Inherent relevance of MRMT models to concentration variance and mixing-induced reactivity

Abstract

Several anomalous transport approaches have been developed to model the interaction between fast advectively-dominated transport in well-connected porosity and fracture structures and slow diffusively-dominated transport in poorly-connected or low-permeability ones. Among them, the Multi-Rate Mass Transfer approach (MRMT) represents the anomalous dispersion along the main flow paths (mobile zone) induced by a large distribution of first-order exchanges with immobile zones. Even though MRMTs have been developed for conservative transport processes in the mobile zone, we demonstrate that they also conserve the variance of the concentration distribution in the immobile zones, and, hence, pertain to mixing induced reactivity. This property is established whatever the organization of the immobile zones and whatever the injection and sampling conditions in the mobile zone. It inherently derives from the symmetry properties of the diffusion operator in the immobile zones, but cannot be directly extended to heterogeneous dispersive processes in the mobile zone.