Pore-Scale Modeling of Mixing-Induced Reaction Transport through a Single Self-Affine Fracture

Abstract

This pore-scale modeling study in single self-affine fractures showed that the heterogeneous flow field had a significant influence on the mixing-induced reaction transport. We generated the single self-affine fracture by the successive random additions (SRA) technique. The pore-scale model was developed by coupling the Navier-Stoke equation (NSE) and advection-diffusion equation with reaction (ADER). Eddies were captured in the self-affine fracture due to the increasing Reynolds number and the sudden expansion of aperture. The flux-weighted breakthrough curves (BTCs) of reaction product showed the typical non-Fickian characteristics (i.e., “early arrival” and “heavy tail”). It was found that the reactant was involved in eddies and then reacted inside the eddy-controlled domain. Consequently, eddies played a significant role in delaying the mass exchange process between the eddy-controlled domain and the main flow channel, which resulted in the “heavy tail” in BTCs. As the Reynolds number increased, the breakthrough time increased while the concentration peaks of BTCs decreased. Furthermore, the dilution index presenting the exponential of the Shannon entropy of a concentration probability distribution was used to quantify the degree of reactant mixing. The results showed that the quantification of dilution for nonreaction transport was in good agreement with the outcomes of mixing-induced reaction transport. The high Reynolds number and Peclet number had a negative influence on the mixing process at the early time whereas they led to the enhanced mixing process at the late time.