Calculation of the effective permeabilities of held-scale porous media

The problem of estimating the effective grid block permeabilities of a fiel d-scale porous medium with long-range correlations is studied. Both isotrop ic and anisotropic porous media are considered. The grid blocks are represe nted by networks of bonds the permeabilities of which are distributed accor ding to three different stochastic functions that generate long-range corre lations, two of which are fractal distribution. A new perturbation expansio n for estimating the effective permeabilities of the system is presented wh ich, at the lowest order, yields an anisotropic effective-medium approximat ion (AEMA). The effective permeabilities are also estimated by a renormaliz ation group (RG) method, as well as computer simulations. The RG method and AEMA both provide reasonable estimates of the effective permeabilities. Ho wever, 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 i ncreases, the anisotropy of the medium decreases. (C) 2000 Published by Els evier Science Ltd. All rights reserved.