A fast algorithm for the estimation of the equivalent hydraulic conductivity of heterogeneous media

Abstract

Fast upscaling of hydraulic conductivity is a recurrent problem in modeling flow through heterogeneous porous media. We propose a new renormalization technique. It is based on the iterative application of the Cardwell and Parsons [1945] bounds on elementary groups of cells. The combination of the bounds with a heuristic formula allows anisotropy to be taken into account. The new technique is tested and compared with other fast techniques. Among the tested techniques the two most reliable ones are the tensorial renormalization and the new simplified renormalization. The numerical efficiency of the simplified renormalization leads us to recommend it when a diagonal tensor of equivalent conductivity is sufficient.