Calculation of the effective permeabilities of field-scale porous media

Abstract

The problem of estimating the effective grid block permeabilities of a field-scale porous medium with long-range correlations is studied. Both isotropic and anisotropic porous media are considered. The grid blocks are represented by networks of bonds the permeabilities of which are distributed according to three different stochastic functions that generate long-range correlations, two of which are fractal distribution. A new perturbation expansion for estimating the effective permeabilities of the system is presented which, at the lowest order, yields an anisotropic effective-medium approximation (AEMA). The effective permeabilities are also estimated by a renormalization group (RG) method, as well as computer simulations. The RG method and AEMA both provide reasonable estimates of the effective permeabilities. However, if the porous medium contains zones of very low permeabilities, then the predictions of the two methods are not very accurate. Two methods are suggested to increase the accuracy of the predictions. We also show that as the volume fraction p of the low-permeability zones of the porous medium increases, the anisotropy of the medium decreases.