Effective transport dynamics in porous media with heterogeneous retardation properties

We study a transport model that is characterized by a spatially distributed retardation coefficient. The latter accounts for linear instantaneous mass transfer between a mobile and immobile phases as well as instantaneous equilibrium adsorption. Using a Lagrangian framework we upscale the local scale transport problem to an observation scale that is much larger than the variation scale of spatial heterogeneity. The derived effective Lagrangian transport equation describes the effective particle motion as a random walk in space-time, or in other words, a continuous time random walk, which is characterized by a joint transition length and time distribution. The transition time distribution is obtained by an exact map from the spatial distribution of retardation coefficients. The effective model compares well with numerical simulations of the small scale transport problem. For broad disorder distributions transport is highly non-Fickian and an (constant) effective retardation coefficient may not exist at practically relevant time and length scales. Copyright 2009 by the American Geophysical Union.