Comment on “Comparison of Methods for Estimating Critical

Comment/Reply pubs.acs.org/jced

Comment on “Comparison of Methods for Estimating Critical Properties of Alkyl Esters and Its Mixtures” Xiangzan Meng,† Ming Jia,‡ and Tianyou Wang†,* †

State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, China

‡

S Supporting Information *

ecently, Garciá et al.1 quantitatively compared three different packages in predicting the critical properties (Pc, Tc, Vc) and the normal boiling points (Tnb) of pure methyl esters (FAMEs) and ethyl esters (FAEEs). The three packages were composed of the following methods: Constantinou and Gani (CG), Marrero and Pardillo (MP), Wilson and Jasperson (WJ), Ambrose (A), Joback (J), Lee-Kesler equations (LK), and the Yuan correlation (Y). However, the authors have perhaps accidently made several mistakes in the application of these methods, which leads to some erroneous results. The significant issues are detailed briefly in this comment. (1) The CG method was used to estimate the Tnb, critical temperature (Tc), and critical volume (Vc) in package 1 in their study. We recalculated the Tnb, Tc, and Vc with the CG method. Our results are consistent with those obtained by the embedded CG method in the Aspen plus software.2 However, the values of Tnb and Tc in Table 3 and Table 4 are unexpectedly high while the values of Vc are unexpectedly low for all the compounds in their paper. Additionally, the CG method was used to compute the Tnb for ethyl esters in package 3. The values of Tnb for ethyl esters listed in Table 8 are also erroneous. (2) The MP method was used to estimate the Tnb, Tc, and Vc in package 2. The application of the MP method in predicting the Tnb for most methyl esters is correct, but errors are found for a few methyl esters and all the ethyl esters. The authors have misused the molecular weight of methyl ester C14:0 to calculate the Tnb for methyl esters C8:0, C10:0, and C12:0, which leads to erroneous Tnb. The values of Tnb are also erroneous for methyl esters C24:0, C17:1, C18:1 OH, C22:1, and C24:1, but the reason for their miscalculations is unclear. The erroneous Tnb leads to erroneous values for the corresponding Tc by the MP method and the critical pressure (Pc) by the WJ method. Additionally, the predicted critical volumes of methyl esters C18:1 OH and C24:1 are unexpectedly wrong, although those of the remainder methyl esters are correct. As for the ethyl esters, the mistakes in the calculation of the properties of methyl esters are inherited. What is worse, the authors mistook the molecular weights of methyl esters for those of ethyl esters. Additionally, the group CH2 and COO[] should be used for the application of the MP method for ethyl esters, but the authors still used the group CH3 and COO[], which is a fatal error. (3) The authors stated that the Yuan correlation (eq 7 in their paper) was used to estimate the Tnb for methyl esters in package 3. We recalculated the Tnb for methyl esters with eq 7, but the results are inconsistent with those listed in Table 7. We

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© 2013 American Chemical Society

found that the authors actually have applied the following equation3 to calculate the Tnb for most methyl esters rather than eq 7. Tnb = 206.9 ln(CN ) + 27.0

(1)

For methyl esters C16:0 and C18:1, the authors took the values reported by Graboski and McCormick4 instead of those calculated by the above equation. Additionally, the method for the prediction of Tnb for C18:1 OH in Table 7 is unclear. Obviously, it should be neither the CG method nor the MP method, because the Tnb for C18:1 OH in Table 7 is inconsistent with that in Table 3 or Table 5 in their paper. (4) The Ambrose method was used to estimate the Tc and Pc in package 3, but it was not applied correctly by the authors. They took the number of carbon atoms in the molecule as the number of carbon atoms in alkyl groups for all the compounds except for the methyl and ethyl ester C18:1 OH. In fact, the number of carbon atoms in alkyl groups should be the number of carbon atoms in the molecule excluding the carbon atom of the aliphatic functional group CO−O. Moreover, one double bond is missing when it was applied by the authors to calculate the Tc and Pc of methyl linolenate (C18:3) and ethyl linolenate (C18:3). We recalculated the Tc and Pc with the Ambrose method. Our results are consistent with those obtained by the embedded Ambrose method in the Aspen plus software.2 (5) The Joback method was used to estimate the Vc in package 3. The application of the Joback method is correct for methyl esters, but incorrect for ethyl esters. For a certain methyl ester, one more >CH2 group should be added for the corresponding ethyl ester. However, the authors added one more CH3 group instead, which leads to the erroneous critical volumes for all the ethyl esters. (6) The Lee−Kesler equations were used to compute the acentric factor, but the authors failed to use the method properly. First, the constant 0.160347 in eq 4 in their paper should be 0.169347.5 Therefore, eq 4 should be written as α = −ln Pci − 5.92714 + 6.09648θ −1 + 1.28862 ln θ − 0.169347θ 6

(2)

Second, the critical pressure, Pci in the above equation is actually in the unit of atmosphere.5 To enable Pci using the SI Received: April 10, 2013 Accepted: August 20, 2013 Published: September 3, 2013 2687

dx.doi.org/10.1021/je400342e | J. Chem. Eng. Data 2013, 58, 2687−2688

Journal of Chemical & Engineering Data

Comment/Reply

The recalculated properties with different packages are presented in the Supporting Information.

unit, for example kPa, the above equation should be rearranged as

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α = −ln(Pci/101.325) − 5.92714 + 6.09648θ −1 + 1.28862 ln θ − 0.169347θ

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ASSOCIATED CONTENT

* Supporting Information S

(3)

Tables of the recalculated properties with different packages. This material is available free of charge via the Internet at http://pubs.acs.org.

In fact, the authors may have directly applied eq 2 with Pci in bar, which leads to the erroneous acentric factors despite the correct predictions on critical properties and normal boiling points. The aforementioned errors have led to unreasonable predictions. For example, the unexpectedly low acentric factors of C18:0 OH in Table 5 and Table 6 calculated with package 2 in their paper. Misleading conclusions were also drawn. For example, the authors stated that “the error of the methods increase slightly in the case of low molecular weight methyl esters (C8:0 and C10:0)”1 as shown in Figure 2 in their paper. However, from Figure 1 in this comment, in which the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86-22-27403434. Fax: +86-22-27403434. Funding

The study is supported by the National Natural Science Foundation of China (No. 51076114). Notes

The authors declare no competing financial interest.

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REFERENCES

(1) García, M.; Alba, J.-J.; Gonzalo, A.; Sánchez, J. L.; Arauzo, J. Comparison of Methods for Estimating Critical Properties of Alkyl Esters and Its Mixtures. J. Chem. Eng. Data 2012, 57 (1), 208−218. (2) Aspentech. Aspen Plus V7 Reference Manual; Aspen Technology, Inc.: Cambridge, MA 02141, 2009. (3) Yuan, W.; Hansen, A. C.; Zhang, Q. Vapor Pressure and Normal Boiling Point Predictions for Pure Methyl Esters and Biodiesel Fuels. Fuel 2005, 84 (7−8), 943−950. (4) Graboski, M. S.; McCormick, R. L. Combustion of Fat and Vegetable Oil Derived Fuels in Diesel Engines. Prog. Energy Combust. Sci. 1998, 24 (2), 125−164. (5) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids. 4th ed.; McGraw-Hill: New York, 1987. (6) Santander, C. M. G.; Rueda, S. M. G.; da Silva, N. D.; de Camargo, C. L.; Kieckbusch, T. G.; Maciel, M. R. W. Measurements of Normal Boiling Points of Fatty Acid Ethyl Esters and Triacylglycerols by Thermogravimetric Analysis. Fuel 2012, 92 (1), 158−161.

Figure 1. Experimental4,6 and estimated values of Tnb/K for pure methyl and ethyl esters using CG and MP methods: □, exp. FAME; ○, CG; Δ, MP; ■, exp. FAEE; ●, CG; ▲, MP. CG FAME ARD = 2.79 %, MP FAME ARD = 1.72 %, CG FAEE ARD = 0.97 %, MP FAEE ARD = 8.27 %.

recalculated normal boiling points of some esters by the CG method and the MP method are plotted with experimental data taken from the literature, it is evident that both the CG method and the MP method can give accurate predictions on normal boiling points for low molecular weight methyl esters. The average relative deviation (ARD %) defined the same as eq 8 in their paper is also recalculated and shown in Figure 1. It should be pointed out that the experimental normal boiling points of methyl esters are from reference 6 (reference 4 in this comment) rather than reference 7 indicated by Garciá et al.1 On the basis of the recalculated properties, we further calculated the densities of methyl esters, ethyl esters, and biodiesels. It is found that several conclusions drawn by Garciá et al.1 should be corrected. First, it is package 3 (ARD = 3.68 %), rather than package 2 (ARD = 4.90 %) concluded by the authors, that showed the highest accuracy in predicting the densities of 14 pure methyl esters. Second, package 1 is not able to predict methanol-based biodiesel density with ARD lower than 2.1 % because it has an ARD of 5.55 % according to our recalculation. Finally, since package 1 has the highest ARD (4.53 %) in predicting the ethanol-based biodiesel density, it is not a good option to estimate the properties of ethanol-based biodiesel. 2688

dx.doi.org/10.1021/je400342e | J. Chem. Eng. Data 2013, 58, 2687−2688