| A new method for scaling up subgrid scale reservoir heterogeneity to coarser finite difference simulation cells has been developed. It uses a fine-grid full-field Laplace solution and the one dimensional Buckley-Leverett profile as input. The requirement of positive dissipation for intercell fluxes produces a reshaped coarse grid system with strictly non-negative transmissibilities. Effective two phase relative permeability is derived for each reshaped coarse grid interface using streamtube information from the fine-grid results. The method is compared with existing upscaling techniques for cross-sectional horizontal well problems. The reservoir model is a computer-generated extremely heterogeneous sand shale sequence with a permeability contrast of 1,000. Although existing methods fail, coarse grid simulations using the new system successfully reproduce fine-grid pressure distributions for single-phase problems and approximate fine-grid pressure and saturation distributions for two phase problems within a range of mobility ratios. Total computation time that includes solving the Laplace equation, calculating transmissibilities, and deriving relative permeabilities, as well as coarse grid simulation is on order of 1/1,000 of a fine grid simulation. Accuracy in well performance is related to mobility ratio at the displacement front. Although being based on fixed streamtube geometries, this method is shown to be applicable to transient pressure problems where rock and fluid compressibilities are important, and infill well problems where initial water saturation is nonuniform. These are advantages over streamtube mapping methods in addition to the fact that the method can make use of existing facilities in commercial finite difference simulators. |
