(364e) Systematic Development of an Artifact-Free SAFT Eos

Recent work by Jaubert, Polishuk, Alsaifi, and coworkers has demonstrated several artifacts in the most popular implementations of SAFT EOSs. For example, Jaubert and coworkers showed that the PC-SAFT EOS trends to negative critical pressures in the long chain limit and indicates an artificial pure component liquid-liquid separation and critical point at high densities.[1] Polishuk addressed the high density artifacts by regressing new coefficients for PC-SAFT, but his proposed EOS gave poor results for vapor pressures of heavy n-alkanes.[2] Alsaifi et al. developed a “bifurcation” algorithm that mapped artifacts throughout the T-ρ plane, demonstrating artifacts in HR-SAFT, Soft-SAFT, and SAFT-VR at intermediate densities and temperatures.[3] On the other hand, the cubic SAFT formulation of the ESD EOS[4] and the multiparameter formulation of the SPEAD11 EOS[5] were free of artifacts at T > 40K. Artifacts can be quite problematic when solving for global free energy minima during phase equilibrium calculations of complex mixtures. Artificial density roots inside the binodal envelop also cause classical density functional theories for interfaces to fail. Altogether, these observations suggest a need and an opportunity for a protocol by which artifacts can be avoided and robust SAFT EOSs provided.

To develop a systematic protocol, we begin by revisiting the ESD EOS to examine how a cubic SAFT EOS can be developed while matching molecular simulation results developed since 1990. We find that the denominator of the repulsive contribution can be improved by recognizing that heavy branched hydrocarbons may remain as liquid at much higher packing fractions than spherical molecules. This suggests generalizing the factor of 1.9 to a function of molecular weight and functionality. Analysis of the attractive contribution shows that agreement with simulations of long chains can be improved by eliminating the temperature dependence of the denominator, resulting in an EOS that is practically first order in temperature. The resulting cubic SAFT EOS is shown to be free of artifacts at all temperatures, densities, and chain lengths.

The next step is to add features to the cubic EOS that enhance accuracy relative to molecular simulations while retaining freedom from artifacts. Naturally, the resulting EOS is no longer cubic. Analyzing the derivative behavior similar to the SPEAD11 EOS analysis leads to identification of several constraints that must be satisfied when characterizing the higher order contributions to thermodynamic perturbation theory (TPT). These constraints are much easier to satisfy when the higher order TPT contributions decay monotonically from their critical value to zero at high density, as in the Weeks-Chandler-Andersen (WCA) split of the potential function. An infinite order EOS is demonstrated that is free of artifacts while reproducing simulation results for Lennard-Jones chains with reasonable accuracy.

Finally, a simplified association contribution is added to the chain EOS to examine whether artifacts may arise in the presence of association. This leads to a modification of the constraints developed for non-associating molecules. The protocol is complete in cases where the WCA split of the potential function is acceptable.

References

[1] R. Privat, R. Gani, and J. Jaubert, “Fluid Phase Equilibria Are safe results obtained when the PC-SAFT equation of state is applied to ordinary pure chemicals ?,” vol. 295, pp. 76–92, 2010.

[2] I. Polishuk, “Standardized critical point-based numerical solution of statistical association fluid theory parameters: The perturbed chain-statistical association fluid theory equation of state revisited,” Ind. Eng. Chem. Res., vol. 53, no. 36, pp. 14127–14141, 2014.

[3] N. M. Alsaifi, M. Alkhater, H. Binous, I. Al Aslani, Y. Alsunni, and Z. G. Wang, “Nonphysical Behavior in Several Statistical Mechanically Based Equations of State,” Ind. Eng. Chem. Res., vol. 58, no. 3, pp. 1382–1395, 2019.

[4] J. R. Elliott, S. J. Suresh, M. D. Donohue, and M. D. Donohue, “A Simple Equation of State for Nonspherical and Associating Molecules,” Ind. Eng. Chem. Res., vol. 29, no. 7, 1990.

[5] A. F. Ghobadi and J. R. Elliott, “Evaluating perturbation contributions in SAFT models by comparing to molecular simulation of n-alkanes,” Fluid Phase Equilib., vol. 306, pp. 57–66, 2011.