Effects of surface roughness and Reynolds number on the solute transport through three-dimensional rough-walled rock fractures under different flow regimes

In this study, the effects of surface roughness and Reynolds number (Re) on fluid flow and solute transport are investigated based on a double rough-walled fracture model that precisely represents the natural geometries of rock fractures. The double rough-walled fracture model is composed of two three-dimensional(3D) self-affine fracture surfaces generated using the improved successive random additions (SRA). Simulation of fluid flow and solute transport through the models were conducted by directly solving the Navier-Stokes equation and advection-diffusion equation (ADE), respectively. The results indicate that as the Re increases from 0.1 to 200, the flow regime changes from linear flow to nonlinear flow accompanied with the tortuous streamlines and significant eddies. Those eddies lead to the temporary stagnant zones that delay the solute migration. The increment of Re enhances the transport heterogeneity with the transport mode changing from the diffusion-dominated to the advection-dominated behavior, which is more significant in the fracture with a larger joint roughness coefficient (JRC). All breakthrough curves (BTCs) of rough-walled fractures exhibited typical non-Fickian transport characteristics with "early arrival" and "long tailing" of BTCs. Increasing the JRC and/or Re will enhances the non-Fickian transport characteristics. The ADE model is able to accurately fit the numerical BTCs and residence time distributions (RTDs) at a low Re, but fails to capture the non-Fickian transport characteristics at a large Re. In contrast, the continuous time random walk (CTRW) model provides a better fit to the numerical simulation results over the whole range of Re. Whereas, the fitting error gradually increases with increasing Re.