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The Thermodynamic Properties of Non-Associating and Associating Fluids: A Systematic Evaluation of SAFT-Type Equations of State

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Abstract

Statistical Associating Fluid Theory (SAFT) equations of state (EoSs) have been extensively used for estimating thermodynamic properties of fluids. However, the predicted performance of SAFT-type EoSs for associating and non-associating fluids under the same thermodynamic conditions is poorly understood. In this work, four typical SAFT-type EoSs including the CPA, CK-SAFT, PC-SAFT, and SAFT-VR Mie EoSs are mainly employed and then a systematic evaluation is performed for the phase equilibria and derivative properties of the common non-associating (alkanes and carbon dioxide) and associating fluids (methanol and water). The results show that the misdescription of the residual Helmholtz free energy by SAFT-type EoSs is the major cause for the prediction accuracy of vapor–liquid equilibria (VLE). SAFT-VR Mie outperforms the others when predicting VLE of all the considered compounds, especially in conditions near the critical point, with an average absolute relative deviation (AARD) below 0.5%. PC-SAFT provides satisfactory enthalpy of vaporization (ΔHv) predictions of alkanes, but its performance is inferior to PR due to the inaccurate description of the liquid-phase ∂A/∂T derivatives. Adopting a reasonable association scheme or including the ΔHv experimental data into the parameter regression routine can effectively improve the predictions accuracy of ΔHv for associating fluids. Overall, SAFT-VR Mie performs the best performance in correlating isobaric heat capacity (CP) due to the improved description of the ∂2A/∂V∂T and ∂2A/∂V2 derivatives. Re-optimizing the universal constants of the dispersion term or employing higher-order perturbations can effectively improve the CP predictions.

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Abbreviations

AARD:

Average absolute relative deviation

CEoSs:

Cubic equations of state

CK-SAFT:

Chen and Kreglewski-SAFT

CPA:

Cubic-Plus-Association

EoSs:

Equations of state

NBP:

Normal boiling point

PC-SAFT:

Perturbed Chain-SAFT

PR:

Peng–Robinson

RK:

Redlich–Kwong

SAFT:

Statistical associating fluid theory

SAFT-VR Mie:

SAFT-Variable Range Mie

SRK:

Soave–Redlich–Kwong

vdW:

Van der Waals

VLE:

Vapor–liquid equilibria

A:

Helmholtz free energy, J·mol−1

CP :

Isobaric heat capacity, J·mol−1·K−1

N:

Number of data points

P:

Pressure, Pa

Ps :

Saturated pressure, Pa

R:

Universal gas constant, J·mol−1·K−1

T:

Temperature, K

V:

Volume, m3·mol−1

X:

Property used to calculate AARD in Eq. 6

XA i :

Fraction of A sites of molecule i that are not bonded

Z:

Compressibility factor

ρs :

Saturated liquid density, mol·m−3

ΔHv :

Enthalpy of vaporization, J·mol−1

a:

Energy parameter of cubic equations of state

b:

Co-volume parameter of cubic equations of state

g:

Radial distribution function

h:

Enthalpy, J·mol−1

k:

Boltzmann’s constant, J·K−1

m:

Segment number

ε :

Depth of pair potential, J

η :

Packing fraction

ρ :

Number density

σ :

Segment diameter, Å

ω :

Acentric factor

assoc:

Association contribution

c:

Critical

calc:

Calculated property

chain:

Contribution due to the formation of chains

disp:

Contribution due to the dispersive attraction

exp:

Experimental property

hs:

Contribution of hard-sphere system

i, j:

Component indexes

ideal:

Ideal gas contribution

mono:

Contribution of monomer system

pert:

Perturbed

r:

Reduced

ref:

Reference

res:

Residual

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Acknowledgements

Financial support from the National Natural Science Foundation of China under Grant No.51976040, Grant No. 51236002 and the Guangdong Special Support Program under Grants No 2017TX04N371 is gratefully acknowledged.

Funding

Financial support from the National Natural Science Foundation of China under Grant No.51976040, Grant No. 51236002 and the Guangdong Special Support Program under Grants No. 2017TX04N371 is gratefully acknowledged.

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Authors and Affiliations

  1. School of Materials and Energy, Guangdong University of Technology, Guangzhou, 510006, China

    Yuanjing Mao, Zhi Yang, Ying Chen, Songping Mo, Xianglong Luo, Jianyong Chen & Yingzong Liang

  2. Guangdong Province Key Laboratory for Functional Soft Matter, Guangdong University of Technology, Guangzhou, 510006, China

    Zhi Yang, Ying Chen, Songping Mo, Xianglong Luo, Jianyong Chen & Yingzong Liang

  3. Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, 100190, China

    Hao Guo

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  1. Yuanjing Mao
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Contributions

Y.M. contributed to data curation; formal analysis; investigation; methodology; Software; writing of the original draft; and writing, reviewing, & editing of the manuscript. Z.Y. contributed to investigation; software; supervision; funding acquisition; and writing, reviewing, & editing of the manuscript. H.G. contributed to investigation and writing, reviewing, & editing of the manuscript. Y.C. contributed to investigation and writing, reviewing, & editing of the manuscript. S.M. contributed to investigation; supervision; funding acquisition; and writing, reviewing, & editing of the manuscript. X.L. contributed to investigation and writing, reviewing, & editing of the manuscript. J.C. contributed to investigation and writing, reviewing, & editing of the manuscript. Y.L. contributed to investigation and writing, reviewing, & editing of the manuscript.

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Correspondence to Zhi Yang or Songping Mo.

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Mao, Y., Yang, Z., Guo, H. et al. The Thermodynamic Properties of Non-Associating and Associating Fluids: A Systematic Evaluation of SAFT-Type Equations of State. Int J Thermophys 44, 32 (2023). https://doi.org/10.1007/s10765-022-03131-9

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