Power Law Expressions for Predicting Lower and Upper Flammability

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Power Law Expressions for Predicting Lower and Upper Flammability Limit Temperatures Didier Mathieu* CEA, DAM, Le Ripault, F-37260 Monts, France S Supporting Information *

ABSTRACT: By analogy with recent models for flash point, the lower and upper flammability limit temperatures of organic compounds are represented as power law expressions in terms of fragment contributions. The predictive value of the resulting models compares well with recently published methods. A major advantage of the present approach is the fact it provides better insight into the relationships between flammability limit temperatures and molecular structure.

1. INTRODUCTION In view of the large variety of compounds involved in chemical industry, there is currently much interest in computational methods to predict the main safety characteristics and explosivity properties of new molecules,1 including heats of decomposition,2 shock sensitivities,3 flash point4−6 or flammability limits.7−9 For the design of safe processes avoiding fire onset and explosion, the knowledge of the lower and upper flammability limit temperatures (LFLT and UFLT) is more convenient than flammability limits in the form of concentrations. The LFLT value for a given compound is defined as the temperature at which a flame will propagate if its vapors in equilibrium in air under standard conditions are successfully ignited.4,10 Therefore, it is closely related to the flash point (FP) value, which is defined as the temperature at which the same vapors may be ignited. A significant advantage of LFLT is that it does not depend on the strength of an external ignition source. In fact, LFLT was recently put forward as a good measure for explosion prevention.10 On the other hand, UFLT is the temperature at which the concentration of a saturated vapor of the compound in air under ambient conditions is equal to the upper flammability limit. Methods to predict LFLT and UFLT have been developed only very recently.11−16 The best results are obtained using a corresponding states model.16 However, as it requires a knowledge of critical properties, the latter is not suitable for new compounds or potential synthesis targets. Therefore, we focus in what follows on the two other techniques previously used to estimate LFLT/UFLT. The first one (GA-MLR) consists in carrying out a multilinear regression (MLR) against a set of input variables selected among a large pool of descriptors with the help of a genetic algorithm (GA).11,12 The second one (GC-ANN) uses an artificial neural network (ANN) with chemical group occurences as input variables.13−15 Such fragmental descriptors are typically used in group contribution (GC) additivity methods. The large number of empirical parameters involved and the implicit nature of resulting models were reported as the two main drawbacks of the GC-ANN technique.16 In fact, as emphasized by Patel et al. in the context of flash point prediction,17 they are some limitations associated with the use of either GA-MLR or GC© XXXX American Chemical Society

ANN techniques in computer aided molecular design (CAMD). Moreover, to compute the descriptors (GA-MLR) or to implement a neural network (GC-ANN), both techniques require specialized software not necessarily available to chemical engineers. The present paper reports alternative models for both LFLT and UFLT that overcome the abovementioned limitations and can be easily implemented by chemical engineers in their own CAMD system. Furthermore, these models demonstrate that the influence of a molecular substructure on LFLT and UFLT is to some extent transferable, and point to functional groups most efficiently contributing to increase the values of these temperatures.

2. METHODOLOGY The present work takes advantage of a small set of fragmental descriptors that proved highly successful in predicting increasingly complex properties, from crystal volumes18 to sublimation enthalpies19 and flash points.20,21 A detailed description of how these descriptors are defined is provided in these earlier papers.18−20 The definition of the additive fragments is basically guided by geometrical considerations.18 Focusing on an atom in a molecule, the local molecular geometry depends primarily on the element under consideration and on the number and sizes of chemically bonded atoms. Because most atoms in organic compounds exhibit similar sizes, except for hydrogen atoms, this local geometry may be characterized for any non-hydrogen atom by a label Xnc-nH where X stands for the atomic symbol, nc for the coordination number, and nH for the number of attached hydrogen atoms. A distinctive feature of this scheme, compared to standard chemical groups, lies in the fact that bond orders are ignored. The use of such simple fragments assumes that the local geometry is the primary determinant of intermolecular interactions, as it is associated with the exposed surface area of the atoms. By contrast, the role of bond orders should be less Received: January 21, 2013 Revised: May 21, 2013 Accepted: June 7, 2013

A

dx.doi.org/10.1021/ie4002348 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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and root-mean-square error (RMSE). For comparison with earlier methods, the average relative error (AAE%) is also reported. While models fitted against the training set make comparison with previous methods easier, the parameters are eventually fitted against all data at hand. The predictive values of the methods thus obtained for predicting LFLT and UFLT are further assessed on the basis of a leave-ten-out crossvalidation procedure (CV-10).

significant as they are more directly associated with the reactive behavior of the compound. In addition to atomic fragments, the present schemes relies on structural corrections, namely, crowding and ring corrections. The former account for crowding effects associated with any non-hydrogen atom bonded to big atoms, that is, to atoms beyond the first row of the periodic table. They are denoted B2 and B3 for atoms bonded to two or three big atoms, respectively. For sublimation enthalpy, it is clear that these corrections should be negative as they reflect a decreased accessibility of the atom under consideration. On the other hand, no explicit B1 correction is used as it would only introduce redundancies in the description of the molecule.19 Ring corrections depend on ring size and aromatic character. Corrections R3 to R6 are introduced for ring sizes r = 3 to r = 6, and R>6 for larger rings. Aromatic rings exhibit a specificity with regard to intermolecular forces owing to the possibility of πstacking interactions. Therefore, two specific corrections R5a and R6a are used for aromatic rings, instead of the general corrections R5 and R6. In addition to these seven ring corrections, the present work introduces another one denoted Rfused and defined as the number of bonds belonging to at least two rings. This is motivated by the fact that from the standpoint of surrounding molecules, a fused rings system may be viewed as a single rigid extended ring. Since flash point is a concave function of molecular size,20 a similar behavior is expected for FLTs. Therefore, it comes as no surprise that a linear expression of these properties in terms of the numbers of occurences νi of constitutive groups i yields poor results13 To account for this concavity, the following expressions are used: LFLT = (NLFLT)2/5

and

UFLT = (NUFLT)2/5

3. RESULTS Because it relies on molecular fragments whose definition is primarily based on geometrical considerations, with associated additive contributions derived from multilinear regression, the present approach is hereafter denoted GF-MLR where GF stands for geometrical fragments. The quality of present fits and the predictive value of the corresponding GF-MLR models are summarized and compared to previous studies in Table 1 for Table 1. Performance of Available Methods for Predicting LFLT GA-MLR

GC-AAN

GF-MLR

∑ νiNLFLT,i i

and

NUFLT =

∑ νiNUFLT,i i

N

R2

train. test whole train. test whole train. test whole CV-10

937 234 1171 1144 285 1429 934 233 1167 1155

0.946 0.953 0.947 0.981 0.970 0.979 0.965 0.949 0.963 0.956

AAE (K)

RMSE (K)

AAE%

10 12 10 11

16 15 16 10 13 11 12 16 13 14

4.0 3.9 4.0 2.3 2.6 2.4 3.0 3.8 3.1 3.3

(1)

where the intermediary quantities NLFLT and NUFLT are simply obtained as sums of additive contributions associated with the above-mentioned atomic fragments and structural corrections, collectively labeled with indices i: NLFLT =

set

Table 2. Performance of Available Methods for Predicting UFLTa GA-MLR

(2)

The value of the exponent 2/5 in eq 1 is empirically found to yield good results. Such a value slightly below 1/2 was previously observed to be optimal for predicting flash points of organosilicon compounds.21 All in all, the present models require only 41 linear parameters to estimate LFLT and 37 to estimate UFLT, because of the lower diversity of the data set. While GC-ANN methods require respectively 125 and 122 chemical groups to predict both properties, the number of parameters involved is much larger because of the need for several parameters to describe the nonlinear dependence of the property with respect to every input variable. Thus, the extent of empiricism is dramatically decreased on going from GCANN to the present method. To make comparison with previous work easier, present models are developed on the basis of data sets already used in previous studies. More specifically, the training and test sets introduced in ref 11 for LFLT and in ref 12 for UFLT are used.22 The model parameters NLFLT,i and NUFLT,i involved in eq 2 have been fitted through a multilinear regression based on a singular value decomposition procedure.23 The performances of the methods are characterized by various statistical criteria: determination coefficient (R2), average absolute error (AAE),

GC-AAN

GF-MLR

eq 3b eq 3c

set

N

R2

AAE (K)

RMSE(K)

AAE%

train. test whole train. test whole train. test whole CV-10 whole whole

1036 258 1294 1100 65 1294 1228 64 1292 1286 1292 1292

0.949 0.954 0.950 0.99 0.98 0.990 0.956 0.962 0.956 0.951 0.987 0.944

6 7 6 12 12 12 13 6 14

17 8 10 9 16 16 16 17 8 18

3.6 1.5 1.9 1.7 3.4 3.4 3.4 3.5 1.6 3.8

a

The last row reports the performance of eq 3 with calculated LFLT values as input. bUsing experimental LFLT values as input. cUsing GFMLR LFLT values as input.

LFLT and in Table 2 for UFLT. With regard to previous investigations, GC-ANN appears to perform significantly better than GA-MLR. For instance, the root-mean-square error (RMSE) increases from 11 to 16 K for LFLT and from 9 to 17 K for UFLT on going from GC-ANN to GA-MLR. However, a close examination of the data for GC-ANN models reveals that about one-third of the groups fed to the ANN are not involved in the external predictions for compounds in the B



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test set. For instance, among the 122 groups introduced to estimate UFLT, 36 do not arise at all in the test set. While the smallest groups arise in both the training and test set, the model relies on many specialized groups encountered only within the training set (for instance, highly specific groups associated with cyclic structures such as oxiranes, oxolanes, pyrrolidines, thiophenes,...). In other words, the external test set contains only relatively simple compounds. Therefore, the corresponding predictions do not necessarily reflect the reliability of the method when it comes to molecules with more unusual moieties. The numerous specialized descriptors effectively increase the flexibility of the model, allowing for a better fit of the data, but their predictive value is unknown. Finally, the superior reliability of GC-ANN over MLR-GA predictions thus remains to be established. Assuming that the statistics reported for GC-ANN methods do effectively reflect their predictive value, the relative performance of the models are GA-MLR < GF-MLR < GCANN for both LFLT and UFLT. The fact that GF-MLR yields better fits of the data than GA-MLR comes as no surprise since the former approach involves a larger number of adjustable parameters. However, the fact that it yields equally good predictions is more unexpected, considering the simplicity of present geometrical fragments and the fact that the input variables are given a priori rather than obtained as the outcome of an intensive search among many possible combinations of descriptors. Although the GC-ANN methods appear somewhat superior to the others, significant deviations from experiment are observed with this method, ranging from −33% to +29% for LFLT and from −12% to +24% for UFLT. For present GFMLR methods, the deviations range from −14% to +20% for LFLT and from −20% to +31% for UFLT. Using the present GF-MLR approach, AAE, RMSE, and AAE % values are remarkably constant on going from the training set to the test set for UFLT, while a modest increase is observed for LFLT. Furthermore, the leave-ten-out cross-validation (CV10) of the models fitted against the whole data sets confirm the conclusions drawn from the statistics for the test sets. These results show that present parameters are essentially transferable. In what follows, only the final models for both LFLT and UFLT are considered. Their performances are illustrated by the plots of calculated versus observed values in Figure 1 and Figure 2. In contrast to previous approaches, GF-MLR yields somewhat better results for LFLT compared to UFLT. Moreover, the procedure for LFLT is more widely applicable owing to the larger number of presently fitted parameters. While predictive models for LFLT and UFLT have been so far developed independently, it is clear from their definition that both temperatures are closely related. Considering present data, it may be noted that the difference UFLT−LFLT is always positive and ≤94 K. In addition, it tends to increase with molecular size, the maximum value of 94 K being obtained for a compound with empirical formula C22H42O4. As a result, UFLT may be estimated from LFLT according to

Figure 1. Calculated versus observed LFLT data.

Figure 2. Calculated versus observed UFLT data.

using the present GF-MLR method yields a reasonable procedure to estimate UFLT, as shown on the last row in Table 2. The values of the model parameters are reported in Table 3. Associated standard deviations are not listed in this table as they are close to 1 K5/2 for the few parameters depending on a single experimental value, and much lower otherwise. In other words, they are systematically ≪1% of the actual NLFLT,i or NUFLT,i values. In view of the close relationship between LFLT and UFLT, it comes as no surprise that both sets of parameters exhibit a significant correlation, with R = 0.948. Table 3 shows that −OH groups (with contributions denoted O2-1) are especially efficient to increase flammability limit temperatures (FLTs), followed by −CN groups (N1-0 and C2-0 contributions) and some heavy atoms, especially I, Br, S, and trivalent P atoms. In contrast, crowded atoms bound to three atoms heavier than fluorine yield a dramatic decrease of FLTs, as is clear from the values of the corresponding B3 parameters. This might be due to the corresponding bonds being particularly strained owing to crowding effects, and

UFLT = (1.0946 ± 0.0000)LFLT + (9.843 ± 0.024) (3) 2

With a predictive value characterized by R = 0.987, AAE = 6 K and RMSE = 8 K, this equation performs somewhat better than any available model for UFLT using molecular structure as input.12,14 Of course, this relation is of little practical value as it requires LFLT data. However, using the LFLT value calculated C



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while the present work is one of the very first attempts to model FLTs, there is already a wealth of experience available with regard to FP modeling. For the latter property, AAE values 10 K, even for those involving advanced techniques.28,29 In this respect, the fact that present GF-MLR models predict FLTs with AAEs close to 12 K is quite encouraging. This is precisely the AAE obtained recently for FP using a similar GF-MLR approach, despite the fact that the exponent in eq 1 was taken from a preliminary work on alkanes rather than optimized for the studied data set.21 However, this result was obtained for a rather homogeneous data set of organosilicon compounds. According to present experience, LFLT might prove easier to model than FP. In that case, this would provide a further incentive to adopt the former as a criterion to assess explosion risks.

Table 3. Parameters of the Present Model (K5/2) and Associated Numbers of Occurences in Parentheses i

NLFLT,i

C2−0 C2−1 C3−0 C3−1 C3−2 C4−0 C4−1 C4−2 C4−3 N1−0 N2−0 N3−0 N3−1 N3−2 O1−0 O2−0 O2−1 F1−0 Cl1−0 Br1−0 I1−0 Si4−0 Si4−1 Si4−2 P3−0 P4−0 S1−0 S2−0 S2−1 S3−0 S4−0

214410 122122 264710 227704 59898 198879 194082 194137 88290 926324 276757 281569 523163 749239 421704 184129 1090258 135948 392017 610671 889631 74033 159239 164819 686599 83058 563739 614242 654332 534751 317691

R3 R4 R5 R5a R6 R6a R>6 Rfused

150305 61338 27925 −111814 48480 −18727 −96484 200963

B2 B3

16405 −289011

Nocc,i

NUFLT,i

Atomic Groups: (51) 404031 (10) 263045 (565) 259763 (521) 283162 (140) 157123 (97) 112395 (308) 181258 (834) 257444 (920) 161795 (26) 955387 (23) 317610 (27) 585359 (27) 743231 (48) 842787 (333) 537775 (301) 314375 (250) 1368564 (4) 215972 (76) 494976 (7) 734827 (2) 1074955 (15) 52254 (5) 108639 (3) 488351 (1) (2) 457108 (1) (43) 824801 (26) 860192 (1) (1) Ring Corrections: (10) 317547 (5) 169478 (37) 16219 (20) 154378 (53) 99532 (301) 250690 (8) −97778 (45) 305026 Crowding Corrections: (13) 109257 (3) −394944

Nocc,i (57) (15) (622) (592) (158) (114) (341) (898) (1003) (23) (23) (51) (37) (47) (375) (331) (289) (3) (93) (13) (4) (17) (2) (2)

4. CONCLUSION To conclude, GF-MLR methods reported in this work are probably the most attractive for engineers needing LFLT or UFLT estimates, considering their simplicity and reduced empiricism. In the future, the more complicated GC-ANN methods might prove valuable as a means to obtain even more accurate predictions, in spite of the fact that they yield little insight into the contributions of the various groups to these properties. However, these methods require further assessment to make sure that the many specialized groups involved do not cause overfitting issues.

(4) (39) (16)

5. EXAMPLES This section illustrates the present approach for three compounds, namely, n-butane, toluene, and hexadecamethylcyclooctasiloxane. n-Butane. The molecule exhibits two C atoms in methyl groups (C4-3) and two in methylene groups (C4-2), no ring and no heavy atom. Thus, using the parameters reported in Table 3:

(13) (6) (46) (18) (70) (345) (7) (52)

NLFLT = 2 × (88290) + 2 × (194137) = 564854 TLFLT = 5648542/5 = 199.9 K

(13) (5)

NUFLT = 2 × (161795) + 2 × (257444) = 838478 TUFLT = 8384782/5 = 234.1 K (Experimental value: 223 K)

therefore especially unstable. Cyclic structures tend to exhibit somewhat higher FLTs, but their influence is especially significant for UFLT, while it is smaller for LFLT. A significant UFLT increase is observed for fused ring systems and, more surprisingly, for three-membered rings, despite their relatively high reactivity. Such systematic trends cannot be derived from earlier GA-MLR or GC-ANN models. This is because GA-MLR models do not directly express the properties of interest in term of simple molecular structural features, while the GC-ANN technique yields complex algebraic expressions from which the influence of any given input variable is not immediately clear. It is interesting to compare modeling approaches for FLTs with those for flash point (FP). As stated in the introduction, FP is closely related to FLTs and especially to LFLT. However,

Toluene. The molecule exhibits one C atom in the methyl group (C4-3), five aromatic C atoms bound to an hydrogen atom (C3-1), one aromatic carbon atom with no H atom attached, and one aromatic ring: NLFLT = 1 × (88290) + 5 × (227704) + 1 × (264710) + 1 × ( −18727) = 1472793 TLFLT = 14727932/5 = 293.3 K (Experimental value: 278 K) D



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(8) Rowley, J.; Rowley, R.; Wilding, W. Estimation of the lower flammability limit of organic compounds as a function of temperature. J. Hazard. Mater. 2011, 186, 551−557. (9) Pan, Y.; Jiang, J.; Wang, R.; Cao, H.; Cui, Y. A novel QSPR model for prediction of lower flammability limits of organic compounds based on support vector machine. J. Hazard. Mater. 2009, 168, 962− 969. (10) Brandes, E.; Mitu, M.; Pawel, D. The lower explosion point - A good measure for explosion prevention: Experiment and calculation for pure compounds and some mixtures. J. Loss Prev. Process Ind. 2007, 20, 536−540. (11) Gharagheizi, F. A QSPR model for estimation of lower flammability limit temperature of pure compounds based on molecular structure. J. Hazard. Mater. 2009, 169, 217−220. (12) Gharagheizi, F.; Ilani-Kashkouli, P.; Mirkhani, S. A.; Mohammadi, A. H. Computation of Upper Flash Point of Chemical Compounds Using a Chemical Structure-Based Model. Ind. Eng. Chem. Res. 2012, 51, 5103−5107. (13) Gharagheizi, F. New Neural Network Group Contribution Model for Estimation of Lower Flammability Limit Temperature of Pure Compounds. Ind. Eng. Chem. Res. 2009, 48, 7406−7416. (14) Gharagheizi, F.; Abbasi, R. A New Neural Network Group Contribution Method for Estimation of Upper Flash Point of Pure Chemicals. Ind. Eng. Chem. Res. 2010, 49, 12685−12695. (15) Lazzús, J. Prediction of flammability limit temperatures from molecular structures using a neural network-particle swarm algorithm. J. Taiwan Inst. Chem. Eng. 2011, 42, 447−453. (16) Gharagheizi, F.; Ilani-Kashkouli, P.; Mohammadi, A. H. Corresponding States Method for Estimation of Upper Flammability Limit Temperature of Chemical Compounds. Ind. Eng. Chem. Res. 2012, 51, 6265−6269. (17) Patel, S. J.; Ng, D.; Mannan, M. S. QSPR Flash point prediction of solvents using topological indices for application in computer aided molecular design. Ind. Eng. Chem. Res. 2009, 48, 7378−7387. (18) Beaucamp, S.; Mathieu, D.; Agafonov, V. Optimal partitioning of molecular properties into additive contributions: the case of crystal volumes. Acta Crystallogr., Sect. B 2007, 63, 277−284. (19) Mathieu, D. Simple Alternative to Neural Networks for Predicting Sublimation Enthalpies from Fragment Contributions. Ind. Eng. Chem. Res. 2012, 51, 2814−2819. (20) Mathieu, D. Inductive modeling of physico-chemical properties: flash point of alkanes. J. Hazard. Mat. 2010, 179, 1161−1164. (21) Mathieu, D. Flash Points of Organosilicon Compounds: How Data for Alkanes Combined with Custom Additive Fragments can Expedite the Development of Predictive Models. Ind. Eng. Chem. Res. 2012, 51, 14309−14315. (22) In practice, a few entries in the original source files are not used here owing to missing compound names. On the other hand, since present models aim at providing FLT estimates for pure compounds, the data included in the original data sets for the equimolar mixture of bis-(1-methylethyl)-phenyl and hydroperoxide is not used either. (23) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in C; Cambridge University Press: Cambridge, U.K., 1992. (24) Carroll, F. A.; Lin, C.-Y.; Quina, F. H. Simple Method to Evaluate and to Predict Flash Points of Organic Compounds. Ind. Eng. Chem. Res. 2011, 50, 4796−4800. (25) Gharagheizi, F.; Eslamimanesh, A.; Mohammadi, A. H.; Richon, D. Empirical Method for Representing the Flash-Point Temperature of Pure Compounds. Ind. Eng. Chem. Res. 2011, 50, 5877−5880. (26) Lee, C. J.; Ko, J. W.; Lee, G. Flash point prediction of organic compounds using a group contribution and support vector machine. Korean J. Chem. Eng. 2012, 29, 145−153. (27) Saldana, D. A.; Stark, L.; Mougin, P.; Rousseau, B.; Pidol, L.; Jeuland, N.; Creton, B. Flash Point and Cetane Number Predictions for Fuel Compounds using Quantitative Structure Property Relationship (QSPR) Methods. Energy Fuels 2011, 25, 3900−3908.

NUFLT = 1 × (161795) + 5 × (283162) + 1 × (259763) + 1 × (250690) = 2088058 TUFLT = 20880582/5 = 337.2 K (Experimental value: 311 K)

Hexadecamethylcyclooctasiloxane. The molecule exhibits 16 C atoms in methyl groups (C4-3), 8 sp3 O atoms with no hydrogen attached (O2-0), 8 sp3 Si atoms with no hydrogen attached (Si4-0), and one 16-membered ring (R>6). In addition, 8 B2 corrections must be applied as every oxygen atom is bonded to two big Si atoms. Therefore NLFLT = 16 × (88290) + 8 × (184129) + 8 × (74033) + 1 × ( −96484) + 8 × (16405) = 3512692 TLFLT = 35126922/5 = 415.2 K (Experimental value: 405 K)

NUFLT = 16 × (161795) + 8 × (314375) + 8 × (52254) + 1 × ( −97778) + 8 × (109257) = 6298030

■

TUFLT = 62980302/5 = 524.4 K

ASSOCIATED CONTENT

* Supporting Information S

A table summarizing experimental and calculated LFLT and UFLT values in K as well as the corresponding numbers of fragments. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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(28) Bagheri, M.; Borhani, T. N. G.; Zahedi, G. Estimation of flash point and autoignition temperature of organic sulfur chemicals. Energy Convers. Manage. 2012, 58, 185−196. (29) Bagheri, M.; Bagheri, M.; Heidari, F.; Fazeli, A. Nonlinear molecular based modeling of the flash point for application in inherently safer design. J. Loss Prev. Process Ind. 2012, 25, 40−51.

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Power Law Expressions for Predicting Lower and Upper Flammability

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