A comprehensive mechanism for the pyrolysis and oxidation of ethylene

Nineteenth Symposium (International) on Combustion/The Combustion Institute, 1982/pp. 153-166

A COMPREHENSIVE MECHANISM FOR THE PYROLYSIS A N D OXIDATION OF ETHYLENE CHARLES K. WESTBROOK University of California, Lawrence Livermore National Laboratory Livermore, California 94550 FREDERICK L, DRYER

Princeton University, Princeton, New Jersey K. E SCHUG DFVLR-Institut fur Physikalische Chemic der Verbrennung, Stuttgart, West Germany A detailed chemical kinetic reaction mechanism is developed for the intermediate and high temperature pyrolysis and oxidation of ethylene. The mechanism, consisting of 93 elementary reactions among 26 chemical species, is validated by comparison between computed results and measured data from shock tube and turbulent flow reactor experiments. New rate expressions are determined for a number of reactions between C~H4 molecules and H, O, and OH radicals. The comprehensive mechanism accurately reproduces available experimental data for pressures ranging from 1 to 12 atmospheres and for fuel-air equivalence ratios from 0.125 to pyrolysis conditions. The resulting mechanism then predicts correctly laminar flame and detonation properties for ethylene-air mixtures. Introduction

Ethylene is an important fuel molecule and is used extensively in studies of flame structure and propagation, shock tube ignition, and detonation. It is also an intermediate species in the combustion of many higher molecular weight hydrocarbons, being formed by fuel fragmentation processes in early flame stages or in zones of high pyrolysis rate, Consequently, ethylene oxidation is a common subelement in the combustion of many hydrocarbon fuels. In addition, formation of ethylene and its subsequent reactions to acetylenic derivatives are believed to play important roles in the kinetics of gas phase soot formation. Detailed kinetic modeling of ethylene pyrolysis and oxidation may therefore provide a valuable computational tool to assist in the analysis of a wide variety of combustion systems. Experimental data on ethylene combustion are available from shock tubes, laminar flames, detonations, and flow reactors. With this variety of information, ethylene is a promising subject for development of a comprehensive detailed reaction mechanism [1] similar in concept and scope to that developed previously for methanol [2]. This type of reaction mechanism is validated by requiring

that it reproduce experimental results in a variety of combustion environments, not just in a single experimental regime. The value of this approach has been illustrated effectively through applications of the resulting mechanisms to studies of laminar flames [3,4] and detonations [5]. In the present paper, we detail the development of such a comprehensive kinetic mechanism for ethylene pyrolysis and oxidation. Detailed Reaction Mechanism

Previous modeling studies have included ethylene as an intermediate constituent [6-10]; however, relatively little attention has been directed towards situations where ethylene is itself the principal fuel [10-13]. The present mechanism for ethylene combustion is an extension of our earlier work [2], including within it submodels for combustion of moist CO [7], methane [7,14], and methanol [2,3] over extended ranges of temperatare, pressure, and fuel-air equivalence ratio 4. The final reaction mechanism developed in this paper is given in Table I. Reverse reaction rates are calculated from the forward rates and the appropriate equilibrium coefficients [15,16]. 153

154

REACTION MECHANISMS AND M O D E L I N G II TABLE I Fuel oxidation mechanism. Reaction rates in cm~-mole-sec-kcal units, k = AT~ exp (-E~/RT)

Reaction 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20, 21. 22. 23. 24. 25. 26. 27. 28. 29, 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.

H + 02 H2 + O H20 + O H20 + H H202 + OH H20 + M H + O2 + M HO2 + O HO2 + H HO2 + H HO2 + OH H202 + 02 H202 + M H202 + H O + H + M 02 + M H2 + M CO + OH CO + HO 2 CO + O + M CO2 + O HCO + OH HCO + M HCO + H HCO + O HCO + HO 2 HCO + 02 CH20 + M CH20 + OH CHzO + H CH20 + O CH20 + HO2 CH4 + M CH~ + H CH 4 + OH CH4 + O CH4 + HOz CH3 + HOz CH3 + OH CH3 + O CH~ + Oz CH20 + CH3 CH3 + HCO CH~ + HO2 CH30 + M CH,O + 02 CzH6 C~H6 + CH~ C~H6 + H C~H~ + OH C2H~ + O C2H5 + M CzH~ + Oz

log A ---~O + OH 14.27 --~H + OH 10.26 ---~OH + OH 13.53 --~H2 + OH 13.98 ---*H20 + HO2 13.00 ---~H + OH + M 16.34 ---~HO2 + M 15.22 ---~OH + O2 13.70 ---~OH + OH 14.40 ---~H2 + 02 13.40 ---~H20 + 02 13.70 --*HO2 + HO 2 13.60 ---~OH + OH + M 17.08 ---~HO2 + H2 12.23 ---~OH+ M 16.00 --~O + O + M 15.71 ---~H + H + M 14.34 ---~CO2 + H 7.11 ---~CO2 + OH 14.18 ---~CO2 + M 15.77 ---~CO + 02 12.44 ---~CO + H20 14.00 ---~H + CO + M 14.16 --*CO + H2 14.30 ---~CO + OH 14.00 ---~CH20 + 02 14.00 ---~CO + HO2 12.60 --~HCO + H + M 16.52 ---~HCO+ H20 12.88 ---~HCO + H 2 14.52 ---~HCO + OH 13.70 ---~HCO + H20~ 12.00 ---~CH3 + H + M 17.15 --~CH3 + H2 14.10 --~CH3 + H20 3.54 ---~CH3 + OH 13.20 ---~CH3 + H202 13.30 --~CH30 + OH 13.51 --~CH20 + H2 12.60 --~CH20 + H 14.11 --~CH30 + O 13.68 ---~CH4+ HCO 10.00 ---~CH4+ CO 11.48 ---~CH4 + O~ " 12.00 ---~CH20 + H + M 13.70 ---~CH20 + HOz 12.00 ---~CH3 + CH 3 19.35 ---~C2H5+ CH4 -0.26 ---~C2H5 + H~ 2.73 ---~C2H~+ H20 13.05 ---~C2H5 + OH 13.40 ---~C2H~ + H + M 15.30 ---~C2H~ + HO~ 12.00

Forward rate n Ea 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.08 0 0 0 0 0 0 0.5 0.5 0 0 0 -1 4 3.5 0 0 0 0

16.79 8.90 18.35 20.30 1.80 105.00 -1.00 1.00 1.90 0.70 1.00 42.64 45.50 3.75 0.00 115.00 96.00 -0.77 23.65 4.10 43.83 0.00 19.00 0.00 0.00 3.00 7.00 81.00 0.17 10.50 4.60 8.00 88.40 11.90 2.00 9.20 18.00 0.00 0.00 2.00 29.00 6.00 0.00 0.40 21.00 6.00 88.31 8.28 5.20 2.45 6.36 30.00 5.00

log A 13.17 9.92 12.50 13.34 13.45 23.15 15.36 13.81 13.08 13.74 14.80 13.00 14.96 11.86 19.90 15.67 15.48 9.15 15.23 21.74 11.50 15.45 11.70 15.12 14.46 15.56 12.95 11.15 12.41 13.42 12.24 11.04 11.45 12.68 2.76 11.43 12.02 10.00 14.08 15.23 14.48 10.32 13.71 13.88 9.00 11.11 12.95 10.48 2.99 13.30 12.66 10.62 11.12

Reverse rate n E~ 0 1 0 0 0 -2 0 0 0 0 0 0 0 0 -1 -0.28 0 1.3 0 -1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 3.08 0 0 0 0 0 0 0.5 0.5 0 1 0 0 0 3.5 0 0 0 0

0.68 6.95 1.10 5.15 32.79 0.00 45.90 56.61 40.10 57.80 73.86 1.00 -5.07 18.70 103.72 0.00 0.00 21.58 85.50 131.78 37.60 105.15 1.55 90.00 87.90 46.04 39.29 -11.77 29.99 25.17 17.17 6.59 -19.52 11.43 16.68 6.64 1.45 0.00 71.73 71.63 0.73 21.14 90.47 58.59 -2.56 ' 32.17 0.00 12.50 27.32 24.57 11.23 -11.03 13.70

Ref. 54 55 55 55 55 55 55 56 55 55 56 56 55 55 57 58 55 59 60 61 62 63 7 33 64 65 7 17 66 17 18 56 67 68 31 69 70 37 71 72 73 74 74 70 73 75 76 29 29 77 78 25 14

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PYROLYSIS AND OXIDATION O F ETHYLENE TABLE I (continued) Fuel oxidation mechanism. Reaction rates in cma-mole-sec-kcal units, k = AT" exp ( - E d R T )

Reaction 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93.

CnH4 + CzH4 C~H4 + M C~H4 + M C2H4 + O C~H4 + O C2H4 + H CzH4 + OH C~H4 + OH C~H~ + M C~H3 + On C2H2 + M C2Hn + O~ C2H~ + H C~Hz + OH C~H2 + OH C~H2 + O C~H 2 + O C~H + Oz CnH + O CHn + On CH2 + O CH~ + H CH2 + OH CH + Oz CH + O2 CH3OH + M CHaOH + OH CHsOH + O CH3OH + H CHaOH + H CH3OH + CH3 CH~OH + HO~ CH2OH § M CHzOH + O z C2H ~ + CzH 4 C~Hn + C ~ H ~ C4Ha + M CzH~ + CnH C4H2 + M C2H3 + H

log A ---*C~H5 + C~H3 ---*C~H2 + Hn + M ---~C~H3 + H + M --->CH3 + HCO ---~CHzO + CHz --*C2H3 + H2 ---->C~H3+ H20 --->CH3 + CHzO ---~C~Hz + H + M ---~C~H~ + HO~ --~C2H + H + M --->HCO + HCO ---*C2H + H2 --->C2H + H~O --->CH3 + CO --->C~H + O H ---~CH2 + CO ---~HCO + CO ---~CO + CH ---~HCO + O H --->CH + OH --->CH + H~ --->CH + H~O --->CO + OH --->HCO + O ---~CH3+ OH + M --->CH~OH + H~O --->CH~OH + OH --->CHzOH + Hz --*CHa + H~O --*CH~OH + CH4 --->CHzOH + H~O~ --*CH~O + H + M --->CHzO + HO2 -->C4H ~ + H -->C4H~ + H "->C4H~ + H + M -">C4H~+ H --->C,H + H + M -'->CzH2 + H2

Forward rate n E,

14.70 16.97 18.80 12.52 13.40 7.18 12.68 12.30 14.90 12.00 14.00 12.60 14.30 12.78 12.08 15.51 13.83 13.00 13.70 14.00 11.28 11.43 11.43 11.13 13.00 18.48 12.60 12.23 13.48 12.72 11.26 12.80 13.40 12.00 12.00 13.00 16.00 13.60 17.54 13.30

0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 -0.6 0 0 0 0 0.68 0.67 0,67 0.67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

64.70 77.20 108.72 1.13 5.00 6.00 1.23 0.96 31.50 10.00 114.00 28.00 19.00 7.00 0.50 17.00 4.00 7.00 0.00 3.70 25.00 25.70 25.70 25.70 0.00 80.00 2.00 2.29 7.00 5.34 9.80 19.36 29.00 6.00 7.30 45.00 60.00 0.00 80.00

2.50

log A 14.17 12.66 17.30 11.20 12.48 6.24 12.08 11.78 11.09 12.00 9.04 11.00 13.62 12.73 12.41 14.47 13.10 12.93 13.50 13.61 10.77 11.28 11.91 11.71 13.13 13.16 7.27 5.90 7.51 12.32 6.70 7.00 16.69 17.94 13.00 13.18 11.92 14.65 12.30 13.12

Reverse rate n E, 0 1 0 0 0 2 0 0 1 0 1 0 0 0 0 -0.6 0 0 0 0 0.68 0.67 0.67 0.67 0 1 1.66 1.66 1.66 0 1.66 1.66 -0.66 -1.66 0 0 1 0 1.0 0

Ref,

-2.61 12 36.52 23 0.00 * 31.18 35 15.68 * 5.11 * 14.00 * 16.48 * -10.36 12 17.87 * 0.77 13 63.65 79 13.21 80 16.36 81 58.00 19 0.91 80 54.67 . 81 138.40 80 59.43 80 76.58 7 25.93 82 28.72 82 43.88 83 185.60 83 71.95 13 -10.98 2 25.31 2 8.35 84 15.16 2 36.95 2 18.43 85 11.44 86 7.58 2 28.32 86 4.70 12 0.00 21 2.54 21 0.55 21 -16.40 21 68.08 11

*This study. The mechanism differs from that of Reference [2] in several respects:

Formaldehyde Submodel Rate expressions recommended by Dean et al. [17] for Reactions 28-30 have been adopted. The rate for Reaction 29 CH20 + OH = HCO + HzO

(29)

is smaller than that used earlier [18] over the temperature range considered in this paper, but the revised rates of Reactions 28 and 30 are not significantly different from those used previously.

Acetylene Submodel The elementary reactions and rate expressions for acetylene oxidation used previously [2] have

REACTION MECHANISMS AND MODELING II

156

been retained, except for the addition of Reaction 68 C2H2 + OH = CH 3 + CO

(68)

with a rate expression determined by Smith and Zellner [19]. Uncertainty remains concerning the rates and product species distributions of many of the reactions of acetylene and its fragment species, and improvements may be necessary to develop a comprehensive mechanism for acetylene oxidation [20]. However, for ethylene oxidation the sensitivity of the computed results to variations in the rates of the acetylene submechanism reactions was small. The polyacetylene Reactions 89-92 are based on the acetylene pyrolysis modeling studies of Tanzawa and Gardiner [21,22].

Ethylene Submodel Most of the modifications of the mechanism involve reactions of ethylene molecules and vinyl radicals. For Reaction 55, a rate expression obtained C2H4 + M = C2H2 + H 2 + M

(55)

recently by Franck [23] from shock tube ethylene decomposition experiments was adopted. This rate expression is slightly lower than earlier measurements and has some impact on the evaluation of k56 C2H4 + M = C2H3 + H + M

been the subject of considerable study. At high temperatures abstraction reactions can be expected to be important, including

(56)

reported by Just et al. [24]. Modeling results discussed below produced the expression given for k~, which is still consistent with the experimental data of Just et al. Radical dissociation Reactions 52 and 62 involving ethyl and vinyl C2H ~ + M = C2H4 + H + M

(52)

C2H 3 + M = C z H 2 + H + M

(62)

radicals have been written as second order decompositions, although it is recognized that both are in the pressure falloff region under some experimental conditions of interest. Future improvements should include the deviation from a second order rate expression with both temperature and pressure to account for the falloff region. For high temperature flame, shock tube and detonation conditions, the second order rate expressions are probably appropriate [9,11,25,26], but under flow reactor conditions they may be somewhat too large. The rates and product distributions for reactions between ethylene and O, OH and H radicals have

C2H4 + H = C2H3 + H 2

(59)

C2H4 + OH = C2H3 + HzO

(60)

Expressions from the literature for k59 are summarized in Fig. 1. These data suggest [27] that the composite rate expression may be curved. The expression given in Table I represents an analytic fit to the experimental data and is shown as the dashed curve in Figure 1. This was derived by requiring that k 59 agree with the shock tube results at 2000 K and with the value at 817 K given by Baldwin [28]. Non-Arrhenius temperature dependence for reactions involving H atoms has been determined for reactions with acetylene [21] and with methane and ethane [29], so the same type of behavior for k59 is not unexpected. Computed results agreed best with experimental data using the above expression for k~9. The rate expression for Reaction 60 was constructed by combining several measurements at different temperatures. At 813 K Baldwin et al., [28] found k6o = 1.1 • 1013 cm3 -mole -1 - s -1, while Bradley et al., [30] found k6o/k35 = 2.33 at 1300 K. Using the expression of Zellner and Steinert [31] for k35, k~o at 1300 K was estimated to be 1.5 • 1013 cm3 -mole -1 s-!. Combining these gave k~o = 2.4 • 1013 exp (-1230/RT). In subsequent comparisons between computed and experimental results, the activation energy was held fixed while the pre-exponential was varied along with other rate expressions to provide the best overall agreement. The resulting rate expression shown in Table I is larger than the original estimate by about a factor of two. The sum of the two C2H4 + OH reactions 60 and 61, evaluated at 300 K, agrees closely with the experimental value measured by Smith and Zellner [19]. At intermediate temperatures most reactions between C2H4 and radical species including Reactions 57, 58, and 61, appear to involve the formation of an activated complex followed by a rearrangement and subsequent fragmentation [19]. At low temperatures recent experiments [32] indicate that C2H30 is a major product of reactions between C2H4 and O atoms, although this path has not been included in the present mechanism. At somewhat higher temperatures, Reaction 57 is most important [33]. The total rate of reaction between C2H 4 and O has been found to be curved on an Arrhenius diagram [34,35], suggesting that Reaction 58 may have a slightly larger activation energy than Reaction 57. With Ess = 5 kcal/mole, the sum of Reactions 57 and 58 reproduces the observed curvature [34], where E a (total) increases from 1.1 kcal/

PYROLYSIS AND OXIDATION OF ETHYLENE

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FIC. 1. Rate expressions for C~H4 + H = C2H3 + H2, including experimental values from the references cited in the legend. mole at 250 K to about 2.8 kcal/mole at 1000 K. In addition to Reaction 62, vinyl radicals are assumed to react with Oz molecules. The relative rates of Reactions 62 and 63 were found to be important, since Reaction 62 produces H atoms which are much more reactive than the HO 2 radicals produced by Reaction 63. These H atoms provide subsequent chain branching from Reaction 1, accelerating fuel oxidation in all of the experimental regimes studied. Earlier modeling studies [2,14] demonstrated similar sensitivity to analogous reactions of hydroxymethyl and ethyl radicals.

Minor Species Several minor species were not included in the mechanism (Table I). At room temperature, Bradley et al. [36] found mass spectrometer peaks for C H + OH products corresponding to acetaldehyde or ethylene oxide. Baldwin et al. [28] suggested that acetaldehyde or ethylene oxide were plausible products of reactions between molecular oxygen and excited ethyl radicals from H + C2H 4 recombination. In some of the simulations described below reactions forming acetaldehyde were combined with an acetaldehyde consumption mechanism [37]. However the inclusion of this submechanism had little effect on the computed results and was not included in other calculations. Recombi-

nation reactions of methyl, vinyl, and ethyl radicals to produce propane, propene, butane, and butene have not been included. Reactions involving ketene (CH2CO) have not been included, although other studies [10,20] indicate that ketene may be important in the oxidation of rich ethylene and acetylene. Shock Tube Pyrolysis Tanzawa and Gardiner [11] recently reviewed thermal decomposition of ethylene in shock tubes, developing a detailed mechanism which reproduced their own and other available experimental results [38-43]. Table I includes the reactions in Reference [11], although some rate expressions are slightly different. The present mechanism provides good agreement with all of the experimental results and with the modeling results of Tanzawa and Gardiner, including the observed three-halves order overall rate constant for ethylene consumption. However, Tanzawa and Gardiner were unable to reproduce the variations in H atom concentrations measured by Just et al. [24]. Those data provide a unique test of the mechanism since only the chain initiating Reactions 55 and 56, and the vinyl decomposition Reaction 62 are involved. Comparison between computed and experimental H atom

REACTION MECHANISMS AND MODELING II

158

50 p p m C H

T=~o7baro~'

P = 1.95

//

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by the model. Ethylene consumption is approximately linear, with predicted H a levels slightly higher than for Calla. Computed C4H6 levels are lower than H a and Call 2 by an order of magnitude. The overall pyrolysis consists primarily of a chain reaction involving Reactions 59 and 62 C2H4 + H = C2H3 + H a

(59)

C2H3 + M = C a H a + H + M

(62)

However, approximately 10% of the vinyl radicals react with ethylene to produce butadiene by means of Reaction 88. Therefore the production rate of acetylene is about 90% that of H a, with C4H 6 production accounting for the remainder.

20 p p m C H T = 2 0 6 0 ~( 4 P = 1.77 bar

Shock Tube Oxidation 4 0 0 pore C. ~ I T = 1655 KP = 1,94 bar

f v

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400

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FIG. 2. H atom concentration profiles from shock tube pyrolysis of CzH4. Open circles show experimental data of Just et al. [24], solid curves are computed results from the present work, dashed curves from Reference [11]. profiles provides a measure of the magnitude and relative distributions of Reactions 55 and 56. Computed results in Figure 2 show that the present mechanism provides a very accurate reproduction of the H atom data. In order to reproduce the experimental results, which cover a temperature range of 1655 K to 2060 K, it was necessary to increase the activation energy for Reaction 56 from 98.16 kcal/mole to 108.72 kcal/mole. With E56 = 98.16 kcal/mole, the model predicts too high a value for the rate of H atom production at 1655 K and too low a rate at 2060 K. The resulting expression for k56 still agrees very closely with the measurements of Just et al. [24].

A number of recent experimental studies of ethylene oxidation in shock tubes have appeared [13,40,45-49]. Jachimowski [13] developed a reaction mechanism which reproduced the overall features of his shock tube experiments but was not applied to data from other sources. White and Gardiner [26], noting that methane oxidation mechanisms contain within them submechanisms for oxidation of C a species, applied a CH 4 oxidation mechanism [9] to many of the Call 4 shock tube oxidation data, with mixed but generally unsatisfactory results. From the experimental results, the data of Baker and Skinner [48] were selected for detailed modeling analysis. The data covered a temperature range between 1058 K and 1876 K, with equivalence ratios between 0.125 and 2.0. The initial conditions are summarized in Reference [48]. For each mixture, Baker and Skinner computed a correlation function which best represented the observed ignition delay times, with effective activation energies ranging systematically from about 28 kcal/mole at d~ = 2 to nearly 40 kcal/mole at qb = 0.125. An overall correlation function for all of the results was given in terms of the induction time ~r as "r = 10n'9[CaHa]~

~ exp (34200/RT).

Flow Reactor Pyrolysis Schug et al. [44] reported experimental results on ethylene pyrolysis and oxidation in the Princeton University turbulent flow reactor. In the pyrolysis experiments, dilute mixtures of ethylene in nitrogen react in a cylindrical flow system. Call 2 and Ha are produced in approximately equal amounts, with butadiene being the only detectable minor product. Computed results indicate that the experimentally observed trends are reproduced well

Induction time calculations were carried out for each mixture at initial post-shock temperatures between 1100 K and 1800 K. In the experiments the induction time was defined as the time of maximum OH emission. In the model, the times for maximum OH concentration (which would correspond to the maximum in OH absorption) and the product of the CO and O concentrations are both very nearly equal to the time of maximum rate of pressure increase, and any of these definitions could

PYROLYSIS AND OXIDATION OF ETHYLENE

0

37

7 104/1-

FIG. 3. Correlation functions using 13 = r[C2H~]-~ [Oz]lt [Ar]-~ Dashed curves indicate computed results for lean mixtures, solid curves for stoichiometric and rich mixtures, with initial compositions taken from data of Baker and Skinner [48]. The numbers beside each symbol in the legend refer to the Mixture number (see Reference [48]).

be used to evaluate the induction time in the computations. The computed results are summarized in Figure 3, together with the experimental correlation function. Although there is some spread in the computed results, the experimental correlation function appears to represent a reasonable average of all the computed data, particularly at the higher temperatures. More importantly, there is a systematic trend with computed induction times for most of the lean mixtures lying above the correlation function and those for most of the rich mixtures below the line. Combined with the fact that the experimentally determined effective activation energies vary continuously with equivalence ratio from about 28 to 40 kcal/mole, it is clear that the use of a single correlation function to describe all of the data is an oversimplification. Ethylene oxidation in shock tubes has been found to exhibit a complex temperature dependence. Homer and Kistiakowski [40] discuss variations in overall activation energy from 17 to more than 24 kcal/ mole at temperatures from 1500 K to 2300 K at an initial ethylene level of 0.5%. Suzuki et al. [49]

159

found large variations in overall activation energy with both temperature and ethylene concentration. The same variations were observed in the computed results, indicated by the" curved lines for each mixture in Figure 3. Although the experimental data were represented by a single activation energy, the effective activation energy from each computed model increases as temperature decreases, varying from values as low as 17 kcal/ mole at 1600 K to more than 40 kcal/mole at 1100 K for some mixtures. It is difficult to trace the changes in overall induction behavior to one or even a few elementary reactions. Computed histories for each mixture show a complicated inter-relationship between groups of reactions. The initiation is dominated by Reaction 55. However, the initiation phase is only a very small fraction (-1%) of the total induction period. During the remainder of this time ethylene consumption reactions determine the behavior of the shocked gas. Of particular importance are the relative rates of competing reactions, including Reactions 62 and 63 of vinyl radicals, Reactions 1 and 7 between H and Oz, and the reactions between ethylene and O, OH, and H radicals. For example, due to differences in activation energy (E62 = 31.5 kcal/mole, E63 = 10 kcal/mole) and dependence on O z concentration, the relative importance of Reactions 62 and 63 changes with equivalence ratio and temperature. The ratio of Vinyl radical consumption from Reactions 62 and 63 varies from 2/ 1 for Mixture 35 at 1100 K to 66/1 for Mixture 31 at 1600 K. Since the same reactions do not dominate at all temperatures, one would not expect a straight line correlation in plots such as those in Figure 3.

Flow Reactor Oxidation From the ethylene oxidation experiments of Schug et al. [44], one fuel-rich ((b = 1.8) and one fuellean (qb = 0.19) example were selected for comparison with computed results. Species concentrations and temperature for the lean case are shown in Figure 4 as functions of axial distance along the reactor. In addition to the indicated species, small amounts (-100 ppm) of CH20, C2H 6, CzHz, CH3OH, and CH3CHO (or C2H40 ) were also identified. Further details concerning the experimental techniques are described by Dryer [50] and Schug et al. [44]. It is assumed that combustion occurs at atmospheric pressure, that plug flow conditions prevail, and that no heat transfer to the reactor walls takes place [2,7]. Some reaction occurs in the reactor inlet duct before the first measurement location. This is taken into account by determining an appropriate delay time after which the computed species con-

REACTION MECHANISMS AND MODELING II

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lean case, Reaction 61 with H atoms provides a smaller fraction of the CzH4 consumption. In the rich case, the large amounts of H 2 which are present make Reaction 61 effectively balanced, so that very little ethylene is actually consumed by reactions with H atoms. Reactions with O atoms consume about one-tenth as much fuel as OH radicals. Computed results for flow reactor conditions also depend strongly on the relative rates of consumption of vinyl radicals by Reactions 62 and 63. Their relative rates are about equal in the rich case, while Reaction 63 with 0 2 consumes about 80% of the vinyl radicals in the lean case. The same trends were observed for the hydroxymethyl radical in methanol oxidation in the flow reactor [2]. As a result the HO z level in the lean case is quite large (i.e., ->25 ppm).

Pomion cm

FIG. 4. Species composition profiles for fuel-lean flow reactor oxidation of C2H4. Symbols indicate experimental data of Schug et al. [44], solid curves are computed results from the present work, longdashed curves computed using mechanism in Ref. [2], short-dashed curves computed with mechanism in Ref. [10]. Calculations are normalized to the first experimental data points (see text). centration and temperature profiles match the values recorded at the first measurement location. The detailed reaction mechanism from Reference [2] was used to make an initial prediction of the results of the flow reactor experiments. Computed spatial profiles are summarized in Figure 4. Overall agreement is poor, with the computed fuel consumption being too rapid. Agreement is also poor for the CO and H 2 profiles. Flow reactor simulations using the mechanism developed by Warnatz [10] also resulted in poor agreement with the experimental data, with virtually no conversion of fuel to intermediate or product species. Detailed examination of these preliminary results led to the modifications to the reaction mechanism discussed earlier, involving particularly Reactions 57-63. With the final mechanism from Table I, agreement between computed and experimental results is good, as indicated in Figure 4. Predicted temperature profiles are close to the measured data, although the computed maximum rate of temperature increase in the lean model (at about 70 cm) is greater than observed. This is consistent with the fact that the computed CO profile is somewhat narrower and falls more rapidly than the experimental results, although both the maximum CO concentration and its spatial location are predicted well by the model. Similar agreement was obtained for the rich case. For both rich and lean cases, the principal reaction consuming C2H 4 is Reaction 60, followed by Reaction 61, both involving OH radicals. In the

Discussion

The comprehensive mechanism developed and validated above was then used to examine the properties of ethylene oxidation in laminar flames and detonation waves. The laminar burning velocity in a stoichiometric ethylene-air mixture at atmospheric pressure is predicted to be 71 -+ 2 cm/s, in agreement with previously reported experimental [51,52] and theoretical [10] values. Additional flame modeling, including effects of variations in pressure, temperature, equivalence ratio, dilution, and inhibitor concentration are discussed elsewhere [53]. The same mechanism has also been shown [5] to predict many of the detonation properties of ethylene-oxidizer mixtures. Both studies [5,53] demonstrate the wide applicability of the comprehensive mechanism. Earlier mechanisms, including those designed specifically for ethylene oxidation in flames [10] and comprehensive mechanisms for simpler fuels [2] were shown (Fig, 4) to be inadequate for describing ethylene oxidation in regimes different from those for which the mechanisms were designed. Since this comprehensive mechanism contains within it earlier mechanisms for simpler fuels, it is simultaneously a comprehensive mechanism for C2H4, CH 4, CH3OH, CO, and H 2 oxidation. Further improvements are still needed for the acetylene submechanism, and refinements in individual reaction rates will also improve the overall model, but the present mechanism provides a useful computational tool for the analysis of combustion systems involving the pyrolysis and oxidation of ethylene and simpler hydrocarbon fuels. Acknowledgments

The authors are grateful for the computer programming assistance of Ms. Lila L. Chase. This work was carried out in part under the auspices of

PYROLYSIS AND OXIDATION OF ETHYLENE the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48.

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46. GAY, I. D., GLASS, G. P., KERN, R. D., AND KISTIAKOWSKY,G. B., J. Chem. Phys. 47, 313 (1967). 47. HIDAKA,Y., KATAOKA,T., AND SUGA, M., Bull. Chem. Soc. Japan 47, 2166 (1974). 48. BAKER,J. A., AND SKINNER, G. B., Combustion and Flame 19, 347 (1972). 49. SUZUKI,M., MORIWhgI, T., OKAZAKI,S., OKUDA, T., AND TANZAWA,T., Astronautica Acta 18, 359 (1973). 50. DRYER, F. L., Ph.D. thesis, Department of Aerospace and Mechanical Sciences, Princeton University, 1972. 51. RAEZER,S. D. AND OLSEN, H. L., Combustion and Flame, 6, 227 (1962). 52. GUNTHER, R., AND JANISCH, G., Chemie-Ing.Techn. 43, 975 (1971). 53. WESTBROOK,C. K., DRYER, F. L., AND SCHUG, K. P., in preparation, 1982. 54. BAULCH,D. L., DRYSDALE, D. D., ANDHORNE, D. G., Fourteenth Symposium (International) on Combustion, p. 107, The Combustion Institute, Pittsburgh, 1973. 55. BAULCH, D. L., DRYSDALE, D. D., HORSE, D. G., AND LLOYD, A. C., Evaluated Kinetic Data for High Temperature Reactions, Vol. 1 Butterworths, London, 1973. 56. LLOYD, A. C., Int. J. Chem. Kinet. 6, 169 (1974). 57. MOREa'n, G., AIAA J. 3, 223 (1965). 58. JENKINS, D. R.,, YUMLU,V. S., AND SPALDING, D. B., Eleventh Symposium (International)on Combustion, p. 779, The Combustion Institute, Pittsburgh, 1967. 59. BAULCH,D. L., AND DRYSDALE, D. D., Combustion and Flame 23, 215 (1974). 60. ATRI, G. M., BALDWIN, R. R., JACKSON, D., AND WALKER, R. W., Combustion and Flame 30, 1 (1977). 61. SIMONAITIS, R. AND HEICKLEN, J.,. J. Chem. Phys. 56, 2004 (1972). 62. GARDISER, W. C., JR., McFAaLAND, M., MORINAGA, K., TAKEYAMA,T., AND WALKER, B. F., J. Phys. Chem. 75, 1504 (1971). 63. BOWMAN, C. T.,, Combust. Sci. and Technol. 2, 161 (1970). 64. WESTENBERG,A. A., AND DE HAAS, N., J. Phys. Chem. 76, 2215 (1972). 65. BALDWIN, R. R., AND WALKER, R. W., Fourteenth Symposium (International) on Combustion, p. 241, The Combustion Institute, Pittsburgh, 1973. 66. ATKINSON,R. ANDPlVrs, J. N., J. Chem. Phys. 68, 3581 (1978). 67. HARTIC, R., TROE, J., AND WAGNER, H. GG., Thirteenth Symposium (International) on Combustion, p. 147, The Combustion Institute, Pittsburgh (1971). 68. BALDWIN, R. R., HOPKINS, D. E., NORRIS, A.

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C., AND WALKER,R. W., Combustion and Flame 15, 33 (1970). HERRON, J. T., Int. J. Chem. Kinet. 1, 527 (1969). SKINNER, G. B., LIFSHITZ, A., SCHELLER, K., AND BURCAT,A., J. Chem. Phys. 56, 3853 (1972). FENIMORE, C. P., Twelfth Symposium (International) on Combustion, p. 463, The Combustion Institute, Pittsburgh, 1969. PEETERS,J. AND MAHNEN, G., Fourteenth Symposium (International) on Combustion, p. 133, The Combustion Institute, Pittsburgh, 1973. BaASBS, T. A. AND BROKAW, R. S., Fifteenth Symposium (International) on Combustion, p. 893, The Combustion Institute, Pittsburgh (1975). TUNDER, R., MAYER S., COOK, E., AND SCHIELEa, L., Aerospace Corporation Report TR-1001 (9210-02)- 1(AD813485), 1966. ENCLEMAN, V. S., EPA report EPA-600/2-76003, 1976. PACEY,P. D., Chem. Phys. Lett. 23, 394 (1973). GREINER,N. R., J. Chem. Phys. 53, 1070 (1970). HEro,ON, J. T. AND Hum, R. E., J. Phys. Chem. Ref. Data 2, 467 (1973). GARDINER,W. C., JR., AND WALKER, B. F., J. Chem. Phys. 48, 5279 (1968). BROWNE,W. B., PORTER, R. P., VERLIN, J. D., AND CLARK, A. H., Twelfth Symposium (International) on Combustion, p. 1035, The Combustion Institute, Pittsburgh, 1969. VANDOOREN, J. AND VAN TIGGELEN, P. J.~ Sixteenth Symposium (International) on Combustion, p. 1133, The Combustion Institute, Pittsburgh, 1977. MAYER,S. W., 8CHIELER, L., AND JOHNSTON, H. S., Eleventh Symposium (International) on Combustion, p. 837, The Combustion Institute, Pittsburgh, 1967. PEETERS, J. AND VINCKIER, C., Fifteenth Symposium (International) on Combustion~ p. 969, The Combustion Institute, Pittsburgh, 1975. LEFEVRE, H. F., MEAGHEB, J. F., AND TIMMOSS, R. B., Int. J. Chem. Kinet. 4, 103 (1972). GRAY, P. AND HEROD, A. A . , Trans. Faraday Soc. 64, 2732 (1968). ARONOWITZ,D., SANTORO, R. J., DRYER, F. L., AND GLASSMAN,I., Seventeenth Symposium (International) on Combustion, p. 633, The Combustion Institute, Pittsburgh, 1979. SCHOFIELD,K., Planet. Space Sci. 15, 643 (1967). TIKHOMIROVA, N. N., AND VOEVODSKII, V. V., Chain Reactions of Hydrocarbon Oxidation in the Gaseous Phase, Izd. AN SSR (1975). AZArYAN,A., NALRANDYAN,N., AND MENG-YUAN, S., DokL Akad. Nauk SSSR 149, 1095 (1963). YAMPOLSKII,Y. P., Izv. Akad. Nauk SSSR, Ser. Khim., 564 (1974).

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COMMENTS Dr. David Hsu, Naval Research Laboratory, Washington, DC. You mentioned that for your reaction n u m b e r (29): CH20 + OH ~ H~O + CHO, you used the rate constant compiled by Tony Dean. I believe that was the low temperature rate constant measured by Atkinson and Pitts, which might be inappropriate for high temperature modeling. In the kinetic modeling for CO production in our shock tube experiment on CHa + 02, we found that the CH~O + OH ~ H20 + HCO reaction is one of the most sensitive reactions. In order to arrive at a dependable rate constant at high temperatures, we carried out a transition state theory calculation, fitting Atkinson and Pitts' rate constant at 426 K (the highest temperature in their experiment) and extending the calculation to high as well as lower temperatures. We found that the calculated Arrhenius plot curved up sharply at high temperatures and agreed well with three sets of high temperature data and one l o w temperature data point. The parametrized TST rate expressed is given by: k = 6.9 x 104 T z~ exp (+ 1900/RT);

cc/mole-sec

Linear extrapolation of the Arrhenius plot based on Atkinson and Pitts' low temperature data to 2000 K can give a rate constant too low by a factor of 20. It should be emphasized that it is risky to linearly extrapolate low temperature Arrhenius plots to high temperatures.

Author's Reply. We are certainly most interested to learn of this recent experimental and modeling work which is relevant to our paper. While we agree with the warning about the use of extrapolated rate expressions, we feel that this type of error is not serious in the present paper with respect to the reaction CH20 + OH = HCO + H20. The reason is that only in the flow reactor were the computed results for ethylene oxidation at all sensitive to variations in this rate expression. At the temperatures of these experiments, about 1000 K, the extrapolation errors are quite small.

Prof. Fred Kaufman, University of Pittsburgh, PA. I would like to pose these identical questions to the authors of these four excellent modeling papers on inhibition, ethylene oxidation, and acetylene combustion processes. There seems to exist, suddenly, an embarassment of success. A great va-

riety of experimental results is well modeled so that one may be tempted to claim that most combustion problems are solved. Yet, our knowledge of the ~100-200 reaction rate constants is far from satisfactory. My questions are: 1. Are the mechanisms much too large so that most of the more complicated steps could be omitted? 2: How should sensitivity analysis be used in these problems and how has it been used? 3. The state of affairs of rate constant coUeetion, evaluation, and selection seems to be chaotic. Can the authors suggest improvements, regularized interactions with kinetics practitioners, etc. so that they will use the best, most up-to-date information, and so that the kineticists will be made aware of priority orderings of rate problems?

Author's Reply. It would be naive to claim, as a result of recent successes in kinetics modeling, that most combustion problems have been solved. It is probably fair to say that these advances have been very rapid and that kinetics models are having a significant impact on p r e s e n t combustion research, contributing a new and powerful tool to those already available for this type of work. However, it is important to place this kinetics modeling work in proper perspective. Chemical kinetics is only one of the many physical/chemical processes contributing to the behavior of practical combustion systems. Fluid mechanics, radiation and other forms of heat transfer, multiphase phenomena, turbulence, and other very difficult and complex problems related to interactions of these processes also must be addressed. It may be true that the kinetics field (and the modeling of kinetic behavior) has experienced rapid progress in the past few years, but many problems still remain. Kinetic mechanisms exist only for the simplest hydrocarbon and other fuels, rate data and product distributions are often uncertain, and interactions between kinetics and fluid mechanical processes including turbulence are not yet understood. Even for the simplest fuel molecules, examination o f the fine structure of the mechanism leads to new areas which cannot yet be explained. Examples of this at present include soot precursor formation and destruction, ion generation, chemical kinetics of CH, CHz, and C2H radicals, and many others. Dealing specifically with the questions raised: 1. The mechanisms discussed in this session of the Symposium are not too large if they are expected to describe fuel oxidation in practical combustion environments. The question of determining a "smallest necessary" mechanism is often raised. While this has some logical appeal, it is a poten-

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REACTION MECHANISMS AND M O D E L I N G II

tially dangerous trap. Many elementary reactions are important only in a restricted range of conditions. For example, in methane oxidation, the reaction

which the computed results are most dependent and which therefore warrant the greatest scrutiny. Perhaps the best example of the success of early "brute force" sensitivity analysis is the famous reaction

CH 4 + H = CHa + H 2 CH3 + 02 = products is a dominant reaction for fuel-rich conditions but can often be neglected in fuel-lean conditions, while the reaction c a 4 q- O = CH3 + OH is important only in lean conditions. Many recombination reactions become significant only at elevated pressures and can be neglected when modeling low pressure laminar flames, for example. If one wishes to provide a reaction mechanism which is valid only for one restricted experimental regime (low pressure, fuel-lean laminar methane-air flames, for example), then some elementary reactions need not be considered. On the other hand, we are developing "comprehensive" reaction mechanisms which are valid simultaneously, with no ad hoc "'adjustments" or other special treatments or assumptions, over wide ranges of fuel-oxidizer equivalence ratio, pressure, t e m p e r a t u r e , fuel type, amount of dilution, inhibitor type and concentration, and other parameters of interest experienced in conventional combustion. In practical terms, there is no good reason to reduce the size of a given reaction mechanism for the sake of compactness alone. The computational cost of kinetics modeling depends almost entirely on the n u m b e r of species included, n o t on the number of elementary reactions. It is very seldom possible to omit a given species entirely from a mechanism. The one case where this can often be done is the NOx reactions, which do not contribute to the radical levels or heat release rate in practical combustors. Therefore if one is not concerned with NO x production in a given model, the species such as NO, NO2, NzO, N, and perhaps other N-containing species can safely be omitted. The same is not true for hydrocarbon oxidation species such as CH 3, HCO, CO, or others. Those species must be retained; since they determine the computer costs there is no benefit to omitting individual elementary reactions. 2. Sensitivity analysis in varous forms has been used for as long as detailed mechanism development has been in existence. Only recently have convenient, powerful, and automated formalisms become available for simplifying the task of determining linear sensitivity parameters. In principle, sensitivity analysis identifies those elementary steps in a given reaction mechanism on

Extensive calculations with varied rate parameters pointed to this reaction step as the key to methane oxidation. Subsequent experimental investigation showed that it is actually a very slow reaction and the high temperature products most commonly being assumed were in fact incorrect. Eventually, it was realized that methyl radical recombination

CH3+ CH3= C2H6 had not been considered in early methane mechanisms and was required to account properly for methyl radical consumption. Sensitivity analysis has its limitations, however. While this can identify the steps to which computed results are sensitive, it cannot clearly identify paths which are completely missing from a given mechanism. Thus in the above example of methyl radical consumption, sensitivity analysis pointed to CH 3 + O2 as a highly sensitive reaction, but it could not identify the methyl radical consumption path required to achieve reasonable results with appropriate rates and products for CH3 + 02. However, sensitivity analysis can point to reactions which need experimental attention. This analysis, presented in our paper, suggests that the rates and product distributions of the reactions CzH 3 + M

=C2H 2+H+

C2H 3 + O 3

= C 2 H 2 + HO2

C2H4 + O

= products

M

C2H4 + OH = products need attention in experiments at elevated temperatures (T -> 1000 K). Other papers at this Symposium point to the same needs for related reactions in acetylene combustion. Finally, we again wish to point out that the term "elementary reaction" must be used advisedly with regard to any kinetic mechanism. Each mechanism represents an approximation in which all intermediates with characteristic lifetimes too small to be resolved or to affect the observable features of interest are neglected. Occasionally this level of approximation results in distortions of the mechanistic description as in the case of the CH 3 + 02 reaction. Sensitivity analysis helps to locate and identify such anomalies, and it is the explanation and re-

PYROLYSIS AND OXIDATION O F ETHYLENE moval of these anomalies which is a constant force driving the evolution of kinetics modeling. 3. We do not agree with the suggestion that the state of affairs in rate constant use is "'chaotic." There is a fairly small community of researchers carrying out this type of modeling work, and most of us are quite aware of experimental advances in kinetics research. Recalling that the time lag in preparing, editing, and presenting symposium papers is often appreciable, the present papers represent work that is more than a year old. Our own current mechanisms reflect recent developments of several types and will continue to evolve and grow as additional elementary reaction data and combustion chemistry experiments become available. All of our publications, including those at this symposium, present detailed discussions indicating which elementary reactions have the greatest importance in determining the model solutions. This information should then be helpful to experimental kineticists by suggesting areas in which their work can be of greatest benefit to modeling efforts. We believe this process works very well. A good example of this symbiosis between modeling and experimental kinetics is provided by the current experinaental interest in the reaction rates and product distributions for reactions C~H4 or C2H2 and radical species including H, O, and OH. Those steps, identified in modeling papers during the past year or two as needing attention, have received some intense experimental and theoretical analysis, and the results are now finding their way back into the models.

Dr. Ji~rgen Warnatz, Tenische Hochschule Darmstadt, West Germany. You compare experiments in the turbulent flow reactor with results of your mechanism and a mechanism developed by me. 1 As explicitly mentioned in the paper cited, this latter mechanism should b e applied only to high t e m p e r a t u r e flame propagation, whereas it cannot explain processes including induction phenomena or pyrolysis. Of course, this mechanism must lead to exorbitant discrepancies between calculations and the experiments cited. An extended mechanism including pyrolysis steps to explain induction processes has been given elsewhere, z3

165

Colloquium on Gas Dynamics of Explosions and Reactive Systems, Minsk, USSR, 1981, in press. 3. J. WARNATZ, in: W. C. Gardiner (ed.), Combustion Chemistry, Springer, in press.

Author's Reply. We agree wholeheartedly with the comment from Professor Warnatz. Although it is often done in practice, the use of detailed reaction mechanisms to predict or interpret experimental results u n d e r conditions for which the mechanism was not developed, validated, or intended should be strongly discouraged. In the present paper we make this point explicitly by taking the only available ethylene oxidation mechanism, that of Prof. Warnatz, and expressly des i g n e d only for e t h y l e n e o x i d a t i o n in h i g h temperature laminar flames, and trying to apply it to other parameter ranges. The inability of that mechanism to predict such data 'from shock tubes or the flow reactor was expected and should not be interpreted in any way as a criticism of the beautiful work of Prof. Warnatz. It does, however, motivate perfectly the mechanism development described in the present paper. For some years we have been developing comprehensive reaction mechanisms which simultaneously describe experimental data from all available types of regimes, including laminar flames, flow reactors, shock tubes, detonations, and any other relevant experiments. The flow reactor data are particularly important, since they represent a lower temperature range than the other experiments. No mechanism can be truly comprehensive unless it considers experiments in this range around 1000 K. With such a mechanism that has been validated over all conceivable parameter ranges, one can apply it to any set of experimental combustion data and expect it to give reliable overall results. Even so, there will be experimental ranges in which this type of mechanism will still be invalid, such as in cool flame regimes. Finally, it is possible to take one of these comprehensive mechanisms and simplify-it considerably to deal with only one experimental regime, such as laminar flames or shock tubes. Elementary reactions and species which are unimportant in that regime of interest can be eliminated, reducing the size and complexity of the mechanism. However, that simplified mechanism cannot then be used properly to model other experimental regimes, as pointed Out by Professor Warnatz.

REFERENCES 1. J. WA•NATZ, E i g h t e e n t h Symposium (International) on Combustion, p. 369, The Combustion Institute, Pittsburgh, 1981. 2. W. C. GARDINER, C. S. EUBANK, J. M. SIMMIE, R. ZELLNER, K. J. NIEMI'FZ, J. WARNATZ, 8th Int.

Dr. J. V. Michael, Brookhaven National Labs, Upton, NY. Professor Hoyermann has pointed out that under very low pressure conditions in his experiments OH + C2H 2 ~ CH2CO + H in agreement with an earlier assertion by Gutman. We

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REACTION MECHANISMS AND M O D E L I N G II

measured the overall rate constant for this reaction a couple of years ago and found a significant pressure dependence. This means that an alternative channel for the reaction will be the formation of the stabilized adduct radical. This unfortunately suggests that still another species, C2H~OH, must be considered in this reaction. Our specific view on this reaction is given in detail i n our already published paper.

Author's Reply. Both the formation of an adduct species C2H~OH and the product channel produc-

i n g CH2CO are considered in other mechanisms presented at this symposium and elsewhere. We did not include them in the present paper because, like other details of the acetylene oxidation submechanism, they did not have any appreciable effect on burning rates and other features of ethylene oxidation in the cases we considered, Their importance in describing acetylene oxidation has been recognized by those modeling such systems, however.