Ind. Eng. Chem. Res. 1994,33, 1086-1089
1086
KINETICS, CATALYSIS, AND REACTION ENGINEERING Are Aromatic Diluents Used in Pyrolysis Experiments Inert? Phillip E. Savaget Chemical Engineering Department, University
of
Michigan, Ann Arbor, Michigan 48109-2136
Hydrogen abstraction from compounds such as benzene and biphenyl is a potential complication when these aromatics are used as diluents in hydrocarbon pyrolysis experiments. This paper presents a general methodology for quantitatively assessing the likelihood that substrate-derived radicals abstract hydrogen from a nominally inert diluent. The key variables are the concentration of the substrate, the pyrolysis temperature, and the dissociation energies of the C-H bonds attacked. Hydrogen abstraction from an aromatic diluent becomes more important as the temperature increases, the substrate concentration decreases, and the C-H bond dissociation energy of the substrate increases. All other factors being equal, the relative rate of hydrogen abstraction from an aromatic diluent is about 10 times higher during the pyrolysis of an n-alkane than during the pyrolysis of an n-alkylbenzene. Introduction Aromatic compounds such as benzene, biphenyl, and terphenyl have been used as diluents in pyrolysis experiments (Khorasheh and Gray, 1993; Poutsma and Dyer, 1982; Savage and Korotney, 1990; Smith and Savage, 1991a,b; Billmers et al., 1989; Senthilnathan and Stein, 1988). These compounds are generally regarded as being unreactive at temperatures around 400 "C because the phenyl C-H bond is much stronger than the C-H bonds in substrates such as alkanes, alkylaromatics, diarylalkanes, and diary1 ethers, which are frequent subjects of pyrolysis studies. Khorasheh and Gray (1993),however, recently reported that biphenyl (presumably formed from phenyl radicals) was a major product from the pyrolysis of n-hexadecanein benzene. They concluded that benzene was not an inert diluent in the thermal cracking of alkanes at temperatures around 400 "C. The present paper presents a general methodology that enables one to determine just how "inert" aromatic diluents are for specific applications. The kinetics analysis that follows identifiesthe important variables and allows one to answer the question posed in the title. Kinetic Analysis An aromatic diluent could be reactive during hydrocarbon pyrolysis if a substrate-derived radical (R')abstracts hydrogen from the diluent. The importance of hydrogen abstraction from the diluent can be assessed by examining the ratio of the rate (P) of abstraction from the diluent (d) relative to the rate of abstraction from the substrate (9).
The rate constants were written in Arrhenius form to obtain the final expression. ~~
+ E-mail
address:
[email protected] Activation energies for hydrogen abstraction reactions can be correlated with their heats of reaction using the Evans-Polanyi relation (Boudart, 1991).
E = E, + (1- a!)AHo E = E,, + aAH0
endothermic reactions exothermic reactions
(2)
The parameter a! typically ranges from 0.25 to 0.50 for hydrogen abstraction reactions (Semenov, 1958;Boudart, 1991; Russell, 1973; Malhotra and McMillen, 1990; Poutsmaand Dyer, 1982;Nigam and Klein, 1993). To use the Evans-Polanyi relation in this analysis, we need to determine the heats of reaction for hydrogen abstraction from an aromatic diluent and from the substrate. Examining the mechanism of hydrocarbon pyrolysis at low substrate concentrationswill permit evaluation of the heat of reaction for these key abstraction steps. The pyrolysis of alkanes and many alkylarenesproceeds through free-radical chain reactions. The propagation sequence in these chains comprises a hydrogen abstraction step and a @-scissionstep as shown below, where RH and Q are molecular products, and 1.1 is a substrate-derived free radical. R'
+ pH -1.1 + RH jL'R'+Q
(3)
In the first step, the radical R' will preferentially attack the substrate C-H bond with the lowest bond dissociation energy (BDE). In n-alkylarenes, the benzylic hydrogens have the lowest C-H BDE. In n-alkanes, secondary aliphatic hydrogens have the lowest C-H BDE. The resultant substrate-derived radical (1.1) then decomposes by 8-scissionto form a primary aliphatic radical and either an a-olefin (for n-alkane substrates) or a vinylarene (for alkylarene substrates). Thus, the free-radical-chaincarrier (R') for the pyrolysis of alkanes and alkylaromatics at low concentrations is typically a primary aliphatic radical. It is this primary radical (or a secondary radical formed via isomerizationof the primary radical) that then participates in hydrogen abstraction steps (Smith and Savage, 1993;
0088-5885/94/2633-1086$04.50/00 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 5,1994 1087 Khorasheh and Gray, 1993;Freund and Olmsted, 1989). The key abstraction reactions, then, are the attack of a primary or secondary alkyl radical on a C-H bond in the aromatic diluent and on a secondary aliphatic or secondary benzylic C-H bond in the substrate. Now, the heat of reaction for a hydrogen abstraction step is equal to the difference between the BDE of the C-H bond broken and the BDE of the C-H bond formed in the reaction. Consequently, one can relate the heats of reaction to the C-H bond dissociation energies as
Equation 4 shows that hydrogen abstraction reactions are endothermic if the C-H bond broken is stronger than the C-H bond formed by the reaction. The converse is true for exothermic abstraction reactions. The values of the bond dissociation energies for the C-H bonds central to this analysis are in the order of phenyl > primary alkyl > secondary alkyl > secondary benzylic (Tsang, 1992; McMillen and Golden, 1982;Benson, 1976). Therefore, hydrogen abstraction from an aromatic diluent (by a primary or secondary alkyl radical) is an endothermic reaction, whereas abstraction from the substrate is an exothermic (or thermoneutral) reaction. The difference in the activation energies for abstraction from the diluent and from the substrate can then be estimated from the Evans-Polanyi relation as
= (1 - a ) m d 0- amso
(5)
Substituting eq 4 into eq 5 gives the difference in activation energies.
The ratio of abstraction rates is then given by
($) (7) This final equation provides a basis for making a quantitative assessment of the significance of hydrogen abstraction from a diluent for any set of reaction conditions. Before employing eq 7,we note that the present analysis has not explicitly considered the fate of the aryl radical formed by hydrogen abstraction from the aromatic diluent. We briefly consider this issue here and take benzene as a representative aromatic diluent. One would expect phenyl radicals (4.) to either abstract hydrogen from the substrate (NH)or form biphenyl (6-4) by either adding to benzene (4H) or by recombination, as illustrated in the reactions below.
4.
+ pH
-. + ebs
p
-
4H
rec
4. + 4'
4-4
Clearly, there is a competition between hydrogen abstraction by and addition of phenyl radicals. The relative rates of these two steps will determine whether the diluentderived aryl radicals lead to additional products. The rate constants for the abstraction and addition steps are both substrate- and diluent-dependent, and for benzene they appear to be of roughly the same order of magnitude (Chen et al., 1989;Duncan and Trotman-Dickenson, 1962;Fahr and Stein, 1988, 1989). Thus, for cases in which the concentration of benzene greatly exceeds the substrate concentration, one would expect the addition reaction to be dominant. This expectation is consistent with the high biphenyl selectivities Khorasheh and Gray (1993)reported for the thermal cracking of n-hexadecane (1-5mol %) in benzene. Note too that although the abstraction step may not lead to measurable amounts of diluent-derived products, it can nevertheless influence the pyrolysis kinetics (Rebick, 1980). We will now illustrate the utility of eq 7 by briefly examining the effects of temperature, concentration, and substrate C-H BDE on the importance of hydrogen abstraction (by a primary alkyl radical) from an aromatic diluent. To simplify this general illustration, we will take the ratio of preexponential factors to be equal to unity. If eq 7 were applied to a specific substrate and diluent, one would use thermochemical kinetics techniques (Benson, 1976)and also account for the reaction path degeneracy to estimate this ratio of preexponential factors. The C-H bond dissociation energies required in eq 7 are available in the literature (Tsang, 1992;McMillen and Golden, 1982; Benson, 1976). We will use Tsang's (1992)values of 113 kcal/mol for the BDE of the C-H bond in benzene as BDEd and 100.5 kcal/mol for the BDE of a primary C-H bond in an alkane as BDE,. Effect of Substrate. Equation 7 shows that the ratio of the rate of hydrogen abstraction from an aromatic diluent relative to that from the substrate will depend on the BDE of the C-H bond(s) in the substrate. Abstraction from benzene should become less important as the BDE of the substrate C-H bond attacked decreases. Thus, qualitatively, one would expect abstraction from benzene to be less important for the pyrolysis of alkylbenzenes, where secondary benzylic hydrogens are abstracted, than for the pyrolysis of n-alkanes, where secondary aliphatic hydrogens are abstracted. A quantitative analysis is consistent with this expectation. Figure 1 shows the rate ratio at 400 OC as a function of the BDE of the C-H bond attacked in the substrate. We have also indicated the value of the BDE (from Tsang) for the most easily abstracted hydrogen atom for n-alkanes, n-alkylbenzenes, and n-alkylpyrenes. The three lines in Figure 1 correspond to values of the Evans-Polanyi a of 0.25,0.35,and 0.50. The mole fraction of the substrate is 0.01. Figure 1 shows that, under these specific conditions, a primary radical will abstract hydrogen from an aromatic diluent a t roughly 10% of the rate at which it will abstract hydrogen from an n-alkane. The rate ratio for an n-alkane is a strong function of CY. The highest ratios correspond to a = 0.50,where 36% of the hydrogen abstraction reactions will be from the aromatic diluent. Thus, abstraction from an aromatic diluent does appear
1088 Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994 ~-]oOlxl
1x10'
1
l
a = 0.5
x
l
o
0
7
1x10'-
/'
8 1x102-
d
3 iX10*-
1x104-
lxlo-~o 75 ' 80 85 90 95 100 C-H Bond Dissociation Energy "
Figure 1. Rate of abstraction of phenyl hydrogen relative to rate of abstraction of substrate hydrogen as a function of the substrate C-H BDE at 400"C with a substrate mole fraction of 0.01. The three lines correspond to values of the Evans-Polanyi a of 0.25,0.35,and 0.50.
IO
-;01x1
C-H Bond Dissociation Energy
Figure 3. Rate of abstraction of phenyl hydrogen relative to rate of abstraction of substrate hydrogen aa a function of the substrate C-H BDE at 400 "C with an Evans-Polanyi a of 0.35. The three lines correspond to substrate mole fractions of 0.01,0.03,and 0.10.
important as the temperature increases. The effect of temperature is more significant for substrates with lower C-H bond dissociation energies. Figure 3 shows that if all other factors are equal, abstraction from the aromatic diluent becomes more important as the substrate concentration (or mole fraction) decreases. Indeed, the form eq 1shows that the rate ratio is inversely proportional to the substrate concentration. This reciprocal relationship is clearly evident in the study of n-hexadecane cracking in benzene by Khorasheh and Gray (1993). These authors report biphenyl selectivities of 45,16, and 9 mo1/100 mol of n-hexadecanedecomposed at initial n-hexadecanemole fractions of 0.01, 0.03, and 0.05, respectively.
1x100
1x10-1
Summary and Conclusions 1x10470
75
80 85 90 95 100 C-H Bond Dissociation Energy
Figure 2. Rate of abstraction of phenyl hydrogen relative to rate of abstraction of Substrate hydrogen as a function of the Substrate C-H BDE with a substrate mole fraction of 0.01 and an EvansPolanyi a of 0.35. The three lines correspond to temperatures of 350,400,and 460 "C.
to be significant during the pyrolysis of n-alkanes at low concentrations. This observation is consistent with Khorasheh and Gray's (1993) report of biphenyl as a major product from n-hexadecane cracking in benzene. Note, however, that the percentage of abstraction reactions that involve an aromatic diluent drops to less than 1% for alkylbenzene substrates, and to nearly 0.1% for alkylpyrene substrates. Regardless of the precise value of a, then, it is clear that the rate ratio is about an order of magnitude smaller for the pyrolysis of alkylbenzenesthan it is for the pyrolysis of alkanes. Abstraction from an aromatic diluent becomes even less significant for the pyrolysis of polycyclic alkylaromatics that have additional resonance stabilization energy and benzylic C-H bonds with even lower BDEs. Effect of Temperature and Concentration. Figures 2 and 3 show the effects of temperature and substrate mole fraction on the rate ratio for pyrolyses a t 400 "C. The Evans-Polanyi a was set equal to 0.35 for these calculations. Figure 2 shows that if all other factors are equal, abstraction from the aromatic diluent becomes more
Equation 7 allows one to determine whether benzene and related aromatic hydrocarbons such as biphenyl can be employed as "inert" diluenta in hydrocarbon pyrolysis studies under a given set of conditions. The key variables to consider are the substrate concentration, the dissociation energy of the substrate C-H bond attacked, and the pyrolysis temperature. The general illustration presented here showed that taking an aromatic diluent to be inert becomes a poorer approximation as the pyrolysis temperature increases, as the substrate concentration decreases, and as the BDE of the substrate C-H bond attacked increases. Abstraction from an aromatic diluent would be about an order of magnitude more likely during the pyrolysis of an n-alkane than during the pyrolysis of an n-alkylbenzene or an n-alkylpyrene. This analysis is consistent with the recent report (Khorasheh and Gray, 1993) of biphenyl as a major product from n-hexadecane pyrolysis in benzene. Finally, eq 7 shows that the BDE of the diluent is an important factor in determining inertness. This link is well recognized, and it is precisely the reason that aromatic hydrocarbons, which have very high C-H BDEs, are typically used as diluenta. We note, however, that diluenta with a BDE greater than the dissociation energy of the phenyl C-H bond would be even more Kinertn than aromatic hydrocarbons. Aromatic fluorocarbons may be one such class of compounds. Aromatic C-F bonds are about 15 kcal/mol stronger than aromatic C-H bonds (Benson, 1976).
Ind. Eng. Chem. Res., Vol. 33, No. 5, 1994
Acknowledgment
I thank Dr. C. Michael Smith for helpful discussions and the donors of the Petroleum Research Fund (ACSPRF 23744-AC41, administered by the American Chemical Society, for partial support of our pyrolysis research. Nomenclature A = Arrhenius preexponential factor BDE = bond dissociation energy C = concentration d = diluent E = Arrhenius activation energy Eo = intrinsic barrier height for thermoneutral reaction AH = heat of reaction k = rate constant Q = molecular product r = rate of hydrogen abstraction R = gas constant R' = free radical RH = molecular product s = substrate T = absolute temperature (K) Greek Symbols a = parameters in Evans-Polanyi relation 4 = phenyl radical
4H = benzene 4-4 = biphenyl = free radical that decomposes unimolecularly
p
pH = substrate molecule Literature Cited Benson, S. W. Thermochemical Kinetics, 2nd ed.; John Wiley & Sons: New York, 1976. Billmers, R.; Brown, R. L.; Stein, S. E. Hydrogen Transfer from 9,lO-Dihydrophenanthreneto Anthracene. Int. J. Chem. Kinet. 1989, 21,-375-386. Boudart. M. Kinetics of Chemical Processes: Butterworth-Heinemann'Reprint Series; Stoneham, MA, 1991. Chen, R. H.; Kafafi, S. A.; Stein, S. E. Reactivity of Polycyclic Aromatic Aryl Radicals. J. Am. Chem. SOC.1989,111, 1418. Duncan, F. J.; Trotman-Dickenson, A. F. The Reactions of Phenyl Radicals from the Photolysis of Acetophenone and the Strength of the C-H Bond in Benzene. J. Chem. SOC.1962,4672. Fahr, A.; Stein, S. E. Gas Phase Reactions of Phenyl Radicals with Aromatic Molecules. J. Phys. Chem. 1988, 92, 4951. ~
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Fahr, A.; Stein, S. E. Reactions of Vinyl and Phenyl Radicals with Ethyne, Ethene, and Benzene. Proc. Znt. Symp. Combust. 1989, 22, 1023. Freund, H.; Olmsted, W. N. Detailed Chemical Kinetic Modeling of Butylbenzene Pyrolysis. Znt. J. Chem. Kinet. 1989,21,561-574. Khorasheh, F.; Gray, M. R. High-pressure Thermal Cracking of n-Hexadecane in Aromatic Solvents. Znd. Eng. Chem. Res. 1993, 32, 1864-1876. Malhotra, R.; McMillen, D. F. A Mechanistic Numerical Model for Coal Liquefaction Involving Hydrogenolysis of Strong Bonds. Rationalization of Interactive Effects of Solvent Aromaticity and Hydrogen Pressure. Energy Fuels 1990,4, 184-193. McMillen, D. F.; Golden, D. M. Hydrocarbon Bond Dissociation Energies. Annu. Rev. Phys. Chem. 1982,33,493-532. Nigam, A.; Klein, M. T. A Mechanism Oriented Lumping Strategy for Heavy Hydrocarbon Pyrolysis: Imposition of Quantitative Structure-Reactivity Relationships for Pure Components. Znd. Eng. Chem. Res. 1993,32, 1297-1303. Poutsma, M. L.; Dyer, C. W. Thermolysis of Model Compounds for Coal. 3. Radical Chain Decomposition of 1,3-Diphenylpropane and 1,4-Diphenylbutane. J. Org. Chem. 1982, 47, 4903-4914. Rebick, C. Hydrogen Transfer Catalysis in Hydrocarbon Pyrolysis. In Frontiers of Free Radical Chemistry; Academic Press: New York, 1980; pp 117-137. Russell. G. A. Reactivitv. Selectivitv. and Polar Effects in Hvdrogen Atom Transfer Reactions. In Fiee Radicals; John Wile;& SGns: New York, 1973; pp 275-326. Savage, P. E.; Korotney, D. J. Pyrolysis Kinetics for Long-chain n-Alkylbenzenes: Experimental and Mechanistic Modeling Results. Ind. Eng. Chem. Res. 1990,29,499-502. Semenov,N. N. SomeProblems in Chemical Kinetics and Reactivity; Princeton University Press: Princeton, NJ, 1958. Senthilnathan, V. P.; Stein, S. E. Mechanisms of Condensation of Biaryl Hydrocarbons. J. Org. Chem. 1988,53, 3000-3007. Smith, C. M.; Savage, P. E. Reactions of Polycyclic Alkylaromatics. 1. Pathways, Kinetics, and Mechanisms for 1-Dodecylpyrene Pyrolysis. Ind. Eng. Chem. Res. 1991a, 30,331-339. Smith, C. M.; Savage, P. E. Reactions of Polycyclic Alkylaromatics. 2. Pyrolysis of 1,3-Diarylpropanes. Energy Fuels 1991b,5,146155. Smith, C. M.; Savage, P. E. Reactions of Polycyclic Alkylaromatics. 6. Detailed Chemical Kinetic Modeling. Chem. Eng. Sci. 1994, 49,259-270. Tsang, W. Kinetic Stability of Unsaturated Organics at High Temperatures. Prepr. Pap.-Am. Chem. SOC.,Diu. Fuel Chem. 1992,37, 367-374.
Received for review October 12, 1993 Revised manuscript received February 10, 1994 Accepted February 28, 1994' Abstractpublishedin Advance ACSAbstracts, April 1,1994.
