- Email: [email protected]
Detailed kinetic modeling of C1 — C3 alkane diffusion flames
Detailed Kinetic Modeling of C, Diffusion Flames K. M. LEUNG
C, Alkane
and R. P. LINDSTEDT*
Department of Mechanical Engineeting, Imperial College of Science, Technology and Medicine, Exhibition Road. London SW7 2BX, UK
A study of detailed chemical kinetics in coflow and counterflow diffusion flames is presented. The chemistry of diffusion flames is of fundamental importance from a practical as well as a mechanistic viewpoint. The present study uses systematic reaction path flux and sensitivity analyses to determine the crucial reaction paths in methane and propane diffusion flames. The formation of benzene and intermediate hydrocarbons via C, and C, species has been given particular attention and the relative importance of reaction channels has been assessed. The developed mechanism considers singlet and triplet CH,, isomers of C,H,, C,H,, C,H,, C,H, and C,H,. Computational results show that benzene in methane-air diffusion flames is formed mainly via reactions involving propargyl radicals and that reaction paths via C, species are insignificant. It is also shown that uncertainties in thermodynamic data may significantly influence predictions and that the reaction of acetylene with the hydroxyl radical to produce ketene may be an important consumption path for acetylene in diffusion flames. Quantitative agreement has been achieved between computational results and experimental measurements of major and minor species profiles, including benzene, in methane-air and propane-air flames. It is also shown that the mechanism correctly predicts laminar burning velocities for results for a two-dimensional methane-air flame on a stoichiometric C, -C, flames. Finally, Wolfhard-Parker burner obtained with full detailed chemistry are presented along with flamelet computations and the accuracy of the latter are discussed.
1. INTRODUCTION Chemical kinetic modeling has become an important tool for interpreting and understanding observed combustion phenomena. Its application require as an input a valid chemical reaction mechanism. A large amount of effort has been devoted to the development of detailed kinetic mechanisms of varying complexity for hydrocarbon combustion. Detailed kinetic mechanisms found in the literature covers most of the C,-C, hydrocarbons [l-18] as well as higher hydrocarbons such as benzene 1191, toluene 1201, heptane, and octane [21, 221. However, it is well recognized that the rates of many elementary reactions are uncertain and vary strongly depending on flame type and combustion conditions. As a result the development of comprehensive detailed kinetic mechanisms requires validation under a wide variety of regimes. Previous mechanism validation studies have mainly focused on premixed systems (e.g., premixed flames, shock tubes, and flow reactors), with comparatively little attention given to nonpremixed reactants. The
* Corresponding
author.
COMBUSTIONAND FLAME 102: 129-160 (1995) Copyright 0 1995 by The Combustion Institute Published by Elsevier Science Inc.
complex transport and chemical kinetic interactions that occur in nonpremixed combustion result in significant differences in flame structures compared to premixed combustion. Moreover, pyrolysis reactions play a more important role for fuel consumption in nonpremixed combustion. These differences makes it desirable to extend the validation of detailed chemistry further through the application to non-premixed systems. To date modeling studies of diffusion flames have mainly concentrated on simple fuels [23-251. However, some detailed numerical studies of heptane-air [26] and propane-air [27, 281 diffusion flames have been reported recently. In many cases good agreement has been obtained between predictions and measurements for major species profiles. However, it has been found [27] that even the predictions of stable intermediate species are very sensitive towards the rates of a number of reactions. The difficulty in formulating a well balanced kinetic scheme is further increased by the considerable scatter in rate constants of reactions which are important for the prediction of intermediate species in diffusion flames. The objective of the present study is to further develop and refine a detailed kinetic OOlO-2180/95/$9.50 SSDI 0010-2180(94)00254-P
130
K. M. LEUNG
mechanism to make it suitable for the modeling of C,-C, hydrocarbon combustion under diffusion flame conditions. Particular attention has been given to improvements of the quantitative predictions of species such as benzene and acetylene which are of fundamental importance for the further development of soot formation models [28]. Refinement of the mechanism has been achieved by a systematic computational sensitivity analysis conducted initially on laminar counterflow methane-air and propane-air diffusion flames and subsequently on coflowing methane-air flames. Propane and methane were chosen as fuels because of the significant differences in the amounts of intermediate species produced during the pyrolysis of the two fuels and as experimental measurements of many of these species are available for comparison [29, 301. In hydrocarbon diffusion flames with nonaromatic fuels the formation of benzene can be expected to precede the formation of PAII and soot and several benzene formation paths via C,-C, hydrocarbons have been suggested [9, 32-371. The possible reaction paths have here been investigated using experimental data obtained by Smyth and co-workers [38, 40-431 and Miller and Taylor [39], who measured concentration profiles of a number of species including acetylene and benzene, in a coflowing methane-air diffusion flame on a Wolfhard Parker burner. Detailed kinetic calculations, as well as flamelet computations, have been performed for this flame, and comparisons with measurements are reported. In all cases the major reaction paths and the sensitivity of the predictions of intermediate species towards individual reactions in the detailed mechanism are quantified through reaction path flux and sensitivity analyses. The uncertainties in the rate constants are related to the predictions of intermediate species. 2. MATHEMATICAL
AND R. P. LINDSTEDT
point streamline. The basic boundary layer equations for the counterflow geometry may be written in a similarity transformed coordinate system. The mechanics of the actual transformation of the steady equations has been discussed by Peters and Kee [44], and the corresponding governing time-dependent equations are only briefly repeated below.
where
The corresponding boundary layer equations for the two-dimensional flame on the Wolfhard-Parker burner are JP u -+ dx
dP * = 0, dy
dU
dZ4
pudx+pv-=-
dY
d
(
dY \
dP
au\
u-
dY
I
-z,
MODEL
The numerical representation of the structure of counterflow diffusion flames has been discussed by many authors [24, 25, 441. The structure of this flame is obtained from the solution of the equations of conservation of momentum, species and energy along a stagnation
-Jk---
x i ayk
puax
+ puz
= 2
+ MkRk.
KINETIC
MODELING
OF ALKANE
DIFFUSION
In the above equations the components of velocity are denoted by u and v in the x and y directions, p is the fluid density, h is the mixture enthalpy, p is the fluid viscosity, Y, is the mass fraction and Mk is the molar mass of species k. For the counterflow flames a is the rate of strain and the subscript e denotes values prevailing in the potential flow at the “edge” of the boundary layer. The buoyancy term was evaluated in a similar way to that used by Jones and Lindstedt 1451.The reaction rate source term may be written as nreac R, =
nsP
c
Sik k/n
j=l
i
nsP
(I+
- k; n
I= 1
@,‘lk .
I= 1
i
The expression for the flux term is as suggested by Jones and Lindstedt [45] and may for example in the counterflow case be written as,
J,=-!c
dYk --
i a
USC
1 dn
Yp---
i
-
41r,. Ll
The evaluation of the transport coefficients were made using the same technique as outlined by Jones and Lindstedt [45]. The above equation system was solved using an implicit difference formulation involving two point backward time differencing and central differences for the spatial derivatives. The resulting set of algebraic equations are nonlinear, and a Newton linearization was used for the source terms in the species transport equations,
131
FLAMES
To obtain steady flow solutions the above equations were integrated in time until steady conditions prevailed or until a sufficient distance downstream had been reached. Mesh distributions in the flames were set to ensure a large number of mesh nodes in the portion of the flame where the maximum gradients occur. This was achieved by using distributed mesh spacing with a minimum of 110 nodes for the counterflow case and 165 nodes for the coflow case. The applied boundary conditions for the counterhow case consisted of an adiabatic wall with a prescribed mass flux at the cylinder surface and zero gradient conditions at the free stream boundary for all variables except I/. Calculations for the coflowing cases were performed with initial conditions for the axial velocity, the temperature and the species concentrations as prescribed at the burner exit. Zero gradient conditions were assumed for all variables at the symmetry line. The air side was treated as a free stream boundary condition. An ad hoc modification of the buoyancy term was found necessary in order to produce reasonable agreement with the measured velocity profiles as discussed below. The coflowing flame was also computed using a flamelet approximation. For this case the species and enthalpy equations were replaced by an equation for the mixture fraction Z, dZ dZ d pudx +pv- JY JY
The mixture fraction equation was solved based on mean mixture properties with species concentrations and temperature profiles obtained from flamelets generated in the counterflow geometry. The resulting block tridiagonal equation system for the species transport equations was solved using a direct method 1461, and in an outer sweep the transport equations were iterated with respect to the nonlinear contributions (rate expressions, diffusion correction velocity). The enthalpy and momentum equations were solved using a conventional tridiagonal equation solver. Finally, the transformed continuity equation is used to solve for V by numerical integration for the counterflow case.
3. THE REACTION
MECHANISM
The present detailed mechanism is an extension of the C, -C, mechanism developed by Leung et al. [27, 281. Rate constants for the reactions in the former mechanism were mainly obtained from the compilation of Baulch and co-workers [471, Tsang and Hampson 1481 and Tsang [49-511. Many additional features have been incorporated into the present mecha-
132
K. M. LEUNG
nism. The present mechanism also includes a reaction submechanism for C, species based predominantly on the work by Miller and Melius [361, Kiefer et al. [52, 531 and Kern et al. [54]. A detailed benzene formation mechanism has been formulated based on the work of Alkemade and Homann [34], Stein et al. [35] and Melius et al. [37]. A benzene oxidation mechanism, validated independently by Lindstedt and Skevis [55], has also been included. The details of the benzene formation mechanism are discussed below. The current mechanism differentiates between methylene in the ground and excited states c3CH, and ‘CH,), isomers of C,H, (CH,CCH,, CHCCH,, and cyclopropene), C,H, (CH,CHCH,, CH,CHCH, and CH,CCH,). In addition the following isomers of C, and C, species are considered: I-C,H,
= CH,CHCHCHCHCH,
(1,5)-&H,
= CHCCH,CH,CCH,
(1,2)-C,H,
= CH,CCHCH,CCH,
(1,2,4,5)-C,H,
= CH,CCHCHCCH,,
(Ml-C,H,
= 1,2-dimethylene-3-
AND R. P. LINDSTEDT
A complete referenced listing of the reaction mechanism consisting of 87 species and 451 reactions can be found in Table 1. All reactions were assumed reversible with the reverse rates calculated from the appropriate equilibrium constants. The thermodynamic data coefficients adopted for the calculation of the equilibrium constants were obtained mainly from the compilation of Burcat and McBride [llO] or from the CHEMKIN [ill] database. For species not found in these sources thermodynamic data was estimated using Benson’s method [112]. A critical review of the heats of formation for some species was also required as discussed below and a list of the final values used for all the species considered can be found in Table 2. The treatment of pressuredependent reactions was according to the formalism of Troe [114] and transport coefficients for viscosity and binary diffusivity were evaluated using the kinetic theory of Chapman and Enskog (see Reid et al. [115]>. The thermal conductivity was evaluated using the Mason and Monchick [1161 approximation including rotational collision efficiency, but ignoring the vibrational contributions. Lennard-Jones potential parameters were taken from the compilations of Kee et al. [117].
cyclobutene, (1,3&H,
= CH,CHCHCHCCH,
(1,3&H,
= CHCCH,CHCCH,
(1,5&H,
= CHCCHCHCHCH,
(1,2)-C,H,
= CH,CHCCH,,
(1,3)-C,H,
= CH,CHCHCH,,
c-C,H, (1,2)-C,H,
= l-methyl-cyclopropane, = CH,CHCCH, (radical site at terminal carbon),
(1,3)-C,H,
= CH,CHCCH,
X,H,
= CH,CHCCH, (radical site at interior carbon),
n-C,H,
= CHCCHCH,
X,H,
= CH,CCCH.
4. REACTION ANALYSIS
SENSITMTY
AND PATH
As a starting point for further development the C,-C, mechanism described above was evaluated using experimental data from methane-air and propane-air counterflow diffusion flames obtained at ambient pressure by Tsuji and Yamaoka [29, 301. Reaction path flux analysis was used to identify the main species consumption paths in both methane and propane flames. Sensitivity analysis was also conducted to determine which rate coefficients had the greatest influence on the computed results. The sensitivity analyses were performed by multiplying the rate constant of each reaction of interest by a factor of 5 or l/5 and followed by a complete flame computation for every perturbation. This variation of the reaction rate covers in most cases the range of scatter in rate constants reported in the literature. Logarithmic response sensitivities are used in the
KINETIC MODELING OF ALKANE DIFFUSION FLAMES
133
TABLE 1
Reaction Mechanism Rate Coefficients in the Form k, = AT”exp( -E/RT)
n
E (kJ/mol)
0.00 2.67 1.60 1.14 - 0.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 1.00 -0.60 - 1.25 - 2.00 - 2.00 - 1.00 1.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
70.34 26.27 13.80 0.42 0.00 3.66 5.90 - 2.08 7.20 0.00 6.44 14.96 15.71 16.63 5.57 190.00 0.00 0.00 0.00 0.00 0.00 0.00 - 2.08 98.94 - 19.00 199.54 0.00 2.89 0.00 0.00 0.00 -2.16 0.00 0.00 0.00 41.84 41.84 0.00 0.00 0.00 0.00 0.00 71.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
A
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. 54.
(m3, kmol, s-
Reactions
No.
H + Oz 0 + Hz OH + H, 20H O?+H+M HO, + H HO, + H HO, + OH HO, + H HOz + 0 HO, + HO, H,O, + H H,O, + H H,O, + 0 H20, + OH H,Oz + M 2H + M 2H + H, 2H + H,O 2H + CO, H+OH+M 20 + M CO+OH CO + HO, CO+O+M co + 0, CH + 0, CH + CO, CH + 0 CH+OH CH + H,O CH + CH,O CH +3CH, CH+CH, CH + CH, CH + C,H, CH + C,H2 CHO + H CHO + 0 CHO + 0 CHO + OH CHO + 0, CHO + M ‘CH, + Hz ‘CH, + H ‘CH2 + 0 ‘CH, + 0 ‘CH, + OH ‘CH, + 0, ‘CH, + CO, ‘CHZ + CH, ‘CH, + CH, ‘CH, + C,H, ‘CH, + C,H,
OH + 0 OH+H H,O + H H,O + 0 HO, + M” 20H H, + Oz H,O + 0, Hz0 + 0 OH + 0, H20, + 0, H,O + OH HO, + H, HO, + OH H,O + HO, 20H + Mb Hz + MC Hz + H, Hz + H,O Hz + CO* Hz0 + Mb OX + Mb CO, + H CO, + OH CO, + Mb co2 + 0 CHO + 0 CHO + CO CO + H CHO+H CH,O + H CH,CO + H C2H, + H C,H, + H C,H, + H C,H + H, C,H, + H CO + H, CO + OH CO, + H CO + H,O CO + HO, CO + H + Mb CH, + H CH + Hz CO + 2H CO + Hz CH,O+H CO + OH + H CH,O + CO C,H, + H CH, + CH, C,H, + H c-C3H,
1.989E + 5.120E + 1.025E + 1.500E + 2.000E + 1.686E + 4.280E + 2.890E + 3.000E + 3.190E + 1.870E + 1.024E + 1.686E + 6.620E + 7.830E + 1.200E + 6.530E + 9.200E + 6.000E + 5.490E + 2.213E + l.OOOE + 6.320E + 1SOOE + 5.300E + 2.530E + 3.300E + 3.430E + 4.000E + 3.000E + 1.170E + 9.640E + 4.OOOE+ 3.000E + 6.000E + l.OOOE + l.OOOE + 9.030E + 3.000E + 3.000E + 1.024E + 3.000E + 1.860E + 7.230E + 7.000E + 1.500E + 1.5OOE + 3.000E + 3.130E + 3.000E + 1.800E + 4.280E + 8.000E + 8.000E +
’)
11 01 05 06 12 11 10 10 10 10 09 10 09 08 09 14 11 10 13 14 16 11 03 11 07 09 10 09 10 10 12 10 10 10 10 11 11 10 10 10 11 09 14 10 10 10 10 10 10 09 10 10 10 10
Ref. I471 [471 I471 [471 [21 [471 [471 [471 [471 [471 I471 [471 [471 [471 I471 I21 [471 I361 I361 [361 [471 Dl I471 1481 Bl [481 [471 I471 [471 1361 I361 [471 [361 [361 I361 est., [57] est., 1571 [471 I471 [471 [471 [471 I581 [481 [591 I481 [481 I481 [481 I481 [481 [481 est., [60] est., [601
TABLE 1 Reaction Mechanism Rate Coefficients in the Form kj = AT”exp( -E/W) A (m3, kmol, s- ‘1
Reactions
No. 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.
‘CH, ‘CH, ‘CH, ‘CH, 3CH2 3CH2 3CH, 3CH, 3CH, 3CH, 3CH, 3CH2 3CH, 3CH2 3CH, 3CH, 3CH, 3CH, 3CH, 3CH, 3CH, CH,O CH,O CH,O CH,O CH,O CH,O CH,O 2CH, 2CH,
+ CH,CO + C,H, + C,H, + M + H, + H + 0 + 0 + OH + OH + 0, + O2 + 0, + 0, + 0, + CO, +3CH, + CH, + C,HO + C,H, + C,H, + H + 0 + OH + 0, + HO, + CH, + M
85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109.
CH, + 0 CH, + OH CH, + OH CH, + OH CH, + OH CH, + 0, CH, + 0, CH, + HO, CH,+CHO CH, + M CH, + M CH,OH+M CH,OH + M CH,OH + M CH,OH + H CH,OH + H CH,OH + H CH,OH + 0 CH,OH + 0 CH,OH + OH CH,OH + OH CH,OH + CH, CH,OH + CH,O CH,O + H CH,O+O
C,H,
+ CO
C3H6
C,H, + CH, 3CH, + Md CH, + H CH + H, CO + 2H CO + H, CH + H,O CH,O + H CO + H + OH CO, + 2H CH,O + 0 CO, + H, CO + H,O CH,O + CO C,H, + 2H C,H, + H C,H, + CO c-C,H, C3H6
CHO+H, CHO + OH CHO + H,O CHO + HO, CHO + H,O, CHO + CH, CHO+H+M C25 C2H6’
,+
H
k, = k, =
CH,O + H CH,OH + H ‘CH? + H,O CH,O + H, CH,O + H CH,O + 0 CH,O + OH CH,O + OH CH, + CO ‘CH, + H + M CH + H, + M CH, + OH + M CH,OH + H + M ‘CH, + H,O + M CH,OH + H, CH,O + H, CH, + H,O CH,OH + OH CH,O + OH CH,OH + H,O CH,O + H,O CH,OH + CH, CH,OH + CH,OH CH,O + H, CH,O + OH
1.260E + 11 6.600E + 10 1.140E + 11 l.OOOE + 10 3.000E + 06 l.lOOE + 11 7.220E + 10 3.610E + 10 1.130E + 04 2.5OOE + 10 6.580E + 09 6.580E + 09 6.580E + 09 2.630E + 09 2.630E + 09 l.lOOE -I- 08 1.2OOE + 11 4.210E + 10 3.000E + 10 1.2OOE + 10 1.800E + 07 2.29OE + 07 4.150E + 08 3.430E + 06 6.000E + 10 2.000E + 09 4.090E + 09 1.260E + 13 5.000E + 09 3.613E + 10 1.270E + 35 8.430E + 10 1.500E + 11 4.000E + 10 1.024E + 09 5.740E + 09 1.320E + 11 3.300E + 08 1.800E + 10 1.200E + 11 1.900E + 13 6.900E + 11 1.900E + 16 2.000E + 14 7.0OOE + 12 4.000E + 10 4.000E + 09 5.010E + 09 3.880E + 02 l.OOOE + 10 3.000E + 01 5.300E + 00 3.190E - 02 3.000E + 08 2.000E -t 10 6.000E + 09
(Continued) E
n 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.05 0.57 1.18 0.00 0.00 0.00 0.00 0.10 0.00 - 7.00 0.00 0.00 0.00 0.00 - 0.23 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.50 0.00 2.65 2.65 3.20 0.00 0.00 0.00
W/mol)
Ref.
0.00
[601
0.00 0.00 0.00 0.00 0.00 0.00 0.00 12.55 0.00 6.24 6.24 6.24 6.24 6.24 4.18 3.32 0.00 0.00 27.70 0.00 13.72 11.56 - 1.87 170.10 48.80 37.00 325.91 44.36 0.00 11.56 0.00 34.46 10.47 0.00 58.28 131.36 37.41 0.00 0.00 382.44 345.03 384.04 315.89 278.00 25.50 25.50 22.17 12.89 19.60 - 3.70 -3.70 30.00 17.04 0.00 0.00
[471 [481 [471 [481 est., [61] est., 1471 est., [471 [361 [361 [621 [621 [621 1621 1621 [361 [471 t471 1361 1631 [481 1471 [471 [471 1471 [621 1471 [471
[641 [471 I471 [621 1621 [651 [661 [471 [471 t471 I481 t671 I671 I491 [681 t691 [621 [621 [701 [621 Dl 1621 [621 I491 t491 I481 [481
TABLE 1 Reaction Mechanism Rate Coefficients in the Form k, = AT”exp( -E/RT)
110. 111. 112. 113. 114. 115. 116. 117. 118.
CH,O + CH,O + CH,O + CH,OH CH,OH CH,OH CH,OH CHzOH
119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158.
CH, + H CH, + 0 CH, + OH CH, + HO, CH, + 0, C2H + H, C,H + 0 C,H + OH C,H + 0, C2H + CH, CHCO + H CHCO + 0 CHCO + OH CHCO + 0, CHCO + 0, CHCO + CH 2CHC0 CHCO + C,H, CHCO + M C20 + H c,o + 0 C,O + OH c*o + 0, C2H,+0 C,H, = 0 C,H, + OH C,H, + OH C,H, + OH C,H, + OH
159. 160. 161. 162. 163. 164. 165.
A (m3, kmol, s- ‘)
Reactions
No. OH 0, M + H + 0 + OH + O2 + M
CH,
CzH, + C2H, + C2H, + CHCOH CH,CO CH,CO CH,CO CH,CO CH,CO CH,CO C,H, +
0, 0, M + H + M + H + 0 + 0 + OH + CH, H
C,H, C,H, C,H,
+ H + 0 + OH
GH3
=
C,H, C,H, C,H,
+ CH + C,H + H
0,
CHZO + H,O CH,O + HO, CH?O+H+M CH,O + H, CH,O + OH CH,O + H,O CH,O + HO, CH,O + H + M CH, + H’s2 CH, + H, CH, + OH CH, + H,O CH, + H,O, CH, + HO, C,H, + H CO + CH CHCO + H 2C0 + H C,H, + H ‘CH, + CO 2C0 + H C,O + H,O 2C0 + OH CO, + CHO C,H, + CO C,H, + 2C0 C,H, + CO CH + CO + M CH + CO co + co CO + CO + H co + co + 0 3CH2 + CO CHCO + H C,H + H,O CHCOH + H CH,CO + H CH, + CO C,H + HO, CHCO + OH C,H + H + M CH,CO + H 3CH, + CO + M CH, + CO CO, +3CH2 CHCO + OH CHCO + H,O C,H, + CO CzHjf.’ C,H, + Hz CH,CO + H C,H? + H,O CH,O + CHO C,H, +3CH, C,H, + C,H, C2H3 + H,
k, = k, =
k, = k, =
1.800E + 6.6208 + 5.45OE + 3.000E + 4.210E + 2.410E + l.OOOE + 1.220E + 2.4OOE + 4.516E + 1.325E + 9.033E + 1.560E + 9.033E + 3.970E + 4.074E + 1.024E + 2.OOOE+ 3.520E + 2.410E + 1.5OOE + 9.640E + 3.0OOE + l.OOOE + l.OOOE + 5.0OOE + l.OOOE + l.OOOE + 6.000E + 5.0OOE -t 5.000E + 2.0OOE + 2.000E + 1.080E + 1.080E + 3.370E + 5.040E + 2.180E 4.830E 1.200E + 2.0OOE + 4.0OOE + l.OOOE + 3.600E + 1.800E + 1.750E + l.OOOE + 7.500E + 5.000E + 5.540E + 2.670E + 4.0OOE + 3.000E + 2.000E + 3.970E + 5.000E + 3.0OOE + 1.325E +
10 07 10 10 10 10 11 25 16 14 01 05 04 09 10 02 10 10 10 10 11 10 10 10 10 10 10 08 12 10 10 10 10 01 01 04 02 07 07 10 05 13 10 12 10 09 10 09 09 09 21 10 10 10 09 10 10 03
(Continued) E
n 0.00 0.00 0.00 0.00 0.00
0.00 0.00 - 4.00 0.00 0.00 3.00 1.56 1.83 0.00 0.00 2.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.80 2.80 2.00 2.30 4.50 4.00 0.0) 1.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 3.50 0.00 0.00 0.00 0.00 0.00 0.00 2.53
&J/mol) 0.00 10.89 56.50 0.00 0.00 0.00 21.00 133.42 438.98 379.95 33.63 35.50 11.64 103.09 238.03 0.84 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 12.55 246.10 0.00 0.00 0.00 0.00 2.08 2.08 58.58 56.48 -4.18 - 8.37 311.78 125.94 447.00 0.00 248.00 14.13 5.65 8.37 8.37 0.00 10.08 10.08 0.00 0.00 0.00 - 1.05 0.00 0.00 51.21
Ref. [481 [481 Lb21 121 [491 [491 [621 [621 [851 [471 [471 [471 [471 [471 [531 I471 [361 [361 [481 [471 [471 [361 est., [21 est., [2] [361 [361 1361 [711 [361 1361 [361 1361 est., [47] est., [471 1361 1361 [361 1361 1481 [361 PI [361 El [471 [361 [361 Ml [721 Ml [361 [361 1361 [731 [361 [361 [481
136
K. M. LEUNG AND R. P. LINDSTEDT TABLE 1 Reaction Mechanism Rate Coefficients in the Form k, = AZ’“exp(-E/RT)
(Continued)
A
Reactions
No.
166. 167. 168. 169. 170. 171. 172.
C,H, C,H, C,H, C,H, C,H, C,H,
+ + + + + +
0 OH M O? 0 M
173. 174. 17.5. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195. 196. 197. 198. 199. zoo. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211.
C,H, + H C,H, + 0 C,H, + OH C,H + 0 C,H + OH C,H + 0, c-C,H, + 0 c-C,H, + OH c-C,H, + 0, c-C3H, + M
CH, + CHO C,H, + H,O C,H, + H + M
C,H,O C,H,O C,H, + C,H, + C,H2 + C,H, + a-C,H, a-C3H, a-C,H, a-C3H, a-C,H, a-C,H, a-C,H, a-C,H, a-C3H, a-C,H, a-C3H, a-C,H, c-C3HI, c-C,H, p-C,H, p-C,H, p-C,H,
+ 0 + OH CH, CH, CH, CH, + H + H + H + 0 + OH + OH + 0, + CH, + C,H + a-C3H, + a-C3H, + M
212. 213. 214. 215. 216. 217. 218. 219.
p-C,H, p-C,H, p-C,H, p-C,H, p-C,H,
+ + + + +
0 0 0 OH OH
0
P-C,H,
+
0,
o
P-C,&
+
0,
P-C,&
+
CH3
0 0
C,H, + HO, CH, + CH,O C,H, + H + M C,H, + He,3
C,H,
C,H, C,H, C,H,
+ H + 0 + OH
C3H3
+
C,H,
(m3, kmol, s-
k, = k, =
C,H, + Hz C,H, + OH C,H, + Hz0 C,H + CO C,H, + CO CHCO + CO C,H + CO + H C,H, + CO + H C,H, + CO, C,H + H + M c-C3H2 + Hz C,H,O + H C,H,O + H, CH$O + CHO c-C,H2 + H + M C,H, + CO C,HO + CHO CH,CO + CHO a - C,H, + H p-C,H, + H a-C3HS s-C,H, t-C,H, a-C,H,
0,
+ M
C3HzO
C3H3
+
C,H, + CH,CO C,H, + C,H, + C,H, +
Hz
CHO + CH, H,O HO, CH,
C,H, + C,Hz a-C,H, + C,H, C3H3
+
C,H,
+
Hz
C,H, + H + M a-C3H, P-C,&
+ H + H + H
t-C,H, s-C,H, C3H3
CH,CO +3CH, C,H, + CHO CHCO + CH, CH,CO + CH, C3H3
+H@
CHCO +%H2 C,H, + HO, C,H, +CH,
+ OH
’1
1.325E + 1.570E + 2.600E + 1.020E + 6.620E + 2.000E + 8.850E + 4.900E + 1.445E + l.OOOE + 7.226E + 6.800E + 6.8OOE + 2.000E + 6.800E + 5.000E + 2.000E + l.OOOE + 5.000E + 1.400E + 2.000E + 3.000E + 2.000E + 8.500E + l.OOOE + l.OOOE + 6.7408 + 2.730E + 2.620E + 1.610E + 8.500E + 4.000E + 2.000E + l.lOOE + 3.120E + 1.445E + 4.000E + 2.000E + l.OOOE + 5.000E + 2.000E + 2.000E + 1.513E + 7.080E + 6.5OOE + 5.800E + 2.000E +
05 01 14 07 10 12 20 39 06 06 03 10 10 09 10 10 09 12 09 11 09 07 45 14 10 10 16 15 43 37 09 09 11 05 09 10 10 09 10 11 09 15 14 13 09 09 11
6.400E 3.200E 6.300E 5.000E 3.000E 2.000E 5.000E 2.000E
09 09 09 07 00 05 09 09
+ + + + + + +
n
-
-
-
E &J/m00
1.55 2.15 0.00 0.00 0.00 0.00 1.23 6.43 1.50 1.50 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8.50 0.00 0.00 0.00 2.08 1.96 9.82 8.58 0.00 0.00 0.00 4.61 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1.79 17.46 404.00 -9.14 0.00 125.00 427.70 448.40 31.01 24.28 3.62 0.00 0.0) 0.00 0.00 0.00 0.00 424.80 0.00 0.00 0.00 12.00 409.95 297.06 0.00 0.00 132.18 86.16 154.60 85.06 8.37 11.30 62.84 - 17.75 - 1.66 17.46 257.32 32.22 0.00 270.70 32.22 334.72 210.87 182.84 8.37 12.98 62.84
0.00 0.00 0.00 4.50 3.00 1.50 0.00 0.00
8.41 8.41 8.41 -4.18 0.84 125.94 213.38 32.22
Ref. 1481
[481 PI [471 I471 [I61 I61 [471 [471 [471 est. est. est. est., [741 est., 1361 est. est. est.
[751 est. 1761
I571 t771 est. est.
I661 I661 [661 [661 t791 I791 est., [801
I151 [151 [151 u51 [811 I811 [151 1151 t821 [831 is31 [781 [781 [801 [151 [151 1151 I151 1151 t151 I151 [811
KINETIC MODELING
OF ALKANE
137
DIFFUSION FLAMES TABLE 1
Reaction Mechanism Rate Coefficients in the Form ki = AT”exp( -E/RT)
220. 221. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233. 234. 235. 236. 237. 238. 239. 240. 241. 242. 243. 244. 24.5. 246. 247. 248. 249. 250. 251. 252. 253. 254. 255. 256. 257. 258. 259. 260. 261. 262. 263. 264. 265. 266. 267. 268. 269. 270. 271. 272. 273.
A (m3, kmol, s-l)
Reactions
No. p-C,H, + C,H p-C,H, + a-C,H, p-&H, + M a-C,H, + H a-C,H, + 0 n-C,H, + 0, a-C3H, + CH, a-CJH, + C,H, a-C,HS + C,H, 2u-C,HS s-C,H, + H s-C,H, + 0 s-C,H, + 0, s-C,H, + CH, s-C3H, + C,H, s-C,H, + C,H, t-C,H, + H t-C,H, + 0 t-C,H, + O2 K,H, + CH, r-C,H, + C,H, K,H, + C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H,
+ + + + + + + + + + + + + + +
GH, + C,H, n-C,H, + H n-C,H, + 0, n-&H, C,H, + H i-C,H, + H i-C,H, + 0, i-C,H, i-C,H,
C,H, C,H, C,H,
+ H + H + 0
+
C2H2
C3H3
+
C3Fi
C,H, + H + M a-C3H, + H, C,H, + CH,O C,H, + CH,O + OH a-C,H, + CH, a-C,H, + C,H, a-C3H, + C,H, a+H, + C,H, a-C$H, + H, CH,CO + CH, CH, + CHO + CHO a-C3H, + CH, a-C3H, + C,H, a-C3H, + C,H, a-C,H, + H, CHCO+CH,+H CH, + CO + CH,O a-C,H, + CH, a-C3H, + C,H, a-C,H, + C,H, C,H, + CH, a-C,H, + H s-&H, + H t-C,H, + H a-C,H, + Hz s-&H5 + H, t-C,H, + H, C,H, + CHO C,H, + CH,O 2CH, + CO a-C,H, + H,O s-C,HS + H,O t-C,H, + H,O a-C,H, + HO, s-C,H, + HO, t-C,H, + HO, a-C,H5 + CH, s-C,H, + CH, t-C,H, + CH, a-C3HS + C,H,
H H H 0 0 0 OH OH OH 02 02 02 CH, CH, CH,
C3W3
C3H3
C3H,
C,H, + HO, C,H, + CH, n-C3H, C3%
-
C,H, C,H, C,H, C,H,
+ + + +
HO, CH, H CH35
0 e 0
n-C,H7 + H, X,H, + H, n-C,H, + OH
k, = k, =
l.OOOE + 2.0OOE + 4.7OOE + 3.333E + 1.807E + 1.700E + 3.000E + 2.410E + 9.640E + 8.43OE + 3.333E + 1.807E + 4.335E + l.OOOE + l.OOOE + l.OOOE + 3.333E + 1.807E + 4.335E + l.OOOE + l.OOOE + l.OOOE + l.lOOE + 4.500E + 7.590E + 1.450E + 1.728E + 4.65OE + 8.036E + 5.219E + 3.484E + 6.960E + 3.120E + l.llOE + 2.138E + 1.950E + 2.0OOE + 2.000E + 2.216E 8.420E 1.351E 2.220E 2.000E + l.OOOE + 3.0OOE + 7.230E + 2.000E + l.OOOE + 2.000E + 6.300E + l.lOOE + 7.828E + 1.3OOE + l.OOOE + 3.000E +
10 09 15 09 11 09 09 09 08 07 09 11 08 08 08 08 09 11 08 08 08 08 21 14 14 15 02 02 02 04 04 04 03 03 03 09 10 10 03 04 03 03 10 09 14 09 10 09 10 13 17 15 11 11 10
(Continued) Ref.
n 0.00 0.00 0.00 0.00 0.00 0.00 - 0.32 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 1.20 0.00 0.00 0.00 2.50 2.50 2.50 1.57 1.57 1.57 2.00 2.00 2.00 0.00 0.00 0.00 3.50 3.50 3.50 3.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 32.22 334.72 0.0) 0.00 0.00 - 0.55 0.00 - 0.55 - 1.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 408.84 371.96 423.84 410.28 10.42 40.98 51.39 - 2.63 - 2.63 - 2.63 - 1.25 6.07 11.62 163.18 199.16 184.10 23.74 48.77 53.76 27.77 0.00 20.90 138.10 12.14 0.00 12.50 123.43 154.39 353.10 271.87 40.60 34.90 24.10
WI 1151 1821 D51 [841 est.
[511 [511 [511 [511 1151 [151 est., 1151
WI [I51 [151 [I51 [I51 est., [15]
[I51 D51 [I51 [511 [151 1151 [151 [511 [511 [511 D51 D51 est., [15]
[511 [511 [511 D51 1151 D51 [511 [511 [511 [511 [I61 M
[161 [511 [161
[161 [I71 [I71 B51
[I61 [I61 [161
138
K. M. LEUNG AND R. P. LINDSTEDT TABLE 1 Reaction Mechanism Rate Coefficients in the Form ki = AT”exp( -E/RT) A (m3, kmol, s- ’)
Reactions
No.
274. 27.5. 276. 277. 278. 279. 280. 281. 282. 283. 284. 285. 286. 287. 288. 289. 290. 291. 292. 293. 294. 295. 296. 297. 298. 299. 300. 301. 302. 303.
C,Hs C,Hs C,Hs C,H, C,Hs C,H,
+ + + + + +
CzH,
+ CzHz
C2H2
+
304. 305. 306. 307.
n-C,H, n-C,H3 I-C,H, I-C,H,
308. 309. 310. 311. 312. 313. 314. 315. 316. 317.
i-C,H, I-C,H, i-C,H, i-C,H,
C,H, C,H, + H C,H, + 0 C,H, + OH C,H, + C,H (1,2)-C,H,
CH,CO + C,H C,H, + H,O CH,CO + C,HO i-&H, + H n-C,H3 + H, a-C3H, + CO n-C,H, + H,O i-C,H, + C,H, C,H, + H*
318. 319. 320. 321.
(1,2&H, (1,2)-C,H, (1,2&H, (1,3)-C,H,
GH, + H2 C,H, + H,O (1,3)-C,H, C,H, + H*
322. 323. 324.
(1,3)&H, (1,3)-C,H, (1,3)-C,H,
0 OH OH CH, CH, C,H, CzHz
i-C,H, n-C,H, i-C,H, n-C,H, i-C,H, r&H3 i-C,H, GH2
c-C,H, +3CH2 C,H, + CH C,H, + CH C,H, +3CH2 C,H + C2H2 C,H + C,Hz C,H + C,H2 2C,H C,H + H, C,H + C,H2 C,H + C,H2 GH2
+ OH + H,O + H,O + CH, + CH, + H + H +
H2
i-C,H, + H n-C,H, + H I-C,H3 + H C,H4 + H C,H2 + H C,H2 + H C,H2 + H C,H + H C,H, + H C,H, + H C,H, + H C,H + H
GH,
+
C,Hz
C,H2
+
C4H2
+
C,Hz
C,H2
+ 2H
C2H2
+
GH2
C&2
+
C2H2
+
C,H2
C,H,
+ 2H
C2H2
+
C,H2
C,H2
+
C2H2
+
C&2
C,H2 CO + C,H,O C,H, C,H,
+ 2H C,H, + H + 2C0 + H + H* k, = k, =
C,H2
+
C,H2 r&H, C,H,!
+ H,O
C,H2
+
C,H, + 0 C,H, + OH C,H,O + OH n-C,H, + H + OH
+ + + +
H 0 OH O2
+ H + OH
+ H + OH
H2
H2
H2
H2
+ H*
k, = k, =
H2
C2H3
+
C2H2
C,H,
+
H2
C,H,
+ H,O
k, = k, =
k, = k, =
2.600E + 5.750E + 4.786E + 9.OOOE1.510E l.OOOE + 2.000E + 1.513E + 3.000E + 7.000E + 7.OOOE+ 4.000E + 1.200E + 1.200E + 1.200E + l.OOOE + 4.074E + 1.200E + 1.200E + 7.800E + 1.513E + 1.513E + 1.513E + 1.513E + 1.513E + 1.513E + 2.800E + 6.680E + l.OOOE + l.OOOE + l.OOOE + 5.000E + 3.000E + 1.500E + 1.000E + 2.000E + 5.000E + 2.000E + 3.0OOE + l.OOOE + 8.630E + 2.OOOE+ 3.000E + l.OOOE + 3.980E + l.OOOE + 2.OOOE+ l.OOOE + 2.OOOE+ 1.500E + l.OOOE + l.OOOE + 2.000E + l.OOOE + 2.000E +
10 05 05 04 03 09 09 10 10 10 10 10 11 11 11 11 02 11 11 14 10 11 10 11 10 11 10 09 12 14 11 10 10 13 14 12 10 10 10 09 09 04 10 04 10 14 12 11 04 13 14 11 12 11 04
(Continued) E
n
0.00 1.40 1.40 3.65 3.46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 2.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 2.00
&J/m00 18.70 3.56 3.56 29.93 22.93 276.14 268.00 178.66 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.84 0.00 0.00 502.08 178.66 234.30 178.66 234.30 178.66 234.30 7.23 - 1.72 0.00 150.62 125.52 0.00 0.00 283.26 230.12 200.83 0.00 0.00 0.00 0.00 246.86 25.17 7.57 12.60 0.00 209.20 175.73 0.00 4.18 283.26 154.81 125.52 192.46 0.00 4.18
Ref.
[I61 [861 [861 [501 [501 [871 [SSI 1531 [361 [361 [361 [361 1531 1531 [531 [531 1531 [531 1531 [891 [531 [531 t531 1531 1531 [531 [901 [911 [921 t361 est., 1361 est., 1361 est., [541 [361 [361 [361 [361 [361 [891 est., [361 [901 est., t361 [931 est., [361 est. est., [361 t541 [361 est., t941 est. [361
KINETIC MODELING
OF ALKANE
139
DIFFUSION FLAMES TABLE 1
Reaction Mechanism Rate Coefficients in the Form ki = AT”exp( -E/RT)
325. 326.
i-C,H, i-C,H,
327. 328. 329. 330. 331. 332. 333. 334. 335. 336. 337. 338. 339. 340. 341. 342. 343. 344. 345. 346. 347. 348. 349. 350. 351. 352. 353. 354. 355. 356. 357. 358. 359. 360. 361. 362. 363. 364. 365. 366. 367. 368. 369. 370. 371. 372. 373. 374.
i-C,H, + H i-C,H, + OH (1,2)-C,H, (1,2&H, (1,2)-C,H, + (1,2)-C,H, + (1,2)-C,H, + (1,2)-C,H, +
376. 377. 378.
A (m”, kmol, s-l)
Reactions
No.
e w
C,H, + H,O C,H, -t CH, i-C,H, + H H H OH CH,
C2H3
+
C3H3
+
C3H3
C,H,
+
C&3
C,H, (1,3&H, (1,3)-C,H, (1,3&H, (1,3)-C,H, (1,3&H, (1,5)-C,H, (1,5)-C,H, (1,3)-C,H, (1,5)-C,H,
+ H + 0 + OH
+ H + 0 + OH
C,H,
C,H,O (1,3)-C,H, + (1,3)-C,H, + (1,3)-C,H, + (1,3)-C,H, + (1,3)-C,H, + c-C,H, (1,3)-C,H, (1,2)-C,H, CO + C,H, I-C,H, + H (1,2&H, (1,5)-C,H, (1,2,4,5&H, l-&H, (1,3)-C,H, l-C,H, I-C,H,
C,H, + a-C3H, n-C,H, + C,H, C,H, + C,H3 (1,3)-C,H, + C,H, C,H, + H C,H; + 0 C,H, + OH I-C,H, + H I-C,H, + 0 I-C,H, + OH
+
(1,2)-C,H, + (1,2)-C,H, + (1,2)-C,H, + (1,3&H, i-C,H, + H (1,3)-C,H, + C?H, + C,H,
C,H,O C,H, + C,H, C3H3
k, = k, =
C,H, + H,
2C,H, (1,3&H, (1,3)-C,H, + H (1,3)-C,H, + H (1,3)-C,H, + 0 (1,3)-C,H, + OH (1,3)&H, + 0, (1,3)-C,H, + C,H, (1,3)-C,H, + CH, (1,3&H, + C,H, ‘CH2 + p-C,H, c-C,H, c-C,H,
C3H3
(1,3)-C4H, C,H, + H*
-
C&
0 0
C,H,+OH C,H, +H,O
a 0 0 0 0 0 w = 0 0 Q 0 0 0 =
GH, + Hz C,H,+OH C,H, +H,O I-C,H, I-C,H, + H I-C,H, + H, I-C,H, + OH I-C,H, + H,O (1,5)-C,H, I-C,H, + H I-C,H, + H, I-C,H, + OH f-&H, + H,O (1,3&H, C,H, +H C,H,+H, C,H, + OH C,H, + H,O C,H,O + OH
C,H, C,H, C,H, C,H, C,H,
+ H + 0 + OH
t, 0 t)
C,H,
+ HO>
e
+ H2
H, H,O CH,
H,
H,O HO, C2H, CH, a-C3H,
1.500E + l.OOOE + 2.000E + l.OOOE + 2.0OOE + l.OOOE + 4.2OOE + 4.000E + l.OOOE + 1.620E + 7.000E + 2.0OOE + 4.200E + 6.3OOE + 5.0OOE + 6.020E + 8.430E + 4.000E + 6.310E + 7.000E + l.OOOE + 1.800E + 3.OOOE+ 3.000E + 1.090E + l.OOOE + l.OOOE + l.OOOE + l.OOOE + 3.000E + 4.120E + 3.000E + 1.724E + l.OOOE + 2.0OOE + 2.000E + l.OOOE + 2.000E + 2.000E + l.OOOE + 2.500E + l.OOOE + 2.000E + 2.000E + l.OOOE + 6.0OOE + l.OOOE + 2.000E + 2.000E + 4.000E + 3.000E + 1.5OOE + 2.000E + 2.0OOE + 5.000E +
13 14 12 11 04 12 15 08 11 10 10 10 15 07 08 05 09 10 10 10 10 11 13 13 16 10 10 10 10 08 03 08 03 11 10 10 11 10 10 12 58 11 10 10 11 11 11 10 10 13 13 11 10 10 10
(Continued) E
II 0.00 0.00 0.00 1.00 2.00 0.00 0.00 0.00 0.0) 0.00 0.00 0.00 0.00 0.70 0.00 1.45 0.0) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.65 0.00 1.79 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 13.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
W/mol) 283.26 209.20 175.73 0.00 4.18 248.95 387.10 0.00 60.67 0.00 0.00 0.00 414.21 25.10 0.00 3.59 - 3.66 242.00 60.68 1.20 75.31 0.00 177.00 183.00 305.43 0.00 0.00 0.00 0.0) 12.55 10.46 12.55 9.38 0.00 0.00 0.00 0.00 0.00 0.00 138.07 208.36 0.00 0.00 0.00 0.00 188.00 0.00 0.00 0.00 305.12 372.38 0.00 0.00 0.00 4.18
Ref. est., [54] [361 est. est., 1361 [541 est., 1941 [541 [541 [951 est., [541 1871 est., 1941 [961 1521 [971 [981 est. 1521 est., 1541 est., [54] est., 1991 DO01 DO01 DO11 est. est., 1341 est., [34] est., 1341 [331 [331 1331 1331 est. est. est. est. est. est. est. [lo21 est. est. est. est. est. est. est. est. 1471 est. est. est. est. [191
K. M. LEUNG AND R. P. LINDSTEDT TABLE 1 Reaction Mechanism Rate Coefficients in the Form 5 = AT”exp(-E/RT)
319. 380. 381. 382. 383. 384. 385. 386. 387. 388. 389. 390. 391. 392. 393. 394. 395. 396. 397. 398. 399. 400. 401. 402. 403. 404. 405. 406. 407. 408. 409. 410. 411. 412. 413. 414. 415. 416. 417. 418. 419. 420. 421. 422. 423. 424. 425. 426. 427. 428. 429. 430. 431. 432. 433.
A (m3, kmol, s- ‘)
Reactions
No.
C,H,O + 0 K&4.5)-C,H, (M&H, Fulvene Fulvene Fulvene (1,3&H, (1,3&H,
Cd& + 02
(IS&H, (1,2,4,5)-C& (1,2/WC&I, WC,H, (1,2&H, (1,2)-C,H, Fulvene (1,3)-C,H, Fulvene (l,S)-C,H, U,2)-C,H, (1,5&H, (l,S)-C,H, (l,S)-C,H, (1,2)-C,H, (1,2&H, (1,2)-C,H, (1,3)-C,H, (1,3&H, (1,3)-C,H, C,H, C,H, C,H, C,H, C,H, C,H,
+ + + + +
+ + + + + + + + +
H 0 OH H 0 OH H 0 OH
H 0 0 OH OH
C,H, + 02 C,H, + CH, C,H,O + H C,H,OH -t C,H, C,H,OH + H C,H,OH + 0 C,H,OH + OH C,H,O C,H, + H Cd7
a-C,HS C,H, + C,H, + C,H, + C,H, + C,H, tC,H, + C,H, + C,H, + C,H, +
+ C,H, H 0 0 OH HO, H 0 OH HO,
C,H,
+
02
C,H,
+
02
VW C&OH C&W C,H, C,H,
C,H,
+ C,H,
C,H, CA (1,5)-C,H5 (1,5)-C,H, (1,5)-C,H, (1,5&H, (l,S)-C,H, (1,5&H, (l,S)-C,H, (l,S)-C,H, (1,3)-C,H, (1,3&H, (1,3&H, C,H, + H CA + C,H,OH C,H, + C,H, + C,H,OH C,H, + C,H, + C,H,OH C,H,O C,H,O C,H,O C,H,O C,H, +
+ + + + + + + + + + +
H H Hz OH H,O H, HO H,O H, OH H,O
H2
OH H,O + H HO, CH, + C,H, + H, + OH + Hz0 CO
GH7
I-C,H, C,H, + H C,H, (1,3)-C,H,
+ CO
CsH,O C,H,OH + H C,H,O + OH C,H, + Hz C,H, + OH C,H, + Hz0 C,H, + H,O, C,H, + HO, C,H,O + OH (1,3)-C,H, + CO C,H,O -t H C,H, + C,H, + CO I-C,H, l-C,H, I-CsH,
2.090E + 5.400E + 5.000E + S.OOOE+ 4.260E + S.OOOE+ l.OOOE + l.OOOE + 5.000E + 7.580E + 1.400E + 7.OOOE+ l.OOOE + 2.000E + 2.000E + l.OOOE + 2.000E + 2.000E + l.OOOE + 2.000E + 2.000E + 4.570E + 2.SlOE + 2.400E + 2.000E + 1.630E + 1.320E + 6.300E + 4.365E 2.530E + 2.67OE + 1.150E + 2.810E + 6.000E + 4.500E + 4.040E + 3.020E + 4.000E + l.OOOE + l.OOOE + l.OOOE + 3.000E + 3.OOOE+ 2.190E + 1.810E + 3.430E + 1.990E + 2.000E + l.OOOE + 2.510E + 2.100E + l.OOOE + l.OOOE + l.OOOE + l.OOOE +
09 11 11 11 13 11 12 13 11 13 15 14 11 10 10 11 10 10 11 10 10 13 11 10 10 OS 10 10 07 11 11 11 10 09 11 10 14 11 11 11 10 10 10 05 10 06 09 10 10 11 13 15 14 14 06
(Continued)
n
E (kJ/mol)
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.42 0.00 0.00 5.00 0.00 0.00 0.0) 0.00 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 1.77 0.00 1.18 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
31.25 149.66 92.30 132.40 206.00 144.00 224.00 342.00 200.00 309.00 326.60 326.60 0.00 0.00 0.00 0.00 0.00 0.00 46.00 0.00 12.60 372.38 66.94 19.54 61.52 6.07 44.31 251.04 51.46 0.00 105.55 51.88 30.76 0.00 183.74 18.04 209.20 104.14 0.00 0.00 0.00 0.00 0.00 12.55 12.89 - 1.87 48.78 104.60 86.66 183.68 200.83 326.35 235.00 334.00 0.00
Ref. 1191 1351 est., [371 est., [37] est., est., est., est.,
[371 [37] [37] [37] [371 [371 est. est. est. est. est. est. est. est. est. est. est.
11031 DO41 DO51 t1051 [471 1471
[201 hod 1471 [lo71 DO1 r201
[201
est., [lo81 1471 DO91 [Sll DO1 PO1 [191 DO1 DOI
[201 WI t201 t201 [201 [191 BOI DOI
1201 est. est. est., [341
KINETIC
MODELING
OF ALKANE
DIFFUSION
141
FLAMES
TABLE 1 Reaction
Mechanism
No.
Rate Coefficients
in the Form
Reactions
434. 435. 436. 437. 438. 439.
I-C,H, I-C,H, I-C,H, I-C,H, K,H, I-C,H,
+ + + + + +
H H 0 OH H 0
= 0 = e 0 0
440. 441. 442. 443. 444. 445. 446. 447. 448. 449. 450. 451.
I-C,H, + OH l-C,H, + Oz I-C,H, + H I-C,H, + OH I-C,H, + H I-C,H, + H I-C,H, + 0 I-C,H, + OH I-C,H? + OH C,H, +‘CH, C,H, +3CH, C,H,+CH
0 0 0 0 0 0 0 0 0 0 0 0
k, = AT”exp(
(m3,
I-C,H, I-C,H, C,H,O I-C,H, I-C,H,
+ Hz + C,H, + H + H,O + H,
i-C,H, + CO I-C,H, + H,O C2H3 + C,HO I-C,H, + H, I-C,H, + H,O I-C,H, I-C,H, + H, i-C,H, + CO I-C,Hz + H,O C,H, + CHO l-C,H, + H I-C,H, + H I-C,H, + H
+ CHO
-E/RT) (Continued)
A kmol, s- ‘)
n
E W/m00
l.OOOE+ l.OOOE+ 2.000E + l.OOOE+ l.OOOE+
10 09 10 10 10
0.00 0.00 0.00 0.00 0.00
0.00 0.00 126.00 0.00 0.00
l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE 3.000E 1.3OOE l.OOOE
11 10 09 10 10 10 10 11 10 09 10 10 11
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 155.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 18.10 0.00
+ + + + + + + + + + + + +
Ref. est. est. est. est. est. est. est. est. est. est. est. est. est. est. est. [361
[361 [361
** All third-body
collision efficiencies are equal to 1 unless otherwise stated. * Reaction in Lindemann form. a Enhanced Collision Efficiencies: H,O = 6.5:0, = 0.3:CO = 0.7:C02 = 1.5:N, = 0.4 h Enhanced Collision Efficiencies: H,O = 12.0:H, = 2.5:CO = 1.9:C02 = 3.8 ’ Enhanced Collision Efficiencies: H,O = O.O:H, = O.O:CO, = 0.0 d Enhanced Collision Efficiencies: H,O = 4.0:N, = 0.4:CO = 0.4:CO, = 0.4:CH, = 0.7:C,H, = 5.0:C,H, = 2.2 e Enhanced Collision Efficiencies: H,O = 5.7:0, = 1.9:CO = 1.9:C02 = 3.3:H, = l.l:N, = 1.6 I Enhanced Collision Efficiencies: H,O = 5.O:CO = 2.O:CO, = 3.0:H, = 2.0 ’F, = 0.38 exp( - T/23) + 0.63 exp( - T/ 1180). ‘F, = 0.31 exp( - T/90) + 0.69 exp( - T/2210). ‘F, = 0.4761 exp(-16182/T) + exp( - T/3371). ’ log(k/k,) = -0.349 + 1.349E - 3*T - 1.408E - 06*T* + 2.132E - lO*T’. 5 F, = 0.76 exp( - T/38) + 0.24 exp( - T/1946).
present study with a sensitivity fined as
coefficient
de-
= 1.4:CzH,
of these species towards the rate of reactions in the mechanism and the uncertainty in rate constants of these reactions is also assessed.
X = In(Y,/Y,)/ln(S). 4.1. Reaction Paths for C, Species In the above expression Y0 is the computed peak concentration of a particular species using the rate constants as shown in Table 1. Similarly, Y, is the peak concentration of the same species computed at the same condition but with the rate coefficient of a certain reaction k increased or decreased by a factor of 5. The following paragraphs focus on the main formation and consumption paths for the intermediate species of interest in propane-air diffusion flames. The sensitivity of predictions
Computational results show that propane consumption mainly occurs through thermal decomposition and reactions with H radicals. Reactions with 0 radicals are insignificant due to low concentrations in the fuel-rich pyrolysis region. Abstraction by CH, and OH radicals consumes only around 15% of the fuel at a strain rate of 600 s- ’ and less than 7% at strain rate of 50 s- ’. The most important fuel breakdown reactions can therefore be summa-
142
K. M. LEUNG AND R. P. LINDSTEDT TABLE II Thermodynamic Data for C, Ah; W/mole)
Species H OH 0
217.999 39.343 249.170 12.552 0.00 - 241.826 - 136.310 0.00 - 110.530 -393.510 0.00 597.360 42.00 424.732 390.417 - 108.580 146.858 16.318 - 8.900 - 200.940 - 74.600 566.932 161.084 227.400 -51.871 93.186 299.740 52.294 118.658 - 83.863 684.084 477.000 346.000 190.920 185.431 276.991 112.968 161.921 270.704 255.224 20.413 100.500 93.286 - 103.854
HO, HZ Hz0 H@, 0, co co2 N2
CH CHO ‘CH, ‘CH, CH,O CH, CH,O CH,OH CH,OH CH, C2H
CHCO C2H2
CHrCO CHCOH C2H, C2H4 C2H5 C2H.s C3H C3H2 WI3
a-C,H, p-C3H4
b-C,H, C,H,O a-C,H, s-C,H, t-C,H, C3H6 nC,H,
i-C,H, C3H,
So (J/mole) 114.718 183.737 161.060 229.106 130.679 188.829 234.527 205.144 197.657 213.787 191.607 183.037 224.345 166.716 194.899 218.764 193.965 229.390 243.919 239.810 186.371 213.304 246.674 200.917 241.923 249.142 233.953 219.180 247.119 229.080 226.742 235.308 253.300 243.431 248.298 243.616 301.917 258.738 275.474 277.608 266.538 289.465 289.341 270.182
rized as
(270)
Reference
HlOl
11101 11101 HlOl [1101 HlOl HlOl HlOl ill01 DlOl [1101 [1101 11101
[1101 MO1 t1101 HlOl [1101 [1101 t1101 [1101 [531,[1101 DlOl HlOl HlOl [1101 11101 [1101 DlOl [1101 DlOl [651 t1101 [1101 [1101 D101 est., [112] est., [36] est., [361 est., [36] [1101 [1101 [1101 11101
C, species
Species C4H C4H2
n-C,H, I-C,H, C4H4 W)-C,H,
(1,3)-C,H, I’-C,H, (1,2)-C,H, (1,3)-C,H, c-C,H, C4H60 C6H2 WI2 C6H3
I-C,H, c-C,H, C6H5 C6H50 C6H6
C,H,OH C,H,
I-C,H, (1,5)-C,H, (1,2)-C,H, (1,31-C,H, (1,2,4,51-C,H, CM)-C,H, fulvene (1,3)-C,H, (1,5)-C,H, C5H6 C5H5 C5H50 C5H40
C,H,OH I-C,H, I-C,H, I-C,H, I-C,H, C5H2
Ah; (kJ/mole)
803.328 464.424 523.380 476.976 280.328 302.184 345.157 330.157 164.593 108.983 243.509 - 103.763 700.820 934.287 663.164 514.632 481.160 328.456 47.716 82.811 - 96.375 200.589 389.150 414.300 410.100 334.550 394.969 334.400 218.500 542.664 588.270 134.300 266.102 103.300 17.363 87.446 249.366 374.468 435.136 566.513 691.615
So (J/mole)
254.638 255.977 272.922 273,550 278.654 289.212 288.540 283.217 291.618 278.191 289.951 333.046 299.190 347.690 319.323 321.331 291.093 288.337 307.816 269.065 314.864 305.835 353.270 340.300 339.197 332.800 328.900 299.993 299.993 332.335 339.197 274.154 279.485 307.805 280.872 310.016 320.494 318.109 293.298 295.139 266.521
Reference
t1101,D111 t531,DlOl [1091,[llll [531,ml1 1531, D111 [I101 DlOl t1101 DlOl [1101 [lOOI est., 11121 [1101 [1101 t1131 [W [1101 DlOl DlOl [1101 t1101 DlOl [1101 est., [37] est., [371 est., 1371 est., [37] est., [371 est., [371 W31 [361,[1101 [1101 [1101 um 1201 11101 est., [112] [361,[I121 est., [1121 11131 ill31
with secondary channels provided by
C,H, = C,H,
(271)
C,H, + H = n-C,H,
(272)
C,H,
+ CH,,
(275)
C,H, + OH = n - C,H, + H,O,
(276)
C,H, + OH = I’-C,H, + H,O,
+ H,,
(277)
C,H, + CH, = n-C,H,
+ H = I’-C,H, + H,,
(278)
C,H, + CH, = I’-C,H, + CH,.
+ CH,,
KINETIC
MODELING
OF ALKANE
DIFFUSION
lc shows that the computed ethylene concentrations are also sensitive to the rate of reactions 270-272 and 277. The major product of ethylene consumption in diffusion flames is acetylene and a similar sensitivity to the above, reactions in the computed acetylene concentrations can be observed in Fig. Id. Ethane and methane are formed mainly through the recombination of methyl radicals in the fuel-rich region. The methyl radical is a primary pyrolysis product of propane and n-propyl radicals and the predictions for ethane and methane concentration are sensitive to reactions 270-272 as shown in Figs. lb and le. Figure le also shows that the predicted methane concentration is sensitive to the rate constants of reaction 277 and 278 which produce methane directly from propane through H atom abstraction. Rate constants of the propane consumption reactions reported in the literature [16-18, 50, 1181 are somewhat scattered. There are differences not only in reaction rates for hightemperature conditions but also in their rela-
The formation of C,H, and C,H, and the regeneration of H and CH, radicals are the result of the alkyl radical decomposition reactions, (171)
C,H,
= C,H,
+ H,
(264)
n-C,H,
= C,H,
+ CH,,
(269)
X,H,
= C,H,
+ H.
143
FLAMES
Analysis shows that the decomposition reactions are not the rate-limiting steps in the present mechanism. Therefore the product distribution of intermediate species is dependent on the relative formation rate of the n- and iso-propyl radicals. The sensitivity analysis, see Fig. la, shows that the computed peak concentration of propene is sensitive to the rate constants of reactions 272 and 278 which produce the iso-propyl radical and to the competitive reaction 271-forming the n-propyl radical. Ethylene is mainly produced through the decomposition of ethyl and n-propyl radicals. Figure
Logarithmic Response Sensitivity In(Y,r/,)/in(5.0)
-0.5
(a) I
R03 R84 Fill9 RI65 RI91 R192 R242 R243 R246 R247 R248 R264 R265 R270 R271 R.272 R.275 R276 R277 R270
0-N 0.5
0.0
I ; I 6 4 ; 9: - s; b I
-0.4
1
-
-
,
R03 R&I R85 R119 R165 Al73 R193 R242 R246 R247 R248 R264 R265 R270 R271 R272 R275 A276 R277 R278
0.0 I
% 0 -w ( ) 9 ; + P 4
(4
(c) 0.4 1
-0.2
0.0
0.2
( (
-
!
-
; 4 8
-
i
-
;
-
-
R83 R84 Rll8 Rl19 R142 RI43 R165 .-R167 R173 R242 A246 R264 R265 -
-
R270 y;
& - c?
R275 R276 R277 R278
-
-
-
-
f
-
-0.2 R83 R118 Rl19 R142 R143 R146 R165 R167 R173 Rl91 Rl92 R193 R194 R242 R246 R247 R248 R270 R271 R272
0.0 I
; / ; - & P $ ; ; q f I
(e) 0.2
-
-
-
-0.2 R83 R04 R85 Rll8 R119 R142 R143 R165 R173 R193 R242 R246 R265 R270 R271 R272 R275 R276 R277 R278
-
0.0 , 9
0.2
s
-
; 63
-
;
-
4
-
]I
-
(
-
I
Fig. 1. Logarithmic response sensitivities computed using the detailed mechanism for the maximum concentrations of (a) C,H,, (b) C,H,, (c) C,H,, (d) C,H, and (e) CH, in counterflow propane-air diffusionflames. The light bare represent the sensitivities for the rate coefficients increased by a factor of 5. The dark bars represent the sensitivities for the rate coefficients decreased by a factor of 5.
144 tive importance for propane consumption. The rate constant for the thermal decomposition reaction of propane has received a number of studies [118-1231. Among the rate constants reported in the literature [16-l& 50, 1181 there is still disagreement around a factor of ten at a temperature of 1600 K which is the temperature of the region in the flames where the propane consumption rate is highest. The major difficulties in the evaluation of the rate expression for this reaction are caused by its pressure dependence and the influence of secondary chain decomposition reactions. Comparison of computed intermediate species profiles with measurements indicates that a comparatively slow rate for reaction (270) is favoured to reduce excessive levels of intermediate species. Thus the pressure dependent rate of Baulch et al. [851 was adopted for reaction 270. This results in a rate 14 times slower at 1600 K compared with the highpressure limit suggested by Tsang t.501. As discussed above the relative formation rate of n-propyl and iso-propyl radicals also affects the distribution of ethylene and propene in propane-air diffusion flames. However, the ratio between the rates of reactions 271 and 272 reported in the literature [16-l& 50, 1181 varies from 0.44 [18] to 3 [17, 1181 at 1600 K. Computational results indicate that a ratio of 1.8 between the rates of reactions 271 and 272 does reproduce the measured distribution of ethylene and propene. The suggestion of Warnatz [16] was adopted for reactions 271 and 272 but with the rate constants of reaction 272 decreased by a factor of 2 to give better agreement with propene profiles. Rate constants suggested by Tsang [50] for the abstraction reactions 277 and 278 are slower by a factor of 3 compared to other suggestions [17, 18, 1181 but were used in the present mechanism to reduce overpredictions of methane concentrations. Among the various propene consumption reactions considered in the present mechanism, it was found that reactions with the H radical are the dominant consumption paths. Reactions with CH, and OH radicals account for less than 15% of propene consumption. Propene is either consumed by H-atom abstraction reaction to form isomers of the C,H,
K. M. LEUNG
AND R. P. LINDSTEDT
radical or addition reaction to produce n-propyl radical. (246)
C,H,
+ H = a-C,H,
+ H,,
(247)
C,H,
+ H = s-C,H,
+ H,,
(248)
C,H,
+ H = t-C,H,
+ H,,
(265)
C,H,
+ H = n-C,H,.
The C,H, isomers considerd in the present mechanism are ally1 (CH,CHCH,), l-methyl vinyl (CH ,CCH,) and 2-methyl vinyl (CH,CHCH) radicals. They are coded as aC,H,, t-C,H,, and s-C,H, respectively. Reaction 246, which produces the ally1 radical, is the major abstraction reaction. Since the npropyl radical quickly decomposes into C,H, and CH, via reaction (2641, the balance between abstraction and addition reactions is important for the relative balance of the C, and C, chains in the consumption of propene. Significant sensitivity of the computed propene concentrations to the rates of these reactions can be observed in Fig. la. Computational result with rate constant listed in Table 1 indicate that about 90% of propene consumption goes through the C, chain. The effect of two thermal decomposition reactions of propene was also investigated. (243)
C,H,
= a-C,H,
(242)
C,H,
= C,H,
-t H, + CH,.
A wide range of rate constants for these reactions has been reported in the literature [51] and suggestions differ by up to two orders of magnitude, predominantly due to the pressure dependence. Previous modeling work [16-181 has used the high pressure limit rate expressions for these reactions. However, Rao and Skinner [124] have suggested that these reactions are in the intermediate fall-off region under combustion conditions. In the present mechanism the rate expressions proposed by Tsang [51], which agree very well with the results of Rao and Skinner 11241, have been used. Computational results show that reactions 242 and 243 only account for a small fraction of propene consumption in propaneair diffusion flames.
KINETIC
MODELING
OF ALKANE
DIFFUSION
Thermal decomposition reactions constitute the dominant consumption paths for the C,H, radicals. Ally1 and 2-methyl-vinyl radicals mainly decompose to form C,H, and CH, via the reverse of reaction 193 and 194. The decomposition of the l-methyl vinyl radical has been assumed to yield both allene and propyne. (-193)
a-C,HS = C,H,
+ CH,,
(-194)
s-C,HS = C,H,
+ CH,,
(-195)
t-C,H,
= a-C,H,
+ H,
(-196)
a-C,HS = a-C,H,
+ H,
c-209)
t-C,H,
=p-C,H,
+ H,
C-210)
s-C,H,
=p-C,H,
+ H.
Due to the fast decomposition of a-C,H, and s-C,H, to the &-chain, only 30% of C,H, radical consumption produces C,H, isomers. However, this is compensated by the fast insertion reaction of ‘CH, into C,H,. Here this insertion reaction has been postulated to produce the propargyl radical and cyclopropene as discussed below. (53)
‘CH, + C,H,
= C,H,
+ H,
(54)
‘CH, + C,H,
= c-C,H,,
(207)
c-&H,
= a-C3H,,
(208)
c-&H,
= p-C,H,.
Allene and propyne are mainly consumed by H, OH, and CH, abstraction reactions to form the propargyl radical. (197) (200) (202) (211) (216) (219)
a-C,H, a-C,H, a-C,H, p-C,H, p-C,H, p-C,H,
+ H = C,H, + OH = C,H,
+ H,, + H,O,
+ CH, = C3H, + CH,, + H = C,H,
+ H,,
+ OH = C,H,
+ H,O,
+ CH, = C,H,
+ CH,.
Propargyl is subsequently consumed through reactions with H, 0, and OH radicals to form cycle-propenylidene (c-C,H,) and propynal (C,H,O). Computational results show that these consumption channels proceed with comparable rates. Cyclopropenylidene is mainly
145
FLAMES
consumed through reaction with the OH radical, whereas propynal decomposes quickly to form acetylene. (183)
C,H,
+ H = c-C,H,
+ H,,
(184)
C,H,
+ 0 = C,H,O
+ H,
+ OH = C,H,O
+ H,,
(185)
C,H,
(1801 c-C,H,
+ OH = C2HZ + CO + H, C,H,O
(188)
= C,H,
+ CO.
There are considerable uncertainties in many of the above reactions due to the lack of direct measurements of rate constants and product channels. While the propargyl chemistry is too minor to have any significant effect on the overall flame structure, it is of paramount importance to benzene formation as discussed below. 4.2. Reaction
Paths for C,H,
and C,H,
The reaction paths in the C, chain are better established than the C, chemistry discussed above. However, as ethylene and acetylene are major products of propane combustion it is desirable to quantify the major uncertainties. Ethylene is mainly consumed by H radical attack to produce vinyl radical. Reactions with 0 and OH radicals account only for a fraction of ethylene consumption at low strain rate conditions. However, the reactions with 0 and OH radicals may be responsible for up to 30% of ethylene consumption at high strain rates in the counterflow geometry. At the high temperatures of the present study the vinyl radical decomposes quickly into acetylene. (165) (-158)
C,H,
+ H = C,H, C,H,
= C,H,
+ H,, + H.
The rate of reaction 165 actually determines the ratio between computed concentrations of ethylene and acetylene. High sensitivity can be observed in the prediction of ethylene and acetylene concentrations to the rate of this reaction as shown in Figs. lc and Id, respectively. Literature data for reaction 165 has an uncertainty factor of about 3. However, variation in the rate of reaction 165 by this amount can result in significant change in the balance
146
K. M. LEUNG
between the computed concentrations of ethylene and acetylene. The selection of a rate constant for reaction 165 is also dependent on the formation rate of ethylene from alkyl radicals in propane-air diffusion flames. The rate constant for this reaction was therefore determined using the computation for methane-air diffusion flames where the effects of reactions involving C, species are insignificant. The suggestion of Tsang and Hampson [48] for reaction 165 was found to give reasonable agreement for ethylene concentrations in both methane-air and propane-air diffusion flames. The consumption paths of acetylene have been problematic in combustion modeling. There are uncertainties not only in the reaction rate parameters but also in product channels of the reactions. Miller and Melius [36] have suggested that reactions with 0 atom are the major acetylene consumption paths even in slightly rich acetylene premixed flames. However, Levy and Sarofim [ll] and Woods and Haynes [72] suggested that the reaction with the OH radical, producing ketene, is responsible for acetylene consumption in fuel-rich premixed ethylene flames. A large number of reactions for acetylene consumption are included in the present mechanism to test the contributions of the various consumption paths in diffusion flames. A branching ratio of 1 was adopted for the two product channels for the reaction betwen acetylene and the 0 atom. The product channels for the reaction of OH with acetylene were adopted from the work by Miller and Melius [36]. Computational results show that the reaction of acetylene with the H radical is in equilibrium. Reactions with the 0 atom form the dominant paths and are responsible for about 80% of the overall acetylene consumption rate. The remaining contributions come from reactions with the OH radical and methylene. (142)
C,H,
+ 0 =3CH,
(143)
C2H2
+ 0 = CHCO
+ CO, + H,
(144)
C,H,
+ OH = C,H
+ H,O,
(145)
C,H,
+ OH = CHCOH
(146)
C,H,
+ OH = CH,CO
+ H, + H.
AND
R. P. LINDSTEDT
There is still uncertainty relating to the rate of reaction 146. Recently. Woods and Haynes [72] proposed a rate constant for this reaction which is ten times faster than the rate by Miller and Melius [36] adopted in the present study. Computations using the faster rate show that for this case the OH channel becomes competitive. Clearly the uncertainty in the reaction between acetylene and the OH radical is still unresolved. 4.3 Reaction
Paths for ‘CH,
and 3CH,
One of the most important features of methylene chemistry is its role in addition reactions with acetylene leading to the formation of higher hydrocarbon fragments [36, 59-61, 631. Reactions of both singlet and triplet methylene were considered in the present mechanism. Rate constants for these reactions have mainly been obtained from the compilation of Miller and Melius [36], Baulch et al. [47], and Tsang and Hampson [48]. Computational results for methane and propane flames show that singlet methylene is mainly formed by H and OH radical attack on CH, and the reaction between CHCO and the H radical. CH,
C-44) (87)
CH,
(129)
CHCO
+ H =‘CH,
+ H,,
+ OH =‘CH,
+ H,O,
+ H =‘CH,
+ CO.
Among the various consumption paths for singlet methylene, it was found that about 60% of singlet methylene isomerises to the triplet form, 25% reacts with acetylene to form C, species with the reminder consumed through reactions with OH, O,, and CO,. (481 (491 (50)
‘CH,
+ OH = CH,O
‘CH, ‘CH,
+ 0, + CO,
= CO + OH + H, = CO + CH,O,
(53)
‘CH,
+ C,H,
=
(54)
‘CH,
+ C,H,
= c-&H,,
(58)
‘CH,
+ H,
C,H,
+ M =3CH2
+
I-L
+ M.
KINETIC
MODELING
OF ALKANE
DIFFUSION
FLAMES
147
Canosa-Mas et al. [60] observed that propyne, allene and propargyl are all possible products of the singlet methylene reaction with acetylene. Since cyclopropene isomerises to propyne and allene quickly, the choice of cyclopropene as a product for this addition reaction provides a branching ratio for the formation of the two linear C,H, isomers. Triplet methylene is a major product of the reaction between acetylene and the 0 atom:
and theoretical work [37] also suggests that linear C, species are the initial products of propargyl recombination followed ring closure. However, there is uncertainty with respect to whether the rate-limiting step is the formation of the linear C, species or the subsequent cyclization reactions to form benzene. The following linear C, species formation paths have been considered in the present study, (350)
C,H,
+ C,H,
= (1,2)-C,H,,
(142)
(351)
C,H,
+ C,H,
= (1,5)-C,H,,
(352)
C,H,
+ C,H,
= (l&V)-C,H,,
C,H,
+ 0 =3CH,
+ CO.
Computational results show that several reactions with comparable rates are responsible for the consumption of triplet methylene. In total about 40% of triplet methylene is consumed by reaction with the H radical, 20% by reactions with 0, molecule, and the remaining contributions come from reactions with 0, OH, and CH, radicals. (60)
3CH, + H = CH + H,,
(61)
3CH, + 0 = CO + H + H,
(62)
3CH,+O=CO+H,,
(63)
3CH, + OH = CH + H,O,
(64)
3CH, + OH = CH,O + H,
(72)
3CH, + CH, = C,H,
+ H.
Reaction 60 is also the dominant formation path for CH radicals. Triplet methylene also reacts with acetylene to produce cyclopropene at a rate about three times slower than the equivalent singlet methylene reaction path. 4.4. Formation
of C, Species and Benzene
Benzene is of crucial importance as the first single-ring aromatic formed from smaller nonaromatic hydrocarbons. While reaction paths involving recombination reactions of linear C, and C, species have been favored in the past to account for the formation of benzene and other soot-precursors [9, 32, 33, 1091, recent work [34-37, 54, 811 suggests that propargyl radical recombination may in fact be a major contributor to the formation of benzene in flames. Recent experimental [34, 351
(353)
C,H,
+ a-C,H,
= I-&H,,
(354)
n-C,H,
+ C,H,
= (1,3)-&H,,
(355)
C,H,
+ C,H,
= Z-&H,,
(356) (1,3)-C,H,
+ C,H,
= I-&H,.
The rate constants for reactions 350-352 were obtained from Alkemade and Homann [34] with an equal branching ratio between the three product channels. The rate constants for reactions 353-356 were adopted from the work of Westmoreland et al. [33]. The chemistry of the C, chain is important since it contains potential benzene precursors. Computational results from methane and propane flames show that there are four paths leading to the formation of C,H, isomers. (-329)
C,H,
+ CH, = (1,2)-C,H,,
(335)
C,H,
+ C,H,
= (1,3)-C,H,,
(-338)
C,H,
+ C,H,
= (1,3&H,
(345)
‘CH, +p-C,H,
+ H,
= c-C,H,.
The recombination reaction (-329) between propargyl and methyl radicals is the dominant path for butadiene formation in both methane and propane flames. The other paths are significant only in propane flames because of the higher C, and C, species concentrations. The product of single methylene addition to propyne is specified as l-methyl-cycle-propane. This compound quickly isomerises to form (1,2)-C,H, and (1,3)-C,H,. (345)
c-C,H,
= (1,31-C,H,,
(3471
c-C,H,
= (1,2)-C,H,.
148
IS. M. LEUNG
The oxidation of 1,3 butadiene has been extensively studied by Lindstedt and Skevis [125]. In the present flames the C,H, isomers are predominantly consumed via abstraction reactions with CH, radicals. However, reactions with H and OH radicals also contribute to the consumption of (1,3)-C,H,: .
AND R. P. LINDSTEDT
The n-C,H, radical isomerizes quickly to iC,H, and the latter is mainly consumed by hydrogen abstraction and thermal decomposition reactions to produce C,H,. c-306)
n-C,H,
= i-C,H,,
(307)
i-C,H3 = C,H,
I
(334)
(1,2)-C,H,
+ CH, = (1,2)-&H,
(337)
(340)
(343)
(1,3)-C,H,
+ CH,,
+ H
(1,3)-C,H,
= (1,3&H,
+ H,,
= (1,3)-C,H,
+ H,O,
+ OH
(1,3)-C,H,
+ CH, = (1,3)-C,H,
+ CH,.
The 1,3-butadienyl radical readily decomposes to C,H, and C,H, at flame temperatures with isomerization to i-C,H, and (1,2)-C,H, accounting for less than 20% of the total consumption rate. (322)
(1,3)-C,H,
= C,H,
+ C,H,.
Consumption of the 1,2-butadienyl and isobutadienyl radicals proceeds mainly via the abstraction reactions with H and OH radicals to form C,H,. (318) (319)
(1,2)-C,H, (1,2)-C,H, i-C,H,
(327)
i-C,H,
(328)
+ H = C,H, + OH = C,H, + H = C,H, + OH = C,H,
+ H,, + H,O,
(313) (315)
3CH, + C,H, C,H, C,H,
= C,H,
+ H = n-C,H, + OH = n-&H,
i-C,H,
+ H = C,H,
= H,.
Computed concentrations of the (1,3)-C,H, and n-C,H, isomers are very small even in propane diffusion flame. This is mainly due to the high reversibility of the reactions responsible for the formation of C, species. As a result benzene formation paths via the C, species are not important in the present study. In fact, computational results show that reaction 354 proceeds in the reverse direction and becomes a formation path for n-C,H,. With the present mechanism benzene formation occurs mainly through radical recombination reactions of propargyl and the subsequent cyclization of the linear C, species. Among the three recombination paths considered in the present mechanism, reaction 352 forming (1,2,4,5&H, is the dominant formation path: (350)
C,H,
+ C,H,
= (1,2&H,,
(351)
C,H,
+ C,H,
= (1,5)-C,H,
(352)
C,H,
+ C,H,
= (1,2,4,5&H,.
+ H,, + H,O.
Vinyl-acetylene is also produced from the reaction 285 between propargyl and triplet methylene. This reaction is actually the dominant formation path for C,H, in methane flames where the C, intermediate concentrations are lower than in propane flames. Vinyl-acetylene is consumed by abstraction reactions producing the n-C,H, radical. (285)
(308)
+ H,
+ H, + H,, + H,O.
Reactions 350 and 351 are in partial equilibrium and consequently their net rates are controlled by the thermodynamic properties of the linear C&H, species involved. Melius et al. 1371 have suggested that the heats of formation of the linear C,H, species have an uncertainty of at least 20 kJ/mol. The heats of formation adopted in the present study are in good agreement with those suggested by Alkemade and Homann [34] with (1,2,4,5)-C,H, more stable than (1,2&H, and (1,5)-C,H, by 80 kJ/mol. Computational results show that with the current thermodynamic data, reaction 352 is faster than reactions 350 and 351 by factors of 15 and 5, respectively.
KINETIC
MODELING
OF ALKANE
DIFFUSION
Stein et al. [35] observed that the isomerization product of 1,5-hexadiyne was 1,2-dimethylene-cycle-butene which subsequently isomerizes to benzene and fulvene. They also suggested that 1,2,4,5_hexatetraene is a possible intermediate of this cyclization reaction. Melius et al. [37] studied the unimolecular rearrangement processes of various C,H, compounds and concluded that concerted reaction mechanisms involving ringed transition state structures provide low-activation-energy pathways for the cyclization reactions of linear C,H, isomers. Following these suggestions an isomerization reaction submechanism for the linear C,H, species was formulated:
but at a slower rate. Benzene is eventually formed from fulvene through reaction 388. Benzene is mainly consumed via the thermal decomposition reaction 400 and abstraction reactions 401 and 407 to form the phenyl radical. C,H,
(400) (401) (407)
C,H, C,H,
= C,H,
+ H,
+ H = C,H,
+ H,,
+ CH,
= C,H,
+ CH,.
In methane flames the reverse of reaction 407 also contributes to benzene formation due to the high CH, concentrations. A detailed discussion of the benzene oxidation mechanismn can be found elsewhere 1551.
(380)
(1,5)-C,H,
(381)
(1,2,4,5)-C&H,
= (Ml-C,H,,
5. MECHANISM
(382)
(1,2,4,5)-C,H,
= Fulvene,
The reaction mechanism, listed in Table 1, has been applied in the modeling of both nonpremixed and premixed combustion. For diffusion flames the reaction mechanism was initially tested by comparison of computational results with experimental data for methane-air and propane-air counterflow flames obtained by Tsuji and Yamaoka 129, 301. Subsequently, computations of a coflowing methane-air flame on a Wolfhard-Parker burner were made. The latter flame has been extensively measured by Smyth and co-workers [38-431. The comparison of computed results with measured species concentration profiles is a major part of the present study and provides a severe test on the validity of the reaction mechanism. For premixed combustion the present mechanism has been used to calculate laminar burning velocities of a number of premixed stoichiometric fuel-air mixtures. The results of these calculations for freely propagating flames are here compared with the experimental results of Egolfopoulos et al. [126] and the predictions with mechanisms of other authors [2-51 in Table 3. It can be observed that the present mechanism reproduces experimental results successfully at least for this limited selection of conditions. However, the main focus of the present study is non-premixed flames and detailed comparisons with measurements are made below.
(383)
CM)-C,H,
= (1,2,4,5)-C&H,,
149
FLAMES
= Fulvene,
(384)
(1,2)-C,H,
= Fulvene,
(385)
(1,2)-C,H,
= (1,3)-C,H,,
(386) (387) (388)
Fulvene (1,3)-C,H, Fulvene
= (1,3)-C,H,, = C,H,, = C,H,.
The rate constant for reaction 380 was adopted from the work of Stein et al. [35] while the rate constants for the isomerization reactions 383 and 388 were adopted from the work by Melius et al. [37]. The preexponential factors for reactions 381, 382, 384, and 387 were assigned a value of 5*1011 arguably typical for this type of rearrangement reactions. Energy barriers for these reactions were estimated following the formalism of Melius et al. [37]. Computational results show that (1,5)-C,H, mainly isomerizes to form (1,2,4,5&H,, which is subsequently converted to fulvene and 1,2-di-methylene-cycle-butene via reactions 381 and 382. At the high temperatures of the present calculations 1,2-di-methylene-cycle-butene isomerises quickly to fulvene. Fulvene is also produced via (1,2X,H, through reaction 384
EVALUATION
K. M. LEUNG
1.50
AND
R. P. LINDSTEDT
TABLE III Comparison
of Measured and Calculated Laminar Premixed Stoichiometric Hydrocarbon-Air
CH,
C2H,
Burning Velocities Mixtures
of
39.0 40.2 38.5
38.0 42.5 51.0
67.4 65.8 81.0
142.5 135.4 151.0
Glarborg et al. [3] Kee et al. [4] Sloane [5]
39.0 41.0 42.5
58.9 61.0 46.8
84.1 81.8 73.9
129.6 136.8 126.1
39.2
42.1
66.1
132.6
Egolfopoulos
et al. [6]
5.1. Counterflow Flames
Methane-Air
Diffusion
Tsuji and Yamaoka [29, 301 have reported two sets of experimental data for methane-air diffusion flames in the counterflow geometry with rates of strain of 100 s- ’ and 150 s- ‘. The former flame is well documented with measurements of velocity, temperature and species profiles. Presentation of the measured data on physical distance scale is also available [31]. Measured species profiles of this flame are here used for comparison with computational results. Detailed calculation of the structure of this flame has previous been done by DixonLewis et al. [24]. It has been suggested that for comparison between the measurements and computational results a slight increase in the velocity gradient is necessary to account for the additional pressure gradient imposed by the combustion chamber geometry. However, the differences in the flame structure were found to be small over the relevant strain rate range and the nominal velocity gradient was therefore used. A fuel injection velocity of 0.12 m/s was found to locate the flame properly in the physical domain. Comparisons between the measured and computed concentration profiles for major species, C, intermediates and the OH radical are shown in Figs. 2-4. There is clearly good quantitative agreement for absolute concentrations, locations of the peak concentration and profile shapes for major species. However, H,O profiles are over-predicted in the reaction zone of the flame and it is difficult to explain such discrepancy in terms of the computation results. Profiles of C,H,, C,H,, C,H, as well as for the OH radical are shown in Fig. 4. Agreement
C3H,
C2H2
C,H,
Present study Experimental data [126] Warnatz [2]
47.0 45.0 -
-
is again satisfactory. The OH concentration measurements were performed by Sick et al. 11271 for a flame with strain rate of 125 s-l and a fuel injection velocity of 0.114 m/s. The slightly different flow field parameters give rise to a small misalignment with respect to the computed profiles and for comparison purposes the measured OH profile was aligned with the computed profile. There are also some differences in the shape of the ethane profile. However, considering that the formation of C,H, proceeds mainly via methyl radical recombination on the fuel-rich side of the flame, the location of the peak C,H, concentration 0.25
!
I
I
I
OCHJ4 00, ANJ4
L_ 2.0
4.0
6.0
Distance (mm) Fig. 2. Comparison between calculations (lines) and measurements (symbols) by Tsuji and Yamaoka [30] of CH,, Oz, N, and Hz0 profiles in a counterflow methane-air diffusion flame with a strain rate of 100/s. Mole fractions are presented on a wet basis.
KINETIC
MODELING
OF ALKANE
DIFFUSION
1.51
FLAMES
should arguably appear on the rich side, rather than near the flame front as indicated by the measurements. The successful prediction of intermediate C2 profiles shows that the C, -Cz chemistry in the present mechanism is kinetically correct for combustion in diffusion flames. It also indicates that the treatment for the pressuredependent methyl radical recombination reaction producing ethane and that the rate constants used for the consumption reactions for acetylene and ethylene are adequate. 5.2. CounterBow Propane-Air Flames
Distance (mm) Fig. 3. Comparison between calculations (lines) and measurements (symbols) by Tsumi and Yamaoka [30] of CO, CO, and H, profiles in a counterflow methane-air diffusion flame with a strain rate of 100/s. Mole fractions are presented on a wet basis.
0.006
I
I
I
I
I
0 CA
0W A CA
OH
??
0.006 ~.-
0.0
C,“,
C,H, C,H, OH
2.0
4.0
6.0
Distance (mm) Fig. 4. Comparison between calculations (lines) and measurements (symbols) by Tsuji and Yamaoka [30] of C,H,, C2H,, C,H, and OH radical profiles in a counterflow methane-air diffusion flame with a strain rate of 100/s. Mole fractions are presented on a wet basis.
Diffusion
Tsuji and Yamaoka [29] also measured two counterflow propane-air diffusion flames at a medium strain rate of 1.50 ss’ and higher strain rate of 3.50 s- ‘. Species concentrations were reported on dry basis in both cases. The detailed kinetic model reproduces the features of the experimental results faithfully. Propane was found to be consumed rapidly on the fuel rich side of the flame to generate a pool of intermediates. Computational results for the case with a rate of strain of 150 s- ’ show that the peak consumption rate of propane occurs at temperature of around 1500 K which is well below the maximum temperature of 1900 K calculated for this flame. The observed separation of the fuel consumption region from the flame front was not found in methane-air diffusion flames in which the location of maximum fuel consumption was found to coincide with the location of maximum temperature. Such a separation is mainly due to the thermal decomposition of propane in the pyrolysis region which accelerates the fuel consumption. This feature could be typical for higher hydrocarbon diffusion flames because the rates of thermal decomposition reactions of higher hydrocarbons are typically comparable to, or greater than, those observed for propane. Computed major species profiles for the case with a rate of strain of 150 s-l are compared with measurements in Figs. 5 and 6. Good agreement can be observed for all the major species except a slight over-prediction of CO and CO, profiles as shown in Fig. 6. There is
152
K. M. LEUNG
1 0.8
C 0.6 .o % Ii 1 %
0.4
if ,A I’
B i
I’
0.2
ri
0
O0
/
0
AND
R. P. LINDSTEDT
also quantitative agreement for intermediate species, see Fig. 7, except that the computed CH, and C,H, concentrations are somewhat higher than the measurements. Similar agreement for the intermediate species in the higher strain rate case can be found in Fig. 8. It can be observed that in both cases the ratios between the C, -C, intermediate species have been predicted correctly. As discussed previously, the computed concentrations for the intermediate species are very sensitive to the rates of major pyrolysis reactions of propane. Considering the amount of uncertainty in the rate expressions for these reactions and in the experimental data the agreement can be regarded as satisfactory.
P
f
0.0 CI.0
P/
ri
1
1.0
2.0
3.0
4.0
Distance (mm) Fig. 5. Comparison between calculations (lines) and measurements (symbols) by Tsuji and Yamaoka [29] of C,Hs, O?, and N, profiles in a counterflow propane-air diffusion flame with a strain rate of 150/s. Mole fractions are presented on a dry basis.
5.3. Extinction Flames
Limit of Counterflow
Diffusion
Tsuji and Yamaoka 129-311 also reported extensive measurement to establish extinction parameters for counterflow diffusion flames. As discussed by Jones and Lindstedt [ 1281 there is some uncertainty concerning the experimen-
0.030
0.020 E 'J 8 t i? 8 0.010
1.0
2.0
3.0
Distance (mm) Fig. 6. Comparison between calculations (lines) and measurements (symbols) by Tsuji and Yamaoka [29] of H,, CO and COT profiles in a counterflow propane-air diffusion flame with a strain rate of 150/s. Mole fractions are presented on a dry basis.
0.000 3.0
Distance (mm) Fig. 7. Comparison between calculations (lines) and measurements (symbols) by Tsumi and Yamaoka [291, of CH,, C2H,, C,H,, C,H, and C,H, profiles in a counterflow propane-air diffusion flame with a strain rate of 150/s. Mole fractions are presented on a dry basis.
KINETIC
MODELING I
I
o
I
OF ALKANE I
I
I
DIFFUSION I
1
CH, '3,
0 0 C;H;
A CA
*CA --- CH, ---- C,H. A
2.l
2.0
Distance (mm) Fig. 8. Comparison between calculations (lines) and measurements (symbols) by Tsuji and Yamaoka [29] of CH,, C,H,, C,H,, C2H, and C,H, profiles in a counterflow propane-air diffusion flame with a strain rate of 350/s. Mole fractions are presented on a dry basis.
tal extinction point which has been found to be dependent upon the cylinder radius to a considerable degree. Within the framework of a similarity solution where effects such as any additional pressure gradients caused by the apparatus cannot be taken into account, the value obtained with the smallest cylinder is likely to provide the most accurate comparison. Measured extinction limits for methaneair and propane-air diffusion flames are therefore taken as 375 and 675 s-l, respectively. In the present study the extinction limit was determined by increasing strain rate for calculation until no stable solution could be achieved. The computed extinction limits for methaneair and propane-air diffusion flames were found to be 480 and 650 s-i, respectively, which is in acceptable agreement with the measurements. 5.4. Coflowing Methane-Air
Diffusion Flame
Smyth and co-workers [38-431 have conducted a detailed experimental investigation of a laminar coflowing methane-air diffusion flame on
FLAMES
153
a rectangular Wolfhard Parker burner. Measurements have been made of species concentrations, ve!ocity and temperature at different heights above the burner exit. Concentration profiles for a number of compounds including acetylene, benzene and radicals such as CH,, CH, 0, OH, and H have been reported. However, to date no detailed kinetic computations of the flame structure have been carried out for this geometry. In previous modeling works comparisons were made either with flamelets derived from the counterflow geometry [1291 or with flamelets derived from kinetic computations of the chemical structure of axisymmetric laminar diffusion flames [130]. In the present study, calculations have been made with full detailed chemical kinetics as well as with a laminar flamelet approach. Direct comparison of measured and computed species profiles on a physical distance scale provides a critical and demanding test of the present mechanism. Moreover, the measured acetylene and benzene profiles can be used to validate the benzene formation paths considered in the mechanism. The acetylene and benzene data has recently been reevaluated [43] and the new values are used here. Computations were performed with initial conditions similar to those reported by Smyth et al. [38] in their experimental investigation. The velocities for the fuel and the air flows reported earlier 1381have recently been recalibrated [130] to 11.0 and 21.7 cm/s, respectively. The calculations were initiated with a flamelet approach to generate the initial flame structure. Once a sufficient number of high temperature nodes was obtained, typically after a distance of 0.4 mm above the burner, the computation switched to use of the full kinetic scheme. Preliminary calculations show the vertical velocity profiles to be overpredicted near the centerline region. In order to improve the flow field predictions, the buoyancy term was adjusted near the centre-line region. The measured velocity profiles at 9 mm above the burner exit are compared in Fig. 9 with the corresponding results of the calculations. The agreement is reasonable considering the simplified boundary layer approximation employed in the numerical calculation. There is also good agreement for the temperature and mixture
154
K. M. LEUNG
AND
R. P. LINDSTEDT
Velocity profiles at 9mm above burner
‘j;
0.60
0.6
z
c4
0 Mixture Mixture
fraction fraction
ATemperature Temperature
2500
0 B S
0.40
B e z
0.20
0.00
-0.10 z .e8
-0.20
z g
Lateral Position (mm)
-0.30
w ‘Z I” -0.40
-0.50
i 0.0
2.0
4.0 Lateral
6.0 Position
6.0
10.0
12.0
Fig. 10. Comparision between calculations (lines) and measurements (symbols) by Smyth [43] of profiles of mixture fraction (solid line, circle) and temperature (dotted line, triangle) at a height of 9 mm above the exit of a Wolfhard-Parker burner.
(mm)
Fig. 9. Comparision between calculations (lines) and measurements (symbols) by Smyth [43] of velocity profiles at a height of 9 mm above the exit of a Wolfhard Parker burner.
fraction profiles in terms of magnitude and shape as shown in Fig. 10. The definition of mixture fraction used follows the suggestion by Bilger et al. [131]. Figure 11 compares measured stable species (CH,, O,, N,, and H,O) with calculated profiles. There is excellent agreement in terms of their absolute concentrations, the locations and the profile shapes. Similar agreement for H, profiles can be observed in Figure 12. However, there are some discrepancies in the CO and CO, profiles. The computed CO? concentrations are lower than the measurements in the fuel rich region while there is an overprediction of the CO profiles. Computational results from the counterflow geometry show that the peak CO concentrations vary from 5.7% to 4.5% as the strain rate is increased from 10 to 100 s-r. The variation of computed peak concentrations of H,, CO, and CO, with flame
0.25
2.0
4.0
6.0
6.0
10.0
Lateral Position (mm) Fig. 11. Comparision between calculations (lines) and measurements (symbols) by Smyth [43] of CH,, O,, N,, and H,O profiles at a height of 9 mm above the exit of a Wolfhard-Parker burner.
KINETIC
0.10
MODELING
/
0.06
i
/
,
oco, oco A “2 co, ~.~ co H*
OF ALKANE
I
,
DIFFUSION
FLAMES
,
-H
o’tb
o”
155
0
OH
0.006
0
A AA
g 0.06 'ij 0 !!! LL u
A
r" 0.04
0.02
0.00 0.0
2.0
4.0
6.0
6.0
6.0
Fig. 12. Comparison between calculations (lines) and measurements (symbols) by Smyth 1431 of C02, CO, and HZ profiles at a height of 9 mm above the exit of a Wolfhard Parker burner.
height above the burner is moderate. For example, the computed peak CO concentration increases from a value of 4.6% to 5.3% from a height of 1 mm to 9 mm above the burner. The variation is similar in the flamelet computation. Figure 13 compares measured profiles of H, 0 and OH radicals with computational results. The overall agreement in the shape and locations of the profiles is good. The results of detailed kinetic calculations show that the computed 0 and OH profiles are slightly narrower than the measurements and the computed H profiles appear somewhat misaligned. However, the agreement in the peak concentration is reasonable. The computed peak OH radical concentration is less sensitive to increasing height than the computed H and 0 atoms concentrations which decrease by around 12% and 25% respectively-in agreement with experimental observations. Figure 14 compares measured profiles of CH and CH, radicals with the computational results. Experimental CH concentrations were normalised assuming an arbitrary peak concentration of 1 ppm and the experimental methyl
8.0
Lateral Position (mm)
Lateral Position (mm)
Fig. 13. Comparison between detailed kinetic and flamelet calculations (lines) and measurements (symbols) by Smyth [43] of H, 0 and OH radical profiles at a height of 9 mm above the exit of a Wolfhard-Parker burner.
0.00:
-
OCH;20 *CH'2000 CH, CH'lOOO
t
0.00:
E
‘i;
8 t
a,
2
0.001
0.000
w
LO
4.0
6.0
Lateral Position (mm) Fig. 14. Comparison between detailed kinetic calculations (lines) and measurements (symbols) by Smyth [43] of CH and CH, radical profiles at height of 9 mm above the exit of a Wolthard-Parker burner.
156
K. M. LEUNG
radical concentrations reported by Miller and Taylor [39] arguably provide a lower limit only. Therefore, to illustrate the similarity in profile shapes the peak concentration of the experimental data are scaled to the same values as the calculated profiles for comparison. There is a good agreement in the location and profile shape for the methyl radical. The computed CH profile is narrower and appears closer towards the air side than the measurements. Computational results show that the peak concentrations of CH and CH, radicals are sensitive to the rate of strain, and their values were reduced by 55% and 45%, respectively, when the height increases from 1 mm to 9 mm above the burner exit. Figures 15 and 16 compare the evolution of measured and computed acetylene and benzene profiles with flame height. Benzene concentrations at the beginning of calculation were set to zero to ensure that the flamelet did not impose unrealistically high initial concentrations. There is good agreement in the locations and shape of the profiles and both measurements and predictions show that acetylene and benzene concentrations increase with increas-
0.0060
-
0.0070
~
-‘1
_ 0.0060
-
0.0050
-
0.0040
-
0.0030
-
-
07mm 09mm *llmm 7mm 9mm ~ llmm
,“\ ,/,‘A,
s ‘Z
0’0°051
0.0004
-
AND
03mm 07mm n9mm 3mm - 7mm -9mm
R. P. LINDSTEDT
%A a n n 1
n g ‘Z
0.0003
~
0.0002
-
0.0001
~
I
n 0
n
8 t a, 9
1
2.0
4.0
6.0
Lateral Position (mm) Fig. 16. Comparison between detailed kinetic calculations (lines) and measurements (symbols) by Smyth [43] of C,H, profiles at heights of 3, 7, and 9 mm above the exit of a Wolfhard-Parker burner.
ing flame height. However, Figure 15 shows that the computed C,H, profiles are consistently higher than the measurements by around 30%. The variation of computed peak benzene concentration with flame height is less than that observed in experiments, see Figure 16. Previous modeling studies [129, 1301 linked flamelets to the scalar dissipation rate (~1, to account for the variation of the chemical structure due to local strain rate in a flame. The scalar dissipation rate can be expressed as [129]
8 t s? r”
where 0.0020
0.0000
~
T0.0
D = -
A
and the mixture
fraction
is Z.
PC,
I
, 2.0
I
,
I
4.0
,
6.0
8.0
Lateral Position (mm) Fig. 15. Comparison between detailed kinetic and flamelet calculations (lines) and measruements (symbols) by Smyth [43] of C,H, profiles at heights of 7, 9, and 11 mm above the exit of a Wolfhard-Parker burner.
The variation of the scalar dissipation rate at the stoichiometric plane ( x,,> and the position of maximum temperature ( xT) take values in the range 1.5 to 0.7 /s. The computed results show that the scalar dissipation rates decrease with increasing flame height as expected. The corresponding ,yst from flamelets of counterflow geometry with strain rates of 15 and 50 ski are 0.75 and 2.25, respectively.
KINETIC
MODELING
OF ALKANE
DIFFUSION
The coflowing flame was also computed using a flamelet approach with flamelet data generated in the counterflow geometry with rates of strain of 10 s-l and 200 s-l. This large variation in strain rate helps to exemplify the effect of strain on the flame structure. The results of flamelet calculations for radicals (H, 0 and OH), acetylene and benzene at a height of 9 mm above the burner are compared in Figure 17 with the corresponding results of detailed kinetic computation and measurements. It can be observed that predictions for all the species shown, except for the OH radical, are sensitive to the rate of strain. Computation results show the computed peak concentrations for acetylene and benzene are reduced by 50% and 90%, respectively, when the strain rate is increased from 10 to 200 s-‘. Calculations using the flamelet with a low rate of
FLAMES
157
strain provide better agreement in profile shapes with the result of detailed kinetic computation than the computational results generated with high strain rage flamelet data. However, all the profiles of the flamelet calculations appear shifted towards the rich side. Finally, the sensitivity of the benzene prediction to the propargyl recombination reaction was investigated. Flamelet data were generated for a rate of strain of 10 s-l in which the contributions of propargyl recombination reactions were removed from the mechanism. The results of the flamelet calculation using this flamelet data in the coflowing case can be found in Fig. 17. The peak benzene concentration was reduced by two orders of magnitude. This observation establishes the importance of propargyl recombination reactions for benzene formation. CONCLUSIONS
2.0e-03
0.0
2.0
4.0
6.0
6.0
10.0
Lateral Position (mm) Fig. 17. Comparison between detailed kinetic and flamelet calculations (lines) with experimental measurements (symbols) by Smyth [43] at a height of 9 mm above the exit of a Wolfhard-Parker burner. Also shown is a computation in which all benzene formation paths involving the propargyl radical have been removed.
An extensive kinetic model for the combustion of C, -C, hydrocarbons in diffusion flames has been described. The major reaction paths for intermediate species have been determined by conducting systematic sensitivity analysis. The validity of the C, -C, chemistry has been shown by quantitative agreement between computed results and experimental measurements of both major and minor species in ambient pressure methane-air and propane-air counterflow diffusion flames. Detailed kinetic and flamelet computations for a coflowing methane-air diffusion flame on a Wolfhard-Parker burner have shown that quantitative agreement between predictions and measurements for major specie, acetylene, benzene and radical species profiles has been achieved. The investigation of benzene formation shows that propargyl radical recombination is the major formation path for benzene in C, -C, hydrocarbons diffusion flames. Benzene formation from C, species appears insignificant by comparison due to their low concentration caused by isomerization reactions and the high reversibility of the reactions responsible for the formation of these species. The results of flamelet computations show that the predictions for benzene are very sensitive to the rate of strain.
K. M. LEUNG
158
The results of sensitivity analysis reveal that there are still significant uncertainties in some reaction rate data which can affect the quality of predictions with the present mechanism. A brief summary of the most urgent problem areas is as follows: Computational results of the potential portance of the reaction
im-
7. 8. 9. 10. 11. 12.
(146)
C,H,
+ OH = CH,CO
+ H
for acetylene consumption in diffusion flames. The scatter in available rate constants in the literature for this reaction leads to the need for further investigation. Although there is good agreement between the computed and measured concentration profiles for C, -C, species in propane flames, it has not been possible, to quantify the relative importance of the consumption paths for in the present study. Propene is an important intermediate for higher hydrocarbon combustion and experimental work including the measurement of C, species will be helpful in clarifying this uncertainty. It has been shown that the thermodynamic properties for minor C, species along with isomerization reactions for C, and C, species are of considerable importance in the determination of benzene formation paths in diffusion flames. Further data are urgently required to resolve remaining uncertainties. The authors are grateful for the financial support of the Defence Research Agency (Aerospace Division) RAE Pyestock for this work. REFERENCES 1.
2. 3. 4.
5. 6.
Warnatz, J., Eighteenth Symposium (International) Institute, 1981, p. on Combustion, The Combustion 369. Wamatz, J., Combustion Chemistry (W. C. Gardiner, Jr., Ed.), Springer-Verlag, New York, 1984, p. 197. Glarborg, P., Miller, J. A., and Kee, R. J., Combust. Flame 65:177 (1986). Kee, R. J., Miller, J. A., Evans, G. H., and DixonLewis, G., Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1989, p. 1479. Sloane, T. M., Combust. Sci. Technol. 63:287 (1989). Frenklach, M., Wang, H., and Rabinowitz, M. J., Prog. Ener. Combust. Sci. 18:47 (1992).
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AND R. P. LINDSTEDT
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K. M. LEUNG AND R. P. LINDSTEDT Baulch, D. L., Cobos, C. J., Cox, R. A., Esser, C., Frank, P., Just, Th., Kerr, J. A., Pilling, M. J., Troe, J., Walker, R. W., and Warnatz, J., Combust. Flame 98:59 (1994). Tully, F. P., Ravishankara, A. R., and Carr, K., Int. J. Chem. Kinet. 15:llll (1983). Benson, S. W., ht. .I. Chem. Kinet. 21:233 (19891. Duran, R. P., Amorebieta, V. T., and Colussi, A. J., J. Phys. Chem. 92:636 (1988). Kern, R. D., Xie, K., Chen, H., and Kiefer, J. H., Twenty-Third Symposium (International) on Combustion, The Combustion Institute, 1990, p. 69. Homann, K. H., and Wellmann, Ch., Ber. Bunsenges. Phys. Chem. 87:527 (1983). Perry, R. A., Combust. Flame 68:221 (1984).
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102. Braun-Unkhoff,
M., Frank,
P., and
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Th.,
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Twentieth Symposium (International) on Combustion,
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C, Alkane
and R. P. LINDSTEDT*
Department of Mechanical Engineeting, Imperial College of Science, Technology and Medicine, Exhibition Road. London SW7 2BX, UK
A study of detailed chemical kinetics in coflow and counterflow diffusion flames is presented. The chemistry of diffusion flames is of fundamental importance from a practical as well as a mechanistic viewpoint. The present study uses systematic reaction path flux and sensitivity analyses to determine the crucial reaction paths in methane and propane diffusion flames. The formation of benzene and intermediate hydrocarbons via C, and C, species has been given particular attention and the relative importance of reaction channels has been assessed. The developed mechanism considers singlet and triplet CH,, isomers of C,H,, C,H,, C,H,, C,H, and C,H,. Computational results show that benzene in methane-air diffusion flames is formed mainly via reactions involving propargyl radicals and that reaction paths via C, species are insignificant. It is also shown that uncertainties in thermodynamic data may significantly influence predictions and that the reaction of acetylene with the hydroxyl radical to produce ketene may be an important consumption path for acetylene in diffusion flames. Quantitative agreement has been achieved between computational results and experimental measurements of major and minor species profiles, including benzene, in methane-air and propane-air flames. It is also shown that the mechanism correctly predicts laminar burning velocities for results for a two-dimensional methane-air flame on a stoichiometric C, -C, flames. Finally, Wolfhard-Parker burner obtained with full detailed chemistry are presented along with flamelet computations and the accuracy of the latter are discussed.
1. INTRODUCTION Chemical kinetic modeling has become an important tool for interpreting and understanding observed combustion phenomena. Its application require as an input a valid chemical reaction mechanism. A large amount of effort has been devoted to the development of detailed kinetic mechanisms of varying complexity for hydrocarbon combustion. Detailed kinetic mechanisms found in the literature covers most of the C,-C, hydrocarbons [l-18] as well as higher hydrocarbons such as benzene 1191, toluene 1201, heptane, and octane [21, 221. However, it is well recognized that the rates of many elementary reactions are uncertain and vary strongly depending on flame type and combustion conditions. As a result the development of comprehensive detailed kinetic mechanisms requires validation under a wide variety of regimes. Previous mechanism validation studies have mainly focused on premixed systems (e.g., premixed flames, shock tubes, and flow reactors), with comparatively little attention given to nonpremixed reactants. The
* Corresponding
author.
COMBUSTIONAND FLAME 102: 129-160 (1995) Copyright 0 1995 by The Combustion Institute Published by Elsevier Science Inc.
complex transport and chemical kinetic interactions that occur in nonpremixed combustion result in significant differences in flame structures compared to premixed combustion. Moreover, pyrolysis reactions play a more important role for fuel consumption in nonpremixed combustion. These differences makes it desirable to extend the validation of detailed chemistry further through the application to non-premixed systems. To date modeling studies of diffusion flames have mainly concentrated on simple fuels [23-251. However, some detailed numerical studies of heptane-air [26] and propane-air [27, 281 diffusion flames have been reported recently. In many cases good agreement has been obtained between predictions and measurements for major species profiles. However, it has been found [27] that even the predictions of stable intermediate species are very sensitive towards the rates of a number of reactions. The difficulty in formulating a well balanced kinetic scheme is further increased by the considerable scatter in rate constants of reactions which are important for the prediction of intermediate species in diffusion flames. The objective of the present study is to further develop and refine a detailed kinetic OOlO-2180/95/$9.50 SSDI 0010-2180(94)00254-P
130
K. M. LEUNG
mechanism to make it suitable for the modeling of C,-C, hydrocarbon combustion under diffusion flame conditions. Particular attention has been given to improvements of the quantitative predictions of species such as benzene and acetylene which are of fundamental importance for the further development of soot formation models [28]. Refinement of the mechanism has been achieved by a systematic computational sensitivity analysis conducted initially on laminar counterflow methane-air and propane-air diffusion flames and subsequently on coflowing methane-air flames. Propane and methane were chosen as fuels because of the significant differences in the amounts of intermediate species produced during the pyrolysis of the two fuels and as experimental measurements of many of these species are available for comparison [29, 301. In hydrocarbon diffusion flames with nonaromatic fuels the formation of benzene can be expected to precede the formation of PAII and soot and several benzene formation paths via C,-C, hydrocarbons have been suggested [9, 32-371. The possible reaction paths have here been investigated using experimental data obtained by Smyth and co-workers [38, 40-431 and Miller and Taylor [39], who measured concentration profiles of a number of species including acetylene and benzene, in a coflowing methane-air diffusion flame on a Wolfhard Parker burner. Detailed kinetic calculations, as well as flamelet computations, have been performed for this flame, and comparisons with measurements are reported. In all cases the major reaction paths and the sensitivity of the predictions of intermediate species towards individual reactions in the detailed mechanism are quantified through reaction path flux and sensitivity analyses. The uncertainties in the rate constants are related to the predictions of intermediate species. 2. MATHEMATICAL
AND R. P. LINDSTEDT
point streamline. The basic boundary layer equations for the counterflow geometry may be written in a similarity transformed coordinate system. The mechanics of the actual transformation of the steady equations has been discussed by Peters and Kee [44], and the corresponding governing time-dependent equations are only briefly repeated below.
where
The corresponding boundary layer equations for the two-dimensional flame on the Wolfhard-Parker burner are JP u -+ dx
dP * = 0, dy
dU
dZ4
pudx+pv-=-
dY
d
(
dY \
dP
au\
u-
dY
I
-z,
MODEL
The numerical representation of the structure of counterflow diffusion flames has been discussed by many authors [24, 25, 441. The structure of this flame is obtained from the solution of the equations of conservation of momentum, species and energy along a stagnation
-Jk---
x i ayk
puax
+ puz
= 2
+ MkRk.
KINETIC
MODELING
OF ALKANE
DIFFUSION
In the above equations the components of velocity are denoted by u and v in the x and y directions, p is the fluid density, h is the mixture enthalpy, p is the fluid viscosity, Y, is the mass fraction and Mk is the molar mass of species k. For the counterflow flames a is the rate of strain and the subscript e denotes values prevailing in the potential flow at the “edge” of the boundary layer. The buoyancy term was evaluated in a similar way to that used by Jones and Lindstedt 1451.The reaction rate source term may be written as nreac R, =
nsP
c
Sik k/n
j=l
i
nsP
(I+
- k; n
I= 1
@,‘lk .
I= 1
i
The expression for the flux term is as suggested by Jones and Lindstedt [45] and may for example in the counterflow case be written as,
J,=-!c
dYk --
i a
USC
1 dn
Yp---
i
-
41r,. Ll
The evaluation of the transport coefficients were made using the same technique as outlined by Jones and Lindstedt [45]. The above equation system was solved using an implicit difference formulation involving two point backward time differencing and central differences for the spatial derivatives. The resulting set of algebraic equations are nonlinear, and a Newton linearization was used for the source terms in the species transport equations,
131
FLAMES
To obtain steady flow solutions the above equations were integrated in time until steady conditions prevailed or until a sufficient distance downstream had been reached. Mesh distributions in the flames were set to ensure a large number of mesh nodes in the portion of the flame where the maximum gradients occur. This was achieved by using distributed mesh spacing with a minimum of 110 nodes for the counterflow case and 165 nodes for the coflow case. The applied boundary conditions for the counterhow case consisted of an adiabatic wall with a prescribed mass flux at the cylinder surface and zero gradient conditions at the free stream boundary for all variables except I/. Calculations for the coflowing cases were performed with initial conditions for the axial velocity, the temperature and the species concentrations as prescribed at the burner exit. Zero gradient conditions were assumed for all variables at the symmetry line. The air side was treated as a free stream boundary condition. An ad hoc modification of the buoyancy term was found necessary in order to produce reasonable agreement with the measured velocity profiles as discussed below. The coflowing flame was also computed using a flamelet approximation. For this case the species and enthalpy equations were replaced by an equation for the mixture fraction Z, dZ dZ d pudx +pv- JY JY
The mixture fraction equation was solved based on mean mixture properties with species concentrations and temperature profiles obtained from flamelets generated in the counterflow geometry. The resulting block tridiagonal equation system for the species transport equations was solved using a direct method 1461, and in an outer sweep the transport equations were iterated with respect to the nonlinear contributions (rate expressions, diffusion correction velocity). The enthalpy and momentum equations were solved using a conventional tridiagonal equation solver. Finally, the transformed continuity equation is used to solve for V by numerical integration for the counterflow case.
3. THE REACTION
MECHANISM
The present detailed mechanism is an extension of the C, -C, mechanism developed by Leung et al. [27, 281. Rate constants for the reactions in the former mechanism were mainly obtained from the compilation of Baulch and co-workers [471, Tsang and Hampson 1481 and Tsang [49-511. Many additional features have been incorporated into the present mecha-
132
K. M. LEUNG
nism. The present mechanism also includes a reaction submechanism for C, species based predominantly on the work by Miller and Melius [361, Kiefer et al. [52, 531 and Kern et al. [54]. A detailed benzene formation mechanism has been formulated based on the work of Alkemade and Homann [34], Stein et al. [35] and Melius et al. [37]. A benzene oxidation mechanism, validated independently by Lindstedt and Skevis [55], has also been included. The details of the benzene formation mechanism are discussed below. The current mechanism differentiates between methylene in the ground and excited states c3CH, and ‘CH,), isomers of C,H, (CH,CCH,, CHCCH,, and cyclopropene), C,H, (CH,CHCH,, CH,CHCH, and CH,CCH,). In addition the following isomers of C, and C, species are considered: I-C,H,
= CH,CHCHCHCHCH,
(1,5)-&H,
= CHCCH,CH,CCH,
(1,2)-C,H,
= CH,CCHCH,CCH,
(1,2,4,5)-C,H,
= CH,CCHCHCCH,,
(Ml-C,H,
= 1,2-dimethylene-3-
AND R. P. LINDSTEDT
A complete referenced listing of the reaction mechanism consisting of 87 species and 451 reactions can be found in Table 1. All reactions were assumed reversible with the reverse rates calculated from the appropriate equilibrium constants. The thermodynamic data coefficients adopted for the calculation of the equilibrium constants were obtained mainly from the compilation of Burcat and McBride [llO] or from the CHEMKIN [ill] database. For species not found in these sources thermodynamic data was estimated using Benson’s method [112]. A critical review of the heats of formation for some species was also required as discussed below and a list of the final values used for all the species considered can be found in Table 2. The treatment of pressuredependent reactions was according to the formalism of Troe [114] and transport coefficients for viscosity and binary diffusivity were evaluated using the kinetic theory of Chapman and Enskog (see Reid et al. [115]>. The thermal conductivity was evaluated using the Mason and Monchick [1161 approximation including rotational collision efficiency, but ignoring the vibrational contributions. Lennard-Jones potential parameters were taken from the compilations of Kee et al. [117].
cyclobutene, (1,3&H,
= CH,CHCHCHCCH,
(1,3&H,
= CHCCH,CHCCH,
(1,5&H,
= CHCCHCHCHCH,
(1,2)-C,H,
= CH,CHCCH,,
(1,3)-C,H,
= CH,CHCHCH,,
c-C,H, (1,2)-C,H,
= l-methyl-cyclopropane, = CH,CHCCH, (radical site at terminal carbon),
(1,3)-C,H,
= CH,CHCCH,
X,H,
= CH,CHCCH, (radical site at interior carbon),
n-C,H,
= CHCCHCH,
X,H,
= CH,CCCH.
4. REACTION ANALYSIS
SENSITMTY
AND PATH
As a starting point for further development the C,-C, mechanism described above was evaluated using experimental data from methane-air and propane-air counterflow diffusion flames obtained at ambient pressure by Tsuji and Yamaoka [29, 301. Reaction path flux analysis was used to identify the main species consumption paths in both methane and propane flames. Sensitivity analysis was also conducted to determine which rate coefficients had the greatest influence on the computed results. The sensitivity analyses were performed by multiplying the rate constant of each reaction of interest by a factor of 5 or l/5 and followed by a complete flame computation for every perturbation. This variation of the reaction rate covers in most cases the range of scatter in rate constants reported in the literature. Logarithmic response sensitivities are used in the
KINETIC MODELING OF ALKANE DIFFUSION FLAMES
133
TABLE 1
Reaction Mechanism Rate Coefficients in the Form k, = AT”exp( -E/RT)
n
E (kJ/mol)
0.00 2.67 1.60 1.14 - 0.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 1.00 -0.60 - 1.25 - 2.00 - 2.00 - 1.00 1.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 0.75 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
70.34 26.27 13.80 0.42 0.00 3.66 5.90 - 2.08 7.20 0.00 6.44 14.96 15.71 16.63 5.57 190.00 0.00 0.00 0.00 0.00 0.00 0.00 - 2.08 98.94 - 19.00 199.54 0.00 2.89 0.00 0.00 0.00 -2.16 0.00 0.00 0.00 41.84 41.84 0.00 0.00 0.00 0.00 0.00 71.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
A
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. 54.
(m3, kmol, s-
Reactions
No.
H + Oz 0 + Hz OH + H, 20H O?+H+M HO, + H HO, + H HO, + OH HO, + H HOz + 0 HO, + HO, H,O, + H H,O, + H H,O, + 0 H20, + OH H,Oz + M 2H + M 2H + H, 2H + H,O 2H + CO, H+OH+M 20 + M CO+OH CO + HO, CO+O+M co + 0, CH + 0, CH + CO, CH + 0 CH+OH CH + H,O CH + CH,O CH +3CH, CH+CH, CH + CH, CH + C,H, CH + C,H2 CHO + H CHO + 0 CHO + 0 CHO + OH CHO + 0, CHO + M ‘CH, + Hz ‘CH, + H ‘CH2 + 0 ‘CH, + 0 ‘CH, + OH ‘CH, + 0, ‘CH, + CO, ‘CHZ + CH, ‘CH, + CH, ‘CH, + C,H, ‘CH, + C,H,
OH + 0 OH+H H,O + H H,O + 0 HO, + M” 20H H, + Oz H,O + 0, Hz0 + 0 OH + 0, H20, + 0, H,O + OH HO, + H, HO, + OH H,O + HO, 20H + Mb Hz + MC Hz + H, Hz + H,O Hz + CO* Hz0 + Mb OX + Mb CO, + H CO, + OH CO, + Mb co2 + 0 CHO + 0 CHO + CO CO + H CHO+H CH,O + H CH,CO + H C2H, + H C,H, + H C,H, + H C,H + H, C,H, + H CO + H, CO + OH CO, + H CO + H,O CO + HO, CO + H + Mb CH, + H CH + Hz CO + 2H CO + Hz CH,O+H CO + OH + H CH,O + CO C,H, + H CH, + CH, C,H, + H c-C3H,
1.989E + 5.120E + 1.025E + 1.500E + 2.000E + 1.686E + 4.280E + 2.890E + 3.000E + 3.190E + 1.870E + 1.024E + 1.686E + 6.620E + 7.830E + 1.200E + 6.530E + 9.200E + 6.000E + 5.490E + 2.213E + l.OOOE + 6.320E + 1SOOE + 5.300E + 2.530E + 3.300E + 3.430E + 4.000E + 3.000E + 1.170E + 9.640E + 4.OOOE+ 3.000E + 6.000E + l.OOOE + l.OOOE + 9.030E + 3.000E + 3.000E + 1.024E + 3.000E + 1.860E + 7.230E + 7.000E + 1.500E + 1.5OOE + 3.000E + 3.130E + 3.000E + 1.800E + 4.280E + 8.000E + 8.000E +
’)
11 01 05 06 12 11 10 10 10 10 09 10 09 08 09 14 11 10 13 14 16 11 03 11 07 09 10 09 10 10 12 10 10 10 10 11 11 10 10 10 11 09 14 10 10 10 10 10 10 09 10 10 10 10
Ref. I471 [471 I471 [471 [21 [471 [471 [471 [471 [471 I471 [471 [471 [471 I471 I21 [471 I361 I361 [361 [471 Dl I471 1481 Bl [481 [471 I471 [471 1361 I361 [471 [361 [361 I361 est., [57] est., 1571 [471 I471 [471 [471 [471 I581 [481 [591 I481 [481 I481 [481 I481 [481 [481 est., [60] est., [601
TABLE 1 Reaction Mechanism Rate Coefficients in the Form kj = AT”exp( -E/W) A (m3, kmol, s- ‘1
Reactions
No. 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.
‘CH, ‘CH, ‘CH, ‘CH, 3CH2 3CH2 3CH, 3CH, 3CH, 3CH, 3CH, 3CH2 3CH, 3CH2 3CH, 3CH, 3CH, 3CH, 3CH, 3CH, 3CH, CH,O CH,O CH,O CH,O CH,O CH,O CH,O 2CH, 2CH,
+ CH,CO + C,H, + C,H, + M + H, + H + 0 + 0 + OH + OH + 0, + O2 + 0, + 0, + 0, + CO, +3CH, + CH, + C,HO + C,H, + C,H, + H + 0 + OH + 0, + HO, + CH, + M
85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109.
CH, + 0 CH, + OH CH, + OH CH, + OH CH, + OH CH, + 0, CH, + 0, CH, + HO, CH,+CHO CH, + M CH, + M CH,OH+M CH,OH + M CH,OH + M CH,OH + H CH,OH + H CH,OH + H CH,OH + 0 CH,OH + 0 CH,OH + OH CH,OH + OH CH,OH + CH, CH,OH + CH,O CH,O + H CH,O+O
C,H,
+ CO
C3H6
C,H, + CH, 3CH, + Md CH, + H CH + H, CO + 2H CO + H, CH + H,O CH,O + H CO + H + OH CO, + 2H CH,O + 0 CO, + H, CO + H,O CH,O + CO C,H, + 2H C,H, + H C,H, + CO c-C,H, C3H6
CHO+H, CHO + OH CHO + H,O CHO + HO, CHO + H,O, CHO + CH, CHO+H+M C25 C2H6’
,+
H
k, = k, =
CH,O + H CH,OH + H ‘CH? + H,O CH,O + H, CH,O + H CH,O + 0 CH,O + OH CH,O + OH CH, + CO ‘CH, + H + M CH + H, + M CH, + OH + M CH,OH + H + M ‘CH, + H,O + M CH,OH + H, CH,O + H, CH, + H,O CH,OH + OH CH,O + OH CH,OH + H,O CH,O + H,O CH,OH + CH, CH,OH + CH,OH CH,O + H, CH,O + OH
1.260E + 11 6.600E + 10 1.140E + 11 l.OOOE + 10 3.000E + 06 l.lOOE + 11 7.220E + 10 3.610E + 10 1.130E + 04 2.5OOE + 10 6.580E + 09 6.580E + 09 6.580E + 09 2.630E + 09 2.630E + 09 l.lOOE -I- 08 1.2OOE + 11 4.210E + 10 3.000E + 10 1.2OOE + 10 1.800E + 07 2.29OE + 07 4.150E + 08 3.430E + 06 6.000E + 10 2.000E + 09 4.090E + 09 1.260E + 13 5.000E + 09 3.613E + 10 1.270E + 35 8.430E + 10 1.500E + 11 4.000E + 10 1.024E + 09 5.740E + 09 1.320E + 11 3.300E + 08 1.800E + 10 1.200E + 11 1.900E + 13 6.900E + 11 1.900E + 16 2.000E + 14 7.0OOE + 12 4.000E + 10 4.000E + 09 5.010E + 09 3.880E + 02 l.OOOE + 10 3.000E + 01 5.300E + 00 3.190E - 02 3.000E + 08 2.000E -t 10 6.000E + 09
(Continued) E
n 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.05 0.57 1.18 0.00 0.00 0.00 0.00 0.10 0.00 - 7.00 0.00 0.00 0.00 0.00 - 0.23 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.50 0.00 2.65 2.65 3.20 0.00 0.00 0.00
W/mol)
Ref.
0.00
[601
0.00 0.00 0.00 0.00 0.00 0.00 0.00 12.55 0.00 6.24 6.24 6.24 6.24 6.24 4.18 3.32 0.00 0.00 27.70 0.00 13.72 11.56 - 1.87 170.10 48.80 37.00 325.91 44.36 0.00 11.56 0.00 34.46 10.47 0.00 58.28 131.36 37.41 0.00 0.00 382.44 345.03 384.04 315.89 278.00 25.50 25.50 22.17 12.89 19.60 - 3.70 -3.70 30.00 17.04 0.00 0.00
[471 [481 [471 [481 est., [61] est., 1471 est., [471 [361 [361 [621 [621 [621 1621 1621 [361 [471 t471 1361 1631 [481 1471 [471 [471 1471 [621 1471 [471
[641 [471 I471 [621 1621 [651 [661 [471 [471 t471 I481 t671 I671 I491 [681 t691 [621 [621 [701 [621 Dl 1621 [621 I491 t491 I481 [481
TABLE 1 Reaction Mechanism Rate Coefficients in the Form k, = AT”exp( -E/RT)
110. 111. 112. 113. 114. 115. 116. 117. 118.
CH,O + CH,O + CH,O + CH,OH CH,OH CH,OH CH,OH CHzOH
119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158.
CH, + H CH, + 0 CH, + OH CH, + HO, CH, + 0, C2H + H, C,H + 0 C,H + OH C,H + 0, C2H + CH, CHCO + H CHCO + 0 CHCO + OH CHCO + 0, CHCO + 0, CHCO + CH 2CHC0 CHCO + C,H, CHCO + M C20 + H c,o + 0 C,O + OH c*o + 0, C2H,+0 C,H, = 0 C,H, + OH C,H, + OH C,H, + OH C,H, + OH
159. 160. 161. 162. 163. 164. 165.
A (m3, kmol, s- ‘)
Reactions
No. OH 0, M + H + 0 + OH + O2 + M
CH,
CzH, + C2H, + C2H, + CHCOH CH,CO CH,CO CH,CO CH,CO CH,CO CH,CO C,H, +
0, 0, M + H + M + H + 0 + 0 + OH + CH, H
C,H, C,H, C,H,
+ H + 0 + OH
GH3
=
C,H, C,H, C,H,
+ CH + C,H + H
0,
CHZO + H,O CH,O + HO, CH?O+H+M CH,O + H, CH,O + OH CH,O + H,O CH,O + HO, CH,O + H + M CH, + H’s2 CH, + H, CH, + OH CH, + H,O CH, + H,O, CH, + HO, C,H, + H CO + CH CHCO + H 2C0 + H C,H, + H ‘CH, + CO 2C0 + H C,O + H,O 2C0 + OH CO, + CHO C,H, + CO C,H, + 2C0 C,H, + CO CH + CO + M CH + CO co + co CO + CO + H co + co + 0 3CH2 + CO CHCO + H C,H + H,O CHCOH + H CH,CO + H CH, + CO C,H + HO, CHCO + OH C,H + H + M CH,CO + H 3CH, + CO + M CH, + CO CO, +3CH2 CHCO + OH CHCO + H,O C,H, + CO CzHjf.’ C,H, + Hz CH,CO + H C,H? + H,O CH,O + CHO C,H, +3CH, C,H, + C,H, C2H3 + H,
k, = k, =
k, = k, =
1.800E + 6.6208 + 5.45OE + 3.000E + 4.210E + 2.410E + l.OOOE + 1.220E + 2.4OOE + 4.516E + 1.325E + 9.033E + 1.560E + 9.033E + 3.970E + 4.074E + 1.024E + 2.OOOE+ 3.520E + 2.410E + 1.5OOE + 9.640E + 3.0OOE + l.OOOE + l.OOOE + 5.0OOE + l.OOOE + l.OOOE + 6.000E + 5.0OOE -t 5.000E + 2.0OOE + 2.000E + 1.080E + 1.080E + 3.370E + 5.040E + 2.180E 4.830E 1.200E + 2.0OOE + 4.0OOE + l.OOOE + 3.600E + 1.800E + 1.750E + l.OOOE + 7.500E + 5.000E + 5.540E + 2.670E + 4.0OOE + 3.000E + 2.000E + 3.970E + 5.000E + 3.0OOE + 1.325E +
10 07 10 10 10 10 11 25 16 14 01 05 04 09 10 02 10 10 10 10 11 10 10 10 10 10 10 08 12 10 10 10 10 01 01 04 02 07 07 10 05 13 10 12 10 09 10 09 09 09 21 10 10 10 09 10 10 03
(Continued) E
n 0.00 0.00 0.00 0.00 0.00
0.00 0.00 - 4.00 0.00 0.00 3.00 1.56 1.83 0.00 0.00 2.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.80 2.80 2.00 2.30 4.50 4.00 0.0) 1.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 3.50 0.00 0.00 0.00 0.00 0.00 0.00 2.53
&J/mol) 0.00 10.89 56.50 0.00 0.00 0.00 21.00 133.42 438.98 379.95 33.63 35.50 11.64 103.09 238.03 0.84 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 12.55 246.10 0.00 0.00 0.00 0.00 2.08 2.08 58.58 56.48 -4.18 - 8.37 311.78 125.94 447.00 0.00 248.00 14.13 5.65 8.37 8.37 0.00 10.08 10.08 0.00 0.00 0.00 - 1.05 0.00 0.00 51.21
Ref. [481 [481 Lb21 121 [491 [491 [621 [621 [851 [471 [471 [471 [471 [471 [531 I471 [361 [361 [481 [471 [471 [361 est., [21 est., [2] [361 [361 1361 [711 [361 1361 [361 1361 est., [47] est., [471 1361 1361 [361 1361 1481 [361 PI [361 El [471 [361 [361 Ml [721 Ml [361 [361 1361 [731 [361 [361 [481
136
K. M. LEUNG AND R. P. LINDSTEDT TABLE 1 Reaction Mechanism Rate Coefficients in the Form k, = AZ’“exp(-E/RT)
(Continued)
A
Reactions
No.
166. 167. 168. 169. 170. 171. 172.
C,H, C,H, C,H, C,H, C,H, C,H,
+ + + + + +
0 OH M O? 0 M
173. 174. 17.5. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195. 196. 197. 198. 199. zoo. 201. 202. 203. 204. 205. 206. 207. 208. 209. 210. 211.
C,H, + H C,H, + 0 C,H, + OH C,H + 0 C,H + OH C,H + 0, c-C,H, + 0 c-C,H, + OH c-C,H, + 0, c-C3H, + M
CH, + CHO C,H, + H,O C,H, + H + M
C,H,O C,H,O C,H, + C,H, + C,H2 + C,H, + a-C,H, a-C3H, a-C,H, a-C3H, a-C,H, a-C,H, a-C,H, a-C,H, a-C3H, a-C,H, a-C3H, a-C,H, c-C3HI, c-C,H, p-C,H, p-C,H, p-C,H,
+ 0 + OH CH, CH, CH, CH, + H + H + H + 0 + OH + OH + 0, + CH, + C,H + a-C3H, + a-C3H, + M
212. 213. 214. 215. 216. 217. 218. 219.
p-C,H, p-C,H, p-C,H, p-C,H, p-C,H,
+ + + + +
0 0 0 OH OH
0
P-C,H,
+
0,
o
P-C,&
+
0,
P-C,&
+
CH3
0 0
C,H, + HO, CH, + CH,O C,H, + H + M C,H, + He,3
C,H,
C,H, C,H, C,H,
+ H + 0 + OH
C3H3
+
C,H,
(m3, kmol, s-
k, = k, =
C,H, + Hz C,H, + OH C,H, + Hz0 C,H + CO C,H, + CO CHCO + CO C,H + CO + H C,H, + CO + H C,H, + CO, C,H + H + M c-C3H2 + Hz C,H,O + H C,H,O + H, CH$O + CHO c-C,H2 + H + M C,H, + CO C,HO + CHO CH,CO + CHO a - C,H, + H p-C,H, + H a-C3HS s-C,H, t-C,H, a-C,H,
0,
+ M
C3HzO
C3H3
+
C,H, + CH,CO C,H, + C,H, + C,H, +
Hz
CHO + CH, H,O HO, CH,
C,H, + C,Hz a-C,H, + C,H, C3H3
+
C,H,
+
Hz
C,H, + H + M a-C3H, P-C,&
+ H + H + H
t-C,H, s-C,H, C3H3
CH,CO +3CH, C,H, + CHO CHCO + CH, CH,CO + CH, C3H3
+H@
CHCO +%H2 C,H, + HO, C,H, +CH,
+ OH
’1
1.325E + 1.570E + 2.600E + 1.020E + 6.620E + 2.000E + 8.850E + 4.900E + 1.445E + l.OOOE + 7.226E + 6.800E + 6.8OOE + 2.000E + 6.800E + 5.000E + 2.000E + l.OOOE + 5.000E + 1.400E + 2.000E + 3.000E + 2.000E + 8.500E + l.OOOE + l.OOOE + 6.7408 + 2.730E + 2.620E + 1.610E + 8.500E + 4.000E + 2.000E + l.lOOE + 3.120E + 1.445E + 4.000E + 2.000E + l.OOOE + 5.000E + 2.000E + 2.000E + 1.513E + 7.080E + 6.5OOE + 5.800E + 2.000E +
05 01 14 07 10 12 20 39 06 06 03 10 10 09 10 10 09 12 09 11 09 07 45 14 10 10 16 15 43 37 09 09 11 05 09 10 10 09 10 11 09 15 14 13 09 09 11
6.400E 3.200E 6.300E 5.000E 3.000E 2.000E 5.000E 2.000E
09 09 09 07 00 05 09 09
+ + + + + + +
n
-
-
-
E &J/m00
1.55 2.15 0.00 0.00 0.00 0.00 1.23 6.43 1.50 1.50 2.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8.50 0.00 0.00 0.00 2.08 1.96 9.82 8.58 0.00 0.00 0.00 4.61 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1.79 17.46 404.00 -9.14 0.00 125.00 427.70 448.40 31.01 24.28 3.62 0.00 0.0) 0.00 0.00 0.00 0.00 424.80 0.00 0.00 0.00 12.00 409.95 297.06 0.00 0.00 132.18 86.16 154.60 85.06 8.37 11.30 62.84 - 17.75 - 1.66 17.46 257.32 32.22 0.00 270.70 32.22 334.72 210.87 182.84 8.37 12.98 62.84
0.00 0.00 0.00 4.50 3.00 1.50 0.00 0.00
8.41 8.41 8.41 -4.18 0.84 125.94 213.38 32.22
Ref. 1481
[481 PI [471 I471 [I61 I61 [471 [471 [471 est. est. est. est., [741 est., 1361 est. est. est.
[751 est. 1761
I571 t771 est. est.
I661 I661 [661 [661 t791 I791 est., [801
I151 [151 [151 u51 [811 I811 [151 1151 t821 [831 is31 [781 [781 [801 [151 [151 1151 I151 1151 t151 I151 [811
KINETIC MODELING
OF ALKANE
137
DIFFUSION FLAMES TABLE 1
Reaction Mechanism Rate Coefficients in the Form ki = AT”exp( -E/RT)
220. 221. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233. 234. 235. 236. 237. 238. 239. 240. 241. 242. 243. 244. 24.5. 246. 247. 248. 249. 250. 251. 252. 253. 254. 255. 256. 257. 258. 259. 260. 261. 262. 263. 264. 265. 266. 267. 268. 269. 270. 271. 272. 273.
A (m3, kmol, s-l)
Reactions
No. p-C,H, + C,H p-C,H, + a-C,H, p-&H, + M a-C,H, + H a-C,H, + 0 n-C,H, + 0, a-C3H, + CH, a-CJH, + C,H, a-C,HS + C,H, 2u-C,HS s-C,H, + H s-C,H, + 0 s-C,H, + 0, s-C,H, + CH, s-C3H, + C,H, s-C,H, + C,H, t-C,H, + H t-C,H, + 0 t-C,H, + O2 K,H, + CH, r-C,H, + C,H, K,H, + C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H, C,H,
+ + + + + + + + + + + + + + +
GH, + C,H, n-C,H, + H n-C,H, + 0, n-&H, C,H, + H i-C,H, + H i-C,H, + 0, i-C,H, i-C,H,
C,H, C,H, C,H,
+ H + H + 0
+
C2H2
C3H3
+
C3Fi
C,H, + H + M a-C3H, + H, C,H, + CH,O C,H, + CH,O + OH a-C,H, + CH, a-C,H, + C,H, a-C3H, + C,H, a+H, + C,H, a-C$H, + H, CH,CO + CH, CH, + CHO + CHO a-C3H, + CH, a-C3H, + C,H, a-C3H, + C,H, a-C,H, + H, CHCO+CH,+H CH, + CO + CH,O a-C,H, + CH, a-C3H, + C,H, a-C,H, + C,H, C,H, + CH, a-C,H, + H s-&H, + H t-C,H, + H a-C,H, + Hz s-&H5 + H, t-C,H, + H, C,H, + CHO C,H, + CH,O 2CH, + CO a-C,H, + H,O s-C,HS + H,O t-C,H, + H,O a-C,H, + HO, s-C,H, + HO, t-C,H, + HO, a-C,H5 + CH, s-C,H, + CH, t-C,H, + CH, a-C3HS + C,H,
H H H 0 0 0 OH OH OH 02 02 02 CH, CH, CH,
C3W3
C3H3
C3H,
C,H, + HO, C,H, + CH, n-C3H, C3%
-
C,H, C,H, C,H, C,H,
+ + + +
HO, CH, H CH35
0 e 0
n-C,H7 + H, X,H, + H, n-C,H, + OH
k, = k, =
l.OOOE + 2.0OOE + 4.7OOE + 3.333E + 1.807E + 1.700E + 3.000E + 2.410E + 9.640E + 8.43OE + 3.333E + 1.807E + 4.335E + l.OOOE + l.OOOE + l.OOOE + 3.333E + 1.807E + 4.335E + l.OOOE + l.OOOE + l.OOOE + l.lOOE + 4.500E + 7.590E + 1.450E + 1.728E + 4.65OE + 8.036E + 5.219E + 3.484E + 6.960E + 3.120E + l.llOE + 2.138E + 1.950E + 2.0OOE + 2.000E + 2.216E 8.420E 1.351E 2.220E 2.000E + l.OOOE + 3.0OOE + 7.230E + 2.000E + l.OOOE + 2.000E + 6.300E + l.lOOE + 7.828E + 1.3OOE + l.OOOE + 3.000E +
10 09 15 09 11 09 09 09 08 07 09 11 08 08 08 08 09 11 08 08 08 08 21 14 14 15 02 02 02 04 04 04 03 03 03 09 10 10 03 04 03 03 10 09 14 09 10 09 10 13 17 15 11 11 10
(Continued) Ref.
n 0.00 0.00 0.00 0.00 0.00 0.00 - 0.32 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 1.20 0.00 0.00 0.00 2.50 2.50 2.50 1.57 1.57 1.57 2.00 2.00 2.00 0.00 0.00 0.00 3.50 3.50 3.50 3.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 32.22 334.72 0.0) 0.00 0.00 - 0.55 0.00 - 0.55 - 1.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 408.84 371.96 423.84 410.28 10.42 40.98 51.39 - 2.63 - 2.63 - 2.63 - 1.25 6.07 11.62 163.18 199.16 184.10 23.74 48.77 53.76 27.77 0.00 20.90 138.10 12.14 0.00 12.50 123.43 154.39 353.10 271.87 40.60 34.90 24.10
WI 1151 1821 D51 [841 est.
[511 [511 [511 [511 1151 [151 est., 1151
WI [I51 [151 [I51 [I51 est., [15]
[I51 D51 [I51 [511 [151 1151 [151 [511 [511 [511 D51 D51 est., [15]
[511 [511 [511 D51 1151 D51 [511 [511 [511 [511 [I61 M
[161 [511 [161
[161 [I71 [I71 B51
[I61 [I61 [161
138
K. M. LEUNG AND R. P. LINDSTEDT TABLE 1 Reaction Mechanism Rate Coefficients in the Form ki = AT”exp( -E/RT) A (m3, kmol, s- ’)
Reactions
No.
274. 27.5. 276. 277. 278. 279. 280. 281. 282. 283. 284. 285. 286. 287. 288. 289. 290. 291. 292. 293. 294. 295. 296. 297. 298. 299. 300. 301. 302. 303.
C,Hs C,Hs C,Hs C,H, C,Hs C,H,
+ + + + + +
CzH,
+ CzHz
C2H2
+
304. 305. 306. 307.
n-C,H, n-C,H3 I-C,H, I-C,H,
308. 309. 310. 311. 312. 313. 314. 315. 316. 317.
i-C,H, I-C,H, i-C,H, i-C,H,
C,H, C,H, + H C,H, + 0 C,H, + OH C,H, + C,H (1,2)-C,H,
CH,CO + C,H C,H, + H,O CH,CO + C,HO i-&H, + H n-C,H3 + H, a-C3H, + CO n-C,H, + H,O i-C,H, + C,H, C,H, + H*
318. 319. 320. 321.
(1,2&H, (1,2)-C,H, (1,2&H, (1,3)-C,H,
GH, + H2 C,H, + H,O (1,3)-C,H, C,H, + H*
322. 323. 324.
(1,3)&H, (1,3)-C,H, (1,3)-C,H,
0 OH OH CH, CH, C,H, CzHz
i-C,H, n-C,H, i-C,H, n-C,H, i-C,H, r&H3 i-C,H, GH2
c-C,H, +3CH2 C,H, + CH C,H, + CH C,H, +3CH2 C,H + C2H2 C,H + C,Hz C,H + C,H2 2C,H C,H + H, C,H + C,H2 C,H + C,H2 GH2
+ OH + H,O + H,O + CH, + CH, + H + H +
H2
i-C,H, + H n-C,H, + H I-C,H3 + H C,H4 + H C,H2 + H C,H2 + H C,H2 + H C,H + H C,H, + H C,H, + H C,H, + H C,H + H
GH,
+
C,Hz
C,H2
+
C4H2
+
C,Hz
C,H2
+ 2H
C2H2
+
GH2
C&2
+
C2H2
+
C,H2
C,H,
+ 2H
C2H2
+
C,H2
C,H2
+
C2H2
+
C&2
C,H2 CO + C,H,O C,H, C,H,
+ 2H C,H, + H + 2C0 + H + H* k, = k, =
C,H2
+
C,H2 r&H, C,H,!
+ H,O
C,H2
+
C,H, + 0 C,H, + OH C,H,O + OH n-C,H, + H + OH
+ + + +
H 0 OH O2
+ H + OH
+ H + OH
H2
H2
H2
H2
+ H*
k, = k, =
H2
C2H3
+
C2H2
C,H,
+
H2
C,H,
+ H,O
k, = k, =
k, = k, =
2.600E + 5.750E + 4.786E + 9.OOOE1.510E l.OOOE + 2.000E + 1.513E + 3.000E + 7.000E + 7.OOOE+ 4.000E + 1.200E + 1.200E + 1.200E + l.OOOE + 4.074E + 1.200E + 1.200E + 7.800E + 1.513E + 1.513E + 1.513E + 1.513E + 1.513E + 1.513E + 2.800E + 6.680E + l.OOOE + l.OOOE + l.OOOE + 5.000E + 3.000E + 1.500E + 1.000E + 2.000E + 5.000E + 2.000E + 3.0OOE + l.OOOE + 8.630E + 2.OOOE+ 3.000E + l.OOOE + 3.980E + l.OOOE + 2.OOOE+ l.OOOE + 2.OOOE+ 1.500E + l.OOOE + l.OOOE + 2.000E + l.OOOE + 2.000E +
10 05 05 04 03 09 09 10 10 10 10 10 11 11 11 11 02 11 11 14 10 11 10 11 10 11 10 09 12 14 11 10 10 13 14 12 10 10 10 09 09 04 10 04 10 14 12 11 04 13 14 11 12 11 04
(Continued) E
n
0.00 1.40 1.40 3.65 3.46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.00 0.00 2.00 0.00 0.00 0.00 0.00 2.00 0.00 0.00 0.00 0.00 0.00 2.00
&J/m00 18.70 3.56 3.56 29.93 22.93 276.14 268.00 178.66 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.84 0.00 0.00 502.08 178.66 234.30 178.66 234.30 178.66 234.30 7.23 - 1.72 0.00 150.62 125.52 0.00 0.00 283.26 230.12 200.83 0.00 0.00 0.00 0.00 246.86 25.17 7.57 12.60 0.00 209.20 175.73 0.00 4.18 283.26 154.81 125.52 192.46 0.00 4.18
Ref.
[I61 [861 [861 [501 [501 [871 [SSI 1531 [361 [361 [361 [361 1531 1531 [531 [531 1531 [531 1531 [891 [531 [531 t531 1531 1531 [531 [901 [911 [921 t361 est., 1361 est., 1361 est., [541 [361 [361 [361 [361 [361 [891 est., [361 [901 est., t361 [931 est., [361 est. est., [361 t541 [361 est., t941 est. [361
KINETIC MODELING
OF ALKANE
139
DIFFUSION FLAMES TABLE 1
Reaction Mechanism Rate Coefficients in the Form ki = AT”exp( -E/RT)
325. 326.
i-C,H, i-C,H,
327. 328. 329. 330. 331. 332. 333. 334. 335. 336. 337. 338. 339. 340. 341. 342. 343. 344. 345. 346. 347. 348. 349. 350. 351. 352. 353. 354. 355. 356. 357. 358. 359. 360. 361. 362. 363. 364. 365. 366. 367. 368. 369. 370. 371. 372. 373. 374.
i-C,H, + H i-C,H, + OH (1,2)-C,H, (1,2&H, (1,2)-C,H, + (1,2)-C,H, + (1,2)-C,H, + (1,2)-C,H, +
376. 377. 378.
A (m”, kmol, s-l)
Reactions
No.
e w
C,H, + H,O C,H, -t CH, i-C,H, + H H H OH CH,
C2H3
+
C3H3
+
C3H3
C,H,
+
C&3
C,H, (1,3&H, (1,3)-C,H, (1,3&H, (1,3)-C,H, (1,3&H, (1,5)-C,H, (1,5)-C,H, (1,3)-C,H, (1,5)-C,H,
+ H + 0 + OH
+ H + 0 + OH
C,H,
C,H,O (1,3)-C,H, + (1,3)-C,H, + (1,3)-C,H, + (1,3)-C,H, + (1,3)-C,H, + c-C,H, (1,3)-C,H, (1,2)-C,H, CO + C,H, I-C,H, + H (1,2&H, (1,5)-C,H, (1,2,4,5&H, l-&H, (1,3)-C,H, l-C,H, I-C,H,
C,H, + a-C3H, n-C,H, + C,H, C,H, + C,H3 (1,3)-C,H, + C,H, C,H, + H C,H; + 0 C,H, + OH I-C,H, + H I-C,H, + 0 I-C,H, + OH
+
(1,2)-C,H, + (1,2)-C,H, + (1,2)-C,H, + (1,3&H, i-C,H, + H (1,3)-C,H, + C?H, + C,H,
C,H,O C,H, + C,H, C3H3
k, = k, =
C,H, + H,
2C,H, (1,3&H, (1,3)-C,H, + H (1,3)-C,H, + H (1,3)-C,H, + 0 (1,3)-C,H, + OH (1,3)&H, + 0, (1,3)-C,H, + C,H, (1,3)-C,H, + CH, (1,3&H, + C,H, ‘CH2 + p-C,H, c-C,H, c-C,H,
C3H3
(1,3)-C4H, C,H, + H*
-
C&
0 0
C,H,+OH C,H, +H,O
a 0 0 0 0 0 w = 0 0 Q 0 0 0 =
GH, + Hz C,H,+OH C,H, +H,O I-C,H, I-C,H, + H I-C,H, + H, I-C,H, + OH I-C,H, + H,O (1,5)-C,H, I-C,H, + H I-C,H, + H, I-C,H, + OH f-&H, + H,O (1,3&H, C,H, +H C,H,+H, C,H, + OH C,H, + H,O C,H,O + OH
C,H, C,H, C,H, C,H, C,H,
+ H + 0 + OH
t, 0 t)
C,H,
+ HO>
e
+ H2
H, H,O CH,
H,
H,O HO, C2H, CH, a-C3H,
1.500E + l.OOOE + 2.000E + l.OOOE + 2.0OOE + l.OOOE + 4.2OOE + 4.000E + l.OOOE + 1.620E + 7.000E + 2.0OOE + 4.200E + 6.3OOE + 5.0OOE + 6.020E + 8.430E + 4.000E + 6.310E + 7.000E + l.OOOE + 1.800E + 3.OOOE+ 3.000E + 1.090E + l.OOOE + l.OOOE + l.OOOE + l.OOOE + 3.000E + 4.120E + 3.000E + 1.724E + l.OOOE + 2.0OOE + 2.000E + l.OOOE + 2.000E + 2.000E + l.OOOE + 2.500E + l.OOOE + 2.000E + 2.000E + l.OOOE + 6.0OOE + l.OOOE + 2.000E + 2.000E + 4.000E + 3.000E + 1.5OOE + 2.000E + 2.0OOE + 5.000E +
13 14 12 11 04 12 15 08 11 10 10 10 15 07 08 05 09 10 10 10 10 11 13 13 16 10 10 10 10 08 03 08 03 11 10 10 11 10 10 12 58 11 10 10 11 11 11 10 10 13 13 11 10 10 10
(Continued) E
II 0.00 0.00 0.00 1.00 2.00 0.00 0.00 0.00 0.0) 0.00 0.00 0.00 0.00 0.70 0.00 1.45 0.0) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.65 0.00 1.79 0.00 0.00 0.00 0.00 0.00 0.00 0.00 - 13.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
W/mol) 283.26 209.20 175.73 0.00 4.18 248.95 387.10 0.00 60.67 0.00 0.00 0.00 414.21 25.10 0.00 3.59 - 3.66 242.00 60.68 1.20 75.31 0.00 177.00 183.00 305.43 0.00 0.00 0.00 0.0) 12.55 10.46 12.55 9.38 0.00 0.00 0.00 0.00 0.00 0.00 138.07 208.36 0.00 0.00 0.00 0.00 188.00 0.00 0.00 0.00 305.12 372.38 0.00 0.00 0.00 4.18
Ref. est., [54] [361 est. est., 1361 [541 est., 1941 [541 [541 [951 est., [541 1871 est., 1941 [961 1521 [971 [981 est. 1521 est., 1541 est., [54] est., 1991 DO01 DO01 DO11 est. est., 1341 est., [34] est., 1341 [331 [331 1331 1331 est. est. est. est. est. est. est. [lo21 est. est. est. est. est. est. est. est. 1471 est. est. est. est. [191
K. M. LEUNG AND R. P. LINDSTEDT TABLE 1 Reaction Mechanism Rate Coefficients in the Form 5 = AT”exp(-E/RT)
319. 380. 381. 382. 383. 384. 385. 386. 387. 388. 389. 390. 391. 392. 393. 394. 395. 396. 397. 398. 399. 400. 401. 402. 403. 404. 405. 406. 407. 408. 409. 410. 411. 412. 413. 414. 415. 416. 417. 418. 419. 420. 421. 422. 423. 424. 425. 426. 427. 428. 429. 430. 431. 432. 433.
A (m3, kmol, s- ‘)
Reactions
No.
C,H,O + 0 K&4.5)-C,H, (M&H, Fulvene Fulvene Fulvene (1,3&H, (1,3&H,
Cd& + 02
(IS&H, (1,2,4,5)-C& (1,2/WC&I, WC,H, (1,2&H, (1,2)-C,H, Fulvene (1,3)-C,H, Fulvene (l,S)-C,H, U,2)-C,H, (1,5&H, (l,S)-C,H, (l,S)-C,H, (1,2)-C,H, (1,2&H, (1,2)-C,H, (1,3)-C,H, (1,3&H, (1,3)-C,H, C,H, C,H, C,H, C,H, C,H, C,H,
+ + + + +
+ + + + + + + + +
H 0 OH H 0 OH H 0 OH
H 0 0 OH OH
C,H, + 02 C,H, + CH, C,H,O + H C,H,OH -t C,H, C,H,OH + H C,H,OH + 0 C,H,OH + OH C,H,O C,H, + H Cd7
a-C,HS C,H, + C,H, + C,H, + C,H, + C,H, tC,H, + C,H, + C,H, + C,H, +
+ C,H, H 0 0 OH HO, H 0 OH HO,
C,H,
+
02
C,H,
+
02
VW C&OH C&W C,H, C,H,
C,H,
+ C,H,
C,H, CA (1,5)-C,H5 (1,5)-C,H, (1,5)-C,H, (1,5&H, (l,S)-C,H, (1,5&H, (l,S)-C,H, (l,S)-C,H, (1,3)-C,H, (1,3&H, (1,3&H, C,H, + H CA + C,H,OH C,H, + C,H, + C,H,OH C,H, + C,H, + C,H,OH C,H,O C,H,O C,H,O C,H,O C,H, +
+ + + + + + + + + + +
H H Hz OH H,O H, HO H,O H, OH H,O
H2
OH H,O + H HO, CH, + C,H, + H, + OH + Hz0 CO
GH7
I-C,H, C,H, + H C,H, (1,3)-C,H,
+ CO
CsH,O C,H,OH + H C,H,O + OH C,H, + Hz C,H, + OH C,H, + Hz0 C,H, + H,O, C,H, + HO, C,H,O + OH (1,3)-C,H, + CO C,H,O -t H C,H, + C,H, + CO I-C,H, l-C,H, I-CsH,
2.090E + 5.400E + 5.000E + S.OOOE+ 4.260E + S.OOOE+ l.OOOE + l.OOOE + 5.000E + 7.580E + 1.400E + 7.OOOE+ l.OOOE + 2.000E + 2.000E + l.OOOE + 2.000E + 2.000E + l.OOOE + 2.000E + 2.000E + 4.570E + 2.SlOE + 2.400E + 2.000E + 1.630E + 1.320E + 6.300E + 4.365E 2.530E + 2.67OE + 1.150E + 2.810E + 6.000E + 4.500E + 4.040E + 3.020E + 4.000E + l.OOOE + l.OOOE + l.OOOE + 3.000E + 3.OOOE+ 2.190E + 1.810E + 3.430E + 1.990E + 2.000E + l.OOOE + 2.510E + 2.100E + l.OOOE + l.OOOE + l.OOOE + l.OOOE +
09 11 11 11 13 11 12 13 11 13 15 14 11 10 10 11 10 10 11 10 10 13 11 10 10 OS 10 10 07 11 11 11 10 09 11 10 14 11 11 11 10 10 10 05 10 06 09 10 10 11 13 15 14 14 06
(Continued)
n
E (kJ/mol)
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.42 0.00 0.00 5.00 0.00 0.00 0.0) 0.00 0.00 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 0.00 1.77 0.00 1.18 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
31.25 149.66 92.30 132.40 206.00 144.00 224.00 342.00 200.00 309.00 326.60 326.60 0.00 0.00 0.00 0.00 0.00 0.00 46.00 0.00 12.60 372.38 66.94 19.54 61.52 6.07 44.31 251.04 51.46 0.00 105.55 51.88 30.76 0.00 183.74 18.04 209.20 104.14 0.00 0.00 0.00 0.00 0.00 12.55 12.89 - 1.87 48.78 104.60 86.66 183.68 200.83 326.35 235.00 334.00 0.00
Ref. 1191 1351 est., [371 est., [37] est., est., est., est.,
[371 [37] [37] [37] [371 [371 est. est. est. est. est. est. est. est. est. est. est.
11031 DO41 DO51 t1051 [471 1471
[201 hod 1471 [lo71 DO1 r201
[201
est., [lo81 1471 DO91 [Sll DO1 PO1 [191 DO1 DOI
[201 WI t201 t201 [201 [191 BOI DOI
1201 est. est. est., [341
KINETIC
MODELING
OF ALKANE
DIFFUSION
141
FLAMES
TABLE 1 Reaction
Mechanism
No.
Rate Coefficients
in the Form
Reactions
434. 435. 436. 437. 438. 439.
I-C,H, I-C,H, I-C,H, I-C,H, K,H, I-C,H,
+ + + + + +
H H 0 OH H 0
= 0 = e 0 0
440. 441. 442. 443. 444. 445. 446. 447. 448. 449. 450. 451.
I-C,H, + OH l-C,H, + Oz I-C,H, + H I-C,H, + OH I-C,H, + H I-C,H, + H I-C,H, + 0 I-C,H, + OH I-C,H? + OH C,H, +‘CH, C,H, +3CH, C,H,+CH
0 0 0 0 0 0 0 0 0 0 0 0
k, = AT”exp(
(m3,
I-C,H, I-C,H, C,H,O I-C,H, I-C,H,
+ Hz + C,H, + H + H,O + H,
i-C,H, + CO I-C,H, + H,O C2H3 + C,HO I-C,H, + H, I-C,H, + H,O I-C,H, I-C,H, + H, i-C,H, + CO I-C,Hz + H,O C,H, + CHO l-C,H, + H I-C,H, + H I-C,H, + H
+ CHO
-E/RT) (Continued)
A kmol, s- ‘)
n
E W/m00
l.OOOE+ l.OOOE+ 2.000E + l.OOOE+ l.OOOE+
10 09 10 10 10
0.00 0.00 0.00 0.00 0.00
0.00 0.00 126.00 0.00 0.00
l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE l.OOOE 3.000E 1.3OOE l.OOOE
11 10 09 10 10 10 10 11 10 09 10 10 11
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 155.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 18.10 0.00
+ + + + + + + + + + + + +
Ref. est. est. est. est. est. est. est. est. est. est. est. est. est. est. est. [361
[361 [361
** All third-body
collision efficiencies are equal to 1 unless otherwise stated. * Reaction in Lindemann form. a Enhanced Collision Efficiencies: H,O = 6.5:0, = 0.3:CO = 0.7:C02 = 1.5:N, = 0.4 h Enhanced Collision Efficiencies: H,O = 12.0:H, = 2.5:CO = 1.9:C02 = 3.8 ’ Enhanced Collision Efficiencies: H,O = O.O:H, = O.O:CO, = 0.0 d Enhanced Collision Efficiencies: H,O = 4.0:N, = 0.4:CO = 0.4:CO, = 0.4:CH, = 0.7:C,H, = 5.0:C,H, = 2.2 e Enhanced Collision Efficiencies: H,O = 5.7:0, = 1.9:CO = 1.9:C02 = 3.3:H, = l.l:N, = 1.6 I Enhanced Collision Efficiencies: H,O = 5.O:CO = 2.O:CO, = 3.0:H, = 2.0 ’F, = 0.38 exp( - T/23) + 0.63 exp( - T/ 1180). ‘F, = 0.31 exp( - T/90) + 0.69 exp( - T/2210). ‘F, = 0.4761 exp(-16182/T) + exp( - T/3371). ’ log(k/k,) = -0.349 + 1.349E - 3*T - 1.408E - 06*T* + 2.132E - lO*T’. 5 F, = 0.76 exp( - T/38) + 0.24 exp( - T/1946).
present study with a sensitivity fined as
coefficient
de-
= 1.4:CzH,
of these species towards the rate of reactions in the mechanism and the uncertainty in rate constants of these reactions is also assessed.
X = In(Y,/Y,)/ln(S). 4.1. Reaction Paths for C, Species In the above expression Y0 is the computed peak concentration of a particular species using the rate constants as shown in Table 1. Similarly, Y, is the peak concentration of the same species computed at the same condition but with the rate coefficient of a certain reaction k increased or decreased by a factor of 5. The following paragraphs focus on the main formation and consumption paths for the intermediate species of interest in propane-air diffusion flames. The sensitivity of predictions
Computational results show that propane consumption mainly occurs through thermal decomposition and reactions with H radicals. Reactions with 0 radicals are insignificant due to low concentrations in the fuel-rich pyrolysis region. Abstraction by CH, and OH radicals consumes only around 15% of the fuel at a strain rate of 600 s- ’ and less than 7% at strain rate of 50 s- ’. The most important fuel breakdown reactions can therefore be summa-
142
K. M. LEUNG AND R. P. LINDSTEDT TABLE II Thermodynamic Data for C, Ah; W/mole)
Species H OH 0
217.999 39.343 249.170 12.552 0.00 - 241.826 - 136.310 0.00 - 110.530 -393.510 0.00 597.360 42.00 424.732 390.417 - 108.580 146.858 16.318 - 8.900 - 200.940 - 74.600 566.932 161.084 227.400 -51.871 93.186 299.740 52.294 118.658 - 83.863 684.084 477.000 346.000 190.920 185.431 276.991 112.968 161.921 270.704 255.224 20.413 100.500 93.286 - 103.854
HO, HZ Hz0 H@, 0, co co2 N2
CH CHO ‘CH, ‘CH, CH,O CH, CH,O CH,OH CH,OH CH, C2H
CHCO C2H2
CHrCO CHCOH C2H, C2H4 C2H5 C2H.s C3H C3H2 WI3
a-C,H, p-C3H4
b-C,H, C,H,O a-C,H, s-C,H, t-C,H, C3H6 nC,H,
i-C,H, C3H,
So (J/mole) 114.718 183.737 161.060 229.106 130.679 188.829 234.527 205.144 197.657 213.787 191.607 183.037 224.345 166.716 194.899 218.764 193.965 229.390 243.919 239.810 186.371 213.304 246.674 200.917 241.923 249.142 233.953 219.180 247.119 229.080 226.742 235.308 253.300 243.431 248.298 243.616 301.917 258.738 275.474 277.608 266.538 289.465 289.341 270.182
rized as
(270)
Reference
HlOl
11101 11101 HlOl [1101 HlOl HlOl HlOl ill01 DlOl [1101 [1101 11101
[1101 MO1 t1101 HlOl [1101 [1101 t1101 [1101 [531,[1101 DlOl HlOl HlOl [1101 11101 [1101 DlOl [1101 DlOl [651 t1101 [1101 [1101 D101 est., [112] est., [36] est., [361 est., [36] [1101 [1101 [1101 11101
C, species
Species C4H C4H2
n-C,H, I-C,H, C4H4 W)-C,H,
(1,3)-C,H, I’-C,H, (1,2)-C,H, (1,3)-C,H, c-C,H, C4H60 C6H2 WI2 C6H3
I-C,H, c-C,H, C6H5 C6H50 C6H6
C,H,OH C,H,
I-C,H, (1,5)-C,H, (1,2)-C,H, (1,31-C,H, (1,2,4,51-C,H, CM)-C,H, fulvene (1,3)-C,H, (1,5)-C,H, C5H6 C5H5 C5H50 C5H40
C,H,OH I-C,H, I-C,H, I-C,H, I-C,H, C5H2
Ah; (kJ/mole)
803.328 464.424 523.380 476.976 280.328 302.184 345.157 330.157 164.593 108.983 243.509 - 103.763 700.820 934.287 663.164 514.632 481.160 328.456 47.716 82.811 - 96.375 200.589 389.150 414.300 410.100 334.550 394.969 334.400 218.500 542.664 588.270 134.300 266.102 103.300 17.363 87.446 249.366 374.468 435.136 566.513 691.615
So (J/mole)
254.638 255.977 272.922 273,550 278.654 289.212 288.540 283.217 291.618 278.191 289.951 333.046 299.190 347.690 319.323 321.331 291.093 288.337 307.816 269.065 314.864 305.835 353.270 340.300 339.197 332.800 328.900 299.993 299.993 332.335 339.197 274.154 279.485 307.805 280.872 310.016 320.494 318.109 293.298 295.139 266.521
Reference
t1101,D111 t531,DlOl [1091,[llll [531,ml1 1531, D111 [I101 DlOl t1101 DlOl [1101 [lOOI est., 11121 [1101 [1101 t1131 [W [1101 DlOl DlOl [1101 t1101 DlOl [1101 est., [37] est., [371 est., 1371 est., [37] est., [371 est., [371 W31 [361,[1101 [1101 [1101 um 1201 11101 est., [112] [361,[I121 est., [1121 11131 ill31
with secondary channels provided by
C,H, = C,H,
(271)
C,H, + H = n-C,H,
(272)
C,H,
+ CH,,
(275)
C,H, + OH = n - C,H, + H,O,
(276)
C,H, + OH = I’-C,H, + H,O,
+ H,,
(277)
C,H, + CH, = n-C,H,
+ H = I’-C,H, + H,,
(278)
C,H, + CH, = I’-C,H, + CH,.
+ CH,,
KINETIC
MODELING
OF ALKANE
DIFFUSION
lc shows that the computed ethylene concentrations are also sensitive to the rate of reactions 270-272 and 277. The major product of ethylene consumption in diffusion flames is acetylene and a similar sensitivity to the above, reactions in the computed acetylene concentrations can be observed in Fig. Id. Ethane and methane are formed mainly through the recombination of methyl radicals in the fuel-rich region. The methyl radical is a primary pyrolysis product of propane and n-propyl radicals and the predictions for ethane and methane concentration are sensitive to reactions 270-272 as shown in Figs. lb and le. Figure le also shows that the predicted methane concentration is sensitive to the rate constants of reaction 277 and 278 which produce methane directly from propane through H atom abstraction. Rate constants of the propane consumption reactions reported in the literature [16-18, 50, 1181 are somewhat scattered. There are differences not only in reaction rates for hightemperature conditions but also in their rela-
The formation of C,H, and C,H, and the regeneration of H and CH, radicals are the result of the alkyl radical decomposition reactions, (171)
C,H,
= C,H,
+ H,
(264)
n-C,H,
= C,H,
+ CH,,
(269)
X,H,
= C,H,
+ H.
143
FLAMES
Analysis shows that the decomposition reactions are not the rate-limiting steps in the present mechanism. Therefore the product distribution of intermediate species is dependent on the relative formation rate of the n- and iso-propyl radicals. The sensitivity analysis, see Fig. la, shows that the computed peak concentration of propene is sensitive to the rate constants of reactions 272 and 278 which produce the iso-propyl radical and to the competitive reaction 271-forming the n-propyl radical. Ethylene is mainly produced through the decomposition of ethyl and n-propyl radicals. Figure
Logarithmic Response Sensitivity In(Y,r/,)/in(5.0)
-0.5
(a) I
R03 R84 Fill9 RI65 RI91 R192 R242 R243 R246 R247 R248 R264 R265 R270 R271 R.272 R.275 R276 R277 R270
0-N 0.5
0.0
I ; I 6 4 ; 9: - s; b I
-0.4
1
-
-
,
R03 R&I R85 R119 R165 Al73 R193 R242 R246 R247 R248 R264 R265 R270 R271 R272 R275 A276 R277 R278
0.0 I
% 0 -w ( ) 9 ; + P 4
(4
(c) 0.4 1
-0.2
0.0
0.2
( (
-
!
-
; 4 8
-
i
-
;
-
-
R83 R84 Rll8 Rl19 R142 RI43 R165 .-R167 R173 R242 A246 R264 R265 -
-
R270 y;
& - c?
R275 R276 R277 R278
-
-
-
-
f
-
-0.2 R83 R118 Rl19 R142 R143 R146 R165 R167 R173 Rl91 Rl92 R193 R194 R242 R246 R247 R248 R270 R271 R272
0.0 I
; / ; - & P $ ; ; q f I
(e) 0.2
-
-
-
-0.2 R83 R04 R85 Rll8 R119 R142 R143 R165 R173 R193 R242 R246 R265 R270 R271 R272 R275 R276 R277 R278
-
0.0 , 9
0.2
s
-
; 63
-
;
-
4
-
]I
-
(
-
I
Fig. 1. Logarithmic response sensitivities computed using the detailed mechanism for the maximum concentrations of (a) C,H,, (b) C,H,, (c) C,H,, (d) C,H, and (e) CH, in counterflow propane-air diffusionflames. The light bare represent the sensitivities for the rate coefficients increased by a factor of 5. The dark bars represent the sensitivities for the rate coefficients decreased by a factor of 5.
144 tive importance for propane consumption. The rate constant for the thermal decomposition reaction of propane has received a number of studies [118-1231. Among the rate constants reported in the literature [16-l& 50, 1181 there is still disagreement around a factor of ten at a temperature of 1600 K which is the temperature of the region in the flames where the propane consumption rate is highest. The major difficulties in the evaluation of the rate expression for this reaction are caused by its pressure dependence and the influence of secondary chain decomposition reactions. Comparison of computed intermediate species profiles with measurements indicates that a comparatively slow rate for reaction (270) is favoured to reduce excessive levels of intermediate species. Thus the pressure dependent rate of Baulch et al. [851 was adopted for reaction 270. This results in a rate 14 times slower at 1600 K compared with the highpressure limit suggested by Tsang t.501. As discussed above the relative formation rate of n-propyl and iso-propyl radicals also affects the distribution of ethylene and propene in propane-air diffusion flames. However, the ratio between the rates of reactions 271 and 272 reported in the literature [16-l& 50, 1181 varies from 0.44 [18] to 3 [17, 1181 at 1600 K. Computational results indicate that a ratio of 1.8 between the rates of reactions 271 and 272 does reproduce the measured distribution of ethylene and propene. The suggestion of Warnatz [16] was adopted for reactions 271 and 272 but with the rate constants of reaction 272 decreased by a factor of 2 to give better agreement with propene profiles. Rate constants suggested by Tsang [50] for the abstraction reactions 277 and 278 are slower by a factor of 3 compared to other suggestions [17, 18, 1181 but were used in the present mechanism to reduce overpredictions of methane concentrations. Among the various propene consumption reactions considered in the present mechanism, it was found that reactions with the H radical are the dominant consumption paths. Reactions with CH, and OH radicals account for less than 15% of propene consumption. Propene is either consumed by H-atom abstraction reaction to form isomers of the C,H,
K. M. LEUNG
AND R. P. LINDSTEDT
radical or addition reaction to produce n-propyl radical. (246)
C,H,
+ H = a-C,H,
+ H,,
(247)
C,H,
+ H = s-C,H,
+ H,,
(248)
C,H,
+ H = t-C,H,
+ H,,
(265)
C,H,
+ H = n-C,H,.
The C,H, isomers considerd in the present mechanism are ally1 (CH,CHCH,), l-methyl vinyl (CH ,CCH,) and 2-methyl vinyl (CH,CHCH) radicals. They are coded as aC,H,, t-C,H,, and s-C,H, respectively. Reaction 246, which produces the ally1 radical, is the major abstraction reaction. Since the npropyl radical quickly decomposes into C,H, and CH, via reaction (2641, the balance between abstraction and addition reactions is important for the relative balance of the C, and C, chains in the consumption of propene. Significant sensitivity of the computed propene concentrations to the rates of these reactions can be observed in Fig. la. Computational result with rate constant listed in Table 1 indicate that about 90% of propene consumption goes through the C, chain. The effect of two thermal decomposition reactions of propene was also investigated. (243)
C,H,
= a-C,H,
(242)
C,H,
= C,H,
-t H, + CH,.
A wide range of rate constants for these reactions has been reported in the literature [51] and suggestions differ by up to two orders of magnitude, predominantly due to the pressure dependence. Previous modeling work [16-181 has used the high pressure limit rate expressions for these reactions. However, Rao and Skinner [124] have suggested that these reactions are in the intermediate fall-off region under combustion conditions. In the present mechanism the rate expressions proposed by Tsang [51], which agree very well with the results of Rao and Skinner 11241, have been used. Computational results show that reactions 242 and 243 only account for a small fraction of propene consumption in propaneair diffusion flames.
KINETIC
MODELING
OF ALKANE
DIFFUSION
Thermal decomposition reactions constitute the dominant consumption paths for the C,H, radicals. Ally1 and 2-methyl-vinyl radicals mainly decompose to form C,H, and CH, via the reverse of reaction 193 and 194. The decomposition of the l-methyl vinyl radical has been assumed to yield both allene and propyne. (-193)
a-C,HS = C,H,
+ CH,,
(-194)
s-C,HS = C,H,
+ CH,,
(-195)
t-C,H,
= a-C,H,
+ H,
(-196)
a-C,HS = a-C,H,
+ H,
c-209)
t-C,H,
=p-C,H,
+ H,
C-210)
s-C,H,
=p-C,H,
+ H.
Due to the fast decomposition of a-C,H, and s-C,H, to the &-chain, only 30% of C,H, radical consumption produces C,H, isomers. However, this is compensated by the fast insertion reaction of ‘CH, into C,H,. Here this insertion reaction has been postulated to produce the propargyl radical and cyclopropene as discussed below. (53)
‘CH, + C,H,
= C,H,
+ H,
(54)
‘CH, + C,H,
= c-C,H,,
(207)
c-&H,
= a-C3H,,
(208)
c-&H,
= p-C,H,.
Allene and propyne are mainly consumed by H, OH, and CH, abstraction reactions to form the propargyl radical. (197) (200) (202) (211) (216) (219)
a-C,H, a-C,H, a-C,H, p-C,H, p-C,H, p-C,H,
+ H = C,H, + OH = C,H,
+ H,, + H,O,
+ CH, = C3H, + CH,, + H = C,H,
+ H,,
+ OH = C,H,
+ H,O,
+ CH, = C,H,
+ CH,.
Propargyl is subsequently consumed through reactions with H, 0, and OH radicals to form cycle-propenylidene (c-C,H,) and propynal (C,H,O). Computational results show that these consumption channels proceed with comparable rates. Cyclopropenylidene is mainly
145
FLAMES
consumed through reaction with the OH radical, whereas propynal decomposes quickly to form acetylene. (183)
C,H,
+ H = c-C,H,
+ H,,
(184)
C,H,
+ 0 = C,H,O
+ H,
+ OH = C,H,O
+ H,,
(185)
C,H,
(1801 c-C,H,
+ OH = C2HZ + CO + H, C,H,O
(188)
= C,H,
+ CO.
There are considerable uncertainties in many of the above reactions due to the lack of direct measurements of rate constants and product channels. While the propargyl chemistry is too minor to have any significant effect on the overall flame structure, it is of paramount importance to benzene formation as discussed below. 4.2. Reaction
Paths for C,H,
and C,H,
The reaction paths in the C, chain are better established than the C, chemistry discussed above. However, as ethylene and acetylene are major products of propane combustion it is desirable to quantify the major uncertainties. Ethylene is mainly consumed by H radical attack to produce vinyl radical. Reactions with 0 and OH radicals account only for a fraction of ethylene consumption at low strain rate conditions. However, the reactions with 0 and OH radicals may be responsible for up to 30% of ethylene consumption at high strain rates in the counterflow geometry. At the high temperatures of the present study the vinyl radical decomposes quickly into acetylene. (165) (-158)
C,H,
+ H = C,H, C,H,
= C,H,
+ H,, + H.
The rate of reaction 165 actually determines the ratio between computed concentrations of ethylene and acetylene. High sensitivity can be observed in the prediction of ethylene and acetylene concentrations to the rate of this reaction as shown in Figs. lc and Id, respectively. Literature data for reaction 165 has an uncertainty factor of about 3. However, variation in the rate of reaction 165 by this amount can result in significant change in the balance
146
K. M. LEUNG
between the computed concentrations of ethylene and acetylene. The selection of a rate constant for reaction 165 is also dependent on the formation rate of ethylene from alkyl radicals in propane-air diffusion flames. The rate constant for this reaction was therefore determined using the computation for methane-air diffusion flames where the effects of reactions involving C, species are insignificant. The suggestion of Tsang and Hampson [48] for reaction 165 was found to give reasonable agreement for ethylene concentrations in both methane-air and propane-air diffusion flames. The consumption paths of acetylene have been problematic in combustion modeling. There are uncertainties not only in the reaction rate parameters but also in product channels of the reactions. Miller and Melius [36] have suggested that reactions with 0 atom are the major acetylene consumption paths even in slightly rich acetylene premixed flames. However, Levy and Sarofim [ll] and Woods and Haynes [72] suggested that the reaction with the OH radical, producing ketene, is responsible for acetylene consumption in fuel-rich premixed ethylene flames. A large number of reactions for acetylene consumption are included in the present mechanism to test the contributions of the various consumption paths in diffusion flames. A branching ratio of 1 was adopted for the two product channels for the reaction betwen acetylene and the 0 atom. The product channels for the reaction of OH with acetylene were adopted from the work by Miller and Melius [36]. Computational results show that the reaction of acetylene with the H radical is in equilibrium. Reactions with the 0 atom form the dominant paths and are responsible for about 80% of the overall acetylene consumption rate. The remaining contributions come from reactions with the OH radical and methylene. (142)
C,H,
+ 0 =3CH,
(143)
C2H2
+ 0 = CHCO
+ CO, + H,
(144)
C,H,
+ OH = C,H
+ H,O,
(145)
C,H,
+ OH = CHCOH
(146)
C,H,
+ OH = CH,CO
+ H, + H.
AND
R. P. LINDSTEDT
There is still uncertainty relating to the rate of reaction 146. Recently. Woods and Haynes [72] proposed a rate constant for this reaction which is ten times faster than the rate by Miller and Melius [36] adopted in the present study. Computations using the faster rate show that for this case the OH channel becomes competitive. Clearly the uncertainty in the reaction between acetylene and the OH radical is still unresolved. 4.3 Reaction
Paths for ‘CH,
and 3CH,
One of the most important features of methylene chemistry is its role in addition reactions with acetylene leading to the formation of higher hydrocarbon fragments [36, 59-61, 631. Reactions of both singlet and triplet methylene were considered in the present mechanism. Rate constants for these reactions have mainly been obtained from the compilation of Miller and Melius [36], Baulch et al. [47], and Tsang and Hampson [48]. Computational results for methane and propane flames show that singlet methylene is mainly formed by H and OH radical attack on CH, and the reaction between CHCO and the H radical. CH,
C-44) (87)
CH,
(129)
CHCO
+ H =‘CH,
+ H,,
+ OH =‘CH,
+ H,O,
+ H =‘CH,
+ CO.
Among the various consumption paths for singlet methylene, it was found that about 60% of singlet methylene isomerises to the triplet form, 25% reacts with acetylene to form C, species with the reminder consumed through reactions with OH, O,, and CO,. (481 (491 (50)
‘CH,
+ OH = CH,O
‘CH, ‘CH,
+ 0, + CO,
= CO + OH + H, = CO + CH,O,
(53)
‘CH,
+ C,H,
=
(54)
‘CH,
+ C,H,
= c-&H,,
(58)
‘CH,
+ H,
C,H,
+ M =3CH2
+
I-L
+ M.
KINETIC
MODELING
OF ALKANE
DIFFUSION
FLAMES
147
Canosa-Mas et al. [60] observed that propyne, allene and propargyl are all possible products of the singlet methylene reaction with acetylene. Since cyclopropene isomerises to propyne and allene quickly, the choice of cyclopropene as a product for this addition reaction provides a branching ratio for the formation of the two linear C,H, isomers. Triplet methylene is a major product of the reaction between acetylene and the 0 atom:
and theoretical work [37] also suggests that linear C, species are the initial products of propargyl recombination followed ring closure. However, there is uncertainty with respect to whether the rate-limiting step is the formation of the linear C, species or the subsequent cyclization reactions to form benzene. The following linear C, species formation paths have been considered in the present study, (350)
C,H,
+ C,H,
= (1,2)-C,H,,
(142)
(351)
C,H,
+ C,H,
= (1,5)-C,H,,
(352)
C,H,
+ C,H,
= (l&V)-C,H,,
C,H,
+ 0 =3CH,
+ CO.
Computational results show that several reactions with comparable rates are responsible for the consumption of triplet methylene. In total about 40% of triplet methylene is consumed by reaction with the H radical, 20% by reactions with 0, molecule, and the remaining contributions come from reactions with 0, OH, and CH, radicals. (60)
3CH, + H = CH + H,,
(61)
3CH, + 0 = CO + H + H,
(62)
3CH,+O=CO+H,,
(63)
3CH, + OH = CH + H,O,
(64)
3CH, + OH = CH,O + H,
(72)
3CH, + CH, = C,H,
+ H.
Reaction 60 is also the dominant formation path for CH radicals. Triplet methylene also reacts with acetylene to produce cyclopropene at a rate about three times slower than the equivalent singlet methylene reaction path. 4.4. Formation
of C, Species and Benzene
Benzene is of crucial importance as the first single-ring aromatic formed from smaller nonaromatic hydrocarbons. While reaction paths involving recombination reactions of linear C, and C, species have been favored in the past to account for the formation of benzene and other soot-precursors [9, 32, 33, 1091, recent work [34-37, 54, 811 suggests that propargyl radical recombination may in fact be a major contributor to the formation of benzene in flames. Recent experimental [34, 351
(353)
C,H,
+ a-C,H,
= I-&H,,
(354)
n-C,H,
+ C,H,
= (1,3)-&H,,
(355)
C,H,
+ C,H,
= Z-&H,,
(356) (1,3)-C,H,
+ C,H,
= I-&H,.
The rate constants for reactions 350-352 were obtained from Alkemade and Homann [34] with an equal branching ratio between the three product channels. The rate constants for reactions 353-356 were adopted from the work of Westmoreland et al. [33]. The chemistry of the C, chain is important since it contains potential benzene precursors. Computational results from methane and propane flames show that there are four paths leading to the formation of C,H, isomers. (-329)
C,H,
+ CH, = (1,2)-C,H,,
(335)
C,H,
+ C,H,
= (1,3)-C,H,,
(-338)
C,H,
+ C,H,
= (1,3&H,
(345)
‘CH, +p-C,H,
+ H,
= c-C,H,.
The recombination reaction (-329) between propargyl and methyl radicals is the dominant path for butadiene formation in both methane and propane flames. The other paths are significant only in propane flames because of the higher C, and C, species concentrations. The product of single methylene addition to propyne is specified as l-methyl-cycle-propane. This compound quickly isomerises to form (1,2)-C,H, and (1,3)-C,H,. (345)
c-C,H,
= (1,31-C,H,,
(3471
c-C,H,
= (1,2)-C,H,.
148
IS. M. LEUNG
The oxidation of 1,3 butadiene has been extensively studied by Lindstedt and Skevis [125]. In the present flames the C,H, isomers are predominantly consumed via abstraction reactions with CH, radicals. However, reactions with H and OH radicals also contribute to the consumption of (1,3)-C,H,: .
AND R. P. LINDSTEDT
The n-C,H, radical isomerizes quickly to iC,H, and the latter is mainly consumed by hydrogen abstraction and thermal decomposition reactions to produce C,H,. c-306)
n-C,H,
= i-C,H,,
(307)
i-C,H3 = C,H,
I
(334)
(1,2)-C,H,
+ CH, = (1,2)-&H,
(337)
(340)
(343)
(1,3)-C,H,
+ CH,,
+ H
(1,3)-C,H,
= (1,3&H,
+ H,,
= (1,3)-C,H,
+ H,O,
+ OH
(1,3)-C,H,
+ CH, = (1,3)-C,H,
+ CH,.
The 1,3-butadienyl radical readily decomposes to C,H, and C,H, at flame temperatures with isomerization to i-C,H, and (1,2)-C,H, accounting for less than 20% of the total consumption rate. (322)
(1,3)-C,H,
= C,H,
+ C,H,.
Consumption of the 1,2-butadienyl and isobutadienyl radicals proceeds mainly via the abstraction reactions with H and OH radicals to form C,H,. (318) (319)
(1,2)-C,H, (1,2)-C,H, i-C,H,
(327)
i-C,H,
(328)
+ H = C,H, + OH = C,H, + H = C,H, + OH = C,H,
+ H,, + H,O,
(313) (315)
3CH, + C,H, C,H, C,H,
= C,H,
+ H = n-C,H, + OH = n-&H,
i-C,H,
+ H = C,H,
= H,.
Computed concentrations of the (1,3)-C,H, and n-C,H, isomers are very small even in propane diffusion flame. This is mainly due to the high reversibility of the reactions responsible for the formation of C, species. As a result benzene formation paths via the C, species are not important in the present study. In fact, computational results show that reaction 354 proceeds in the reverse direction and becomes a formation path for n-C,H,. With the present mechanism benzene formation occurs mainly through radical recombination reactions of propargyl and the subsequent cyclization of the linear C, species. Among the three recombination paths considered in the present mechanism, reaction 352 forming (1,2,4,5&H, is the dominant formation path: (350)
C,H,
+ C,H,
= (1,2&H,,
(351)
C,H,
+ C,H,
= (1,5)-C,H,
(352)
C,H,
+ C,H,
= (1,2,4,5&H,.
+ H,, + H,O.
Vinyl-acetylene is also produced from the reaction 285 between propargyl and triplet methylene. This reaction is actually the dominant formation path for C,H, in methane flames where the C, intermediate concentrations are lower than in propane flames. Vinyl-acetylene is consumed by abstraction reactions producing the n-C,H, radical. (285)
(308)
+ H,
+ H, + H,, + H,O.
Reactions 350 and 351 are in partial equilibrium and consequently their net rates are controlled by the thermodynamic properties of the linear C&H, species involved. Melius et al. 1371 have suggested that the heats of formation of the linear C,H, species have an uncertainty of at least 20 kJ/mol. The heats of formation adopted in the present study are in good agreement with those suggested by Alkemade and Homann [34] with (1,2,4,5)-C,H, more stable than (1,2&H, and (1,5)-C,H, by 80 kJ/mol. Computational results show that with the current thermodynamic data, reaction 352 is faster than reactions 350 and 351 by factors of 15 and 5, respectively.
KINETIC
MODELING
OF ALKANE
DIFFUSION
Stein et al. [35] observed that the isomerization product of 1,5-hexadiyne was 1,2-dimethylene-cycle-butene which subsequently isomerizes to benzene and fulvene. They also suggested that 1,2,4,5_hexatetraene is a possible intermediate of this cyclization reaction. Melius et al. [37] studied the unimolecular rearrangement processes of various C,H, compounds and concluded that concerted reaction mechanisms involving ringed transition state structures provide low-activation-energy pathways for the cyclization reactions of linear C,H, isomers. Following these suggestions an isomerization reaction submechanism for the linear C,H, species was formulated:
but at a slower rate. Benzene is eventually formed from fulvene through reaction 388. Benzene is mainly consumed via the thermal decomposition reaction 400 and abstraction reactions 401 and 407 to form the phenyl radical. C,H,
(400) (401) (407)
C,H, C,H,
= C,H,
+ H,
+ H = C,H,
+ H,,
+ CH,
= C,H,
+ CH,.
In methane flames the reverse of reaction 407 also contributes to benzene formation due to the high CH, concentrations. A detailed discussion of the benzene oxidation mechanismn can be found elsewhere 1551.
(380)
(1,5)-C,H,
(381)
(1,2,4,5)-C&H,
= (Ml-C,H,,
5. MECHANISM
(382)
(1,2,4,5)-C,H,
= Fulvene,
The reaction mechanism, listed in Table 1, has been applied in the modeling of both nonpremixed and premixed combustion. For diffusion flames the reaction mechanism was initially tested by comparison of computational results with experimental data for methane-air and propane-air counterflow flames obtained by Tsuji and Yamaoka 129, 301. Subsequently, computations of a coflowing methane-air flame on a Wolfhard-Parker burner were made. The latter flame has been extensively measured by Smyth and co-workers [38-431. The comparison of computed results with measured species concentration profiles is a major part of the present study and provides a severe test on the validity of the reaction mechanism. For premixed combustion the present mechanism has been used to calculate laminar burning velocities of a number of premixed stoichiometric fuel-air mixtures. The results of these calculations for freely propagating flames are here compared with the experimental results of Egolfopoulos et al. [126] and the predictions with mechanisms of other authors [2-51 in Table 3. It can be observed that the present mechanism reproduces experimental results successfully at least for this limited selection of conditions. However, the main focus of the present study is non-premixed flames and detailed comparisons with measurements are made below.
(383)
CM)-C,H,
= (1,2,4,5)-C&H,,
149
FLAMES
= Fulvene,
(384)
(1,2)-C,H,
= Fulvene,
(385)
(1,2)-C,H,
= (1,3)-C,H,,
(386) (387) (388)
Fulvene (1,3)-C,H, Fulvene
= (1,3)-C,H,, = C,H,, = C,H,.
The rate constant for reaction 380 was adopted from the work of Stein et al. [35] while the rate constants for the isomerization reactions 383 and 388 were adopted from the work by Melius et al. [37]. The preexponential factors for reactions 381, 382, 384, and 387 were assigned a value of 5*1011 arguably typical for this type of rearrangement reactions. Energy barriers for these reactions were estimated following the formalism of Melius et al. [37]. Computational results show that (1,5)-C,H, mainly isomerizes to form (1,2,4,5&H,, which is subsequently converted to fulvene and 1,2-di-methylene-cycle-butene via reactions 381 and 382. At the high temperatures of the present calculations 1,2-di-methylene-cycle-butene isomerises quickly to fulvene. Fulvene is also produced via (1,2X,H, through reaction 384
EVALUATION
K. M. LEUNG
1.50
AND
R. P. LINDSTEDT
TABLE III Comparison
of Measured and Calculated Laminar Premixed Stoichiometric Hydrocarbon-Air
CH,
C2H,
Burning Velocities Mixtures
of
39.0 40.2 38.5
38.0 42.5 51.0
67.4 65.8 81.0
142.5 135.4 151.0
Glarborg et al. [3] Kee et al. [4] Sloane [5]
39.0 41.0 42.5
58.9 61.0 46.8
84.1 81.8 73.9
129.6 136.8 126.1
39.2
42.1
66.1
132.6
Egolfopoulos
et al. [6]
5.1. Counterflow Flames
Methane-Air
Diffusion
Tsuji and Yamaoka [29, 301 have reported two sets of experimental data for methane-air diffusion flames in the counterflow geometry with rates of strain of 100 s- ’ and 150 s- ‘. The former flame is well documented with measurements of velocity, temperature and species profiles. Presentation of the measured data on physical distance scale is also available [31]. Measured species profiles of this flame are here used for comparison with computational results. Detailed calculation of the structure of this flame has previous been done by DixonLewis et al. [24]. It has been suggested that for comparison between the measurements and computational results a slight increase in the velocity gradient is necessary to account for the additional pressure gradient imposed by the combustion chamber geometry. However, the differences in the flame structure were found to be small over the relevant strain rate range and the nominal velocity gradient was therefore used. A fuel injection velocity of 0.12 m/s was found to locate the flame properly in the physical domain. Comparisons between the measured and computed concentration profiles for major species, C, intermediates and the OH radical are shown in Figs. 2-4. There is clearly good quantitative agreement for absolute concentrations, locations of the peak concentration and profile shapes for major species. However, H,O profiles are over-predicted in the reaction zone of the flame and it is difficult to explain such discrepancy in terms of the computation results. Profiles of C,H,, C,H,, C,H, as well as for the OH radical are shown in Fig. 4. Agreement
C3H,
C2H2
C,H,
Present study Experimental data [126] Warnatz [2]
47.0 45.0 -
-
is again satisfactory. The OH concentration measurements were performed by Sick et al. 11271 for a flame with strain rate of 125 s-l and a fuel injection velocity of 0.114 m/s. The slightly different flow field parameters give rise to a small misalignment with respect to the computed profiles and for comparison purposes the measured OH profile was aligned with the computed profile. There are also some differences in the shape of the ethane profile. However, considering that the formation of C,H, proceeds mainly via methyl radical recombination on the fuel-rich side of the flame, the location of the peak C,H, concentration 0.25
!
I
I
I
OCHJ4 00, ANJ4
L_ 2.0
4.0
6.0
Distance (mm) Fig. 2. Comparison between calculations (lines) and measurements (symbols) by Tsuji and Yamaoka [30] of CH,, Oz, N, and Hz0 profiles in a counterflow methane-air diffusion flame with a strain rate of 100/s. Mole fractions are presented on a wet basis.
KINETIC
MODELING
OF ALKANE
DIFFUSION
1.51
FLAMES
should arguably appear on the rich side, rather than near the flame front as indicated by the measurements. The successful prediction of intermediate C2 profiles shows that the C, -Cz chemistry in the present mechanism is kinetically correct for combustion in diffusion flames. It also indicates that the treatment for the pressuredependent methyl radical recombination reaction producing ethane and that the rate constants used for the consumption reactions for acetylene and ethylene are adequate. 5.2. CounterBow Propane-Air Flames
Distance (mm) Fig. 3. Comparison between calculations (lines) and measurements (symbols) by Tsumi and Yamaoka [30] of CO, CO, and H, profiles in a counterflow methane-air diffusion flame with a strain rate of 100/s. Mole fractions are presented on a wet basis.
0.006
I
I
I
I
I
0 CA
0W A CA
OH
??
0.006 ~.-
0.0
C,“,
C,H, C,H, OH
2.0
4.0
6.0
Distance (mm) Fig. 4. Comparison between calculations (lines) and measurements (symbols) by Tsuji and Yamaoka [30] of C,H,, C2H,, C,H, and OH radical profiles in a counterflow methane-air diffusion flame with a strain rate of 100/s. Mole fractions are presented on a wet basis.
Diffusion
Tsuji and Yamaoka [29] also measured two counterflow propane-air diffusion flames at a medium strain rate of 1.50 ss’ and higher strain rate of 3.50 s- ‘. Species concentrations were reported on dry basis in both cases. The detailed kinetic model reproduces the features of the experimental results faithfully. Propane was found to be consumed rapidly on the fuel rich side of the flame to generate a pool of intermediates. Computational results for the case with a rate of strain of 150 s- ’ show that the peak consumption rate of propane occurs at temperature of around 1500 K which is well below the maximum temperature of 1900 K calculated for this flame. The observed separation of the fuel consumption region from the flame front was not found in methane-air diffusion flames in which the location of maximum fuel consumption was found to coincide with the location of maximum temperature. Such a separation is mainly due to the thermal decomposition of propane in the pyrolysis region which accelerates the fuel consumption. This feature could be typical for higher hydrocarbon diffusion flames because the rates of thermal decomposition reactions of higher hydrocarbons are typically comparable to, or greater than, those observed for propane. Computed major species profiles for the case with a rate of strain of 150 s-l are compared with measurements in Figs. 5 and 6. Good agreement can be observed for all the major species except a slight over-prediction of CO and CO, profiles as shown in Fig. 6. There is
152
K. M. LEUNG
1 0.8
C 0.6 .o % Ii 1 %
0.4
if ,A I’
B i
I’
0.2
ri
0
O0
/
0
AND
R. P. LINDSTEDT
also quantitative agreement for intermediate species, see Fig. 7, except that the computed CH, and C,H, concentrations are somewhat higher than the measurements. Similar agreement for the intermediate species in the higher strain rate case can be found in Fig. 8. It can be observed that in both cases the ratios between the C, -C, intermediate species have been predicted correctly. As discussed previously, the computed concentrations for the intermediate species are very sensitive to the rates of major pyrolysis reactions of propane. Considering the amount of uncertainty in the rate expressions for these reactions and in the experimental data the agreement can be regarded as satisfactory.
P
f
0.0 CI.0
P/
ri
1
1.0
2.0
3.0
4.0
Distance (mm) Fig. 5. Comparison between calculations (lines) and measurements (symbols) by Tsuji and Yamaoka [29] of C,Hs, O?, and N, profiles in a counterflow propane-air diffusion flame with a strain rate of 150/s. Mole fractions are presented on a dry basis.
5.3. Extinction Flames
Limit of Counterflow
Diffusion
Tsuji and Yamaoka 129-311 also reported extensive measurement to establish extinction parameters for counterflow diffusion flames. As discussed by Jones and Lindstedt [ 1281 there is some uncertainty concerning the experimen-
0.030
0.020 E 'J 8 t i? 8 0.010
1.0
2.0
3.0
Distance (mm) Fig. 6. Comparison between calculations (lines) and measurements (symbols) by Tsuji and Yamaoka [29] of H,, CO and COT profiles in a counterflow propane-air diffusion flame with a strain rate of 150/s. Mole fractions are presented on a dry basis.
0.000 3.0
Distance (mm) Fig. 7. Comparison between calculations (lines) and measurements (symbols) by Tsumi and Yamaoka [291, of CH,, C2H,, C,H,, C,H, and C,H, profiles in a counterflow propane-air diffusion flame with a strain rate of 150/s. Mole fractions are presented on a dry basis.
KINETIC
MODELING I
I
o
I
OF ALKANE I
I
I
DIFFUSION I
1
CH, '3,
0 0 C;H;
A CA
*CA --- CH, ---- C,H. A
2.l
2.0
Distance (mm) Fig. 8. Comparison between calculations (lines) and measurements (symbols) by Tsuji and Yamaoka [29] of CH,, C,H,, C,H,, C2H, and C,H, profiles in a counterflow propane-air diffusion flame with a strain rate of 350/s. Mole fractions are presented on a dry basis.
tal extinction point which has been found to be dependent upon the cylinder radius to a considerable degree. Within the framework of a similarity solution where effects such as any additional pressure gradients caused by the apparatus cannot be taken into account, the value obtained with the smallest cylinder is likely to provide the most accurate comparison. Measured extinction limits for methaneair and propane-air diffusion flames are therefore taken as 375 and 675 s-l, respectively. In the present study the extinction limit was determined by increasing strain rate for calculation until no stable solution could be achieved. The computed extinction limits for methaneair and propane-air diffusion flames were found to be 480 and 650 s-i, respectively, which is in acceptable agreement with the measurements. 5.4. Coflowing Methane-Air
Diffusion Flame
Smyth and co-workers [38-431 have conducted a detailed experimental investigation of a laminar coflowing methane-air diffusion flame on
FLAMES
153
a rectangular Wolfhard Parker burner. Measurements have been made of species concentrations, ve!ocity and temperature at different heights above the burner exit. Concentration profiles for a number of compounds including acetylene, benzene and radicals such as CH,, CH, 0, OH, and H have been reported. However, to date no detailed kinetic computations of the flame structure have been carried out for this geometry. In previous modeling works comparisons were made either with flamelets derived from the counterflow geometry [1291 or with flamelets derived from kinetic computations of the chemical structure of axisymmetric laminar diffusion flames [130]. In the present study, calculations have been made with full detailed chemical kinetics as well as with a laminar flamelet approach. Direct comparison of measured and computed species profiles on a physical distance scale provides a critical and demanding test of the present mechanism. Moreover, the measured acetylene and benzene profiles can be used to validate the benzene formation paths considered in the mechanism. The acetylene and benzene data has recently been reevaluated [43] and the new values are used here. Computations were performed with initial conditions similar to those reported by Smyth et al. [38] in their experimental investigation. The velocities for the fuel and the air flows reported earlier 1381have recently been recalibrated [130] to 11.0 and 21.7 cm/s, respectively. The calculations were initiated with a flamelet approach to generate the initial flame structure. Once a sufficient number of high temperature nodes was obtained, typically after a distance of 0.4 mm above the burner, the computation switched to use of the full kinetic scheme. Preliminary calculations show the vertical velocity profiles to be overpredicted near the centerline region. In order to improve the flow field predictions, the buoyancy term was adjusted near the centre-line region. The measured velocity profiles at 9 mm above the burner exit are compared in Fig. 9 with the corresponding results of the calculations. The agreement is reasonable considering the simplified boundary layer approximation employed in the numerical calculation. There is also good agreement for the temperature and mixture
154
K. M. LEUNG
AND
R. P. LINDSTEDT
Velocity profiles at 9mm above burner
‘j;
0.60
0.6
z
c4
0 Mixture Mixture
fraction fraction
ATemperature Temperature
2500
0 B S
0.40
B e z
0.20
0.00
-0.10 z .e8
-0.20
z g
Lateral Position (mm)
-0.30
w ‘Z I” -0.40
-0.50
i 0.0
2.0
4.0 Lateral
6.0 Position
6.0
10.0
12.0
Fig. 10. Comparision between calculations (lines) and measurements (symbols) by Smyth [43] of profiles of mixture fraction (solid line, circle) and temperature (dotted line, triangle) at a height of 9 mm above the exit of a Wolfhard-Parker burner.
(mm)
Fig. 9. Comparision between calculations (lines) and measurements (symbols) by Smyth [43] of velocity profiles at a height of 9 mm above the exit of a Wolfhard Parker burner.
fraction profiles in terms of magnitude and shape as shown in Fig. 10. The definition of mixture fraction used follows the suggestion by Bilger et al. [131]. Figure 11 compares measured stable species (CH,, O,, N,, and H,O) with calculated profiles. There is excellent agreement in terms of their absolute concentrations, the locations and the profile shapes. Similar agreement for H, profiles can be observed in Figure 12. However, there are some discrepancies in the CO and CO, profiles. The computed CO? concentrations are lower than the measurements in the fuel rich region while there is an overprediction of the CO profiles. Computational results from the counterflow geometry show that the peak CO concentrations vary from 5.7% to 4.5% as the strain rate is increased from 10 to 100 s-r. The variation of computed peak concentrations of H,, CO, and CO, with flame
0.25
2.0
4.0
6.0
6.0
10.0
Lateral Position (mm) Fig. 11. Comparision between calculations (lines) and measurements (symbols) by Smyth [43] of CH,, O,, N,, and H,O profiles at a height of 9 mm above the exit of a Wolfhard-Parker burner.
KINETIC
0.10
MODELING
/
0.06
i
/
,
oco, oco A “2 co, ~.~ co H*
OF ALKANE
I
,
DIFFUSION
FLAMES
,
-H
o’tb
o”
155
0
OH
0.006
0
A AA
g 0.06 'ij 0 !!! LL u
A
r" 0.04
0.02
0.00 0.0
2.0
4.0
6.0
6.0
6.0
Fig. 12. Comparison between calculations (lines) and measurements (symbols) by Smyth 1431 of C02, CO, and HZ profiles at a height of 9 mm above the exit of a Wolfhard Parker burner.
height above the burner is moderate. For example, the computed peak CO concentration increases from a value of 4.6% to 5.3% from a height of 1 mm to 9 mm above the burner. The variation is similar in the flamelet computation. Figure 13 compares measured profiles of H, 0 and OH radicals with computational results. The overall agreement in the shape and locations of the profiles is good. The results of detailed kinetic calculations show that the computed 0 and OH profiles are slightly narrower than the measurements and the computed H profiles appear somewhat misaligned. However, the agreement in the peak concentration is reasonable. The computed peak OH radical concentration is less sensitive to increasing height than the computed H and 0 atoms concentrations which decrease by around 12% and 25% respectively-in agreement with experimental observations. Figure 14 compares measured profiles of CH and CH, radicals with the computational results. Experimental CH concentrations were normalised assuming an arbitrary peak concentration of 1 ppm and the experimental methyl
8.0
Lateral Position (mm)
Lateral Position (mm)
Fig. 13. Comparison between detailed kinetic and flamelet calculations (lines) and measurements (symbols) by Smyth [43] of H, 0 and OH radical profiles at a height of 9 mm above the exit of a Wolfhard-Parker burner.
0.00:
-
OCH;20 *CH'2000 CH, CH'lOOO
t
0.00:
E
‘i;
8 t
a,
2
0.001
0.000
w
LO
4.0
6.0
Lateral Position (mm) Fig. 14. Comparison between detailed kinetic calculations (lines) and measurements (symbols) by Smyth [43] of CH and CH, radical profiles at height of 9 mm above the exit of a Wolthard-Parker burner.
156
K. M. LEUNG
radical concentrations reported by Miller and Taylor [39] arguably provide a lower limit only. Therefore, to illustrate the similarity in profile shapes the peak concentration of the experimental data are scaled to the same values as the calculated profiles for comparison. There is a good agreement in the location and profile shape for the methyl radical. The computed CH profile is narrower and appears closer towards the air side than the measurements. Computational results show that the peak concentrations of CH and CH, radicals are sensitive to the rate of strain, and their values were reduced by 55% and 45%, respectively, when the height increases from 1 mm to 9 mm above the burner exit. Figures 15 and 16 compare the evolution of measured and computed acetylene and benzene profiles with flame height. Benzene concentrations at the beginning of calculation were set to zero to ensure that the flamelet did not impose unrealistically high initial concentrations. There is good agreement in the locations and shape of the profiles and both measurements and predictions show that acetylene and benzene concentrations increase with increas-
0.0060
-
0.0070
~
-‘1
_ 0.0060
-
0.0050
-
0.0040
-
0.0030
-
-
07mm 09mm *llmm 7mm 9mm ~ llmm
,“\ ,/,‘A,
s ‘Z
0’0°051
0.0004
-
AND
03mm 07mm n9mm 3mm - 7mm -9mm
R. P. LINDSTEDT
%A a n n 1
n g ‘Z
0.0003
~
0.0002
-
0.0001
~
I
n 0
n
8 t a, 9
1
2.0
4.0
6.0
Lateral Position (mm) Fig. 16. Comparison between detailed kinetic calculations (lines) and measurements (symbols) by Smyth [43] of C,H, profiles at heights of 3, 7, and 9 mm above the exit of a Wolfhard-Parker burner.
ing flame height. However, Figure 15 shows that the computed C,H, profiles are consistently higher than the measurements by around 30%. The variation of computed peak benzene concentration with flame height is less than that observed in experiments, see Figure 16. Previous modeling studies [129, 1301 linked flamelets to the scalar dissipation rate (~1, to account for the variation of the chemical structure due to local strain rate in a flame. The scalar dissipation rate can be expressed as [129]
8 t s? r”
where 0.0020
0.0000
~
T0.0
D = -
A
and the mixture
fraction
is Z.
PC,
I
, 2.0
I
,
I
4.0
,
6.0
8.0
Lateral Position (mm) Fig. 15. Comparison between detailed kinetic and flamelet calculations (lines) and measruements (symbols) by Smyth [43] of C,H, profiles at heights of 7, 9, and 11 mm above the exit of a Wolfhard-Parker burner.
The variation of the scalar dissipation rate at the stoichiometric plane ( x,,> and the position of maximum temperature ( xT) take values in the range 1.5 to 0.7 /s. The computed results show that the scalar dissipation rates decrease with increasing flame height as expected. The corresponding ,yst from flamelets of counterflow geometry with strain rates of 15 and 50 ski are 0.75 and 2.25, respectively.
KINETIC
MODELING
OF ALKANE
DIFFUSION
The coflowing flame was also computed using a flamelet approach with flamelet data generated in the counterflow geometry with rates of strain of 10 s-l and 200 s-l. This large variation in strain rate helps to exemplify the effect of strain on the flame structure. The results of flamelet calculations for radicals (H, 0 and OH), acetylene and benzene at a height of 9 mm above the burner are compared in Figure 17 with the corresponding results of detailed kinetic computation and measurements. It can be observed that predictions for all the species shown, except for the OH radical, are sensitive to the rate of strain. Computation results show the computed peak concentrations for acetylene and benzene are reduced by 50% and 90%, respectively, when the strain rate is increased from 10 to 200 s-‘. Calculations using the flamelet with a low rate of
FLAMES
157
strain provide better agreement in profile shapes with the result of detailed kinetic computation than the computational results generated with high strain rage flamelet data. However, all the profiles of the flamelet calculations appear shifted towards the rich side. Finally, the sensitivity of the benzene prediction to the propargyl recombination reaction was investigated. Flamelet data were generated for a rate of strain of 10 s-l in which the contributions of propargyl recombination reactions were removed from the mechanism. The results of the flamelet calculation using this flamelet data in the coflowing case can be found in Fig. 17. The peak benzene concentration was reduced by two orders of magnitude. This observation establishes the importance of propargyl recombination reactions for benzene formation. CONCLUSIONS
2.0e-03
0.0
2.0
4.0
6.0
6.0
10.0
Lateral Position (mm) Fig. 17. Comparison between detailed kinetic and flamelet calculations (lines) with experimental measurements (symbols) by Smyth [43] at a height of 9 mm above the exit of a Wolfhard-Parker burner. Also shown is a computation in which all benzene formation paths involving the propargyl radical have been removed.
An extensive kinetic model for the combustion of C, -C, hydrocarbons in diffusion flames has been described. The major reaction paths for intermediate species have been determined by conducting systematic sensitivity analysis. The validity of the C, -C, chemistry has been shown by quantitative agreement between computed results and experimental measurements of both major and minor species in ambient pressure methane-air and propane-air counterflow diffusion flames. Detailed kinetic and flamelet computations for a coflowing methane-air diffusion flame on a Wolfhard-Parker burner have shown that quantitative agreement between predictions and measurements for major specie, acetylene, benzene and radical species profiles has been achieved. The investigation of benzene formation shows that propargyl radical recombination is the major formation path for benzene in C, -C, hydrocarbons diffusion flames. Benzene formation from C, species appears insignificant by comparison due to their low concentration caused by isomerization reactions and the high reversibility of the reactions responsible for the formation of these species. The results of flamelet computations show that the predictions for benzene are very sensitive to the rate of strain.
K. M. LEUNG
158
The results of sensitivity analysis reveal that there are still significant uncertainties in some reaction rate data which can affect the quality of predictions with the present mechanism. A brief summary of the most urgent problem areas is as follows: Computational results of the potential portance of the reaction
im-
7. 8. 9. 10. 11. 12.
(146)
C,H,
+ OH = CH,CO
+ H
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