Solution Structure of Isoactivity Equations for Liquid–Liquid Equilibrium Calculations Using the Nonrandom Two-Liquid Model

Calculation of the liquid–liquid equilibrium (LLE) based on an activity coefficient model is a common and significant problem in chemical thermodynamics. This is usually carried out by either minimizing the Gibbs free energy of the system coupled with the stability test (tangent plane distance criterion) or solving the isoactivity equations. While established, the stability test requires a very robust algorithm. By contrast, it is easy to solve the isoactivity equations; nevertheless, the solution strongly depends on the initial estimate. This study aims to investigate the structure of the solutions of the isoactivity equations for LLE systems in order to provide a calculation strategy that is not so dependent on the initial estimates while still maintaining its simplicity. A systematic study covering one- and two-phase ternary, quaternary, and quinary LLE systems and three-phase ternary systems has been carried out using the nonrandom two-liquid model, and it has been found that the equation-solving approach can be applied to multiphase systems.