Persistent incomplete mixing in reactive flows

TL;DR

This paper introduces a stochastic advection-diffusion-reaction model that separates mechanical and diffusive mixing, providing a more accurate description of incomplete mixing in reactive flows, especially in porous media.

Contribution

The paper proposes the SADR model that distinguishes mechanical and diffusive mixing, improving accuracy over traditional models in predicting reactive transport.

Findings

SADR model accurately predicts incomplete mixing in reactive flows.

Traditional models overestimate reaction product concentration by up to 60%.

SADR model aligns well with experimental results.

Abstract

We present an effective stochastic advection-diffusion-reaction (SADR) model that explains incomplete mixing typically observed in transport with bimolecular reactions. Unlike traditional advection-dispersion-reaction models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, mechanical mixing is driven by random advective velocity with the variance given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a Fickian diffusion with the effective diffusion coefficient. We demonstrate that the sum of the two coefficients is equal to the dispersion coefficients, but only the effective diffusion coefficient contributes to the mixing-controlled reactions, indicating that such systems do not get fully mixed at the Representative Elementary Volume scale where the deterministic equations and dispersion coefficient are defined. We use the experimental results of Gramling et al. \cite{Gramling} to show that for transport and bimolecular reactions in porous media, the SADR model is significantly more accurate than the traditional dispersion model, which overestimates the concentration of the reaction product by as much as 60\%.