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Nonphysical Behavior in Several Statistical Mechanically Based Equations of State

Alsaifi, Nayef M. and Alkhater, Mohammed and Binous, Housam and Al Aslani, Isa and Alsunni, Yousef and Wang, Zhen-Gang (2019) Nonphysical Behavior in Several Statistical Mechanically Based Equations of State. Industrial & Engineering Chemistry Research, 58 (3). pp. 1382-1395. ISSN 0888-5885. doi:10.1021/acs.iecr.8b04656. https://resolver.caltech.edu/CaltechAUTHORS:20190114-073829851

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Abstract

In this work, we utilize bifurcation diagrams to study the role of mathematical artifacts in deteriorating the physical behavior in statistical mechanically based equations of state of pure fluids. We study the impact of common empirical approximations usually employed to overcome some of the mathematical and physical challenges such as the parametrization of mean field models or pair correlations functions at contact. The proposed diagrams elucidate how the reduced molar volume bifurcates with the variation of temperature at constant pressure. We generate bifurcation diagrams for the modified van der Waals equation of state (EOS) of Poole et al, SAFT-VR Mie, Soft-SAFT, CK-SAFT, and the original SAFT EOSs for spherical and nonspherical molecules. We find that the bifurcation diagram can serve as a useful schematic tool to reveal the unphysical PVT behavior, demonstrate the existence of physical and spurious two-phase separation regions, and illustrate how the number of molar volume roots vary with temperatures. Our method shows that the presence of unphysical branches can cause spurious two-phase separation regions and create erroneous behavior in the stability limit of vapor–liquid equilibrium. We demonstrate that the existence of customary and spurious phase envelopes is accompanied by S-shaped behavior in the volume-temperature bifurcation diagrams. The study reveals that none of the SAFT models is free from producing unphysical behavior. While the SAFT-VR Mie EOS exhibits solid–liquid-like behavior for nonspherical molecules, the CK-SAFT EOS shows liquid–liquid demixing behavior for spherical and nonspherical compounds. For the soft-SAFT EOS, three different two-phase separation regions are observed in addition to the common vapor–liquid phase separation region.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1021/acs.iecr.8b04656DOIArticle
ORCID:
AuthorORCID
Alsaifi, Nayef M.0000-0003-3232-6411
Wang, Zhen-Gang0000-0002-3361-6114
Additional Information:© 2019 American Chemical Society. Received: September 23, 2018; Revised: December 31, 2018; Accepted: January 4, 2019; Published: January 11, 2019. The authors gratefully acknowledge the support of King Fahd University of Petroleum & Minerals through the grant to KFUPM-Caltech Research in Catalysis. The authors declare no competing financial interest.
Funders:
Funding AgencyGrant Number
King Fahd University of Petroleum and Minerals (KFUPM)UNSPECIFIED
Issue or Number:3
DOI:10.1021/acs.iecr.8b04656
Record Number:CaltechAUTHORS:20190114-073829851
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190114-073829851
Official Citation:Nonphysical Behavior in Several Statistical Mechanically Based Equations of State. Nayef M. Alsaifi, Mohammed Alkhater, Housam Binous, Isa Al Aslani, Yousef Alsunni, and Zhen-Gang Wang. Industrial & Engineering Chemistry Research 2019 58 (3), 1382-1395. DOI: 10.1021/acs.iecr.8b04656
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92236
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Jan 2019 21:05
Last Modified:16 Nov 2021 03:48

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