Refined Covolume Approach for Heavy Alkanes in Abel-Noble EOS at High Pressures

Year 2025, Issue: Erken Görünüm - Early Pub Issues, 1 - 10

Houcine Hachoum , Hatem Ksibi

Abstract

A novel formulation was developed to accurately model volume behavior at very high pressures for heavy n-alkanes, based on excluded volume theory. This approach is crucial as several cubic equations of state become inadequate at pressures exceeding several thousand bars. The covolume formulation was applied to the Abel-Noble equation of state (EoS) for real gases to accurately model the specific volume of linear long-chain alkanes. It adjusts the compression limit volume of these heavy alkanes by tuning a small dimensionless parameter, epsilon (), which establishes a numerical relationship between pressure and excluded volume. At high pressure (from 50 MPa), the molar specific volumes of various aliphatic alkanes (CnH2n+2) between 30 and 250 °C were carefully calculated. The proposed formulation was undoubtedly improved by comparing it with experimental data from many peer-reviewed studies, keeping a square error limit of 3% for heavy n-alkanes. Additionally, we notice that attempts to use the presented EoS for low-carbon number hydrocarbons seem unreliable until the fluid is set under very high pressure.

Keywords

covolume, n-alkanes, high pressure, Abel-Noble EoS.

Thanks

Thank you for considering my manuscript for peer review. I appreciate the opportunity to contribute to IJoT and look forward to any feedback from the reviewers. Please let me know if any additional information is required. Best regards,

References

• M. Mohsen-Nia, “A modified MMM EOS for high-pressure PVT calculations of heavy hydrocarbons,” Journal of Petroleum Science and Engineering, vol. 113, pp. 97–103, Jan. 2014, doi: 10.1016/j.petrol.2013.12.008.
• J. C. de Hemptine, P. Mougin, A. Barreau, L. Ruffine, S. Tamouza, and R. Inchekel, “Application to Petroleum Engineering of Statistical Thermodynamics – Based Equations of State,” Oil & Gas Science and Technology - Rev. IFP, vol. 61, no. 3, pp. 363–386, May 2006, doi: 10.2516/ogst:2006039a.
• J. Biet, M. H. Hakka, V. Warth, P.-A. Glaude, and F. Battin-Leclerc, “Experimental and Modeling Study of the Low-Temperature Oxidation of Large Alkanes,” Energy & Fuels, vol. 22, no. 4, pp. 2258–2269, May 2008, doi: 10.1021/ef8000746.
• A. B. Moussa and H. Ksibi, “Numerical Simulation of a One-Dimensional Shock Tube Problem at Supercritical Fluid Conditions,” International Journal of Fluid Mechanics Research, vol. 35, no. 1, pp. 38–50, Jan. 2008, doi:10.1615/interjfluidmechres.v35.i1.30.
• H. Hachoum and H. Ksibi, “On the Generation of an Intense Temperature Gradient Through a Modified Shock Tube Hydrodynamics for a Possible Continuous Sterilization Process,” Strojnícky časopis/Journal of Mechanical Engineering, vol. 72, no. 2, pp. 81–92, Nov. 2022, doi: 10.2478/scjme-2022-0018.
• G. Bikas and N. Peters, “Kinetic modelling of n-decane combustion and autoignition,” Combustion and Flame, vol. 126, no. 1–2, pp. 1456–1475, Jul. 2001, doi: 10.1016/s0010-2180(01)00254-1.
• A. I. Rusanov, “Equation of state theory based on excluded volume,” The Journal of Chemical Physics, vol. 118, no. 22, pp. 10157–10163, May 2003, doi: 10.1063/1.1572455.
• G. M. Kontogeorgis, R. Privat, and J.-N. Jaubert, “Taking Another Look at the van der Waals Equation of State–Almost 150 Years Later,” Journal of Chemical & Engineering Data, vol. 64, no. 11, pp. 4619–4637, Aug. 2019, doi: 10.1021/acs.jced.9b00264.
• K. Liu, Y. Wu, M. A. McHugh, Hseen Baled, R. M. Enick, and B. D. Morreale, “Equation of state modeling of high-pressure, high-temperature hydrocarbon density data,” The Journal of Supercritical Fluids, vol. 55, no. 2, pp. 701–711, Dec. 2010, doi: 10.1016/j.supflu.2010.10.004.
• H. Ksibi, “The Solvent-Solute Interaction in Supercritical Solution at Equilibrium: Modeling and Related Industrial Applications,” International Journal of Thermodynamics, vol. 7, no. 3, pp. 131–140, Sep. 2004, doi: 10.5541/ijot.1034000134.
• G. E. Lindberg, J. L. Baker, J. Hanley, W. M. Grundy, and C. King, “Density, Enthalpy of Vaporization and Local Structure of Neat N-Alkane Liquids,” Liquids, vol. 1, no. 1, pp. 47–59, Dec. 2021, doi: 10.3390/liquids1010004.
• C. Vega, L. G. MacDowell, and P. Padilla, “Equation of state for hard n-alkane models: Long chains,” The Journal of Chemical Physics, vol. 104, no. 2, pp. 701–713, Jan. 1996, doi: 10.1063/1.470867.
• H. Eslami, “A perturbed hard-sphere-chain equation of state: prediction from critical point constants,” Fluid Phase Equilibria, vol. 216, no. 1, pp. 21–26, Feb. 2004, doi: 10.1016/j.fluid.2003.09.002.
• R. A. Orwoll and P. J. Flory, “Equation- of-state parameters for normal alkanes. Correlation with chain length,” Journal of the American Chemical Society, vol. 89, no. 26, pp. 6814–6822, Dec. 1967, doi: 10.1021/ja01002a002.
• B. A. Bamgbade et al., “Measurements and modeling of high-temperature, high-pressure density for binary mixtures of propane with n-decane and propane with n-eicosane,” The Journal of Chemical Thermodynamics, vol. 84, pp. 108–117, May 2015, doi: 10.1016/j.jct.2014.12.015.
• P. Longwell, J. Olin, and B. Sage, “Covolumes for a Number of Common Gases.,” Industrial & Engineering Chemistry Chemical & Engineering Data Series, vol. 3, no. 2, pp. 175–180, Oct. 1958, doi: 10.1021/i460004a001.
• G. A. Arteca, “Interpretation of covolume in an extension of the Redlich–Kwong equation of state for real gases,” Journal of Mathematical Chemistry, vol. 61, no. 9, pp. 1967–1979, Aug. 2023, doi: 10.1007/s10910-023-01497-1.
• G.W.H. Höhne and K. Blankenhorn, “High pressure DSC investigations on n-alkanes, n-alkane mixtures and polyethylene,” Thermochimica acta, vol. 238, pp. 351–370, Jun. 1994, doi: 10.1016/s0040-6031(94)85219-7.
• J. J. B. Machado, Theo, E. Christian Ihmels, K. Fischer, and Jürgen Gmehling, “High pressure solid–solid and solid–liquid transition data for long chain alkanes,” The Journal of Chemical Thermodynamics, vol. 40, no. 12, pp. 1632–1637, Jul. 2008, doi: 10.1016/j.jct.2008.07.017.
• A. Kumar and R. Okuno, “Direct perturbation of the Peng–Robinson attraction and covolume parameters for reservoir fluid characterization,” Chemical Engineering Science, vol. 127, pp. 293–309, May 2015, doi: 10.1016/j.ces.2015.01.032.
• V. F. Baibuz, V. Yu. Zitserman, L. M. Golubushkin, and I. G. Malyshev, “The covolume and equation of state of high-temperature real gases,” Journal of Engineering Physics, vol. 51, no. 2, pp. 955–956, Aug. 1986, doi: 10.1007/bf00871197.
• A. Chiapolino and R. Saurel, “Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point,” Fluids, vol. 3, no. 3, p. 48, Jul. 2018, doi: 10.3390/fluids3030048.
• M. J. Anselme, M. Gude, and A. S. Teja, “The critical temperatures and densities of the n-alkanes from pentane to octadecane,” Fluid Phase Equilibria, vol. 57, no. 3, pp. 317–326, Jan. 1990, doi: 10.1016/0378-3812(90)85130-3.
• D. G. Friend, J. F. Ely, and H. Ingham, “Thermophysical Properties of Methane,” Journal of Physical and Chemical Reference Data, vol. 18, no. 2, pp. 583–638, Apr. 1989, doi: 10.1063/1.555828.
• B. A. Younglove and J. F. Ely, “Thermophysical Properties of Fluids. II. Methane, Ethane, Propane, Isobutane, and Normal Butane,” Journal of Physical and Chemical Reference Data, vol. 16, no. 4, pp. 577–798, Oct. 1987, doi: 10.1063/1.555785.
• R. D. Goodwin and W. M. Haynes, “Thermophysical properties of propane from 85 to 700 K at pressures to 70 MPa,” OSTI ID: 6402039, Jan. 1982, doi: 10.6028/nbs.mono.170.
• E. Kiran and Y. L. Sen, “High-pressure viscosity and density of n-alkanes,” International Journal of Thermophysics, vol. 13, no. 3, pp. 411–442, May 1992, doi: 10.1007/bf00503880.
• S. Glos, Reiner Kleinrahm, and W. Wagner, “Measurement of the (p,ρ,T) relation of propane, propylene, n-butane, and isobutane in the temperature range from (95 to 340) K at pressures up to 12 MPa using an accurate two-sinker densimeter,” The Journal of Chemical Thermodynamics, vol. 36, no. 12, pp. 1037–1059, Dec. 2004, doi: 10.1016/j.jct.2004.07.017.
• S. Herrmann and E. Vogel, “Viscosity and Density of Normal Butane Simultaneously Measured at Temperatures from (298 to 448) K and at Pressures up to 30 MPa Incorporating the Near-Critical Region,” Journal of Chemical & Engineering Data, vol. 60, no. 12, pp. 3703–3720, Oct. 2015, doi: 10.1021/acs.jced.5b00654.
• H.-S. Byun, T. P. DiNoia, and M. A. McHugh, “High-Pressure Densities of Ethane, Pentane, Pentane-d12, 25.5 wt Ethane in Pentane-d12, 2.4 wt Deuterated Poly(ethylene-co-butene) (PEB) in Ethane, 5.3 wt Hydrogenated PEB in Pentane, 5.1 wt Hydrogenated PEB in Pentane-d12, and 4.9 wt Hydrogenated PEB in Pentane-d12+ 23.1 wt Ethane,” Journal of Chemical & Engineering Data, vol. 45, no. 5, pp. 810–814, Sep. 2000, doi: 10.1021/je990308+.
• A. K. Doolittle, “Specific Volumes of n-Alkanes.,” Journal of Chemical & Engineering Data, vol. 9, no. 2, pp. 275–279, Apr. 1964, doi: 10.1021/je60021a048.
• D. R. Caudwell, M. Trusler, Velisa Vesovic, and W. A. Wakeham, “Viscosity and Density of Five Hydrocarbon Liquids at Pressures up to 200 MPa and Temperatures up to 473 K,” Journal of Chemical & Engineering Data, vol. 54, no. 2, pp. 359–366, Feb. 2009, doi: 10.1021/je800417q.
• J. H. Dymond, J. Robertson, and J.D Isdale, “(p, ϱ, T) of some pure n-alkanes and binary mixtures of n-alkanes in the range 298 to 373 K and 0.1 to 500 MPa,” The Journal of Chemical Thermodynamics, vol. 14, no. 1, pp. 51–59, Jan. 1982, doi: 10.1016/0021-9614(82)90123-9.
• T. S. Khasanshin, A. P. Shchamialiou, and O. G. Poddubskij, “Thermodynamic Properties of Heavy n-Alkanes in the Liquid State: n-Dodecane,” International Journal of Thermophysics, vol. 24, no. 5, pp. 1277–1289, Jan. 2003, doi: 10.1023/a:1026199017598.
• M. Kariznovi, H. Nourozieh, J. G. James) Guan, and J. Abedi, “Measurement and modeling of density and viscosity for mixtures of Athabasca bitumen and heavy n-alkane,” Fuel, vol. 112, pp. 83–95, Oct. 2013, doi: 10.1016/j.fuel.2013.04.071.
• Vlastimil Růžička, M. Zábranský, and V. Majer, “Heat capacities of organic compounds in liquid state II. C1 to C18 n-alkanes,” Journal of Physical and Chemical Reference Data, vol. 20, no. 2, pp. 405–444, Mar. 1991, doi: 10.1063/1.555883.
• M. Suceska, H.-G. Ang, and H. Y. Serene Chan, “Study of the Effect of Covolumes in BKW Equation of State on Detonation Properties of CHNO Explosives,” Propellants, Explosives, Pyrotechnics, vol. 38, no. 1, pp. 103–112, Nov. 2012, doi: 10.1002/prep.201100150.