Semi-analytical models of mineral dissolution in rough fractures with permeable walls

Mineral dissolution in fractures is largely affected by the flow field within the fracture opening. The flow field maintains transport of the dissolved solutes and influences the concentration gradient and thermodynamic driving force for the mineral dissolution. In this study, we focus on investigating two factors that influence mineral dissolution in fractures: fracture wall roughness and interporosity fluid exchange or the flux through the fracture walls. The classical cubic law for the flow in parallel-plate channels cannot describe the flow in a fracture with rough permeable walls. The wavy, irregular shape of the rough boundaries can result in local flow features and might cause a shift of the overall flow and dissolution regime. At low Reynolds numbers, roughness simply increases the surface area available for mineral dissolution. Moreover, at higher Reynolds numbers, the inertial effects become important and the non-linear flow, flow instabilities, and reverse flow will form. With the creation of eddies and vorticities in the area adjacent to the walls, a flow dead zone forms that reduces the reactive surface area. In the presence of interporosity fluid exchange between the fracture and its surrounding rock, the non-zero fluid velocity on the fracture walls influences the local concentration gradient. In addition, the newly introduced fluid may facilitate or suppress the fracture wall mineral dissolution depending on its composition. This work highlights the compound effect of roughness and fluid flux through the walls on fracture mineral dissolution. For this purpose, the asymptotic solutions of the steady-state Navier–Stokes equations with non-zero velocity on the borders are used to determine the velocity field within the fracture opening. The quadratic and cubic corrections to Darcy’s law are expected as a result of the wall roughness and the flow through the walls. The flow field is coupled with a transport module and a geochemical model (PHREEQC). As a test case, we investigate calcite dissolution in a single fracture at a different influx rate. For each flow rate, a flat fracture and two sets of rough profiles with and without the permeable walls were compared. The simulation results showed that compared to impermeable walls, the pervious walls result in a non-uniform non-periodic mineral dissolution along the fracture, which is more focused at the inlet. At low Reynolds numbers, the hotspots of dissolution are slightly shifted from the small