Effective Permeability of Heterogeneous Reservoir Regions

Most reservoir heterogeneities, such as detailed crossbedding, are on a scale that is too fine to be directly in cluded in reservoir simulation or reservoir engineering calculations. Therefore, ‘averaging’ procedures are required to scale up permeabilities from the fine scale, over which heterogeneities occur, to the coarser scales appropriate for reservoir engineering computation. The purpose of this paper is to describe the numerical implementation of such an averaging technique and to apply this technique to the scale up of a representative region of a crossbedded eolian depositional system. Toward this end, a triangle based nonconforming finite element approximation of the fine scale pressure equation, subject to appropriately formulated periodic boundary conditions, is salved to give the effective coarse scale permeability. It will be seen that the magnitudes of the cross terms of the effective permeability tensor are significant for the eolian system considered and that the accurate determination of these terms is essential for modeling flow through crossbedded systems.