Editorial to the Special Issue: Mixing in Porous Media

Abstract

Mixing in porous media is a key process for a wide range of natural and engineered systems in geological, biological and synthetic porous media. It is a multi-scale phenomenon with spatial scales ranging from micrometers (pores and capillaries) to kilometers (aquifers and reservoirs), and temporal scales that range from seconds to years. Mixing in porous media is an interdisciplinary subject with a diversity of scientific and engineering applications that include the understanding of karst formation, groundwater and soil remediation, underground hydrogen storage, geological radioactive waste storage, geothermal energy production, mining, oil and gas production, porous reactors and batteries, as well as drug delivery, and nutrient transport in biological tissue and capillaries.The quantitative understanding and prediction of mixing is complicated due to the presence of spatial heterogeneity inherent to natural and engineered porous media. Heterogeneity leads to transport, mixing and reaction behaviors that cannot be accounted for using the conventional upscaling paradigm based on constant hydrodynamic dispersion coefficients. In the past two decades, advances in the imaging of porous media structure and processes, and increased computational capabilities (Blunt et al. 2013) have facilitated new experimental, numerical and theoretical approaches (Rolle and Le Borgne 2019) to probe the mechanisms and controls of mixing, and cast them into predictive mathematical models. These developments were discussed at the Lorentz Center workshop on Mixing in Porous Media that was held in Leiden, The Netherlands, from 3 to 7 February 2020. There, the idea for this Special Issue originated with the aim to give an account of recent developments in the field of Mixing in Porous Media. This special issue consists of twenty-two contributions that cover different aspects of mixing in porous and fractured media at the pore and continuum scales, in single fractures and fracture networks.Two review papers report on concepts and approaches for mixing in porous media (Dentz et al. 2022) and the dynamical system approach to transport in porous media (Metcalfe et al. 2022). Nine articles focus on hydrodynamic flow, mixing and dispersion processes on the pore scale and their upscaling to the continuum scale. The papers by Sole-Mari et al. (2022) andOliveira et al. (2022) investigate mixing, reaction and dispersion in the pore space of highly resolved three-dimensional synthetic porous media. The direct numerical * Marco Dentz