A Comparison of Mixed Multiscale Finite Element Methods for Multiphase Transport in Highly Heterogeneous Media

Abstract

Many practical applications such as nuclear waste storage and reservoir simulations require multiphase transport simulations in porous media. Detailed reservoir models with a wide range of scales are available for more accurate simulations. In this study, we consider a two-phase flow model, in which a pressure equation is coupled with a specific transport equation. As a main component of the model, we consider the permeability that exhibits high heterogeneities with large contrast, which creates a significant difficulty to resolve by traditional approaches. In particular, due to the multiscale nature of the problem, solving on finescale grid that is sufficient to capture the heterogeneity results considerable computation, which motivates upscaled or multiscale methods and some other model reduction methods. The idea in upscaled method involves using one effective media parameter in each coarse block so that the concerned equation can be solved in a reduced model (

A conservative multiscale method for stochastic highly heterogeneous flow

“…In MMsFEM, one velocity multiscale basis is constructed via solving a locally defined flow problem while piecewise constant functions defined in each coarse-element are utilized for the pressure. Although the MMsFEM succeeds in many scenarios, it fails to deal with very complicated porous media, and this motivates the development of the mixed generalized multiscale finite element method (MGMsFEM) [20,41]. In MGMsFEM, multiple multiscale basis functions for velocity are constructed and thus can capture more complicated media information.…”