Time-Domain Random-Walk Algorithms for Simulating Radionuclide Transport in Fractured Porous Rock

Mixing in Porous Media: Concepts and Approaches Across Scales

This review provides an overview of concepts and approaches for the quantification of passive, non-reactive solute mixing in steady uniform porous media flows across scales. Mixing in porous media is the result of the interaction of spatial velocity fluctuations and diffusion or local-scale dispersion, which may lead to the homogenization of an initially segregated system. Velocity fluctuations are induced by spatial medium heterogeneities at the pore, Darcy or regional scales. Thus, mixing in porous media is a multiscale process, which depends on the medium structure and flow conditions. In the first part of the review, we discuss the interrelated processes of stirring, dispersion and mixing, and review approaches to quantify them that apply across scales. This implies concepts of hydrodynamic dispersion, approaches to quantify mixing state and mixing dynamics in terms of concentration statistics, and approaches to quantify the mechanisms of mixing. We review the characterization of stirring in terms of fluid deformation and folding and its relation with hydrodynamic dispersion. The integration of these dynamics to quantify the mechanisms of mixing is discussed in terms of lamellar mixing models. In the second part of this review, we discuss these concepts and approaches for the characterization of mixing in Poiseuille flow, and in porous media flows at the pore, Darcy and regional scales. Due to the fundamental nature of the mechanisms and processes of mixing, the concepts and approaches discussed in this review underpin the quantitative analysis of mixing phenomena in porous media flow systems in general.

Impact of diffusive motion on anomalous dispersion in structured disordered media: From correlated Lévy flights to continuous time random walks

We elucidate the impact of diffusive motion on the nature of anomalous dispersion in layered and fibrous disordered media. We consider two types of disorder characterized by quenched random velocities and quenched random retardation properties. Purely advective particle motion is ballistic in both disorder models. This changes dramatically in the presence of transverse diffusion, which leads to dimension-dependent disorder sampling. For d≤3 dimensions, heavy-tailed velocity distributions render large-scale particle motion a correlated Lévy flight, while transport in the quenched random retardation model behaves as a biased continuous time random walk with correlated time increments.