Abstract
Equations of state (EoSs) have always been one the most interesting field of study for scientists and engineers, due to their extensive applications in various industries and scientific research. Accordingly, scientists have extensively studied useful modifications of the original EoSs. In this study, the temperature dependent part of the Peng–Robinson cubic equation of state is modified. The new dual parameter α-function is able reproduce the vapor pressure data accurately for a large variety of pure components. Mono-atomic and di-atomic molecules, hydrocarbons, polar and associating compounds are well represented by the Peng–Robinson–Saali equation of state with negligible deviation with experimental data. Moreover, the thermodynamic consistency test of P–T–x solubility data based on the fundamental Gibbs–Duhem equation, for binary mixtures including acid gases (CO2 and H2S)/polar and associating solvents at low and high pressure were also investigated. The proposed EoS coupled with a three-parameter binary interaction term, namely the Panagiotopoulos–Reid mixing rule, was used in order to present the PR–Saali EoS as a versatile equation for analyzing thermodynamic consistency of experimental data. Modeling processes were carried out by using MATLAB 2018a.
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References
Chapman, W.G., Gubbins, K.E., Jackson, G., Radosz, M.: SAFT: equation-of-state solution model for associating fluids. Fluid Phase Equilib. 52, 31–38 (1989)
van der Waals, J.D.: On the continuity of the gaseous and liquid states. Doctoral dissertation. Universiteit Leiden (1873)
Soave, G.: Equilibrium constants from a modified Redlich–Kwong equation of state. Chem. Eng. Sci. 27, 1197–1203 (1972)
Robinson, D.B., Peng D.Y.: The characterization of the heptanes and heavier fractions for the gpa peng-robinson programs, research report (Gas Processors Association). Gas Processors Association (1978)
Stryjek, R., Vera, J.H.: PRSV: an improved Peng–Robinson equation of state for pure compounds and mixtures. Can. J. Chem. Eng. 64, 560–570 (1986)
Yokozeki, A.: Solubility of refrigerants in various lubricants. Int. J. Thermophys. 22, 1057–1071 (2001)
Kud, A., Korkel, S., Maixner, S.: A cubic equation of state based on saturated vapor modeling and the application of model-based design of experiments for its validation. Chem. Eng. Sci. 65, 4194–4207 (2010)
Gasem, K.A.M., Gao, W., Pan, Z., Robinson, R.L., Jr.: A modified temperature dependence for the Peng–Robinson equation of state. Fluid Phase Equilib. 25, 113–125 (2001)
Mathias, P.M., Copeman, T.W.: Extension of the Peng–Robinson equation of state to complex mixtures: evaluation of the various forms of the local composition concept. Fluid Phase Equilib. 13, 91–108 (1983)
Kwak, T.Y., Mansoori, G.A.: Van der Waals mixing rules for cubic equations of state. Applications for supercritical fluid extraction modelling. Chem. Eng. Sci. 41, 1303–1309 (1986)
Melhem, G., Saini, A.R., Goodwin, B.M.: A modified Peng–Robinson equation of state. Fluid Phase Equilib. 47, 189–237 (1989)
Søreide, I., Whitson, C.H.: Peng-Robinson predictions for hydrocarbons, CO2, N2, and H2S with pure water and NaCl brine. Fluid Phase Equilib. 77, 217–240 (1992)
Fotouh, K., Shukla, K.: An improved Peng–Robinson equation of state with a new temperature dependent attractive term. Chem. Eng. Commun. 159, 209–229 (1997)
Floter, E.T., De Loos, W., de Swaan Arons, J.: Improved modeling of the phase behavior of asymmetric hydrocarbon mixtures with the Peng−Robinson equation of state using a different temperature dependency of the parameter a. Ind. Eng. Chem. Res. 37, 1651–1662 (1998)
Tsai, J.C., Chen, Y.P.: Application of a volume-translated Peng–Robinson equation of state on vapor–liquid equilibrium calculations. Fluid Phase Equilib. 145, 193–215 (1998)
Catano-Barrera, A.M., Figueira, F.L., Olivera-Fuentes, C., Colina, C.M.: Correlation and prediction of fluid–fluid equilibria of carbon dioxide–aromatics and carbon dioxide–dichlorobenzoates binary mixtures. Fluid Phase Equilib. 311, 45–53 (2011)
Faradonbeh, M.R., Bahramian, A., Masoudi, R.: In: CIPC/SPE Gas Technology Symposium 2008 Joint Conference, Society of Petroleum Engineers, pp.1–11 (2008)
Valiollahi, S., Kavianpour, B., Raeissi, S., Moshfeghian, M.: A new Peng–Robinson modification to enhance dew point estimations of natural gases. J. Nat. Gas Sci. Eng. 34, 1137–1147 (2016)
Van der Stelta, T.P., Nannan, N.R., Colonna, P.: The iPRSV equation of state. Fluid Phase Equilib. 330, 24–35 (2012)
Kaviani, S., Feyzi, F., Khosravi, B.: Modification of the Peng–Robinson equation of state for helium in low temperature regions. Fluid Phase Equilib. 54, 542–551 (2016)
Hosseinifar, P., Jamshidi, S.: An evolved cubic equation of state with a new attractive term. Fluid Phase Equilib. 408, 58–71 (2016)
NIST Scientific and Technical Databases, Thermophysical Properties of Fluid Systems. https://webbook.nist.gov/chemistry/fluid/. Accessed Dec 2018
Dortmund Data Bank Software and Separation Technology. http://www.ddbst.com/free-data.html. Accessed Dec 2018
Gross, J., Sadowski, G.: Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules. Ind. Eng. Chem. Res. 40, 1244–1260 (2001)
Panagiotopoulos, A.Z., Reid, R.C.: New mixing rule for cubic equations of state for highly polar, asymmetric systems. ACS Symp. Ser. 300, 571–582 (1986)
Valderrama, J.O., Faúndez, C.A.: Thermodynamic consistency test of high pressure gas–liquid equilibrium data including both phases. Thermochim. Acta 499, 85–90 (2010)
Eslamimanesh, A., Mohammadi, A.H., Richon, D.: Thermodynamic consistency test for experimental data of sulfur content of hydrogen sulfide. Ind. Eng. Chem. Res. 50, 3555–3563 (2011)
Mashayekhi, M., Sakhaeinia, H., Shokouhi, M.: Analysis of thermodynamic consistency behavior of CO2 solubility in some associating solvents. Int. J. Thermophys. 41, 1–28 (2020)
Valderrama, J.O., Sanga, W.W., Lazzus, J.A.: Critical properties, normal boiling temperature, and acentric factor of another 200 ionic liquids. Ind. Eng. Chem. Res. 47, 1318–1330 (2007)
Saali, A., Shokouhi, M., Sakhaeinia, H., Kazemi, N.: Thermodynamic consistency test of vapor–liquid equilibrium data of binary systems including carbon dioxide (CO2) and ionic liquids using generic Redlich–Kwong equation of state. J. Solution Chem. 49, 383–404 (2020)
Valderrama, J.O., Zavaleta, J.: Thermodynamic consistency test for high pressure gas solid solubility data of binary mixtures using genetic algorithms. J. Supercrit. Fluids 39, 20–29 (2006)
Valderrama, J.O., Alvarez, V.H.: A versatile thermodynamic consistency test for incomplete phase equilibrium data of high-pressure gas–liquid mixtures. Fluid Phase Equilib. 226, 149–159 (2004)
Brunner, E., Hultenschmidt, W., Schlichtharle, G.: Fluid mixtures at high pressures IV. Isothermal phase equilibria in binary mixtures consisting of (methanol + hydrogen or nitrogen or methane or carbon monoxide or carbon dioxide). J. Chem. Thermodyn. 19, 273–291 (1987)
Smith, J.M., Van Ness, H.C., Abbott, M.M.: Introduction to Chemical Engineering Thermodynamics, 6th edn. McGraw-Hill, New York (2003)
Gui, X., Tang, Z.G., Fei, W.: Solubility of CO2 in alcohols, glycols, ethers, and ketones at high pressures from (288.15 to 318.15) K. J. Chem. Eng. Data 56, 2420–2429 (2011)
Jalili, A.H., Shokouhi, M., Samani, F., Hosseini-Jenab, M.: Measuring the solubility of CO2 and H2S in sulfolane and the density and viscosity of saturated liquid binary mixtures of (sulfolane + CO2) and (sulfolane + H2S). J. Chem. Thermodyn. 85, 13–25 (2015)
Chang, C.J., Day, C.Y., Ko, C.M., Chiu, K.L.: Densities and P-x-y diagrams for carbon dioxide dissolution in methanol, ethanol, and acetone mixtures. Fluid Phase Equilib. 131, 243–258 (1997)
Ohgaki, K., Katayama, T.: Isothermal vapor–liquid equilibrium data for binary systems containing carbon dioxide at high pressures: methanol–carbon dioxide, n-hexane–carbon dioxide, and benzene–carbon dioxide systems. J. Chem. Eng. Data 21, 53–55 (1976)
Joung, S.N., Yoo, C.W., Shin, H.Y., Kim, S.Y., Yoo, K.P., Lee, C.S., Huh, W.S.: Measurements and correlation of high-pressure VLE of binary CO2–alcohol systems (methanol, ethanol, 2-methoxyethanol and 2-ethoxyethanol). Fluid Phase Equilib. 185, 219–223 (2001)
Zheng, D.Q., Ma, W.D., Wei, R., Guo, T.M.: Solubility study of methane, carbon dioxide and nitrogen in ethylene glycol at elevated temperatures and pressures. Fluid Phase Equilib. 155, 277–286 (1999)
Chapoy, A., Mohammadi, A.H., Tohidi, B.: Experimental measurement and phase behavior modeling of hydrogen sulfide–water binary system. Ind. Eng. Chem. Res. 44, 7567–7574 (2005)
Shokouhi, M., Rezaierad, A.R., Zekordi, S.M., Abbasghorbani, M., Vahidi, M.: Solubility of hydrogen sulfide in ethanediol, 1,2-propanediol, 1-propanol, and 2-propanol: experimental measurement and modeling. J. Chem. Eng. Data 61, 512–524 (2016)
Yau, J.S., Tsal, F.N.: Solubility of carbon dioxide in phenol and in catechol. J. Chem. Eng. Data 37, 141–143 (1992)
Mak, P.C.: Thermodynamic Properties from Cubic Equations of State. M. Sci., University of British Columbia (1988)
Mohamed, R.S., Holder, G.D.: High pressure phase behavior in systems containing CO2 and heavier compounds with similar vapor pressures. Fluid Phase Equilib. 32, 295–317 (1987)
Sugie, H., Iwahori, Y., Lu, B.C.: On the application of cubic equations of state: Analytical expression for α/Tr and improved liquid density. Fluid Phase Equilib. 50, 1–20 (1989)
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Saali, A., Sakhaeinia, H. & Shokouhi, M. Modification of Peng–Robinson Cubic Equation of State with Correction of the Temperature Dependency Term. J Solution Chem 50, 402–426 (2021). https://doi.org/10.1007/s10953-021-01065-8
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DOI: https://doi.org/10.1007/s10953-021-01065-8