2006b, ‘Multiscale mixed methods on corner-point grids: mimetic versus mixed subgrid solvers

Abstract. Multiscale simulation is a promising approach to facilitate direct simulation of large and complex grid-models for highly heterogeneous petroleum reservoirs. Unlike traditional sim-ulation approaches based on upscaling/downscaling, multiscale methods seek to solve the full flow problem by incorporating sub-scale heterogeneities into local discrete approximation spaces. We consider a multiscale formulation based on a hierarchical grid approach, where basis func-tions with subgrid resolution are computed numerically to correctly and accurately account for subscale variations from an underlying (fine-scale) geomodel when solving the global flow equa-tions on a coarse grid. By using multiscale basis functions to discretise the global flow equations on a (moderately-sized) coarse grid, one can retain the efficiency of an upscaling method, while at the same time produce detailed and conservative velocity fields on the underlying fine grid. For pressure equations, the multiscale mixed finite-element method (MsMFEM) has shown to be a particularly versatile approach. In this paper we extend the method to corner-point grids, which is the industry standard for modelling complex reservoir geology. To implement MsMFEM, one needs a discretisation method for solving local flow problems on the underlying fine grids. To this end, we propose two different subsolvers that both are designed to giv