Quartz precipitation kinetics at 180°C in NaCl solutions—Implications for the usability of the principle of detailed balancing

Abstract

The kinetics of heterogeneous quartz precipitation were determined at 180°C and a pH near 4 as a function of the degree of super saturation and dissolved NaCl concentrations. Stirred batch reactors were used and the changes in H 4SiO 4 concentrations over time were used to model the reaction rates. As the change in concentration in the batch experiment is not linear with time during all sampling intervals, the precipitation rates were retrieved by fitting the experimental observations to a forward model, i.e., a model that uses a prescribed rate law and compares the results with the experiments. Quartz precipitation occurs via an overall reaction, and therefore one can not presuppose the applicability of the predictions of Transition State Theory (TST). Therefore, different functions describing the dependence of the rate on deviation from equilibrium were examined in the forward model. The obtained precipitation rates were within error the same, regardless of the function that was used. By substituting the prediction of TST into the forward model, the change of quartz precipitation rate (at 180°C, pH 4 and ionic strength of 0.1M) with deviation from equilibrium was found to be r a t e = 1.9 ± 0.4 ⋅ 10 − 8 [ 1 − exp ⁡ ( Δ G r R T ) ] mol m − 2 s − 1 Within error, this observed rate agreed with predictions of quartz precipitation rates, which were calculated using the principle of detailed balancing, far from equilibrium quartz dissolution rates of Dove (1994) and equilibrium constant from Kharaka et al. (1988). Similar agreement between observations and predictions was obtained using the BCF (Burton Cabrera and Frank) crystal growth theory (Burton et al., 1951). In contrast to TST and BCF, a more general form of the rate dependence of deviation from equilibrium failed to predict the observed precipitation rates. Based on the observation that the principle of detailed balancing was verified for quartz dissolution and precipitation at 180°C and pH 4, we suggest that the principle of detailed balancing could be fruitfully applied to the huge database of quartz dissolution rates, together with appropriate thermodynamic data, for modeling quartz precipitation under natural conditions.