Pressure-saturation curves and the critical volume fraction for percolation: Accessibility function of percolation theory

Lecture Notes in Physics

Volumn 771, Issue , 2009, Pages 207-231

  Hunt, Allen ^a   Ewing, Robert ^b  

^a WRIGHT STATE UNIVERSITY   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 62849094749     PISSN: 00758450     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-89790-3_7     Document Type: Article

References (29)

1. Wilkinson, D., 1986, Percolation effects in immiscible displacement, Phys. Rev. A 34: 1380-1391. 208,
2. Gist, G. A., A. H. Thompson, A. J. Katz, and R. L. Higgins, 1990, Hydrodynamic dispersion and pore geometry in consolidated rock. Phys. Fluids A. 2: 1533-1544.
3. Clement, E., C. Baudet, and J. Hulin, 1985, Multiple scale structure of non wetting fluid invasion fronts in 3d model porous-media. J. Phy. Lett. 46(24): 1163-1171.
4. Lenhard, R. J., J. C. Parker, and J. J. Kaluarachchi, 1991, Comparing simulated and experimental hysteretic 2-phase transient fluid-flow phenomena. Water Resour. Res. 27: 2113-2124.
5. Lenhard, R. J., 1992, Measurement and modeling of 3-phase saturation pressure hysteresis, J. Contam. Hydrol. 9: 243-169.
6. Heiba, A. A.,M. Sahimi, L. E. Scriven and H. T. Davis, 1982, Percolation theory of two-phase relative permeability, SPE Reservoir Eng. 7 123-132.
7. Wilkinson, D., and J. Willemsen, 1983, Invasion percolation: A new form of percolation theory, J. Phys. A: Math. Gen. 16: 3365-3376.
8. Sahimi, M., and Y. C. Yortsos, 1990, Applications of fractal geometry to porous media: A review, Paper presented at the 1990 Annual FallMeeting of the Society of Petroleum Engineers, New Orleans, LA.
9. Hunt, A. G., 2004, Continuum percolation theory for water retention and hydraulic conductivity of fractal soils: 2. Extension to non-equilibrium, Adv. Water Resour. 27: 245-257.
10. Bauters, T. W. J., D. A. DiCarlo, T. S., Steenhuis, and J.-Y. Parlange, 1998, Preferential flow in water-repellent sands, Soil Sci. Soc. Am. J. 62: 1185-1190.
11. Hunt, A. G., and T. E. Skinner, 2005, Hydraulic conductivity limited equilibration: Effect on water-retention characteristics, Vadose Zone J. 4: 145-150.
12. Rieu, M., and G. Sposito, 1991, Fractal fragmentation, soil porosity, and soil water properties I. Theory, Soil Sci. Soc. Am. J. 55 1231.
13. Blank, L. A., A. G. Hunt, and T. E. Skinner, 2008, A numerical procedure to calculate hydraulic conductivity for an arbitrary pore size distribution, Vadose Zone J. 7: 461-472.
14. Hunt, A. G., and G. W. Gee, 2002, Water retention of fractal soil models using continuum percolation theory: Tests of Hanford site soils, Vadose Zone J, 1: 252-260.
15. Moldrup, P., T. Oleson, T. Komatsu, P. Schjonning, and D. E. Rolston, 2001, Tortuosity, diffusivity, and permeability in the soil liquid and gaseous phases. Soil Sci. Soc. Am. J. 65: 613-623.
16. Hunt, A. G., 2004, Percolative transport and fractal porous media, Chaos Solitons Fractals 19: 309-325.
17. Khaleel, R., and J. F. Relyea, 2001. Variability of Gardner's alpha for coarse-textured sediments. Water Resour. Res. 37: 1567-1575.
18. Khaleel, R., and E. J. Freeman, 1995. Variability and scaling of hydraulic properties for 200 area soils, Hanford site, Westinghouse Hanford Company Report WHC-EP-0883.
19. Hunt, A. G., and G. W. Gee, 2003, Wet-end deviations from scaling of the water retention characteristics of fractal porous media, Vadose Zone J. 2: 759-765.
20. Hunt, A. G., 2004, Continuum percolation theory for water retention and hydraulic conductivity of fractal soils: 1. Estimation of the critical volume fraction for percolation, Adv. Water Resour. 27: 175-183.
21. Manwart, C., S. Torquato, and R. Hilfer, 2000, Stochastic reconstruction of sandstones. Phys. Rev. E 62: 893-899.
22. Bittelli, M., G. S. Campbell, and M. Flury, 1999, Characterization of particle-size distribution in soils with a fragmentation model. Soil Sci. Soc. Am. J. 63: 782-788.
23. Luckner, L., M. Th. van Genuchten, and D. R. Nielsen, 1989, A consistent set of parametric models for the two-phase flow of immiscible fluids in the subsurface, Water Resour. Res. 25: 2187-2193.
24. Hunt, A., 1993, A general treatment of 1-dimensional hopping conduction, Sol. State Commun. 86: 765-768.
25. Hunt, A. 1991, Transport in ionic conducting glasses, J Phys Condens Matter 3(40): 7831-7842.
26. Hunt, A., 1991, The calorimetric glass transition: A simple model, Phil. Mag. B 64, 563-567.
27. Hunt, A., 1991, One-dimensional hopping conductivity calculations, Phil. Mag. B 64: 327-334.
28. Chandler, R., J. Koplik, K. Lerman, and J. F. Willemsen, 1982, Capillary displacement and percolation in porous media, J. Fluid Mech., 119, 249-267.
29. Freeman, E. J., 1995. Fractal Geometries Applied to Particle Size Distributions and Related Moisture Retention Measurements at Hanford, Washington, M. A. Thesis, University of Idaho, Moscow.