There is a distinct need for predictive equations of state for supercritical aqueous solutions, both for understanding fluids in deeper levels of Earth’s crust or in subduction zones, as well as in experimental work on mineral solubility. Here we develop a semi-empirical approach introduced by Gerya & Perchuk (1997) based on the P-T partition function of statistical thermodynamics, using experimental data on quartz and wollastonite solubility, as well as data on speciation of dissolved solution components derived from first principles molecular dynamics simulations. Two approaches are possible, differing in the degree of explicit information provided on the nature of the solution modelled and also in the amount of basic data needed to implement them. Both have their potential fields of application. A “simple” model using only the semi-empirical formulation for the H2O solvent is useful if independent data on speciation are lacking, overall neutrality of the dissolving species can be assumed, and the number of components is relatively low. Computation is fairly straightforward, because the system can be treated as a simple “mixing” problem, and adopted effective dissolved species are characterized by conventional thermodynamic properties that allow interpolation and extrapolation of fitted experimental solubility data. Application to the system CaO–SiO2–H2O shows that experimental data on fluids coexisting with wollastonite + quartz/coesite can be successfully modelled up to 900 °C and 4 GPa. This simple semi-empirical formulation can lay the groundwork for an “internally consistent data set” allowing descriptions of fluids in relatively simple fluid-rock systems at high pressures. With the addition of independent data on actual speciation, and an optimized model for the dissociation of H2O from available literature data, the semi-empirical approach can be extended to a comprehensive description of aqueous solutions in the CaO–SiO2–H2O system. Both models have one positive feature in common. Because standard thermodynamic properties for dissolved species, oxides or fictive aggregates/clusters can be derived, solutions of arbitrary compositions can be modelled from data obtained from experiments in which fluids are saturated with a given solid phase or phases.

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