Thermodynamic model of aqueous Mg²⁺ – Na⁺ – K⁺ – Cl⁻ quaternary system

We present a thermodynamic model for the aqueous Mg²⁺ – Na⁺ – K⁺ – Cl⁻ quaternary system based on symmetric electrolyte Non-Random Two Liquid (eNRTL) theory. This work is a continuation of our previous study on the aqueous Ca²⁺ – Na⁺ – K⁺ – Cl⁻ quaternary system and part of a larger effort to develop a comprehensive engineering thermodynamic model for high salinity produced water in oil and gas production. The eNRTL theory requires two binary interaction parameters for each molecule-molecule, molecule-electrolyte, and electrolyte-electrolyte pair to correlate composition dependence of the solution nonideality. The binary interaction parameters, including their temperature coefficients, are identified for the (Mg²⁺-Cl⁻):H₂O pair, (Mg²⁺-Cl⁻):(K⁺-Cl⁻) pair, and (Mg²⁺-Cl⁻):(Na⁺-Cl⁻) pair using available thermodynamic data. The binary parameters for the other pairs are taken directly from the literature. Together, the eNRTL model and the binary parameters yield a satisfactory thermodynamic model for the quaternary system and its subsystems with temperatures ranging from 273.15 to 473.15 K and salt concentrations up to saturation.