Energy Fuels 2010, 24, 4854–4856 Published on Web 08/20/2010
: DOI:10.1021/ef1005836
Improved Prediction of Hydrocarbon Flash Points from Boiling Point Data 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 May 8, 2010. Revised Manuscript Received July 19, 2010
Flash points (TFP) of hydrocarbons are calculated from their flash point numbers, NFP, with the relationship TFP ðKÞ ¼ 23:369NFP 2=3 þ 20:010NFP 1=3 þ 31:901 In turn, the NFP values can be predicted from experimental boiling point numbers (YBP) and molecular structure with the equation NFP ¼ 0:987YBP þ 0:176D þ 0:687T þ 0:712B - 0:176 where D is the number of olefinic double bonds in the structure, T is the number of triple bonds, and B is the number of aromatic rings. For a data set consisting of 300 diverse hydrocarbons, the average absolute deviation between the literature and predicted flash points was 2.9 K.
using eq 1 had R2 = 0.985 and an average absolute deviation (AAD) of 3.4 K. We have now extended the use of flash point numbers to the prediction of the TFP values of hydrocarbons in general and report here a simple and highly accurate way to predict hydrocarbon flash points.
Introduction The flash point (TFP) of a liquid is the lowest temperature at which the mixture of vapor and air above the surface of the liquid can be ignited. Therefore, flash points are the most frequently specified measure of the fire hazard associated with the storage, transport, and use of flammable substances.1,2 For this reason, methods for evaluating reported TFP values and for predicting the flash points of new substances continue to be of interest. Recently, we introduced the flash point number, NFP, as a new parameter to characterize the flammability hazards of acyclic alkanes. Flash points of the paraffins were calculated from their flash point numbers using the relationship in eq 1. TFP ðKÞ ¼ 23:369NFP 2=3 þ 20:010NFP 1=3 þ 31:901
Method and Results The data set used in this study consisted of 300 hydrocarbons, which included 130 linear and branched, cyclic and acyclic alkanes having from 5 to 17 carbon atoms, 96 cyclic and acyclic, linear and branched alkenes having from 5 to 18 carbon atoms and up to 4 double bonds, 21 linear and branched alkynes and diynes having from 5 to 12 carbon atoms, and 53 benzene derivatives having linear and branched alkyl and alkenyl substituents with up to 17 carbon atoms total.5 Their YBP values were calculated from reported boiling points using eq 3. Their NFP values were calculated from literature flash points using eq 4, where the constants a, b, and c are 23.369, 20.010, and 31.901, respectively, as reported in ref 3. " pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# - b þ b2 - 4aðc - TFP Þ 1=3 ð4Þ ¼ NFP 2a
ð1Þ
For the alkanes, NFP values were found to correlate with boiling point numbers (YBP) as shown in eq 2.3 NFP ¼ 1:020YBP - 1:083
ð2Þ
The YBP values were determined from experimental or predicted boiling points (TB) via eq 3, where the constants a, b, and c are -16.80, 337.38, and -437.88, respectively.4 " pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# - b þ b2 - 4aðc - TB Þ 1=3 ð3Þ YBP ¼ 2a
We first considered whether YBP values alone could be used to predict TFP values of all hydrocarbons as accurately as was the case for just the acyclic alkanes. Indeed, the NFP values for the hydrocarbons did correlate well with YBP values, as shown in eq 5.
For a set of 102 linear and branched acyclic alkanes, the correlation of literature flash points with TFP values predicted
NFP ¼ 0:998 ð(0:006ÞYBP - 0:197 ð(0:164Þ ðn ¼ 300, F ¼ 26815, SE ¼ 0:697Þ
*To whom correspondence should be addressed. Telephone: 704-894-2544. Fax: 704-894-2709. E-mail:
[email protected]. (1) Zalosh, R. G. Industrial Fire Protection Engineering; John Wiley and Sons, Ltd.: New York, 2003. (2) Jones, J. C. Hydrocarbon Process Safety; Whittles Publishing: Caithness, Scotland, 2003. (3) Carroll, F. A.; Lin, C.-Y.; Quina, F. H. Energy Fuels 2010, 24, 392. (4) 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. r 2010 American Chemical Society
ð5Þ
After YBP values were calculated from literature boiling points and eq 3, NFP values calculated via eq 5 were used in (5) TB and TFP values were rounded to the nearest degree Kelvin for this study. A listing of the compounds, along with their literature TB and TFP values, is provided in the Supporting Information.
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Energy Fuels 2010, 24, 4854–4856
: DOI:10.1021/ef1005836
Carroll et al.
eq 1 to predict the flash points of the hydrocarbons, and a very good correlation was obtained (R2 of 0.988). The AAD between literature and predicted values was 3.3 K, and the standard error for the correlation was 4.2 K. As we noted earlier,3 an empirical method based on just one variable (in this case, boiling point number) is unlikely to produce a smaller standard error than is inherent in the data set from which it is derived. Therefore, we suggest that 4.2 K may be taken as the upper limit of the experimental uncertainty of the reported flash points of these hydrocarbons. It is notable that eq 5 is so similar to eq 2, which confirms that boiling point plays the primary role in determining the flash point of a hydrocarbon. Nevertheless, a closer examination of the data pointed to an even more accurate correlation. Many compounds with similar boiling points but belonging to different chemical families were observed to have significantly different literature flash points. For example, 2,2,4-trimethylpentane, cis-2-heptene, and 1-heptyne all boil at 372 K, but their TFP values are 261, 265, and 271 K, respectively. Similarly, the TB values of 2,3,3,4-tetramethylhexane, (þ)-β-pinene, and R-methylstyrene are all 438 K, but their respective flash points are 304, 309, and 318 K. Thus, we found that an even closer correspondence between literature and predicted flash points could be obtained by incorporating a limited number of functional group-specific parameters into the equation for NFP. This approach led to the correlation shown in eq 6
Figure 1. Correlation between literature flash points of 300 hydrocarbons and those predicted from the structure and boiling point via eq 6. The diagonal line represents perfect correlation between literature and predicted values, and the size of the data points indicates the standard error in the correlation.
An even more complex relationship was proposed by Satyanarayana and Rao (eq 9), where temperatures are in K.8 Using the values of a, b, and c recommended for hydrocarbons (225.1, 537.6, and 2217, respectively), our set of 300 hydrocarbons gave an AAD of 6.6 K.
NFP ¼ 0:987 ð(0:006ÞYBP þ 0:176 ð(0:061ÞD þ 0:687 ð(0:122ÞT þ 0:712 ð(0:104ÞB - 0:176 ð(0:167Þ ðn ¼ 300, F ¼ 8241, SE ¼ 0:629Þ
ð6Þ
TFP
2 - c c b e TB TB ¼ aþ c ð1 - e TB Þ2
ð9Þ
where D is the number of olefinic double bonds in the structure, T is the number of triple bonds, and B is the number of aromatic rings. Using YBP values determined from literature boiling points and eq 3, we calculated the NFP values of the hydrocarbons with eq 6 and then used these NFP values to predict TFP values with eq 1. The correlation of literature and predicted flash points is shown in Figure 1. The R2 value is 0.99, and the AAD is 2.9 K.
A linear correlation of the flash point with the boiling point reported by Butler and co-workers9 (eq 10) actually gave more accurate results for the 300 compounds in the present study (AAD=3.7 K) than any of eqs 7-9. Nevertheless, the method that we report here is substantially better than any of these methods.
Discussion
TFP ð°FÞ ¼ 0:683TB ð°FÞ - 119
A number of authors have reported hydrocarbon flash point prediction methods that are based on the boiling point as the only experimental physical property, but none is as accurate as the method reported here. Hshieh proposed the relationship in eq 7, where temperatures are in °C.6 With our data set, that method produced an AAD of 10.2 K.
There are also methods for predicting the flash points of hydrocarbons that do not require any experimental data but are instead directly based on the structure. Suzuki and co-workers reported a method based on the first-order molecular connectivity index and functional group counts, and it produced an reported AAD of 9.5 K for a set of 59 hydrocarbons.10 Albahri P the group contribution method shown in eq 11, where (Φ)i is the sum of molecular structure group contribution parameters.11 This approach was found to give an AAD of 5 K for a group of hydrocarbons included in that study. X X ðΦÞi - 5:6345ð ðΦÞi Þ2 TFP ¼ 84:65 þ 64:18
TFP ¼ - 54:5377 þ 0:5883TB þ 0:00022TB 2
ð7Þ
Riazi and Daubert suggested a relationship for hydrocarbons in the form of eq 8, where temperatures are in K.7 That approach gave an AAD of 6.8 K with the 300 compounds in our data set.
i
i
X X þ 0:360ð ðΦÞi Þ3 - 0:0101ð ðΦÞi Þ4
1 2:84947 ¼ -1:4568 10- 2 þ TFP TB þ 1:903 10- 3 ln TB
ð10Þ
i
ð8Þ
ð11Þ
i
(8) Satyanarayana, K.; Rao, P. G. J. Hazard. Mater. 1992, 32, 81. See also the comment about eq 9 in ref 3. (9) Butler, R. M.; Cooke, G. M.; Lukk, G. G.; Jameson, B. G. Ind. Eng. Chem. 1956, 48, 808. (10) Suzuki, T.; Ohtaguchi, K.; Koide, K. J. Chem. Eng. Jpn. 1991, 24, 258. (11) Albahri, T. A. Chem. Eng. Sci. 2003, 58, 3629.
(6) Hshieh, F.-Y. Fire Mater. 1997, 21, 277. See also Patil, G. S. Fire Mater. 1988, 12, 127. (7) Riazi, M. R.; Daubert, T. E. Hydrocarbon Process. 1987, 81.
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with the length of the alkyl chain is quite good (R = 0.997) for all of the compounds, except n-decylbenzene. The NFP value of ndecylbenzene calculated from its reported 380 K flash point15 is an outlier, however. Because there is no obvious chemical reason why the flammability of n-decylbenzene should vary dramatically from the trend exhibited by other n-alkylbenzenes, we suggest that the experimental flash point of n-decylbenzene should be redetermined (A 405 K TFP value for n-decylbenzene would be consistent with the correlation in Figure 2). Examining the NFP values of other hydrocarbon families in this way may reveal additional possibly erroneous literature flash points, which in turn could lead to an even more accurate correlation of TFP values with the structure. Conclusions The method for predicting hydrocarbon flash points from NFP values presented here is not only simpler than any method, except that in eq 10, but also more accurate than any of the other methods discussed above. Furthermore, this approach provides a new way to evaluate literature flash point data for hydrocarbons. We expect our general approach to be useful in predicting the flash points of non-hydrocarbons also, and work in this area is underway.
Figure 2. Correlation of NFP values for the n-alkylbenzenes with the number of carbons in the n-alkyl group. The diagonal line is the best-fit line through all of the data points, except for that of ndecylbenzene, which is indicated by . The bars indicate the standard error in NFP values for this correlation.
Patil reported the correlation in eq 12, where 0χ, 1χ, 2χ, 3χ, and 4χ are zero-, first-, second-, third-, and fourth-order molecular connectivities, respectively.12 For a set of 40 alkanes, alkenes, alkynes, and aromatics, this approach gave an AAD of 6.4 K. Thus, flash points predicted from NFP values calculated with eq 6 also correlate with literature values better than those obtained with these methods based only on the structure.13,14
Acknowledgment. Financial and fellowship support from Davidson College and Conselho Nacional de Desenvolvimento Cientı´ fico e Tecnol ogico are gratefully acknowledged. F.H.Q. is affiliated with the Brazilian National Institute for Catalysis in Molecular and Nanostructured Systems (INCT-Catalysis).
TFP ðKÞ ¼ 173:67 þ 38:14ð0 χÞ - 31:96ð1 χÞ - 31:62ð2 χÞ þ 34:73ð3 χÞ þ 34:28ð4 χÞ
ð12Þ
Supporting Information Available: Data set of hydrocarbons along with their literature boiling points, YBP values, reported flash points, counts of the structural parameters used in eq 6, and predicted flash points. This material is available free of charge via the Internet at http://pubs.acs.org.
Another advantage of the method reported here is that the use of NFP values provides a simple way to evaluate the reliability of literature flash point data. Consider the NFP values of the n-alkylbenzenes from toluene to n-undecylbenzene, which are shown in Figure 2. The correlation of NFP
(14) There are also neural network methods based on connectivity or group counts for the prediction of the flash points of organic compounds in general. Among these are Tetteh, J.; Suzuki, T.; Metcalfe, E.; Howells, S. J. Chem. Inf. Comput. Sci. 1999, 39, 491; Gharagheizi, F.; Alamdari, R. F. QSAR Comb. Sci. 2008, 27, 679; and Gharagheizi, F.; Alamdari, R. F.; Angaji, M. T. Energy Fuels 2008, 22, 1628. Furthermore, Katritzky, A. R.; Petrukhin, R.; Jain, R.; Karelson, M. J. Chem. Inf. Comput. Sci. 2001, 41, 1521 and Katritzky, A. R.; Stoyanova-Slavova, I. B.; Dobchev, D. A.; Karelson, M. J. Mol. Graphics Modell. 2007, 26, 529 reported a QSPR method for organic compounds in general based on structural, computed, and experimental properties. Although the differing data sets make exact comparisons impossible, these methods do not appear to be as accurate as the method reported here. (15) http://ull.chemistry.uakron.edu/erd/.
(12) Patil, G. S. Fire Mater. 1988, 12, 159. (13) There are flash point prediction methods for organic compounds in general that can be applied to hydrocarbons but which require knowledge of some physical property other than or in addition to the boiling point. These physical properties include enthalpy of vaporization (Catoire, L.; Naudet, V. J. Phys. Chem. Ref. Data 2004, 33, 1083), specific gravity (Satyanarayana, K.; Kakati, M. C. Fire Mater. 1991, 15, 97. Metcalfe, E.; Metacalfe, A. E. M. Fire Mater. 1992, 16, 153), and vapor pressure (Mack, E.; Boord, C. E.; Barham, H. N. Ind. Eng. Chem. 1923, 15, 963. Prugh, R. W. J. Chem. Educ. 1973, 50, A85. Fujii, A.; Hermann, E. R. J. Saf. Res. 1982, 13, 163.) Of these, only the method of Catoire and Naudet seems to approach the accuracy of the method reported here.
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