Abstract
Based on the extended three-parameter corresponding-states principle and the most reliable experimental data of \(n\)-alkanes, a generalized fundamental equation of state for technical calculations has been developed. This equation is in the form of the reduced Helmholtz free energy and takes the reduced density, reduced temperature, and acentric factor as variables. The proposed equation satisfies the critical conditions and Maxwell rule, shows correct behavior for the ideal curves and for the derivatives of the thermodynamic potentials, and allows the calculation of all thermodynamic properties including phase equilibrium of \(n\)-alkanes from \(n\)-pentane \((\hbox {C}_{5})\) to \(n\)-pentacontane \((\hbox {C}_{50})\) over a temperature range from the triple point to 700 K with pressures up to 100 MPa. The new equation differs from the previous generalized equations of other authors by a wider range of variation of the acentric factor \(\omega =0.25\) to 1.8, and by more accurately predicting thermal properties.
Similar content being viewed by others
References
R. Span, Multiparameter Equation of State: An Accurate Source of Thermodynamic Property Data (Springer, Berlin, 2000)
O. Redlich, J.N.S. Kwong, Chem. Rev. 44, 233 (1949)
G.S. Soave, Chem. Eng. Sci. 27, 1197 (1972)
D.-Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fund. 15, 59 (1976)
A.I. Brusilovsky, Phase Transformations in Developing Oil and Gas (Graal, Moscow, 2002)
S.B. Kiselev, Ind. Eng. Chem. Res. 38, 4993 (1999)
P. Paricaud, A. Galindo, G. Jackson, Fluid Phase Equilib. 194, 87 (2002)
M. Benedict, G.B. Webb, L.C. Rubin, J. Chem. Phys. 8, 334 (1940)
S.M. Walas, Phase Equilibria in Chemical Engineering (Butterworth Publishers, Boston, 1989)
B.I. Lee, M.G. Kessler, AIChE J. 21, 510 (1975)
K.S. Pitzer, R.F. Curl, Ind. Eng. Chem. 50, 265 (1958)
B. Saager, R. Hennenberg, J. Fisher, Fluid Phase Equilib. 72, 41 (1992)
B. Saager, J. Fisher, Fluid Phase Equilib. 72, 67 (1992)
A. Muller, J. Winkelmann, J. Fisher, AIChE J. 42, 1116 (1996)
S. Calero, M. Wendland, J. Fisher, Fluid Phase Equilib. 152, 1 (1998)
B. Platzer, G. Maurer, Fluid Phase Equilib. 51, 223 (1989)
E. Bender, in Proceedings of 5th Symposium on Thermophysical Properties (American Society of Mechanical Engineers, New York, 1970), pp. 227–235
L. Sun, J.E. Ely, Fluid Phase Equilib. 222/223, 107 (2004)
E.W. Lemmon, A.R.H. Goodwin, J. Phys. Chem. Ref. Data 29, 1 (2000)
A.S. Teja, R.J. Lee, D. Rosenthal, M. Anselme, Fluid Phase Equilib. 56, 153 (1990)
E.W. Lemmon, M.L. Huber, Energy Fuels 18, 960 (2004)
B. Schmidt, Wiss. Zeitschr. Tech. Univ. Leuna-Merseburg 20, 506 (1978)
D.S. Kurumov, Thermal Properties of n-Alkanes and Fractions of Mangyshlak Oil in Liquid and Gaseous States (Dr. Sci. Thesis, Grozny Petroleum Institute, Russia, 1991)
A.A. Gerasimov, Caloric Properties Of Normal Alkanes and Multi-Component Hydrocarbon Mixtures in a Liquid and Gas Phases, Including a Critical Region (Thesis, Kaliningrad State Technical University, Russia, Dr. Sci, 2000)
I.S. Alexandrov, A.A. Gerasimov, E.B. Grigor’ev, Defense complex. Sci Tech Prog Russ 4, 56 (2010)
B.A. Grigor’ev, Thermophysical Properties of Oil, Oil Products, Gas Condensates and Fractions (Moscow Power Engineering Institute, Moscow, 1999)
P.A. Chmykhalo, DSSDD (Ukrainian State Standard) 7-2005: The Procedure for Calculating the Saturated Vapor Pressure of n-Alkanes \((\text{ C }_{1}{-}\text{ C }_{100})\) and Hydrogen on the Boiling Line (Derzhspozhivstandard Ukrainy, Kiev, 2005)
P.A. Chmykhalo, DSSDD (Ukrainian State Standard) 10-2006: The Procedure for Calculating the the Density of Liquid n-Alkanes \((\text{ C }_{1}{-}\text{ C }_{100})\) and Hydrogen on the Boiling Line (Derzhspozhivstandard Ukrainy, Kiev, 2006)
L. Sun, J.E. Ely, Int. J. Thermophys. 26, 705 (2005)
B.H. Sage, W.N. Lacey, Ind. Eng. Chem. 34, 730 (1942)
J.A. Beattie, S.W. Levine, D.R. Douslin, J. Am. Chem. Soc. 74, 4778 (1952)
K. Li, L.N. Canjar, Chem. Eng. Prog., Symp. Ser. 49, 147 (1953)
W.G.S. Scaife, C.G.R. Lyons, Proc. R. Soc. London 370, 193 (1980)
H. Kratzke, S. Muller, M. Bohn, R. Kohlen, J. Chem. Thermodyn. 17, 283 (1985)
B.A. Grigor’ev, D.S. Kurumov, I.M. Abdulagatov, YuL Vasilev. Teplofiz. Vys. Temp. 24, 1096 (1986)
E. Kiran, Y.L. Sen, Int. J. Thermophys. 13, 411 (1992)
H. Poehler, E. Kiran, J. Chem. Eng. Data 42, 389 (1997)
I.M. Abdulagatov, A.R. Bazaev, E.A. Bazaev, S.P. Khokhlachev, M.B. Saidakhmedova, A.E. Ramazanova, J. Sol. Chem. 27, 729 (1998)
B. Tohidi, R.W. Burgass, A. Danesh, A.C. J. Chem. Eng. Data 46, 385 (2001)
S. Young, Proc. Roy. Irish Acad. 38B, 65 (1928)
C.B. Willingham, W.J. Taylor, J.M. Pignocco, F.D. Rossini, J. Res. Natl. Bur. Stand. 35, 219 (1945)
E.R. Nicolini, Ann. Chim. 6, 582 (1951)
J.A. Beattie, S.W. Levine, D.R. Douslin, J. Am. Chem. Soc. 73, 4431 (1951)
D.A. Zanolini, Measurements of Vapor Pressures of Volatile Hydrocarbons (Masters Thesis, Pennsylvania State University, 1964)
D.R. Douslin, Proc. Div. Ref., Am. Petrol. Inst. 50, 189 (1970)
A.G. Osborn, D.R. Douslin, J. Chem. Eng. Data 19, 114 (1974)
C. Horner, A. Hopfner, B. Schmeiser, Ber. Bunsenges. Phys. Chem. 79, 222 (1975)
I.A. Hossenlopp, D.W. Scott, J. Chem. Thermodyn. 13, 415 (1981)
A. Olivares Fuentes, J. Suarez Cansino, A. Trejo Redriquez, Rev. Mex. Fis. 30, 63 (1983)
H.N. Maia de Oliveira, J. Chem. Eng. Data 47, 1384 (2002)
R.W. Dornte, C.P. Smyth, J. Am. Chem. Soc. 52, 3546 (1930)
B.R. Carney, Pet. Ref. 21, 84 (1942)
I.S. Alexandrov, Fundamental Equations of State of Petroleum Hydrocarbons (Ph.D. Thesis, Kaliningrad State Technical University, 2012)
C.D. Holcomb, J.W. Magee, W.M. Haynes, Density Measurements on Natural Gas Liquids (Gas Processors Association Research, Report RR-147, 1995)
V.A. Mirskaya, I.K. Kamilov, Fluid Phase Equilib. 125, 169 (1996)
I.M. Abdulagatov, Experimental Results for the Isochoric Heat Capacity of n-Heptane and n-Octane, private communication (National Institute of Standards and Technology, Boulder, Colorado, 1998)
KhI Amirkhanov, B.G. Alibekov, D.I. Vikhrov, V.A. Mirskaya, L.N. Levina. High Temp. 9, 1211 (1971)
G.H. Messerly, R.M. Kennedy, J. Am. Chem. Soc. 62, 2988 (1940)
J.F. Messerly, G.B. Guthrie, S.S. Todd, H.L. Finke, J. Chem. Eng. Data 12, 338 (1967)
E.G. Richardson, R.I. Tait, J. Philos. Mag. 2, 441 (1957)
A. Lainez, J.A. Zollweg, W.B. Streett, J. Chem. Thermodyn. 22, 937 (1990)
E.A. Kelso, W.A. Felsing, J. Am. Chem. Soc. 62, 3132 (1940)
J. Schaffenger, On the Nonideal Behavior of Some Hydrocarbons in the Vapor Phase (Ph.D. Thesis, Ruhr-Universitat Rostock, 1963)
D. Oeder, G.M. Schneider, Ber. Bunsenges. Phys. Chem. 74, 580 (1970)
B.A. Grigor’ev, D.S. Kurumov, Viniti Deposited, Publication (1981)
T. Moriyoshi, T. Aono, J. Chem. Thermodyn. 20, 185 (1988)
S.S. Susnar, C.J. Budziak, H.A. Hamza, A.W. Neumann, Int. J. Thermophys. 13, 443 (1992)
P. Sauermann, K. Holzapfel, J. Oprznski, F. Kohler, W. Poot, T.W. de Loos, Fluid Phase Equilib. 112, 249 (1995)
J.L. Daridon, B. Lagourette, J.-P.E. Grolier, Int. J. Thermophys. 19, 145 (1998)
I. Brown, Aust. J. Sci. Res. A5, 530 (1952)
I.P.-C. Li, B.C.-Y. Lu, E.C. Chen, J. Chem. Eng. Data 18, 305 (1973)
A.H.N. Mousa, J. Chem. Thermodyn. 9, 1063 (1977)
S.A. Wieczorek, J. Stecki, J. Chem. Thermodyn. 10, 177 (1978)
J.M. Genco, A.S. Teja, W.B. Kay, J. Chem. Eng. Data 25, 355 (1980)
T.W. de Loos, W. Poot, J. de Swaan Arons, Fluid Phase Equilib. 42, 209 (1988)
H.S. Wu, S.I. Sandler, J. Chem. Eng. Data 33, 157 (1988)
E. Bich, T. Lober, J. Millat, Fluid Phase Equilib. 75, 149 (1992)
R.L. Schmidt, J.C. Randall, H.L. Clever, J. Phys. Chem. 70, 3912 (1966)
M.S. Rozhnov, Khim. Prom. 43, 48 (1967)
G.H. Findenegg, Monatshefte Chem. 101, 1081 (1970)
E. Aicart, G. Tardajos, M. Diaz Pena, J. Chem. Eng. Data 25, 140 (1980)
J.H. Dymond, K.J. Young, Int. J. Thermophys. 1, 331 (1980)
C.-H. Yu, F.-N. Tsai, J. Chem. Eng. Data 40, 601 (1995)
B. Garcia, R. Alcalde, S. Aparicio, J.M. Leal, Ind. Eng. Chem. Res. 41, 4399 (2002)
H.M. Huffman, G.S. Parks, M. Barmore, J. Am. Chem. Soc. 53, 3876 (1931)
D.R. Douslin, H.M. Huffman, J. Am. Chem. Soc. 68, 1704 (1946)
G. Waddington, D.R. Douslin, J. Am. Chem. Soc. 69, 2275 (1947)
R. Paramo, M. Zouine, C. Casanova, J. Chem. Eng. Data 47, 441 (2002)
J.W.M. Boelhouwer, Physica 34, 484 (1967)
V.N. Verveiko, G.A. Melnikov, YaF Melikhov, Teplofizicheskiye svoystva veshchestv i materialov 30, 5 (1991)
T.S. Khasanshin, A.P. Shchemelev, High Temp. 39, 60 (2001)
S.J. Ball, J.P.M. Trusler, Int. J. Thermophys. 22, 427 (2001)
L.B. Smith, J.A. Beattie, W.C. Kay, J. Am. Chem. Soc. 59, 1587 (1937)
W.B. Nichols, H.H. Reamer, B.H. Sage, Ind. Eng. Chem. 47, 2219 (1955)
J.W.M. Boelhouwer, Physica 26, 1021 (1960)
A.K. Doolittle, J. Chem. Eng. Data 9, 275 (1964)
A.Z. Golik, I.I. Adamenko, M.G. Makhno, Fiz. Zhidk. Sostoyaniya 10, 3 (1982)
A. Zawisza, J. Vejrosta, J. Chem. Thermodyn. 14, 239 (1982)
M.J.P. Muringer, N.J. Trappeniers, S.N. Biswas, Phys. Chem. Liq. 14, 273 (1985)
S. Toscani, P. Figuiere, H. Szwarc, J. Chem. Thermodyn. 21, 1263 (1989)
E.R. Smith, J. Res. Natl. Bur. Stand. 24, 229 (1940)
A.F. Forziati, W.R. Norris, F.D. Rossini, J. Res. Natl. Bur. Stand. 43, 555 (1949)
L.A. Weber, J. Chem. Eng. Data 45, 173 (2000)
M.B. Ewing, J.C.S. Ochoa, J. Chem. Eng. Data 50, 1543 (2005)
P.M. Christopher, W.L.S. Laukhuf, C.A. Plank, J. Chem. Eng. Data 21, 443 (1976)
K. Stephan, H. Hildwein, Dechema 4, 1/2 (1987)
H. Kahl, T. Wadewitz, J. Winkelmann, J. Chem. Eng. Data 48, 580 (2003)
J.L. San Jose, G. Mellinger, R.C. Reid, J. Chem. Eng. Data 21, 414 (1976)
B. Kalinowska, J. Jedlinska, W. Woycicki, J. Stecki, J. Chem. Thermodyn. 12, 891 (1980)
M. Zabransky, V. Ruzicka Jr, J. Phys. Chem. Ref. Data 23, 55 (1994)
N.S. Osborne, D.C. Ginnings, J. Res. Nat. Bur. Stand. 39, 453 (1947)
L. Becker, O. Aufderhaar, J. Gmehling, J. Chem. Eng. Data 45, 661 (2000)
N.G. Polikhronidi, I.M. Abdulagatov, R.G. Batyrova, Fluid Phase Equilib. 201, 269 (2002)
R. Kling, E. Nicolini, J. Tissot, Rech. Aeronaut. 31, 31 (1953)
W.A. Felsing, G.M. Watson, J. Am. Chem. Soc. 64, 1822 (1942)
J.H. Dymond, J.D. Isdale, N.F. Glen, Fluid Phase Equilib. 20, 305 (1985)
T.S. Banipal, S.K. Garg, J.C. Ahluwalia, J. Chem. Thermodyn. 23, 923 (1991)
Y. Tanaka, H. Hosokawa, H. Kubota, T. Makita, Int. J. Thermophys. 12, 245 (1991)
A.R.H. Goodwin, C.H. Bradsell, L.S. Toczylkin, J. Chem. Thermodyn. 28, 637 (1996)
A.G.A. Badalyan, A.S. Keramidi, D.S. Kurumov, Izv. Vyssh. Uchebn. Zaved., Neft Gaz 29, 54 (1986)
P. Gierycz, J. Gregorowicz, S. Malanowski, J. Chem. Thermodyn. 20, 385 (1988)
A. Dejoz, V. Gonzalez-Alfaro, P.J. Miguel, M.I. Vazquez, J. Chem. Eng. Data 41, 93 (1996)
M.B. Ewing, J.C. Sanchez Ochoa, Fluid Phase Equilib. 210, 277 (2003)
T.R. Das, N.R. Kuloor, Indian J. Technol. 5, 51 (1967)
C.C. Chappelow, P.S. Snyder, J. Winnick, J. Chem. Eng. Data 16, 440 (1971)
J.F. Connolly, G.A. Kandalic, J. Chem. Eng. Data 7, 137 (1962)
H.L. Finke, M.E. Gross, G. Waddington, H.M. Huffman, J. Am. Chem. Soc. 76, 333 (1954)
T. Takagi, H. Teranishi, Fluid Phase Equilib. 20, 315 (1985)
Z.S. Ding, J. Alliez, C. Boned, P. Xans, Meas. Sci. Technol. 8, 154 (1997)
L.T. Carmichael, B.H. Sage, W.N. Lacey, Ind. Eng. Chem. 45, 2697 (1953)
J.D. White, F.W. Rose, J. Res. Natl. Bur. Stand. 7, 907 (1931)
H.-I. Paul, J. Krug, H. Knapp, Thermochim. Acta 108, 9 (1986)
J. Ortega, C. Gonzalez, S. Galvan, J. Chem. Eng. Data 46, 904 (2001)
T. Grindley, J.E. Lind Jr, J. Chem. Phys. 68, 5046 (1978)
T. Plebanski, M. Wozniak, K. Wilanowska, Nauchn. Appar. 1, 47 (1986)
H.I. Amirkhanov, Isochoric Heat Capacity and Other Caloric Properties of the Hydrocarbons of Methane Series (Makhachkala, Dagestan, 1981)
G.S. Parks, H.M. Huffman, S.A. Thomas, J. Am. Chem. Soc. 52, 1032 (1930)
C.A. Tovar, E. Carballo, C.A. Cerdeirina, J.L. Legido, L. Romani, Int. J. Thermophys. 18, 761 (1997)
B.S. Kiryakov, Acoustic and Elastic Properties of n-Paraffins at Pressures up to 2000 at (Ph.D. Thesis, Kursk State Pedagogical Institute, 1981)
S. Lago, P.A. Giuliano Albo, D. Madonna Ripa, Int. J. Thermophys. 27, 1083 (2006)
B.H. Sage, H.M. Lavender, W.N. Lacey, Ind. Eng. Chem. 32, 743 (1940)
H.H. Reamer, R.H. Olds, B.H. Sage, W.N. Lacey, Ind. Eng. Chem. 34, 1526 (1942)
P.S. Snyder, J. Winnick, in Proceedings of 5th Symposium on Thermophysical Properties, vol. 5 (American Society of Mechanical Engineers, New York, 1970), pp. 115–129
M. Gehrig, H. Lentz, J. Chem. Thermodyn. 15, 1159 (1983)
D.R. Caudwell, J.P.M. Trusler, V. Vesovic, W.A. Wakeham, Int. J. Thermophys. 25, 1339 (2004)
A. Zuniga-Moreno, L.A. Galicia-Luna, L.E. Camacho-Camacho, J. Chem. Eng. Data 50, 1030 (2005)
R.D. Chirico, A. Nguyen, W.V. Steele, M.M. Strube, J. Chem. Eng. Data 34, 149 (1989)
D.L. Morgan, R. Kobayashi, Fluid Phase Equilib. 97, 211 (1994)
E.C. Bingham, H.J. Fornwalt, J. Rheol. 1, 372 (1930)
J.H. Dymond, K.J. Young, Int. J. Thermophys. 2, 237 (1981)
J.A. Gates, R.H. Wood, J.C. Cobos, C. Casanova, A.H. Roux, G. Roux-Desgranges, J.P.E. Grolier, Fluid Phase Equilib. 27, 137 (1986)
J. Peleteiro, D. Gonzalez-Salgado, C.A. Cerdeirina, L. Romani, J. Chem. Thermodyn. 34, 485 (2002)
T.M. Aminabhavi, B. Gopalakrishna, J. Chem. Eng. Data 39, 529 (1994)
L.M. Casas, A. Tourino, B. Orge, G. Marino, M. Iglesias, J. Tojo, J. Chem. Eng. Data 47, 887 (2002)
R. Landau, A. Wuerflinger, Ber. Bunsen Ges. Phys. Chem. 84, 895 (1980)
D.L. Camin, F.D. Rossini, J. Phys. Chem. 59, 1173 (1955)
Anonymous, Properties of Hydrocarbons of High Molecular Weight (American Petroleum Institute Research Project 42, Pennsylvania State University, 1968)
A.I. Vogel, J. Chem. Soc. 146, 133 (1946)
M. Garcia, C. Rey, V.P. Villar, J.R. Rodriguez, J. Chem. Eng. Data 33, 46 (1988)
O.Z. Golik, I.I. Ivanova, Zh Fiz. Khim. 36, 1768 (1962)
Y.P. Melikhov, Ultrasound and Thermodynamic Properties of Substances (Kursk State Pedagogical Institute, Kursk, Russia, 1985)
F. Plantier, J.-L. Daridon, B. Lagourette, C. Boned, High Temp.-High Press. 32, 305 (2000)
W.G. Cutler, R.H. McMickle, W. Webb, R.W. Schlessler, J. Chem. Phys. 29, 727 (1958)
P. Gierycz, M. Rogalski, S. Malanowski, Fluid Phase Equilib. 22, 107 (1985)
D. Bessieres, H. Saint-Guirons, J.-L. Daridon, High Press. Res. 18, 279 (2000)
M.R. Fenske, W.G. Braun, R.V. Wiegand, D. Quiggle, R.H. McCormick, D.H. Rand, Ann. Chem. 19, 700 (1947)
C. Viton, M. Chavret, E. Behar, J. Jose, Int. Electron. J. Phys.-Chem. Data 2, 215 (1996)
R.W. Schiessler, C.H. Herr, A.W. Rytina, C.A. Weisel, F. Fischl, R.L. McLaughlin, H.H. Kuehner, Proc. Am. Pet. Inst., Sect. 3 26, 254 (1946)
J. Wu, Z. Shan, A.-F.A. Asfour, Fluid Phase Equilib. 143, 263 (1998)
J. Peleteiro, D. Gonzalez-Salgado, C.A. Cerdeirina, J.L. Valencia, L. Romani, Fluid Phase Equilib. 191, 83 (2001)
A.A. Gerasimov, I.S. Alexandrov, B.A. Grigor’ev, E.B. Grigor’ev, Defense Complex - Scientific and Technical Progress of Russia 1, 43 (2001)
P. Gouel, Bull. Cent. Rech. Explor.- Prod. Elf-Aquitaine 2, 211 (1978)
K. Holzapfel, G. Goetze, A.M. Demiriz, F. Kohler, Int. Data Ser., Sel. Data Mixtures, Ser. A 30,(1987)
E. Gawronska, L. Dordain, J.-Y. Coxam, J.R. Quint, J.-P. Grolier, J. Chem. Eng. Data 40, 1257 (1995)
P. Kneisl, J.W. Zondlo, J. Chem. Eng. Data 32, 11 (1987)
F. Krafft, Ber. Dtsch. Chem. Ges. 15, 1687 (1882)
G. Calingaert, H.A. Beatty, R.C. Kuder, G.W. Thoson, Ind. Eng. Chem. 33, 103 (1941)
V.V. Roshchupkin, Nek. Vopr. Fiz. Tekh. Yad. Reakt. 151, (1965)
J.L. Daridon, B. Lagourette, High Temp.-High Press. 32, 83 (2000)
J.M. Pardo, C.A. Tovar, D. Gonzalez, E. Carballo, L. Romani, J. Chem. Eng. Data 46, 212 (2001)
J.L. Daridon, H. Carrier, B. Lagourette, Ind. Eng. Chem. 23, 697 (2002)
S. Landa, J. Romovacek, H. Romovackova, Chem. Listy 49, 313 (1955)
P.M. Diaz Pena, G. Tardajos, J. Chem. Thermodyn. 10, 19 (1978)
J.H. Dymond, K.J. Young, J.D. Isdale, J. Chem. Thermodyn. 11, 887 (1979)
J.S. Chang, M.J. Lee, H.M. Lin, J. Chem. Eng. Data 43, 233 (1998)
P.L. Mills, R.L. Fento, J. Chem. Eng. Data 32, 266 (1987)
M.F. Grenier-Loustalot, M. Potin-Gautier, P. Grenier, Anal. Lett. 14, 1335 (1981)
R.W. Schiessler, The Synthesis and Properties of Hydrocarbons of High Molecular Weight, American Petroleum Institute Research Project 42 (1947)
H.S. Myers, M.R. Fenske, Ind. Eng. Chem. 47, 1652 (1955)
Buckland, W.F. Seyer, Personal Commun. Dec. 21 (1950)
P. Gray, P.L. Smith, J. Chem. Soc. 769, (1954)
J.F. Eykman, Recl. Trav. Chim. Pays-Bas 15, 52 (1986)
J.W.J. McKinney, Am. Chem. Soc. 46, 968 (1924)
L.T. Chu, C. Sindilariu, A. Freilich, V. Fried, Can. J. Chem. 64, 481 (1986)
K. Sasse, J. Jose, J.-C. Merlin, Fluid Phase Equilib. 42, 287 (1988)
J.B. Rodden, C. Erkey, A. Akgerman, J. Chem. Eng. Data 33, 344 (1988)
W.M. Mazee, Recl. Trav. Chim. 67, 197 (1948)
A.W. Schmidt, Ber. Dtsch. Chem. Ges. B75, 1399 (1942)
E.F. Meyer, K.S. Stec, J. Am. Chem. Soc. 93, 5451 (1971)
D.L. Wakefield, K.N. Marsh, Int. J. Thermophys. 8, 649 (1987)
H.I. Waterman, J.J. Leendertse, D.W. Van Krevelen, Rev. Pet. Technol. (London) 25, 801 (1939)
E.W. Lemmon, R. Span, J. Chem. Eng. Data 51, 785 (2006)
Acknowledgments
The authors would like to thank Dr. Eric W. Lemmon at the National Institute of Standards and Technology for his help in collecting experimental data and for his valuable comments. The authors are grateful to the Russian Foundation for Basic Research (RFBR) for financial support under Grant No. 09-08-00683a.
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix 1: Definitions of Common Thermodynamic Properties and their Relation to the reduced Helmholtz Energy
The functions used for calculating pressure \((p)\), compressibility factor \((Z)\), internal energy \((u)\), enthalpy \((h)\), entropy \((s)\), Gibbs energy \((g)\), isochoric heat capacity \((c_{v})\), isobaric heat capacity \((c_{p})\), Joule–Thomson coefficient (\(\mu \)), and the speed of sound \((w) \) from Eq. 1 are given below.
The fugacity coefficient and second and third virial coefficients are given in the following equations:
Other derived properties, given below, include the first derivative of pressure with respect to density at constant temperature \((\partial p/\partial \rho )_{T}\), the second derivative of pressure with respect to density at constant temperature \((\partial ^{2} p/\partial \rho ^{2})_{T}\), and the first derivative of pressure with respect to temperature at constant density \((\partial p/\partial T)_{\rho }\).
The derivatives of the residual Helmholtz energy are given in the following equations.
Appendix 2: Comparison of Thermodynamic Properties of Selected \(n\)-alkanes \((\hbox {C}_{7},\,\hbox {C}_{8},\,\hbox {C}_{10},\,\hbox {C}_{12})\) calculated by Individual Equations of State with the Generalized Fundamental Equation of State, Eq. 3
Rights and permissions
About this article
Cite this article
Alexandrov, I., Gerasimov, A. & Grigor’ev, B. Generalized Fundamental Equation of State for the Normal Alkanes \((\hbox {C}_{5}{-}\hbox {C}_{50})\) . Int J Thermophys 34, 1865–1905 (2013). https://doi.org/10.1007/s10765-013-1512-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10765-013-1512-1