A Modified Nested-Gridding for Upscaling–Downscaling in Reservoir Simulation

Abstract

The upscaled models of reservoirs result in coarse representation of flow for simulation gridblocks. This representation discards subgrid heterogeneities and flow complexities which can lead to an inaccurate performance prediction for reservoir processes. To tackle the problem, reconstruction techniques such as multiscale or upscaling–downscaling methods have been developed to recapture the subgrid flow details which have been approximated at the upscaling stage. In this study, we propose a modified downscaling procedure applied on local–global upscaling method. The modification accounts for using approximate fine-scale velocities obtained from the upscaling stage to partition the coarse-scale fluxes to local boundary conditions in the reconstruction of fine-scale solutions. This modification enhances quality of saturation profiles obtained by resultant reconstructed velocities. In this stage, we also investigate the application of basis functions for velocity reconstruction. These functions are computed numerically by solving at initial time a set of decomposed Neumann boundary condition problems for each coarse block. The values of boundary fine fluxes are derived from apportioning a unit-value coarse flux over that boundary. These functions are stored and reused for the rest of the simulation. This leads to computational gain compared to conventional downscaling where velocity is refined at any time and any where. We simulate incompressible tracer and multiphase flow in two and three dimensions on a range of test cases by fine-scale reference model and upscaling–downscaling model. For comparison purposes a pressure solver upscaling is used as a base method. The results show a better reconstruction quality for saturation profiles obtained by modified scheme and the practicality of application of basis functions with minimal deterioration of results.