The chemical continuous time random walk framework for upscaling
fluid--solid reactions under advection--diffusion
- Tomás Aquino,
- Tanguy Le Borgne
Abstract
The spatial distribution of reactants in heterogeneous media plays a
central role in chemical reactions, which, as contact processes, depend
on mixing. For fast reactions, diffusion is unable to smooth out
structure in reactant distributions on scales relevant for reaction,
leading to incomplete mixing. Thus, well-mixed reaction models tend to
overestimate reaction rates, as they assume that all solute is available
for reaction and do not take into account mass-transfer limitations.
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 develop a novel theoretical framework to quantify these dynamics for
fluid--solid reactions, with the fluid phase undergoing
advective--diffusive transport. Our approach is based on the concept of
inter-reaction times, which result from the waiting times between
contacts of transported reactants with the solid phase. We use this
formulation to quantify the time evolution of total mass for a catalytic
degradation reaction, and test its predictions against numerical
simulations of advective--diffusive transport in stratified channel flow
and Stokes flow through a beadpack.