Efficient Incorporation of Global Effects in Upscaled Models of Two-Phase Flow and Transport in Heterogeneous Formations

Abstract

Geological variability occurring over multiple length scales can significantly affect fluid flow in subsurface formations. In this paper we explore the impact of large scale (global) information on the accuracy of coarse scale models for two-phase flow and transport. Based on these findings, a new methodology for generating coarse models is introduced. This approach, which avoids any global fine scale calculations, entails adaptive local-global single-phase parameter upscaling coupled with subgrid models for two-phase parameters. Two related subgrid treatments for two-phase flow effects---a pseudorelative permeability model and a generalized convection-diffusion model---are investigated and applied. The upscaled single-phase parameters (transmissibilities), computed using the adaptive local-global procedure, account explicitly for global boundary conditions as they are adapted for a specific flow scenario. The two-phase coarse scale functions are computed from local simulations using effective flux boundary conditions (EFBCs), which account approximately for global effects in the local computations. The advantages of the adaptive local-global upscaled single-phase parameters, as well as the superior accuracy of EFBCs relative to standard treatments for two-phase parameters, are demonstrated for several challenging two-dimensional example cases. The overall method is also applied to highly heterogeneous systems with global boundary conditions that vary in time. Using standard upscaling methods, errors for some of these cases are very large, though the new methodology is shown to consistently provide reasonably accurate coarse models.