Skip to main content
SpringerLink
Log in

Porous Media Primer for Physicists

  • Chapter
  • First Online:
Percolation Theory for Flow in Porous Media

Part of the book series: Lecture Notes in Physics ((LNP,volume 771))

The study of soils and rocks is the province of many different disciplines. These disciplines have historically focused on applications rather than understanding, and this pragmatic approach has led to some cutting of corners. Furthermore, the different disciplines have different goals, so they have developed their own peculiar vocabulary, insights, and biases. For example, petroleum engineers generally work with consolidated rock, so the concept of a particle size distribution is not as central to their thinking as it is to a soil scientist. Meanwhile, soil scientists working with just two fluids – air and water – can frequently get away with assuming that air is infinitely compressible (and has density and viscosity of zero); petroleum engineers working with multiple flowing gases and liquids must consider all fluid phases in concert. Insofar as the structure of the medium is concerned, the material presented here tends to be centered on soil physics, but we have attempted to make contact with other disciplines in important cases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bear, J., 1972,Dynamics of Fluids in Porous Media, American Elsevier Publishing Co. Inc., New York.

    Google Scholar 

  2. Dullien, F.A.L. 1992.Porous Media, Fluid Transport and Pore Structure. Academic, London.

    Google Scholar 

  3. Warrick, A. A., 2002,Soil Physics Companion, CRC Press, Boca Raton.

    Google Scholar 

  4. Marshall, T. J., J. W. Holmes, and C. W. Rose, 1996,Soil Physics, 3rd edition, 469 pages ISBN:0521451515 | ISBN13:9780521451512.

    Google Scholar 

  5. Hillel, D., 1998,Environmental Soil Physics, Academic Press. (Elsevier?), San Diego, CA

    Google Scholar 

  6. Sahimi, M., 1995,Flow and Transport in Porous Media and Fractured Rock from Classical Methods to Modern Approaches, Wiley VCH Weinheim, Germany, 500 pp.

    Google Scholar 

  7. Surkov, V. V., and H. Tanaka, 2005, Electrokinetic effect in fractal pore media as seismoelectric phenomena, in:Fractal Behavior of the Earth System, Ed. V. P. Dimri, Springer, Heidelberg.

    Google Scholar 

  8. Sen, P. N., C. Scala, and M. H. Cohen, 1981, A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads,Geophysics 46: 781–795.

    Article  Google Scholar 

  9. Krohn, C. E., and A. H. Thompson, 1986, Fractal sandstone pores: automated measurements using scanning-electron-microscope images,Phys. Rev. B 33: 6366–6374.

    Article  Google Scholar 

  10. Katz, A. J., and A. H. Thompson, 1985, Fractal sandstone pores: implications for conductivity and pore formation,Phys. Rev. Lett.54: 1325–1328.

    Article  Google Scholar 

  11. Turcotte, D. L., 1986, Fractals and fragmentation.J. Geophys. Res.91: 1921–1926.

    Article  Google Scholar 

  12. Thompson, A. H., A. J. Katz, and C. E. Krohn, 1987, Microgeometry and transport in sedimentary rock,Adv. Phys.36: 625.

    Article  Google Scholar 

  13. Balberg, I., 1987, Recent developments in continuum percolation,Philos. Mag. B 30: 991–1003.

    Google Scholar 

  14. de Gennes, P. G., 1985,Phys. of Disordered Materials, Adler, D., H. Fritzsche, and S. R. Ovshinsky (eds.) Plenum Press, New York.

    Google Scholar 

  15. Tyler, S. W., and S. W. Wheatcraft, 1990, Fractal processes in soil water retention.Water Resour. Res.26: 1045–1054.

    Google Scholar 

  16. Tyler S. W., and S. W. Wheatcraft, 1992, Fractal scaling of soil particle-size distributions – analysis and limitations,Soil Sci. Soc. Am. J.56: 362–369.

    Google Scholar 

  17. Rieu, M., and G. Sposito, 1991, Fractal fragmentation, soil porosity, and soil water properties I. Theory,Soil Sci. Soc. Am. J.55: 1231.

    Google Scholar 

  18. 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.

    Google Scholar 

  19. Bird, N. R. A., E. Perrier, and M. Rieu, 2000, The water retention function for a model of soil structure with pore and solid fractal distributions,Eur. J. Soil Sci.,51: 55–63.

    Article  Google Scholar 

  20. Gimenez, D., E. Perfect, W. J. Rawls, and Ya A. Pachepsky, 1997, Fractal models for predicting soil hydraulic properties: a review,Eng. Geol.,48: 161–183.

    Google Scholar 

  21. Filgueira, R. R., Ya. A. Pachepsky, L. L. Fournier, G. O. Sarli, and A. Aragon, 1999, Comparison of fractal dimensions estimated from aggregate mass-size distribution and water retention scaling,Soil Sci.164: 217–223.

    Article  Google Scholar 

  22. 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.

    Google Scholar 

  23. Baveye, P., J.-Y. Parlange, and B. A. Stewart (ed.), 1998,Fractals in Soil Science, CRC Press, Boca Raton, FL.

    Google Scholar 

  24. Kozeny, J., 1927, Ueber Kapillare Leitung des Wasssers im Boden,Sitzungsber. Adak. Wiss. Wien,136: 271–306.

    Google Scholar 

  25. Childs, E. C., and N. Collis-George, 1950, The permeability of porous materials,Proc. Royal Soc. London, Ser. A 201: 392–405.

    Article  Google Scholar 

  26. Carman, P. C. 1956,Flow of Gases Through Porous Media, Butterworths, London.

    Google Scholar 

  27. Wyllie, M. R. J., and G. H. F. Gardner, 1958, World Oil (March and April Issues), p. 2.

    Google Scholar 

  28. Millington, R. J., and J. P. Quirk, 1959, Permeability of porous media.Nature (London)183: 387–388.

    Article  Google Scholar 

  29. Millington, R. J., and J. P. Quirk, 1961, Permeability of porous media,Trans. Faraday Soc.57: 1200–1208.

    Article  Google Scholar 

  30. Brooks, R. H., and A. T. Corey, 1964, Hydraulic properties of porous media, Colorado State Univ. Hydrology Paper 3.

    Google Scholar 

  31. Mualem, Y., 1976, A new model for predicting the hydraulic conductivity of unsaturated porous media,Water Resour. Res.12: 513–522.

    Article  Google Scholar 

  32. Mualem, Y., 1976. A catalogue of the hydraulic properties of unsaturated soils, Res. Proj. No. 442, Technion, Israel Institute of Technology, Haifa.

    Google Scholar 

  33. Mualem,Y., and G. Dagan, 1978, Hydraulic conductivity of soils: unified approach to the statistical models,Soil Sci. Soc. Am. J.42: 392–395.

    Google Scholar 

  34. van Genuchten, M. T., 1980, A closed form equation for predicting the hydraulic conductivity of unsaturated soils,Soil Sci. Am. J.,44: 892–898.

    Google Scholar 

  35. 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.

    Article  Google Scholar 

  36. van Genuchten, M. Th., F. J. Leij, and S. R. Yates, 1991, The RETC code for quantifying the hydraulic functions of unsaturated soils, US EPA 000/091/000, ADA OK, 83 pp.

    Google Scholar 

  37. Hassanizadeh, S. M., and W. G. Gray, 1993, Toward an improved description of two-phase flow,Adv. Water Res.16: 53–67.

    Article  Google Scholar 

  38. Burdine, N. T., 1953, Relative permeability calculations from pore-size distribution data.Petrol. Trans. Am Inst. Min. Eng.198: 71–77.

    Google Scholar 

  39. Ewing, R. P., 2004, Soil water potential (I), Soil Physics Lecture Notes,http://www.agron.iastate.edu/soilphysics/a577pot1.html

  40. Danielson, R. E. and P. L. Sutherland, 1986, Porosity, pp. 443–461 in A. Klute (ed.), Methods of Soil Analysis. Part 1. Agron. Monogr. 9 (2nd ed.), ASA and SSSA, Madison, WI.

    Google Scholar 

  41. Lindquist, W. B., 2002, Network flow model studies and 3D pore structure,Contemp. Math.295: 355–366.

    Google Scholar 

  42. Vogel, H.-J., 2002, Topological characterization of porous media. In K. R. Mecke and D. Stoyan (eds.), Lecture Notes in Physics 600, pp. 75–92, Springer-Verlag, Berlin.

    Google Scholar 

  43. Silin, D., and T. Patzek, 2006, Pore space morphology analysis using maximal inscribed spheres, Physica A. 371: 336–360.

    Google Scholar 

  44. Ham, K., H. Jin, R. Al-Raoush, X. G. Xie, C. S. Willson, G. R. Byerly, L. S. Simeral, M. L. Rivers, R. L. Kurtz, and L. G. Butler, 2004, Three-dimensional chemical analysis with synchrotron tomography at multiple x-ray energies: brominated aromatic flame retardant and antimony oxide in polystyerene,Chem. Mater.16: 4032–4042.

    Article  Google Scholar 

  45. Lehmann, P., P. Wyss, A. Flisch, P. Vontobel, M. Krafczyk, A. Kaestner, F. Beckmann, A Gvgi, and H. Fluhler, 2006, Tomographical imaging and mathematical description of porous media used for the prediction of fluid distribution,Vadose Zone J. 5: 80–97.

    Google Scholar 

  46. Glantz, R., and M. Hilpert, 2007, Dual models of pore spaces,Adv. Water Resour.30(2): 227–248.

    Article  Google Scholar 

  47. Mohanty, K. K, H. T. Davis, and L. E. Scriven, 1987, Physics of oil entrapment in water-wet rock.SPE Reserv. Eng.2: 113–128.

    Google Scholar 

  48. Weisstein. E. W., 2003, Hexagonal Close Packing. FromMathWorld–A Wolfram Web Resource.http://mathworld.wolfram.com/HexagonalClosePacking.html

  49. Finney, J. L., 1970, Random packings and the structure of simple liquids I. The geometry of random close packing.Proc. Roy. Soc. London A 319: 479–494.

    Article  Google Scholar 

  50. Al-Raoush R., K. Thompson, and C. S. Willson, 2003, Comparison of network generation techniques for unconsolidated porous media,Soil Sci. Soc. Am. J.67: 1687–1700.

    Google Scholar 

  51. Scher, H., and R. Zallen, 1970, Critical density in percolation processes,J. Chem. Phys.53: 3759.

    Article  Google Scholar 

  52. Miller, E. E., and R. W. Miller, 1956, Physical theory for capillary flow phenomena,J. Appl. Phys.,27: 324–332.

    Article  Google Scholar 

  53. Fatt, I., 1956, The network model of porous media,Trans. Am. Inst. Min. Metall. Pet. Eng.,207: 144–177.

    Google Scholar 

  54. Eshel, G., G. J. Levy, U. Mingelgrin and M. J. Singer, 2004, Critical evaluation of the use of laser diffraction for particle-size distribution analysis, Soil Sci. Soc. Am. J. 68:736–743.

    Google Scholar 

  55. Raine, D. A., and J. S. Brenizer, 1997, The analysis and correction of neutron scattering effects in neutron imaging,Mater. Eval. 55: 1174–1178.

    Google Scholar 

  56. Tija, J. S., and P. V. Moghe, 1998, Analysis of 3-D microstructure of porous poly(lactide-glycolide) matrices using confocal microscopy,J. Biomed. Mater. Res.43: 291–299.

    Article  Google Scholar 

  57. MacDonald, I. F., G. D. Yadav, I. Chatzis, amd F. A. L. Dullien, 1988, 2-phase flow in porous media – obtaining sharp digitized images of serial sections for subsequent quantitative analysis,J. Microscopy – Oxford,150: 191–198.

    Google Scholar 

  58. Peth, S., R. Horn, F. Beckman, T. Donath, J. Fischer, and A. J. M. Smucker, 2008, Three-dimensional quantification of intra-aggregate pore-space features using synchrotron radiation-based microtomography,Soil Sci. Soc. Am. J.72: 897–907.

    Article  Google Scholar 

  59. Arya, L. M., and J. F. Paris, 1981, A physicoempirical model to predict the soil moisture characteristic from particle size distribution and bulk density data,Soil Sci. Soc. Am. J.45: 1023–1080.

    Google Scholar 

  60. Gvirtzman, H., and P. V. Roberts, 1991, Pore scale spatial analysis of two immiscible fluids in porous media.Water Resour. Res. 27: 1167.

    Article  Google Scholar 

  61. Gee, G. W., and J. W. Bauder, 1986, Particle-size analysis, pp. 383–411.In A. Klute. (ed.)Methods of Soil Analysis. Part 1. 2nd ed. Agron. Monogr. 9. ASA and SSSA, Madison, WI.

    Google Scholar 

  62. Fatt, I., 1956, The network model of porous media. Petrol. Trans. AIME 207: 144–181.

    Google Scholar 

  63. Lago, M., and M. Araujo, 2001, Threshold pressure in capillaries with polygonal cross-section,J. Colloid Interface Sci. 243: 219–226.

    Article  Google Scholar 

  64. Camassel, B., N. Sghaier, M. Prat, and S. Ben-Nasrallah, 2005, Evaporation in a capillary tube of square cross-section: application to ion transport,Chem Eng Sci. 60: 815–826.

    Article  Google Scholar 

  65. Lindquist, W. B., 2006, The geometry of primary drainage,J. Colloid and Interface Science,296: 655–668.

    Article  Google Scholar 

  66. Toledo, P. G., L. E. Scriven, and H. T. Davis, 1989, Pore space statistics and capillary pressure curves from volume controlled porosimetry,Paper SPE 19618, 64th Ann. Tech. Conf. and Exhib. of the SPE, Oct. 8–11, San Antonio, Texas.

    Google Scholar 

  67. Hilpert, M., C. T. Miller, and W. G. Gray, 2003, Stability of a fluid-fluid interface in a biconical pore segment,J. Colloid Interface Sci 267: 397–407.

    Article  Google Scholar 

  68. Bakke, S., and P-E. Øren, 1997, 3-D pore-scale modelling of sandstones and flow simulations in the pore networks,SPE J.2: 136–149.

    Google Scholar 

  69. Knackstedt, M. A., A. P. Sheppard, and M. Sahimi, 2001, Pore network modelling of two-phase flow in porous rock: the effect of correlated heterogeneity,Adv. Water Res.24: 257–277.

    Article  Google Scholar 

  70. Chatzis, I. and F. A. L. Dullien, 1977, Modelling pore structures by 2-D and 3-D networks with application to sandstones,Can. J. Petrol. Tech. 16: 97–108.

    Google Scholar 

  71. Levine, S., P. Reed, G. Shutts, and G. Neale, 1977, Some aspects of wetting/dewetting of a porous medium,Powder Tech.17: 163–181.

    Article  Google Scholar 

  72. Wu, Q., M. Borkovec, and H. Sticher, 1993, On particle-size distributions in soils,Soil Sci. Soc. Am. J.57: 883–890.

    Google Scholar 

  73. Posadas, A. N. D., D. Gimenez, M. Bittelli, C. M. P. Vaz, and M. Flury, 2001, Multifractal characterization of soil particle-size distributions.Soil Sci. Soc. Am. J.65: 1361–1367.

    Google Scholar 

  74. 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.

    Article  Google Scholar 

  75. Bird, N. R. A., E. Perrier, and M. Rieu, 2003, The water retention function for a model of soil structure with pore and solid fractal distributions. Eur. J. Soil Sci. 51: 55–63.

    Google Scholar 

  76. Mandelbrot, B. B., 1983,The Fractal Geometry of Nature, W. H. Freeman, San Francisco.

    Google Scholar 

  77. Jullien, R. and R. Botet, 1987,Aggregation and Fractal Aggregates, World Scientific, Singapore.

    Google Scholar 

  78. Nigmatullin, R. R., L. A. Dissado, and N. N. Soutougin, 1992, A fractal pore model for Archie’s law in sedimentary rocks,J. Phys. D. Appl. Phys.25: 32–37.

    Article  Google Scholar 

  79. Hunt, A. G., 2007, Comments on “Fractal Fragmentation, Soil Porosity, and SoilWater Properties: I. Theory”, Soil Sci. Soc. Am. J. 71:1418–1419.

    Google Scholar 

  80. Narasimhan, T. N., 2007, Central ideas of Buckingham, 1906: a century later,Vadose Zone J. 6: 687–693

    Article  Google Scholar 

  81. Haines, W. B., 1930, Studies in the physical properties of soil: V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith.J. Agric. Sci.20: 97–116.

    Article  Google Scholar 

  82. Sears, F. W., and G. L. Salinger, 1975,Thermodynamics, Kinetic Theory, and Statistical Thermodynamics, 3rd edition, Addison-Wesley, Reading, MA.

    Google Scholar 

  83. Cole, K. S., 1941, Dispersion and absorption in dielectrics I. Alternating current characteristics,J. Chem. Phys. 9: 341.

    Article  Google Scholar 

  84. Havriliak, S., and S. Negami, 1966, Analysis of α-dispersion in some polymer systems by the complex variables method, J. Polymer Science (C) 14, 99–117.

    Google Scholar 

  85. Wilkinson, D., 1986, Percolation effects in immiscible displacement,Phys. Rev. A 34: 1380–1391.

    Article  Google Scholar 

  86. Blunt, M. J., and H. Scher, 1995, Pore-level model of wetting,Phys. Rev. E,52: 6387–403.

    Article  Google Scholar 

  87. Tokunaga, T., and J. Wan, 1997, Water film flow along fracture surfaces of porous rock,Water Resour. Res.33: 1287–1295.

    Article  Google Scholar 

  88. Topp, G. C., A. Klute, and D. B. Peters, 1967, Comparison of water content-pressure head data obtained by equilibrium, steady-state and unsteady state methods.Soil Sci. Soc. Am. Proc.31: 312–314.

    Article  Google Scholar 

  89. 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.

    Article  Google Scholar 

  90. Wildenschild, D., and J. W. Hopmans, 1999, Flow rate dependence of hydraulic properties of unsaturated porous media, in:Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media, ed. M. Th. van Genuchten, F. J. Leij, and L. Wu, U.S. Salinity Laboratory, Agricultural Research Service, U.S. Department of Agriculture, Riverside, CA, pp. 893–904.

    Google Scholar 

  91. Hansen, D., 2004, Discussion of ‘‘On the use of the Kozeny-Carman equation to predict the hydraulic conductivity of soils’’, NRC Research Press Web site athttp://cgj.nrc.ca (Appears inCan. Geotech. J. 40: 616–628).

  92. Marshall, T.J., 1958, A relation between permeability and size distribution of pores,J. Soil Sci.9: 1–8.

    Article  Google Scholar 

  93. Scheibe, T., and S. Yabusaki, 1998, Scaling of flow and transport behavior in heterogeneous groundwater systems,Adv. Water Resour.22: 223–238.

    Article  Google Scholar 

  94. Deutsch, C. V., 1989, Calculating effective absolute permeability in sandstone/shale sequences,SPE Form Eval,4(3): 343–348.

    Google Scholar 

  95. Desbarats, A., 1992, Spatial averaging of hydraulic conductivity in 3-dimensional heterogeneous porous-media.Math Geol.24(3): 249–267.

    Article  Google Scholar 

  96. Amyx, J. W., D. M. Bass, and R. L. Whiting, 1960,Petroleum Reservoir Engineering. Physical Properties, McGraw-Hill Book C., New York.

    Google Scholar 

  97. Sahimi, M., 1993, Fractal and superdiffusive transport and hydrodynamic dispersion in heterogeneous porous media,Transp. Porous Media 13: 3–40.

    Article  Google Scholar 

  98. 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.

    Article  Google Scholar 

  99. Hasimoto, H., 1959, On the periodic fundamental solutions of the Stokes equations and their applications to viscous flow past a cubic array of cylinders, J. Fluid Mech. 5(2): 317–328.

    Google Scholar 

  100. Sangani, A. S., and A. Acrivos, 1983, The effective conductivity of a periodic array of spheres, Proc. R. Lond. A 386: 263–275.

    Google Scholar 

  101. Zick, A. A. and G. M. Homsy, 1982, Stokes flow through periodic arrays of spheres, pp. 13–26.J. Fluid Mech.115: 13.

    Google Scholar 

  102. Larson, R. E., and J. J. L. Higdon, 1989, A periodic grain consolidation model of porous media, pp. 38–46. Phys. Fluids A 1: 38.

    Google Scholar 

  103. Childress, S., 1972, Viscous flow past a random array of spheres, pp. 2527–2539. J. Chem. Phys.,56: 2527.

    Google Scholar 

  104. Howells, I. D., 1974, Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects, pp. 449–476.J. Fluid Mech. 64: 449.

    Google Scholar 

  105. Hinch, E. J., 1977,An averaged-equation approach to particle interactions in a fluid suspension, Ref. 83(4): 695–720. J. Fluid Mech.,83: 695.

    Google Scholar 

  106. Kim, S., and W. B. Russell, 1985,1985, Modelling of porous media by renormalization of the Stokes equations, pp. 269–286. J. Fluid Mech.154: 269.

    Google Scholar 

  107. Prager, S., 1961, Viscous flow through porous media, pp. 1477–1482. Phys. Fluids 4: 1477.

    Google Scholar 

  108. Weissberg, H. L., and S. Prager, 1962, Viscous flow through porous media. II. Approximate three-point correlation function, pp. 1390–1392. Phys. Fluids,5: 1390.

    Google Scholar 

  109. Berryman, J. G., and G. W. Milton, 1985, Normalization constraint for variational bounds on fluid permeability, pp. 754–760. J. Chem. Phys.83: 745.

    Google Scholar 

  110. Katz, A. J., and A. H. Thompson, 1986, Quantitative prediction of permeability in porous rock,Phys. Rev. B 34: 8179–8181.

    Article  Google Scholar 

  111. Johnson, D. L., and L. M. Schwartz, 1989, Unified theory of geometric effects in transport properties of porous media. In Paper presented at SPWLA, 30th Annual Logging Symposium, Soc. of Prof. Well Log. Anal. Houston, TX.

    Google Scholar 

  112. Bernabe, Y., and A. Revil, 1995, Pore-scale heterogeneity, energy dissipation and the transport properties of rocks,Geophys. Res. Lett.22: 1529–1532.

    Article  Google Scholar 

  113. Bernabe, Y., and C. Bruderer, 1998, Effect of the variance of pore size distribution on the transport properties of heterogeneous networks,J. Geophys. Res.,103: 513.

    Article  Google Scholar 

  114. Torquato, S., and B. Lu, 1990, Rigorous bounds on the fluid permeability: effect of polydispersivity in grain size,Phys. Fluids A 2: 487–490.

    Article  Google Scholar 

  115. Hunt, A. G., and G. W. Gee, 2002, Application of critical path analysis to fractal porous media: comparison with examples from the Hanford site,Adv. Water Resour.,25: 129–146.

    Article  Google Scholar 

  116. Pollak, M., 1987, In.Non-Crystalline Semiconductors, CRC Press, Boca Raton, FL, Chapter 5ab.

    Google Scholar 

  117. Mallory, K., 1993, Active subclusters in percolative hopping transport,Phys. Rev. B 47: 7819–7826.

    Article  Google Scholar 

  118. Gingold, D. B., and C. J. Lobb, 1990, Percolative conduction in three dimensions.Phys. Rev. B 42(13): 8220–8224.

    Article  Google Scholar 

  119. Clerc, J. P., V. A. Podolskiy, and A. K. Sarychev, 2000, Precise determination of the conductivity exponent of 3D percolation using exact numerical renormalization.Eur. Phys. J. B 15: 507–516.

    Article  Google Scholar 

  120. Hunt, A. G., 2004, A note comparing van Genuchten and percolation theoretical formulations of the hydraulic properties of unsaturated media,Vadose Zone J. 3: 1483–1488.

    Article  Google Scholar 

  121. Khaleel, R., and J. F. Relyea, 2001. Variability of Gardner’s alpha for coarse-textured sediments.Water Resour. Res. 37: 1567–1575.

    Article  Google Scholar 

  122. Sahimi, M., and Y. C. Yortsos, 1990, Applications of fractal geometry to porous media: a review, Paper presented at the 1990 Annual Fall Meeting of the Society of Petroleum Engineers, New Orleans, LA.

    Google Scholar 

  123. Verboven, P., G. Kerkhofs, H. K. Mebatsion, Q. T. Ho, K. Temst, M. Wevers, P. Cloetens, and B. M. Nicolaï, 2008, Three-dimensional gas exchange pathways in pome fruit characterized by synchrotron X-ray computed tomography,Plant Physiol. 147: 518–527.

    Article  Google Scholar 

  124. Mendoza, F., P. Verboven, H. K. Mebatsion, G. Kerckhofs, M. Wevers, and B. Nicolaï, 2007, Three-dimensional pore space quantification of apple tissue using X-ray computed microtomography,Planta 226: 559–570.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Physics and Geology, Wright State University, Dayton, OH 45431, USA

    Allen Hunt

  2. Dept. Agronomy, Iowa State University, Ames, IA 50011-1011, USA

    Robert Ewing

Authors
  1. Allen Hunt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert Ewing
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Allen Hunt .

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hunt, A., Ewing, R. (2009). Porous Media Primer for Physicists. In: Percolation Theory for Flow in Porous Media. Lecture Notes in Physics, vol 771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89790-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89790-3_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89789-7

  • Online ISBN: 978-3-540-89790-3

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation