Correspondence Cite This: Ind. Eng. Chem. Res. 2019, 58, 5743−5743
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Comment on “Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules” Wilson A. Cañas-Marín,*,† Doris L. Gonzaĺ ez,‡ and Bibian A. Hoyos† †
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Departamento de Procesos y Energía, Facultad de Minas, Universidad Nacional de Colombia Sede Medellín, Carrera 80 No. 65-223, 050041 Medellín, Colombia ‡ BP America, Inc., Houston, Texas 77079, United States e find a typographical mistake in the original paper by Gross and Sadowski.1 These authors presented in an appendix all the mathematical equations needed for using their PC-SAFT EoS model. For instance, the residual reduced Helmholtz free energy (i.e., eq A4) was given as
W
hs a ̃hc = ma ̅ ̃ −
∑ xi(mi − 1)ln giihs i
They also gave the mathematical expression for the compositional derivative of ãhc (eq A.35) as ij ∂a ̃hc yz ij ∂a ̃hs yz hs jj zz j z = + m a m ̃ k jj zz ̅ jjj x zzz x k k {T , ρ , xj≠k k k {T , ρ , xj≠k −
ij ∂g hs yz ii z zz j xk zzz k {T , ρ , xj≠k
∑ xi(mi − 1)(giihs)−1jjjjj i
But that equation is incorrect, with the following expression being the correct one: ij ∂a ̃hs yz ij ∂a ̃hc yz zz zz jj = mk a ̃hs + m̅ jjj − (mk − 1)ln gkkhs zz jj j x zz x k k {T , ρ , xj ≠ k k k {T , ρ , xj ≠ k −
ij ∂g hs yz ii z zz j xk zzz {T , ρ , xj ≠ k k
∑ xi(mi − 1)(giihs)−1jjjjj i
In short, the third term on the right-hand side was missing in the original paper, and this typographical mistake could contribute to produce erroneous or extraneous predictions by using PC-SAFT without checking before the consistence of the respective mathematical equations.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Gross, J.; Sadowski, G. Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules. Ind. Eng. Chem. Res. 2001, 40, 1244−1260.
Published: March 28, 2019 © 2019 American Chemical Society
5743
DOI: 10.1021/acs.iecr.8b06349 Ind. Eng. Chem. Res. 2019, 58, 5743−5743
