A Group Contribution Method for Predicting the Alkyl Ester and Biodiesel Densities at Various Temperatures
Abstract
:1. Introduction
2. Methods
2.1. Experimental Database
2.2. Predictive Model for the Alkyl Ester Density
2.3. Predictive Model for the Biodiesel Density
2.4. Statistical Analysis
3. Results
4. Discussion
5. Conclusions
Supplementary Materials
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Appendix A
Compound | Chemical Structure | -CH3 | -CH2 | =CH- | -COO- |
---|---|---|---|---|---|
Methyl octadecanoate | 2 | 16 | 0 | 1 | |
Methyl cis-9-octadecanoate | 2 | 14 | 2 | 1 | |
Methyl (9Z,12Z)-octadeca-9,12-dienoate | 2 | 12 | 4 | 1 | |
Methyl (9Z,12Z,15Z)-octadeca-9,12,15-trienoate | 2 | 10 | 6 | 1 |
Appendix B
- (a)
- MWmethyl hexadecanoate = [17(12.0107) + 34(1.00794) + 2(15.9994)] g/mol = 270.4507 g/mol.
- (b)
- MWmethyl octadecanoate = [19(12.0107) + 38(1.00794) + 2(15.9994)] g/mol = 298.5038 g/mol.
- (c)
- MWmethyl cis-9-octadecenoate = [19(12.0107) + 36(1.00794) + 2(15.9994)] g/mol = 296.4879 g/mol.
- (d)
- MWmethyl (9Z,12Z)-octadeca-9,12-dienoate = [19(12.0107) + 34(1.00794) + 2(15.9994)] g/mol = 294.4721 g/mol.
- (a)
- n-CH3 = 2, n-CH2 = 14, n=CH- = 0, n-COO- = 1 (methyl hexadecanoate).
- (b)
- n-CH3 = 2, n-CH2 = 16, n=CH- = 0, n-COO- = 1 (methyl octadecanoate).
- (c)
- nCH3 = 2, n-CH2 = 14, n=CH- = 2, n-COO- = 1 (methyl cis-9-octadecenoate).
- (d)
- nCH3 = 2, n-CH2 = 12, n=CH- = 4, n-COO- = 1 (methyl (9Z,12Z)-octadeca-9,12-dienoate).
- (a)
- Vmethyl hexadecanoate = {2[15.74 + 1.62 × 10−3(303.15) + 10.01 × 10−5(303.15)2] + 14[14.42 + 5.1 × 10−3(303.15) + 0.76 × 10−5(303.15)2] + 0[11.98 + 1.19 × 10−3(303.15) + 0.89 × 10−5(303.15)2] + 1[30.77 + 1.31 × 10−3(303.15) + 1.08 × 10−5(303.15)2]} cm3/mol = 316.3233 cm3/mol.
- (b)
- Vmethyl octadecenoate = {2[15.74 + 1.62 × 10−3(303.15) + 10.01 × 10−5(303.15)2] + 16[14.42 + 5.1 × 10−3(303.15) + 0.76 × 10−5(303.15)2] + 0[11.98 + 1.19 × 10−3(303.15) + 0.89 × 10−5(303.15)2] + 1[30.77 + 1.31 × 10−3(303.15) + 1.08 × 10−5(303.15)2]} cm3/mol = 349.6523 cm3/mol.
- (c)
- Vmethyl cis-9-octadecenoate = {2[15.74 + 1.62 × 10−3(303.15) + 10.01 × 10−5(303.15)2] + 14[14.42 + 5.1 × 10−3(303.15) + 0.76 × 10−5(303.15)2] + 2[11.98 + 1.19 × 10−3(303.15) + 0.89 × 10−5(303.15)2] + 1[30.77 + 1.31 × 10−3(303.15) + 1.08 × 10−5(303.15)2]} cm3/mol = 342.6406 cm3/mol.
- (d)
- Vmethyl (9Z,12Z)-octadeca-9,12-dienoate = {2[15.74 + 1.62 × 10−3(303.15) + 10.01 × 10−5(303.15)2] + 12[14.42 + 5.1 × 10−3(303.15) + 0.76 × 10−5(303.15)2] + 4[11.98 + 1.19 × 10−3(303.15) + 0.89 × 10−5(303.15)2] + 1[30.77 + 1.31 × 10−3(303.15) + 1.08 × 10−5(303.15)2]} cm3/mol = 335.6289 cm3/mol.
- (a)
- ρmethyl hexadecanoate = [270.4507 ÷ 316.3233] g/cm3 = 0.85498 g/cm3.
- (b)
- ρmethyl octadecenoate = [298.5038 ÷ 349.6523] g/cm3 = 0.85372 g/cm3.
- (c)
- ρ methyl cis-9-octadecenoate = [296.4879 ÷ 342.6406] g/cm3 = 0.8653 g/cm3.
- (d)
- ρmethyl (9Z,12Z)-octadeca-9,12-dienoate = [294.4721 ÷ 335.6289] g/cm3 = 0.87737 g/cm3.
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Group | Group Contribution Parameters | Statistical Parameters | ||||
---|---|---|---|---|---|---|
A (cm3/mol) | 103·B (cm3/mol·K) | 105·C (cm3/mol·K2) | R | AAD (%) | σ (g/cm3) | |
This work | 0.9941 | 0.36 | 0.00339 | |||
-CH3 | 15.74 | 1.62 | 10.01 | |||
-CH2 | 14.42 | 5.1 | 0.76 | |||
=CH- | 11.98 | 1.19 | 0.89 | |||
-COO- | 30.77 | 1.31 | 1.08 | |||
Elbro et al. [51] | 0.9788 | 0.83 | 0.00866 | |||
-CH3 | 18.96 | 45.58 | - | |||
-CH2 | 12.52 | 12.94 | - | |||
=CH- | 6.761 | 23.97 | - | |||
-COO- | 14.23 | 11.93 | - | |||
Ihmels and Gmehling [52] | 0.9894 | 0.44 | 0.00457 | |||
-CH3 | 16.43 | 55.62 | - | |||
-CH2 | 12.04 | 14.1 | - | |||
=CH- | −1.651 | 93.42 | −14.39 | |||
-COO- | 61.15 | −248.2 | 36.81 | |||
Pratas et al. [8] | 0.9911 | 0.81 | 0.00827 | |||
-CH3 | 18.96 | 45.58 | - | |||
-CH2 | 12.52 | 12.94 | - | |||
=CH- | 11.43 | 6.756 | - | |||
-COO- | 14.23 | 11.93 | - |
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Ramírez-Verduzco, L.F. A Group Contribution Method for Predicting the Alkyl Ester and Biodiesel Densities at Various Temperatures. Sustainability 2022, 14, 6804. https://doi.org/10.3390/su14116804
Ramírez-Verduzco LF. A Group Contribution Method for Predicting the Alkyl Ester and Biodiesel Densities at Various Temperatures. Sustainability. 2022; 14(11):6804. https://doi.org/10.3390/su14116804
Chicago/Turabian StyleRamírez-Verduzco, Luis Felipe. 2022. "A Group Contribution Method for Predicting the Alkyl Ester and Biodiesel Densities at Various Temperatures" Sustainability 14, no. 11: 6804. https://doi.org/10.3390/su14116804