Prediction of the thermodynamic properties for <italic style="font-style: italic">ortho</italic>-, <italic style="font-style: italic">para</italic>-and normal hydrogen using an equation of state with quantum effects for square-well chain fluid with variable range

Jia Yuqian; Hu Song; Li Jiashu; Liu Yingjie; Ye Qing; Li Jinlong

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Prediction of the thermodynamic properties for ortho-, para-and normal hydrogen using an equation of state with quantum effects for square-well chain fluid with variable range

Updated：2026-08-24

- Prediction of the thermodynamic properties for ortho-, para-and normal hydrogen using an equation of state with quantum effects for square-well chain fluid with variable range
- Prediction of the thermodynamic properties for ortho-, para-and normal hydrogen using an equation of state with quantum effects for square-well chain fluid with variable range
- 中国化学工程学报（英文） 2026年94卷第6期页码：232-248
- Affiliations：
  
  Jiangsu Key Laboratory of Advanced Catalytic Materials and Technology and School of Petrochemical Engineering, Changzhou University, Changzhou 213164, China
  PetroChina Petrochemical Research Institute, Beijing 102206, China
- Author bio：
  
  Corresponding authors. E-mail addresses: husong024@petrochina.com.cn(S. Hu)
  lijinlong@cczu.edu.cn(J. Li)
- Funds：
  
  the National Natural Science Foundation of China(22078026;21878025;22178030)
- DOI：
  中图分类号：
- 收稿：2025-08-17，
  
  修回：2025-12-17，
  
  录用：2025-12-23，
  
  网络首发：2026-03-07，
  
  纸质出版：2026-06
- Accepted：
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Jia Yuqian, Hu Song, Li Jiashu, 等. Prediction of the thermodynamic properties for ortho-, para-and normal hydrogen using an equation of state with quantum effects for square-well chain fluid with variable range[J]. 中国化学工程学报（英文）, 2026,94(6):232-248.

Jia Yuqian, Hu Song, Li Jiashu, et al. Prediction of the thermodynamic properties for ortho-, para-and normal hydrogen using an equation of state with quantum effects for square-well chain fluid with variable range[J]. Chinese Journal of Chemical Engineering, 2026, 94(6): 232-248.
Jia Yuqian, Hu Song, Li Jiashu, 等. Prediction of the thermodynamic properties for ortho-, para-and normal hydrogen using an equation of state with quantum effects for square-well chain fluid with variable range[J]. 中国化学工程学报（英文）, 2026,94(6):232-248. DOI：

Jia Yuqian, Hu Song, Li Jiashu, et al. Prediction of the thermodynamic properties for ortho-, para-and normal hydrogen using an equation of state with quantum effects for square-well chain fluid with variable range[J]. Chinese Journal of Chemical Engineering, 2026, 94(6): 232-248. DOI：

摘要

Abstract

The use of hydrogen as an energy carrier depends closely on its thermodynamic properties. In our previous work

a novel equation of state with quantum effects for square-well chain fluid with variable range (QSWCF-VR) has been presented and it was successfully used to represent the experimental phase equilibrium and pressure-volume-temperature (PVT) of quantum fluids such as helium

hydrogen

deuterium

etc

. To validate the predictive accuracy of the QSWCF-VR model

we calculated various thermodynamic properties (phase diagrams

isochoric and isobaric heat capacities

Joule-Thomson coefficients

speed of sound

enthalpy of evaporation

and internal energies) for

ortho

para

and normal hydrogen isomers over a broad range of temperatures and pressures. These predictions were based on transferable molecular parameters derived from experimental PVT data. Meanwhile

the comparisons of predicted results between the statistical associating fluid theory for Mie potentials of variable range corrected for quantum effects (SAFT-VRQ Mie) and this model were carried out. The results demonstrate that theQSWCF-VRmodel accurately predicts hydrogen's thermodynamic properties across a broad range of temperatures and pressures

with excellent agreement to published data.

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Keywords

references

M.L. Yue, H. Lambert, E. Pahon, R. Roche, S. Jemei, D. Hissel, Hydrogen energy systems: a critical review of technologies, applications, trends and challenges, Renew. Sustain. Energy Rev. 146 (2021) 111180.

T.T. Le, P. Sharma, B.J. Bora, V.D. Tran, T.H. Truong, H.C. Le, P.Q.P. Nguyen, Fueling the future: a comprehensive review of hydrogen energy systems and their challenges, Int. J. Hydrogen Energy 54 (2024) 791-816.

International Energy Agency, Prospects for Hydrogen and Fuel Cells, OECD, 2005, https://doi.org/10.1787/9789264109582-en.

M.A. Ifticene, K.J. Yan, Q.W. Yuan, Governing chemical reactions and mechanisms of hydrogen generation during in-situ combustion gasification of heavy oil, Int. J. Hydrogen Energy 92 (2024) 37-46.

M.Y. Wang, L. Fei, J.W. Wang, Y.P. Yuan, J.Z. Zhou, Experimental investigation on the electrical and hydrogen-production performance of a novel PEM electrolyzer driven by CdTe PV with a tracking system, Int. J. Hydrogen Energy 92 (2024) 482-493.

W.B. Tang, J. Shen, Z.J. Shen, J.W. Wang, Z.Z. Dong, J.L. Xu, H.F. Liu, Reaction kinetics and product evolution of hydrolysis in copper-chlorine thermochemical cycle for hydrogen production, Int. J. Hydrogen Energy 92 (2024) 409-418.

J.Q. Li, Y. Chen, Y.B. Ma, J.T. Kwon, H. Xu, J.C. Li, A study on the Joule-Thomson effect of during filling hydrogen in high pressure tank, Case Stud. Therm. Eng. 41 (2023) 102678.

A.K. Aadhithiyan, R. Sreeraj, S. Anbarasu, Multi-objective optimization and absorption prediction of complete 3-D design modeled MmNi 4.6 Al 0.4 based hydrogen storage reactor, Int. J. Hydrogen Energy 87 (2024) 641-656.

Y. Ye, Z.Y. Zhang, Y.W. Ma, Y.Y. Zhang, J.J. Liu, K. Yan, H.H. Cheng, Performance optimization of hydrogen storage reactors based on PCM coupled with heat transfer fins or metal foams, Int. J. Hydrogen Energy 92 (2024) 392-400.

S. Dahri, A. Jabar, L. Bahmad, L.B. Drissi, R.A. Laamara, First principles investigation of structural, elastic, thermoelectric, electronic and optical properties XH3 (X=Ac, La) for hydrogen storage, Int. J. Hydrogen Energy 92 (2024) 147-156.

M.P. Sukhorukov, Y.A. Kremzukov, A.N. Puchkov, A.G. Yudintsev, V.M. Rulevskiy, Experimental studies of using the digital control system in power conversion equipment of high-voltage power supply systems in spacecrafts with a hydrogen energy accumulator, Int. J. Hydrogen Energy 48 (86) (2023) 33644-33655.

P. Mojaver, S. Khalilarya, Sustainable waste-to-hydrogen energy conversion through face mask waste gasification integrated with steam methane reformer and water-gas shift reactor, Int. J. Hydrogen Energy 85 (2024) 947-961.

A. Ahmad, E. Oko, A. Ibhadon, Comparative energy and exergy analysis of ortho-para hydrogen and non-ortho-para hydrogen conversion in hydrogen liquefaction, Int. J. Hydrogen Energy 78 (2024) 991-1003.

T.T. Zhang, J. Uratani, Y.X. Huang, L.J. Xu, S. Griffiths, Y.L. Ding, Hydrogen liquefaction and storage: recent progress and perspectives, Renew. Sustain. Energy Rev. 176 (2023) 113204.

A. Ahmad, S.G. Nnabuife, E. Oko, A. Ibhadon, Comprehensive review of advances and challenges in hydrogen liquefaction, Sustain. Times 6 (2025) 100192.

P. Xu, J. Wen, K. Li, S.M. Wang, Y.Z. Li, Review of the continuous catalytic ortho-para hydrogen conversion technology for hydrogen liquefaction, Int. J. Hydrogen Energy 62 (2024) 473-487.

I. Veza, Fuel-cell thermal management strategies for enhanced performance:review of fuel-cell thermal management in proton-exchange membrane fuel cells (PEMFCs) and solid-oxide fuel cells (SOFCs), Hydrogen 6 (3) (2025) 65.

S.C. Gao, F. Ju, W.C. Zhuang, Q. Wang, Y.H. Zong, L.M. Wang, Cooperative energy management and fuel cell thermal management of fuel cell hybrid electric buses via multi-agent reinforcement learning, Energy 337 (2025) 138534.

B.A. Younglove, Thermophysical Properties of Fluids. 1: Argon, Ethylene, Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen, American Chemical Society, New York, N.Y,1982.

B. Younglove, Interactive Fortran Program to Calculate Thermophysical Properties of Six Fluids, 0 ed., National Bureau of Standards, Gaithersburg, MD, 1982, https://doi.org/10.6028/NBS.TN.1048.

R.T. Jacobsen, J.W. Leachman, S.G. Penoncello, E.W. Lemmon, Current status of thermodynamic properties of hydrogen, Int. J. Thermophys. 28 (3) (2007) 758-772.

J.W. Leachman, R.T. Jacobsen, S.G. Penoncello, E.W. Lemmon, Fundamental equations of state for parahydrogen, normal hydrogen, and orthohydrogen, J. Phys. Chem. Ref. Data 38 (3) (2009) 721-748.

K. Nasrifar, Comparative study of eleven equations of state in predicting the thermodynamic properties of hydrogen, Int. J. Hydrogen Energy 35 (8) (2010) 3802-3811.

A. Aasen, M. Hammer, S. Lasala, J.N. Jaubert, Ø. Wilhelmsen, Accurate quantum-corrected cubic equations of state for helium, neon, hydrogen, deuterium and their mixtures, Fluid Phase Equilib. 524 (2020) 112790.

A. Alanazi, M. Ali, S. Bawazeer, N. Yekeen, H. Hoteit, Evaluation of cubic, PC-SAFT, and GERG2008 equations of state for accurate calculations of thermophysical properties of hydrogen-blend mixtures, Energy Rep. 8 (2022) 13876-13899.

J. Gross, G. Sadowski, Perturbed-chain SAFT: an equation of state based on a perturbation theory for chain mole cules, Ind. Eng. Chem. Res. 40 (4) (2001) 1244-1260.

O. Kunz, W. Wagner, The GERG-2008 wide-range equation of state for natural gases and other mixtures: an expansion of GERG-2004, J. Chem. Eng. Data 57 (11) (2012) 3032-3091.

J. Schwartzentruber, H. Renon, Extension of UNIFAC to high pressures and temperatures by the use of a cubic equation of state, Ind. Eng. Chem. Res. 28 (7) (1989) 1049-1055.

V.M. Trejos, A. Gil-Villegas, Semiclassical approach to model quantum fluids using the statistical associating fluid theory for systems with potentials of variable range, J. Chem. Phys. 136 (18) (2012) 184506.

A. Aasen, M. Hammer, Å. Ervik, E.A. Müller, Ø. Wilhelmsen, Equation of state and force fields for Feynman-Hibbs-corrected Mie fluids. I. Application to pure helium, neon, hydrogen, and deuterium, J. Chem. Phys. 151 (6) (2019) 064508.

A. Aasen, M. Hammer, E.A. Müller, Ø. Wilhelmsen, Equation of state and force fields for Feynman-Hibbs-corrected Mie fluids. II. Application to mixtures of helium, neon, hydrogen, and deuterium, J. Chem. Phys. 152 (7) (2020) 074507.

J.L. Li, H.H. He, C.J. Peng, H.L. Liu, Y. Hu, A new development of equation of state for square-well chain-like molecules with variable width 1.1≤ λ ≤3, Fluid Phase Equilib. 276 (1) (2009) 57-68.

J.L. Li, H.H. He, C.J. Peng, H.L. Liu, Y. Hu, Equation of state for square-well chain molecules with variable range. I: application for pure substances, Fluid Phase Equilib. 286 (1) (2009) 8-16.

J.L. Li, M. Tong, C.J. Peng, H.L. Liu, Y. Hu, Equation of state for square-well chain molecules with variable range II. Extension to mixtures, Fluid Phase Equilib. 287 (1) (2009) 50-61.

J.S. Li, S.L. Wang, Q.C. He, Q. Ye, J.L. Li, Equation of state with quantum effects for square-well chain fluid with variable range, Sci. Sin.-Chim. 54 (7) (2024) 1135-1142.

N.F. Carnahan, K.E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51 (2) (1969) 635-636.

C. Serna, A. Gil-Villegas, Molecular thermodynamics of quantum square-well fluids using a path-integral perturbation theory, Mol. Phys. 114 (18) (2016) 2700-2716.

J.A. Barker, D. Henderson, Perturbation theory and equation of state for fluids: the square-well potential, J. Chem. Phys. 47 (8) (1967) 2856-2861.

I. Anoune, Z. Mimoune, H. Madani, A. Merzougui, New modified PC-SAFT pure component parameters for accurate VLE and critical phenomena description, Fluid Phase Equilib. 532 (2021) 112916.

Z. Mimoune, I. Anoune, H. Madani, Implementation of PC-SAFT for predicting thermodynamic properties of pure refrigerants and vapor-liquid equilibria of refrigerants binary mixtures, Fluid Phase Equilib. 573 (2023) 113868.

A. Pakravesh, F. Zarei, H. Zarei, PρT parameterization of SAFT equation of state: developing a new parameterization method for equations of state, Fluid Phase Equilib. 538 (2021) 113024.

T. Lafitte, A. Apostolakou, C. Avendaño, A. Galindo, C.S. Adjiman, E.A. Müller, G. Jackson, Accurate statistical associating fluid theory for chain molecules formed from Mie segments, J. Chem. Phys. 139 (15) (2013) 154504.

T. Lafitte, D. Bessieres, M.M. Piñeiro, J.L. Daridon, Simultaneous estimation of phase behavior and second-derivative properties using the statistical associating fluid theory with variable range approach, J. Chem. Phys. 124 (2) (2006) 024509.

T. Lafitte, M.M. Piñeiro, J.L. Daridon, D. Bessières, A comprehensive description of chemical association effects on second derivative properties of alcohols through a SAFT-VR approach, J. Phys. Chem. B 111 (13) (2007) 3447-3461.

T. Lafitte, F. Plantier, M.M. Piñeiro, J.L. Daridon, D. Bessières, Accurate global thermophysical characterization of hydrofluoroethers through a statistical associating fluid theory variable range approach, based on new experimental high-pressure volumetric and acoustic data, Ind. Eng. Chem. Res. 46 (21) (2007) 6998-7007.

Y.W. Pang, N. Hu, Z.W. Ding, Q.S. Li, Evaluation of volume translation models inPC-SAFT EoS for carbon dioxide, Fluid Phase Equilib. 584 (2024) 114145.

M.J. Assael, J.A.M. Assael, M.L. Huber, R.A. Perkins, Y. Takata, Correlation of the thermal conductivity of normal and parahydrogen from the triple point to 1000 K and up to 100 MPa, J. Phys. Chem. Ref. Data 40 (3) (2011) 033101.

Parahydrogen Orthohydrogen, Heavy hydrogen, Nature 135 (1935) 601-602.

N. Sakoda, K. Shindo, K. Shinzato, M. Kohno, Y. Takata, M. Fujii, Review of the thermodynamic properties of hydrogen based on existing equations of state, Int. J. Thermophys. 31 (2) (2010) 276-296.

P.J. Linstrom, W.G. Mallard, The NIST chemistry WebBook: a chemical data resource on the internet, J. Chem. Eng. Data 46 (5) (2001) 1059-1063.

Ø. Wilhelmsen, A. Aasen, G. Skaugen, P. Aursand, A. Austegard, E. Aursand, M. A. Gjennestad, H. Lund, G. Linga, M. Hammer, Thermodynamic modeling with equations of state: present challenges with established methods, Ind. Eng. Chem. Res. 56 (13) (2017) 3503-3515.

A.J. de Villiers, C.E. Schwarz, A.J. Burger, G.M. Kontogeorgis, Evaluation of the PC-SAFT, SAFTand CPA equations of state in predicting derivative properties of selected non-polar and hydrogen-bonding compounds, Fluid Phase Equilib. 338 (2013) 1-15.

N.I. Diamantonis, I.G. Economou, Evaluation of statistical associating fluid theory (SAFT) and perturbed chain-SAFT equations of state for the calculation of thermodynamic derivative properties of fluids related to carbon capture and sequestration, Energy Fuel. 25 (7) (2011) 3334-3343.

G.L. Shen, C. Held, X.H. Lu, X.Y. Ji, Modeling thermodynamic derivative properties of ionic liquids with ePC-SAFT, Fluid Phase Equilib. 405 (2015) 73-82.

S.S. Ashrafmansouri, Modeling the density and the second-order thermodynamic derivative properties of imidazolium-, cyano-based ionic liquids using the SAFT-γ EoS, Fluid Phase Equilib. 548 (2021) 113190.

H. Quinteros-Lama, F. Llovell, Global phase behaviour in carbon dioxide plus n-alkanes binary mixtures, J. Supercrit. Fluids 140 (2018) 147-158.

G.M. Kontogeorgis, M.L. Michelsen, G.K. Folas, S. Derawi, N. von Solms, E.H. Stenby, Ten years with the CPA (cubic-plus-association) equation of state. part 1. pure compounds and self-associating systems, Ind. Eng. Chem. Res. 45 (14) (2006) 4855-4868.

X.X. Yang, Viscosity and thermal conductivity models of 151 common fluids based on residual entropy scaling and cubic equations of state, ACS Omega 10 (6) (2025) 6124-6134.

C.Y. Zhu, X.Y. Liu, M.G. He, G.M. Kontogeorgis, X.D. Liang, Heat capacities of fluids: the performance of various equations of state, J. Chem. Eng. Data 65 (12) (2020) 5654-5676.

R.L. Gardas, J.A.P. Coutinho, A group contribution method for heat capacity estimation of ionic liquids, Ind. Eng. Chem. Res. 47 (15) (2008) 5751-5757.

J.O. Valderrama, A. Toro, R.E. Rojas, Prediction of the heat capacity of ionic liquids using the mass connectivity index and a group contribution method, J. Chem. Thermodyn. 43 (7) (2011) 1068-1073.

F.O. Cedeño, M.M. Prieto, J. Xiberta, Measurements and estimate of heat capacity for some pure fatty acids and their binary and ternary mixtures, J. Chem. Eng. Data 45 (1) (2000) 64-69.

K. Anand, R.P. Sharma, P.S. Mehta, A comprehensive approach for estimating thermo-physical properties of biodiesel fuels, Appl. Therm. Eng. 31 (2-3) (2011) 235-242.

N. Tarom, M.M. Hossain, A. Rohi, A new practical method to evaluate the Joule-Thomson coefficient for natural gases, J. Pet. Explor. Prod. Technol. 8 (4) (2018) 1169-1181.

M.X. Li, Y.F. Bai, C.Z. Zhang, Y.X. Song, S.F. Jiang, D. Grouset, M.J. Zhang, Review on the research of hydrogen storage system fast refueling in fuel cell vehicle, Int. J. Hydrogen Energy 44 (21) (2019) 10677-10693.

X.D. Liang, B. Maribo-Mogensen, K. Thomsen, W. Yan, G.M. Kontogeorgis, Approach to improve speed of sound calculation within PC-SAFT framework, Ind. Eng. Chem. Res. 51 (45) (2012) 14903-14914.

F. Llovell, C.J. Peters, L.F. Vega, Second-order thermodynamic derivative properties of selected mixtures by the soft-SAFT equation of state, Fluid Phase Equilib. 248 (2) (2006) 115-122.

D.H. Yu, Z. Chen, A theoretical analysis on enthalpy of vaporization:Temperature-dependence and singularity at the critical state, Fluid Phase Equilib. 516 (2020) 112611.

M.F. Gord, M. Roozbahani, H.R. Rahbari, S.J.H. Hosseini, Modeling thermodynamic properties of natural gas mixtures using perturbed-chain statistical associating fluid theory, Russ. J. Appl. Chem. 86 (6) (2013) 867-878.

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Prediction of the thermodynamic properties for ortho-, para-and normal hydrogen using an equation of state with quantum effects for square-well chain fluid with variable range

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摘要

Abstract

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