Disorder Versus Correlation Control: Non-Fickian Transport in Heterogeneous Porous Media and Correlated Continuous Time Random Walks
Résumé
Medium and flow heterogeneities lead to global transport patternsthat cannot be captured by large scale transport models that arebased on Fickian transport mechanisms. Early and late solute and particle arrivals, and non-linear evolution of dispersion arenon-Fickian manifestations of spatial heterogeneity on large scale transport. Such behaviors can be modeled by approaches thatare 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, andheterogeneity and flow correlation on global non-Fickian transport.We identify the signatures of disorder and correlation dominatedlarge scale transport in the distributions of solute arrival times,solute dispersion and spatial solute distributions. Starting fromwell-defined small scale stochastic flow and transport descriptions,we quantify large scale transport by ensemble averaging over the Lagrangianparticle dynamics, which leads to a global transport modelthat is given by a coupled continuous time random walk (CTRW) characterizedby correlated particle velocities. We formalize this correlated CTRW in terms of an evolution equation for the global particle distribution, anddiscuss the impact of the correlation of subsequent particle velocitieson the transport behavior, as well as the limits of perfect and nocorrelation.