Cubic Plus GE (CPGE): Cubic equation of state with simple mixing rule plus excess Gibbs energy that satisfies low-density condition

Abstract

The excess Gibbs energy calculated by activity coefficient model GE,M is added to a cubic equation of state. The additional term containing GE,M is obtained by a dimensional analysis. A simple mixing rule such as a/b = Σ(ai/bi)xi and b = Σbixi is adopted. The equation of state satisfies the low-density boundary condition that the second virial coefficient be quadratic in composition. The activity coefficient derived from the equation of state is expressed as the sum of Flory-Huggins term and interaction term, which has the same form as UNIQUAC, UNIFAC, and ASOG models at low pressure in liquid phase. Peng-Robinson equation of state was used for an example of cubic equation of state, and NRTL, CDSAP, and r-CDSAP models were adopted for GE,M for examples of activity coefficient models. The vapor-liquid equilibria for 2-propanol (1) + water (2), acetone (1) + water (2), benzene (1) + 2,2,4-trimethylpentane (2), methane (1) + pentane (2), and ethane (1) + heavy alkanes (2) systems were calculated to test the temperature dependency. The parameter values in the activity coefficient models were fitted to the experimental data of each binary system at the lowest temperature. Then, the vapor-liquid equilibria were calculated at higher temperatures with the parameter values. The calculated results at higher temperatures by the proposed model are better than those by Peng-Robinson + Wong-Sandler + NRTL mixing rule or Peng-Robinson + Huron-Vidal + NRTL mixing rule. The vapor-liquid equilibria for acetone (1) + acetonitrile (2) + benzene (3) + ethanol (4) system and its sub-binary and sub-ternary systems were calculated to test the estimation performance. The parameter values in the activity coefficient models were fitted to the experimental data of sub-binary systems. Then, the vapor-liquid equilibria for ternary and quaternary systems were estimated. The average deviations between the experimental data and the calculated results by the proposed model are 0.7% for pressure and 0.005 to 0.006 for mole fraction in vapor phase.