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

Abstract

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.

Parametrization of PC-SAFT EoS for Solvents Reviewed for Use in Pharmaceutical Process Design: VLE, LLE, VLLE, and SLE Study

“…of Fouad et al 19 and Chapman and Fouad. 33 The good results of the false VLLE calculations by the UNIQUAC model are also shown in Figure 7. Also, the NRTL model with adjustable parameters does not explicitly account for specific chemical associations such as hydrogen bonding.…”

“…If the values of k ij and k A i B j are provided as a result of fitting against experimental data of two nonassociating solvents, this implies that the cross-association does occur. Chapman and Fouad 33 showed that the phase behavior of solvating systems is dominated by cross-associating interactions between unlike species so that the solvation parameters were fitted to the experimental data. The conceptual representation of the PC-SAFT interaction parameters between 62 ICH-reviewed solvents is represented in Figure 4.…”

“…48 In contrast, the PC-SAFT model with a fitted value of k ij = 0.1276 − 0.001/T r and k A i B j = −0.0912 + 0.0871T r could accurately describe the VLE phase behavior of the ethanol + n-hexane mixture at different temperatures (25−55 °C). Chapman and Fouad 33 have shown that self-association interactions play a major role in the phase equilibrium of the ethanol + normal hexane mixture. Hence, the PC-SAFT equation of state (EoS) is a suitable model to describe such solutions.…”

“…The activity coefficient models such as UNIFAC and UNIQUAC fail to accurately describe the VLE phase behavior of alcohols + alkanes, unless using false vapor–liquid–liquid (VLLE) calculations. Results are in agreement with the finding of Fouad et al and Chapman and Fouad . The good results of the false VLLE calculations by the UNIQUAC model are also shown in Figure .…”

Wertheim’s Association Theory for Phase Equilibrium Modeling in Chemical Engineering Practice

“…To appreciate the connection between activity models and EOSs based on TPT1, the expansion rule provides thermodynamically consistent terms for individual contributions, as shown by eq . , An especially convenient assumption is constant packing fraction for all compositions and compounds. This leads to variation of the pressure, of course, but repulsive (rep) terms usually go to zero in that reference frame, helping to focus on the more interesting effects.…”