Flow and transport phenomena in porous media are the governing processes in many technical and environmental systems. These processes occur on different spatial and temporal scales, and may also differ locally: in most cases, complex flow regimes occur in only small regions within the domain of interest. Inside these regions, a detailed description of the physics involved is essential, while a simpler model abstraction is sufficient where simpler physical processes prevail. There is also a high variability of scales, with regard to both the temporal and the spatial scale: the porous medium is a very heterogeneous material. These heterogeneities give rise to complex flow regimes, with channelling flowpaths or blocking enclosures.
If we want to understand and describe the flow processes in porous media, we need to identify the dominating physical processes on the one hand and the dominant temporal and spatial scales on the other. A multi-physics framework has been developed which combines individual models of varying numerical complexity and attempts to use the best available model abstraction locally. Multi-scale methods allow for the reduction of the global degrees of freedom while maintaining the highly resolved properties of the heterogeneous porous medium. While the multi-physics concept faces the challenge of modelling thermodynamically and thus numerically complex systems and coupling different types of model, the multi-scale methods have to maintain small-scale features while remaining globally efficient.
Our vision is a consistent framework that combines both methods,resulting in a multi-scale-multi-physics model. Complex flow and transport phenomena can then be efficiently modelled with a high accuracy.