Mixed-Hybrid and Vertex-Discontinuous-Galerkin Finite Element Modeling of Multiphase Compositional Flow on 3D Unstructured Grids

摘要

Problems of interest in hydrogeology and hydrocarbon resources involvecomplex heterogeneous geological formations. Such domains are most accuratelyrepresented in reservoir simulations by unstructured computational grids.Finite element methods accurately describe flow on unstructured meshes withcomplex geometries, and their flexible formulation allows implementation ondifferent grid types. In this work, we consider for the first time thechallenging problem of fully compositional three-phase flow in 3D unstructuredgrids, discretized by any combination of tetrahedra, prisms, and hexahedra. Weemploy a mass conserving mixed hybrid finite element (MHFE) method to solve forthe pressure and flux fields. The transport equations are approximated with ahigher-order vertex-based discontinuous Galerkin (DG) discretization. We showthat this approach outperforms a face-based implementation of the samepolynomial order. These methods are well suited for heterogeneous and fracturedreservoirs, because they provide globally continuous pressure and flux fields,while allowing for sharp discontinuities in compositions and saturations. Thehigher-order accuracy improves the modeling of strongly non-linear flow, suchas gravitational and viscous fingering. We review the literature onunstructured reservoir simulation models, and present many examples thatconsider gravity depletion, water flooding, and gas injection in oil saturatedreservoirs. We study convergence rates, mesh sensitivity, and demonstrate thewide applicability of our chosen finite element methods for challengingmultiphase flow problems in geometrically complex subsurface media.