Implementation of a Vertex-Centered Method Inside an Industrial Reservoir Simulator: Practical Issues and Comprehensive Comparison With Corner-Point Grids and Perpendicular-Bisector-Grid Models on a Field Case

Abstract

Summary Corner-point grids (CPGs) and pillar-based unstructured grids do not provide an effective work flow for translating Earth models into simulation models. Such a work flow requires grids that allow an accurate representation of the near-well flow, preserve geological accuracy, and offer flexible resolution control. Hence, a 3D unstructured approach is required. Significant work has been performed for generating unstructured grids, and modeling hydraulic-fracture flow for gas-shale simulation has given a new impulse for unstructured gridding. Recent methods such as vertex-approximate gradient (VAG) or more-mature ones such as multipoint flux approximation (MPFA) provide a numerical scheme dependent on multipoint stencil more physical than two-point flux-approximation (TPFA) methods. This paper presents the implementation of VAG and MPFA schemes inside a next-generation reservoir simulator starting from a source code calculating multipoint flux nonneighbor connections (NNCs) for any polygonal-shaped control volume. The unstructured-scheme approach has been developed as an in-house extension to a next-generation multicompany collaborative reservoir simulator that is designed for handling unstructured grids. The main issues addressed are the introduction of vertices unknowns among the usual cell-center variables, the assignment of vertices properties in the reservoir-simulator model, and the link with the well model. Incidentally, the definition of an exchange format to describe the unstructured geometry (vertices, edges, faces, control volumes) on a large reservoir-simulation model is proposed. Three simulation examples are presented, and we compare results, accuracy, and performance of multipoint-scheme methods such as VAG and MPFA on unstructured grids. Results are compared with TPFA methods on refined structured CPGs and TPFA methods on unstructured Voronoi grids. The two first test cases are academic models, and the third one is a field model.