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

journal contribution

posted on 2016-02-18, 00:00 authored by Zheng Li, Kathryn A. Mumford, Kathryn
H. Smith, Jian Chen, Yong Wang, Geoffrey W. StevensCalculation
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.