Energy Fuels 2010, 24, 392–395 Published on Web 11/04/2009
: DOI:10.1021/ef900883u
Calculating Flash Point Numbers from Molecular Structure: An Improved Method for Predicting the Flash Points of Acyclic Alkanes Felix A. Carroll,*,† Chung-Yon Lin,† and Frank H. Quina‡ †
Department of Chemistry, Davidson College, Davidson, North Carolina 28035, and ‡Instituto de Quı´mica, Universidade de S~ ao Paulo, CP 26077, S~ ao Paulo 05513-970, Brazil Received August 13, 2009. Revised Manuscript Received October 14, 2009
We report a novel method for calculating flash points of acyclic alkanes from flash point numbers, NFP, which can be calculated from experimental or calculated boiling point numbers (YBP) with the equation NFP ¼ 1:020YBP -1:083 Flash points (FP) are then determined from the relationship 2=3
1=3
FPðKÞ ¼ 23:369NFP þ 20:010NFP þ 31:901 For a data set of 102 linear and branched alkanes, the correlation of literature and predicted flash points has R2 = 0.985 and an average absolute deviation of 3.38 K. NFP values can also be estimated directly from molecular structure to produce an even closer correspondence of literature and predicted FP values. Furthermore, NFP values provide a new method to evaluate the reliability of literature flash point data.
Methods to predict closed cup flash points continue to be of interest because they allow estimation of flash points for which experimental data are not available,5 and they can provide some measure of the reliability of reported flash points.6 Flash points of alkanes are of particular interest because paraffins are present in fuels and other petroleum products. One of the earliest prediction methods, reported by Butler and co-workers, is a linear correlation of flash point with boiling point (TB).7 FPð°FÞ ¼ 0:683TB ð°FÞ -119 ð1Þ
Introduction The flash point (FP) of a liquid is the lowest temperature of a bulk liquid at which the mixture of air and vapor near its surface can be ignited. As a result, the flash point is the most frequently specified measure of the fire hazard associated with the transport, storage, and use of flammable substances.1,2 Depending upon the design of the test apparatus, flash points are classified as being either closed cup or open cup. The closed cup flash point of a substance is generally lower than the open cup flash point, often by several degrees.1,3 Combustion of vapor above the surface of a liquid requires that the concentration of vapor be equal to or greater than the lower concentration limit in air required for combustion to occur but less than the upper concentration limit, beyond which combustion cannot occur. The lower concentration limit is typically measured in volume percent and is often called the lower explosion limit (LEL). LEL values of liquid hydrocarbons vary inversely with molecular weight. For example, the LEL values of hexane, decane, and tetradecane are 1.2 vol. %, 0.8 vol. %, and 0.5 vol. %, respectively. The LEL values of isomeric branched alkanes are relatively similar, however, and the LEL values of more than 70 branched decanes are all reported to be 0.7 vol. %.4 As a result, variation of vapor pressure with molecular structure is usually considered to be a more significant determinant of hydrocarbon flash points than is variation of LEL with structure.
As part of the study reported here, we assembled a data set consisting of 102 acyclic alkanes containing from 5 to 18 carbon atoms.8 For these compounds, the correlation between literature flash points and those predicted with eq 1 had an R2 of 0.979 and an average absolute deviation (AAD) of 5.4 K. Because the relationship of flash points and boiling points is not entirely linear, a number of authors have reported more complex relationships between the two. Riazi and Daubert suggested a relationship for hydrocarbons in the form of eq 2, where temperatures are in °R and the constants a, b, and c have the values -1.4568 10-2, 2.84947, and 1.903 10-3, respectively.9 That relationship gave an AAD of 8.3 K with our data set. 1 b ¼aþ þ c lnTB ð2Þ FP TB
*To whom correspondence should be addressed. Fax: 704-894-2709. E-mail:
[email protected]. (1) Zalosh, R. G. Industrial Fire Protection Engineering; John Wiley & Sons Ltd.: West Sussex, 2003. (2) Jones, J. C. Hydrocarbon Process Safety; Whittles Publishing: Caithness, Scotland, 2003. (3) Higman, C.; van der Burgt, M. Gasification, 2nd ed.; Elsevier: Oxford, 2008. (4) Yaws, C. L. Handbook of Chemical Compound Data for Process Safety; Gulf Publishing Company: Houston, 1997. r 2009 American Chemical Society
(5) For reviews, see (a) Vidal, M.; Rogers, W. J.; Holste, J. C.; Mannan, M. S. Proc. Saf. Prog. 2004, 23, 47. (b) Hristova, M.; Tchaoushev, S. J. U. Chem. Tech. Metal. 2006, 41, 291. (6) For example, see Catoire, L.; Naudet, V. J. Phys. Chem. Ref. Data 2004, 33, 1083. (7) Butler, R. M.; Cooke, G. M.; Lukk, G. G.; Jameson, B. G. Ind. Eng. Chem. 1956, 48, 808. (8) A listing of the compounds and their literature flash points is provided in the Supporting Information. (9) Riazi, M. R.; Daubert, T. E. Hydrocarbon Process 1987, 81.
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Energy Fuels 2010, 24, 392–395
: DOI:10.1021/ef900883u
Carroll et al.
Building upon a concept originally proposed by Kinney,21 we predicted boiling points through use of boiling point numbers (YBP). The relationship is shown in eq 5, where the constants a, b, and c are -16.802, 337.377, and -437.8835, respectively.22
For organic compounds other than acids and alcohols, Patil suggested a relationship in the form of eq 3, where temperatures are in K and the constants a, b, and c have the values 4.656, 0.844, and -2.34 10-3, respectively.10 That equation gave a correlation with an AAD of 19.7 K for the set of 102 alkanes. FP ¼ a þ bTB þ
cTB2
2=3
1=3
TB ðKÞ ¼ aYBP þ bYBP þ c
ð3Þ
ð5Þ
Values of YBP were determined from molecular structure according to eq 6. YBP ¼ 1:726 þ 2:779C þ 1:716M3 þ 1:564M þ
An even more complex relationship was proposed by Satyanarayana and Rao (eq 4), where temperatures are in K.11,12 Using the values of a, b, and c recommended for hydrocarbons (225.1, 537.6, and 2217, respectively), our set of 102 alkanes gave an AAD of 7.8 K. The methods discussed above require only experimental boiling points. Other investigators have developed correlations including as variables specific gravity,13 enthalpy of vaporization at 25°,6 or infrared spectra.14 2 b TcB e -c=TB FP ¼ a þ ð4Þ ð1 - e -c=TB Þ2
4:204E3 þ 3:905E þ 5:007P - 0:329D þ 0:241G þ 0:479V þ 0:967T þ 0:574S
ð6Þ
Here C is the number of carbon atoms in the longest or main chain, M3 is the number of methyl groups on carbon 3 of this chain (counting from either end), M is the number of methyl groups at other positions, E3 and E are the number of corresponding ethyl groups, P is the number of propyl groups, D is the number of 2,2-dimethyl groupings, G is the number of geminal substitutions at other positions, V is the number of vicinal relationships, T is the number of instances of two methyl substituents on both carbons one and three of a threecarbon segment of the main chain, and S is the square of the ratio of total number of carbons to the number of carbons in the longest chain. This approach gave a correlation of experimental and predicted boiling points with R2=0.999 for acyclic alkanes containing 6-30 carbons. The important conceptual advantage of eq 6 is that YBP provides a measure of alkane boiling points that varies linearly with the number of structural increments among a series of homologous compounds. We therefore hypothesized that an analogous relationship might also exist for a new measure of alkane flash points, which we designated the flash point number, NFP. Thus, we would expect to find a relationship in the form of eq 7.
In addition to methods based entirely on experimental data, there are also flash point prediction methods based on molecular connectivity.15,16 Several investigators have reported quantitative structure-property relationships (QSPR) for flash points of organic compounds that incorporate properties computed from molecular structure.17,18 Neural network methods have also been developed.19 None of these methods appear to be substantially more accurate for the acyclic alkanes than is eq 1, however. For example, Pan et al.20 reported a group bond contribution neural network approach with an AAD of 4.8 K for the alkanes. Except for eq 1, all of the methods discussed above are nonlinear with boiling point, require knowledge of additional experimental data, or are based on approaches (connectivity or neural network) that may not be familiar to those who use flash point data. We report here a novel method for predicting the flash points of paraffins directly from molecular structure (and/or from their normal boiling points, when available) that is distinctly superior to the methods previously reported. Furthermore, our approach provides a useful new method to evaluate the reliability of literature flash point data.
2=3
1=3
FPðKÞ ¼ aNFP þ bNFP þ c
ð7Þ
In order to determine the appropriate constants in eq 7, we considered first the flash points of the n-alkanes from pentane to octadecane. Because of the close correspondence of FP values with BP values discussed above, we initially used YBP values for NFP values in eq 7. Then we used the Solver add-in of Microsoft Excel to find values of a, b, and c that minimized the AAD between the literature flash points of the n-alkanes and the flash points calculated with eq 7. The values obtained in this way were 23.369, 20.010, and 31.901 for a, b, and c, respectively. These values gave a very good correlation between literature and calculated flash points, as shown in Figure 1. The R2 value was 0.996, and the AAD was 2.5 K. Next we calculated experimental NFP values for all of the 102 alkanes from their literature flash points using eq 8 and the constants a, b, and c indicated above. " pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# -b þ b2 - 4aðc - FPÞ 1=3 ð8Þ NFP ¼ 2a
Method and Results The approach for predicting flash points developed here is an extension of our improved method for the prediction of alkane boiling points directly from molecular structure. (10) Patil, G. S. Fire Mat. 1988, 12, 127. (11) Satyanarayana, K.; Rao, P. G. J. Hazard. Mater. 1992, 32, 81. (12) Equation 4 as given here is the correct form of the equation. It reproduces the values reported in ref 11 and was used in ref 5b. (13) Satyanarayana, K.; Kakati, M. C. Fire Mater. 1991, 15, 97. Metcalfe, E.; Metcalfe, A. E. M. Fire Mater. 1992, 16, 153. (14) Vazhev, V. V.; Aldabergenov, M. K.; Vazheva, N. V. Pet. Chem. 2006, 46, 136. The AAD reported for this method with a different data set was 3.2 K. (15) Patil, G. S. Fire Mater. 1988, 12, 159. (16) Albahri, T. A. Chem. Eng. Sci. 2003, 58, 3629. (17) Katritzky, A. R.; Petrukhin, R.; Jain, R.; Karelson, M. J. Chem. Inf. Comput. Sci. 2001, 41, 1521. Katritzky, A. R.; Stoyanova-Slavova, I. B.; Dobchev, D. A.; Karelson, M. J. Mol. Graphics Modell. 2007, 26, 529. (18) Gharagheizi, F.; Alamdari, R. F. QSAR Comb. Sci. 2008, 27, 679. (19) See, for example Gharagheizi, F.; Alamdari, R. F.; Angaji, M. T. Energy Fuels 2008, 22, 1628. (20) Pan, Y.; Jiang, J.; Wang, Z. J. Haz. Mat. 2007, 147, 424. See also. Tetteh, J.; Suzuki, T.; Metcalfe, E.; Howells, S. J. Chem. Inf. Comput. Sci. 1999, 39, 491. (21) Kinney, C. R. J. Am. Chem. Soc. 1938, 60, 3032.
In the case of the n-alkanes, the method of calculation of a, b, and c resulted in NFP values that were nearly equal to the corresponding YBP values. We therefore asked whether there might be a linear relationship between YBP values and NFP (22) Palatinus, J. A.; Sams, C. M.; Beeston, C. M.; Carroll, F. A.; Argenton, A. B.; Quina, F. H. Ind. Eng. Chem. Res. 2006, 45, 6860.
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: DOI:10.1021/ef900883u
Carroll et al.
Figure 1. Correlation of predicted FP values for the n-alkanes with their literature values. The predicted FP values were calculated using eq 7. The diagonal line represents perfect correlation between literature and predicted values. The size of the data points represents the standard error of the correlation.
Figure 2. Correlation of predicted and literature FP values for 102 acyclic alkanes. The predicted values were calculated using eq 7 with NFP values obtained from eq 9 and experimental YBP values. The diagonal line represents perfect correlation between literature and predicted values. The size of the data points represents the standard error of the correlation.
values for the branched alkanes as well. This was indeed found to be the case, and the resulting correlation for all 102 compounds is shown in eq 9.
flash points had R2 = 0.988, and the AAD was 2.9 K.
NFP ¼ 1:020ð ( 0:012ÞYBP - 1:083ð ( 0:316Þ ðN ¼ 102, R2 ¼ 0:987, F ¼ 7637Þ
NFP ¼ 1:754ð ( 0:305Þ þ 2:792ð ( 0:030ÞC þ 1:997ð ( 0:102ÞM3 þ 1:790ð ( 0:071ÞM þ
ð9Þ
4:770ð ( 0:195ÞE3 þ 4:554ð ( 0:397ÞE þ 0:322ð ( 0:073ÞV
Furthermore, the flash points predicted using eq 7 with the NFP values calculated with eq 9 correlated well with literature flash point values (Figure 2). The R2 was 0.985, and the AAD was 3.38 K. These results demonstrate that eq 9 provides a way to predict acyclic alkane flash points that correlate with literature flash points as well as or better than any other reported method, yet it requires only knowledge of YBP values. Furthermore, because the YBP values can be calculated from structure with eq 6, the method reported here provides a simple way to predict the flash points of paraffins from molecular structure. The success of this approach pointed to an even more direct method of predicting alkane flash points from structure. The branched alkanes have LEL values that are very similar, but often not identical, to those of the corresponding linear alkanes.23 For example, the LEL of n-nonane is reported to be 0.7 vol. %, while that of 2,3-dimethylheptane is 0.8 vol. % and that of 2-methyloctane is 0.9 vol. %.4 Therefore, it seemed reasonable that the structural components used to predict YBP values with eq 6 might correlate in a slightly different way with NFP values so as to reflect both the volatility and the LEL contributions to flash points. Indeed, we found that NFP values correlate very well with structure, as shown in eq 10.24,25 The overall correlation of predicted and literature
ð10Þ
ðN ¼ 102, R2 ¼ 0:9898, F ¼ 1540Þ As an example of the application of eq 10, consider 2,2,3,4tetramethylpentane. There are five carbons in the main chain, so C = 5. There is one methyl group on C3 (M3 = 1), and there are two methyl groups on C2 and one methyl on C4 (M = 3). There are also three vicinal relationships (two between the methyl group on C3 with the two methyls on C2 plus one between the methyl on C3 and the methyl on C4), so V = 3. Therefore NFP ¼ 1:754 þ ð5 2:792Þ þ 1:997 þ ð3 1:790Þ þ ð3 0:322Þ ¼ 24:03
ð11Þ
Using this value in eq 7 gives a predicted FP of 284 K, which agrees with the literature value.8 Discussion Equation 10 includes fewer parameters than does eq 6, suggesting that some structural variations (such as the number of geminal bonding relationships) may be less important in determining LEL values than in determining boiling points.26 Alternatively, the greater experimental uncertainty of flash point data than boiling point data may mask minor contributions from some of the parameters used in eq 6. It is not possible to determine which of these factors is more important, however, because flash points are usually reported without an indication of the uncertainties in the reported values.27
(23) Bodurtha, F. T. Industrial Explosion Prevention and Detection; McGraw-Hill: New York, 1980. (24) Our data set did not include compounds with propyl or larger substituents, so parameters for such groups are not included in eqs 6 or ref 10. In the event flash points for compounds with such substituents are needed, they may be predicted with eq 9 and either experimental boiling points or values estimated by any of a number of the boiling point estimation methods discussed in ref 22. (25) It is notable that the ratios of the coefficients for M, M3, E, and E3 in eq 6 to those in equation 10 are all close to 1.15, whereas the ratio of coefficients for the V parameter is 0.67. These ratios are consistent with the smaller dependence of NFP values than YBP values on branching.
(26) Inclusion of the D, G, and S parameters in the correlation gave a negligible improvement to the overall correlation (R2 = 0.9899), and the coefficients for these parameters were not statistically significant. (27) A reviewer noted that even replicates of flash points determined by the same standard method can show uncertainties of 2 K or more. We are grateful to the reviewer for suggesting that we discuss the inherent uncertainties of flash point data.
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: DOI:10.1021/ef900883u
Carroll et al.
alkane, as shown in Figure 3. While the overall correlation is very good (R2 = 0.995), the data point for n-tridecane is a significant outlier. Since there is no obvious chemical reason why the structure of tridecane should make its flammability characteristics unique among the n-alkanes, it is reasonable to suggest that its experimental flash point should be checked for accuracy. Taking this approach to identify other possibly erroneous literature flash point values should lead to an even better correlation of NFP values with structure. The use of NFP values can also provide a measure of the uncertainties of flash point data that result from random experimental error. The standard error for the correlation of FP values predicted via eq 9 is less than 4.4 K for all 102 compounds in the data set. Since an empirical method based on just one variable (in this case, boiling point) is unlikely to produce a smaller standard error than is inherent in the data set from which it is derived, we suggest that 4.4 K may be taken as the upper limit of the experimental uncertainty of the literature flash points of the paraffins.
Figure 3. Correlation of NFP values for the n-alkanes from pentane to octadecane with the number of carbon atoms in the alkane. The NFP values were calculated with eq 8 and the literature flash points of the alkanes. The diagonal line is the best-fit line through the data points. The error bars indicate the standard error in NFP values for this correlation.
Conclusion
The primary objective in pursing an empirical correlation of an important physical property is to be able to predict values when experimental data are not available. Such correlations can offer a secondary benefit, however, by providing a method to evaluate the reliability of the experimental data that are available. Specifically, when the properties of one member of a homologous series are inconsistent with those predicted by the method but the properties of all other members of the series are consistent with prediction, one has to ask whether there is something unique about that particular compound or whether the discrepancy could be attributed to an erroneous experimental value. A significant conceptual advantage of flash point numbers in this regard is that, unlike FP values, NFP values make such comparisons easy because they are additive with structural increments.28 As an example of this approach, consider the correlation of the NFP values of the linear alkanes (calculated using eq 8 and their literature flash points) with the number of carbons in the
The use of flash point numbers provides a straightforward means to predict alkane flash points, either from experimental boiling points or directly from molecular structure, and to evaluate the reliability of literature flash point data. We expect NFP values to be useful in predicting the flash points of other organic compounds as well, and work in this area is underway. Acknowledgment. Financial and fellowship support from Davidson College and from CNPq (Conselho Nacional de Desenvolvimento Cientı´ fico e Tecnol ogico) are gratefully acknowledged. Note Added after ASAP Publication. Equation 2 was modified in the version of this paper published ASAP November 4, 2009; the corrected version published ASAP December 17, 2009. Supporting Information Available: Data set of acyclic alkanes along with their literature boiling points, YBP values, counts of the structural parameters used in eq 10, literature and predicted flash points, and examples of NFP and FP calculations. This material is available free of charge via the Internet at http:// pubs.acs.org.
(28) This additivity is explicit in eq 10 and is implicit in eq 9 because YBP values vary with structure as shown in eq 6.
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