Effective Absolute Permeability in the Presence of Sub-Grid Heterogeneities: An Analytical Approach

An effective permeability tensor is derived, which can be assigned to a grid block under the assumption that the sub-grid permeability is a scalar, bounded random function in the spatial coordinates with given covariance function. The effective permeability tensor depends on both the nature of the spatial heterogeneities and the considered flow system operating within the grid-block flow domain. Examples are given substantiating the theoretical results. Attention is restricted to single-phase flow.