Mixing in Porous Media

Mixing in porous and fractured media is a key process in a diversity of systems including biological, engineered and geological porous media. These processes span spatial scales from nanometers to kilometers and temporal scales from seconds to geological time scales and include applications in hydrology, geological storage, geothermal energy production, subsurface mining and petroleum engineering, chemical engineering, biology and medicine. Thus the qualitative and quantitative understanding of the mechanisms of mixing in porous media – including flow, transport, chemical reactions and biological activity – across a diversity of spatial and temporal scales is essential for myriad applications with high scientific, technological and societal relevance.

This understanding is complicated by the inherently heterogeneous nature of porous media, which leads to flow, mixing, transport and reaction beyond conventional Fickian modelling approaches. Novel theoretical, modelling and experimental approaches have emerged that facilitate much deeper understanding of these processes and a greater ability to predict and control them. This includes stochastic transport models for heterogeneous media, Lagrangian methods for transport analyses and advanced volume-averaging modelling approaches as well as state-of-the-art experimental techniques and dedicated computational methods for detailed characterization of key processes in porous media at both the pore and Darcy scale in laboratory and field set-ups. These advances enable new insights, avenues of research and developments toward a thorough understanding of mixing processes in porous media. This, in turn, may motivate further development of experimental and numerical approaches and data-analysis methods.

Key challenges to advance this field are: (i) development of a thorough understanding of flow, mixing, reaction and transport processes in realistic porous media; (ii) cross-disciplinary development of new theoretical, numerical and experimental approaches; (iii) their translation and integration into analysis, modeling and design strategies. The workshop aims to address these challenges by bringing together physicists, mathematicians, engineers, and hydrogeologists with expertise in theoretical, experimental and numerical research in order to exchange ideas, approaches, methods and views on all relevant aspects of mixing in porous media. This concentrates on two urgent questions:

1. New developments in experimental techniques provide unprecedented capabilities for a deeper understanding of mixing, transport and reactions in porous media beyond the classical Fickian paradigm. What experimental protocols, observables and data-analysis methods are needed to identify and quantify relevant microscale, and heterogeneity-induced macroscale behaviors?

2. Upscaling of mixing, anomalous transport and reaction is being studied with approaches ranging from volume averaging and homogenization theory via stochastic descriptions to models based on laminar mixing or non-equilibrium transport models. How can these approaches be united to obtain a new physics-based understanding of mixing in porous media?