Objective functions analysis in the minimization of binary VLE data for asymmetric mixtures at high pressures

Five different objective functions were studied with the purpose of analyzing their performance for parameters estimation of vapor–liquid equilibrium models for a series of 13 non-polar and 13 polar asymmetric binary mixtures at high pressures. Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the VLE in all cases. The first two objective functions are based on the calculation of the distribution coefficients for each component in the mixture and the remaining objective functions involve additional calculations of other quantities such as the bubble point pressure. In general, the optimal parameters obtained from all objective functions showed a good prediction capacity of the behavior of the vapor phase. It is also demonstrated that a good prediction of the pressure depends on the form of the objective function. It was found that one objective function has slight advantages over the other analyzed objective functions: first, it does not involve additional iterative calculations as the bubble point or isothermal flash for each data point; second, the optimal second virial coefficient interaction parameter shows to be in concordance with the statistical thermodynamic postulates; and finally, VLE predictions using the optimal parameters obtained with the help of this objective function show very good representations of both the vapor phase and pressure.