Critical points calculation with a cubic equation of state and excess free energy mixing rules

This paper presents analytical partial derivative equations required for multicomponent critical point calculation. These partial derivative equations follow the computational scheme developed by Heideman and Khalil, but extended to excess free energy mixing rules. The mixing rules implemented in this paper are the Wong–Sandler (WS), the modified Huron–Vidal first and second orders mixing rules. The Peng–Robinson equation of state and the NRTL activity model are used in all calculations. However, the calculation based on the derivative is not limited to the mixing rules referred in this paper. It can also be applied to any other mixing rules. It is found that the calculations using these analytical partial derivative equations are superior, in computation time and reliability, that using the numerical partial derivative equations.