# Equation of State of the H_{2}O–CO_{2}–CaCl_{2} Fluid System and Properties of Fluid Phases at *Р-Т* Parameters of the Middle and Lower Crust

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### Abstract

A numerical thermodynamic model is proposed for one of the most important geological fluid system, ternary H_{2}O–CO_{2}–CaCl_{2} system, at *P-T* conditions of the middle and lower crust and crust–mantle boundary. The model is based on the previously proposed equation for concentration dependence of the excess Gibbs free energy and on the first obtained *P-T* dependencies of the coefficients of the equation of state (EOS) expressed via molar volumes of the components. The EOS allows to predict the properties of the fluid participating in the majority of deep petrogenetic processes: its phase state (homogeneous or multi-phase), densities of fluid phases, concentrations of components in the co-existing phases, and the chemical activities of the components. The model precisely reproduces all available experimental data on the phase state of the ternary H_{2}O–CO_{2}–CaCl_{2} fluid system in the ranges of temperatures 773.15–1073.15 K and pressures 0.1–0.9 GPa and also allows the correct application of the EOS beyond the experimentally studied range of temperatures and pressures up to *P* = 2 GPa and *T* = 1673.15 K. The possibility of the correct extrapolation of our EOS is ensured by using the parametrization of *P-T* dependencies via the molar volume of water. The latter remains in the experimental domain of values or falls slightly beyond its boundaries, when increasing temperatures and pressures.

## Keywords:

fluid equation of state H_{2}O–CO

_{2}–CaCl

_{2}phase splitting high temperature high pressure lower crust mantle

## Notes

### ACKNOWLEDGMENTS

We are grateful to L. Ya. Aranovich (IGEM RAS) for useful and productive comments.

### FUNDING

This work was supported by the State Task of the Institute of Precambrian Geology and Geochronology of the Russian Academy of Sciences (project no. 0153-2019-0004).

### CONFLICT OF INTEREST

The authors declare that they have no conflict of interest.

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