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

Flow and transport processes in porous media occur on different spatial and temporal scales and may also be locally different. Additionally, the structure of the porous medium itself generally shows a high dependence on the spatial scale. As an example, the contamination of the unsaturated zone with a light non-aqueous phase liquid is studied, corresponding to a domain with randomly distributed heterogeneities where complex three-phase–three-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 three-phase–three-component processes as well as heterogeneities in the whole (global) model domain, data collection is expensive and computational time is long. Therefore, we developed a general multi-scale concept where on the one hand, the global flow field influences the local three-phase–three-component processes on the fine-scale. On the other hand, a coarse-scale saturation equation is solved where the effects of the fine-scale multi-phase–multi-component processes in the subdomain are captured by source/sink terms and the effects of fine-scale heterogeneities by a macrodispersion term. It turned out that the new multi-scale algorithm represents a flexible and extendable tool for incorporating processes of different complexity occurring at different locations in one model domain, while reducing the amount of required data. Using a simplified numerical example, it could be shown that the multi-scale algorithm functions very well. However, more research has to be done in order to further improve its computational efficiency.