Extension of the Nrtl Model for Accurate Plait Point Prediction in Ternary Liquid–liquid Equilibria

Abstract

The accurate prediction of the plait point in ternary liquid–liquid equilibrium (LLE) systems is essential for the reliable analysis and optimal design of separation processes. While the Non-Random Two-Liquid (NRTL) model is extensively employed for phase equilibrium calculations, its conventional formulation relies primarily on binary interaction parameters and may exhibit limitations when describing highly non-ideal ternary mixtures, particularly in the vicinity of the critical demixing region. In this work, a straightforward extension of the NRTL model is proposed through the introduction of an additional term that explicitly accounts for ternary interactions in the excess Gibbs free energy expression. This modification is governed by a single adjustable parameter, denoted (λ0), which enables the model to capture cooperative interaction effects among the three components while preserving the mathematical structure and computational simplicity of the original formulation. The performance of the modified model is evaluated using experimental LLE data for several ternary systems reported in the literature. Comparison with the conventional NRTL model reveals a marked improvement in the prediction of plait point compositions. The proposed approach therefore provides a practical, efficient, and physically consistent enhancement of the NRTL framework for modeling ternary liquid–liquid equilibria.