Pore-scale numerical investigation of the impacts of surface roughness: Upscaling of reaction rates in rough fractures

The roughness of solid surfaces influences mineral dissolution rates by affecting flow and transport in the near-surface regions and by increasing the surface area available for reaction. The impact of surface area is commonly accounted for by using the surface roughness factor (SRF), which is the ratio between the total surface area and the nominal or geometric surface area. The coupled impacts of hydrodynamics and transport, however, are rarely considered. In this study, we performed pore-scale reactive transport simulations in a series of synthetic 2D rough fractures to investigate the compound effects of surface roughness on the reaction rates in fractures. Simulation results show that while reaction rates increase with SRF, the increase is not linearly proportional to that of the surface area. Rather, local concentration gradients resulting from flow and transport processes limit the increase in the rate. In addition, surface roughness gives rise to concentration gradients that do not otherwise develop in the flat-surface geometries typically considered in modeling studies. To describe the impacts of the surface area increase on reaction rate at different roughness and flow velocities, three distinct regimes were identified. A unified mathematical relationship was also developed that allows the reaction rate in a rough fracture to be approximated by the well-mixed reactor reaction rate and a correction factor. The correction factor follows a power-law function of SRF, with the multiplying factor and exponent expressed as exponential functions of the Péclet and Damköhler number. This mathematical formulation provides a valuable upscaling approach for effective integration of sub-grid scale surface roughness in larger scale continuum models.