Thermodynamic Modeling of the Solubility of Quartz in Water up to High Temperatures and Pressures

Abstract

Available data on speciation of silica in aqueous solutions show that the main forms of silica are the monomer Si­(OH)4 and the dimer Si2O­(OH)6, with shares of higher polymers growing with an increase of temperature and the total concentration of silica in solution. Thermodynamic properties of the monomer and dimer in the ideal gas state are determined from the quantum-chemical calculations. The fugacity coefficients of these species in water up to water densities of 1200 kg m–3 and temperatures of up to 1350 K are estimated from an empirical correlation based on the stoichiometry of hydroxide species. The fine-tuning of the model is made by comparing calculations with the experimental solubility and speciation data. It was found that to match the speciation results reported as the share of the monomer, it is necessary to consider polymerization of silica beyond the dimer, which can be achieved without increasing the number of fitting parameters. The resulting model reproduces well the experimental results on the solubility of quartz in water, on the distribution of silica between the vapor and liquid phases of water at subcritical temperatures, and on the speciation of silica in water in equilibrium with quartz.

Thermochemistry of SinOx(OH)y Vapor Species from Quantum Chemical Calculations

“…Brady deduced that orthosilicic acid vapor, Si­(OH) 4 , is the major form of silica in steam from his analysis of the experimental results of Kennedy, Morey and Hesselgesser . Subsequent experimental ,,, and theoretical ,, work by several groups confirms his conclusions and also shows that dimers Si 2 O­(OH) 6 and trimers Si 3 O 2 (OH) 8 of silicic acid vapor comprise more of total gaseous silica with increasing fluid density along isotherms . On Earth, silica transport by “steam” above the critical point of water occurs in high-pressure steam turbines and in hydrothermal systems in the crust .…”

“…8 Subsequent experimental 3,9,17,18 and theoretical 13,19,23 vapor comprise more of total gaseous silica with increasing fluid density along isotherms. 49 On Earth, silica transport by "steam" above the critical point of water occurs in highpressure steam turbines 11 and in hydrothermal systems in the crust. 4 However, silica solubility in steam may be observable on some of the several thousand exoplanets discovered around other stars in our Milky Way galaxy.…”

Thermodynamic Modeling of Solubility of Corundum in Water at Supercritical Conditions

“…On the other hand, numerical values of K 0 ( T ) and ϕ 2 ∞ have to be evaluated, and this is one of the goals of this study. The model to evaluate fugacity coefficients of hydroxides of metals and metalloids in water was presented elsewhere and already used for Si­(OH) 4 and Si 2 O­(OH) 6 . In this work, it will be used to estimate ϕ 2 ∞ for various charge-neutral species of aluminum hydroxide.…”

“…The model for fugacity coefficients of hydroxides of metals and metalloids at infinite dilution in water was already presented. , An example of its use to evaluate of ϕ 2 ∞ for a species of a formula Al 2 m (OH) 6 m · ( r – 3 m )­H 2 O, see eq , will be given here. At water densities, ρ 1 * , below 300 kg m –3 (decreasing to 100 kg m –3 in the near-critical range, see ref ), the following approximation is proposed to estimate ϕ 2 ∞ where ϕ 1 * is the fugacity coefficient of pure water, and the parameter k corresponds to the stoichiometry of the dissolved species as follows: that is, by counting the groups (OH, H 2 O) that can form hydrogen bonds with water.…”