Effective permeability of sandstone-shale reservoirs by a random walk method

A random walk algorithm for calculating the effective permeability of random mixtures of two finite permeability components (e.g. sandstone and shale) is introduced. It is an extension of the 'ant in a labyrinth' algorithm, which only applies when one of the components has zero permeability. Numerical results obtained from the proposed random walk algorithm are shown to be in close agreement with those obtained from the conventional finite difference method on three-dimensional cubic lattices. In contrast, it is shown that the hybrid random walk algorithms which have been used in the past to study the critical behaviour of two-component random conductor mixtures are inadequate for the problem under consideration. The proposed random walk algorithm provides a computationally efficient method for calculating the effective permeability and does not require the explicit solution of the fluid flow through the random mixture.