The impact of microscale physics in continuous time random walks for hydrodynamic dispersion in disordered media

Abstract

The continuous time random walk (CTRW) approach has been widely applied to model large-scale non-Fickian transport in the flow through disordered media. Often, the underlying microscopic transport mechanisms and disorder characteristics are not known, and their effect on large-scale solute dispersion is encoded by a heavy-tailed transition time distribution. Here we study how the microscale physics manifests in the CTRW framework, and how it affects solute dispersion. To this end, we consider transport in disordered media with random sorption and random flow properties. Both disorder mechanisms can give rise to anomalous particle transport. We present the CTRW models corresponding to each of these physical scenarios to discuss the different manifestations of microscale heterogeneity on large-scale dispersion depending on the particle injection modes. The combined impact of random sorption and advection is studied with a novel CTRW model that explicitly represents both microscale disorder mechanisms. While random advection and sorption may show similar large-scale transport behaviors, they can be clearly distinguished in their response to uniform injection conditions, and, in general, to initial particle distributions that are not flux-weighted. These findings highlight the importance of the microscale physics for the interpretation and prediction of anomalous dispersion phenomena in disordered media.