Upscaling immiscible gas displacements: Quantitative use of fine-grid flowdata in grid-coarsening schemes

This paper presents and assesses grid-coarsening schemes based on the quant itative use of fine-scale two-phase-flow information. The basic approach is motivated from a volume-average analysis of the fine-scale saturation equa tion including gravitational effects. Extensive results for layered systems are presented. We show that coarse-grid simulation error correlates closel y with specific subgrid quantities involving higher moments of fine-grid va riables, which can be computed from the fine-scale simulations. With format ion of a coarse grid that minimizes the appropriate subgrid property, optim al coarse-scale descriptions can be generated. The overall approach is show n to be applicable to coarse-scale descriptions with either rock or pseudor elative permeability curves. The accuracy of the coarse-grid calculations i s, however, significantly better when pseudofunctions are used. The method is applied to determine the optimal number and configuration of coarse-grid layers in more general cases and it is shown that coarse-grid results do n ot always improve as the number of coarse layers is increased.