A lattice percolation model of an inhomogeneous medium  introducing f(r), the probability density function of the microcapillaries with respect to their radius r, is employed. The calculation scheme described makes it possible to determine the dependence of the permeability K on the pressure gradient G for media with arbitrary f(r). It is shown that for inhomogeneous media the behavior of K(G) is mainly determined by the form of f(r). The question of the effect of the state of stress on the permeability of the medium is considered.
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 84–94, March–April, 1989.
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Rostovskii, N.S., Selyakov, V.I. Effect of the microinhomogeneity of the medium on the flow law in porous media. Fluid Dyn 24, 232–242 (1989). https://doi.org/10.1007/BF01075153
- Porous Medium
- Density Function
- Probability Density
- Pressure Gradient