A self‐consistent approach for calculating the effective hydraulic conductivity of a binary, heterogeneous medium

In this paper, we consider an approach for estimating the effective hydraulic conductivity of a 3D medium with a binary distribution of local hydraulic conductivities. The medium heterogeneity is represented by a combination of matrix medium conductivity with spatially distributed sets of inclusions. Estimation of effective conductivity is based on a self-consistent approach introduced by Shvidler (1985). The tensor of effective hydraulic conductivity is calculated numerically by using a simple system of equations for the main diagonal elements. Verification of the method is done by comparison with theoretical results for special cases and numerical results of Desbarats (1987) and our own numerical modeling. The method was applied to estimating the effective hydraulic conductivity of a 2D and 3D fractured porous medium. The medium heterogeneity is represented by a combination of matrix conductivity and a spatially distributed set of highly conductive fractures. The tensor of effective hydraulic conductivity is calculated for parallel- and random-oriented sets of fractures. The obtained effective conductivity values coincide with Romm's (1966) and Snow's (1969) theories for infinite fracture length. These values are also physically acceptable for the sparsely-fractured-medium case with low fracture spatial density and finite fracture length. Verification of the effective hydraulic conductivity obtained for a fractured porous medium is done by comparison with our own numerical modeling for a 3D case and with Malkovsky and Pek's (1995) results for a 2D case.

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