolation processes, 1. Crystals and mazes. Proc Cambridge Philos Soc 1957, 53, 629-641.
7. Ambegaokar, V.N., Halperin, B.I.; Langer, J.S. Hopping conductivity in disordered systems. Phys Rev B 1971, 4, 2612-2621.
8. Pollak, M. A percolation treatment of dc hopping conduction. J Non-Cryst Solids 1972, 11, 1-24.
9. Skal, A.; Shklovskii, B. Topology of an infinite cluster in the theory of percolation and its relationship to the theory of hopping conduction. Sov Phys Semicond 1975, 8, 1029-1032.
10. Hunt, A.G. Applications of percolation theory to porous media with distributed local conductances Adv Water Res 2001, 24(3,4), 279-307.
11. Hunt, A.G.; Gee, G.W. Application of critical path analysis to fractal porous media: comparison with examples from the Hanford site. Adv Water Res 2002a, 25, 129-146.
12. Hunt, A.G.; Gee, G.W. Water retention of fractal soil models using continuum percolation theory: Tests of Hanford site soils. Vadose Zone J 2002b, 1, 252-260.
13. Hunt, A.G.; Gee, G.W. Wet-end deviations from fractal scaling of water retention characteristics. Vadose Zone J 2003, 2, 759-765.
14. Hunt, A.G. Continuum percolation theory for pressure-saturation characteristics of fractal porous media: Extension to non-equilibrium, Adv Water Resour 2004c, 27, 245-257.
15. Hunt, A.G.; Ewing, R.P. On the vanishing of solute diffusion at a finite moisture content. Soil Sci Soc Am J 2003, 67, 1701-1702.
16. Rockhold, M.L., Fayer, M.J.; Gee, G.W. Characterization of unsaturated hydraulic conductivity at the Hanford Site, PNL 6488 Pacific Northwest National Laboratory, Richland, WA 99352, 1988.
17. Khaleel, R.; Freeman, E.J. 1995. Variability and scaling of hydraulic properties for 200 area soils, Hanford site. Westinghouse Hanford Company Report WHC-EP-0883.
18. Khaleel, R., Relyea, J.F.; Conca, J.L. Evaluation of van Genuchten Mualem relationship to estimate unsaturated hydraulic conductivity of at low water content. Water Resour Res 1995, 31, 2659-2668.
19. Freeman, E.J. Fractal Geometries Applied to Particle Size Distributions and Related Moisture Retention Measurements at Hanford, Washington, M.A. Thesis, University of Idaho, 1995.
20. Moldrup, P., Oleson, T.; Komatsu, T.; Schjoning, P.; Rolston, D.E. Tortuosity, diffusivity, and permeability in the soil liquid and gaseous phases. Soil Sci Soc Am J 2001, 65, 613-623.
21. Bauters, T.W.J.; DiCarlo, D.A.; Steenhuis, T.S.; Parlange, J.-Y. Preferential flow in water-repellent sands. Soil Sci Soc Am J 1998, 62, 1185-1190.
22. Moldrup, P.; Yoshikawa, S.; Oleson, T.; Komatsu, T.; Rolston, D.E. Air permeability in undisturbed volcanic ash soils: Predictive model test and soil structure fingerprint. Soil Sci Soc Am J 2003, 67, 32-40.
23. Steriotis, T.A.; Katsaros, F. K.; Stubos, A. K.; Mitropoulos, A.Ch.; Kanellopoulos, N.K. A novel experimental technique for the measurement of the single-phase gas relative permeability of porous solids. Meas Sci Technol 1997, 8, 168-173.
24. Hunt, A.G. Continuum percolation theory for saturation dependence of air permeability. Vadose Zone J, accepted. 2004e,
25. Hunt, A.G. Continuum percolation theory and Archie's law. Geophys Res Lett accepted, 2004d.
26. Hunt, A.G. Continuum percolation theory for pressure-saturation characteristics of fractal porous media: Critical volume fraction for percolation. Adv Water Resour 2004b, 27, 175-183.
27. Arya, L.M.; Paris, J.F. A physicoempirical model to predict the soil moisture characteristic from particle size distribution and bulk density data. Soil Sci Soc Am J 1981, 45, 1023-1080.
28. Gevirtzman, H.; Roberts, P.V. Pore scale spatial analysis of two immiscible fluids in porous media. Water Resour Res 1991, 27, 1167.
29. Tyler S.W.; Wheatcraft, S.W. Fractal scaling of soil particle-size distributions - Analysis and limitations. Soil Sci Soc Am J 1992, 56, 362-369.
30. Nigmatullin, R.R.; Dissado, L.A.; Soutougin, n.N. A fractal pore model for Archie's law in sedimentary rocks. J Phys D Appl Phys 1992, 25, 32-37.
31. Kirkpatrick, S. Hopping conduction: Experiment versus theory. 5th Annual Conference on Amorphous and Liquid Semiconductors: Proceedings, Stuke, J.; Brenig, W., Eds.; Taylor & Francis: London, 1973; 103-107.
32. Seager, C.H.; Pike, G.E. Percolation and conductivity: A computer study II. Phys Rev B 1974, 10, 1435-1436.
33. Katz, A.J.; Thompson, A.H. Quantitative prediction of permeability in porous rock. Phys Rev B 1986, 34, 8179-8181.
34. Bernabe, Y.; Bruderer, C. Effect of the variance of pore size distribution on the transport properties of heterogeneous networks. J Geophys Res 1998, 1998, 103, 513.
35. Shah, C.B.; Yortsos, Y.C. The permeability of strongly disordered systems. Phys. Fluids 1996, 8, 280-282.
36. Berkowitz, B.; Balberg, I. Percolation theory and its application to groundwater hydrology. Water Resour Res 1993, 29, 775-794.
37. Derrida, B.; Vannimenus. 1982, A transfer matrix approach to random resistor networks, J Phys A Math Gen 13 L557-L562.
38. Fatt, I. The network model of porous media. Trans Am Inst Min Metall Pet Eng 1956, 207, 144-177.
39. Friedman, S.P.; Seaton, N.A. Critical path analysis of the relationship between permeability and electrical conductivity of three-dimensional pore networks. Water Resour Res 1998, 34, 1703-1710.
40. Stauffer, D.; Aharony, A. Introduction to Percolation Theory, 2nd Edition; Taylor & Francis: London, 1994.
41. Sahimi, M. Flow and Transport in Porous Media and Fractured Rock. Classical Methods to Modern Approaches; VCH Weinheim, Federal Republic of Germany, 1995.
42. Matheron, G. Elements pour une Theorie des Milieux Poreux, Masson et Cie, Paris, 1967.
43. Vyssotsky, V.A.; Gordon, S.B.; Frisch, H.L.; Hammersley, J.M. Critical percolation probabilities (bond problem). Phys Rev 1961, 123, 1566-1567.
44. Stauffer, D. Scaling theory of percolation clusters. Phys Rep 1979, 54, 1-74.
45. Hunt, A.G. Percolative transport in fractal porous media. Chaos Solitons Fractals 2004a, 19, 309-325.
46. Golden, K.M. Critical behavior of transport in lattice and continuum percolation models. Phys Rev Lett 1997, 78, 3935-3938.
47. Golden, K.M. Brine percolation and the transport properties of sea ice. Ann Glaciology 2001, 33, 28-36.
48. Khaleel, R.; Relyea, J.F. Variability of Gardner's alpha for coarse-textured sediments. Water Resour Res 2001, 37, 1567-1575.
49. Mualem, Y. A Catalogue of the Hydraulic Properties of Unsaturated Soils. Research Project No. 442, Technion, Israel Institute of Technology, Haifa, 1976.
50. van Genuchten, M.T. A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Am J 1980, 44, 892-898.
51. Thompson, A.H.; Katz, A. J.; Krohn, C.E. The microgeometry and transport of sedimentary rock. Adv Phys 1987, 36, 625.
52. Kuentz, M.; Mareschal, J.C.; Lavallee, P. Numerical estimation of electrical conductivity in saturated porous media with a 2-D lattice gas. Geophysics 2000, 65, 766-772.
53. Krohn, C.E.; Thompson, A.H. Fractal sandstone pores: Automated measurements using scanning-electron-microscope images. Phys Rev B 1986, 33, 6366-6374.
54. Lenhard, R.J. Measurement and modeling of 3-phase saturation pressure hysteresis. J Contam Hydrol 1992, 9, 243-169.
55. Lenhard, R.J.; Parker, J.C.; Kaluarachchi, J.J. Comparing simulated and experimental hysteretic 2-phase transient fluid-flow phenomena. Water Resour Res 1991, 27, 2113-2124.
56. Blunt, M. J.; Scher, H. Pore-level model of wetting, Phys Rev E 1995, 52, 6387-6403.
57. Tokunaga, T.; Wan, J. Water film flow along fracture surfaces of porous rock. Water Resour Res 1997, 33, 1287-1295.
58. Ewing, R.P.; Horton, R. Scaling in diffusive transport. In: Scaling Methods in Soil Physics; Pachepsky, Ya., et al., Eds.; CRC Press: Boca Raton, FL, 2003.