Transport properties: part 1 – permeability

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The permeability, noted by κ, is one of the most important properties of porous materials. It relates the vector of flux of fluid's flow q through the pore network of a porous medium and the fluid pressure gradient ∇p such as: q = -(κ/μ) ∇p where μ is the fluid's viscosity. This tool provides some basic calculations of the permeability of porous media including the famous Kozeny-Carman's theory and its deviations (Kozeny, 1927; Carman, 1937; Mavko and Nur, 1997; Carrier, 2003; Costa, 2006; Xu and Yu, 2008; Bear, 2013). These semi-empirical models relate the permeability to the porosity (effective porosity or connected porosity that excludes the closed pores) of the medium. They could be employed to extrapolate, for each type of material, data measured on several samples to a large porosity range.


References
Kozeny, J. (1927). Uber kapillare leitung der wasser in boden. Royal Academy of Science, Vienna, Proc. Class I, 136, 271-306.
Carman, P. C. (1937). Fluid flow through granular beds. Transactions-Institution of Chemical Engineeres, 15, 150-166.
Mavko, G., & Nur, A. (1997). The effect of a percolation threshold in the Kozeny-Carman relation. Geophysics, 62(5), 1480-1482.
Xu, P., & Yu, B. (2008). Developing a new form of permeability and Kozeny–Carman constant for homogeneous porous media by means of fractal geometry. Advances in water resources, 31(1), 74-81.
Costa, A. (2006). Permeability‐porosity relationship: A reexamination of the Kozeny‐Carman equation based on a fractal pore‐space geometry assumption. Geophysical research letters, 33(2).
Carrier III, W. D. (2003). Goodbye, hazen; hello, kozeny-carman. Journal of geotechnical and geoenvironmental engineering, 129(11), 1054-1056.
Bear, J. (2013). Dynamics of fluids in porous media. Courier Corporation.
Coussy, O. (1987). Acoustics of porous media. Editions Technip.
Bourbie, T., Coussy, O., & Zinszner, B. (1987). Acoustics of porous media. Institut francais du petrole publications.
Connolly, J. A. D., & Podladchikov, Y. Y. (2000). Temperature-dependent viscoelastic compaction and compartmentalization in sedimentary basins. Tectonophysics, 324(3), 137-168.

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