A Multiscale Method for Modeling Transport in Porous Media on Unstructured Corner-Point Grids

Abstract

Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine-scale permeability variations through the calculation of specialized coarse-scale basis functions. Most of the multiscale techniques presented to date address subgrid capturing in pressure solution (elliptic/parabolic equations). In this paper we propose a multiscale method for solving transport equations on a coarse grid. In this method the global flow is computed on a coarse grid scale, but information from a fine scale velocity field is used to improve accuracy. The method is applied to incompressible and immiscible two-phase flow on a synthetic geological model with corner-point grid geometry. Although corner-point grids are given on a logically Cartesian format, the resulting grids are unstructured in physical space. The numerical results demonstrate that the multiscale method gives nearly the same flow characteristics as simulations where the transport equation is solved on the scale of an underlying fine grid.