The chemical continuous time random walk framework for upscaling transport limitations in fluid–solid reactions

Abstract

Fluid-solid reactions play a key role in a large range of biogeochemical processes. Transport limitations at the pore scale limit the amount of solute available for reaction, so that reaction rates measured under well-mixed conditions tend to strongly overestimate rates occurring in natural and engineered systems. Although different models have been proposed to capture this phenomenon, linking pore-scale structure, flow heterogeneity, and local reaction kinetics to upscaled effective kinetics remains a challenging problem. We present a new theoretical framework to quantify these dynamics based on the chemical continuous time random walk framework. We study a fluid–solid reaction with the fluid phase undergoing advective–diffusive transport. We consider a catalytic degradation reaction, AF+BS→BS, where AF is in fluid phase and BS is in solid phase and homogeneous over the fluid–solid interface, allowing us to focus on the role of transport limitations and medium structure. Our approach is based on the concept of inter-reaction times, which result from the times between contacts of transported reactants with the solid phase. We use this formulation to quantify the global kinetics of fluid-reactant mass and test our predictions against numerical simulations of advective–diffusive transport in stratified channel flow and Stokes flow through a beadpack. The theory captures the decrease of effective reaction rates compared to the well-mixed prediction with increasing Damköhler number due to transport limitations. Although we consider simple kinetics and media, these findings will contribute to the understanding and modeling of the effect of transport limitations in more complex reactive transport problems.