Upscaling immiscible gas displacements: Quantitative use of fine grid flow data in grid coarsening schemes

Grid coarsening schemes based on the quantitative use of fine scale two-phase flow information are presented and assessed. 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. It is shown that coarse grid simulation error correlates closely with specific sub-grid quantities involving higher moments of fine grid variables, which can be computed from the fine scale simulations. By forming a coarse grid that minimises the appropriate sub-grid quantity, optimal coarse scale descriptions can be generated. The overall approach is shown to be applicable to coarse scale descriptions using either rock or pseudo relative permeability curves. The accuracy of the coarse grid calculations is, however, significantly better when pseudo functions 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.