Upscaling Calcite Growth Rates from the Mesoscale to the Macroscale

Abstract

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 {1014} 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.

Growth Rate and Morphology of a Single Calcium Carbonate Crystal on Polysulfone Film Measured with Time Lapse Raman Micro Spectroscopy

“…The growth rate depends on solution parameters, such as: the supersaturation index (SI), the ionic strength (I), the pH and the [Ca 2+ ]/[CO 3 2-] ratio [8,[32][33][34][35]. Table 1 compares the results from this study with results from the literature [33][34][35].…”

“…Table 1 compares the results from this study with results from the literature [33][34][35]. Experimental conditions for crystal growth rates vary widely in the literature and importantly influence observed growth rates.…”

Precipitation in Pores: A Geochemical Frontier

“…In the extreme case of dilute water however, this theory predicts that the pore sizes where electric double layer effects would be seen could be substantial. In natural systems pure water is not reasonably expected to be observed, but in experiments researchers will sometimes minimize the ionic strength since the composition and concentration of the electrolyte affects mineral precipitation reaction mechanisms and rates (e.g., Ruiz-Agudo et al 2011;Kubicki et al 2012;Bracco et al 2013).…”

“…The rate constants and mechanism for attachment of these ions vary depending on the ion and the mineral. For example, the rate constants for attachment of calcium and carbonate to calcite are ~6.7 × 10 6 s -1 and 3.6 × 10 7 s -1 (Bracco et al 2013), whereas those for attachment of magnesium and carbonate ions to magnesite (MgCO 3 ) are 4.0 × 10 5 s -1 and 2.0 × 10 6 s -1 (Bracco et al 2014). From this, one would expect that the zone over which surface kinetics and transport are both important depends not just on the fl ow rate and the reactivity of the mineral, but the identity of the constituent ions will affect how much of a reaction is transport controlled.…”

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

“…AFM has been used successfully to quantify mineral reaction rates for calcite growth and to develop macroscopic reaction rates for use in RTM studies (Bracco et al 2013). However, these models also need to account for the heterogeneity of the crystal surface.…”