Scale dependence of mineral dissolution rates within single pores and fractures

The possibility that gradients in concentration may develop within single pores and fractures, potentially giving rise to scale-dependent mineral dissolution rates, was investigated with experimentally validated reactive transport modeling. Three important subsurface mineral phases that dissolve at widely different rates, calcite, plagioclase, and iron hydroxide, were considered. Two models for analyzing mineral dissolution kinetics within a single pore were developed: (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 within the pore, and (2) a Well-Mixed Reactor model that assumes complete mixing within the pore, while maintaining the same reactive surface area, average flow rate, geometry, and multicomponent chemistry as the Poiseuille Flow model. For the case of a single fracture, a 1D Plug Flow Reactor model was also considered to quantify the effects of longitudinal versus transverse mixing. Excellent agreement was obtained between results from the Poiseuille Flow model and microfluidic laboratory experiments in which pH 4 and 5 solutions were flowed through a single 500 μm diameter by 4000 μm long cylindrical pore in calcite. The numerical modeling and time scale analysis indicated that rate discrepancies arise primarily where concentration gradients develop under two necessary conditions: (1) comparable rates of reaction and advective transport, and (2) incomplete mixing via molecular diffusion. For plagioclase and iron hydroxide, the scaling effects are negligible at the single pore and fracture scale because of their slow rates. In the case of calcite, where dissolution rates are rapid, scaling effects can develop at high flow rates from 0.1 to 1000 cm/s and for fracture lengths less than 1 cm. Under more normal flow conditions where flow is usually slower than 0.001 cm/s, 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. The analysis suggests that concentration gradients are unlikely to develop within single pores and fractures under typical geological/hydrologic conditions, implying that the discrepancy between laboratory and field rates must be attributed to other factors.