Influence of eddies on conservative solute transport through a 2D single self-affine fracture

Abstract

The solute transport regime is highly dependent upon the heterogeneity of the flow field. In this study, the influence of eddies on conservative solute transport through a two-dimensional (2D) single self-affine fracture was investigated by the Navier-Stokes flow and solute transport simulations. The self-affine rough fracture was generated by the successive random additions (SRA) technique. The simulations showed that eddies had significant influence on the spatial evolution of the solute plume through the fracture. Analysis of breakthrough curves (BTCs) and residence time distributions (RTDs) presented that the solute transport through the fracture was non-Fickian and the developing eddies enhanced the typical non-Fickian characteristics (i.e., “early arrival” and “heavy tail”) in BTCs for a step tracer injection. Increasing the Reynolds number caused the increasing exponent of the power-law tail with the developing eddies. Fitting the non-Fickian BTCs with the classical inverse model (advection–dispersion-equation, ADE) led to a non-negligibleerror due to the presence of eddies. The continuous time random walk (CTRW) inverse model with truncated power law transition rate probability was alternatively employed and the fitting results showed the robust capability of CTRW in capturing the eddy-induced non-Fickian transport. It was found that the value of parameter β of CTRW decreased as the total eddy volume increased, indicating that the developing eddies might increase the magnitude of non-Fickian transport. Furthermore, the dilution index presenting the exponential of the Shannonentropyof a concentration probability distribution was used to quantify the uniformity of concentration distribution within the fracture. We could conclude that eddies provided strong resistance for solute transport and significantly delayed the mass exchange between the main flow channel and the eddy-controlled zones. Consequently, the delayed mass exchange process directly determined the magnitude of tails in BTCs. The results may enhance our understanding of the role of eddies in the solute transport through fractures.