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Comprehensive Detailed Chemical Kinetic Modeling Study of Toluene Oxidation W. K. Metcalfe,*,† S. Dooley, and F. L. Dryer Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States

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bS Supporting Information ABSTRACT: A detailed chemical kinetic model containing 329 species and 1888 reversible reactions has been developed to describe the oxidation of toluene and its intermediates. The model has been validated over a wide range of experimental conditions, including flow reactor, shock tube, jet-stirred reactor, and flame studies, and for toluene, phenol, benzene, and cyclopentadiene as initial reactants. Good agreement is obtained between predictions and experimental results for all venues and initial reactants. The model is of utility not only for predictions of toluene and benzene chemistry but also for providing a needed submodel to describe higher molecular-weight alkyl aromatics more typical of those found in higher molecular-weight fuels.

1. INTRODUCTION Alkyl aromatic hydrocarbons comprise a significant fraction of the molecular components found in petroleum-derived gasoline, diesel, and gas turbine fuels. Their chemical reactivity is markedly different from other chemical functional classes. Alkyl aromatics typically inhibit the oxidation of alkane/cycloalkane components and, in addition, have potential to form soot precursors much more readily. While eliminating aromatics in transportation fuels has been considered as a means of reducing raw particulate emissions, full hydrogenation of these components in fuel refining is expensive and reduces the energy density of the fuel produced. Moreover, it appears that some level of aromatics is required in some fuels, for example, gasoline, to control autoignition and also to maintain seals in fuel systems (for example, in aircraft applications). Thus, the detailed understanding of the aromatic pyrolysis and oxidation processes remains important to understanding the combustion properties of real fuels. This is especially the case as recent advancements in surrogate fuel formulation1,2 make the accurate kinetic modeling of real fuel combustion behavior achievable. Toluene has been used in producing component blends along with n-heptane and iso-octane to emulate real gasolines,29 and it has recently been used in developing a surrogate mixture for gas turbine fuels.2 However, one would wish to use alkyl benzenes with higher carbon numbers to emulate the average molecular weights found in gas turbine fuels. This work is focused on developing a thoroughly validated detailed chemical kinetic model for toluene, the major aromatic found in gasolines, and for the major intermediates of its combustion, namely, benzene, cyclopentadiene, and phenol. This model can also be used as a base submodel for future developments to describe the combustion chemistry of more complex, higher molecular-weight alkyl aromatics. These aromatics include dimethyl, trimethyl, and ethyl benzenes. Brezinsky and co-workers3,4 conducted pioneering experiments on toluene oxidation with flow reactor studies. The early work3 was performed using an atmospheric pressure flow reactor with a constant toluene concentration of 0.14%. Both lean and r 2011 American Chemical Society

rich conditions were examined by varying the oxygen concentration, with temporal profiles reported for fuel and product concentrations as well as the identified major intermediate species. Later investigations4 used the same atmospheric pressure flow reactor, measuring species concentration profiles at lean conditions (ϕ = 0.76) at 1173 K. Later, Dagaut et al.5 studied toluene oxidation in a jet-stirred reactor over the temperature range of 10001375 K at 1 atm at various equivalence ratios, 0.5 e ϕ e 1.5. Bounaceur et al.6 also performed a jet-stirred reactor study over the temperature range of 873923 K, at 1 bar and fuel equivalence ratios from 0.45 to 0.91, with concentrations of toluene from 1.4 to 1.7% diluted in helium. In both studies, reactant, product, and many intermediate species were identified and quantified. Numerous toluene-reflected shock tube ignition delay experiments have also been carried out. Early work was performed by Burcat et al.,7 who studied toluene oxidation behind reflected shockwaves between 1.95 and 8.85 atm and high temperatures ranging from 1339 to 1797 K, with initial toluene concentrations from 0.5 to 1.5%. Pengloan et al.8 carried out a shock tube study at 1.1 atm, with a toluene concentration of 0.4%; this work characterized the ignition delay times for temperatures between 1400 and 1920 K at lean, stoichiometric, and rich conditions by varying the oxygen concentration. Davidson et al.9 performed an ignition delay study of toluene oxidation at conditions of 8551269 K and 1459 atm, studying equivalence ratios of 0.5 and 1.0 in synthetic air. Sakai et al.11 also measured the toluene ignition delay using a shock tube at reflected shock temperatures of 12701755 K and a reflected shock pressure of 2.4 atm for mixtures of 0.12.0% toluene at equivalence ratios of 0.51.5. Recently, Shen et al.12 performed a high-pressure shock tube study of toluene/air mixtures at 10211400 K and 1061 atm for equivalence ratios of 0.25, 0.5, and 1.0. Sivaramakrishnan et al.13 used single-pulse reflected shock tube methods to determine Received: June 20, 2011 Revised: September 9, 2011 Published: September 12, 2011 4915

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Energy & Fuels species concentration profiles as a function of the reaction temperature for an approximately fixed reaction time at very high pressures (22550 bar). Equivalence ratios at ϕ = 1.0 and 5.0 were studied at reaction temperatures from 1210 to 1480 K. Ignition delay studies have also been performed in rapid compression machines. Roubaud et al.14 measured ignition delay times for a variety of alkylbenzenes (including toluene) for stoichiometric mixtures of fuel in air at compressed gas conditions up to 25 bar, over a range of compression temperatures from 600 to 900 K. These experiments are somewhat difficult to model well, because no information exists for correcting the pressure and temperature variations during the ignition period as a result of heat loss. On the other hand, Mittal and Sung28 performed a rapid compression machine ignition delay study at compressed conditions of approximately 25 and 45 bar and 9201100 K for a variety of equivalence ratios from 0.5 to 1.0, for which corrections reflecting heat loss are available. A number of laminar premixed flame studies of toluene oxidation have been performed, including those of Davis et al.15 and more recently those of Zhang et al.16 and Li et al.17 Using the counter-flow flame technique, Davis et al. measured the laminar burning velocity of toluene/air mixtures at atmospheric pressure for a range of equivalence ratios. Zhang et al. measured the pyrolysis products from 1.24% toluene (by volume) in premixed, argon-diluted, laminar flames at low pressure using tunable synchrotron vacuum ultraviolet (VUV) photoionization and molecular-beam mass spectrometry (MBMS) to detect species concentrations. Li et al. investigated a rich (ϕ = 1.9) low-pressure premixed toluene/O2/Ar flame using tunable synchrotron VUV photoionization mass spectrometry. Intermediate species up to C19H12 were identified by measurements of the photoionization mass spectrum and photoionization efficiency spectrum. Several detailed kinetic models have been proposed to simulate and analyze results from the various experimental studies described above. Emdee et al.18 developed a model to explain previous flow reactor experiments of toluene3 and benzene.19 Lindstedt and Maurice20 developed a more detailed model composed of 743 elementary reactions and 141 species, and they validated the model over a wide range of conditions through predictions of counter-flow diffusion flames, premixed flames, plug-flow reactors, and shock tubes. Coupled with their flow reactor study, Klotz et al. updated the work by Emdee et al. to explain their additional experimental observations, producing a model consisting of 529 reversible reactions and 97 species. Dagaut et al.5 proposed a different detailed scheme consisting of 120 species and 920 reactions to simulate their jet-stirred reactor species data, toluene/oxygen/argon shock tube ignition delay measurements, and toluene/air laminar flame speed data. Sivaramakrishnan et al.13 modified the earlier Klotz model to simulate their high-pressure shock tube speciation measurements. Bounaceur et al. developed a detailed kinetic model based on a previous benzene submechanism21 that explained their companion low-temperature jet-stirred reactor data. This model was also validated against higher temperature shock tube ignition delay data and the flow reactor data by Brezinsky et al. and Klotz et al. Andrae et al.23 developed a large detailed model to describe the oxidation of n-heptane/toluene mixtures. The toluene submechanism was validated against high-pressure shock tube ignition delay measurements9 and the species measurements presented by Sivaramakrishnan et al. Recently, Sakai et al.24 presented a combined n-heptane/iso-octane/toluene kinetic

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Table 1. Mixture Composition (mol %) and Conditions for the 12.5 atm Flow Reactor Study29 mix number toluene

O2

N2

ϕ

Tresidence (s) temperature (K)

1

0.14

2.15 97.71 0.59

≈1.8

450950

2 3

0.14 0.14

1.29 98.57 0.98 0.85 99.01 1.48

≈1.8 ≈1.8

450950 450950

2

0.14

1.29 98.57 0.98

≈0.32.5

920

model. The toluene submechanism was based on the work by Pitz et al.22 and was validated against their previous reported shock tube data.11 Narayanaswamy et al.25 produced a hightemperature substituted aromatic mechanism, including the chemistry of toluene, styrene, ethylbenzene, 1,3-dimethylbenzene (m-xylene), and 1-methylnaphthalene. Recently, Tian et al.26 developed a mechanism to explain the low-pressure toluene flame speciation data of Li et al., compiling a scheme containing 273 species and 1740 reactions, including descriptions of polyaromatic hydrocarbons up to chrysene (C18), which are formed under the conditions of the low-pressure rich flame. In this study, we build on the above previous works on toluene oxidation, including our unpublished work, summarized in ref 29, on n-heptane/iso-octane/toluene mixtures to emulate gasoline. Further details of high-pressure flow reactor data on toluene oxidation at temperatures of 6001000 K partially reported in ref 29 are provided here and used in validation of the present model. Recent works in quantum chemical rate constant determinations are used to assemble this new kinetic model for toluene oxidation, which, in the course of the work, has been validated by comparing predictions with a variety of combustion phenomena encompassing wide ranges of temperature, pressure, and fuel/oxygen concentrations.

2. EXPERIMENTAL SECTION The flow reactor experiments reported in this work were performed in the Princeton variable-pressure flow reactor (VPFR) and were originally reported at the 5th U.S. Combustion Meeting by Chaos and coworkers.29 The conditions studied are summarized in Table 1. Only a brief discussion of the experimental details are given here because there exist several other publications providing detailed information on the VPFR instrumentation and experimental methodology, for example, ref 30. In the VPFR experiments, liquid-phase toluene (99.5%, Aldrich Chemical Co., Ltd.) is volumetrically metered to a liquid vaporizer system located within the VPFR pressure shell. The metered liquid flow is gas blast atomized using heated nitrogen. The nitrogen and fuel vapor mixture then flows into the center tube of a fuel injector. At the entrance to a conical-shaped silica foam mixer/diffuser, the diluted fuel vapor is rapidly mixed with additional nitrogen carrier gas and an oxygen stream. The reacting mixture is sampled at axial positions downstream of the mixer/diffuser using a hot-water-cooled, stainless-steel sampling probe. The sampled stream is continuously extracted and convectively quenched by wall heat transfer. The reaction temperature of flow at the sampling location, with all flows established except the fuel flow, varied by less than (3 K, independent of the location of the mixer diffuser in the test section. During operation of the VPFR, all flow rates of carrier, diluent, and reactants are metered and held constant for the entire duration of each set of experiments reported. The reactor section is surrounded by thermostatted electrical resistance heaters that establish reactor wall temperatures at the initial reaction temperature entering the mixer/test section. The reaction zone itself is nearly adiabatic, and changes in the reacting gas temperature reflect heat release as a result of the reaction of 4916

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Energy & Fuels the fuel and oxidizer. The reaction pressure is held constant for the entire experiment. The reaction temperature at the sampling location and all sample analytical readings are allowed to achieve steady state before the data are recorded. 2.1. Residence Time. The reaction time for a specific location of the mixer/diffuser was calculated using experimental axial velocity profile information downstream of the mixer/diffuser, determined under cold-flow conditions, and corrected for reaction conditions using a Reynolds number correlation technique. The reaction time for the reactants is varied by moving the location of the mixer/diffuser relative to the fixed sampling location. Two types of experiments were performed, termed reactivity experiments and species time history experiments. In the reactivity experiments, temperature and sample composition are determined after a fixed reaction residence time at different initial reaction (and wall) temperatures. The residence time from the mixer to sampling location is held constant by varying the actual location of the mixer/diffuser to correct for changes in the reactor gas density with the established initial reaction temperature. In the species time history experiments, the initial reaction (and wall) temperatures were held fixed and samples of the reacting flow and the reaction temperature were obtained at discrete locations downstream of the mixer/diffuser by varying the diffuser/mixer location. The resulting data were then assembled to produce the species time histories reported for a given set of initial mixture conditions, initial temperature, and reaction pressure. 2.2. Sample Analysis. The sampled gas flow is transferred through heated Teflon lines to a series of analytical equipment, including a Fourier transform infrared (FTIR) spectrometer (Nicolet model 560), an electrochemical oxygen (O2) analyzer (Infrared Industries model 2200), and nondispersive carbon monoxide (CO) and carbon dioxide (CO2) analyzers (Horiba model PIR 2000). Upon exiting the probe, the gas sample travels to heated multiport sampling valves. This system is used to trap and hold individual gas samples for subsequent off-line gas chromatographic analysis. The uncertainties in the measurements reported here are O2 e 4%, CO e 3%, and CO2 e 3% of the reading. The major species identified during the oxidation of toluene by FTIR spectroscopy were H2O (water) and CH2O (formaldehyde). The FTIR spectrometer was calibrated to measure the concentration of these species by recording the FTIR spectra for known mole fractions evaporated in hot nitrogen. The calibrations use the FTIR response signal at wavelengths where only the species in question is the major absorber. Estimated uncertainties in the measurements of H2O (water) and CH2O (formaldehyde) are e5 and e10%, with respect to the reported value. The gas chromatograph used in this study is equipped with flame ionization detectors and is primarily used to detect and measure heavier hydrocarbons, such as CH4 (methane), C2H4 (ethylene), C6H6 (benzene), and C6H5CH3 (toluene). The respective uncertainties in these measurements are e4% of the reported reading. All scanned FTIR wavelengths were digitally recorded.

3. MECHANISM DEVELOPMENT 3.1. Toluene Submechanism. The toluene submechanism developed in this work is primarily based on the work by Bounaceur et al.6 This model was chosen as a starting point because it had been optimized in a similar temperature regime to the flow reactor measurements reported in this study. Several important changes were made to this mechanism based on recent literature rate constant values, and the resulting kinetic scheme was then optimized to best reproduce the body of available experimental data, including the flow reactor data. All of the changes/ additions to the Bounaceur et al. submechanism are shown

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in Table 2, and the most important alterations are discussed below. 3.1.1. Unimolecular Decomposition. Recently reported rate constants for the toluene unimolecular decomposition reactions forming a benzyl radical and a hydrogen atom and a phenyl radical and a methyl radical were taken by Klippenstein et al.,36 who calculated the rate constants in the reverse (addition) direction. The high-pressure-limit rate constants for the forward (decomposition) reactions adopted here are calculated from the reverse reactions by Klippenstein et al. and the internally consistent thermochemistry used in this work. Both decomposition reactions were treated using the quantum RiceRamsperger Kassel theory implemented in CHEMDIS37 to account for pressure falloff, and a Troe fit38 was generated to fit the determined rate constants over the studied temperature and pressure range. 3.1.2. Hydrogen Abstraction. The rate constants for hydrogen abstraction from the benzylic position were updated where possible from recent literature recommendations. Hydrogen abstraction from the phenylic position is adopted from the model by Bounaceur et al., who estimated rate constants from similar reactions involved in benzene oxidation. In this study, a small correction has been made to account for the replacement of one of the phenyl H atoms by the methyl group of toluene by decreasing the A factor of each reaction by 1/6. Three substitution reactions are also considered, two replacing a phenyl hydrogen atom and one replacing the methyl group. The rate constant for the reaction between toluene and atomic oxygen producing a cresoxy radical and a hydrogen atom is consistent with the study by Bounaceur et al., who adopted the work by Tappe et al.39 The rate expressions for toluene plus hydrogen atom producing benzene and methyl radical and _ radical producing a cresoxy radical and a toluene plus OH hydrogen atom were taken from the literature. 3.1.3. Benzyl Radical Chemistry. The decomposition of the benzyl radical (C6H5CH2) has been studied in recent years. Oehlschlaeger et al.40 measured the rate constant for the decomposition of the benzyl radical to a hydrogen atom and a C7H6 fragment of unknown structure. More recently, Cavallotti et al.41 performed a computational study of the potential energy surface of benzyl radical decomposition, determining the C7H6 fragment to be fulvenallene and calculating the rate constant for its production. They estimated that fulvenallene reacts with hydrogen atoms quickly to produce the cyclopentadienyl radical and acetylene. The study concludes that further work is required to understand this complicated system. More recent work from da Silva et al.42 reaffirms that fulvenallene is the major product of benzyl decomposition and provides a rate constant for this reaction. Because the chemistry of fulvenallene is not explicitly known, a more simple description is required for modeling purposes. Therefore, the rate constants for benzyl radical decomposition as estimated by Colket et al.43 have been adopted. In a shock tube study, Colket et al. observed primarily the cyclopentadienyl radical and acetylene to be formed from toluene pyrolysis. The rate constants for the reactions of the benzyl radical with atomic oxygen are taken from the study by Sakai et al.,44 and the addition reaction with a hydroxyl radical is taken from the study by Hippler et al.45 Previous works, e.g., refs 3, 6, and 45, have noted that the reaction between benzyl and hydroperoxy radicals is very important for the oxidation of toluene. The description used in this 4917


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Table 2. Reaction Changes to the Bounaceur et al.6 Toluene Submechanisma number 1500

A

reaction

n

EA

reference 36

C6H5CH3 (+M) = C6H5CH2 + H (+M)

2.78 1015

0.17

91168

low-pressure limit

1.00 1098

22.86

99882

a = 0.065, T3 = 15.1, T1 = 1.00 1010, T2 = 7.6 107 1501

C6H5CH3 (+M) = C6H5 + CH3 (+M)

1.95 1027

3.16

107447

low-pressure limit

1.00 1098

22.97

122080

36

a = 0.71, T3 = 1.00 1010, T1 = 460.0, T2 = 8.21 109 1502

C6H5CH3 + O2 = C6H5CH2 + HO2

2.18 107

2.5

46045

67

1504 1505

C6H5CH3 + H = C6H5CH2 + H2 C6H5CH3 + OH = C6H5CH2 + H2O

6.47 10 1.77 105

4.0 2.4

3384 602

68 69

1507

C6H5CH3 + CH3 = C6H5CH2 + CH4

2.94 1011

0.0

9245

70

1508

C6H5CH3 + HCO = C6H5CH2 + CH2O

3.77 1013

0.0

23787

44

1516

C6H5CH3 + C6H5O = C6H5CH2 + C6H5OH

5.43 1012

0.0

20923

44

1522

C6H5CH3 + H = C6H4CH3 + H2

5.00 108

1.0

16800

6b

1523

C6H5CH3 + O = C6H4CH3 + OH

1.66 1013

0.0

14700

6b

1524

C6H5CH3 + OH = C6H4CH3 + H2O

1.33 108

1.4

1450

6b

1525 1526

C6H5CH3 + HO2 = C6H4CH3 + H2O2 C6H5CH3 + CH3 = C6H4CH3 + CH4

3.33 1011 1.60 1012

0.0 0.0

28900 15000

6b 6b

1528

C6H5CH3 + OH = HOC6H4CH3 + H

1.10 102

3.2

5590

69c

1529

C6H5CH3 + H = C6H6 + CH3

9.49 105

2.0

944

71

1530

C6H5CH2 = C5H5 + C2H2

6.00 1013

0.0

70000

43

1531

C6H5CH2 = C3H3 + C4H4

2.00 1014

0.0

83600

43

1532

C6H5CH2 + O = C6H5CHO + H

2.11 1014

0.0

0

44

1533

C6H5CH2 + O = C6H5 + CH2O

1.19 1014

0.0

0

44

1534 1535

C6H5CH2 + OH = C6H5CH2OH C6H5CH2 + HO2 = BZCOOH

2.00 1013 6.75 1044

0.0 17.5

0 45232

45 46d

1536

C6H5CH2 + HO2 = C6H5CH2O + OH

1.00 1013

0.0

0

46e

1537 1545

C6H5CH2 + CH3 = C6H5C2H5

1.19 10

13

0.0

221

72

C6H5CH2OO (+M) = C6H5CH2 + O2 (+M)

4.17 1036

7.1

32235

47

low-pressure limit

1.80 106

5.40

7630

a = 0.61, T = 1.00 10 , T = 1.04, T = 1.79 10 3

10

1

2

9

1550

C6H5CH2O + OH = BZCOOH

2.00 1013

0.0

0

1551 1552

C6H5CH2O = C6H5CHO + H C6H5CH2O = C6H5 + CH2O

1.99 1013 8.55 1013

0.0 0.0

18728 26017

1556

C6H5CH2 + C6H5CH2 = C14H14

5.00 1012

0.0

454

48

1557

C14H14 = C14H13 + H

1.00 1016

0.0

83660

45

1558

C14H14 + H = C14H13 + H2

3.16 1012

0.0

0

49

1567

C14H14 + C6H5O = C14H13 + C6H5OH

5.43 1012

0.0

20923

44

1568

C14H13 = C14H12 + H

7.90 1015

0.0

51864

50

1569

C14H13 + O2 = C6H5CHO + C6H5CH2O

3.94 1050

11.5

42250

44

1570 1571

C14H13 + HO2 = C6H5CH2 + C6H5CHO + OH C14H12 + O2 = HO2 + C14H11

1.92 1013 4.00 1013

0.0 0.0

0 58200

44 44

1572

C14H12 + H = C14H11 + H2

8.42 103

4.6

2583

44

1573

C14H12 + OH = C14H11 + H2O

2.02 1013

0.0

5955

44

1574

C14H12 + O = C6H5CO + C6H5CH2

7.95 103

1.7

657

44

1575

C14H11 = C6H5 + C2H + C6H5

1.07 1025

2.2

88474

44

1576

C14H11 + O2 = C6H5CO + C6H5CHO

1.70 1029

5.3

6500

44

1577

C14H12 + O = C14H11 + OH

4.20 1011

0.0

1940

f

1578 1579

C14H12 + HO2 = C14H11 + H2O2 C14H12 + CH3 = C14H11 + CH4

2.70 1011 1.10 1012

0.0 0.0

11640 8827

f f

1580

C14H12 + C3H5-a = C14H11 + C3H6

1.10 1012

0.0

8827

f

1581

C14H12 + C6H5O = C14H11 + C6H5OH

5.43 1012

0.0

20923

f

1582

C14H12 + C6H5CH2 = C14H11 + C6H5CH3

1.10 1011

0.0

8827

f

1583

C14H13 + O2 = C14H13OO

8.00 1012

0.0

0

f

1584

C14H13 + HO2 = C14H13O + OH

7.00 1012

0.0

1000

f

4918

f 44g 44g


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Table 2. Continued number

A

reaction

n

EA

reference

1585 1586

C6H5CH2 + C6H5CHO = C14H13O C14H13OOH + C6H5CH2 = C14H13OO + C6H5CH3

1.00 10 1.44 1010

0.0 0.0

12900 17700

f f

1587

C14H13OO + HO2 = C14H13OOH + O2

1.75 1010

0.0

3275

f

1588

C14H13OO + H2O2 = C14H13OOH + HO2

2.40 1012

0.0

10000

f

1589

C14H13O + OH = C14H13OOH

2.00 1013

0.0

0

f

1590

C14H13OO = C14H12OOH

2.59 1012

0.0

21374

f

1591

C14H12 + HO2 = C14H12OOH

1.00 1011

0.0

10530

f

1680

C6H5C2H5 + H = C6H6 + C2H5

1.20 1013

0.0

5100

53

1681 1682

C6H5C2H5 + H = C6H5CHCH3 + H2 C6H5C2H5 + OH = C6H5CHCH3 + H2O

3.97 102 5.17 109

3.4 1.0

3120 870

52 52

1683

C6H5C2H5 + O2 = C6H5CHCH3 + HO2

1.81 1012

0.0

39740

52

1707

C6H5C2H5 = C6H5CHCH3 + H

2.51 1015

0.0

81262

54

1708

C6H5CHCH3 = C6H5C2H3 + H

3.16 1013

0.0

50669

54

1709

C6H5C2H3 = C6H6 + C2H2

1.58 1011

0.0

58440

54

1710

C6H5 + C2H4 = C6H5C2H3 + H

2.51 1012

0.0

6200

55

1711

C6H5C2H3 + O = C6H5 + CH2CHO

3.50 1013

0.0

2832

56

1712 1713

C6H5C2H3 + H = C6H5CCH2 + H2 C6H5C2H3 + OH = C6H5CCH2 + H2O

3.23 107 2.11 1013

2.1 0.0

15842 4571

52 52

1714

C6H5CCH2 + O2 = C6H5O + CH2CO

1.88 1012

0.0

7469

56

1715

C6H5CCH2 + H = C6H5C2H3

1.11 1016

0.8

690

52

1716

C6H5 + C2H2 = C6H5CCH2

1.10 1041

8.6

18152

57

1717

C6H5C2H3 + H = C6H5CHCH + H2

5.07 107

1.9

12951

52

1718

C6H5C2H3 + OH = C6H5CHCH + H2O

2.02 1013

0.0

5955

52

1719

C6H5C2H3 + O = C6H5CHCH + OH

7.55 106

1.9

3736

56

1720

C6H5 + C2H2 = C6H5CHCH

6.70 1034

7.0

10987

57

11

a The number in the first column corresponds to the reaction number in the mechanism. Units = cm3 mol1 s1 cal1. b A factor reduced by 1/6 to account for one less abstraction site. c A factor reduced by 1/6 to account for one less substitution site. d Single expression fitted to results by ref 46. e On the basis of ref 46. See the text. f This study. g High-pressure-limit value.

study is based on the work by da Silva and Bozzelli.46 In their study, da Silva and Bozzelli calculate the products and reaction rate constants for this system, concluding that, above 700 K, the dominant products are benzoxyl and hydroxyl radicals. Below 700 K, the addition reaction forming benzylhydroperoxide becomes important. Because this system exhibits an unusual temperature dependence, they provide separate rate expressions for each reaction between 300 and 700 K and between 700 and 2000 K. The recommended rate constant producing benzoxyl and hydroxyl radicals is approximately 5.0 1012 cm3 mol1 s1 and was originally tested in this study. However, to improve model agreement with toluene shock tube ignition delays, the rate constant was increased by a factor of 2 to 1.0 1013 cm3 mol1 s1. A single three-parameter modified Arrhenius expression was fit to the two expressions calculated by da Silva and Bozzelli describing the formation of benzylhydroperoxide and adopted in this work. This approach does not create errors that are of significance within the range of validation efforts of this study. Murakami et al.47 performed an ab initio study of the potential energy surface of the reaction of the benzyl radical with molecular oxygen and confirmed that it proceeds to form the benzylperoxyl radical with zero energy barrier. The reaction schemes for the methylphenyl (C_ 6H4CH3), _ alkoxybenzyl (C6H5CH2O), _ and peroxylbenzyl (C6H5CH2OO), _ 6H4CH3) radicals as well as those of benzyl hydroperoxide cresoxy (OC (BZCOOH), benzaldehyde (C6H5CHO), cresol (HOC6H4CH3),

Figure 1. Bond dissociation energies used in this study: (a) toluene and (b) bibenzyl (kcal mol1) at 298.15 K.

and benzyl alcohol (C6H5CH2OH) are adopted from the work by Bounaceur et al. The benzyl radical is the most abundant radical formed during the initial stages of toluene oxidation. Because it is resonantly stabilized, it is important to consider the formation of the bibenzyl species that may be readily formed from the association of two benzyl radicals. The reactions describing the chemistry of bibenzyl (C14H14) were also primarily taken from the work by Bounaceur et al., while the chemistry of its primary radical (C_ 14H13) and major intermediate, stilbene (C14H12), were taken from the work by Sakai et al.44 Additional abstraction reactions _ not found in the Sakai et al.44 mechanism were included here (O, _ 3, C_ 3H5-a, C6H5O, _ 2, CH _ and C6H5CH2). The rate expresHO sions were prescribed in consistent fashion with those of the benzyl system, with the pre-exponential factors reduced by a factor of 2, because of the change in the number of abstractable hydrogen atoms. The activation energies were reduced to reflect the small difference in bond dissociation energies between the 4919


Energy & Fuels two compounds (Figure 1). On the basis of the work by Curran et al.,51 low-temperature chemistry pathways were also included for bibenzyl but are shown to be largely unimportant under the studied condtions, with the exception being the primary addition of molecular oxygen, internal isomerization, followed by β-scission to produce stillbene (C14H12) and hydroperoxyl radical. The second addition of molecular oxygen and, thus, true lowtemperature chemistry was not observed to occur. The chemical kinetics of ethylbenzene and styrene was updated from the work by Bounaceur et al. to the more recent recommendations by Ergut et al.52 3.2. Aromatic Submechanism. The kinetic mechanism describing the important intermediates formed during toluene oxidation has been critically assembled from the literature and thoroughly validated against a variety of experimental targets for phenol, benzene, and cyclopentadiene. Mechanism performance and important reactions are discussed in section 5. 3.3. C0C4 Submechanism. The C4 submechanism used in this study is part of a continuous development of the primary constituents of which are the H2/CO and C1 chemistry from the work by Li et al.58 and C2C4 chemistry from the work by Healy et al.59 The chemistry of some important unsaturated species, including 1,3-butadiene, 1,2-butadiene, butenyne, propene, allene, allyl, 1,2-propadiene, and propyne, are taken from the work by Laskin et al.,60 primarily on the basis of the earlier work by Davis et al.61 The performance of this base mechanism is detailed in the Supporting Information. 3.4. Thermochemistry. The thermochemistry of the small species considered in this study has been compiled from the respective constituent studies by Li et al., Healey et al., and Laskin et al.5860 Thermochemical properties of the species of the aromatic submodel have been obtained wherever possible from the recommendations by Burcat and Ruscic.62 Unavailable thermochemistry was estimated using group additivity methods63 implemented through the THERM program.64 The used parameters result in a set of bond dissociation energies, as shown in Figure 1 for the important examples of toluene and bibenzyl. Group values used in this study are available from the authors. Thermochemical properties calculated using group additivity are in good agreement with available experimental values.65 3.5. Transport. Transport parameters of the small species submodel are adopted from the Lawrence Livermore National Laboratory (LLNL)66 database. LennardJones parameters for aromatic species were estimated in accordance with the study by Wang and Frenklach27 and are very similar to those estimated from the principle of corresponding states, where sufficient data are available. The fully referenced detailed chemical kinetic mechanism, thermochemistry, and transport parameters developed in this work are available in the Supporting Information.

4. COMPUTATIONAL SIMULATIONS The modeling computations in this study were carried out using the CHEMKIN suite of programs.31 The fundamental modeling assumptions used in comparing the kinetic calculations to experiments are detailed as follows. 4.1. VPFR. The dilute nature of the reacting mixtures studied in the VPFR limit the departure of the reaction temperatures from the initial temperature to e50 K for all VPFR experiments. Reactor wall temperatures are closely maintained at the initial reaction temperature using electrical resistance heating,

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minimizing heat transfer to and from the reacting gases. Consequently, changes in chemical enthalpy correspond closely to changes in sensible enthalpy, i.e., adiabatic reaction conditions. High convective velocities in the test section and high dilution suppress axial spatial gradients, and thus, axial diffusive terms may be neglected in the governing equations relative to the convective and chemical rate terms. Radial diffusion is negligible because the core reacting flow is radially uniform,30 and the reacting system therefore meets plug-flow conditions. Thus, the experiment can be modeled as a zero-dimensional system with isobaric and adiabatic approximations.32 We have previously discussed the extent of experimental departures from homogeneous plug-flow conditions and the use of approximations developed to treat these in zero-dimensional calculations.33 The primary difficulty being that the experimental device relies on in situ mixing of fuel/oxygen at reaction temperatures. Therefore, it is impossible to ensure that chemical reaction commences under homogeneous conditions. The hot mixing of individual reactant streams results in a region of inhomogeneous composition and chemical reaction until such time as homogeneous conditions are met. The result is that the initial reaction time condition is ill-defined. In this study, zero-dimensional model computations are compared to experimental data by the time-shifting technique, which is thoroughly discussed by Zhao et al.33 Flow reactor modeling simulations in this study are time-shifted by +0.3 s. 4.2. Jet-Stirred Reactor. The jet-stirred reactor is simulated by the Aurora package of the CHEMKIN suite as a homogeneous, constant volume reactor assumed to be at constant temperature and pressure, with a prescribed influx of fresh reactants such that the residence time is constant within the reactor. Solutions were iterated until such point that no change in species concentration occurred (convergence). These species concentrations were then compared to experimental measurements. 4.3. Shock Tube. Shock tube simulations are zero-dimensional and begin at the onset of the reflected shock period. The reflected shock pressure and temperature are inputted as the initial pressure and temperature, respectively. Constant volume and homogeneous adiabatic conditions are assumed behind the reflected shock wave. For ignition delay computations, the simulated ignition delay time is defined consistent with the particular diagnostic used in each set of measurements. For the speciation measurements by Sivamarakrishnan et al.,13 an average pressure and residence time is used based on the reported conditions for each individual experiment. This small approximation has almost no effect on the simulation results. 4.4. Rapid Compression Machine. Model computations of a rapid compression machine that measured ignition delay times assume homogeneous adiabatic conditions. The compression heating and post-compression heat loss phases are accounted for by considering the full pressure history of nonreactive mixtures of identical Cp/Cv, as described by Mittal and Sung.28,77 The simulated ignition delay time is defined by the occurrence of an inflection point in the pressure history during the pressure rise because of ignition.28 4.5. Flame Simulation. For a model of this size, it is not possible to obtain solutions that are completely independent of the grid size at reasonable computational expense. Thus, to test the model against flame phenomena, a reduced model has been produced from a methodology based on the work by Wang and Frenklach.35 The reduced model is valid over the temperature range of 13002000 K and is of 139 species and 525 reactions. 4920


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Figure 2. Oxidation in the VPFR of 0.14% C6H5CH3 in N2, ϕ = 0.586, P = 12.5 atm, and residence time (τ) = 1.8 s. (a) (9) O2, (O) CO2, (4) CO, and (1) H2O. (b) (9) CH2O and (O) heat release as a result of the reaction (K). Symbols are experimental results, and lines are model predictions. Dashed lines correspond to open symbols.

Figure 3. Oxidation in the VPFR of 0.14% C6H5CH3 in N2, ϕ = 0.977, P = 12.5 atm, and residence time (τ) = 1.8 s. (a) (9) O2, (O) CO2, (4) CO, and (1) H2O. (b) (9) CH2O and (O) heat release as a result of the reaction (K). Symbols are experimental results, and lines are model predictions. Dashed lines correspond to open symbols.

4.5.1. Laminar Burning Velocity. Laminar burning velocities are calculated by simulating freely propagating flames using the PREMIX31 module. Simulations are performed over a constant domain size and consider both multicomponent transport and thermal diffusive effects. The use of 1000 grid points assures that stringent increments of 0.01 for both CURV and GRAD are met and that the reported solutions are independent of the grid size. 4.5.2. Diffusion Flame Extinction. Numerical calculations of counter flow flames are performed using the OPPDIFF module of the CHEMKIN package. First, a solution for a flame of low strain rate is achieved. The computed extinction strain rate is obtained in an iterative manner using the previous reacting solution as a starting point, increasing the flow velocity of fuel and oxidizer streams at each iteration until a nonreacting flow is achieved. As instructed by Won et al.,34 the momentum of opposing streams is matched to allow for the computed stagnation plane to be located halfway between each boundary with the use of the plug-flow assumption. Grid-independent solutions are obtained, and multicomponent transport and thermal diffusive effects have been considered.

All figures in this study depict experimental measurements as symbols and kinetic modeling simulations as lines.

5. RESULTS AND DISCUSSION 5.1. Toluene. 5.1.1. Flow Reactor. Toluene oxidation has been studied in the VPFR at 12.5 atm between temperatures of 450 and 1000 K with a residence time of 1.8 s. Stoichiometries from ϕ ≈ 0.6 to 1.5 were examined. Experimental observations are compared to model computations in Figures 25. All mixtures show the onset of reactivity at approximately 900 K, although the oxygen-lean and -rich mixtures do show reactions at slightly higher and lower temperatures compared to the near stoichiometric case, respectively. The kinetic model reproduces the global reactivity, reactants/products (O2, CO, CO2, and H2O), and the change in temperature because of heat release quite well. There is only a significant discrepancy arising in the prediction of formaldehyde under lean conditions (Figure 2a), some of which may be attributed to the inherent difficulties in quantifying this species. 4921


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Figure 4. Oxidation in the VPFR of 0.14% C6H5CH3 in N2, ϕ = 1.48, P = 12.5 atm, and residence time (τ) = 1.8 s. (a) (9) O2, (O) CO2, (4) CO, and (1) H2O. (b) (9) CH2O and (O) heat as a result of the reaction (K). Symbols are experimental results, and lines are model predictions. Dashed lines correspond to open symbols.

Figure 5. Oxidation in the VPFR of 0.14% C6H5CH3 in N2, ϕ = 0.977, T = 920 K, and P = 12.5 atm. (a) (9) O2, (4) CO2, (O) CO, and (1) H2O. (b) (9) C6H5CH3, (O) C6H6. () C2H4, (2) CH4, and (3) CH2O. Symbols are experimental results, and lines are model predictions. Dashed lines correspond to open symbols. Data have been time-shifted by +0.3 s.

Detailed intermediate species profiles are shown in Figure 5, which are collected at near stoichiometric conditions, 12.5 atm, and a constant temperature of 920 K, with a varying residence time. Benzene, ethylene, formaldehyde, and methane are observed to be the major intermediate species formed from the oxidation of toluene at these conditions (Figure 5a). The model accurately computes the major product species and also satisfactorily computes intermediate species concentrations, particularly the rate of toluene consumption and the rate of benzene production/ consumption. However, the model significantly underpredicts the formation of formaldehyde and methane. The average carbon balance in these experiments was 95%, with the lowest recovered carbon of 70% occurring at approximately 1.9 s on the time scale of Figure 5b. To fundamentally understand the mechanism of toluene oxidation, a rate of production analysis is performed at this condition, at the point where the model shows 50% of the fuel consumed (Figure 6). At this condition, the mechanism of toluene oxidation may be simplified into essentially two pathways, proceeding through benzyl and cresoxy radicals. This analysis shows the major pathway to be through the abstraction of the relatively weak (89.9 kcal mol1) benzylic hydrogen

atoms, accounting for 45% of fuel consumption. Although stronger, abstraction of the phenylic CH bonds also makes a significant contribution to fuel consumption. The resulting radical subsequently predominantly reacts with molecular oxygen to form the cresoxy radical. The remaining fuel fraction is also converted to the cresoxy radical by the substitution reaction of toluene and O_ atoms; thus, only two distinct oxidation pathways are shown to occur. The hydroxyl radical is the major abstracting species, consuming ≈60% of fuel, although there are also small contribu_ atom and HO _ 2 radicals. tions from the O At this flow reactor condition, the benzyl radical predominately reacts with itself to form bibenzyl or with the hydroperoxy radical to form the benzoxyl radical and a hydroxyl radical. The benzoxyl radical mostly decomposes to form benzaldehyde, which is consumed to eventually form the phenyl radical. Bibenzyl undergoes hydrogen atom abstraction by the hydroxyl radical to also eventually form a molecule of benzaldehyde along _ with an alkoxy radical (C6H5CO). A sensitivity analysis is also performed at this condition to further understand the governing kinetics. Sensitivity coefficients are calculated using a metric of the carbon monoxide concentration, because CO is an intrinsic measure of reactivity. 4922


Energy & Fuels If increasing a particular reaction caused an increase in the concentration of carbon monoxide, it has a positive sensitivity coefficient. Conversely, a negative sensitivity coefficient was assigned to those reactions that, when increased, caused a

Figure 6. Rate of production analysis of toluene oxidation in a flow reactor at 50% fuel consumption. Initial conditions are C6H5CH3 = 0.14%, ϕ = 0.977, P = 12.5 atm, and T = 920 K.

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subsequent decrease in the carbon monoxide concentration. Figure 7 depicts the 20 most sensitive reactions to the carbon monoxide concentration under flow reactor conditions of 0.14% C6H5CH3, ϕ = 0.977, T = 920 K, and P = 12.5 atm at 50% fuel consumed. Figure 7 clearly shows that the most important promoting reaction under these conditions is the radicalradical reaction of benzyl radical plus hydroperoxyl radical to form benzoxyl and hydroxyl radicals. This reaction is effectively chain-branching because it converts two relatively unreactive radicals into two significantly more reactive species. The decomposition of the cresoxy radical to benzene, carbon monoxide, and hydrogen atom is also an important promoting reaction because it produces reactive hydrogen atoms. The model also predicts that this is the main formation pathway for benzene under these conditions. A recent computational study on methylphenyl radicals has been performed by da Silva et al.73 However, the rate constants describing this decomposition and other cresol reactions are taken from Bounaceur et al. because this model is adequately able to reproduce the experimental benzene formation rates. Another important reaction highlighted by the sensitivity analysis is the addition of the hydroperoxyl radical to the phenoxy radical and subsequent decomposition to form an ortho-quinone _ and a hydroxyl radical (Figure 8). This radical (o-OC6H5O) reaction is described by analogy to the addition of the hydroperoxyl radical to phenyl and is assigned a temperature-independent rate constant of 2.0 10 13 . The enthalpy of formation, H f° _ were (298 K), entropy, S, and heat capacity Cp(T) of o-OC6H5O calculated following methods described by Sebbar et al.74 The enthalpy of formation was calculated at the B3LYP/6-311G(d,p)

Figure 8. Postulated addition of the hydroperoxyl radical to the phenoxy radical. Names correspond to species names in the mechanism.

Figure 7. Reaction rate sensitivity to the CO concentration in toluene oxidation in a flow reactor at 50% fuel consumption. Initial conditions are C6H5CH3 = 0.14%, ϕ = 0.977, P = 12.5 atm, and T = 920 K. 4923


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Figure 9. Oxidation in the VPFR of a 0.14% C6H5CH3 in N2, ϕ = 0.977, T = 920 K, and P = 12.5 atm. (9) O2, (b) C6H5CH3, and (2) C6H6. Symbols are experimental results, and lines are model predictions. (—) This study, ( ) Sakai et al., ( 3 3 3 ) Bounaceur et al., (- 3 -) Sivaramakrishnan et al., (- 3 3 ) Andrae et al., and (- - -) Dagaut et al.

level of theory using isodesmic reactions to minimize errors. The frequency analysis was also performed at this level of theory. This radical was then allowed to decompose to form ortho-benzoquinone and a hydrogen atom. The rate constant for this reaction was defined in the reverse addition direction based on the work by Curran.75 The addition of this reaction was important to match the characteristic reaction times observed in the flow reactor but appears to have a limited effect in other temperature regimes. A dedicated analysis of this system is certainly required. As mentioned in the Introduction, a number of toluene mechanisms exist in the literature and the performance of a selection of these previous works against the VPFR data is shown in Figure 9. For clarity and brevity, only one representitive condition and partial result comparisons are shown. Figure 9 shows the toluene, benzene, and molecular oxygen experimental data from the VPFR at a condition of 0.14% C6H5CH3 in N2, ϕ = 0.977, T = 920 K, and P = 12.5 atm. It is evident that these current mechanisms are unable to reproduce the experimental data. The mechanism developed by Bounaceur et al. performs quite well because it was primarily developed to reproduce jet-stirred reactor data at a similar intermediate temperature range. The mechanism by Sakai et al.44 also performs reasonably, matching the slope of the toluene consumption. The work by Dagaut et al. 5 predicts almost no reactivity at this condition. Conversely, the mechanisms by Sivaramakrishnan et al.13 and Andrae et al.23 grossly overpredict reactivity. In the pursuit of a detailed reaction mechanism that is applicable over a wide range of conditions (fuel concentrations, temperatures, and pressures), it is imperative to validate the mechanism against a large range of experimental data. Previous flow reactor experiments exist in the literature, with the most notable being the work by Klotz et al.,4 where fuel and intermediates species concentrations were observed at a constant pressure as a function of the residence time. This work was performed at lower pressures, 1 atm, and higher temperatures, 1173 K, than the current study. The model reproduces the data very well (Figure 10), predicting the rate of fuel consumption and also the formation and consumption of the major intermediates. In particular, the model performance against bibenzyl and ethylbenzene profiles is important. However, the model

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significantly overpredicts the concentration of carbon monoxide, benzaldehyde (C6H5CHO), and propene. 5.1.2. Jet-Stirred Reactor. Toluene has also previously been studied in a jet-stirred reactor by Dagaut et al.5 and Bounaceur et al.6 The work by Dagaut et al. was performed at 1 atm over the temperature range of 10001375 K and equivalence ratios ranging from 0.5 to 1.5. The mechanism developed in this study is unable to reproduce this data set, overpredicting reactivity across the range of conditions. An example of this is shown in Figure 11, with experimental and modeling results shown at ϕ = 1.0. The model predicts significant fuel consumption at approximately 100 K lower than the experiment. Also shown are the fuel profiles predicted by the Dagaut et al. and Bounaceur et al. mechanisms. Unsurprisingly, because it was developed in the study, the Dagaut et al. mechanism performs very well, accurately capturing the consumption of toluene, whereas the Bounaceur et al. mechanism predicts even higher reactivity than our current kinetic scheme. In comparison to the flow reactor data presented here, the mechanism developed by Dagaut et al.5 computes considerably lower reactivity than observed in the experiment and computed by the present model (Figure 9). Regrettably, with the fundamental information on toluene oxidation available at the present time, we have been unable to reconcile both stirred reactor and flow reactor data sets with the same kinetic model. The reason for this discrepancy is unclear. Bounaceur et al. also studied toluene oxidation in a jet-stirred reactor at 1 bar but over a temperature range of 873923 K and between equivalence ratios of 0.45 and 0.91. The detailed chemical kinetic mechanism developed with these data is the basis for the present effort. The current mechanism computes reactivity that is somewhat higher than observed in the Bounaceur et al. stirred reactor, for example, at a temperature very similar to the flow reactor study (Figure 12). At 923 K and 1 bar, the rate of toluene consumption and intermediate formation is higher than observed in the experiment. The overprediction of reactivity by the current model against the Bounaceur experiments is primarily due to the description of the phenoxy radical reaction with the hydroperoxy radical. This was a necessary modification required to match the time scale of the flow reactor experiments. The quality of the model performance degrades further, and discrepancies increase at the lower temperatures of the Bounaceur et al. study, from which one could infer that the rate constant for the addition of the hydroperoxyl radical to the phenoxy radical should have an activation energy associated with it. 5.1.3. Shock Tube. Toluene has been studied quite extensively under shock tube conditions over a wide range of temperatures and pressures. Burcat et al.7 studied toluene oxidation at fuel concentrations between 0.5 and 1.5% and equivalence ratios of 0.33 and 1.0. Figure 13 shows the current model performance against this data set. The model accurately produces the ignition delay measurements across all temperature, pressure, and fuel concentration ranges of the experimental study, reproducing the effect of pressure, equivalence ratio, and mixture composition. More recently, Pengloan et al.8 measured toluene ignition delays at approximately 1 atm and 14151880 K as a function of the equivalence ratio. Model agreement against this data set is also good (Figure 14), although not of the same quality, in agreement with the Burcat et al. data sets, with the effect of the equivalence ratio being well-captured. Higher pressure shock tube studies have also been carried out on toluene/air mixtures by both Davidson et al.9 and Shen et al.12 4924


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Figure 10. Flow reactor species concentration profiles with 0.1514% C6H5CH3, 1.78% O2, in N2, ϕ = 0.76, T = 1173 K, and P = 1.0 atm. (a) (9) C6H5CH3, (2) CO 0.25, (O) C6H6, and (3) CH4. (b) (9) C6H5CHO, (O) C4H6 (1,3-butadiene), and (b) C2H4. (c) (9) C3H6, (O) C14H14 (bibenzyl), and (2) C6H5C2H5 (ethylbenzene). Symbols are experimental data,4 and lines are model predictions. Dashed lines correspond to open symbols. Data have been time-shifted by +0.034 s.

Figure 11. Jet-stirred reactor species concentration profiles of 0.15% C6H5CH3, in N2, ϕ = 1.0, P = 1.0 atm, and residence time (τ) = 0.1 s. (9) C6H5CH3, (O) O2, (2) CO, (1) CO2, (]) CH2O, and (v) H2. (—) This study [( 3 3 3 ) Dagaut et al. and (- 3 -) Bounaceur et al., with toluene concentrations only]. Symbols are experimental data,5 and lines are model predictions. Dashed lines correspond to open symbols.

Figure 12. Jet-stirred reactor species concentration profiles of 1.7% C6H5CH3, in He, ϕ = 0.9, P = 1.0 atm, and T = 923 K. (9) C6H5CH3, (O) CO, (4) C6H5CHO, and (1) C6H6. Symbols are experimental data,6 and lines are model predictions. Dashed lines correspond to open symbols. 4925


Energy & Fuels Shen et al. compares the two studies to show that the experimental results by Davidson et al. have an overall activation energy

Figure 13. Shock tube ignition delay times of C6H5CH3 in Ar. (2) Fuel = 0.5%, ϕ = 1.0, and average P = 2.28 atm. (3) Fuel = 0.5%, ϕ = 1.0, and average P = 6.81 atm. (b) Fuel = 1.5%, ϕ = 1.0, and average P = 2.82 atm. (0) Fuel = 0.5%, ϕ = 0.33, and average P = 2.27 atm. Symbols are experimental data,7 and lines are model predictions. Dashed lines correspond to open symbols.

Figure 14. Shock tube ignition delay times of 0.4% C6H5CH3 in Ar, with P = 1.1 atm. (9) ϕ = 1.5, (O) ϕ = 1.0, and (2) ϕ = 0.5. Symbols are experimental data,8 and lines are model predictions. Dashed lines correspond to open symbols.

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of approximately half of that displayed by the data by Shen et al. The reason for this discrepancy was attributed by Shen et al. to a pre-ignition pressure rise observed in the experiments by Davidson et al., possibly because of contamination of the shock tube or other non-ideal effects. Although Vasu et al.10 later argued that these hypothetical difficulties were absent, Chaos et al.76 incorporated the pre-ignition pressure rise as a polytropic compression and showed that the predicted ignition delays were in good agreement with the experiment. As a result, we have not used comparisons to the Davidson et al. data in the present work. Model performance against the data from Shen et al. is shown in Figure 15. The conditions covered by the experiments range from 1021 to 1400 K and from 10.3 to 61.5 atm. Overall, the model reproduces the experimental observations quite well. Computations are always within approximately a factor of 2 of the experimental measurements. Agreement with the lowpressure data is very good at the higher temperatures, but model computations do become overly long at temperatures approaching 1100 K. However, the experimental trends are excellently captured by the numeric scheme. In Figure 15a, the weak dependence upon the fuel concentration is reproduced by the model. The stoichiometry is increased from 0.25 to 1.0 by varying the initial toluene concentration from 0.5 to 2.28%, but only minor changes in the ignition delay are produced. At the higher pressure conditions (Figure 15b), a clear trend in reactivity is produced by the changing fuel concentration, with reactivity increasing with an increasing toluene concentration. This behavior is also reproduced by the model. Another noteworthy high-pressure shock tube study of toluene oxidation has been performed by Sivaramakrishnan et al.13 This study involved the measurement of intermediate species concentration profiles over the temperature range of 12101480 K and from 22 to 550 bar for stoichiometric and rich mixtures (ϕ = 5.0). The measured species concentration profiles together with the model simulations are plotted together as a function of the temperature in Figures 1621. The kinetic mechanism developed in this study cannot reproduce the reactivity measured in these experiments, but the trends of fuel consumption and intermediate formation are quite well-captured over all of the conditions examined. In the plots shown, the simulations have been performed at higher temperatures than the experiments and then shifted by 26% to match the rate of fuel consumption.

Figure 15. Shock tube ignition delay study in air. (9) ϕ = 0.25, (O) ϕ = 0.5, and (2) ϕ = 1.0. (a) Average pressure = 12.7 atm. (b) Average pressure = 47.2 atm. Symbols are experimental data,12 and lines are model predictions. Dashed lines correspond to open symbols. 4926


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Figure 16. Shock tube species concentration profiles of 72 ppm C6H5CH3, 648 ppm O2, in Ar, ϕ = 1.0, and P = 22.0 bar. (a) (9) C6H5CH3, (O) CO, and (2) CO2. (b) (9) C6H6, (b) C2H2, and (4) C2H4. Symbols are experimental data,13 and lines are model predictions. Dashed lines correspond to open symbols. Simulations were performed using the average experimental pressure and residence time. The simulated temperature has been shifted by 5.0% to match reactivity.


These data have been successfully computed from the models by Sivaramakrishnan et al. and Andrae et al.,23 both of which overpredict reactivity considerably at the flow reactor conditions of this study (Figure 9). The increased reactivity exhibited by the Sivaramakrishnan et al. model is probably due to the considered reactions of the benzyl and hydroperoxyl radicals. The following _ 2 + HO_ 2 f C6H5CHO + H _ + channels are included: C6H5CH _ with a rate expression of 3.67 1014 cm3 mol1 s1, and OH, _ 2 f C_ 6H5 + CH2O + OH, _ with a rate expression _ 2 + HO C6H5CH of 1.17 1014 cm3 mol1 s1. Both of these reactions have very large rate constants at all temperatures and produce reactive radicals that can quickly consume the fuel and reproduce radical species. Andrae et al. included a lumped radical chain-branching reaction with molecular oxygen, which increases the reactivity of _ with _ 2 + O2 f C_ 6H5 + CH2O + O, the toluene system: C6H5CH 11 3 1 1 a rate expression of 6.32 10 exp 14500/RT cm mol s cal1, chosen by fitting model computations to shock tube ignition delay measurements.

None of these reactions or rate constants is consistent with the recent quantum chemical computations by Murakami et al.47 and, in particular, with the efforts by da Silva et al.,42 who have performed a detailed study of the interaction of benzyl and hydroperoxyl radicals. Such apparent inconsistencies highlight the complicated nature of elucidating the mechanism of the oxidation of aromatic systems. To further understand the controlling chemical reactions of the presented kinetic model, a “brute force” sensitivity analysis was performed at high-temperature shock tube conditions. The analysis involves increasing and decreasing each reaction rate expression by a factor of 2 and calculating the effect on the predicted ignition delay time. The sensitivity coefficient (σ) is defined as 0 τ 2:0 σ ¼ log 00 =log 0:5 τ where τ0 is the ignition delay time calculated with the increased rate coefficient and τ00 is the ignition delay time calculated using the 4927


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decreased rate expression. The results of this analysis were performed for a representitive experiment at 2.281% C6H5CH3, 20.53% O2, 77.189% N2 (ϕ = 1.0), 50.9 atm, and 1135 K. Figure 22 shows the 20 most sensitive reactions. It is clear from the results of the sensitivity analysis that two reactions are significantly more important than the others in the oxidation of toluene/air mixtures at elevated pressures. The most important reactivity-promoting reaction involves the conversion of benzyl and hydroperoxyl radicals to benzoxyl and hydroxyl radicals. This converts two relatively stable radicals (particularly the benzyl radical) into two more reactive radicals. As mentioned previously, the rate constant for this reaction is based on the work by da Silva et al.42 The initiation reaction between toluene and molecular oxygen producing benzyl and hydroperoxyl radicals is also important to the reactivity of the system. This analysis also highlights the importance of the small species chemistry to the reactivity of much larger fuels. The chain-branching reaction between hydrogen atom and molecular

oxygen to form oxygen atom and hydroxyl radical is the most important reaction in high-temperature combustion. Despite not being in the high-temperature regime under the conditions of the study by Shen et al., this reaction still asserts a promoting influence on the system. The effect of the pressure is also highlighted by the reactivity-promoting effect associated with the stabilization of hydrogen atom and molecular oxygen to form hydroperoxyl radical, which then couples to the chief reactivitypromoting reaction involved in toluene oxidation. Despite the temperature being relatively high (>1100 K), the elevated pressures force the high-temperature chemistry regime to higher temperatures. The most inhibiting reactions involve the consumption of reactive radicals or provide competition for species that are also involved in prominent reactivity-promoting reactions. The importance of considering some larger aromatic chemistry is also highlighted by the analysis because the reaction leading to the formation of bibenzyl has a large effect on the ignition delay time at this condition. 4928


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Figure 20. Shock tube species concentration profiles of 8 ppm C6H5CH3, 70 ppm O2, in Ar, ϕ = 1.0, and P = 550.0 bar. (a) (9) C6H5CH3, (O) CO, and (2) CO2. (b) (9) C6H6 and (4) C2H4. Symbols are experimental data,13 and lines are model predictions. Dashed lines correspond to open symbols. Simulations were performed using the average experimental pressure and residence time. The simulated temperature has been shifted by 6.0% to match reactivity.

Figure 21. Shock tube species concentration profiles of 14 ppm C6H5CH3, 25 ppm O2, in Ar, ϕ = 5.0, and P = 550.0 bar. (a) (9) C6H5CH3 and (O) CO. (b) (9) C6H6, (b) C2H2, and (4) C2H4. Symbols are experimental data,13 and lines are model predictions. Dashed lines correspond to open symbols. Simulations were performed using the average experimental pressure and residence time. The simulated temperature has been shifted by 2.0% to match reactivity.

5.1.4. Rapid Compression Machine. Mittal and Sung28 also studied the high-pressure ignition of toluene but at lower temperatures. Toluene/O2/N2/Ar mixtures were studied in a rapid compression machine at compressed pressures of approximately 25 and 45 bar and temperatures of 9201100 K. The model performance against the exemplar 45 bar case is shown in Figure 23. The mechanism performs quite well, accurately reproducing the effect of the temperature and oxygen concentration. Reactivity is slightly underpredicted at the highest pressure, with the model showing no ignition occurring at 975 K. 5.1.5. Laminar Burning Velocity. Predictions using the newly developed model are compared to laminar burning velocities of toluene/air mixtures measured by Davis et al.15 using the counterflow flame technique (Figure 24). Simulations were initially performed with PREMIX using the complete mechanism, but because of the large size, a completely converged solution independent of the grid size could not be obtained. The convergence of a flame speed calculation can be routinely

checked by comparing the final temperature calculated at a large distance from the burner to the adiabatic flame temperature of the mixture under study. These two temperatures should coincide within a few degrees ((5 K). To overcome this problem, the reduced high-temperature model was exercised, with the results depicted in Figure 24. The model accurately reproduces the flame speeds as a function of the equivalence ratio. 5.2. Diffusion Flame Strained Extinction. The reduced kinetic model is tested against the diffusive strained extinction measurements by Won et al. in Figure 25. The model reproduces the effect of fuel loading on the strain rate at which extinction occurs very well. As explained by Won et al.,34 because of the existence of both pyrolytic and oxidative flame regimes, diffusive strained extinction is a challenging validation target for kinetic models. The goodness of the model performance against this phenomenon indicates not only the appropriateness of the oxidation model but also that of the transport model, the pyrolytic model, and the interaction of these processes. 4929


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Figure 22. Results of a sensitivity analysis of a shock tube ignition delay at 2.281% C6H5CH3, 20.53% O2, 77.189% N2 (ϕ = 1.0), 50.9 atm, and 1135 K. A negative sensitivity coefficient indicates an increase in reactivity, whereas a positive sensitivity coefficient indicates a decrease in reactivity.

Figure 23. Rapid compression machine ignition delay study at compressed gas pressures, PCP, of approximately 45 bar. (9) C6H5CH3 = 0.96% , O2 = 8.85%, N2 = 10.10%, Ar = 80.29%, and ϕ = 1.00. (O) C6H5CH3 = 0.96%, O2 = 17.31%, N2 = 0.0%, Ar = 81.73%, and ϕ = 0.5. Symbols are experimental data,28 and lines are model predictions. Dashed lines correspond to open symbols.

5.3. Aromatic Submechanism Validation. It has been shown in the above section that the mechanism developed in this study can accurately reproduce experimental measurements for toluene over a wide range of temperatures and pressures. Because this mechanism is intended for use as a stable and validated submechanism for larger aromatic compounds, it is vitally important that the chemistry of the intermediate species is also accurately described. 5.3.1. Benzene. There have been many studies of benzene oxidation ranging from experimental observations, kinetic modeling, and detailed ab initio calculations. These studies are too numerous to discuss in detail in the present work (see the work by Simmie78 and Alzueta et al.79 for more details). Therefore, only the previous work chosen as validation targets for the mechanism will be discussed. The model has been validated against flow reactor data by Lovell et al.19 The experiments were performed at 1 atm pressure

Figure 24. Laminar burning velocities of the C6H5CH3/air mixture as a function of the equivalence ratio at 1 atm. (9) Linear extrapolation. (O) Nonlinear extrapolation. Symbols are experimental data,15 and lines are model predictions.

with the benzene/oxidizer mixture diluted in nitrogen. The benzene concentration used in all experiments was effectively the same (≈1581 ppm), while the oxygen concentration was varied to alter the equivalence ratio. All data were collected at approximately 1100 K. The model accurately captures the experimental results across the range (Figure 26), particularly at lean and stoichiometric conditions, where the benzene consumption rate and phenol, cyclopentadiene, and carbon monoxide production rates are all well-reproduced. At rich conditions, the model agreement with the experiment deteriorates, with the concentration of phenol underpredicted and that of cyclopentadiene overpredicted. These species are intrinsically linked _ which can either through the benzoxyl radical (C 6 H5 O), abstract a hydrogen atom to form phenol or decompose to form cyclopentadiene and carbon monoxide. Alzueta et al.79 also studied benzene oxidation under flow reactor conditions. This study was performed in the temperature range of 9001450 K, with fuel ratios ranging from stoichiometric to very lean and residence times on the order of 150 ms. 4930


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Figure 25. Diffusion flame extinction for toluene/nitrogen in counter flow with air. Tfuel = 500 K, and Tair = 298 K. Symbols are experimental data,34 and lines are model predictions.

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Examples of data and model predictions are shown in Figure 27 at stoichiometric and lean conditions. Model computations are in acceptable agreement with the experiment, matching the consumption of benzene and the production of carbon monoxide and carbon dioxide. The model was also compared to species concentration profiles observed in a jet-stirred reactor by Ristori et al.80 Experimental results were obtained in the temperature range of 9501350 K at 1 atm for equivalence ratios from 0.3 to 1.5. The model again performs well, with exemplar comparison for the equivalence ratio, ϕ = 1.0, shown in Figure 28. The current kinetic scheme correctly captures the consumption rate of benzene and molecular oxygen while also reproducing the rate of formation of carbon dioxide. For the most part, intermediate species concentrations are also well-captured, including carbon monoxide, hydrogen, methane, formaldehyde, and ethane. The model significantly underpredicts the maximum concentration of acetylene and also shows the formation of phenol at lower temperatures than observed experimentally. However, the peak concentration of this species is accurately reproduced. Benzene has also been studied numerous times under shock tube conditions. In a similar work to that mentioned previously

Figure 26. Flow reactor species concentration profiles of C6H6 in N2 and P = 1.0 atm. (9) C6H6, (1) CO, (O) C6H5OH, and (4) C5H6. (a) C6H6 = 1571 ppm, O2 = 15 900 ppm, ϕ = 0.76, and T = 1098 K. (b) C6H6 = 1591 ppm, O2 = 11 700 ppm, ϕ = 1.0, and T = 1096 K. (c) C6H6 = 1581 ppm, O2 = 8700 ppm, ϕ = 1.36, and T = 1096 K. Symbols are experimental data,19 and lines are model predictions. Dashed lines correspond to open symbols. 4931


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Figure 27. Flow reactor species concentration profiles of C6H6 in N2 and P = 1.05 bar. (9) C6H6, (O) CO, and (4) CO2. (a) C6H6 = 111 ppm, O2 = 870 ppm, H2O in N2 = 5300 ppm, and ϕ = 0.96. (b) C6H6 = 107 ppm, O2 = 1290 ppm, H2O = 48700 ppm in N2, and ϕ = 0.62. Symbols are experimental data,79 and lines are model predictions. Dashed lines correspond to open symbols.

Figure 28. Jet-stirred reactor species concentration profiles of 0.15% C6H6, 1.125% O2, in N2, ϕ = 1.0, P = 1.0 atm, and residence time (τ) = 0.07 s. (a) (9) O2, (b) CO2, and (4) CO. (b) (9) C6H6, (O) H2, (4) C6H5OH, and (1) CH2O. (c) (0) C2H2, (b) CH4, and (2) C2H6. Symbols are experimental data,80 and lines are model predictions. Dashed lines correspond to open symbols.

for toluene oxidation, Burcat et al.7 also studied benzene oxidation. Experiments were performed with benzene concentrations ranging from 0.42 to 1.69% with oxygen

concentrations in the range of 3.8720.30% diluted in argon. The experiments were performed in temperature and pressure ranges of 12121748 K and 1.707.78 atm, respectively. 4932


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Figure 29. Shock tube ignition delay times of C6H6 in Ar. (9) Fuel = 1.35%, ϕ = 2.0, and average P = 2.52 atm. (O) Fuel = 0.52%, ϕ = 1.0, and average P = 6.68 atm. (2) Fuel = 1.70%, ϕ = 1.0, and average P = 2.47 atm. (3) Fuel = 0.42%, ϕ = 0.25, and average P = 2.01 atm. ([) Fuel = 1.35%, ϕ = 0.50, and average P = 2.27 atm. Symbols are experimental data,7 and lines are model predictions. Dashed lines correspond to open symbols.

Figure 30. Shock tube ignition delay times of 1.25% C6H6 in Ar and average P = 8.3 atm. (9) ϕ = 1.5, (O) ϕ = 1.0, and (2) ϕ = 0.5. Symbols are experimental data,6 and lines are model predictions. Dashed lines correspond to open symbols.

Model computations against these data are shown in Figure 29. The model accurately predicts the effect of changes in the pressure, temperature, equivalence ratio, and fuel concentration. A similar study was performed by Bounaceur et al.6 at a slightly higher pressure of approximately 8.3 atm. The concentration of benzene was 1.25% diluted in argon, with varying oxygen concentrations used to measure the ignition delay time for stoichiometries of 0.51.5. There is considerable scatter in these data compared to the earlier work by Burcat et al., but the model computations agree quite well (Figure 30). The benzene submechanism was also validated against flame speed measurements from Davis et al.15 The experiments were performed in identical fashion as for toluene, and once again, the mechanism performs very well over the studied range of stoichiometries (Figure 31). 5.3.2. Cyclopentadiene. Despite being an important intermediate in the combustion of benzene (Figure 26), there has been relatively little work performed on cyclopentadiene

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Figure 31. Laminar burning velocities of the C6H6/air mixture as a function of the equivalence ratio at 1 atm. (9) Linear extrapolation. (O) Nonlinear extrapolation. Symbols are experimental data,15 and lines are model predictions.


(C5H6). The majority of previous studies have focused on pyrolysis,8187 with more recent studies performed under oxidative conditions in shock tubes8890 and in a flow reactor.91 Burcat et al.88 performed a shock tube ignition delay study of cyclopentadiene diluted in argon over the temperature range of 12782110 K and pressure range of 2.4312.45 atm. The fuel concentrations were varied from 0.5 to 2.5%, and oxygen concentrations varied from 3.3 to 16.6%. Representative data obtained for 1.0% fuel at an average pressure of approximately 4.0 atm, with different oxygen concentrations to vary the equivalence ratio from 0.5 to 2.0, are shown in Figure 32, together with the model performance. A similar study was performed by Orme and Simmie,89,90 at atmospheric pressure in the temperature range of 13701864 K (Figure 33), with the model reproducing both data sets very well. In the case of the Orme and Simmie fuel-rich data (ϕ = 2.0), the model underpredicts reactivity but is globally in very good agreement. The cyclopentadiene submechanism has been adopted primarily from the work by Zhong and Bozzelli.92 In a recent study, Butler and Glassman91 performed species concentration profile measurements of cyclopentadiene in an atmospheric flow reactor with initial cyclopentadiene concentrations 4933


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from 1000 to 3000 ppm and equivalence ratios from 0.6 to 100.0 in the temperature range of 11001200 K. The model performance against some of the results obtained near stoichiometric

conditions are plotted in Figure 34. The model captures the consumption of the fuel and the formation and destruction of the larger intermediates quite well (panels ad of Figure 34).


Figure 35. Flow reactor species concentration profiles of 28 ppm C6H5OH, 250 000 ppm O2, and 4.70% H2O diluted in N2. (9) CO and (O) CO2. Symbols are experimental data,79 and lines are model predictions. Dashed lines correspond to open symbols.

Figure 34. Flow reactor species concentration profiles of 2243 ppm C5H6, in N2, ϕ = 1.03, T = 1198 K, and P = 1.0 atm. (a) (9) C5H6, (O) CO, and (2) CO2. (b) (9) C6H6, (O) C4H4, and (2) C4H6 (1,3-butadiene). (c) (9) C3H6, (O) C3H4-a, (2) C3H4-p, and (3) C2H5CHO. (d) (9) C2H2, (O) CH4, (2) C2H4, and (3) C2H6. Symbols are experimental data,91 and lines are model predictions. Dashed lines correspond to open symbols. 4934


Energy & Fuels However, some of the smaller unsaturated intermediates, such as propene, allene, and propyne, are poorly predicted by the current scheme. The model assumes the formation of 2,4-cyclopentadiene-1-one as the most important intermediate of cyclopentadiene combustion. However, Butler and Glassman were unable to detect this species and conclude that it is not an important pathway. Further work is required to accurately understand the kinetics governing the intermediate product distribution, despite the current model predictions having captured the reactivity very well. 5.4. Phenol. Phenol (C6H5OH) is another important intermediate produced during benzene oxidation, again shown in the data by Lovell et al. The model is able to reproduce the formation and destruction of this intermediate under flow reactor conditions (Figure 26). Previous studies include flow reactor experiments performed by Alzueta et al.79 during benzene oxidation investigation. Experiments were performed under very lean conditions, monitoring the formation of carbon monoxide and carbon dioxide. Phenol pyrolysis and oxidation experiments were performed by Brezinsky et al.,93 also under flow reactor conditions, identifying a variety of intermediates, including carbon monoxide, carbon dioxide, and unsaturated intermediates, such as acetylene, cyclopentadiene, benzene, 1,3-butadiene, ethene, and also methane. Figure 35 depicts the concentrations of carbon monoxide and carbon dioxide measured by Alzueta et al. The initial conditions were extremely fuel-lean, with 28 ppm phenol, 25% O2, and 4.70% H2O diluted in N2. The model is in acceptable agreement with the experimental data, slightly underpredicting reactivity.

6. CONCLUSION A detailed chemical kinetic mechanism for toluene oxidation and the intermediates of its combustion has been developed and extensively validated against a wide variety of experimental targets and conditions for toluene, benzene, cyclopentadiene, and phenol. These targets include previously unpublished lowtemperature flow reactor speciation profiles obtained during toluene oxidation. Under the conditions of the current study, toluene was shown to be unreactive below 900 K. The mechanism accurately predicts the combustion characteristics of the aforementioned species, including shock tube ignition delay times, flow reactor, and jet-stirred reactor species profiles, and laminar burning velocities. The mechanism developed in this study serves as an essential building block for the development of detailed chemical kinetic mechanisms of more practical substituted aromatic compounds as well as for further refining the submodel components as further validation information emerges. ’ ASSOCIATED CONTENT

bS

Supporting Information. Mechanism and thermochemistry files, with the validation of the current C4 submechanism. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Present Addresses †

Combustion Chemistry Centre, National University of Ireland, Galway, Ireland.

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’ ACKNOWLEDGMENT This work is part of the Multidisciplinary University Research Initiative (MURI) supported by the Air Force Office of Scientific Research under Grant FA9550-07-1-0515 monitored by Dr. Julian Tishkoff. ’ REFERENCES (1) Xu, H.; Yang, Z.; Chaos, M.; Dryer, F. L. Proceedings of the Joint ArmyNavyNASAAir Force (JANNAF) 42nd Combustion Joint Subcommittee Meeting; Hanscom Air Force Base, Newton, MA, May 1216, 2008. (2) Dooley, S.; Won, S. H.; Chaos, M.; Heyne, J.; Ju, Y.; Dryer, F. L.; Kumar, K.; Sung, C.-J.; Wang, H.; Oehlschlaeger, M. A.; Santoro, R. J.; Litzinger, T. A. Combust. Flame 2010, 157, 2333–2339. (3) Brezinsky, K.; Litzinger, T. A.; Glassman, I. Int. J. Chem. Kinet. 1984, 16, 1053–1074. (4) Klotz, S. D.; Brezinsky, K.; Glassman, I. Proc. Combust. Inst. 1998, 27, 337–344. (5) Dagaut, P.; Pengloan, G.; Ristori, A. Phys. Chem. Chem. Phys. 2002, 4, 1846–1854. (6) Bounaceur, R.; Da Costa, I.; Fournet, R.; Billaud, F.; Battin-Leclerc, F. Int. J. Chem. Kinet. 2005, 37, 25–49. (7) Burcat, A.; Snyder, C.; Brabbs, T. NASA TM 87312; National Aeronautics and Space Administration (NASA): Washington, D.C., May 1986. (8) Pengloan, G.; Dagaut, P.; Djebaili-Chaumeix, N.; Paillard, C. E.; Cathonnet, M. Proceedings of the Colloque Combustion Propre; Orleans, France, June 68, 2001; p 9. (9) Davidson, D. F.; Gauthier, B. M.; Hanson, R. K. Proc. Combust. Inst. 2005, 30, 1175–1182. (10) Vasu, S.; Davidson, D. F.; Hanson, R. K. J. Propul. Power 2010, 26, 776–783. (11) Sakai, Y.; Inamura, T.; Ogura, T.; Koshi, M.; Pitz, W. J. SAE [Tech. Pap.] 2007, DOI: 10.4271/2007-01-1885. (12) Shen, H-P. S.; Vanderover, J.; Oehlschlaeger, M. A. Combust. Flame 2009, 32, 165–172. (13) Sivaramakrishnan, R.; Tranter, R. S.; Brezinsky, K. Combust. Flame 2004, 139, 340–350. (14) Roubaud, A.; Minetti, R.; Sochet, L. R. Combust. Flame 2000, 123, 535–541. (15) Davis, S. G.; Wang, H.; Brezinsky, K.; Law, C. K. Proc. Combust. Inst. 1996, 26, 1025–1033. (16) Zhang, T.; Zhang, L.; Hong, X.; Zhang, K.; Qi, F.; Law, C. K.; Ye, T.; Zhao, P.; Chen, Y. Combust. Flame 2009, 156, 2071–2083. (17) Li, Y.; Zhang, L.; Tian, Z.; Yuan, T.; Wang, J.; Yang, B.; Qi, F. Energy Fuels 2009, 23, 1473–1485. (18) Emdee, J. L.; Brezinsky, K.; Glassman, I. J. Phys. Chem. 1992, 96, 2151–2161. (19) Lovell, A. B.; Brezinsky, K.; Glassman, I. Proc. Combust. Inst. 1988, 22, 1063–1074. (20) Lindstedt, R. P.; Maurice, L. Q. Combust. Sci. Technol. 1996, 120, 119–167. (21) Da Costa, I.; Fournet, R.; Billaud, F.; Battin-Leclerc, F. Int. J. Chem. Kinet. 2003, 35, 503–524. (22) Pitz, W. J.; Seiser, R.; Bozzelli, J. W.; Da Costa, I.; Fournet, R.; Billaud, F.; Battin-Leclerc, F.; Seshadri, K.; Westbrook, C. K. Proceedings of the 2nd Joint Meeting of the U.S. Sections of the Combustion Institute; Oakland, CA, March 2528, 2001. (23) Andrae, J. C. G.; Bj€ ornbom, P.; Cracknell, R. F.; Kalghatgi, G. T. Combust. Flame 2007, 149, 2–24. (24) Sakai, Y.; Ozawa, H.; Ogura, T.; Miyoshi, A.; Koshi, M.; Pitz, W. J. SAE [Tech. Pap.] 2007, DOI: 10.4271/2007-01-4104. (25) Narayanaswamy, K.; Blanquart, G.; Pitsch, H. Combust. Flame 2010, 157, 1879–1898. (26) Tian, Z.; Pitz, W. J.; Fournet, R.; Glaude, P.-A.; Battin-Leclerc, F. Proc. Combust. Inst. 2011, 33, 233–241. 4935


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