The scaling of mineral dissolution rates under complex flow conditions

Abstract Mineral dissolution is an important process that provides materials and nutrients to ecosystems. However, a general rate scaling theory has not been developed that can be used to scale mineral dissolution rates from laboratory to field under variable water flow and solute transport conditions. In this study, a mathematical relationship has been derived that can be used to extrapolate the rate of mineral dissolution derived under well-mixed conditions to complex flow systems with spatial heterogeneity and temporal flow velocity transiency. The macroscopic mineral reaction rate in a flow system ( r FT ¯ ) was derived as r FT ¯ = ∫ 0 ∞ r ( τ ) τ f ( τ ) d τ / τ adv ¯ , where f ( τ ) is the fluid travel time distribution (FTTD) function, r ( τ ) is the reaction rate as a function of reaction time in a well-mixed system, and τ adv ¯ is the mean fluid travel time. Reactive transport simulations were performed to generate various scenarios of mineral dissolution under different flow conditions with permeability heterogeneity and flow velocity transiency using magnesite as an example. The macroscopic mineral dissolution rates calculated from the scaling relationship were compared with the rates averaged from the reactive transport simulations. The results indicate that the averaged magnesite dissolution rates decreased significantly in presence of permeability heterogeneity and under transient flow fluctuation conditions as compared to the rate determined from a homogeneous flow-through system with constant flow rate, showing a complex relationship between the averaged dissolution rate, local dissolution rate, and transient flow characteristics. Remarkably all the averaged rates that differ significantly under different flow conditions were converged to the scaling relationship, providing a consistent way to scale the rate of mineral dissolution from well-mixed reactors to complex flow systems. The results in this study were derived under a steady-state of porosity, permeability, and mineral surface reactivity, and further research is to incorporate their temporal variations.