A modified NRTL model for accurate phases equilibria: Part II: application to liquid–liquid equilibrium up to plait point

Abstract

• Modification of NRTL model. • Application in computing Liquid-Liquid Equilibrium (VLE). • LLE correlation for Ternary systems. • LLE Prediction for Quaternary systems. • Plait Points Prediction in LLE. This study presents a modified NRTL model that significantly improves the accuracy of liquid–liquid equilibrium (LLE) predictions for multicomponent systems. Unlike classical thermodynamic models, which based only on binary parameters and often fail near plait points, the proposed modification introduces ternary interaction parameters to account for interactions among three neighboring components. This advancement enables a more physically meaningful representation of complex molecular interactions in ternary and quaternary mixtures. The modified NRTL model performs better across 33 ternary and 4 quaternary systems, showing a substantially lower root-mean-square deviation (RMSD) compared to the classical NRTL model and the other extended NRTL models. It accurately reproduces experimental tie lines, immiscibility regions, and plait point coordinates, and successfully predicts LLE behavior in quaternary systems without requiring additional fitted parameters. The modified NRTL model thus offers a reliable and predictive tool for the design and optimization of liquid–liquid extraction processes, particularly where accurate phase equilibria near critical points are essential.