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Reactive Transport and Mixing in Heterogeneous Media: Chemical Random Walks under Local Non-equilibrium

Periodic Reporting for period 1 - ChemicalWalks (Reactive Transport and Mixing in Heterogeneous Media: Chemical Random Walks under Local Non-equilibrium)

Okres sprawozdawczy: 2019-06-17 do 2021-06-16

Geological media are heterogeneous at a multitude of scales. At the large scale, aquifers are composed of different materials, arranged in different structures; and below the millimeter scale, rocks are porous materials. Heterogeneity in continuum (Darcy)-scale velocity magnitudes in heterogeneous subsurface media (figure left panel) represents an average over pore-scale structural heterogeneity. Dissolved substances, such as contaminants or nutrients, move through these complex porous media in the subsurface, resulting in spatially-variable subscale solute concentrations (figure middle panel). The solid phase at the pore scale is also composed of different minerals and highly heterogeneous from a chemical perspective (figure right panel). The heterogeneity affects the way water flows, which in turn affects the spatial distribution of these dissolved substances and the way in which they interact amongst themselves and with other resident components such as mineral formations. Understanding these processes is key to central societal issues such as water quality control and resources management.

Predicting the amount of dissolved substances present in groundwater and their spatial distribution in geological structures requires modeling transport and reactions in these complex media. Most current models assume that, although the concentration plume of, for example, a contaminant may be complex at the aquifer scale, it is homogeneous at the small scales corresponding to the pore spaces in geological materials. This leads to predictions of reaction rates that are often much larger than those found in real aquifers. The ChemicalWalks project proposed a new way to account for this incomplete mixing at the pore scale, by describing its impact in terms of a reaction slowdown due to the time it takes for different substances to come together and react. The project has led to novel theoretical and numerical frameworks that significantly advance the state-of-the-art understanding of chemical reactions under transport limitations and incomplete mixing.
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.
The results described in the previous section represent significant advances to the state of the art understanding of anomalous transport and reaction processes in the presence of medium heterogeneity and incomplete mixing. In particular, they extend:

1. The theoretical modeling of anomalous transport in heterogeneous velocity fields, by explicitly modeling the interplay between diffusive transport and local shear effects induced by advective heterogeneity.
2. The understanding and predictive modeling of the impact of transport, heterogeneity and incomplete mixing on fluid-solid reaction dynamics, by tying the inter-reaction times of the chemical continuous time random walk framework, previously developed by the ER, to transport dynamics under advection and diffusion.
3. The predictive and efficient numerical modeling of transport and reaction processes, by providing new upscaled methods which model the impact of pore-scale heterogeneity on these processes based on a limited number of physically-meaningful quantities, such as velocity statistics and characteristic lengthscales characterizing medium geometry.

The theoretical and numerical advances have led to an integrated framework for predicting reaction rates under transport limitations which has the potential to become a leading approach in the field. The numerical implementations fill a gap in the availability of efficient and open-source particle tracking algorithms for modeling reactive transport. As expected, the main impacts at this point are academic. Nonetheless, ChemicalWalks serves an important societal role. In particular, providing universal access to clean drinking water and sanitation is a standing United Nations goal. This problem is most severe in rural areas and developing countries, but industrialized countries also face serious challenges, in particular regarding aquifer contamination. A strong quantitative understanding of reactive transport in subsurface media is fundamental to achieving this objective, by providing appropriate models and simulation tools. Thus, a central long-term goal is to test and extend the fundamental results of ChemicalWalks with a view to large-scale applications, which will be of use to consulting companies and decision makers.
Heterogeneity in subsurface media spans multiple scales, affecting transport, reaction, and mixing.