Mechanistic Modeling of the Thermal Cracking of Decylbenzene

Ind. Eng. Chem. Res. 2003, 42, 5791-5808

5791

Mechanistic Modeling of the Thermal Cracking of Decylbenzene. Application to the Prediction of Its Thermal Stability at Geological Temperatures Vale´ rie Burkle´ -Vitzthum and Raymond Michels*,† CNRS-UMR 7566 G2R, Faculte´ des Sciences, BP 236, 54501 Vandoeuvre Les Nancy Cedex, France

Ge´ rard Scacchi and Paul-Marie Marquaire*,‡ De´ partement de Chimie Physique des Re´ actions, CNRS-UMR 7630, ENSIC-INPL, 1 rue Grandville, BP 451, 54001 Nancy Cedex, France

Thermal cracking of decylbenzene is experimentally studied at 330 °C under 70 MPa for 10 h to 1 month, that is, up to 20% of conversion. A detailed kinetic model consisting of 946 freeradical reactions and 1 molecular reaction is developed to describe the results. The formation of main products, namely, toluene, ethylbenzene, nonene, nonane, and octane, is correctly described by the model. The global activation energy is equal to 66 kcal‚mol-1. The molecular reaction, that is, the retroen reaction, is of great importance: it explains the major part of toluene and nonene formation at 330 °C. At 400 °C this reaction becomes negligible but at 200 °C it is predominant. Its activation energy is about 54 kcal‚mol-1 and is confirmed by experimental measurements. The mechanistic kinetic model is applied to the prediction of the thermal stability of decylbenzene at temperatures usually encountered in petroleum sedimentary basins (T < 250 °C). At such temperatures, the main reactive pathway, controlled by the retroen reaction, leads to the formation of toluene. Such conclusion is not intuitive in the geochemistry field and suggests that long-chain alkylbenzenes may inhibit rather than accelerate the cracking of alkanes in natural hydrocarbon mixtures. Introduction An important issue in organic geochemistry and in the petroleum geology community is to predict the survival of hydrocarbon mixtures in sedimentary basin conditions. There, in reservoir rocks, hydrocarbons are subjected to temperatures ranging usually between 100 and 200 °C for several millions of years. One challenge is to be able to estimate the survival of economic oil reserves in deep sections of basins (the hottest) and predict their composition. Because of obvious kinetic reasons, the investigation of the thermal stability and cracking kinetics of hydrocarbon mixtures necessitates the use of pyrolysis techniques at temperatures in the 250-350 °C range and times of several hours to weeks. The extrapolation to geological time-temperature conditions (100-200 °C, several million years) therefore needs a reliable kinetic model based on chemical mechanisms. This is why pyrolysis and modeling of various pure hydrocarbons and hydrocarbon mixtures representative of natural oils have been investigated in the geochemical community.1-23 Our work aims at the construction of a mechanistic kinetic model including most hydrocarbons reactive families present in natural oils. Several steps in the experimentation and modeling have already been performed.5,22,24,25-29 Decylbenzene represents one of these reactive families. Decylbenzene was chosen because it appears that it could highly influence the cracking rate of other com* Authors to whom correspondence should be addressed. † Tel.: 33-383-68-47-50. Fax: 33-383-68-47-01. E-mail: [email protected]. ‡ E-mail: [email protected].

pounds, especially alkanes. In fact, the C-C bond in the β position on the alkyl substituent of the benzene ring has a low bond energy compared to other C-C bonds in the molecule or in alkanes. The cleavage of this C-C bond will create two hydrocarbon radicals, the nonyl radical and the benzyl radical, stabilized by resonance, and lead to the formation of toluene. In a mixture with an alkane, for example, the alkyl radical will induce a faster breakage of the latter, and thus accelerate its thermal decomposition, while toluene is a well-known inhibitor of alkane cracking.30 The determination of the kinetic effect of decylbenzene in a mixture is therefore not a trivial prediction. The investigation of the thermal reactivity and kinetic behavior of pure decylbenzene is a necessary stage in our scientific goal and is an important step in the construction of a kinetic model for complex mixtures, allowing extrapolation to geological time-temperature conditions. Some authors studied the pyrolysis of alkylbenzenes and preliminary attempts to explain the products formed involve free-radical and molecular reactions, but few quantitative tests of the proposed mechanisms were published. Savage and Klein31 pyrolyzed pentadecylbenzene between 375 and 450 °C for various periods from 10 to 180 min, which lead to conversions between 2 and 100%. The major identified products were toluene, tetradecene, styrene, ethylbenzene, and tridecane. These authors wrote a strictly free-radical primary mechanism and explained the observed conversion and productions of toluene and tridecane up to a conversion of 50%.32 They discussed the importance of a molecular reaction, the

10.1021/ie030086f CCC: $25.00 © 2003 American Chemical Society Published on Web 10/10/2003

5792 Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003

retroen reaction, proposed by Mushrush and Hazlett33 and concluded it was negligible.31 Domine´5 studied butylbenzene between 305 and 357 °C and conversions ranged between 0.1 and 48%. The major products were ethane, propane, toluene, propene, and a branched isomer of reactant, methylpropylbenzene. Only traces of styrene were found. The author proposed a brief mechanism that explains qualitatively the observed products. His mechanism includes freeradical reactions and the retroen reaction. Be´har et al.23 carried out experiments on dodecylbenzene from 325 to 425 °C during times ranging from 1 to 72 h. The major products observed are toluene, ethylbenzene, decane, undecene, undecane, and a heavy aromatic fraction. A simplified kinetic scheme was proposed but not quantitatively tested. Despite these studies, the mechanism of decylbenzene cracking remained unclear. Our aim was to bring new information and to compare our results with those already published. The results presented in this paper correspond to the pyrolysis and mechanistic kinetic modeling of pure decylbenzene. The choice of the experimental temperature range (typically 330-350 °C) results from a compromise: Arrhenius parameters are constants in a 150 °C range, so experiment temperature must be as low as possible to permit extrapolation at low temperature (typically 200 °C for the sedimentary basin sections we are interested in). But in the laboratory, experiment durations must remain reasonably long, and therefore it is not possible to operate at geological temperatures. The construction of the mechanism takes into account free-radical reactions as well as retroen reaction and this choice will be discussed. It includes 943 primary free-radical reactions, 3 secondary free-radical reactions, and 1 retroen reaction with kinetic data in Arrhenius form. The quantitative formation of all products is explained up to 20% of conversion. The mechanism is not exhaustive but all simplifications are justified. Furthermore, extrapolation of the kinetic model to low temperatures (150-200 °C) and the consequence on the behavior of decylbenzene is presented.

Figure 1. Major light products (molecular mass less than decylbenzene) obtained by pyrolysis of decylbenzene at 330 °C, 70 MPa.

Figure 2. Major heavy products (molecular mass higher than decylbenzene) obtained by pyrolysis of decylbenzene at 330 °C, 70 MPa.

DB-PETRO J&W Scientific, 0.2-mm i.d, 0.5-µm film fused silica column. The temperature program was 0 °C for 3.5 min followed by a rise in temperature to 300 °C at 6 °C/min. Analysis of the C16+ Fraction. Gold cells were pierced and cut into pieces and products were extracted in hexane under ultrasonication for 1 h. An aliquot fraction was analyzed by GC-FID (same characteristics as above) using a 60-m DB-5 J&W Scientific, 0.25-mm i.d, 0.1-µm film fused silica column. The temperature program was 60-160 °C at 15 °C/min followed by a rise in temperature to 300 °C at 3 °C/min. Quantification was done by using an internal standard. Identification of Products. Gold cells were pierced and cut into pieces and products were extracted in hexane under ultrasonication for 1 h. Products were identified by gas chromatography-mass spectrometry using the same analytical conditions as described above. Experimental Results

Experimental Procedure Samples. Decylbenzene (purity g 99.5%) was obtained from Fluka and used as received. Heating Procedure. Pyrolysis was carried out in gold cells (40-mm length, 5-mm i.d., and 0.5-mm thick). Reactors were loaded with 30 mg of sample, sealed under a helium atmosphere (purity 99.9999%), and welded under cooled nitrogen to not alter hydrocarbons. The gold cells were put in autoclaves kept at a pressure of 70 MPa at 330 °C. Experiment durations were 10 h, 24 h, 72 h, 168 h (1 week), and 720 h (1 month). For each experimental condition 10 cells were pyrolyzed (five for C1-C16 fraction and five for C16+ fraction) to check the reproducibility of the results. At the end of pyrolysis the autoclaves were rapidly (5 min) cooled at room temperature in a water heat exchanger so that the cooling time was negligible relative to heating time. Complete procedure and pyrolysis apparatuses are described elsewhere.34,35 Analysis of the C1-C16 Fraction. Gold cells were placed in an oven thermostated at 250 °C and pierced in a vacuum line. An aliquot fraction was analyzed by a gas chromatography-flame ionization detector (HP 5890 Serie II GC coupled to a HP FID) using a 50-m

Products. The major light products (molecular mass less than decylbenzene, Figure 1) obtained by pure decylbenzene pyrolysis are toluene, nonene, octane, ethylbenzene, and nonane while the major heavy products (molecular mass higher than decylbenzene, Figure 2) are nonadecylbenzene and biaromatics (two aromatic nuclei connected by a chain of 12 carbon atoms). For pyrolysis durations higher than 72 h, branched cyclopentanes and cyclohexanes with 9 atoms of carbon in total were identified and replaced the major part of nonene. Those products here are called cyclo-C9. The minor products (Figure 3) are hexyltetralin and isomers of decylbenzene: (1-methylnonyl)benzene, (1-butylhexyl)benzene, (1-propylheptyl)benzene, and (1-ethyloctyl)benzene. A distribution of other alkylbenzenes from propylbenzene to nonylbenzene and some gases were observed but remain negligible at the studied conversions. Traces of styrene were found in accordance with earlier observations.5 Formation of major products and hexyltetralin and isomers of decylbenzene versus time are presented in Figure 4a,b. All productions increase with time except for nonene and its derived products called cyclo-C9, heavy products, and hexyltetralin, whose formation curves show a maximum.

Ind. Eng. Chem. Res., Vol. 42, No. 23, 2003 5793

Figure 5. µ-Radicals of decylbenzene.

Figure 3. Minor products obtained by pyrolysis of decylbenzene at 330 °C, 70 MPa.

Figure 4. (a) Experimental molar fractions versus time, of major products, obtained by pyrolysis of decylbenzene at 330 °C, 70 MPa. (b) Experimental molar fractions versus time, of heavy products and minor products, obtained by pyrolysis of decylbenzene at 330 °C, 70 MPa.

Model Construction The reaction network of pure decylbenzene cracking includes 947 reactions (943 primary free-radical reactions, 3 secondary free-radical reactions, and 1 molecular reaction) using 49 molecules and 73 radicals and it is presented in the Appendix. Primary Mechanism. It includes all different elementary free-radical reactions: initiations by monomolecular homolysis, monomolecular and bimolecular isomerizations of decylbenzyl radicals called µ-radicals (Figure 5), their decompositions by β-scission, H-transfers and terminations by disproportionation or recombination reactions, and a molecular step: the retroen reaction. This primary mechanism is not fully exhaus-

tive because isomerizations, decompositions, and Htransfers were written only for µ-radicals but it has been proven that reactions for other radicals are negligible because their amounts are largely lower than µ-radical amounts. Some examples from each type of reactions are given in Figure 6a. Initiations by Monomolecular Homolysis. Ten initiations by monomolecular homolysis of C-C bonds were written. One of these is predominant: the C-C bond in the β position (Figure 7) on the alkyl substituent of the benzene ring has a lower bond energy (68 kcal‚mol-1) than all other C-C bonds (82 kcal‚mol-1, except the C-C bond in the R position on the alkyl substituent of the benzene ring that has a higher bond energy, about 96 kcal‚mol-1). Homolysis of C-H bonds were not taken into account because C-H bond energies are higher than 100 kcal‚mol-1 and would need higher temperatures to be activated. Monomolecular Isomerizations. One hundred fortyeight monomolecular isomerizations from µ-radicals and branched isomers of µ-radicals (Figure 5) were included. This type of isomerization corresponds to an H-transfer from the alkyl substituent to the free-radical point with the formation of a 5, 6, or 7-atoms ring as activated complex. Other rings were ruled out because of their high ring strain energy. Another type of monomolecular isomerization was taken into account to explain the formation of branched isomers of decylbenzene (Figure 3). The free radical point from a µ-radical or a branched isomer of a µ-radical attacks the carbon atom on the ipso-position of the aromatic ring (Figure 6a). So the activated complex contains a second 5-, 6-, or 7-atoms ring and aromaticity is temporarily lost. The decomposition by β-scission of the activated complex leads to a branched isomer of a µ-radical. There are 18 isomerizations of that type called “ipso-isomerizations” in the mechanism. Bimolecular Isomerizations. This type of free-radical reaction is identical to H-transfers between µ-radicals and decylbenzene. There are 90 reactions. Decompositions by β-Scission. Mechanism includes 17 decompositions by β-scission of µ-radicals. Two of these are particularly important because they concern radicals stabilized by resonance: decomposition of stabilized µ1radicals and decomposition of µ3-radicals (Figure 5) that lead to stabilized benzyl radicals. H-Transfers. Six hundred forty H-transfers between all radicals (except µ-radicals because the corresponding free-radical reactions are bimolecular isomerizations) and decylbenzene were written. Retroen Reaction. One molecular retroen reaction that directly forms toluene and nonene was added, although some authors31 concluded this reaction is negligible. This choice is discussed below.


Figure 6. (a) Primary mechanism of decylbenzene cracking: typical reactions. (b) Secondary mechanism of decylbenzene cracking.

Figure 7. C-C bond in the β-position of the aromatic ring in the decylbenzene molecule.

“Ortho” Addition. A particular addition was written to explain 1-hexyltetralin formation. The free-radical point from the µ4-radical attacks the C-atom on the R-position in the aromatic ring (Figure 6a). The formed radical contains two 6-atom rings and aromaticity is lost. Terminations. All termination rate constants have about the same value, so only those implying radicals whose concentrations are important were taken into account. Nineteen terminations by disproportionation or recombination reactions were written.

Secondary Mechanism. Three secondary reactions were taken into account to explain the formation of products that were not generated by the primary mechanism. These reactions are as follows: one reverse radical disproportionation (RRD) explaining the formation of the ethylbenzyl radical and therefore ethylbenzene and two additions from major µ-radicals (µ1-radicals) on the two primary alkenes (nonene and styrene) that lead to the formation of heavy products (Figure 6b). Estimation of Rate Constants. Different methods were employed to estimate rate constants in Arrhenius form depending on free-radical reaction type. The method is indicated for each free-radical reaction type and estimation is detailed for some key-reactions. Often the estimated rate constant corresponds to that of the reverse reaction. Thermochemical properties allow calculation of the rate constant of the forward reaction,


Figure 8. Comparison between experimental and simulated parameters of decylbenzene pyrolysis at 330 °C, 70 MPa: (a) conversion of decylbenzene; (b) molar fractions of toluene, nonene, and nonane; (c) molar fractions of ethylbenzene and octane; (d) molar fractions of (1-methylnonyl)benzene and (1-propylheptyl)benzene; (e) molar fractions of (1-butylhexyl)benzene and (1-ethyloctyl)benzene; (f) molar fraction of 1-hexyltetralin.

E1 - E-1 ) ∆rH°(T) - ∆nRT Ln(A1/A-1) ) ∆rS°(T)/R - ∆n‚(1 + ln(R1Tc0/P0)) where ∆rH°(T) is the enthalpy of the reaction (cal‚mol-1), E1 is the activation energy of the forward reaction (cal‚ mol-1), E-1 is the activation energy of the reverse reaction (cal‚mol-1), ∆rS°(T) is the entropy of reaction (cal‚

mol-1‚K-1), A1 is the A factor for the forward reaction (mol, L, s), A-1 is the A factor for the reverse reaction (mol, L, s), ∆n is the variation of the mole number, R ) 1.98 cal‚mol-1‚K-1, R1 ) 0.082 L‚atm‚mol-1‚K-1, P0 ) 1 atm, c0 ) 1 mol‚L-1, and T is the temperature in K. The enthalpy of reaction ∆rH°(T) and entropy of reaction ∆rS°(T) are calculated from enthalpies of formation ∆fH° and entropies S° by


Figure 9. Pathways through which major products are formed.

Figure 10. Determination of global activation energy.

∆rH°(T) ) Σνi∆fHi°(T) ∆rS°(T) ) ΣνiSi°(T) Enthalpies of formation and entropies were calculated by the THERGAS software36 that uses the methods of Benson37 and statistical thermodynamics. Values that could not be calculated by the software were found in the literature or estimated by analogy. Initiations by Monomolecular Homolysis. All initiations by monomolecular homolysis (except homolysis of the C-C bond in the β position on the alkyl substituent) were calculated by the KINGAS software38 that uses modified collisions theory. The homolysis of the C-C bond in the β position is important because it determines the proportion of nonane. Its rate constants were found in the NIST database.39,40 Monomolecular Isomerizations. Their rate constants were calculated by the KINGAS software that uses activated complex theory. Bimolecular Isomerizations and H-Transfers. When no radicals stabilized by resonance or the phenyl radical appear or disappear during reaction, the corresponding constant rates are the same as those commonly used for alkanes pyrolysis at 330 °C. For other reactions, values were found or deduced by analogy from values in the NIST database.39 For reactions that lead to the

formation or consumption of a benzyl radical, a direct measure by Paputa and Price41 and a relative measure by Zhang et al.42 were used. For reactions that lead to the formation and consumption of a radical stabilized by resonance, a direct measure by Louw and Lucas43 was used, and for reactions involving benzene or phenyl radicals, a relative measure by Zhang et al.42 was used. Decompositions by β-Scission. As for bimolecular isomerizations and H-transfers, when no radicals stabilized by resonance appear or disappear, common values of rate constants were used. There are two decompositions by β-scission that involve radicals stabilized by resonance: decomposition of µ1-radical, the major radical, leading to styrene, which determines the RRD rate, and decomposition of the µ3-radical, which leads to the benzyl radical and so to toluene, and to nonene, the major products. For those decompositions, literature values were used.32,39,44,45 Retroen Reaction. Only retroen reactions for alkenes were described until now. The used rate constant was derived from the NIST database46 (direct measure) and from the literature47 and was verified experimentally (see below). RRD. Its rate constant was deducted from the reverse reaction, which is a termination by disproportionation. Additions. Additions are reverse reactions from decomposition by β-scission. Terminations. Rate constants were calculated by KINGAS software using modified collisions theory. Validation of the Model and Kinetic Analysis Experimental Validation. Simulations were performed at experimental conditions using the software CHEMKIN II. The mechanism was tested by comparing model output with experimental data obtained by pure decylbenzene pyrolysis at 330 °C, 70 MPa and from 10 h to 1 week (168 h). The model shows good agreement with experimental data up to 20% conversion for all major products as well as most minor products (Figure 8a-e), except for hexyltetralin (Figure 8f). Results are


Figure 11. First-order plots for the decylbenzene pyrolysis.

Figure 12. Comparisons between simulated molar fractions versus conversion of toluene, nonene, ethylbenzene, and octane at 330, 200, and 150 °C.

Figure 13. Determination of retroen reaction activation energy (ln X versus 1/T where X is the molar production of nonene + nonadecylbenzene divided by initial molar amount of decylbenzene).

shown only up to 12% conversion (72 h) because authors want to focus on low conversions. Flux Distribution. The model was used to elucidate the main reaction pathways in the pyrolysis of decylbenzene. A simulation was performed at 330 °C, 70 MPa, and a residence time of 24 h, which corresponds to 5% conversion. This simulation was used to derive Figure 9, which shows the pathways through which

major products are formed. Considering a flux of consumption of decylbenzene taken equal to 100, the overall flux of production and consumption of the different species was calculated. Arrows and numbers indicate the relative importance of the different pathways. Thirty percent of decylbenzene disappears through the retroen reaction, 27% by H-transfers that lead to µ1-radical, and 28% by H-transfers that lead to the other µ-radicals. Most of the toluene and nonene are directly formed by the retroene reaction. The other pathways are (a) decomposition by β-scission of µ3-radical for both toluene and nonene and (b) homolysis of decylbenzene leading to a benzyl radical (Figure 6a). Decomposition by β-scission of µ1-radicals leads to octane and styrene, which is not observed because it disappears with addition to form biaromatics and with RRD to form the ethylbenzyl radical and so ethylbenzene. Chain Length λ. The kinetic chain length λ is defined as the rate at which radicals propagate the chain to form products relative to their rate of termination. The latter is also equal to the rate of initiation (quasi-steady-state approximation). Hence,


Figure 14. Arrhenius diagram defining the apparent activation energy of decylbenzene pyrolysis deduced from first-order rate law.

λ)

rate of propagation rate of initiation

At 330 °C, 70 MPa, and a residence time of 24 h, the chain length λ is equal to 17. This value is low compared to the chain length of alkane pyrolysis that equals several thousands.26,27 That means that decylbenzene pyrolysis is mainly controlled by initiation reactions. Global Activation Energy. Simulations were performed at 325, 330, and 335 °C. For those temperatures rates of decylbenzene consumption were determined at several but constant conversions (from 1% to 2.5%). The slope of curve representing the logarithm of rate vs temperature inverse (1/T, K-1) is equal to the opposite of global activation energy divided by R (-Ea/R, R ) 1.98 cal‚mol-1‚K-1). Global activation energy has been found to be equal to 66 kcal‚mol-1 and remains constant when conversion increases from 1% to 2.5% (Figure 10). Reaction Order n. Reaction order n is defined by

r ) k[C16H26]n where r is the rate of decylbenzene consumption, k is the global rate constant, and [C16H26] is the decylbenzene concentration. Several simulations were performed with different initial decylbenzene concentrations. For the various concentrations tested and for identical reaction duration, the conversion obtained is constant. This demonstrates that the reaction order is 1. This is graphically confirmed by the linear interpolation of the data points in Figure 11, presenting ln(1 - conv) versus time (s). Mechanism Simulations at 150 and 200 °C. Simulations were performed at 150 and 200 °C. Comparisons between molar fractions of major products versus conversion at 150, 200, and 330 °C are presented in Figure 12. At 150 and 200 °C, for the same conversion, the formation of octane and ethylbenzene is negligible relative to their formations at 330 °C. Free-radical reactions are negligible relative to the retroen reaction, which is responsible for all of the conversion. There are two reasons for this. First is the difference between global activation energy (66 kcal‚mol-1) and the activation energy of the retroen reaction, which is much lower (54 kcal‚mol-1). Thus, the retroen reaction becomes important at low temperature and favors the formation of toluene. The second reason is that free-radical reac-

tions are inhibited by toluene, which is known as a powerful inhibitor of free-radical reactions.30 Therefore, at low temperature, the mechanism could be simplified as a single retroen reaction. Measure of Retroen Reaction Activation Energy. The activation energy of the retroen reaction has been measured because of its importance at low temperature. Experiments at different temperatures (345, 330, and 300 °C) were performed. To isolate the retroen reaction, toluene was added as a reactant to inhibit freeradical reactions. Consequently, after pyrolysis only two products were formed: nonene and toluene. The latter could not be quantified because it is both a product and a reactant. However, quantitation of nonene leads to the measure of the activation energy for the retroen reaction. It was obtained by measuring the slope of the curve corresponding to the logarithm of nonene molar fraction (ln X) vs temperature inverse (1/T, K-1) (Figure 13). The activation energy determined is about 50 kcal‚mol-1. This value is not precise but confirms the value chosen for the mechanism. Discussion About the Retroen Reaction.In contrast to published conclusions31 considering the retroen reaction as negligible, this reaction is important in our model. However, the published results31 are not in contradiction with ours. The published experiments were run at 400 °C.31 We run our reaction mechanism software at this temperature and calculated the flux distribution. Results show that more than 80% of toluene and nonenes are formed by free-radical reactions at 400 °C whereas at 330 °C 80% of toluene and 90% of nonenes are formed through the retroen reaction. An increase of 70 °C changes completely the relative importance of reactions. Moreover, there is still an uncertainty on retroen reaction activation energy: experiments seem to show that it is less than the value chosen. But simulations led to the conclusions that the importance of the retroen reaction decreases at 400 °C when a lesser activation energy is taken. So at 400 °C the retroen reaction is not important and this explains why other authors31 could conclude that the retroen reaction was negligible at 400 °C. These authors31a,b performed another test: they pyrolyzed pentadecylbenzene diluted in deuterium labeled


tetralin and quantified the pyrolysis products. They showed that more important the dilution, the more important the proportion of deutered products. They extrapolated this conclusion to infinite dilution and concluded that all products would be deutered. This means that all of them would be formed by H-transfers, that is, by free-radical reactions, and so no molecular reaction operates. This extrapolation is delicate: a fraction of products could never be deutered what could not be verified by the authors. Moreover, the nondeutered fraction is very small,

Mechanistic Modeling of the Thermal Cracking of Decylbenzene

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