A Finite Element Method for Calculating Transmissibilities in N-point Difference Equations using a Non-Diagonal Permeability Tensor

Abstract

Petroleum reservoir are always heterogeneous. Averaging techniques consist mostly in defining an equivalent homogeneous permeability tensor for a given heterogeneous porous medium whose absolute permeability is a space dependent function. The equivalent permeability tensor is generally symmetric but non-diagonal: three unusual off-diagonal terms Kxy, Kxz and Kyz are to be considered in addition to the standard diagonal permeability terms in x, y and z direction. Non-diagonal tensors arise also in a mesh whose axes are not the principal directions of the permeability tensor: an application for horizontal well simulation is briefly presented.