Percolation theory and the future of hydrogeology

Hydrogeology Journal

Volumn 13, Issue 1, 2005, Pages 202-205

  Hunt, Allen G ^a  

^a WRIGHT STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HYDROGEOLOGY; PERCOLATION;

EID: 17044401397     PISSN: 14312174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10040-004-0405-6     Document Type: Article

References (36)

1. Ambegaokar VN, Halperin BI, Langer JS (1971) Hopping conductivity in disordered systems. Phys Rev B 4:2612-2621 10.1103/PhysRevB.4.2612
2. Berkowitz B, Balberg I (1993) Percolation theory and its application to groundwater hydrology. Water Resour Res 29(4):775-794 10.1029/92WR02707
3. Bernabe Y, Bruderer C (1998) Effect of the variance of pore size distribution on the transport properties of heterogeneous networks. J Geophys Res 103:513 10.1029/97JB02486
4. Chandler R, Koplik J, Lerman K, Willemsen JF (1982) Capillary displacement and percolation in porous media. J Fluid Mech 119:249-267
5. Heiba AA, Sahimi M, Scriven LE, Davis HT (1982) Percolation theory of two-phase relative permeability. SPE 11015:17
6. Hunt AG (1998) Upscaling in subsurface transport using cluster statistics of percolation. Transport in Porous Media 30(2):177-198 10.1023/A:1006534922791
7. Hunt AG (2000) Percolation cluster statistics and conductivity semi-variograms. Transport in Porous Media 39:131-141 10.1023/ A:1006629013418
8. Hunt AG (2001) Applications of percolation theory to porous media with distributed local conductances. Adv Water Res 24:279-308 10.1016/ S0309-1708(00)00058-0
9. Hunt AG (2003) Some comments on the scale dependence of the hydraulic conductivity in the presence of nested heterogeneity. Adv Water Res 26:71-77 10.1016/S0309-1708(02)00096-9
10. Hunt AG (2004a) Percolative transport in fractal porous media. Chaos, Solitons and Fractals 19:309-325
11. Hunt AG (2004b) Continuum percolation theory for pressure-saturation characteristics of fractal porous media: Extension to non-equilibrium. Adv Water Resour 27:245-257 10.1016/j.advwatres.2004.01.002
12. Hunt AG (2004c) Scale-dependent hydraulic conductivity in anisotropic media from dimensional cross-over. Hydrogeol J (in review)
13. Hunt AG (2004d) Continuum percolation theory and Archie's Law. Geophys Res Lett (accepted
14. Hunt AG, Ewing RP (2003) On the vanishing of solute diffusion at a finite moisture content. Soil Sci Soc Am J 67:1701-1702
15. Hunt AG, Gee GW (2002a) Application of critical path analysis to fractal porous media: Comparison with examples from the Hanford site. Adv Water Res 25:129-146 10.1016/S0309-1708(01)00057-4
16. Hunt AG, Gee GW (2002b) Water retention of fractal soil models using continuum percolation theory: Tests of Hanford site soils. Vadose Zone J 1:252-260
17. Hunt AG, Gee GW (2003) Wet-end deviations from fractal scaling of water retention characteristics. Vadose Zone J 2:759-765
18. Katz AJ, Thompson AH (1986) Quantitative prediction of permeability in porous rock. Phys Rev B 34:8179-8181 10.1103/PhysRevB.34.8179
19. Kirkpatrick S (1973) Hopping conduction: Experiment versus theory. In: Stuke J, Brenig W (eds) 5th Annual Conference on Amorphous and Liquid Semiconductors: Proceedings. Taylor & Francis, London, pp 103-107
20. Lenhard RJ, Parker JC, Kaluarachchi JJ (1991) Comparing simulated and experimental hysteretic 2-phase transient fluid-flow phenomena. Water Resour Res 27:2113-2124 10.1029/91WR01272
21. Mallory K (1993) Active subclusters in percolative hopping transport. Phys Rev B 47:7819-7826 10.1103/PhysRevB.47.7819
22. G Matheron 1967 Elements pour une Theorie des Milieux Poreux (Elements of the theory of porous media) Masson et Cie Paris
23. Moldrup P, Oleson T, Komatsu T, Schjoning P, Rolston DE (2001) Tortuosity, diffusivity, and permeability in the soil liquid and gaseous phases. Soil Sci Soc Am J 65:613-623
24. Neuman SP, Di Federico V (2003) Multifaceted nature of hydrogeologic scaling and its interpretation. Rev Geophys 41:aRt. No. 1014 10.1029/ 2003RG000130
25. Pollak M (1972) A percolation treatment of dc hopping conduction. J Non-Cryst Solids 11:1-24 10.1016/0022-3093(72)90304-3
26. Rieu M, Sposito G (1991) Fractal fragmentation, soil porosity, and soil water properties I. Theory Soil Sci Soc Am J 55:1231
27. Sahimi M (1993) Flow phenomena in rocks - from continuum models to fractals, percolation, cellular-automata, and simulated annealing. Rev Mod Phys 65(4):1393-1534
28. M Sahimi 1995 Flow and transport in porous media and fractured rock: from classical methods to modern approaches VCH Weinheim Federal Republic of Germany
29. Seager CH, Pike GE (1974) Percolation and conduction: A computer study II. Phys Rev B 10:1435-1436 10.1103/PhysRevB.10.1435
30. Shah CB, Yortsos Y (1996) The permeability of strongly disordered systems. Phys Fluids 8:280-282 10.1063/1.868835
31. Skaggs TH (2003) Effects of finite system size and finite heterogeneity on the conductivity of broadly distributed resistor networks. Physica B 338:266-269
32. Stauffer D (1979) Scaling theory of percolation clusters. Phys Rep 54:1-74 10.1016/0370-1573(79)90060-7
33. D Stauffer A Aharony 1994 Introduction to percolation theory 2 Taylor & Francis London
34. Tartakovsky DM, Neuman SP (1998) Transient effective hydraulic conductivity under slowly and rapidly varying mean gradients in bounded three-dimensional random media. Water Resour Res 34:21-32 10.1029/ 97WR01965
35. Turcotte DL (1986) Fractals and fragmentation. J Geophys Res 91:1921-1926
36. Vyssotsky VA, Gordon SB, Frisch HL, Hammersley JM (1961) Critical percolation probabilities (bond problem). Phys Rev 123:1566-1567 10.1103/ PhysRev.123.1566