Abstract

Fluid flow in realistic porous media involves global uncertainty in sub-surface properties such as permeability, where the properties are heterogeneous, but only statistical averages of the spatial variation are known. These difficulties make direct simulation methods such as Monte Carlo, expensive to implement in optimisation applications. An attractive alternative solution is to use a fully stochastic model in which uncertainty is embedded from the outset. In this paper an approximation method is developed to solve problems of two-phase flow in a porous medium under global uncertainty. In parallel a Monte Carlo simulation software, which involves building an interface between GSLIB and a commercial flow simulator (FASTFLO 3.0), is constructed. We examine in detail the 2D horizontal producer problem where oil is swept upwards by water from a horizontal injector. The reservoir block is subject to global uncertainty in permeability; The results of applying our approximation to this problem are compared with those obtained from the Monte Carlo simulations, typically over 100 realisations of the random permeability field. Encouraging results are obtained when comparing the predictions of both methods. © 2007 Elsevier B.V. All rights reserved.