Influence of porosity structures on mixing-induced reactivity at chemical equilibrium in mobile/immobile Multi-Rate Mass Transfer (MRMT) and Multiple INteracting Continua (MINC) models

Trapping mechanisms and slow diffusion in poorly connected porosities are well modeled by several anomalous transport models including the Multi-Rate Mass Transfer framework (MRMT). In MRMT, solutes in fast mobile advective zones are slowed down by first-order exchanges with immobile zones. While MRMT models have been used essentially for conservative transport, we investigate their relevance to reactive transport. To this end, we analyze the influence of the structure of the diffusive porosity zone on the distribution of concentrations within the immobile zone and on the reactivity of simple precipitation/dissolution bimolecular reactions at equilibrium. We build Multi-Rate Mass Transfer (MRMT) and Multiple INteracting Continua (MINC) models with equivalent transport characteristics. Both models have the same mobile zone concentrations at any time. They, however, differ by the connectivity structure of their immobile zones. MRMT has a star-shaped connectivity structure with the mobile zone linked to all immobile zones and acting as the sole exchanger. MINC has a chained-type connectivity where immobile zones are mutually connected on a line. We show that both connectivity structures give the same concentration variance whatever the model parameters, dimensionality, and initial conditions. Reaction rates of bimolecular reaction at chemical equilibrium are also highly similar but not equal as long as concentration gradients within the diffusive zone remain low like in the uniform injection case, or at large times when high initial concentration gradients have been reduced. For high initial immobile concentration gradients in the diffusive zone, however, reaction rates are much lower in the star-shaped connectivity structure (MRMT), and consequently depend on the organization of the immobile porosity structure. Negative concentrations also occur in some of the immobile zones of the equivalent MRMT as a result of the direct connection of the mobile and immobile zones. While acceptable for conservative components, negative concentrations limit the relevance of MRMT to model reactivity at high immobile concentration gradients. The concept of immobile zone concentration should thus be taken with great care and systematically be assessed.