Adaptive Homogenization for Upscaling Heterogeneous Porous Medium

Abstract

Abstract One of the major objectives in the development of upscaling approaches is to reduce the computational costs associated with solving fine scale flow and transport problems in heterogeneous porous media. This is due to the availability of reservoir rock property data at fine spatial scales, such as facies distributions, obtained from geological models and field data from well logs. The data sets from each of these sources are themselves at different spatial scales which further adds to the computational challenge. The upscaling approach must not only accommodate these disparate data sets but also capture the flow physics accurately while maintaining computational efficiency. We present a novel upscaling approach which draws upon previous developments of two-scale homogenization (Amaziane et al., 2006) to obtain coarse scale properties in addition to dynamic mesh refinement using an enhanced velocity mixed finite element method (EV MFEM) (Wheeler et al., 2002). A transient region is defined where changes in saturation/concentration are above a chosen threshold compared to a non-transient region where these are relatively small. Since most of the recovery technologies employed in oil and gas field operations involve flooding the subsurface porous medium; as in the case of water-flooding, chemical or gas enhanced oil recovery (EOR), these aforementioned transient regions are usually restricted to much smaller subdomains of the entire reservoir domain. The computational efficiency is achieved by using coarse scale parameters, from numerical homogenization, in the non-transient region. Furthermore, the solution accuracy is preserved by using fine scale information only in the transient region. The numerical results section shows that our adaptive homogenization approach closely captures fine scale flow and transport features while maintaining a computational speedup of approximately 4 times for a variety of permeability distributions extracted from the SPE 10 comparative upscaling project (Christie and Blunt, 2001).