Continuous Time Random Walks and the Causes of Non-Fickian Transport in Heterogeneous Media

Abstract:

Solute transport in heterogeneous porous media is in general
non-Fickian, this means it shows behaviors that do not conform to
advection-dispersion models characterized by constant equivalent transport
parameters. The causes for such behaviors are manifold, while their quantitative
relation to large scale non-Fickian transport is often not known. We address the
questions of (i) how different heterogeneity and microscale transport mechanisms
manifest in large scale transport behavior, (ii) which are their impacts on anomalous
solute dispersion, and (iii) how they can be quantified in terms of large scale dynamics. 
We focus here on the roles of medium and flow heterogeneity, mass transfer between mobile
and immobile zones, as well as spatially variable retardation properties
on large scale anomalous transport. Starting from the different microscale heterogeneity and
transport dynamics, we use a stochastic modeling approach to coarse grain and
average particle transport in a Lagrangian modeling framework, and quantify
the large scale particle dynamics in terms of continuous time random walks (CTRW).
The large scale particle movements are characterized in terms of
a random space increment, which can be related to the heterogeneity structure and
geometry, and a random time increment, which is quantified in terms of the
heterogeneity distribution. We present the CTRW models resulting from the different
heterogeneity scenarios and analyze their transport signatures in terms of solute
dispersion and breakthrough curves.