Thermodynamic modeling of aqueous Na⁺-K⁺-Cl^--SO₄^2- quaternary system with electrolyte NRTL model

A comprehensive thermodynamic model based on electrolyte non-random two-liquid (eNRTL) equation is developed for aqueous Na⁺-K⁺-Cl^--SO₄^2- quaternary system. To account for the composition dependence of the solution nonideality, the eNRTL model requires two binary interaction parameters for each of the four electrolyte-water and four electrolyte-electrolyte pairs. We obtain the eNRTL binary parameters for (K⁺ SO₄^2-):H₂O pair, (K⁺ SO₄^2-):(Na⁺ SO₄^2-) pair and (K⁺ Cl^-):(K⁺ SO₄^2-) pair by regressing literature data. The eNRTL binary parameters for the other electrolyte-water and electrolyte-electrolyte pairs are retrieved from the literature. To account for the temperature dependence, each of the eNRTL binary parameter is correlated with a Gibbs-Helmholtz type expression with up to three temperature coefficients. The eNRTL model accurately represents various thermodynamic properties of the aqueous quaternary system and its subsystems with temperatures up to 473.15K and electrolyte concentrations up to saturation.