Helmholtz Equation of State for Thermodynamic Properties of Isobutane with Comprehensive Assessment

Koemleng Kan¹ , I Made Astina²

1. National Polytechnic Institute of Cambodia, Phnom Penh, Cambodia.
2. Faculty of Mechanical and Aerospace Engineering, Institut Teknologi Bandung, Bandung, Indonesia.

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.5 , pp.26-36, May-2024

Online published on May 31, 2024

Copyright © Koemleng Kan, I Made Astina . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Isobutane is a very interesting hydrocarbon for implementation as a working fluid besides fuel. Thermodynamic properties of isobutane (R-600a) play an important role in analysis and design. Accuracy and reliability of these properties play an important role in the quality of analysis and design results. Helmholtz equation of state for R-600a was developed using a genetic algorithm combined with weighted least square regression. The assessments cover intermolecular potential behavior, extrapolation behavior, and ideal curve characteristics besides deviations concerning experimental data. Deviation distribution was assessed using visualization, as well as statistical interpretation. The average absolute deviation over different data sources is estimated at 0.18% for liquid density, 0.81% for gas density, 0.16% for saturated-liquid density, 0.59% for saturated-vapor except at temperatures near the critical point, and 0.46% at vapor pressure. Meanwhile, the caloric properties have also been evaluated for the average absolute deviation, namely 0.06% for the ideal gas isobaric specific heat, 1.82% for isobaric and isochoric specific heats, 0.018% for the gas phase sound speed, 1.25% for the liquid phase sound speed. This equation has validity from the triple point of 113.73 K up to 700 K with pressure up to 300 MPa.

Key-Words / Index Term :
thermodynamic properties; Helmholtz equation of state; isobutane, refrigerant.

References :
[1] Y. S. Lee, C. C. Su, “Experimental Studies of Isobutane (R600a) as the Refrigerant in Domestic Refrigeration System,” Applied Thermal Engineering, Vol.22, No.5, pp.507-519, 2002.
[2] C. C. Yu, T. P. Teng, “Retrofit Assessment of Refrigerator Using Hydrocarbon Refrigerants,” Applied Thermal Engineering, Vol.66, No.1-2, pp.507-518, 2014.
[3] M. M. Ahmadpour, M. A. Akhavan-Behabadi, B. Sajadi, A. Salehi-Kohestan, “Effect of Lubricating Oil on Condensation Characteristics of R600a inside a Horizontal U-shaped Tube: Experimental Study,” International Journal of Thermal Sciences, Vol.145, No.106007, 2019.
[4] M. M. Ahmadpour, M. A. Akhavan-Behabadi, “Experimental Investigation of Heat Transfer During Flow Condensation of HC-R600a based Nano-Refrigerant Inside a Horizontal U-shaped Tube,” International Journal of Thermal Sciences, Vol.146, No.106110, 2019.
[5] M. Mozafari, M. A. Akhavan-Behabadi, H. Qobadi-Ar, M. Fakoor-Pakdaman, “Condensation and Pressure Drop Characteristics of R600a in a Helical Tube-in-Tube Heat Exchanger at Different Inclination Angles,” Applied Thermal Engineering, Vol.90, pp.571-578, 2015.
[6] X. Jia, H. Wang, X. Wang, “Solubility Measurement, Modeling and Mixing Thermodynamic Properties of R1243zf and R600a in [BMIM][Ac],” The Journal of Chemical Thermdynamics, Vol.164, No.106637, 2022.
[7] B. A. Younglove, J. F. Ely, “Thermophysical Properties of Fluids. II. Methane, Ethane, Propane, Isobutane, and Normal Butane,” J. Phys. Chem. Ref. Data, Vol.16, pp.577-798, 1978.
[8] H. Miyamoto, K. Watanabe, “A Thermodynamic Property Model for Fluid-Phase Isobutane,” International Journal of Thermophysics, Vol.23, No.2, pp.459-475, 2002.
[9] S. Chan, I. M. Astina, P. S. Darmanto, H. Sato, “Helmholtz Equation of State for Wide-Fluid Phase Isobutane,” in Proceedings of the International Conference on Fluid and Thermal Energy Conversion 2006, Jakarta, 2006.
[10] D. Bücker, W. Wagner, “Reference Equations of State for the Thermodynamic Properties of Fluid Phase n-Butane and Isobutane,” J. Phys. Chem. Ref. Data, Vol.35, pp.929-1019, 2006.
[11] R. A. Perkins, J. W. Magee, “Molar Heat Capacity at Constant Volume for Isobutane at Temperatures from (114 to 345) K and at Pressures to 35 MPa,” J. Chem. Eng. Data, Vol.54, pp.2646-2655, 2009.
[12] Q. Liu, X. Feng, K. Zhang, B. An., Y. Duan, “Vapor Pressure and Gaseous Speed of Sound Measurements for Isobutane (R600a),” Fluid phase Equilibria, Vol.382, pp.260-269, 2014.
[13] Y. Liu, X. Zhao, S. Lv, “Heat Capacity of Isobutane in Liquid Phase at Temperatures from 303 K to 413 K and Pressures up to 12 MPa,” J. Chem. Thermodynamics, Vol.111, pp.265-270, 2017.
[14] A. E. Hawary, K. Meier, “Speed-of-Sound Measurements and Derived Thermodynamic Properties of Liquid Isobutane,” J. Chem. Eng. Data, Vol.63, pp.3684-3703, 2018.
[15] P. J. Mohr, D. B. Newell, B. Taylor, “CODATA recommended values of the fundamental physical constants,” Review of Modern Physics, Vol.88, pp.1-73, 2016.
[16] I. M. Astina, H. I. Alfisahri, “New Thermodynamic Equation of State for Refrigerant HFO-1243zf,” International Journal of Thermodynamics, Vol.26, No. 4, pp.19-30, 2023.
[17] I. M. Astina, H. Sato, “A Rapid Genetic Optimization Technique for Rational Thermodynamic Modeling Having Reliable Third Virial Coefficients,” In Proceeding of International Conference of Thermophysics, Boulder, 2002.
[18] G. Budiarso, I. M. Astina, “Development of Helmholtz Equation of State for Thermodynamic Properties of R-1233zd(E),” International Journal of Scientific Research in Science and Technology, Vol.9, No.3, pp.765-776, 2022.
[19] Wikipedia, “Genetic algorithm,” Wikipedia, 20243. [Online]. Available: https://en.wikipedia.org/wiki/Genetic_algorithm. [Accessed 1 4 2024].
[20] S. Dubey, R. Jhaggar, R. Verma and D. Gaur, “Encryption and Decryption of Data by Genetic Algorithm,” International Journal of Scientific Research in Computer Science and Engineering, Vol.5, No.3, pp.42-46, 2017.
[21] A. Yadav, “An Improved Location-Based Genetic Algorithm for Routing in FANETs,” International Journal of Scientific Research in Computer Science and Engineering, Vol. 11, No. 2, pp. 23-30, 2023.
[22] K. Kan, I. M. Astina, P. S. Darmanto, “Simultaneous optimization of saturation equations for two hydrocarbons and four hydrofluoroolefins refrigerants,” In Proceeding of IOP Conference Series: Materials Science and Engineering, Vol. 715, No. 1, p. 012069, 2020.
[23] K. Kan, I. M. Astina, “Development of Thermodynamic Equation of State for Normal Butane with Comprehensive Assessment,” International Journal of Engineering Inventions, Vol. 12, No. 7, pp. 110-122, 2023.
[24] K. Kan, I. M. Astina, “Effective Strategy of Modeling Helmholtz Equation of state,” In Proceeding of the 10th AUN/SEED-Net Regional Conference on Mechanical Engineering and Manufacture Engineering, Phnom Penh, 2019.
[25] T. Ito, Y. Nagata, H. Miyamoto, “Measurement of the (p, ?, T) Properties for Pure Hydrocarbons at Temperatures up to 600 K and Pressures up to 200 MPa,” Int J. Thermophys, Vol. 35, pp. 1636-1646, 2013.
[26] H. Miyamoto, M. Uematsu, “Measurements of (p,v,T) properties for isobutane in the temperature range from 280 K to 440 K at pressures up to 200 MPa,” J. Chem. Thermodynamics, Vol. 36, pp. 360-366, 2006.
[27] Y. Kayukawa, M. Hasumoto, Y. Kano, K. Watanabe, “Liquid-Phase Thermodynamic Properties for Propane (1), n-Butane (2), and Isobutane (3),” J. Chem. Eng. Data, Vol. 50, pp. 556-564, 2005.
[28] S. Glos, R. Kleinrahm, W. Wagner, “Measurement of the (p, ?, T) Relation of Propane, Propylene, n-Butane, and Isobutane in the Temperature Range from (95 to 340) K at Pressure up to 12 MPa Using an Accurate Two-sinker Densimeter,” J. Chem. Thermodynnamics, Vol. 36, pp. 1037-1059, 2004.
[29] W. M. Haynes, “Measurements of Densities and Dielectric Constants of liquid Isobutane from 130 K to 300 K at Pressures to 35 MPa,” J. Chem. Thermodynamics, Vol. 28, No. 4, pp. 367-369, 1983.
[30] W. M. Morris, B. H. Sage, W. N. Lacey, “Tech. Publ. No. 1128,” Na. Bur. Stand., Boulder, 1939.
[31] B. H. Sage, W. N. Lacey, “Phase Equilibrium in Hydrocarbon Systems, Thermodynamic Properties of Isobutane,” Ind. Eng. Chem., Vol. 30, pp. 673-681, 1938.
[32] T. Hondo, Y. Kayukawa, K. Watanabe, “P?Tx Measurements for Gas-Phase Propane + Isobutane System by the Burnett Method,” In Proceeding of Asian Conf. Refrig. and Air Conditioning, Kobe, 2002.
[33] M. Waxman, J. S. Gallagher, “Thermodynamic Properties of Isobutane for Temperatures from 250 to 600 K and Pressures from 0.1 to 40 MPa,” J. Chem. Eng. Data, Vol. 28, No. 2, pp. 224-241, 1983.
[34] B. H. Sage, D. C. Webster, W. N. Lacey, “Phase Equilibrium in Hydrocarbon Systems. XX. Isobaric Heat Capacity of Gaseous Propane, n-Butane, Isobutane, and n-Butane,” Ind. Eng. Chem., Vol. 29, pp. 1309-1314, 1937.
[35] M. Waxman, H. A. Davis, J. M. H. Levelt Sengers and M. Klein, “Interagency Report NBSIR,” Natl. Bur. Stand., Boulder, 1978.
[36] J. E. Orrit, J. M. Lauprete, “Density of Liquefied Natural Gas Components,” Adv. Cryog. Engineering, Vol. 23, pp. 573-579, 1978.
[37] J. A. Beattie, J. S. Marple, D. G. Edwards, “The Vapor Pressure, Orthobaric Liquid Density, and Critical Constants of Isobutane,” J. Chem. Phys., Vol. 17, No. 6, pp. 576-577, 1949.
[38] W. M. Haynes, M. J. Hiza, “Measurements of the Orthobaric Liquid Densities of Methane, Ethane, Propane, Isobutane, and Butane,” J. Chem. Thermodyn., Vol. 9, pp. 179-187, 1977.
[39] C. R. McClune, “Measurement of the Densities of Liquefied Hydrocarbons from 93 to 173 K,” Cryogenics, Vol. 16, No. 5, pp. 289-295, 1976.
[40] L. C. Kahre, “Liquid Density of Light Hydrocarbon Mixtures,” J. Chem. Eng. Data, Vol. 18, No. 3, pp. 267-270, 1973.
[41] P. Sliwinski, “Die Lorentz-Lorenz-Funktion von Dampfförmigem und Flüssigem Äthan, Propan und Butan,” Z. Phys. Chem. Neue. Folge., Vol. 68, pp. 263-279, 1969.
[42] R. C. Wackher, C. B. Linn, A. V. Grosse, “Physical Properties of Butanes and Butenes,” Ind. Eng. Chem., Vol. 37, No. 5, pp. 464-468, 1945.
[43] R. W. Benoliel, “Some Physical Constants of Seven Four-Carbon-Atom Hydrocarbons and Neopentane,” M. S. Thesis, Penn. State Univ., Univ. Park, PA, 1941.
[44] Y. Higashi, “Critical Parameters for 2- Methylpropane (R600a),” J. Chem. Eng. Data, Vol. 51, No. 2, pp. 406-408, 2006.
[45] H. Miyamoto, J. Takemura, M. Uematsu, “Vapour Pressures of Isobutane at T= (310 to 407) K,” J. Chem. Thermodyn., Vol. 36, pp. 919-923, 2004.
[46] B. Y. Lee, J. Y. Park, J. S. Lim, Y. W. Lee, “Vapor-LiquidEquilibria for Isobutane Plus Pentafluoroethane (HFC-125) at 293.15 to 313.15 K and + 1,1,1,2,3,3,3-Heptafluoropropane (HFC-227ea) at 303.15 to 323.15 K,” J. Chem. Eng. Data, Vol. 45, No. 5, pp. 760-763, 2000.
[47] J. S. Lim, J. Y. Park, B. G. Lee, J. D. Kim, “Phase Equilibria of Chlorofluorocarbon Alternative Refrigerant Mixtures. Binary Systems of Trifluoromethane Plus Isobutane at 283.15 and 293.15 K and and 293.15 K and 1,1,1Trifluoroethane Plus Isobutane at 323.15 and 333.15 K,” J. Chem. Eng. Data, Vol. 45, No. 5, pp. 734-737, 2000.
[48] J. S. Lim, J. Y. Park, B. G. Lee, Y. W. Lee, J. D. Kim, “Phase Equilibria of CFC Alternative Refrigerant mixtures: Binary Systems of Isobutane + 1,1,1,2-Tetrafluoroethane + 1,1-Difluorethane, and Plus Difluoromethane,” J. Chem. Eng. Data, Vol. 44, No. 6, pp. 1226-1230, 1999.
[49] L. A. Weber, “Simple Apparatus for Vapor-Lipuid Equilibrium Measurements with Data for the Binary systems of Carbon Dioxide with n-Butane and Isobutane,” J. Chem. Eng. data, Vol.34, pp.171-175, 1989.
[50] L. A. Weber, “Vapour-Liquid Equilibria Measurements for Carbon Dioxide with Normal and Isobutane from 250 to 280 K,” Cryogenics, Vol.25, pp.338-342, 1985.
[51] J. A. Martinez-Ortiz and D. B. Manley, “Vapor Pressures for the System Isobutane-Isobutylene-n-Butane,” J. Chem. Eng. Data, Vol.23, No.2, pp.165-167, 1978.
[52] M. Hirata, S. Suda, “Light Hydrocarbon Vapor-Liquid Equilibria”. Mem. Fac.Technol. Tokyo Metrop. Univ., Vol.19, pp.103-122, 1969.
[53] H. Hipkin, “Experimental Vapor-Liquid Equilibrium Data for Propane-Isobutane,” AIChE J., Vol.12, no.3, pp.484-487, 1966.
[54] G. Ernst, J. Büsser, “Ideal and Real Gas State Heat Capacities CP of C3H8, i-C4H10, C2F5Cl, CH2ClCF3, CF2ClCFCl2, and CHF2Cl,” J. Chem. Thermodyn., Vol.2, pp.787-791, 1970.
[55] J. G. Aston, R. M. Kennedy, S. C. Schumann, “The Heat Capacity and Entropy, Heats of Fusion and Vaporization and the Vapor Pressure of Isobutane,” J. Am.Chem. Soc., Vol.62, pp.2059-2063, 1940.
[56] G. S. Parks, C. H. Shomate, W. D. Kennedy, B. L. J. Crawford, “The Entropies of n-Butane and Isobutane with Some Heat Capacity Data for Isobutane,” J. Chem. Phys., Vol.5, pp.359-363, 1937.
[57] G. S. Parks, C. H. Shomate, W. D. Kennedy, B. L. J. Crawford, “The Entropies of n-Butane and Isobutane with Some Heat Capacity Data for Isobutane,” J. Chem. Phys., Vol.5, pp.359-363, 1937.
[58] J. G. Aston, R. M. Kennedy, S. C. Schumann, “The Heat Capacity and Entropy, Heats of Fusion and Vaporization and the Vapor Pressure of Isobutane,” J. Am.Chem. Soc., Vol.62, pp.2059-2063, 1940.
[59] S. S. Chen, R. C. Wilhoit, B. J. Zwolinski, “Ideal Gas Thermodynamic Properties and Isomerization of n-Butane and Isobutane,” J. Phys. Chem. Ref. Data, Vol. 4, pp. 859-869, 1975.
[60] M. Jaeschke, P. Schley, “Ideal-Gas Thermodynamic Properties for Natural-Gas Applications,” Int. J. Thermophys., Vol.16, pp.1381-1392, 1995.
[61] M. B. Ewing, A. R. H. Goodwin, “Thermophysical Properties of Alkanes from Speeds of Sound Determined Using a Spherical Responator, 4, 2- Methylpropane at Temperatures in the Range 251K to 320K and Pressures in the Range 5 kPa to114 kPa,” J. Chem. Thermodyn., Vol.23, pp.1107-1120, 1991.