An Enriched Galerkin Discretization Scheme for Two Phase Flow on Non-Orthogonal Grids

Abstract

The representation of faults and fractures using cut-cell meshes often results in irregular non-orthogonal grids. Simple finite volume approaches fail to handle complex meshes because they are highly prone to grid orientation effects and only converges for K-orthogonal grids. Wide stencil approaches and higher order methods are computationally expensive and impractical to adopt in commercial reservoir simulators. In this work, we implement an Enriched Galerkin (EG) discretization for the flow and transport problems on non-orthogonal grids. The EG approximation space combines continuous and discontinuous Galerkin methods. The resulting solution lies in a richer space than the the two-point flux approximation (TPFA) method and allows a better flux approximation. It also resolves the inconsistencies that are usually associated with TPFA scheme. The method is tested for various non-orthogonal mesh configurations arising from different fault alignments. The performance of the scheme is also tested for reservoirs with strong anisotropy as well as reservoirs with heterogeneous material properties.