Percolation Approach to the Anisotropy Factor in an Unsaturated Porous Medium |
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Authors: | Igor Grebnev Asya S. Skal |
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Affiliation: | (1) Microsoft Inc., Building, 50/2409 One Microsoft Way, Redmond, WA, 98052, U.S.A.;(2) The Research Institute, The College of Judea and Samaria, Ariel, 44837, Israel |
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Abstract: | The anisotropy factor is defined as the ratio of the effective (macroscopic) conductivities parallel to the bedding plane and perpendicular to it. The anisotropy factor A(p,a) is a function of both the saturation degree, p, in the void space of the disordered medium and the anisotropy parameter, a, that characterizes the ratio of the local conductivities parallel and normal to the bedding plane. There are two opposite behaviors of the anisotropy factor as a function of the saturation degree described in literature. One presents the anisotropy factor as a curve with a maximum and the other as a curve with a minimum. The main result of calculating the conductivities of a uniaxial percolation anisotropic model is that at the saturation threshold value, pc, A(pc, a) = 1, wherefrom it increases at a >1 (or decreases at a < 1) with saturation. An extension of the computed results below the threshold is also proposed. |
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Keywords: | percolation threshold bond percolation model network of capillary tubes anisotropy parameter anisotropy factor |
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