A common challenge in reservoir modelling is to account for highly complex physical processes in critical subregions of a model domain with randomly distributed heterogeneities, whereas within the rest of the domain, the governing processes are physically simpler. Considering for example CO2 sequestration, where supercritical CO2 is injected in deep heterogeneous formations, complex two-phase - two-component processes occur around the injection. It was observed, that considerable mass transfer takes place between the gaseous phase containing CO2 and the surrounding water phase. However, the mass transfer is negligible in large parts of the model domain. One could try to collect all data necessary for a globally comprehensive two-phase - two-component model which could then account for the locally occurring complex processes in the whole domain. This,however, is needlessly challenging, expensive and time consuming. For such globally comprehensive models, the computational power sets drastic limits. Trying to capture the heterogeneous structure down to small scales would further increase the demand for excessive brute-force computer power.
To handle these problems, we need a multi-scale approach, meaning, that we model different processes on different scales. Due to their complexity, the two-phase - two-component processes are modelled on a fine scale, but only in the critical subregion of interest whereas a simpler twophase model can be applied on a coarse scale. The influence of the fine-scale heterogeneities can be transfered to the coarse scale with the help of an upscaling approach for the saturation equation.