Typical methods for calculation of binary liquid-liquid equilibrium compositions such as surfactant systems need proper initial guesses and/or checking the sign of the second derivative of molar Gibbs energy change of mixing, ΔG. Eubank and Hall [1] have shown the equal area rule (EAR) applies to the composition derivative of the Gibbs energy of a binary system at fixed pressure and temperature. Methods based on EAR do not need to check the sign of the second derivative of ΔG because EAR is a necessary and sufficient condition for phase equilibrium. However, the algorithm proposed by Eubank and Hall needs a reasonable initial guess. Furthermore, it is not easy to apply the algorithm to activity coefficient models such as Non-Random Two Liquid (NRTL) because the first and second derivatives of ΔG as a function of composition have various shapes for some sets of NRTL parameters. In this work, we have developed an improved algorithm for calculation of binary liquid-liquid equilibrium compositions based on EAR considering the various shapes of NRTL model. This algorithm needs neither any initial guess nor checking the sign of the second derivative of ΔG.

Binary Mixture Liquid-liquid Equilibria (LLE) Equal Area Rule (EAR) NRTL Algorithm

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