Coupled Continuous Time Random Walks for Anomalous Transport in Media Characterized by Heterogeneous Mass Transfer Properties

Abstract:

Solute transport in geological media is in general non-Fickian as it cannot be explained in terms of equivalent homogeneous media. This anomalous character can be traced back to the existence of multiscale heterogeneity and strong correlations within the medium. Here we investigate the impact of fast heterogeneous mass transfer properties as represented by a spatially varying retardation coefficient (mass exchange between mobile and immobile regions, linear sorption-desorption reactions, variable porosity). In order to estimate the effects of spatial correlation, and disorder distribution on the average transport, we consider 2D media characterized by complex multiscale geometries and point distributions of retardation of increasing heterogeneity. Within a Lagrangian framework, we coarse-grain the Langevin equation for the transport of solute particles due to advection and diffusion in the heterogeneous medium. The large-scale transport properties are derived within a stochastic modeling approach by ensemble averaging of the coarse-grained Langevin equation . This approach shows that the effective particle motion can be described by a coupled CTRW that is fully parametrized by the distribution of the retardation coefficient and the spatial medium organization. This allows for the explicit relation of the heterogeneous medium properties to observed anomalous transport in terms of solute dispersion, breakthrough curves and spatial concentration profiles.