Continuous Time Random Walks for Non-Fickian Solute Transport Under Heterogeneous Flow and Mass Transfer For Uniform and Radial Flow Conditions (Invited)

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. This has been observed in tracer experiments under forced and natural flow conditions. We address the following key questions: (i) how do flow heterogeneity and solute retention by mass transfer manifest in non-Fickian transport models, and (ii) how can non-Fickian solute transport be quantified under non-uniform flow conditions? In order to approach these questions, we present a continuous time random walk (CTRW) formulation for the quantification and interpretation of non-Fickian solute transport under uniform and forced flow conditions. We establish a general CTRW framework in Cartesian and radial coordinates on the basis of the corresponding random walk equations for particle positions and times. The evolution of solute concentration under forced flow conditions is governed by a non-local radial advection-dispersion equation. Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. We then discuss the signatures of flow heterogeneity on one hand and mass transfer between mobile and immobile regions on the other in their impact on large scale non-Fickian transport. On this basis we study their parametrization in the CTRW framework in terms of stochastic particle velocity series and transition times, and their relation to the statistical medium properties. We then derive uniform and radial CTRW implementations that model (i) non-local transport due to heterogeneous advection, (ii) multirate mass transfer (MRMT) between mobile and immobile con- tinua, and (iii) both heterogeneous advection in a mobile and mass transfer between mobile and immobile regions. The transport signatures for the dis- tinct heterogeneity models are analyzed in terms of solute dispersion and breakthrough curves.