Disorder Versus Correlation Control: Non-Fickian Transport in Heterogeneous Porous Media and Correlated Continuous Time Random Walks

Abstract:

Medium and flow heterogeneities lead to global transport patterns
that cannot be captured by large scale transport models that are
based on Fickian transport mechanisms. Early and late solute and particle arrivals, and non-linear evolution of dispersion are
non-Fickian manifestations of spatial heterogeneity on large scale transport. Such behaviors can be modeled by approaches that
are based on time and/or space non-local conservation equations. A key question is the identification and quantification of the heterogeneity controls on global non-Fickian transport patterns.
Here, we focus on the roles of broad heterogeneity distribution, and
heterogeneity and flow correlation on global non-Fickian transport.
We identify the signatures of disorder and correlation dominated
large scale transport in the distributions of solute arrival times,
solute dispersion and spatial solute distributions. Starting from
well-defined small scale stochastic flow and transport descriptions,
we quantify large scale transport by ensemble averaging over the Lagrangian
particle dynamics, which leads to a global transport model
that is given by a coupled continuous time random walk (CTRW) characterized
by correlated particle velocities. We formalize this correlated CTRW in terms of an evolution equation for the global particle distribution, and
discuss the impact of the correlation of subsequent particle velocities
on the transport behavior, as well as the limits of perfect and no
correlation.