Inertia and diffusion effects on reactive transport with fluid-solid reactions in rough fracture flows

Fluid inertia is known to exert a dominant control over transport processes in fracture flows. In particular, recirculating flows readily arise in inertial rough fracture flows and have been shown to cause anomalous transport by trapping particles. However, understanding of the combined effects of fluid inertia and solute diffusion on reactive transport involving fluid-solid reactions has thus far been elusive. This study investigates reactive transport involving an irreversible fluid-solid bimolecular reaction for wide ranges of Reynolds (Re) and Péclet (Pe) numbers and elucidates how the interplay between inertia and diffusion effects controls the dynamics of reactive transport. Solute diffusion (Pe) controls mainly the total reaction amount, whereas fluid inertia (Re) governs the reaction dynamics by inducing complex flow structures such as flow channeling and recirculating flows. Specifically, recirculating flows are shown to facilitate fluid-solid reactions by increasing the residence time of particles near the fluid-solid interfaces, and such trapping effects increase as Pe increases. Further, flow channeling and recirculating flows exert dominant control over the transport of both reactants and products. We elucidate the reactive transport dynamics by analyzing particle trajectories and quantifying Lagrangian velocity statistics and reaction-related measures. Based on the improved understanding, we then propose an upscaled reactive transport model that incorporates Lagrangian velocity statistics and velocity-dependent reaction probability, and show that the upscaled model successfully captures reactive transport over wide ranges of Re and Pe.