Thermodynamic modeling of aqueous Ca²⁺- Na⁺ - K⁺ - Cl^- quaternary system

We present a comprehensive thermodynamic model for the aqueous Ca²⁺ - Na⁺ - K⁺ - Cl^- quaternary system with electrolyte concentrations up to saturation and temperatures up to 473 K. This work is part of a larger effort to develop an engineering thermodynamic model for high salinity produced water in oil and gas production. Built on the thermodynamic framework of symmetric electrolyte Non-Random Two Liquid (eNRTL) theory, the model correlates composition dependency of the solution nonideality with two binary interaction parameters for each of the molecule-electrolyte pairs and the electrolyte-electrolyte pairs present in the system. The model further correlates temperature dependency of the binary parameters through a Gibbs-Helmholtz type equation with three temperature coefficients. We identify the binary parameters and their temperature coefficients for the (Ca²⁺ Cl^-):H₂O pair, the (Ca²⁺ Cl^-):(Na⁺ Cl^-) pair and the (Ca²⁺ Cl^-):(K⁺ Cl^-) pair by regressing experimental phase equilibrium, calorimetric and salt solubility data. These binary parameters are then integrated with published binary parameters for other subsystems present in the quaternary system. Together the eNRTL model and the model parameters offer a comprehensive thermodynamic model for the quaternary system; and it shows excellent agreement with literature data for the quaternary system and its subsystems.