Fault Modelling Aspects Using Unstructured Grid with a Vertex Centered Method

Corner point grids and pillar based unstructured grids do not provide an effective workflow for translating earth models into simulation models. It requires a 3D unstructured grid approach that allow an accurate representation of the near well flow and preserving geological accuracy and offering flexible resolution control. Significant work has been done for generating unstructured grids. Coupled geomechanics simulation and hydraulic fracture flow for gas shale simulation have given a new impulse. The Control Volume Finite Element Method was proposed in the 1990ies (Lemmonier 1979,Fung 1992)as an alternative to the Galerkin Finite Element Method. The hybrid Finite Element-Finite Volume Method (Matthai et al 2004,2011) has been applied successfully to the simulation of fracture réservoirs. Unstructured grids are composed of various types of elements such as tetrahedrons, hexahedrons or any type of volume element with arbitrary number of nodes. Numerical schemes are needed to express the fluxes (phase rates) in terms of primary unknowns. Several schemes have been proposed such as Two Point Flux Approximation (TPFA Heinemann 1988), Multi Point Flux Approximation (MPFA Aavatsmark 2002). Our main focus is the investigation of a recent method, the Vertex Approximate Gradient (Eymard 2012). The novelty of the VAG method is the introduction of cell center unknowns in addition to the vertex unknowns. The method can be written on finite volume form, with explicit cell-vertex fluxes connecting each cell to its vertices which can be used to discretize multiphase Darcy flows. A previous paper SPE 173309 has presented the implementation of VAG and MPFA schemes inside a next generation reservoir simulator starting from a source code calculating multi-point flux non neighbour connections for any polyhedral shaped control volume. The unstructured scheme approach has been developed as an in-house extension to a next generation multi-company collaborative reservoir simulator (designed for handling unstructured grids). This paper presents the application of three multi-point stencil methods (namely VAG, MPFA-O, MPFA-L) on a faulted full field model. Main issues addressed are the fault discretization using unstructured grid and the benefits compared to the usual structured grid and fault multiplier approach. Results, accuracy and performance of multipoint scheme methods on unstructured grids are compared with TPFA methods on structured CPG grids and PEBI method on unstructured Voronoi grids. Two simulation examples are presented and the results are compared in terms of accuracy and performance. The first test case is a Y fault model and the second one is a full field faulted model.