New Empirical Model for the Excess Gibbs Free Energy: Correlation of Liquid–Liquid Equilibrium for Island-Type Ternary Systems

Abstract

Island-type ternary systems, at constant temperature and pressure, present a closed liquid–liquid miscibility gap in the ternary region while the three binary subsystems are completely miscible. Correlation of this type of phase equilibrium behavior is a challenge. Accordingly, correlation results using classical activity coefficient models (as NRTL or UNIQUAC) are not usually reported in the literature for this type of system. In this paper, the limitations of the NRTL model to correlate LLE data sets for island-type ternary systems are discussed. The lack of flexibility and the uncertainty in the equilibrium solution are the main problems. A new expression for the excess Gibbs free energy is proposed to overcome these limitations with a practical aim. The empirical model proposed has two contributions: a Gaussian-like function and a non-ideal homogeneous term. Both are combined to fulfill the topological requirements of the Gibbs energy of mixing surfaces for island-type ternary systems according to the Gibbs common tangent plane criterion along with the phase stability analysis. The model proposed avoids the uncertainty problems of classical activity models for island-type ternary systems. Additionally, in this model, the relations between the parameter values and the calculated LLE are easily interpreted, which allows generating good initial values and guiding the correlation algorithm when convergence problems occur. Some island-type ternary systems have been selected to illustrate this subject.