The Description and Quantification of the Truncation Errors Produced by Local-Grid Refinement in Reservoir Simulation

Abstract

Summary Geologically realistic 3D models yield nonorthogonal simulation grids as a result of grid distortion at faults, steeply dipping horizons, and zonal truncations. Finite-difference (FD) simulators applying discretization principles and volumetric flux calculation use two-point flux approximation (TPFA). On nonorthogonal grids, the TPFA causes numerical errors in the solution of pressure and saturation such that simulation results become inaccurate. These inaccuracies are known as grid-orientation effects. This paper will demonstrate that TPFA applied to grids containing local-grid refinement (LGR) causes identical numerical errors. In the case of a vertically partial LGR, the numerical errors become so severe that they invalidate the simulation results. These results include unphysical oscillations in the fluxes within the LGR and unphysical baffles to flow at the interface between the coarse grid and the LGR. The invalidation of simulation results is demonstrated by two case studies involving the history matching of well tests. To avoid invalid simulation results, any LGR applied in a grid must be extended over the entire vertical extent of the grid such that there exists no TPFA between the coarse- and the refined-grid cells in the vertical direction.