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Ind. Eng. Chem. Res. 2010, 49, 3022–3023
Volume 49, Issue 2 Fragment-Based Approach for Estimating Thermophysical Properties of Fats and Vegetable Oils for Modeling Biodiesel Production Processes. Li Zong, Sundaram Ramanathan, and Chau-Chyun Chen* Pages 879, 880, and 883. The A constant and the ∆Gθvap vap constant in Table 4 (page 879), the ∆Gθ,A constant in Table 6, and eq b in Table 5 (page 880), as previously published, are revised. The revision corrects an unfortunate mistake in our handling of pressure units. Also revised are the mole fractions of soybean oil in Table 11 (page 883). We have misread the soybean oil triglyceride composition data of Ndiaye et al.1 for PPP and SSS.
Table 4. Calculated Physical Constants from Vapor Pressures of Triglycerides material
carbons
A
B
tributyrin tricaproin tricaprylin tricaprin trilaurin trimyristin tripalmitin tristearin 1-capryl-2-lauryl-3-myristin 1-lauryl-2-myristyl-3-palmitin 1-myristyl-2-palmityl-3-stearin 1-myristyl-2-capryl-3-stearin 1-myristyl-2-lauryl-3-stearin 1-palmityl-2-capryl-3-stearin 1-palmityl-2-lauryl-3-stearin
4:4:4 6:6:6 8:8:8 10:10:10 12:12:12 14:14:14 16:16:16 18:18:18 10:12:14 12:14:16 14:16:18 14:10:18 14:12:18 16:10:18 16:12:18
12.495 12.945 14.245 14.205 14.705 14.905 15.525 15.725 14.025 14.925 15.305 15.005 14.965 15.425 15.675
4250 4950 6060 6510 7190 7720 8400 8750 6880 7720 8250 7750 7860 8090 8360
∆Hθvap (J/kmol) ∆Gθvap(J/kmol) 8.137 × 107 9.477 × 107 1.160 × 108 1.246 × 108 1.377 × 108 1.478 × 108 1.608 × 108 1.675 × 108 1.317 × 108 1.478 × 108 1.579 × 108 1.484 × 108 1.505 × 108 1.549 × 108 1.601 × 108
1.004 × 107 2.088 × 107 3.471 × 107 4.355 × 107 5.371 × 107 6.272 × 107 7.220 × 107 7.776 × 107 5.166 × 107 6.261 × 107 7.058 × 107 6.272 × 107 6.506 × 107 6.684 × 107 7.058 × 107
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a
Table 5. Relationship between Fragment-Specific Parameters and Carbon Number of Each Fatty Acid Fragment fragment-specific parameters
R2
trend line equation
equation number
Vapor Pressure vap ∆Hθ,A (J/kmol)
y ) 2093479.64x + 31397826.69
0.988
(a)
vap ∆Gθ,A (J/kmol)
y ) 1653848.04x + 22009767.68
0.994
(b)
A1,A (J/(kmol K))
y ) 21028.920x - 2485.721
0.995
(c)
A2,A (J/(kmol K2))
y ) 31.459476x - 82.038794
0.946
(d)
saturated (kJ/mol)
y ) -59.571x - 1358.7
0.996
(e)
monounsaturated (kJ/mol)
y ) -76.494x - 815.18
1.00
(f)
saturated (kJ/mol)
y ) -76.467x - 1250.8
0.995
(g)
monounsaturated (kJ/mol)
y ) -85.795x - 752.88
0.999
(h)
Heat Capacity
Liquid Enthalpy of Formation
Solid Enthalpy of Formation
Liquid Molar Volume B1,A (kmol/m )
y ) 65.787x-0.9251
0.999
(i)
B2,A (K-1)
y ) 3.6064 × 10-6x2 - 7.7353 × 10-5x
0.720
(j)
C1,A (Pa s)
y ) -1.0172x - 45.8525
0.898
(k)
C2,A (K)
y ) 81.83611x + 2153.99554
0.943
(l)
C3,A (K)
y ) 0.141996x + 20.545285
0.896
(m)
3
-3
+1.6438 × 10
Liquid Viscosity
a Note: In the equations, y represents the fragment-specific parameters in column 1 and x represents the carbon number of each saturated fatty acid fragment. R2 is R-square values of the trend line equations.
vap Table 6. Calculated Vapor Pressure Fragment Parameters ∆Hθ,A vap and ∆Gθ,A
fragments
symbols
glycerol butyric caproic caprylic capric lauric myristic palmitic palmitoleic stearic oleic linoleic linolenic arachidic behenic erucic
Gly-frag Bu-frag Co-frag Cy-frag C-frag L-frag M-frag P-frag Po-frag S-frag O-frag Li-frag Ln-frag A-frag B-frag E-frag
carbons
vap ∆Hθ,A (J/kmol)
vap ∆Gθ,A (J/kmol)
C4:0 C6:0 C8:0 C10:0 C12:0 C14:0 C16:0 C16:1 C18:0 C18:1 C18:2 C18:3 C20:0 C22:0 C22:1
-3.476 × 107 3.862 × 107 4.307 × 107 5.015 × 107 5.292 × 107 5.707 × 107 6.006 × 107 6.550 × 107 6.550 × 107 6.800 × 107 6.800 × 107 6.800 × 107 6.800 × 107 7.327 × 107 7.745 × 107 7.745 × 107
-7.388 × 107 2.789 × 107 3.148 × 107 3.609 × 107 3.904 × 107 4.233 × 107 4.515 × 107 4.877 × 107 4.877 × 107 5.088 × 107 5.088 × 107 5.088 × 107 5.088 × 107 5.509 × 107 5.839 × 107 5.839 × 107
Acknowledgment The authors are grateful to Dr. Gustavo Dassori and Mr. Adam Helton of Sustainable BioEnergy Modeling Center of
Table 11. Triglyceride Composition of Soybean Oil35 fatty acid chain
triglyceride
mole fraction soybean oil
C16:0 C18:0 C18:1 C18:2 C18:3
PPP SSS OOO LiLiLi LnLnLn
0.1221 0.0340 0.2327 0.5425 0.0687
Archer Daniels Midland Company. They found the issues with the reported constants and kindly alerted us these problems. Literature Cited (1) Ndiaye, P. M.; Tavares, F. W.; Dalmolin, I.; Dariva, C.; Oliveira, D.; Oliveira, J. V. Vapor Pressure Data of Soybean Oil, Castor Oil, and Their Fatty Acid Ethyl Ester Derivatives. J. Chem. Eng. Data 2005, 50, 330-333.
IE100160V 10.1021/ie100160v Published on Web 02/16/2010
