(257aw) Thermodynamic Modeling of Quaternary Aqueous Mg2+, Na+, K+, Cl- System

We present a first-ever comprehensive thermodynamic model for the quaternary aqueous Mg²⁺, Na⁺, K⁺, Cl⁻ system with electrolyte concentrations up to saturation and temperatures from 273 to 473 K. This work is a continuation of our previous study on modeling the quaternary aqueous Ca²⁺, Na⁺, K⁺, Cl⁻ system and part of larger efforts to develop a comprehensive 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 with three temperature coefficients that are directly related to excess Gibbs energy, excess enthalpy, and excess heat capacity of the systems. We identify the binary parameters and their temperature coefficients for the MgCl₂-water pair, the MgCl₂-KCl pair, and the MgCl₂-NaCl pair by regressing experimental phase equilibrium, calorimetric, and salt solubility data available in literature. 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 subsystems and the quaternary system. This model is being extended to cover Ba²⁺, Sr²⁺, SO₄²⁻ and HCO₃⁻.