Determination of the effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach: 1. Method

Abstract

A numerical spectral method is described for solving the equations governing the effective hydraulic conductivity of a stationary heterogeneous porous medium. The numerical method is efficient in the sense that the solution can be achieved in order Nt ln (Nt) operations and order Nt storage, where Nt is the total number of sampling points used in an n‐dimensional flow domain. The numerical method is extensively tested and shown to be quite robust. In the test cases, very accurate results are achieved even for an extremely heterogeneous porous medium. The developed numerical algorithm is quite general and can be used to compute effective conductivities for cases where analytic results are unavailable. In the companion paper (Dykaar and Kitanidis, this issue) the method is used to find the effective conductivity of (1) multidimensional isotropic, stationary, lognormally distributed conductivity and (2) core samples of a shale and sandstone formation.