Upscaling Immiscible Gas Displacements: Quantitative Use of Fine-Grid Flow Data in Grid-Coarsening Schemes

Abstract

Summary This paper presents and assesses grid-coarsening schemes based on the quantitative use of fine-scale two-phase-flow information. The basic approach is motivated from a volume-average analysis of the fine-scale saturation equation including gravitational effects. Extensive results for layered systems are presented. We show that coarse-grid simulation error correlates closely with specific subgrid quantities involving higher moments of fine-grid variables, which can be computed from the fine-scale simulations. With formation of a coarse grid that minimizes the appropriate subgrid property, optimal coarse-scale descriptions can be generated. The overall approach is shown to be applicable to coarse-scale descriptions with either rock or pseudorelative permeability curves. The accuracy of the coarse-grid calculations is, 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 not always improve as the number of coarse layers is increased.