Accurate subgrid models for two-phase flow in heterogeneous reservoirs

Subgrid effects can have a strong influence on flow and transport in oil reservoirs. In this work, a new model for the representation of subgrid terms is introduced and applied to two-phase reservoir flows. The model entails a generalized convection-diffusion treatment of the saturation equation as well as an extended representation for total mobility in the pressure equation. Motivation for the form of the model is provided through a consideration of volume averaging and homogenization results. The numerical computation of the subgrid terms and the implementation of the overall method are described. The accuracy of the new subgrid representation is compared to that of coarse-scale models with no subgrid treatment and to coarse models based on pseudorelative permeabilities. The new model consistently provides more accurate overall coarsescale predictions, relative to reference fine-scale results, than the other coarse-scale models, particularly in cases when the global boundary conditions vary in time.