Effective permeabilities for model heterogeneous porous media

This paper presents a rigorous technique to evaluate effective absolute permeabilities for heterogeneous porous media. The technique is based on a perturbation analysis of the equations of motion of a slightly compressible fluid in a homogeneous porous medium at low Reynolds numbers. The effective permeabilities can be calculated once the local geometry of the heterogeneous medium is specified. The technique is used to evaluate two- and three-dimensional effective vertical permeabilities in porous media with shale intercalations. including the case in which the porous matrix is anisotropic. The results indicate that the use of two-dimensional models is not adequate when describing such systems, since three-dimensional calculations differ substantially from two-dimensional ones Effective permeabilities are also reported for the standard 'sugar cubes' model for fractured porous media. In this case, the differences between two- and three-dimensional models are quantitatively insignificant.