Upscaling calcite growth rates from the mesoscale to the macroscale

Quantitative prediction of mineral reaction rates in the subsurface remains a daunting task partly because a key parameter for macroscopic models, the reactive site density, is poorly constrained. Here we report atomic force microscopy (AFM) measurements on the {101Ì.4} calcite surface of monomolecular step densities, treated as equivalent to the reactive site density, as a function of aqueous calcium-to-carbonate ratio and saturation index. Data for the obtuse step orientation are combined with existing step velocity measurements to generate a model that predicts overall macroscopic calcite growth rates. The model is quantitatively consistent with several published macroscopic rates under a range of alkaline solution conditions, particularly for two of the most comprehensive data sets, without the need for additional fit parameters. The model reproduces peak growth rates, and its functional form is simple enough to be incorporated into reactive transport or other macroscopic models designed for predictions in porous media. However, it currently cannot model equilibrium or pH effects and it may overestimate rates at high aqueous calcium-to-carbonate ratios. The discrepancies in rates at high calcium-to-carbonate ratios may be due to differences in pretreatment, such as exposing the seed material to SI ≥ 1.0 to generate/develop growth hillocks, or other factors.