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

Abstract

[1] 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.

On the validity of effective formulations for transport through heterogeneous porous media

“…6 and 7). For HPM, γ max has the same scaling for the initial conditions γ max ∼ 1 √ L 0 and for the diffusion coefficient as γ max ∼ √ Pe (de Dreuzy et al, 2012). Doubling the injection width has a comparable effect to doubling the diffusion coefficient.…”

“…In HPM models, resistance to dispersive mixing, as we can also call γ , is enhanced by heterogeneity and reduced by large diffusion rates (smaller Peclet number) (de Dreuzy et al, 2012). γ sharply increases at initial times to a maximum value γ max , at a time t γ max close to the advection time, and slowly decreases back to 0 (Fig.…”

“…We use simulation results performed in previous studies (de Dreuzy et al, 2012) obtained on 2-D domains of sizes L L and L T in parallel and orthogonal directions, respectively, to the mean flux. L L is large enough to avoid any finite-size effects (from 10 2 to 10 3 correlation lengths λ).…”

“…Notice that, contrary to spreading, we are not concerned here with the spatial distribution, but only with the values of concentration and their time evolution, which are most simply characterized by the second moment. We quantified the deviation from the Gaussian mixing regime as the ratio of the actual concentration second moment M(t) to the second moment M D (t) of the Gaussian profile concentration c D (x,t) minus 1 (de Dreuzy et al, 2012):…”

Equivalence of Finite Dimensional Input–Output Models of Solute Transport and Diffusion in Geosciences

“…They are made up of an infinity of diffusive zones deriving from analytic solutions of the diffusion equation in layered, cylindrical or spherical impervious inclusions (MRMT) or in series (MINC). Between the single and infinite diffusive porosities of the dualporosity and these models, many intermediary models with finite numbers of diffusive porosities have been effectively used and calibrated on synthetic, field, or experimental data showing their relevance and usefulness [10,2,24,32,33].…”