An adaptive multiscale approach for modeling two-phase flow in porous media including capillary pressure

Abstract

[2] Many important applications in porous media require the large-scale simulation of complex physical processes. Due to the limitations of computational resources, huge model domains often have to be simulated on relatively coarse grids. However, depending on the application, a high spatial resolution may be necessary to capture important effects, for example due to small-scale heterogeneities. One solution strategy is multiscale modeling. The idea is to decrease the number of global degrees of freedom while preserving important fine-scale features. In this work, we present a multiscale approach for modeling two-phase flow in porous media, which is applicable in a wide range of flow regimes, but especially if the influence of capillary pressure is significant. In this case, many existing upscaling or multiscale techniques, originally developed and successfully used for advection-dominated systems, fail or are not able to yield sufficiently accurate results. We combine an adaptive grid method based on multipoint flux approximation with various local upscaling techniques. In particular, the numerical method has to be able to treat complex effective parameters like anisotropic phase permeabilities. A crucial point is the development of suitable grid-adaptation strategies to account correctly for important effects. The method is tested and proven to work for various examples including varying heterogeneous parameter fields and different flow regimes.