Activity Coefficients from an Equation of State: Novel Approach for Fast Phase Equilibrium Calculations

Deviation from ideal solution behavior is due to differences in intermolecular interactions, e.g., molecular size, shape, dispersion, multipolar, and hydrogen bonding interactions. Activity coefficients characterize deviations from ideal solution behavior; however, most activity coefficient models lack the physics to explicitly account for intermolecular forces such as hydrogen bonding and multipolar interactions. At the same time, molecular theories (in the form of equations of state) that explicitly account for hydrogen bonding and multipolar interactions have been developed and validated versus molecular simulation results and experiment. In this work, we present a novel approach to calculate activity coefficients using theoretically based equations of state that explicitly describe these molecular interactions. The suggested approach enables phase equilibrium calculations to be performed at a significantly faster rate in comparison to conventional fugacity coefficient approaches. This is attributed to the fact that the molar volume is treated as an input in the approach; hence, iterations over the volume at a given pressure are not required. The polar and perturbed chain form of the statistical associating fluid theory (Polar PC-SAFT) is used in this paper to develop an activity coefficient model (SAFT-AC) for mixtures where self-association, solvation, and dipolar interactions dominate. Excellent agreement with experimental data was observed for all systems. The latter validates the use of the suggested approach as a powerful means for rapid phase equilibrium calculations in process simulators and PVT modeling software, providing consistency between activity coefficient and fugacity coefficient approaches. Extensions should lead to smart simulation methods where the simulation decides when to switch between activity coefficient and fugacity coefficient approaches depending on system conditions.