Unnoticed Pitfalls of Soave-Type Alpha Functions in Cubic Equations of StateClick to copy article linkArticle link copied!
Abstract
Empirical thermal cohesion functions, α(Tr), are frequently used in conventional equations of state (EOS) for fitting the vapor pressures of pure fluids. Accurate vapor pressure predictions are required for correlating and/or predicting the phase equilibrium and interfacial tension of multicomponent mixtures. This is the case for the Redlich−Kwong−Soave and Peng−Robinson models, two well-established models for engineering applications. In this work, we demonstrate that, in the case of pure fluids, the α(Tr) function can potentially predict multiple mechanically stable critical points, thus affecting the global topology of phase equilibrium predictions. A detailed analysis, based on the consistency of the prediction of the Joule−Thomson inversion curve, reveals that these predictions are not reliable from a physical point of view. In fact, conventional cubic EOS are able to predict multiple Joule−Thomson inversion curves, a behavior symptomatic of the prediction of multiple stable critical points for pure fluids. Similar pitfalls have been detected in theoretically based EOS such as SAFT and the model proposed by Johnson et al. (Johnson, J. K.; Zollweg, J. A.; Gubbins, K. E. Mol. Phys.1993, 78, 591−615) for Lennard-Jones fluids, although beyond the range in which such models are usually employed. In the case of conventional cubic EOS with quadratic mixing rules, another pitfall related to conventional α(Tr) functions is the prediction of nondifferentiable critical lines and equilibrium envelopes for mixtures. Such a physical inconsistency might generate a mechanism that predicts closed loops of immiscibility in van der Waals-type EOS that contain a temperature-dependent parameter.
*
To whom correspondence should be addressed. E-mail: [email protected].
†
Universidad de Concepción.
‡
University of Cologne.
§
Ben-Gurion University of the Negev.
‖
Present address: Department of Chemical Engineering & Biotechnology, The College of Judea and Samaria, Ariel, Israel.
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(42)
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(49)
, 21579-21591. https://doi.org/10.1021/acs.iecr.0c04485
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(45)
, 20838-20846. https://doi.org/10.1021/acs.iecr.9b04771
- André
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(20)
, 8856-8870. https://doi.org/10.1021/acs.iecr.9b00817
- Caleb
J. Sisco, Mohammed I. L. Abutaqiya, Francisco M. Vargas, Walter G. Chapman. Cubic-Plus-Chain (CPC). I: A Statistical Associating Fluid Theory-Based Chain Modification to the Cubic Equation of State for Large Nonpolar Molecules. Industrial & Engineering Chemistry Research 2019, 58
(17)
, 7341-7351. https://doi.org/10.1021/acs.iecr.9b00435
- Denise
S. Leal, Marcelo Embiruçu, Gloria M. N. Costa, Karen V. Pontes. Prediction of Thermodynamic Properties of CO2 by Cubic and Multiparameter Equations of State for Fluid Dynamics Applications. Journal of Chemical & Engineering Data 2019, 64
(4)
, 1746-1759. https://doi.org/10.1021/acs.jced.8b01238
- André
M. Palma, António J. Queimada, João A.
P. Coutinho. Modeling of the Mixture Critical Locus with a Modified Cubic Plus Association (CPA) EoS: Aromatics, Ketones, Ethers, Diethyl Carbonate, and THF. Industrial & Engineering Chemistry Research 2018, 57
(46)
, 15857-15868. https://doi.org/10.1021/acs.iecr.8b03657
- Wenying Zhao, Xiaoyan Sun, Li Xia, Shuguang Xiang. Research into the Polynomial Alpha Function for the Cubic Equation of State. Industrial & Engineering Chemistry Research 2018, 57
(38)
, 12602-12623. https://doi.org/10.1021/acs.iecr.8b02549
- André
M. Palma, António J. Queimada, João A.
P. Coutinho. Modeling of the Mixture Critical Locus with a Modified Cubic Plus Association Equation of State: Water, Alkanols, Amines, and Alkanes. Industrial & Engineering Chemistry Research 2018, 57
(31)
, 10649-10662. https://doi.org/10.1021/acs.iecr.8b01960
- André M. Palma, António J. Queimada, and João A. P. Coutinho . Improved Prediction of Water Properties and Phase Equilibria with a Modified Cubic Plus Association Equation of State. Industrial & Engineering Chemistry Research 2017, 56
(51)
, 15163-15176. https://doi.org/10.1021/acs.iecr.7b03522
- André F. Young, Fernando L. P. Pessoa, and Victor R. R. Ahón . Comparison of 20 Alpha Functions Applied in the Peng–Robinson Equation of State for Vapor Pressure Estimation. Industrial & Engineering Chemistry Research 2016, 55
(22)
, 6506-6516. https://doi.org/10.1021/acs.iecr.6b00721
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(9)
, 2865-2871. https://doi.org/10.1021/je500496y
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(24)
, 14175-14185. https://doi.org/10.1021/ie201952n
- Ilya Polishuk . Hybridizing SAFT and Cubic EOS: What Can Be Achieved?. Industrial & Engineering Chemistry Research 2011, 50
(7)
, 4183-4198. https://doi.org/10.1021/ie102420n
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(14)
, 6901-6903. https://doi.org/10.1021/ie900275w
- Ilya Polishuk. Novel Four-Parameter EOS with Temperature-Independent Parameters. Industrial & Engineering Chemistry Research 2007, 46
(26)
, 9248-9256. https://doi.org/10.1021/ie070799o
- Fèlix Llovell and, Lourdes F. Vega. Prediction of Thermodynamic Derivative Properties of Pure Fluids through the Soft-SAFT Equation of State. The Journal of Physical Chemistry B 2006, 110
(23)
, 11427-11437. https://doi.org/10.1021/jp0608022
- Kh. Nasrifar and, O. Bolland, , M. Moshfeghian. Predicting Natural Gas Dew Points from 15 Equations of State. Energy & Fuels 2005, 19
(2)
, 561-572. https://doi.org/10.1021/ef0498465
- Ilya Polishuk and, Juan H. Vera. A Novel Equation of State for the Prediction of Thermodynamic Properties of Fluids. The Journal of Physical Chemistry B 2005, 109
(12)
, 5977-5984. https://doi.org/10.1021/jp046025s
- Kh. Nasrifar and, O. Bolland. Square-Well Potential and a New α Function for the Soave−Redlich−Kwong Equation of State. Industrial & Engineering Chemistry Research 2004, 43
(21)
, 6901-6909. https://doi.org/10.1021/ie049545i
- Ilya Polishuk,, Jaime Wisniak, and, Hugo Segura. Estimation of Liquid−Liquid−Vapor Equilibria in Binary Mixtures of n-Alkanes. Industrial & Engineering Chemistry Research 2004, 43
(18)
, 5957-5964. https://doi.org/10.1021/ie049797j
- Ulrich K. Deiters, Thomas Kraska. Equations of state for pure fluids. 2024, 247-286. https://doi.org/10.1016/B978-0-44-313280-3.00016-3
- . References. 2024, 429-447. https://doi.org/10.1016/B978-0-44-313280-3.00023-0
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(18)
https://doi.org/10.1063/5.0146634
- Pradnya N.P. Ghoderao, Mohan Narayan, Vishwanath H. Dalvi, Hun Soo Byun. Patel-Teja cubic equation of state – A review of modifications and applications till 2022. Fluid Phase Equilibria 2023, 567 , 113707. https://doi.org/10.1016/j.fluid.2022.113707
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- Yunhao Sun, Zhida Zuo, Aatto Laaksonen, Xiaohua Lu, Xiaoyan Ji. How to detect possible pitfalls in ePC-SAFT modelling: Extension to ionic liquids. Fluid Phase Equilibria 2020, 519 , 112641. https://doi.org/10.1016/j.fluid.2020.112641
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- Kaiqiang Zhang, Na Jia, Lirong Liu. Nanoscale-extended alpha functions for pure and mixing confined fluids. Fluid Phase Equilibria 2019, 482 , 64-80. https://doi.org/10.1016/j.fluid.2018.10.018
- Fufang Yang, Qiang Liu, Yuanyuan Duan, Zhen Yang. On the temperature dependence of the α function in the cubic equation of state. Chemical Engineering Science 2018, 192 , 565-575. https://doi.org/10.1016/j.ces.2018.08.014
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- M.A. Ahmadi, A. Bahadori. Retrograde Gas Condensate. 2017, 333-404. https://doi.org/10.1016/B978-0-12-803437-8.00007-5
- Luis A. Forero G, Jorge A. Velásquez J. A generalized cubic equation of state for non-polar and polar substances. Fluid Phase Equilibria 2016, 418 , 74-87. https://doi.org/10.1016/j.fluid.2015.09.045
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(4)
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- José Matías Garrido, Manuel M. Piñeiro, Andrés Mejía, Felipe J. Blas. Understanding the interfacial behavior in isopycnic Lennard-Jones mixtures by computer simulations. Physical Chemistry Chemical Physics 2016, 18
(2)
, 1114-1124. https://doi.org/10.1039/C5CP06562C
- Mirosław Chorążewski, Karel Aim, Ivan Wichterle, Johan Jacquemin, Ilya Polishuk. High-pressure phase equilibrium in the {carbon dioxide (1) + 1-chloropropane (2)} binary system. The Journal of Chemical Thermodynamics 2015, 91 , 165-171. https://doi.org/10.1016/j.jct.2015.07.039
- Romain Privat, Maxime Visconte, Anis Zazoua-Khames, Jean-Noël Jaubert, Rafiqul Gani. Analysis and prediction of the alpha-function parameters used in cubic equations of state. Chemical Engineering Science 2015, 126 , 584-603. https://doi.org/10.1016/j.ces.2014.12.040
- José Matías Garrido, Héctor Quinteros-Lama, Manuel M. Piñeiro, Andrés Mejía, Hugo Segura. On the phase and interface behavior along the three-phase line of ternary Lennard-Jones mixtures: A collaborative approach based on square gradient theory and molecular dynamics simulations. The Journal of Chemical Physics 2014, 141
(1)
https://doi.org/10.1063/1.4885348
- G. Pisoni, M. Cismondi, L. Cardozo-Filho, M.S. Zabaloy. Critical end line topologies for ternary systems. The Journal of Supercritical Fluids 2014, 89 , 33-47. https://doi.org/10.1016/j.supflu.2014.01.014
- Luis A. Forero G., Jorge A. Velásquez J.. A modified Patel–Teja cubic equation of state. Part II: Parameters for polar substances and its mixtures. Fluid Phase Equilibria 2014, 364 , 75-87. https://doi.org/10.1016/j.fluid.2013.12.009
- Ulrich K. Deiters. Comments on the modeling of hydrogen and hydrogen-containing mixtures with cubic equations of state. Fluid Phase Equilibria 2013, 352 , 93-96. https://doi.org/10.1016/j.fluid.2013.05.032
- Luis A. Forero G., Jorge A. Velásquez J.. A modified Patel–Teja cubic equation of state: Part I – Generalized model for gases and hydrocarbons. Fluid Phase Equilibria 2013, 342 , 8-22. https://doi.org/10.1016/j.fluid.2012.12.032
- N. Bender, P. B. Staudt, R. P. Soares, N. S. M. Cardozo. Performance of predictive models in phase equilibria of complex associating systems: PC-SAFT and CEOS/GE. Brazilian Journal of Chemical Engineering 2013, 30
(1)
, 75-82. https://doi.org/10.1590/S0104-66322013000100009
- María José Tardón, José Matías Garrido, Héctor Quinteros-Lama, Andrés Mejía, Hugo Segura. Molar isopycnicity in heterogeneous binary mixtures. Fluid Phase Equilibria 2012, 336 , 84-97. https://doi.org/10.1016/j.fluid.2012.07.034
- Luis A. Forero G., Jorge A. Velásquez J.. The Patel–Teja and the Peng–Robinson EoSs performance when Soave alpha function is replaced by an exponential function. Fluid Phase Equilibria 2012, 332 , 55-76. https://doi.org/10.1016/j.fluid.2012.05.026
- José Matías Garrido, Héctor Quinteros-Lama, Andrés Mejía, Jaime Wisniak, Hugo Segura. A rigorous approach for predicting the slope and curvature of the temperature–entropy saturation boundary of pure fluids. Energy 2012, 45
(1)
, 888-899. https://doi.org/10.1016/j.energy.2012.06.073
- Romain Privat, Elisa Conte, Jean-Noël Jaubert, Rafiqul Gani. Are safe results obtained when SAFT equations are applied to ordinary chemicals? Part 2: Study of solid–liquid equilibria in binary systems. Fluid Phase Equilibria 2012, 318 , 61-76. https://doi.org/10.1016/j.fluid.2012.01.013
- Mauricio E. Flores, María José Tardón, Christian Bidart, Andrés Mejía, Hugo Segura. A topological approach to mass barotropic phenomena in asymmetric mixtures. Fluid Phase Equilibria 2012, 313 , 171-181. https://doi.org/10.1016/j.fluid.2011.09.030
- Ilya Polishuk. Addressing the issue of numerical pitfalls characteristic for SAFT EOS models. Fluid Phase Equilibria 2011, 301
(1)
, 123-129. https://doi.org/10.1016/j.fluid.2010.11.021
- Dan Vladimir Nichita, Claude F. Leibovici. Parametric construction of characteristic curves. Fluid Phase Equilibria 2011, 300
(1-2)
, 83-88. https://doi.org/10.1016/j.fluid.2010.10.017
- Ilya Polishuk, Angel Mulero. The numerical challenges of SAFT EoS models. Reviews in Chemical Engineering 2011, 27
(5-6)
https://doi.org/10.1515/REVCE.2011.009
- Tiziana Fornari, Pilar Luna, Roumiana P. Stateva. The vdW EoS hundred years later, yet younger than before. Application to the phase equilibria modeling of food-type systems for a green technology. The Journal of Supercritical Fluids 2010, 55
(2)
, 579-593. https://doi.org/10.1016/j.supflu.2010.10.021
- Ilya Polishuk. About the numerical pitfalls characteristic for SAFT EOS models. Fluid Phase Equilibria 2010, 298
(1)
, 67-74. https://doi.org/10.1016/j.fluid.2010.07.003
- Romain Privat, Rafiqul Gani, Jean-Noël Jaubert. Are safe results obtained when the PC-SAFT equation of state is applied to ordinary pure chemicals?. Fluid Phase Equilibria 2010, 295
(1)
, 76-92. https://doi.org/10.1016/j.fluid.2010.03.041
- Vladimir Kalikhman, Daniel Kost, Ilya Polishuk. About the physical validity of attaching the repulsive terms of analytical EOS models by temperature dependencies. Fluid Phase Equilibria 2010, 293
(2)
, 164-167. https://doi.org/10.1016/j.fluid.2010.03.003
- F. Abdollahi-Demneh, M.A. Moosavian, M.M. Montazer-Rahmati, M.R. Omidkhah, H. Bahmaniar. Comparison of the prediction power of 23 generalized equations of state: Part II — Parametric evaluation. Fluid Phase Equilibria 2010, 291
(1)
, 48-58. https://doi.org/10.1016/j.fluid.2009.12.017
- Ilya Polishuk, Maxim Katz, Nicolay Pavlov. Prediction of phase equilibria in the systems carbon dioxide (1)–fatty acids (2) by two cubic EOS models and classical mixing rules without binary adjustable parameters. Fluid Phase Equilibria 2010, 289
(1)
, 90-93. https://doi.org/10.1016/j.fluid.2009.11.021
- Evelyne Neau, Otilio Hernández-Garduza, Joan Escandell, Christophe Nicolas, Isabelle Raspo. The Soave, Twu and Boston–Mathias alpha functions in cubic equations of state. Fluid Phase Equilibria 2009, 276
(2)
, 87-93. https://doi.org/10.1016/j.fluid.2008.09.023
- Romain Privat, Jean-Noël Jaubert, Fabrice Mutelet. Addition of the sulfhydryl group (–SH) to the PPR78 model (predictive 1978, Peng–Robinson EOS with temperature dependent kij calculated through a group contribution method). The Journal of Chemical Thermodynamics 2008, 40
(9)
, 1331-1341. https://doi.org/10.1016/j.jct.2008.05.013
- M. Rabiei Faradonbeh, A. Bahramian, R. Masoudi. A New Approach to Improve the Phase Behavior of Supercritical Hydrocarbons Using PR EOS. 2008https://doi.org/10.2118/114567-MS
- Hugo Segura, Diego Seiltgens, Andrés Mejía, Félix Llovell, Lourdes F. Vega. An accurate direct technique for parameterizing cubic equations of state. Fluid Phase Equilibria 2008, 265
(1-2)
, 66-83. https://doi.org/10.1016/j.fluid.2008.01.003
- Hugo Segura, Diego Seiltgens, Andrés Mejía, Félix Llovell, Lourdes F. Vega. An accurate direct technique for parameterizing cubic equations of state. Fluid Phase Equilibria 2008, 265
(1-2)
, 155-172. https://doi.org/10.1016/j.fluid.2008.01.013
- O. Chouaieb, A. Bellagi. New Attraction Term for the Soave‐Redlich‐Kwong Equation of State. The Canadian Journal of Chemical Engineering 2007, 85
(6)
, 854-862. https://doi.org/10.1002/cjce.5450850606
- Marcelo F. Alfradique, Marcelo Castier. Critical points of hydrocarbon mixtures with the Peng–Robinson, SAFT, and PC-SAFT equations of state. Fluid Phase Equilibria 2007, 257
(1)
, 78-101. https://doi.org/10.1016/j.fluid.2007.05.012
- Claude F. Leibovici, Dan Vladimir Nichita. PARAMETRIC GENERATION OF SINGLE-PHASE PROPERTIES (P-T CURVES) FOR MOST CUBIC EQUATIONS OF STATE AND ANY MIXING RULES. Chemical Engineering Communications 2007, 194
(5)
, 648-655. https://doi.org/10.1080/00986440600992768
- Dan Vladimir Nichita, Claude F. Leibovici. Calculation of Joule–Thomson inversion curves for two-phase mixtures. Fluid Phase Equilibria 2006, 246
(1-2)
, 167-176. https://doi.org/10.1016/j.fluid.2006.05.025
- Leonid Yelash, Marcus Müller, Wolfgang Paul, Kurt Binder. A global investigation of phase equilibria using the perturbed-chain statistical-associating-fluid-theory approach. The Journal of Chemical Physics 2005, 123
(1)
https://doi.org/10.1063/1.1948374
- Martín Cismondi, Jørgen Mollerup. Development and application of a three-parameter RK–PR equation of state. Fluid Phase Equilibria 2005, 232
(1-2)
, 74-89. https://doi.org/10.1016/j.fluid.2005.03.020
- Ming-Chung Wang, David Shan-Hill Wong. Calculation of critical lines of hydrocarbon/water systems by extrapolating mixing rules fitted to subcritical equilibrium data. Fluid Phase Equilibria 2005, 227
(2)
, 183-196. https://doi.org/10.1016/j.fluid.2004.11.012
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