1Detailed Kinetic Modeling of Benzene and Toluene Combustion*

Zoran M. Djurisic, Ameya V. Joshi, and Hai WangDepartment of Mechanical Engineering, University of Delaware, Newark, DE 19716

* Presented at the Second Joint Meeting of the U.S. Sections of the Combustion Institute, Oakland, CA, March 25-28, 2001.

Introduction

The high-temperature reaction kinetics ofbenzene and toluene oxidation is of fundamentaland practical importance in combustion. Whilesignificant advances have been made in theunderstanding of the oxidation kinetics ofaliphatic hydrocarbon combustion, comparativelyfewer studies have been conducted on aromatics[1,2]. Such a disparity in emphasis is expectedbecause of the significantly more complex natureof the aromatics' kinetics. It is also obvious thatsince most practical fuel blends consist of largeamounts of aromatics, satisfactory modeling andmanipulation of the combustion processes wouldnot be possible without a quantitative descriptionof their oxidation kinetics. This concern isfurther substantiated by recognizing the role ofaromatic kinetics in engine knock [3], sootproduction [4-12], combustion emissions ofpolycyclic aromatic carcinogen [13] and fullerenesynthesis [14].

Previously, Brezinsky and coworkers [2]proposed a detailed kinetic model of benzene andtoluene oxidation. The model was developed onthe basis of thermochemical considerations andflow-reactor experiments. Several expandedkinetic models have been proposed since thework of Brezinsky et al. [2]. In general, thesemodels were developed for and tested againstdata collected in a single type of experiment only.Specifically, Lindstedt and Skevis [15], Zhangand McKinnon [16], and Tan and Frank [17] haveindependently published reaction models andtested these models against the species profiles ina burner-stabilized benzene flame of Bittner andHoward [18]. There have also been reports ofsimulation studies on the laminar flame speeds ofbenzene and toluene using detailed reactionkinetics and species transport [17, 19, 20]. Wehave seen that these reaction models predicted theindividual experimental data reasonably well.However, a comprehensive model capable ofpredicting all experimental data is still notavailable. Undoubtedly, this situation manifeststhe significant uncertainties in the reaction

kinetics of aromatic compounds.Our work has been largely motivated by the

need of a unified and physically justifiablereaction model to describe one-ring aromatics'combustion. Previously, we proposed [21,22] areaction model for benzene and toluenecombustion and tested this model, for the firsttime, against selected experimental data obtainedunder a variety of combustion conditions,including the oxidation of benzene and toluenein a flow reactor, a stirred reactor, premixedflames and shock tubes. In the present work, wecompared the model predictions to a widervariety of experimental data. Key uncertaintiesof the model were systematically identified.

Methodologies

The current model of benzene and toluenecombustion consists of 65 species and 340elementary reactions. The reaction kinetics ofC1 and C2 species is based on GRI-Mech 1.2[23]. For larger species the reaction pathwaysand rate coefficients were mostly obtained fromliterature data and compilations [e.g., 24].Selected rate parameters were analyzed using theRRKM method [e.g., 25,26].

Calculations of the ignition delay werecarried out using the Sandia Chemkin-II [28-31]codes. The back rate coefficients werecomputed via equilibrium constants. Thethermochemical data of cyclopentadiene and itsderivatives was obtained from quantum chemicalcalculations [27], other data was taken fromRefs. 32 and 33.

Results

We shall first present the modeling resultsfor global combustion properties namely thelaminar flame speed and shock-tube ignitiondelay. This is followed by a comprehensivecomparison between model and experiment fordetailed species profiles during benzene and

2toluene oxidation in a flow reactor and in alaminar premixed burner-stabilized flame.

Figure 1 shows the experimental andcomputed laminar flame speeds of benzene andtoluene at the atmospheric pressure. It is seenthat the flame speed as predicted by the model isin close agreement with the experimental data forboth benzene and toluene and over a wide rangeof equivalence ratios.

In Figure 2, the computed ignition delaytimes are compared to the experimental data ofMiyama [34], collected behind reflected shockwaves for 7 mixtures. The fuel-to-oxygen ratiospans from 0.0256 to 0.379. It is seen that themodel predicts quite well the temperaturedependence of the ignition delay for all mixtures.The model, however, consistently yieldedignition delay times larger than those of theexperimental for mixtures with smaller fuel tooxygen ratio. At the fuel-to-oxygen ratio of0.0256, the model produced ignition delay timeslarger than the experimental counterpart by afactor of two. As this ratio is increased to 1/9 andbeyond, the experimental data are wellreproduced by the current reaction model.

Similar trend was found for the modelprediction of Burcat et al.s experimental data[35], as seen in Figure 3. Specifically, our modeloverpredicted the ignition delay times formixtures with the fuel-to-oxygen ratios smallerthan 0.066, but it reproduced the experimentalresults for higher fuel-to-oxygen ratios. Figure 4presents the comparison between modelpredictions and the experimental data ofThyagarajan and Bhaskaran [36]. It is seen thatthe temperature dependence exhibited by themodel is more pronounced than the experiment.It is most likely that the discrepancy is the resultof experimental inaccuracy because the modelpredicted the temperature dependence for allother mixtures as seen in Figures 2 and 3.

Figure 5 shows the ignition delay times offour toluene-oxygen-argon mixtures, comparingthe present modeling results to the experimentaldata [35]. In all cases, the agreement betweenmodel and experiment is excellent.

Figure 6 shows selected species profilesexperimentally measured [2] and computed forbenzene oxidation in an atmospheric-pressureflow reactor and under the fuel-lean conditionwith the equivalence ratio of 0.65 and thetemperature of ~1108 K. The current modelreproduced the entire mole fraction profiles ofmajor species, including benzene, oxygen, and

carbon monoxide. A very good agreement wasalso found for the concentration profile ofcyclopentadiene. For species with molefractions at a few 100 ppm level, the modelpredictions are accurate to within a factor of ~2.In Figure 7, we present the similar comparisonfor toluene oxidation at the equivalence ratio of1.33. Again the mole fraction profiles of majorspecies are well reproduced by the model. Forminor species, however, the disagreementbetween model and experiment is seen to besignificant. Notably the concentration of phenolwas severely underpredicted.

Figure 8 shows detailed mole fractionprofiles of selected species in a burner-stabilized, low-pressure benzene-oxygen-argonflame. In general, the major species profileswere extremely well reproduced by the currentreaction model. Similar agreement was foundfor major radical species, H and OH. For avariety of minor species, the model is capable ofreproducing their peak concentrations to within afactor of 2 to 3. There are, however, a numberof species for which we found significantdisagreement between the model andexperiment. These species include thecyclopentadienyl radical, cyclopentadiene andphenol. In all cases, the model severely overpredicts the experimental data. The modelingresults also show that for some minor species thepredicted mole fractions may be significantlylower than measured values as in the case ofstyrene, indicating that certain reaction channelsare missing in the model.

We verified the model against several othersets of flame data, including the more recentburner-stabilized flame data of Tregrossi et al.[37]. These are fuel-rich, atmospheric-pressureflames. The species concentration profiles weredetermined by probe sampling and GasChromatography. In general the modelreproduced quite well the measured speciesprofiles. The largest discrepancy is again seen inthe concentrations of phenol andcyclopentadiene. In both cases, the modelpredicts substantially larger mole fractions thanthe experiment.

The model was also tested against thebenzene oxidation data collected in a stirredreactor [38]. While the concentrations of themajor species were well reproduced, the modelover-predicts the phenol concentrations by asmuch as a factor of 5.

3Discussion

The modeling results presented in thepreceding section reveal that there are a numberof important issues concerning the currentreaction model. First, the reaction mechanismseems to capture the main feature of the oxidationprocesses for both benzene and toluene.Specifically, the model reproduced quite well keycombustion properties including the laminarflame speed and shock-tube ignition delay times.The model is also capable of predicting theconcentration profiles of major species duringbenzene and toluene oxidation under quitedifferent reaction conditions. There are, however,several persistent problems. The first is that theignition delay times for mixtures with small fuel-to-oxygen ratios are overpredicted. Secondly, themodel does not reproduce the concentrationprofiles of phenol in all experiments. The degreeof disagreement appears to be dependent on thereactor conditions, and more specifically on theextent of back mixing, as seen in Figure 9. Agreater extent of back mixing causes the model tomore severely overpredict the experimental data.

We have made several attempts to isolate theproblem of ignition delay predictions from that ofthe phenol problem. Specifically, it was thoughtthat the cause for overpredicting the ignitiondelay times for mixtures of small fuel-to-oxygenratio is a missing radical-chain initiation reaction,which involves a 1,2-H shift in benzene to form asinglet carbene species followed by its reactionwith molecular oxygen. Quantum chemicalcalculations, however, suggest that this reactionchannel is not viable. Extensive sensitivityanalyses performed in the present study suggestthat it is very likely that the discrepancy in theignition delay times and the problem of phenolpredictions have the same cause, namely, thekinetic uncertainty in the pathways of the reactionbetween benzene and the oxygen atom. Ouranalysis suggests that to reconcile thediscrepancy between model and experiment thisreaction cannot have a large rate producingphenol. Regardless, a further development of thecurrent reaction model will have to rely on amore accurate knowledge about the detailedkinetics of this reaction.

Summary

A detailed reaction model is proposed in thiswork with the goal to develop a comprehensivemodel, which is capable of predicting a varietyof combustion data of benzene and toluene. Themodel was validated against a large set ofexperimental data. It was found that the reactionmechanism captured the main features of theoxidation processes for both benzene andtoluene. Notable discrepancies between modeland experiment were found to be the ignitiondelay times of mixtures of small fuel-to-oxygenratio and the concentrations of phenol. Thesediscrepancies appear to originate from the samekinetic uncertainty, namely the kinetics of thereaction between benzene and the oxygen atom.

Acknowledgement. The authors wish to thankProfessor Lisa Pfefferle for helpful discussion. Thework was supported by the National ScienceFoundation under Grant CTS9874768 and by the AirForce Office of Scientific Research under GrantF496200110144.

References

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(21) Wang, H.; Djurisic, Z. M., in Chemical andPhysical Processes of Combustion, the 1999Fall Technical Meeting of the Eastern StatesSection of the Combustion Institute,Raleigh, NC, October, 1999, pp. 137-140.

(22) Djurisic, Z. M. MS. Thesis, University ofDelaware, Newark, DE, 1999.

(23) Frenklach, M.; Wang, H.; Goldenberg, M.;Smith, G. P.; Golden, D. M.; Bowman, C.T.; Hanson, R. K.; Gardiner, W. C.;Lissianski, V. GRI-MechAn OptimizedDetailed Chemical Reaction Mechanism forMethane Combustion; GRI Technical ReportNo. GRI-95/0058, November 1, 1995.

(24) Baulch, D. L.; Cobos, C. J.; Cox, R. A.;Frank, P.; Hayman, G.; Just, TH.; Kerr, J.A.; Murrells, T.; Pilling, M. J.; Troe, J.;Walker, R. W.; Warnatz, J. Combust. Flame,1994, 98, 59.

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(28) Kee, R. J.; Rupley, F. M.; Miller, J. A.,Sandia Report SAND 89-8009B; SandiaNational Laboratories: Albuquerque, NewMexico, 1989.

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(30) Kee, R. J.; Rupley, F. M.; Miller, J. A.,Sandia Report SAND 89-8009B; SandiaNational Laboratories: Albuquerque, NewMexico, 1989.

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(38) Chai, Y.; Pfefferle, L. D. Fuel 1998, 77,313.

520

25

30

35

40

45

0.8 0.9 1.0 1.1 1.2 1.3 1.4

Lam

inar

Flam

e Sp

eed

(cm

/s)

Equivalence Ratio

Benzene

Toluene

Figure 1. Experimental (symbols) [19] and computed(lines) laminar flame speed of benzene- and toluene-air mixtures at 1 atm. The experimental data wereobtained from nonlinear extrapolation to zero stretch

101

102

103

104

0.65 0.70 0.75 0.80 0.85 0.90

0.5% C6H

6 - 19.5% O

2 - 80% Ar

p5 = 5.5-7.4 atm

101

102

103

104

0.65 0.70 0.75 0.80 0.85 0.90

1% C6H

6 - 19% O

2 - 80% Ar

p5 = 5.9-7.0 atm

101

102

103

104

0.70 0.75 0.80 0.85 0.90

2% C6H

6 - 18% O

2 - 80% Ar

p5 = 5.5-7.0 atm

100

101

102

103

104

0.60 0.65 0.70 0.75 0.80 0.85

1% C6H

6 - 9% O

2 - 90% Ar

p5 = 5.9-6.6 atm

101

102

103

104

0.65 0.70 0.75 0.80 0.85 0.90

4% C6H

6 - 16% O

2 - 80% Ar

p5 = 5.4-7.4 atm

101

102

103

104

0.60 0.65 0.70 0.75 0.80 0.85 0.90

2% C6H

6 - 8% O

2 - 90% Ar

p5 = 5.6-7.1 atm

101

102

103

0.60 0.65 0.70 0.75 0.80

2.75% C6H

6 - 7.25% O

2 - 90% Ar

p5 = 5.4-6.7 atm

103K/T

Ign

itio

n D

ela

y T

ime ( s

)

Figure 2. Experimental (symbols) [34] and computed(lines) ignition delay times for benzene-oxygen-argonmixtures. Ignition was defined by time lapse from thearrival of a reflected shock wave to the time when fuelconcentration decreased by 3-5% (measured bybenzene light emission at 3.29 m).

101

102

103

104

0.60 0.65 0.70 0.75 0.80

0.419% C6H

6 - 12.57% O

2 - 87.011% Ar

p5 = 2.0 atm

101

102

103

104

0.65 0.70 0.75 0.80 0.85

1.35% C6H

6 - 20.31% O

2 - 78.34% Ar

p5 = 2.27 atm

101

102

103

104

0.60 0.65 0.70 0.75 0.80

1.69% C6H

6 - 12.675% O

2 - 85.635% Ar

p5 = 2.47 atm

101

102

103

104

0.55 0.60 0.65 0.70 0.75

1.35% C6H

6 - 5.09% O

2 - 93.56% Ar

p5 = 2.52 atm

101

102

103

104

0.60 0.65 0.70 0.75

0.516% C6H

6 - 3.87% O

2 - 95.614% Ar

p5 = 6.67 atm

103K/T

Ign

itio

n D

ela

y T

ime

( s

)

Figure 3. Experimental (symbols) [35] and computed(lines) ignition delay times for benzene-oxygen-argonmixtures.

100

101

102

103

104

0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85

1.176% C6H

6 - 8.824% O

2 - 90% Ar

p5 = 4 atm

100

101

102

103

104

0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90

2.353% C6H

6 - 17.647% O

2 - 80% Ar

p5 = 4 atm

103K/T

Igni

tion

D

ela

y T

ime

( s

)

Figure 4. Experimental (symbols) [36] and computed(lines) ignition delay times for benzene-oxygen-argonmixtures.

6101

102

103

0.60 0.65 0.70 0.75

0.497% C7H

8 - 13.51% O

2 - 85.993% Ar

p5 = 2.27 atm

101

102

103

0.55 0.60 0.65 0.70 0.75

0.497% C7H

8 - 4.48% O

2 - 95.023% Ar

p5 = 2.28 atm

100

101

102

103

0.55 0.60 0.65 0.70 0.75

1.495% C7H

8 - 13.45% O

2 - 85.055% Ar

p5 = 2.82 atm

101

102

103

0.55 0.60 0.65 0.70

0.497% C7H

8 - 4.48% O

2 - 95.023% Ar

p5 = 6.81 atm

103K/T

Igni

tion

D

ela

y T

ime

( s

)

Figure 5. Experimental (symbols) [35] and computed(lines) ignition delay times for toluene-oxygen-argonmixtures.

0

1

2

3

4

O2/5

CO

C5H

6 10

O2/5

C6H

6

Mo

le Fr

actio

n

10

3

0

1

2

3

4

5

0 20 40 60 80 100 120

Mo

le Fr

actio

n

10

4

C6H

5OH

C4H

4C

2H

2

Reaction Time (ms)Figure 6. Species profiles experimentally determined(symbols) [2] and computed (lines) for benzeneoxidation (0.14% C6H6-1.61% O2-98.24% N2, =0.65) in a flow reactor at 1 atm and the temperature of1108 K.

0

1

2

C7H

8

C6H

6

CO

Mo

le Fr

ac

tion

10

3

0

2

4

6

8

10

CH4

C2H

4

Mo

le Fr

ac

tion

10

5

C2H

2

0

2

4

6

C6H

5C HOM

ole

Fr

ac

tion

10

4

C6H

5OH

0

1

2

3

4

0 20 40 60 80 100 120

C4H

4+C

4H

6

Mo

le Fr

ac

tion

10

3

Reaction Time (ms)Figure 7. Species profiles experimentally determined(symbols) [2] and computed (lines) for tolueneoxidation (0.16% C7H8-1.09% O2-98.75% N2, =1.33) in a flow reactor at 1 atm and the temperature of1190 K.

70.0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4

Mo

le Fr

actio

n

COO

2

C6H

6

H2 3

H2O

CO2

0

2

4

6

8

10

12

0 1 2

Mo

le Fr

actio

n10

4

CH2O

HO2

0

2

4

6

8

10

0 1 2 3 4

Mol

e Fr

ac

tion

10

4

C3H

3

C3H

4

0

2

4

6

8

10

0 1 2

Mol

e Fr

ac

tion

103

C5H

5C

5H

6

0

1

2

0 1 2

Mol

e Fr

ac

tion

10

3

Distance from Burner Surface (cm)

C6H

5OH

C7H

8

0

2

4

6

8

10

0 1 2 3 4

Mo

le Fr

actio

n10

3

H

OH

0

1

2

3

4

5

0 1 2 3 4

Mo

le Fr

actio

n10

2

C2H

2

C2H

4 5

0

1

2

3

4

5

6

7

0 1 2 3 4

Mol

e Fr

ac

tion

10

3

C4H

2

C4H

4

0

1

2

3

4

0 1 2

Mol

e Fr

ac

tion

104

C6H

5C

6H

4

0

1

2

3

4

0 1 2

Mol

e Fr

ac

tion

10

5

Distance from Burner Surface (cm)

C6H

5C

2H

3

Figure 8. Species profiles experimentally determined (symbols) [7] and computed (lines) for a laminar premixedburner-stabilized benzene flame (13.5% C6H6-56.5% O2-30% Ar, = 1.8, cold gas velocity 50 cm/s, and p = 2.67kPa).

80

5

10

15

20

25

[C6H

5OH]

mo

del/[C

6H5O

H]ex

p

flow reactor

degree of backmixing

burner-stabilized flame

stirred reactor

Figure 9. Influence of back mixing on the prediction of phenyl concentration. While back mixing in the flowreactor is minimal, it is maximum in a stirred reactor. The back mixing in the laminar premixed burner-stabilizedflame is caused by diffusion.