Mineral dissolution rates in the field have been reported to be orders of magnitude slower than those measured in the laboratory, an unresolved discrepancy that severely limits our ability to develop scientifically defensible predictive or even interpretive models for many geochemical processes in the earth and environmental sciences. One suggestion links this discrepancy to the role of physical and chemical heterogeneities typically found in subsurface soils and aquifers in producing scale-dependent rates where concentration gradients develop. In this paper, we examine the possibility that scale-dependent mineral dissolution rates can develop even at the single pore and fracture scale, the smallest and most fundamental building block of porous media. To do so, we develop two models to analyze mineral dissolution kinetics at the single pore scale: (1) a Poiseuille Flow model that applies laboratory-measured dissolution kinetics at the pore or fracture wall and couples this to a rigorous treatment of both advective and diffusive transport, and (2) a Well-Mixed Reactor model that assumes complete mixing within the pore, while maintaining the same reactive surface area, average flow rate, and geometry as the Poiseuille Flow model. For a fracture, a 1D Plug Flow Reactor model is considered in addition to quantify the effects of longitudinal versus transverse mixing. The comparison of averaged dissolution rates under various conditions of flow, pore size, and fracture length from the three models is used as a means to quantify the extent to which concentration gradients at the single pore and fracture scale can develop and render rates scale-dependent. Three important minerals that dissolve at widely different rates, calcite, plagioclase, and iron hydroxide, are considered. The modeling indicates that rate discrepancies arise primarily where concentration gradients develop due to comparable rates of reaction and advective transport, and incomplete mixing via molecular diffusion. The magnitude of the reaction rate is important, since it is found that scaling effects (and thus rate discrepancies) are negligible at the single pore and fracture scale for plagioclase and iron hydroxide because of the slow rate at which they dissolve. In the case of calcite, where dissolution rates are rapid, scaling effects can develop at high flow rates from 0.1 cm/s to 1000 cm/s and for fracture lengths less than 1 cm. At more normal flow rates, however, mixing via molecular diffusion is effective in homogenizing the concentration field, thus eliminating any discrepancies between the Poiseuille Flow and the Well-Mixed Reactor model. This suggests that a scale dependence to mineral dissolution rates is unlikely at the single pore or fracture scale under normal geological/hydrologic conditions, implying that the discrepancy between laboratory and field rates must be attributed to other factors
