Regression of NRTL parameters from ternary liquid–liquid equilibria using particle swarm optimization and discussions

• The PSO was successfully used to regress NRTL parameters from LLE.
• The NRTL model may not represent the real activities of components.
• The normalized random data can be correlated by the NRTL model.

The particle swarm optimization (PSO) method was successfully used to regress the nonrandom two-liquid (NRTL) parameters from liquid–liquid equilibria (LLE) data and the resulting parameters had smaller root-mean square deviations (RMSD) compared with literature values. Analysis of the results reveals that multiple groups of parameters with sufficiently small RMSDs can be found for the same set of LLE data. The activities calculated using these parameters and their corresponding predicted mole fractions can be far beyond the reasonable range of activity, clearly demonstrating that the NRTL model does not represent the real activities of components with parameters regressed from LLE. In addition, five sets of random data that were normalized to resemble LLE data were correlated by the NRTL model equally well as correlations of regular LLE data. Therefore, the model does not have any advantage in correlating LLE data over correlating random data. These limitations of the NRTL model doubt the model’s theoretical validity and should be aware of when the model is used.