Multi-scale modeling of two-phase--two-component processes in heterogeneous porous media

Flow and transport phenomena in porous media are the governing processes in many natural and industrial systems. Not only do these flow and transport phenomena occur on different space and time scales, but it is also the porous medium itself which is heterogeneous where the heterogeneities are present on all spatial scales. We consider a large domain with randomly distributed heterogeneities where complex two-phase--two-component processes are relevant only in a small (local) subdomain. This subdomain needs fine resolution as the complex processes are governed by small-scale effects. For a comprehensive fine-scale model taking into account two-phase--two-component processes as well as heterogeneities in the whole (global) model domain, data collection is expensive and computational time is high. Therefore, we developed a multi-scale concept where on the one hand, the global flow field influences the local two-phase--two-component processes on the fine-scale. On the other hand, a coarse-scale saturation equation is solved where the effects of the fine-scale two-phase--two-component processes in the subdomain are captured by source / sink terms and the effects of fine-scale heterogeneities by a macrodispersion term. The overall algorithm as well as results will be discussed for simplified applications.