Modeling fluid-solid chemical reactions in the subsurface requires a detailed understanding of transport in heterogeneous media. In recent years, it has been found that spatial-Markov models, which model transport in spatially-structured media by considering spatial correlations in velocity, have been very successful in describing advective transport. However, the underlying theoretical models did not account for diffusion, and a modeling framework capable of quantifying the interplay between advection and diffusion was absent. This seriously limited the predictive applicability of such approaches to model transport, mixing, and reaction in realistic subsurface media. We have developed the diffusing-velocity random walk to address this limitation. This novel framework provides a rigorous theory incorporating the interplay of advection and diffusion. The framework provides new insights into the role of shear and diffusion on dispersion and mixing processes in heterogeneous media.
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 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. The ER has mentored Antoine Hubert and Charlotte Le Traon, PhD students in the host group, on mixing theories and the use of stochastic methods to understand and quantify the impact of diffusive transport on reaction rates. This led to novel weakly-coupled descriptions of reaction and diffusion, allowing for a quantitative description of the impact of dilution on nonlinear reaction rates.
A novel theoretical framework to quantify these dynamics for fluid-solid reactions under advective-diffusive transport has also been developed. The 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 have used this formulation to quantify the dynamics of total mass for a fluid-solid reaction, and tested its predictions against numerical simulations of transport in channel flows and flow through a crystalline porous medium. This approach has been used to quantify flow, medium structure, and reaction conditions under which transport limitations play a significant effect on effective reaction rates at the Darcy scale.
ChemicalWalks has led to four main publications in scientific journals, four open-source software repositories for novel reactive particle tracking algorithms, and presentations at six international conferences and workshops. In addition to the core results, ChemicalWalks has led to international collaborations exploring their extension and application to different media and conditions, including unsaturated porous media, bacterial dynamics in the surface and subsurface, and the effect of time-dependent flow fields.
