Thermodynamic Model of the Fluid System H2O–CO2–NaCl–CaCl2 at P-T Parameters of the Middle and Lower Crust

Based on the earlier obtained equations of state for the ternary systems H₂O–CO₂–CaCl₂ and H₂O–CO₂–NaCl, an equation of state for the four-component fluid system H₂O–CO₂–NaCl–CaCl₂ is derived in terms of the Gibbs excess free energy. A corresponding numerical thermodynamic model is built. The main part of the numerical parameters of the model coincides with the corresponding parameters of the ternary systems. The NaCl–CaCl₂ interaction parameter was obtained from the experimental liquidus of the salt mixture. Similar to the thermodynamic models for H₂O–CO₂–CaCl₂ and H₂O–CO₂–NaCl, the range of applicability of the model is pressure 1–20 kbar and temperature from 500 to 1400°C. The model makes it possible to predict the physicochemical properties of the fluid involved in most processes of deep petrogenesis: the phase state of the system (homogeneous or multiphase fluid, presence or absence of solid salts), chemical activities of the components, densities of the fluid phases, and concentrations of the components in the coexisting phases. The model was used for a detailed study of the phase state and activity of water on the H₂O–CO₂–salt sections when changing the ratio \({{{{x}_{{{\text{NaCl}}}}}} \mathord{\left/ {\vphantom {{{{x}_{{{\text{NaCl}}}}}} {({{x}_{{{\text{NaCl}}}}} + {{x}_{{{\text{CaC}}{{{\text{l}}}_{{\text{2}}}}}}})}}} \right. \kern-0em} {({{x}_{{{\text{NaCl}}}}} + {{x}_{{{\text{CaC}}{{{\text{l}}}_{{\text{2}}}}}}})}}\) from 1 to 0. Changes in the composition and density of coexisting fluid phases at a constant activity of water and changes in the total composition of the system are studied. A set of phase diagrams on sections H₂O–NaCl–CaCl₂ for different mole fractions of CO₂ is obtained. Pressure dependencies of the maximal activity of water in the field of coexisting unmixable fluid phases are obtained for several salt compositions of the system. Due to removal of restrictions resulting from a smaller number of components in ternary systems, the thermodynamic behavior of systems with a mixed composition of the salt significantly differs from the behavior of those with a single salt component.