Experimental and modeling study of shock-tube oxidation of acetylene

Article abstract of DOI:10.1002/kin.10141

Nine mixtures of acetylene and oxygen diluted in argon were studied behind reflected shock waves at temperatures of 1150-2132 K and pressures of 0.9-1.9 atm. Initial compositions were varied from very fuel-lean to moderately fuel-rich, covering equivalence ratios of 0.0625-1.66. Two more mixtures with added ethylene were used to boost the sensitivity to reactions of vinyl oxidation. The progress of reaction was monitored by laser absorption of CO molecules. The collected experimental data were subjected to extensive detailed chemical kinetics analysis. The initial kinetic model was assembled based on recent literature data and then optimized using the solution mapping technique. The analysis was extended to include recent experimental observations of Hidaka and co-workers (Combust Flame 1996, 107, 401). The derived model reproduces closely both sets of experimental data, the result obtained by modifying nine rate coefficients and three enthalpies of formation of intermediate species. The identified parameter tradeoffs and justification for the changes are discussed.

Full text of DOI:10.1002/kin.10141

Experimental and Modeling
Study of Shock-Tube
Oxidation of Acetylene
BORIS EITENEER,1 MICHAEL FRENKLACH2
1GE Energy and Environmental Research Corporation, 18 Mason, Irvine, California 92618
2Department of Mechanical Engineering, University of California, Berkeley, California 94720-1740
Received 18 December 2002; accepted 23 April 2003
DOI 10.1002/kin.10141
ABSTRACT: Nine mixtures of acetylene and oxygen diluted in argon were studied behind re-
flected shock waves at temperatures of 1150–2132 K and pressures of 0.9–1.9 atm. Initial com-
positions were varied from very fuel-lean to moderately fuel-rich, covering equivalence ratios
of 0.0625–1.66. Two more mixtures with added ethylene were used to boost the sensitivity to
reactions of vinyl oxidation. The progress of reaction was monitored by laser absorption of CO
molecules. The collected experimental data were subjected to extensive detailed chemical ki-
netics analysis. The initial kinetic model was assembled based on recent literature data and
then optimized using the solution mapping technique. The analysis was extended to include
recent experimental observations of Hidaka and co-workers (Combust Flame 1996, 107, 401).
The derived model reproduces closely both sets of experimental data, the result obtained by
modifying nine rate coefficients and three enthalpies of formation of intermediate species. The
ꢀ
C
identified parameter tradeoffs and justification for the changes are discussed.
Periodicals, Inc. Int J Chem Kinet 35: 391–414, 2003
2003 Wiley
fuel-rich conditions, acetylene becomes a major prod-
uct and plays a critical role in the formation and growth
of carbonaceous matter, like polycyclic aromatic hy-
drocarbons and soot [7–9].
INTRODUCTION
High-temperature oxidation of acetylene appears
prominent in a variety of natural and industrial pro-
cesses, such as fossil-fuel combustion [1,2], materi-
als synthesis [3–5], and astrophysical phenomena [6].
The prominence of acetylene stems from its molecu-
lar compactness and the nature of the triple carbon–
carbon bond, giving rise to the high thermodynamic
stability and, at the same time, the high propensity to
addition reactions. Reactions of O atoms and OH radi-
cals with accumulating acetylene initiate the secondary
chain branching that affects the combustion dynamics
of essentially all fuels, including natural gas. Under
Despite extensive research (see the literature cited
in the article), the kinetics of the high-temperature oxi-
dation of acetylene is not yet established with accuracy
necessaryforpredictivenumericalmodeling. Theprob-
lems associated with the current kinetic models, those
precipitated the present study, are exposed throughout
the article. Difficulties encountered in using these ki-
netics models can be demonstrated, for instance, by a
recent numerical analysis of acetylene ignition [10] as
well as computer simulations of fuel-rich combustion
of natural gas [11].
We report here results of new shock-tube experi-
ments aimed at examining the high-temperature oxi-
dation of acetylene at conditions sensitive to key reac-
tions, and discuss model adopted for the analysis and
Correspondence to: Michael Frenklach; e-mail: myf@me.
berkeley.edu.
Contract grant sponsor: Gas Research Institute.
2003 Wiley Periodicals, Inc.
c
ꢀ

392
EITENEER AND FRENKLACH
document modifications made. We optimize the model,
in a systematic and consistent manner, to fit the present
shock-tube measurements along with literature exper-
imental data, and conclude with recommendations.
and total concentration C5 of gas mixtures behind the
reflected shock waves. The observed shock velocity at-
tenuation was less than 2.5% m−1. The uncertainties of
reflected shock temperature and pressure were 0.35%
and 0.09%, respectively. Corrections for boundary
layer formation were not applied [22].
EXPERIMENTAL APPARATUS
AND PROCEDURES
The concentration of CO was determined by res-
onance laser absorption [13]. A continuous-wave CO
laser was operated at the 2 → 1 P(10) CO transition
(2077.1 cm−1). The intensity of the transmitted laser
beam was collected at 0.5-ꢀs intervals with the over-
all time constant of the electro-optical equipment of
0.6 ꢀs. Absolute CO concentrations were determined
usingtheBeer–Lambertlawwiththecollisionbroaden-
ing half-width parameter 4.8 × 10−2 atm−1 cm−1 ob-
tained earlier in our laboratory from CO calibration
measurements [13]. Further details can be found else-
where [17].
The experimental apparatus and procedures were based
on those described in our previous studies [12–14].
Briefly, the experiments were performed in a con-
ventional stainless-steel double-diaphragm shock tube
with an inner diameter of 8.26 cm, 1.5-m long driver
section, and 4.9-m long driven section. The pumping
system was upgraded to the Varian 600DS dry scroll
mechanical pump, used both as roughing and back-
ing pump, and the Varian Turbo-V 250 turbomolecular
pump. This upgraded pumping system is completely
oil-free and thus excludes contamination of the vac-
uum system by the backstreaming pump oil. Prior to
each experiment, the test section of the shock tube
was evacuated to at least 1 × 10−5 torr. All parts of
the gas handling system were tested for leaks with a
Varian PortaTest II leak detector. The combined leak-
outgassing rate of the driven section was usually about
6 × 10−5 torr min−1. The shock tube was cleaned after
each experiment.
The test mixtures were prepared manometrically,
with a maximum uncertainty in the final reactant con-
centrations of less than 1%, and allowed to mix in a
stainless-steel tank for at least 24 h prior to experi-
ments. Acetylene of a stated purity higher than 99.6%
was obtained from Matheson and was further purified
by passing through a series of activated charcoal fil-
ters (Matheson Model 454) to ensure removal of ace-
tone impurities [15,16]. The estimated efficiency of our
acetone removal technique is 99.9%, much higher than
96% of the dry-ice–acetone cold trap approach [17].
The stated purities for the rest of the gases (all from
Matheson) were as follows: argon, 99.9995%; oxy-
gen, 99.997%; helium, 99.999%; ethylene, 99.99%.
These gases were used as purchased, without further
purification.
EXPERIMENTAL RESULTS
The mixture compositions, experimental conditions,
and obtained characteristic times for CO profiles are
listed in Table I. Kinetic information was deduced from
the experimental data by matching the initial part of
the CO profiles, from the onset of reaction up to the
maximum in the absorption signal. A sensitivity anal-
ysis showed that the remaining part of the CO profiles,
after the maximum, was mostly sensitive to reaction
CO + OH → H + CO2 and hence did not provide
additional information on acetylene reactions. In view
of this, each experimental profile was represented by
three characteristic points, t1/4, t1/2, and t3/4, the times
at which the CO signal reached 1/4, 1/2, and 3/4 of its
maximum value, respectively. Taking three points, not
one, reflected sensitivity to the reaction chemistry of
not just “ignition delay” but also of the shape of the
profile.
For numerical analysis each experimental series was
represented by five to six sets of optimization targets,
{ꢁ1/4, ꢁ1/2, ꢁ3/4}, chosen as follows. The experimental
runs within each series were grouped according to the
total concentration C0, usually into three groups with
C0 around 7, 9, and 11 mol m−3 (see Table I). For each
C0 ≈ const group, experimental characteristic times
t1/4, t1/2, andt3/4 werefittedintoanArrhenius-likeform
and optimization targets ꢁ were selected as represen-
tative points of these fits, typically two points near the
ends of the temperature range. This procedure allowed
us to smoothen experimental variations beforehand and
thus to reduce the amount of numerical simulations re-
quired. Optimization targets developed following this
procedure are listed in Table II.
The progress of reaction was monitored behind re-
flected shock waves. The postshock conditions were
calculated from the incident shock velocity in the usual
manner [18], assuming no chemical reaction and full
vibrational relaxation. The thermodynamic data used
were based on the standard databases, including the
NASA [19] and Technion archives [20,21]. The ve-
locity of the incident shock was extrapolated to the
end plate, and this extrapolated value was then used
in the calculations of the temperature T5, pressure P5,

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
393
Table I Experimental Conditions and Results
a
Experimental Run
T5 (K)
C0 (mol m−3
)
t1/4 (ꢀs)
t1/2 (ꢀs)
t3/4 (ꢀs)
tmax (ꢀs)
Rmax
Series A: 0.25% C2H2–10.00% O2–Ar
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
1288
1303
1336
1383
1395
1463
1477
1495
1519
1590
1626
1702
1727
1731
1767
1818
1869
1954
2081
10.83
10.81
10.80
10.78
10.65
9.04
10.77
8.98
10.62
9.21
9.12
9.12
7.45
9.15
7.58
7.54
7.50
7.53
134.4
136.6
128.6
99.4
83.5
85.8
67.7
74.2
51.5
57.0
52.2
39.2
48.4
34.9
–
145.0
146.4
136.9
105.9
90.1
94.8
73.6
81.1
56.7
63.2
56.8
44.0
53.7
38.6
44.7
40.1
33.9
26.9
21.8
154.1
154.7
144.5
111.4
95.7
102.9
78.6
86.9
61.1
67.8
61.8
47.9
57.8
41.7
49.7
43.8
38.0
30.5
24.6
174.0
171.5
163.7
124.2
111.1
119.0
89.5
99.5
71.4
79.2
–
56.6
67.6
50.3
59.9
54.8
44.7
38.7
32.7
0.953
–
0.826
0.909
0.864
0.876
0.888
0.904
0.902
0.947
0.917
–
0.889
0.874
0.921
0.838
–
36.3
28.3
23.6
19.0
0.839
0.810
7.56
Series B: 0.50% C2H2–10.10% O2–Ar
20
21
22
23
24
25
26
27
28
29
30
31
32
1151
1161
1220
1273
1352
1400
1382
1476
1586
1697
1798
1800
2076
12.30
12.60
12.51
12.80
8.89
8.88
12.50
9.08
9.13
9.11
9.28
7.51
247.2
208.8
156.2
112.4
104.0
88.7
62.1
56.3
42.8
29.5
274.8
223.9
167.2
120.8
111.7
95.0
66.4
60.1
46.0
32.2
295.4
237.6
176.8
127.8
117.8
100.1
70.2
63.5
49.0
34.8
25.8
325.6
259.8
192.4
141.1
129.7
112.1
–
72.2
55.9
41.0
32.6
–
0.819
0.906
0.958
0.920
0.865
0.895
–
0.854
0.857
0.849
0.816
–
21.0
24.3
12.7
23.3
27.0
14.7
28.9
16.6
7.93
22.3
0.783
Series C: 0.50% C2H2–5.00% O2–Ar
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
1182
1247
1401
1401
1416
1470
1480
1589
1622
1656
1702
1713
1718
1747
1820
1900
10.67
10.87
11.32
11.52
11.16
11.15
8.95
9.09
9.05
9.02
9.04
346.0
249.3
99.4
104.7
81.6
64.0
88.1
60.8
55.5
48.2
41.6
50.9
50.1
39.0
38.5
31.6
364.7
274.6
106.4
113.3
87.7
68.3
94.5
65.4
59.3
51.9
45.0
55.0
54.1
42.3
41.8
34.6
382.0
295.3
112.2
120.2
92.7
71.9
99.5
69.3
62.8
55.3
48.1
58.5
57.8
45.2
44.9
37.4
–
0.989
0.957
0.932
0.931
0.914
0.914
0.955
0.908
0.894
0.887
0.894
–
330.0
124.0
131.6
104.0
80.0
110.3
79.1
71.8
63.0
55.1
67.3
67.7
51.5
52.7
44.7
7.33
7.34
9.07
7.41
0.914
0.891
0.891
0.886
7.46
Continued

394
EITENEER AND FRENKLACH
Table I Continued
a
Experimental Run
T5 (K)
C0 (mol m−3
)
t1/4 (ꢀs)
t1/2 (ꢀs)
t3/4 (ꢀs)
tmax (ꢀs)
Rmax
Series D: 0.50% C2H2–2.60% O2–Ar
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
1269
1294
1334
1349
1351
1434
1441
1452
1485
1491
1530
1545
1566
1617
1629
1646
1698
1741
1747
1769
1872
1912
1925
2001
2004
10.85
10.84
8.65
10.79
10.81
10.87
8.99
10.80
9.02
10.87
10.80
10.72
9.09
9.09
8.99
7.34
9.02
9.03
7.43
7.37
7.43
272.0
263.5
206.3
157.6
143.4
125.7
142.5
96.5
98.2
99.3
77.5
76.9
82.3
63.8
65.9
77.7
54.1
50.6
56.1
56.3
43.1
31.6
35.0
31.6
29.1
312.1
299.5
222.2
172.9
162.0
137.9
157.8
105.9
108.5
108.9
85.8
84.7
90.0
69.9
71.7
84.5
59.3
54.9
61.7
341.8
335.5
235.8
184.6
175.7
147.9
172.2
114.0
117.2
118.9
92.9
90.7
96.6
75.2
76.9
90.7
63.7
59.1
67.2
384.9
–
0.941
0.910
0.979
0.929
0.947
0.915
0.900
0.931
0.924
0.939
0.908
0.924
0.915
0.910
0.902
0.928
0.906
0.841
0.888
0.890
0.882
0.885
0.909
0.895
0.885
261.8
209.3
204.0
167.5
197.3
131.2
138.2
133.4
108.3
104.7
112.0
88.8
88.5
104.8
74.8
68.6
79.8
61.8
47.6
34.9
38.9
35.0
32.4
66.6
51.7
37.8
42.5
38.2
35.4
77.0
61.0
44.7
53.3
46.9
43.4
7.22
7.38
7.44
7.37
Series E: 0.50% C2H2–1.25% O2–Ar
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
1405
1406
1412
1472
1515
1520
1567
1588
1600
1630
1643
1713
1729
1734
1745
1811
1881
1887
1916
1977
10.76
10.61
10.65
10.69
9.06
10.70
10.75
10.76
9.11
9.07
9.07
7.33
8.90
7.34
9.03
7.39
7.14
7.47
7.38
7.38
235.9
199.1
171.6
162.4
185.9
134.2
124.4
123.6
153.3
124.4
117.0
112.3
90.4
276.4
235.9
209.4
188.8
212.8
151.6
142.7
140.7
172.7
139.7
130.9
124.8
101.8
114.2
106.4
99.9
308.8
281.0
242.5
211.5
235.4
168.7
154.7
155.3
198.1
154.8
144.1
138.3
112.1
126.5
120.4
110.9
79.5
367.4
–
0.970
0.933
0.938
0.935
0.966
0.952
0.996
–
0.978
0.946
0.939
0.925
0.926
0.909
–
300.5
260.0
283.6
201.2
176.3
185.8
242.0
187.0
173.0
174.0
135.9
154.0
–
101.3
94.0
90.0
64.2
73.5
133.0
106.0
109.0
103.0
91.5
0.904
0.880
0.922
0.883
0.946
72.3
81.5
77.4
67.4
89.0
84.7
74.4
69.8
60.5
Series F: 0.50% C2H2–1.14% O2–Ar
94
95
96
97
98
99
1447
1460
1483
1521
1572
1578
10.72
10.60
10.69
10.62
6.96
203.1
176.8
182.0
165.8
216.8
142.5
236.8
203.5
209.1
190.0
251.1
163.3
273.6
238.0
241.4
211.5
283.5
183.3
344.5
277.4
308.0
252.0
349.0
221.0
0.891
0.876
0.897
0.933
0.930
0.920
10.69
Continued

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
395
Table I Continued
a
Experimental Run
T5 (K)
C0 (mol m−3
)
t1/4 (ꢀs)
t1/2 (ꢀs)
t3/4 (ꢀs)
tmax (ꢀs)
Rmax
100
101
102
103
104
105
106
107
108
109
1607
1656
1714
1774
1813
1820
1826
1950
1973
2052
9.11
8.94
8.98
8.99
7.38
7.43
7.31
7.43
7.39
7.34
148.1
113.8
100.2
91.2
96.7
95.1
84.7
65.9
61.0
54.0
169.1
127.1
112.4
102.5
108.1
105.7
94.4
73.5
68.9
59.6
188.7
140.5
123.7
113.3
119.8
117.2
103.6
81.5
228.4
171.0
149.7
137.0
148.0
143.3
127.4
100.0
95.8
0.902
0.909
0.928
0.904
0.923
0.908
0.908
0.946
0.930
0.827
76.5
65.4
81.5
Series G: 0.50% C2H2–1.00% O2–Ar
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
1436
1457
1487
1541
1591
1632
1674
1699
1737
1747
1812
1832
1882
1882
1987
2006
2037
2092
2132
10.69
10.62
10.53
10.56
9.12
9.02
9.01
8.92
9.01
8.94
6.01
7.41
7.40
7.30
7.40
7.33
6.27
6.27
6.24
261.8
194.3
169.5
132.5
179.1
145.3
125.8
94.6
102.5
100.0
117.3
96.2
83.7
82.4
66.9
57.5
61.2
55.9
44.6
–
381.6
273.8
249.8
184.1
230.8
190.0
166.1
124.8
134.8
127.5
152.4
122.5
108.3
104.1
83.9
477.0
345.5
–
0.993
0.937
0.969
0.937
–
234.8
205.6
158.2
201.6
166.5
146.1
110.3
119.7
113.5
–
109.0
95.3
93.4
75.1
65.0
69.4
63.8
51.1
251.5
284.5
235.0
211.0
157.0
163.0
160.0
194.5
152.0
135.0
133.0
107.5
90.4
0.938
0.945
0.957
0.927
0.918
0.938
0.885
0.934
0.933
0.939
0.929
0.933
0.957
0.889
72.1
77.4
72.2
58.0
99.0
89.5
75.0
Series H: 0.50% C2H2–0.89% O2–Ar
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
1440
1465
1518
1524
1537
1586
1613
1621
1640
1655
1719
1770
1885
1885
1943
1967
2032
10.68
10.63
10.66
9.09
13.93
9.12
9.05
13.97
6.52
9.03
9.17
9.17
6.94
6.90
6.89
6.86
6.88
239.9
226.9
176.6
239.9
142.9
194.2
167.7
105.0
231.0
146.9
125.2
103.9
109.7
92.0
313.5
282.1
213.4
286.4
174.0
232.1
197.7
123.5
266.4
168.9
147.0
119.8
126.7
104.6
96.7
387.3
352.5
259.4
337.0
208.5
281.8
229.5
145.6
292.4
192.1
170.8
138.8
144.2
118.3
110.4
93.4
517.7
473.0
349.0
442.4
289.0
383.3
304.5
206.0
353.6
251.0
218.2
187.3
201.5
154.8
146.2
122.2
110.2
0.931
0.953
0.925
0.939
0.946
0.918
0.937
0.969
0.933
0.936
0.908
0.929
0.929
0.912
0.935
0.923
0.939
85.0
71.0
64.5
82.4
73.6
83.3
Series I: 1.00% C2H2–1.51% O2–Ar
146
147
1847
1943
6.86
6.91
58.3
46.1
66.6
52.8
75.5
59.7
–
–
–
0.842
Series J: 0.346% C2H2–0.087% C2H4–4.323% O2–Ar
148
149
1257
1271
11.13
11.02
177.0
204.5
194.1
230.9
209.3
256.1
238.0
295.0
0.954
0.905
Continued

396
EITENEER AND FRENKLACH
Table I Continued
a
Experimental Run
T5 (K)
C0 (mol m−3
)
t1/4 (ꢀs)
t1/2 (ꢀs)
t3/4 (ꢀs)
tmax (ꢀs)
Rmax
150
160
161
162
163
164
165
166
167
168
169
170
171
172
173
1363
1394
1418
1485
1519
1564
1594
1649
1716
1757
1794
1859
1913
1989
2096
11.45
11.46
11.14
11.24
9.06
9.07
9.03
9.07
9.11
9.09
7.36
7.42
7.44
7.47
7.57
126.8
105.4
77.0
75.1
73.1
66.5
58.0
49.7
43.0
39.5
45.1
36.2
31.9
26.1
17.7
141.8
116.1
84.1
81.0
79.7
72.3
62.9
54.0
47.1
43.1
49.2
40.4
35.0
29.0
20.0
155.1
125.2
89.9
86.7
85.5
77.3
67.3
57.9
50.7
46.4
52.8
43.9
38.0
31.9
22.3
176.0
142.0
102.6
98.0
97.9
88.5
78.8
67.3
58.3
54.9
63.1
54.2
46.2
40.0
28.6
0.981
0.944
0.967
0.918
0.915
0.917
0.926
0.893
0.880
0.872
0.880
0.912
0.900
0.903
0.889
Series K: 0.38% C2H2–0.12% C2H4–1.32% O2–Ar
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
1444
1454
1493
1502
1539
1577
1628
1667
1733
1846
1851
1880
1895
1996
2022
10.93
10.83
10.80
10.65
10.61
8.97
9.01
8.99
8.98
7.42
7.35
7.27
7.33
7.36
7.34
173.2
174.2
150.1
125.5
112.7
137.4
108.1
100.7
76.6
71.2
71.8
62.5
58.0
–
273.3
252.7
198.0
173.1
144.0
181.4
147.4
129.5
96.0
90.3
90.1
76.9
72.5
328.0
310.0
242.0
215.0
176.0
207.0
180.0
159.2
115.4
113.1
105.5
94.5
0.916
0.944
1.031
0.947
0.915
0.959
0.927
0.959
0.937
0.949
0.995
0.900
0.944
0.962
0.950
211.8
173.3
151.0
128.1
160.0
128.2
116.3
87.1
81.2
81.3
70.0
65.4
90.0
71.5
60.0
42.6
37.1
49.0
42.2
56.2
47.1
aObserved ratio of peak CO concentration to total mixture carbon content.
Figure 1 illustrates the CO profile obtained in ex-
perimental run 23, Series B at 1273 K (Table I). Also
shown in Fig. 1 are model predictions obtained with
GRI-Mech 3.0 [23], Hidaka et al.’s mechanism (Model
H) [24], Laskin and Wang’s mechanism (Model LW)
[25], and the trial mechanism assembled in the present
study (Model 0). Model H contains 92 reactions of
36 chemical species assembled by Hidaka et al. [24]
to simulate their acetylene pyrolysis and oxidation re-
sults. Model LW was obtained by adding C3 and C4 hy-
drocarbons’ chemistry to GRI-Mech 1.2 and includes
349 reactions of 52 chemical species. Model 0, assem-
bled in the present study, includes 378 reactions of 52
chemical species.
following reactions:
C2H2 + M → H + C2H + M
O2 + M → O + O + M
(1)
(2)
Also, GRI-Mech 3.0 does not include the chemistry
of C3, C4, and higher unsaturated hydrocarbons and
thus is not suitable for modeling acetylene oxidation,
especially at stoichiometric and fuel-rich conditions.
Performance of Models H, LW, and 0 is further illus-
trated in Fig. 2 for all optimization targets of Table II.
The largest discrepancies were observed for targets
at low temperatures. Model H predicts experimental
characteristic times with an overall accuracy of about
+60/−40%. It predicts the peak CO concentrations to
be only about 70% of the total carbon content (Fig. 1),
while the observed peak CO concentrations accounted
for approximately 90% for all experimental conditions
As can be seen in Fig. 1, GRI-Mech 3.0 overpredicts
the time of CO appearance by a factor of 5. This is
caused mainly by the lack of an initiation step via a
reaction between acetylene and molecular oxygen; in
GRI-Mech 3.0, the chain process is initiated by the

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
397
Table II Optimization Targets
Table II Continued
C5
Target T5 (K) (mol m−3
C5
Target T5 (K) (mol m−3
)
ꢁ1/4 (ꢀs) ꢁ1/2 (ꢀs) ꢁ3/4 (ꢀs)
)
ꢁ1/4 (ꢀs) ꢁ1/2 (ꢀs) ꢁ3/4 (ꢀs)
Series A: 0.25% C2H2–10.00% O2–Ar
46 1640
47 2032
6.57
6.96
234
64.2
270
73.5
297
83.9
1
2
3
4
5
6
1288
1519
1463
1731
1727
2081
10.80
10.67
9.04
9.16
7.50
7.56
147
54.8
86.4
36.4
46.7
18.1
156
59.9
94.8
40.3
51.7
21.0
165
64.1
102
43.8
56.3
23.9
Series I: 1.00% C2H2–1.51% O2–Ar
48 1894 6.89 51.8
Series J: 0.346% C2H2–0.087% C2H4–4.323% O2–Ar
49 1257
50 1394
51 1519
52 1757
53 1794
54 2096
59.3
67.0
11.14
11.35
9.05
9.10
7.36
7.56
197
102
73.6
39.0
46.0
18.5
220
112
79.9
42.6
50.3
20.8
241
121
85.4
45.8
54.0
23.2
Series B: 0.50% C2H2–10.10% O2–Ar
7
8
9
1151
1273
1352
12.50
12.60
8.90
238
111
105
260
119
112
277
127
117
10 1697
11 1923
Series C: 0.50% C2H2–5.00% O2–Ar
12 1182
13 1470
14 1480
15 1747
16 1718
17 1900
9.18
7.71
28.7
17.8
31.4
20.1
34.0
22.1
Series K: 0.38% C2H2–0.12% C2H4–1.32% O2–Ar
55 1444
56 1539
57 1577
58 1733
59 1846
60 2022
10.90
10.60
8.99
8.99
7.35
7.34
182
112
136
77.4
71.6
37.8
227
127
160
88.4
80.9
43.2
272
142
184
97.7
89.4
48.9
10.72
11.36
8.98
9.07
7.33
7.46
367
67.8
88.2
38.0
50.9
31.7
395
418
72.9
94.4
41.1
54.9
34.7
77.1
99.3
43.9
58.6
37.4
Series D: 0.50% C2H2–2.60% O2–Ar
studied. Model LW predicts the peak CO concentra-
tions in good agreement with experiment, and charac-
teristic times with an overall accuracy of about 30%
for equivalence ratios φ ranging from 0.50 to 1.66.
However, the agreement for the very fuel-lean mix-
tures is not so close, overpredicting the experimental
characteristic times by up to a factor of 4 for mixtures
with φ = 0.0625, 0.125, and 0.25. The overall agree-
ment with experimental data of the trial mechanism,
Model 0, is approximately +50/−25%.
18 1269
19 1545
20 1334
21 1741
22 1646
23 2004
10.87
10.80
8.80
9.11
7.37
7.37
262
74.0
205
47.6
76.4
29.8
298
80.9
224
52.1
83.3
33.1
327
86.9
241
56.1
89.7
36.2
Series E: 0.50% C2H2–1.25% O2–Ar
24 1405
25 1588
26 1515
27 1745
28 1713
29 1977
10.67
10.75
8.99
9.11
7.33
7.36
201
118
190
90.1
110
59.3
239
276
134
215
101
123
146
240
113
136
The level of disagreement demonstrated in Figs. 1
and 2 clearly indicates the need for refinement of
65.9
72.3
Series F: 0.50% C2H2–1.14% O2–Ar
30 1483
31 1607
32 1774
33 1572
34 2052
10.66
9.05
8.96
7.06
7.47
179
141
87.8
212
51.7
206
159
98.3
244
57.2
236
177
108
275
62.8
Series G: 0.50% C2H2–1.00% O2–Ar
35 1436
36 1541
37 1591
38 1747
39 1987
40 1812
41 2132
10.65
10.53
9.11
8.96
7.36
6.03
6.29
241
128
175
98.8
63.3
118
47.6
295
153
199
114
71.3
134
54.3
351
180
228
129
79.5
153
61.2
Figure 1 Observed and calculated CO profiles. Experimen-
tal conditions are those of experimental run 23 in Table I:
0.50% C2H2–10.10% O2–Ar, T0 = 1273 K, C0 = 12.80 mol
Series H: 0.50% C2H2–0.89% O2–Ar
42 1572
43 1465
44 1524
45 1770
13.95
10.66
9.06
125
220
239
105
150
278
286
121
178
344
339
139
m
−3. Error bars indicate experimental uncertainty in deter-
mination of maximum CO concentration. ——, Experiment;
9.15
— —, GRI-Mech 3.0; ------, Model H; — —, Model LW;
ꢀ
•
Continued
– - –, Model 0.

398
EITENEER AND FRENKLACH
value essentially rules out reactions
C2H2 + M → H + C2H + M
(3)
(3)
(4)
C2H2 + C2H2 → H + i-C4H3
C2H2 + C2H2 → C2H + C2H3
as efficient initiation steps under the conditions em-
ployed in the present study. Contribution of acetone
impurities, suggested by Colket et al. [15,16] to be im-
portant during acetylene pyrolysis, can be safely ne-
glected at the expected acetone levels of the present
work (see also Kiefer et al. [56]).
Reaction of acetylene with molecular oxygen
C2H2 + O2 → HCO + HCO
→ HCCO + OH
(5a)
(5b)
(5c)
(5d)
→ CH2CO + O
→ C2H + HO2
has been proposed as a chain initiation reaction in high-
temperature acetylene oxidation [24,28,33,57,58]. Re-
action (5d) is generally too slow to compete with chan-
nels (5a)–(5c) [33]. Miller et al. [28] and Hidaka et al.
[24] reached a conclusion that acetylene ignition de-
lays could not be adequately predicted without reac-
tions (5a)–(5c); however, specific reaction channels
cannot be distinguished on the basis of kinetic model-
Figure
2
Relative errors defined as 100 × (ꢁcalc −
ꢁexpt)/ꢁexpt obtained in numerical predictions of ꢁ1/2. The
horizontal axis refers to the experimental targets of Table II.
Top panel: , Model H; , Model LW; ꢁ, Model 0; ꢁ, Model
ꢀ
•
0 with the initiation scheme of Hidaka et al. [24]. Bottom
panel: ꢁ, Model 0; ꢂ, Model 1; , Model 2.
◦
ing alone. Hidaka et al. [24] proposed a rate coefficient
Hidaka
k
= 1.0 × 1012 e−14090/T cm3 mol−1 s−1 as a fit
5a
to their experimental data within the framework of a
complex kinetic mechanism, Model H.
high-temperature acetylene oxidation chemistry. This
refinement constitutes the subject of the present
work.
Laskin and Wang [25] suggested that reaction be-
tween acetylene and molecular oxygen proceeds by
isomerization of acetylene to vinylidene [56,59,60],
TRIAL MECHANISM
C2H2 + M → H2CC + M
(6)
The construction of the trial mechanism, Model 0, for
the present study was based on GRI-Mech 3.0 [23].
Additional reactions of C2Hx , C3Hx , and C4Hx species
weretakenprimarilyfromarecentmechanismofacety-
lene ignition in shock tubes [25] with further mod-
ifications of the kinetic and thermochemical values.
These additional reactions and associated rate coef-
ficients [26–47] are listed in Table III. The modifi-
cations introduced in the present work are described
later.
followed by the reaction between vinylidene and
molecular oxygen,
H2CC + O2 → CH2O + CO
→ CH2 + CO2
(7a)
(7b)
(7c)
(7d)
(7e)
→ HCO + HCO
→ H + CO + HCO
→ CH2CO + O
Initiation Reaction Between C2H2 and O2
They assumed that the energy barrier for the overall re-
action C2H2 + O2 → products is that of the acetylene–
vinylidene rearrangement and derived a rate coefficient
k6LW = 2.45 × 1015T −0.64 e−25010/T cm3 mol−1 s−1 for
Most of the recent theoretical and experimental studies
place the carbon–hydrogen bond energy of acetylene
in the range 131–134 kcal mol−1 [48–55]. Such a high

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
399
Table III Reactions Included in Model 0, Additional to GRI-Mech 3.0
k = AT n exp(−E/RT )a
No.
Reaction
Ab (cm3 mol−1 s−1
)
n
E (cal mol−1
)
Comments/Ref.
R1
R2
R3
R4
R5
R6
R7
C2H2+ M ꢃ H2CC + M
2.45(+15)
1.00(+13)
2.56(+9)
5.14(+9)
4.99(+2)
2.68(+53)
2.50(+13)
4.27(+58)
−0.64
49700
25c
25
36
36
36
36
H2CC + O2 ꢃ CH2 + CO2
CH3 + C2H2 ꢃ p-C3H4 + H
CH3 + C2H2 ꢃ a-C3H4 + H
CH3 + C2H2 ꢃ CH3CCH2
CH3 + C2H2 ꢃ a-C3H5
1.1
1.1
13644
22153
18850
35730
−4.4
−12.8
CH3 + C2H3(+ M) ꢃ C3H6(+M)
33
d
−11.94
−2.8
9770
a = 0.175, T ∗∗∗ = 1341, T ∗ = 60000, T ∗∗ = 10140
R8
R9
e
CH3 + C2H3 ꢃ a-C3H5 + H
1.50(+24)
5.00(+13)
2.41(+13)
5.00(+13)
5.00(+13)
2.00(+13)
2.00(+13)
3.00(+13)
1.00(+13)
5.00(+12)
1.00(+12)
3.60(+13)
9.00(+10)
7.50(+12)
3.00(+13)
1.20(+13)
2.00(+14)
1.77(+13)
4.50(+37)
2.60(+44)
1.51(+5)
18618
33 f
25
33
41
41
41
41
41
28
46
46
46
46
46
30
34
34
See text
42 f
42 f
39
39
45 f
38
33
33
33
28
26
33
33
44
44
33
33
33
CH3 + HCCO ꢃ C2H4 + CO
R10 CH3 + C2H ꢃ C3H3 + H
R11 C2O + H ꢃ CH + CO
R12 C2O + O ꢃ CO + CO
R13 C2O + OH ꢃ H + CO + CO
R14 C2O + O2 ꢃ O + CO + CO
R15 HCCO + OH ꢃ C2O + H2O
R16 HCCO + OH ꢃ H + HCO + CO
R17 CH2CO + OH ꢃ CH2OH + CO
R18 CH2CO + CH2 ꢃ C2H4 + CO
R19 CH2CO + CH2 ꢃ HCCO + CH3
R20 CH2CO + CH3 ꢃ C2H5 + CO
R21 CH2CO + CH3 ꢃ HCCO + CH4
R22 C2H2 + CH ꢃ C3H2 + H
R23 C2H2 + CH2 ꢃ C3H3 + H
R24 C2H2 + CH2(s) ꢃ C3H3 + H
R25 C2H2 + C2H ꢃ C4H2 + H
R26 C2H2 + C2H ꢃ n-C4H3
11000
13000
6620
0.2
−7.7
−9.5
85
7100
14650
5500
42700
10600
3000
−596
R27 C2H2 + C2H ꢃ i-C4H3
R28 C2H2 + C2H2 ꢃ C4H4
R29 C2H2 + C2H2 ꢃ C4H2 + H2
R30 C2H2 + C2H3 ꢃ C4H4 + H
R31 C2H2 + HCCO ꢃ C3H3 + CO
R32 C2H3 + H2O2 ꢃ C2H4 + HO2
R33 C2H3 + HCO ꢃ C2H4 + CO
R34 C2H3 + CH3 ꢃ C2H2 + CH4
R35 CH2CHO + CH3 ꢃ C2H5 + HCO
R36 CH2CHO ꢃ CH3CO
6.31(+13)
2.00(+18)
1.00(+11)
1.21(+10)
9.00(+13)
3.92(+11)
4.90(+14)
1.00(+13)
8.70(+42)
9.60(+13)
3.90(+13)
1.50(+14)
1.20(+13)
3.00(+13)
3.00(+13)
1.80(+11)
1.51(+7)
−1.7
−0.5
−8.6
47000
22420
R37 CH3CO + M ꢃ CH3 + CO + M
R38 CH3CO + H ꢃ CH3 + HCO
R39 CH3CO + O ꢃ CH2CO + OH
R40 CH3CO + O ꢃ CH3 + CO2
R41 CH3CO + OH ꢃ CH2CO + H2O
R42 CH3CO + OH ꢃ CH3 + CO + OH
R43 CH3CO + HO2 ꢃ CH3 + CO2 + OH
R44 CH3CO + H2O2 ꢃ CH3CHO + HO2
R45 C2H4 + O ꢃ OH + C2H3
R46 C2H4 + C2H ꢃ C4H4 + H
R47 C2H4 + O2 ꢃ C2H3 + HO2
R48 C2H5 + HO2 ꢃ C2H6 + O2
R49 C2H5 + HO2 ꢃ C2H4 + H2O2
8226
3740
33
41
33
33
33
33
1.9
1.20(+13)
4.22(+13)
3.00(+11)
3.00(+11)
60800
Continued

400
EITENEER AND FRENKLACH
Table III Continued
k = AT n exp(−E/RT )a
No.
Reaction
Ab (cm3 mol−1 s−1
)
n
E (cal mol−1
)
Comments/Ref.
R50
R51
R52
R53
R54
R55
R56
R57
R58
R59
R60
R61
R62
C2H5 + HO2 ꢃ CH3 + CH2O + OH
C2H5 + H2O2 ꢃ C2H6 + HO2
C2H5 + HCO ꢃ C2H6 + CO
C3H2 + O ꢃ C2H2 + CO
2.40(+13)
8.70(+9)
33
33
33
29
29
25
29
48
25
25
25
25
974
1.20(+14)
6.80(+13)
6.80(+13)
1.00(+13)
6.80(+13)
2.00(+12)
5.00(+13)
5.00(+13)
5.00(+12)
1.00(+13)
2.00(+13)
2.29(+56)
C3H2 + O ꢃ C2H + HCO
C3H2 + H ꢃ C3H3
C3H2 + OH ꢃ HCO + C2H2
C3H2 + O2 ꢃ HCCO + H + CO
C3H2 + CH ꢃ C4H2 + H
1000
7934
C3H2 + CH2 ꢃ n-C4H3 + H
C3H2 + CH3 ꢃ C4H4 + H
C3H2 + HCCO ꢃ n-C4H3 + CO
C3H3 + H(+M) ꢃ a-C3H4(+M)
47
d
−12.55
−12.59
a = 0.234, T ∗∗∗ = 330, T ∗ = 4808, T ∗∗ = 7262
R63
e
C3H3 + H(+M) ꢃ p-C3H4(+M)
3.00(+13)
1.60(+57)
47
d
8376
1000
a = 0.245, T ∗∗∗ = 330, T ∗ = 3706, T ∗∗ = 6777
e
R64
R65
R66
R67
R68
R69
R70
R71
R72
R73
R74
R75
R76
R77
R78
R79
R80
R81
R82
R83
R84
R85
R86
R87
R88
R89
R90
R91
R92
R93
R94
C3H3 + H ꢃ C3H2 + H2
5.00(+13)
2.00(+13)
2.00(+13)
4.00(+13)
3.00(+10)
8.00(+11)
1.90(+11)
3.17(+12)
2.50(+13)
2.50(+13)
5.00(+13)
5.00(+13)
1.20(+44)
5.15(+60)
4.89(+41)
1.30(+6)
41
38
38
47
37
47
47
47
47
47
47
47
36 f
36 f
36 f
47
36 f
47
25
35
35
36 f
36 f
36 f
47
47
47
47
35
47
C3H3 + O ꢃ CH2O + C2H
C3H3 + OH ꢃ C3H2 + H2O
C3H3 + OH ꢃ C2H3 + HCO
C3H3 + O2 ꢃ CH2CO + HCO
C3H3 + HO2 ꢃ OH + CO + C2H3
C3H3 + HO2 ꢃ a-C3H4 + O2
C3H3 + HO2 ꢃ p-C3H4 + O2
C3H3 + HCO ꢃ a-C3H4 + CO
C3H3 + HCO ꢃ p-C3H4 + CO
C3H3 + CH ꢃ i-C4H3 + H
C3H3 + CH2 ꢃ C4H4 + H
p-C3H4 ꢃ c-C3H4
2868
15000
15000
−9.9
−13.9
−9.2
2.0
69250
91117
49594
5500
26949
1000
p-C3H4 ꢃ a-C3H4
c-C3H4 ꢃ a-C3H4
a-C3H4 + H ꢃ C3H3 + H2
a-C3H4 + H ꢃ a-C3H5
1.52(+59)
2.00(+7)
−13.5
a-C3H4 + O ꢃ CH2CO + CH2
a-C3H4 + OH ꢃ C3H3 + H2O
a-C3H4 + CH3 ꢃ C3H3 + CH4
a-C3H4 + C2H ꢃ C2H2 + C3H3
p-C3H4 + H ꢃ a-C3H4 + H
p-C3H4 + H ꢃ CH3CCH2
p-C3H4 + H ꢃ a-C3H5
1.8
5.30(+6)
2.0
2000
7700
2.00(+12)
1.00(+13)
6.27(+17)
1.66(+47)
4.91(+60)
1.30(+6)
−0.9
−10.6
−14.4
2.0
10079
13690
31644
5500
2250
2250
100
p-C3H4 + H ꢃ C3H3 + H2
p-C3H4 + O ꢃ HCCO + CH3
p-C3H4 + O ꢃ C2H4 + CO
p-C3H4 + OH ꢃ C3H3 + H2O
p-C3H4 + CH3 ꢃ C3H3 + CH4
p-C3H4 + C2H ꢃ C2H2 + C3H3
a-C3H5 + H(+M) ꢃ C3H6(+ M)
7.30(+12)
1.00(+13)
1.00(+6)
2.0
2.0
2.00(+12)
1.00(+13)
2.00(+14)
1.33(+60)
7700
40
d
−12.0
5968
Continued

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
401
Table III Continued
k = AT n exp(−E/RT )a
No.
Reaction
Ab (cm3 mol−1 s−1
)
n
E (cal mol−1
)
Comments/Ref.
e
a = 0.200, T ∗∗∗ = 1097, T ∗ = 1097, T ∗∗ = 6860
R95
R96
R97
R98
R99
a-C3H5 + H ꢃ a-C3H4 + H2
a-C3H5 + O ꢃ C2H3CHO + H
a-C3H5 + OH ꢃ C2H3CHO + H + H
C2H3 + HCO ꢃ C2H3CHO
1.80(+13)
6.00(+13)
4.20(+32)
1.80(+13)
1.08(+12)
3.00(+13)
1.90(+7)
3.43(+9)
6.00(+12)
4.99(+15)
1.19(+15)
1.82(+13)
2.66(+12)
3.31(+12)
6.00(+13)
3.00(+12)
7.06(+56)
3.34(+12)
6.00(+13)
5.00(+12)
4.34(+12)
2.00(+13)
9.00(+13)
1.00(+11)
8.00(+21)
1.70(+5)
4.00(+5)
1.20(+8)
3.50(+7)
1.80(+11)
6.00(+10)
3.10(+6)
1.10(+6)
9.60(+3)
2.20(+0)
8.40(−1)
1.00(+17)
3.75(+33)
40
40
40 f
25
25
25
25
25
40
43 f
43 f
43 f
44
44
40
40
36 f
25
25
25
25
25
25
25
36 f
40
40
40
40
40
40
40
40
40
40
40
−5.2
30126
C2H3CHO + H ꢃ C2H4 + HCO
0.5
1820
3540
220
−447
R100 C2H3CHO + O ꢃ C2H3 + OH + CO
R101 C2H3CHO + O ꢃ CH2O + CH2CO
R102 C2H3CHO + OH ꢃ C2H3 + H2O + CO
R103 a-C3H5 + OH ꢃ a-C3H4 + H2O
R104 a-C3H5 + O2 ꢃ a-C3H4 + HO2
R105 a-C3H5 + O2 ꢃ CH3CO + CH2O
R106 a-C3H5 + O2 ꢃ C2H3CHO + OH
R107 a-C3H5 + HO2 ꢃ C3H6 + O2
R108 a-C3H5 + HO2 ꢃ OH + C2H3 + CH2O
R109 a-C3H5 + HCO ꢃ C3H6 + CO
R110 a-C3H5 + CH3 ꢃ a-C3H4 + CH4
R111 a-C3H5 ꢃ CH3CCH2
1.8
1.2
−1.4
−1.0
−0.4
22428
20128
22859
−0.3
−131
−14.1
75868
R112 CH3CCH2 + H ꢃ p-C3H4 + H2
R113 CH3CCH2 + O ꢃ CH3 + CH2CO
R114 CH3CCH2 + OH ꢃ CH3 + CH2CO + H
R115 CH3CCH2 + O2 ꢃ CH3 + CO + CH2O
R116 CH3CCH2 + HO2 ꢃ CH3 + CH2CO + OH
R117 CH3CCH2 + HCO ꢃ C3H6 + CO
R118 CH3CCH2 + CH3 ꢃ p-C3H4 + CH4
R119 C3H6 + H ꢃ C2H4 + CH3
−2.4
2.5
2.5
1.6
1.6
0.7
0.7
2.0
2.0
11180
2490
9790
327
−972
5880
7630
−298
1450
13910
5675
11660
R120 C3H6 + H ꢃ a-C3H5 + H2
R121 C3H6 + H ꢃ CH3CCH2 + H2
R122 C3H6 + O ꢃ CH2CO + CH3 + H
R123 C3H6 + O ꢃ C2H5 + HCO
R124 C3H6 + O ꢃ a-C3H5 + OH
R125 C3H6 + O ꢃ CH3CCH2 + OH
R126 C3H6 + OH ꢃ a-C3H5 + H2O
R127 C3H6 + OH ꢃ CH3CCH2 + H2O
R128 C3H6 + HO2 ꢃ a-C3H5 + H2O2
R129 C3H6 + CH3 ꢃ a-C3H5 + CH4
R130 C3H6 + CH3 ꢃ CH3CCH2 + CH4
R131 C4H + H(+M) ꢃ C4H2(+ M)
2.6
3.5
3.5
−1.0
25
d
−4.8
1900
a = 0.646, T ∗∗∗ = 132, T ∗ = 1315, T ∗∗ = 5566
e
R132 C4H + O ꢃ C2H + C2O
R133 C4H + O2 ꢃ HCCO + C2O
R134 C4H + H2 ꢃ H + C4H2
R135 C4H2 + H ꢃ n-C4H3
5.00(+13)
5.00(+13)
4.90(+5)
1.10(+42)
1.10(+30)
2.70(+13)
6.60(+12)
3.37(+7)
5.00(+13)
1.00(+7)
2.00(+7)
25
25
25
25 f
25 f
29
31
25
41
41
25
1500
560
2.5
−8.7
−4.9
15300
10800
1720
−410
14000
3000
2000
200
R136 C4H2 + H ꢃ i-C4H3
R137 C4H2 + O ꢃ C3H2 + CO
R138 C4H2 + OH ꢃ H2C4O + H
R139 C4H2 + OH ꢃ C4H + H2O
R140 H2C4O + H ꢃ C2H2 + HCCO
R141 H2C4O + OH ꢃ CH2CO + HCCO
R142 H2C4O + O ꢃ CH2CO + C2O
2.0
2.0
1.9
Continued

402
EITENEER AND FRENKLACH
Table III Continued
k = AT n exp(−E/RT )a
No.
Reaction
Ab (cm3 mol−1 s−1
)
n
E (cal mol−1
)
Comments/Ref.
R143
R144
R145
R146
R147
R148
R149
R150
R151
R152
R153
R154
R155
R156
R157
R158
R159
R160
R161
n-C4H3 ꢃ i-C4H3
4.10(+43)
2.50(+20)
6.30(+25)
2.80(+23)
2.00(+47)
3.40(+43)
3.00(+13)
6.00(+13)
2.00(+12)
4.00(+12)
7.86(+16)
6.65(+5)
−9.5
−1.7
−3.3
−2.5
−10.3
−9.0
53000
10800
10014
10780
13070
12120
42 f
42 f
42 f
42 f
42 f
42 f
25
25
25
25
25
25
25
25
25
32
32
27
27
n-C4H3 + H ꢃ i-C4H3 + H
n-C4H3 + H ꢃ C2H2 + C2H2
i-C4H3 + H ꢃ C2H2 + C2H2
n-C4H3 + H ꢃ C4H4
i-C4H3 + H ꢃ C4H4
n-C4H3 + H ꢃ C4H2 + H2
i-C4H3 + H ꢃ C4H2 + H2
n-C4H3 + OH ꢃ C4H2 + H2O
i-C4H3 + OH ꢃ C4H2 + H2O
i-C4H3 + O2 ꢃ HCCO + CH2CO
C4H4 + H ꢃ n-C4H3 + H2
C4H4 + H ꢃ i-C4H3 + H2
C4H4 + OH ꢃ n-C4H3 + H2O
C4H4 + OH ꢃ i-C4H3 + H2O
C4H4 + CH3 ꢃ n-C4H3 + CH4
C4H4 + CH3 ꢃ i-C4H3 + CH4
C4H4 + C2H ꢃ n-C4H3 + C2H2
C4H4 + C2H ꢃ i-C4H3 + C2H2
−1.8
2.5
2.5
2.0
2.0
12240
9240
3430
430
4972
4972
3.33(+5)
3.10(+7)
1.55(+7)
3.98(+11)
3.98(+11)
3.90(+13)
3.90(+13)
a The rate coefficient for the forward direction; the reverse one is calculated via equilibrium constants.
b Numbers in parentheses denote powers of 10.
c Third-body enhancement factors: H2 = 2.0; H2O = 6.0; CH4 = 2.0; CO = 1.5; CO2 = 2.0; C2H6 = 3.0; C2H2 = 2.5; Ar = 0.7.
d Low-pressure limit; third-body enhancement factors: H2 = 2.0; H2O = 6.0; CH4 = 2.0; CO = 1.5; CO2 = 2.0; C2H6 = 3.0; Ar = 0.7.
e Troe’s broadening factor c(T ) = (1 − a) exp(−T/T ∗∗∗) + a exp(−T/T ∗) + exp(−T ∗∗/T ).
f
Calculated at 760 Torr.
reaction (6) from RRKM calculations based on param-
eters of Gallo et al. [61]. Channel (7b) was adopted by
Peeters et al. [63] re-investigated reaction (8), at
2 torr helium and temperatures 287 and 535 K, and
Laskin and Wang [25] for reaction (7) with a rate co-
reported 1.6 × 1012 e−430/T cm3 mol−1
s
−1. The lat-
LW
efficient k = 1.0 × 1013 cm3 mol−1
s
−1. Using the
ter recommendation was adopted by Laskin and Wang
[25]. The same expression was initially assigned in
GRI-Mech and later doubled during the GRI-Mech 3.0
optimization. It should be noted, however, that the sen-
sitivity of the GRI-Mech 3.0 optimization targets to
reaction (8) is only marginal [23]. In a recent shock-
tube study of ketene oxidation, Hidaka et al. [46] re-
ported that the high-temperature recommendation of
Miller et al. [28] gave rise to higher reaction rates
than those observed experimentally. Using their kinetic
mechanism, Hidaka et al. [46] developed a new expres-
sion for the rate coefficient of reaction (8), 4.2 × 1010
7b
set of reactions (6) and (7b), Laskin and Wang [25]
were able to successfully model shock-tube results of
Hidaka et al. [24] on acetylene oxidation.
Our trial mechanism, Model 0, employed the above
acetylene–vinylidene initiation scheme of Laskin and
Wang [25]. We also tested the direct acetylene-oxygen
HHOIA
5a
scheme, using (5a) and k
for the initiation re-
action. This worsen the agreement with experiment
(Fig. 2), producing a deviation of about 8% in the pre-
dicted half-rise times of CO profiles.
e−430/T cm3 mol−1 −1. This latter recommendation
s
Reaction Between HCCO and O2
was adopted for our Model 0.
Kinetic data on this reaction are very limited. Jones and
Bayes [62] carried out an experimental study at 296 K
in the discharge flow of helium at 2 torr, and reported a
Reaction C2H + H2 → H + C2H2
The rate coefficient employed by GRI-Mech 3.0 for
rate constant 1.26 × 1012 cm3 mol−1
s
−1. Miller et al.
[28] adjusted it to 1.46 × 1012 e−1260/T cm3 mol−1 s−1
reaction
and assign the reaction products as
HCCO + O2 → OH + CO + CO
(8)
C2H + H2 → H + C2H2
(9)

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
403
is an extrapolation of Farhat et al.’s recommendation
[64], 5.68 × 1010T 0.9 e−1003/T cm3 mol−1
s
−1, ob-
tained from their experimental data at 295–854 K.
We derived a new expression for this rate coefficient,
4.45 × 106T 2.22 e−461/T cm3 mol−1
s
−1, by fitting re-
cent experimental data [64–71] collected over an ex-
tended temperature range of 180–4000 K (see Fig. 3).
Reaction C2H + C2H2 → H + C4H2
The rate coefficient of reaction
Figure 4 Rate coefficient of reaction C2H + C2H2 → H +
ꢄ
C4H2, k10
.
, Stephens et al. [65]; ×, Shin and Michael [72];
, Koshi et al. [67]; ꢅ, Koshi et al. [68]; , Farhat et al. [64];
◦
•
C2H + C2H2 → H + C4H2
(10)
ꢂ, Pedersen et al. [73]; ꢁ, Frank and Just [34]; , Kruse and
ꢀ
Roth [71]; ——, combined fit, present work.
used in the present study was a three-parameter fit
of recent literature data [64,65,67,68,72,73], 1.94 ×
1013T 0.238 e37/T cm3 mol−1 s−1 (see Fig. 4).
of Clauberg et al. [74] led to the enthalpy of forma-
tion of c-C3H2 ꢀf H2◦98 = 114 4 kcal mol−1. Chyall
and Squires [77] determined an experimental value of
ꢀf H2◦98 = 119.5 2.2 kcal mol−1. On the basis of the
critical literature review, these authors revised the re-
sult of Clauberg et al. [74] to a new value of 120.5 kcal
C3H2
Thermodynamic properties and geometric structures
of C3H2 isomers are subjects of an ongoing contro-
versy [41,74–90]. On almost all levels of theory an ex-
tremely large singlet–triplet split in these compounds
causes singlet cyclopropenylidene and singlet vinyli-
denecarbene to have significantly lower energies than
their triplet counterparts, while triplet propargylene has
lower energy than its singlet. The scatter in the pro-
posed enthalpies of formation of the most stable C3H2
isomers is on the order of several kilocalories [17].
Majority of recent studies has indicated that the
most stable form of C3H2 is its cyclic isomer, singlet
cyclopropenylidene, c-C3H2. An experimental study
mol−1
.
Most of literature sources agree that the second most
stable C3H2 isomer is triplet propargylene, denoted as
C3H2, lying about several kilocalories above singlet c-
C3H2. On the basis of an extensive theoretical study
and comparison to experimental spectral data, Herges
and Mebel [76] concluded that triplet propargylene has
a 1,3-diradicaloid C2 structure rather than Cs carbene
structure, s-C3H2. Ochsenfeld et al. [85] calculated al-
most isoenergetic triplet structures Cs, C2v, and D
∞h
lying 0.12, 0.17, and 0.69 kcal mol−1, respectively,
above the C2 structure. Seburg et al. [86,91] performed
13C labeling of C3H2 photochemical precursors and
also concluded that triplet propargylene has C2 allene
diradical-like geometry rather than the Cs acetylene
carbene-like structure.
The formation of C3H2 is described in Model 0
mostly through the following reactions:
C3H3 + H → C3H2 + H2
C3H3 + OH → C3H2 + H2O
C3H3 → C3H2 + H
C2H2 + CH → C3H2 + H
C4H2 + O → C3H2 + CO
(11)
(12)
(13)
(14)
(15)
Figure 3 Rate coefficient of reaction C2H + H2 → H +
ꢄ
C2H2, k9. , Stephens et al. [65]; ×, Lander et al. [66];
,
◦
Koshi et al. [67]; ꢅ, Koshi et al. [68]; , Farhat et al. [64];
•
Miller and co-workers [79] suggested that triplet
propargylene is the most likely product of reaction
(11), the dominant formation path of C3H2 in their
H2/O2/Ar C3H4 flame. Although these authors did not
ꢂ, Peeters et al. [70]; ꢁ, Opansky and Leone [69]; , Kruse
ꢀ
and Roth [71]; ------, GRI-Mech 3.0 [23]; – - –, transition-
state-theory calculations of Harding et al. [119] as modified
by Peeters et al. [63]; ——, combined fit, present work.

404
EITENEER AND FRENKLACH
exclude the possibility of formation of other C3H2 iso-
mers in their flames, they modeled the C3H2 species
as triplet propargylene in their kinetic scheme [79,81].
Kiefer et al. [84] considered reactions (11) and (13)
as the source of C3H2 in their shock-tube experiments.
These authors showed that even assuming that cyclo-
propenylidene is the most stable isomer energetically,
the triplet propargylene is by far the dominant iso-
mer at equilibrium in the temperature range 1500–
2500 K (see their Fig. 12), with a relative amount of
cyclopropenylidene increasing toward lower temper-
atures. Boullart et al. [92] described reaction (14) as
the source of C3H2 in their C2H2/O/H flames. These
authors compared the approximate ionization potential
9.5 0.4 eV observed for C3H2 with the experimental
value of 9.15 0.03 eV for c-C3H2 [74] and a theo-
retical value of 8.7 eV for triplet propargylene, C3H2
[74]. Based on this comparison, Boullart et al. [92]
concluded that in their system at 600 K the C3H2 is
largely singlet cyclopropenylidene. This conclusion is
in qualitative agreement with equilibrium calculations
of Kiefer et al. [84]. Guadagnini et al. [87] argued that
reaction (11) with an exit barrier for the c-C3H2 chan-
nel should favor formation of linear C3H2. Detailed
microcanonical RRKM master equation calculations
performed by Vereecken and Peeters [90] on product
distribution of reaction (11) showed that the yield of
the triplet HCCCH isomer changed from 90% at 300 K
to 82% at 2000 K for pressures from 0 to 5 atm. In
contrast, Deyerl et al. [93] proposed based on their ex-
perimental data and RRKM analysis that photodisso-
ciation of the propargyl radical results predominantly
in the formation of cyclopropenylidene.
evidence suggests that the major isomer of C3H2
formed under the conditions of the present experi-
mental study should be the triplet propargylene hav-
ing the 1,3-diradicaloid C2 structure. Because of the
large scatter and scarcity of the thermodynamic data for
this species, several high-level ab initio calculations, at
B3LYP/cc-pVTZ, G2, and G3 levels of theory, were
performed in our laboratory [94] to assess the geo-
metric structure and energetics of triplet propargylene.
The G3 results [17], with ꢀf H2◦98 = 130.4 kcal mol−1
,
were adopted for Model 0, and subjected to optimiza-
tion against Hidaka et al.’s experimental data.
C4H3
Model 0 includes reactions of two C4H3 isomers,
n-C4H3 and i-C4H3 (Table III). A review of litera-
ture [16,20,21,24,25,41,47,56,95–97] reveals signifi-
cant scatter in the standard enthalpies of formation for
these species. Recently, a series of quantum ab initio,
density-functional, and Quantum Monte Carlo calcu-
lations were performed for the enthalpy of formation
of n-C4H3 and i-C4H3 radicals [98]. The initial G3 re-
sults, as documented in [17], were adopted for Model
0, and subjected to optimization against Hidaka et al.’s
experimental data.
MODEL OPTIMIZATION
Optimization Variables
Model 0, assembled as discussed earlier, served as the
first trial mechanism for modeling the present shock-
tube experiments on acetylene oxidation. A screening
sensitivity analysis performed for the experimental tar-
gets of Table II are displayed in Fig. 5. The highest
The above information indicates uncertainties as-
sociated with the thermodynamic and kinetic data
of C3H2 isomers. The experimental and theoretical
Figure 5 Logarithmic response sensitivities computed for the half-rise time t1/2 of CO signal with Model 0. The average values
are arithmetic means of absolute sensitivities for all targets included in Table II. Only values above 0.05 are shown.

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
405
sensitivities correspond to reactions
Optimization Runs
The results of a series of optimization runs are summa-
rized in Table IV. The objective function for optimiza-
tion was defined as
H + O2 → O + OH
H + O2 + Ar → HO2 + Ar
(16)
(17)
ꢁ
ꢂ2
ꢀ ꢀ
ꢁi,calc − ꢁi,exp
Their rate coefficients are known with high accuracy
[23,99,100] and hence were fixed at the correspond-
ing GRI-Mech 3.0 expressions and not included into
parameter optimization. Reactions
ꢁ =
.
ꢁi,exp
all
i=1/4,
1/2,
responses
3/4
The first two rows of Table IV document the least-
square residuals computed with Models H and LW. The
next row, Case I, lists the results obtained with Model 0.
Comparison of the respective ꢁ values shows that,
overall, Model H performs close to Model 0, and the
two have much lower ꢁ than Model LW. As discussed
earlier, predictions of Model LW are close to those of
Model 0 for our mixtures D through K, but Model 0
shows a significant improvement over Model LW for
the most fuel-lean mixtures, A, B, and C (Table I). The
improvement comes solely from the replacement of the
GRI-Mech 1.2 module of Model LW with the updated
version, GRI-Mech 3.0. The differences in the ther-
modynamic properties of the C3H2 and C4H3 species
between Model 0 and Model LW result only in minor
changes of model predictions for the current exper-
imental targets. However, their influence grows with
the increase in mixture concentration and equivalence
ratio, as will be witnessed in modeling of Hidaka et al.’s
experiments [24] described in a later section.
HCO + M → H + CO + M
HCO + O2 → HO2 + CO
(18)
(19)
were studied in our previous work [14] as part of the
formaldehyde submechanism. Their rate coefficients
were fixed at the GRI-Mech 3.0 values and excluded
from the present parameter optimization. Reaction
HCCO + OH → C2O + H2O
(20)
displayed only marginal sensitivity and hence was not
included into the optimization.
Optimization against the experimental targets of
Table II included reactions (6), (7b), and
O + C2H2 → CO + CH2
→ H + HCCO
(21a)
(21b)
Case II was a free optimization run with all pre-
exponential factors set free. Its result, ꢁII = 1.53, rep-
resents an effective lower limit of the objective func-
tion. The free optimization shows a moderate reduction
in the objective function from the reference case of
Model 0, ꢁI = 4.27. Yet, as is often the case, several
parameters reached the optimization boundaries dur-
ing free optimization: k23 reached the upper boundary,
while k6, k7b, k21b, and k24b reached lower boundaries of
the respective optimization ranges. Hence, constrained
optimization followed. Case III repeated the free op-
timization of Case II but with k24a and k24b fixed at
the GRI-Mech 3.0 expressions. Comparison of Cases
II and III showed that the influence of rate coefficients
k24a and k24b is marginal, consistent with the sensitiv-
ity analysis (Fig. 5). Cases IV–VI further demonstrate
this conclusion. Therefore, the rate coefficients of re-
actions (24a) and (24b) were fixed at the corresponding
GRI-Mech 3.0 expressions and not included into fur-
ther optimization runs.
OH + C2H2 → C2H + H2O
CH2 + O2 → H + H + CO2
(22)
(23)
C2H3 + O2 → O + CH2CHO
→ HCO + CH2O
(24a)
(24b)
Reaction (24b) does not appear in Fig. 5 due to its
low sensitivity, but was included into the optimization
process to achieve a better control over the total rate
and the branching ratio of reaction (24). The starting
values for k6 and k7b were those of Laskin and Wang
[25], expressions k6LW and k7LbW, respectively. The start-
ing expressions for the rate coefficients of reactions
(21a), (21b), (22), (23), (24a), and (24b) were those of
GRI-Mech 3.0 [23]. Initially, the pre-exponential fac-
tors and activation energies of all listed rate coefficients
were set as free optimization variables. However, it was
noticed in the initial phase of optimization that allow-
ing changes in activation energies of reactions (22),
(23), (24a), and (24b) did not produce much improve-
ment in fitting the experimental targets. Consequently,
activation energies of these reactions were fixed at the
corresponding GRI-Mech 3.0 values.
Cases VII and VIII explored the influence of pre-
exponential factors A6 and A7b, respectively, whereas
Case IX allowed for simultaneous changes in A6 and
A7b. Addition of activation energies of reactions (6) and

406
EITENEER AND FRENKLACH
Table IV Results of Model Optimization Against Targets Listed in Table II
Objective
Function
ꢁ
Optimization Variablesa
Case
A6
E6
A7b
E7b
A21a
E21a
A21b E21b
A22
A23 A24a A24b
Model H
Model LW
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIV
XV
9.25
61.49
4.27
1.45
1.53
3.96
4.21
3.95
4.02
4.10
3.14
2.87
4.00
4.23
4.19
3.80
3.26
2.08
2.09
1.89
1.99
1.68
1.68
2.19
2.38
2.36
2.24
1.46
1.73
2.89
2.68
2.68
2.88
3.10
2.44
2.36
2.52
2.60
2.48
2.52
4.66
1
0.33
0.33
1
1
1
1
0.33
0.33
1
1
1
1
0.68
0.49
1
2.13
2.09
1
1
1
1
1
1
1
1
0.50
0.50
1
1
1
1
1
1
1
1
1
0.67
1
0.50
0.50
0.50
0.50
1
1
1
1
0.39 2.00+ 0.42 0.40
−
−
−
−
−
−
−
0.37 2.00+
1
1
1
1
1
1
1
1
1
1
1.45
1
0.40
1
−
−
1
1
1
1
1
1
1
1.39
1
1
1
1
1.16
1
1
1
0.96 0.40
2.11
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3.00+
2.00+ −2000 0.50
−188
−
−
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.83
1
1
1.47
1.52
1.86
2.10
1.85
2.11
2.69
3.00+
2.17
2.22
1.85
1
−
XVI
1
1
0.33
0.33
1
−
−
−
XVII
XVIII
XIX
XX
XXI
−
3.00+
0.33
0.33
0.33
0.33
0.33
0.33
0.50
0.33
0.33
−
−
−
−
−
−
−
−
−
−
1
1
0.49
1
1
1
0.50
0.50
0.50
0.75
1
1
−
0.49
0.51
1
1
1
1
0.40
1
2.00
2.00
2.00
2.00
2.00
1.50
1.50
1.50
1.50
1.50
1.50
1.50
1
1
1
1
1
1
−
−
XXII
XXIII
XXIV
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
XXXI
XXXII
XXXIII
XXXIV
XXXV
XXXVI
XXXVII
XXXVIII
XXXIX
0.50
−
1
0.33
1.58 −1000 0.75 −1000
−
−
1.46 −1000 0.50
2.00+
−
−
−
−
−
−
−
−
1
1
0.33 2000+ 2.68
0.50
0.50
0.50
0.50
0.50
1
1
1
0.97
0.95
1
1
1
1
1
−
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
0.33
1
1.57
1.37
1.40
1.63
1.55
1.79
1.63
1.61
1.80
1.62
1.80
1
−
−
−
−
−
−
−
−
−
−
−
3.00+
3.00+
1
1
0.75
0.50
1
2.00+
2.00+
1
−
−
0.50
0.70
0.70
0.65
0.60
1
2.00+
1
1
1
1
1
a Entry designations are as follows: 1 for a pre-exponential factor and an empty entry for an activation energy indicates that the corresponding
value was fixed at the Model 0 expression. Numerical entry followed by + (in superscript) or − (in subscript) sign indicates that the optimization
variable reached the upper or lower boundary of the optimization range, respectively. Underlined numerical entry indicates that the value was
fixed during the optimization.
(7b) as optimization variables, Case X, did not produce
a significant improvement in the objective function, yet
forced the rate coefficient k6 above the chosen upper
limit 3.00 of the optimization range. Cases XI–XVII
tested the interplay among the rate coefficients of re-
actions (21a), (21b), (22), and (23). A major improve-
ment in the objective function came from simultane-
ous optimization of rate coefficients k21a, k21b, and k22
(Case XVII). When set free (Cases XVI and XI), the
optimized values of k23 were close to 1; hence the rate
coefficient k23 was fixed at the starting expression and
optimized no further.

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
407
XIX
Cases XVIII–XXI examined the interaction among
of 3 from the base expression leads to k
= 3.3 ×
7b
1012 cm3 mol−1 s−1
.
the rate coefficients of reactions (6), (7b), (21a), (21b),
and (22). Case XIX showed that inclusion of k7b into
optimization instead of k22 resulted in approximately
the same quality of fit to experimental data as Case
XVII. Simultaneous optimization of k21a, k21b, k22, and
k23, Case XX, did not significantly reduce the objective
function compared to Cases XVII and XIX, but resulted
in further departure of k23 from the starting expression.
As the rate coefficient k22 is better established than
simply estimated k7b (see, e.g., Baulch et al. [101] and
references therein), optimization Case XIX is preferred
in the current study to Case XVII.
As mentioned earlier, recommendations [23,34,
102–118] for the total rate coefficient of reaction (21)
are in a reasonable agreement with each other (Fig. 6),
yet there is a significant scatter in the branching ra-
tio of this reaction [17,101,119]. The branching ratio
employed by Model 0 is taken from GRI-Mech 3.0,
GRI-Mech3.0
BR
= 0.66. Optimization Case XIX resulted
21
XIX
21
in BR
= 0.33 while leaving the total rate of reaction
(21) essentially unchanged. We will return to this issue
at our final recommendations.
We will refer to the reaction mechanism with the
Case XIX parameter set as Model 1. A comparison in
performance of Models 0 and 1 against the experimen-
tal data of Table II is shown in the bottom panel of
Fig. 2. As can be seen, Model 1 exhibits substantial
improvements over Model 0, with relative errors in the
predicted half-rise times of CO profiles within 20%
for all experimental conditions studied.
Cases XIX and XXII–XXVII illustrate a trade-
off between changing the branching ratio and the
total rate of reaction (21). Case XIX showed that
ꢁXIX = 1.99, close to the minimum value of ꢁIII
=
1.53, could be reached just by changing the branch-
ing ratio of reaction (21), BR21 = k21b/(k21a + k21b),
and the pre-exponential factor of reaction (7b). Com-
pared to the starting GRI-Mech 3.0 expressions, Case
XIX reversed the branching ratio of channels (21a)
and (21b) while leaving the total rate of reaction
(21) essentially unchanged. Case XXIII resulted in
almost equal rates of channels (21a) and (21b), or
BR21 = 0.5, and an increase in the total rate of reac-
tion (21) by about 40%. Case XXII led to the BR21
value intermediate between Cases XIX and XXIII.
Case XXV gave rise to BR21 = 0.5 while decreas-
ing the activation energy of reaction (21), E21, by 1
kcal mol−1. Such a change in E21 would lead to sig-
nificantly overestimated rate of reaction (21) at low
temperatures.
MODEL VALIDATION AND FURTHER
OPTIMIZATION
Prior to making final conclusions, we tested the tenta-
tive result of our optimization, Model 1, against another
set of experimental data, recently reported shock-tube
Additional optimization runs, Cases XXVIII–
XXXIX, were performed to assess the influence of in-
creasedk22 ontheoptimizedvaluesofk6, k7b, k21a, k21b
,
and k23; its significance will be discussed in the next
section.
Summary of Optimization Results
Considering the trends revealed by the results of op-
timization and taking into account the uncertainties in
literature recommendations, we select Case XIX as a
tentative choice.
Optimization performed over the present acetylene
oxidation targets indicates that a major improvement in
agreement between the model and experiment comes
from optimized rate coefficients of reaction O + C2H2,
channels (21a) and (21b), and reaction (7b). A three-
fold decrease in the rate coefficient of reaction (7b) is
suggested by many optimization runs, and it can be ac-
cepted considering the estimated character of k7b (see
Laskin and Wang [25]). Reduction of k7b by a factor
Figure 6 Literature recommendations for the rate coeffi-
cient of reaction O + C2H2 → products, k21 = k21a + k21b
.
, Sullivan and Warneck [102]; ×, Niki [103]; , Brown and
Thrush [104]; ------, James and Glass [105]; —ꢂ—, Hoyer-
ꢄ
mann et al. [106]; —ꢅ—, Westenberg and de Haas [107];
,
Stuhl and Niki [108]; --ꢁ--, Peeters and Mahnen [109]; –· · ·–,
Vandooren and Van Tigglen [110]; ∇, Westenberg and de
Haas [111]; – –, Aleksandrov et al. [112]; ---∇---, Lohr and
ꢀ
Roth [113]; – –, Homann and Wellman [114]; –+–, Frank
ꢆ
et al. [34]; – - –, Mahmud and Fontijn [115]; --- ---, Russell
◦
ꢄ
et al. [116]; – –, Bohn and Stuhl [117]; –-ꢁ-–, Michael and
Wagner [118]; – –, GRI-Mech 3.0 [23].
•

408
EITENEER AND FRENKLACH
Table V Optimization Targets for Acetylene Oxidation
Based on Experimental Observations of Hidaka et al.
[24]
oxidation of acetylene by Hidaka et al. [24]. It turned
out that essentially all the models we considered—
GRI-Mech 3.0, LW, Model 0, and Model 1—had dif-
ficulty in explaining those observations, as illustrated
in Fig. 7. On the other hand, Model H developed by
the authors [24] by fitting their results does not predict
closely the experimental data of the present work, as
can be seen in the top panel of Fig. 2. To resolve this ap-
parent disagreement, we subjected the Hidaka et al.’s
data to the same type of analysis we applied to our
own data, i.e., we subjected those data to optimization
starting with our Model 1.
C5
ꢁ1/4
ꢁ1/2
ꢁ3/4
Target
T5 (K) (mol m−3
)
(ꢀs) (ꢀs) (ꢀs)
Series 1: 4.0% C2H2–2.0% O2–Ar
HID-6Aa
HID-6Bb
HID-6Cc
1273
1343
1292
12.9
13.4
13.0
–
–
527
871
725
826
543
344
–
Series 2: 1.0% C2H2–2.5% O2–Ar
HID-7Ad
1221 14.5
Series 3: 1.0% C2H2–5.0% O2–Ar
HID-7Bd
1214 14.5
Series 4: 2.0% C2H2–2.5% O2–Ar
HID-7Cd
1179 14.3
339
150
566
421
190
715
655
322
826
Target Development
The derived experimental targets are listed in Table V.
Targets HID-6A and HID-6B were obtained from the
concentration profiles of O2 and C2H2 (Figs. 6a and
6b in [24]); ꢁ1/2 and ꢁ3/4 represent the times when O2
or C2H2 concentration reached 1/2 and 3/4 of the ini-
tial value, respectively. Target HID-6C was developed
based on CO concentration profile (Fig. 6c in [24]);
ꢁ1/4 and ꢁ1/2 represent the times when CO concentra-
tion reached 1/4 and 1/2, respectively, of its maximum
value. The maximum CO concentration, not shown in
Fig. 6c of Hidaka et al. [24], was calculated using
Model H.
Targets HID-7A, HID-7B, and HID-7C were ob-
tained from the reported emission profiles at 4.24 ꢀm
(Figs. 7a–7c in [24]). Hidaka and co-workers [24] con-
cluded that the main source of IR emission observed
at 4.24 ꢀm in their experiments was CO2. We calcu-
lated the CO2 emission intensity using their reported
expression [46] Ie = 10T/2985+7.20 [CO2], where T in
K, [CO2] in cm3 mol−1, and Ie in mV. Calculations
using Model H showed that the experimental emission
profiles could be approximated by CO2 concentration
a O2 decay, mass spectrometry.
b C2H2 decay, mass spectrometry.
c CO rise, mass spectrometry.
d CO2 rise, IR emission.
profiles with an accuracy of about 5% for targets HID-
7A and HID-7C. For target HID-7B, however, the dif-
ferences between the emission and the CO2 concen-
tration profiles were significantly higher, about 15%.
On the basis of this observation, the target HID-7B
of Table V was excluded from the present optimiza-
tion, although the comparisons with the experimental
emission data were performed (see later). For targets
HID-7A and HID-7B, the values of ꢁ1/4, ꢁ1/2 and ꢁ3/4
listed in Table V are the times when emission calcu-
lated using the above expression for Ie and Model H
reached 1/4, 1/2, and 3/4 of its value at 2000 ꢀs, and for
target HID-7C of its maximum value. The compound
errors in determination of the target values, because
of approximations involved, are estimated to be about
5–10%.
Optimization Variables
Figure 8 displays a sensitivity spectrum calculated for
the experimental conditions of Fig. 7 with Model 0.
Reaction (16) has the largest sensitivity for all targets
of Table V, as expected. Its rate coefficient, k16, was
fixed at the GRI-Mech 3.0 expression, as previously,
and not included into optimization. The optimization
variables were chosen according to the rest of the sensi-
tivity ranking and included the pre-exponential factors
of reactions (22), (24a), (24b), and
C4H2 + H → i-C4H3
C3H3 + OH → C2H3 + HCO.
(25)
(26)
Figure 7 Observed and calculated O2 profiles. Experi-
mental conditions: 4.0% C2H2–2.0% O2–Ar; T0 = 1273 K;
C0 = 12.9 mol m−3
. , experiment (Hidaka et al. [24]); – –,
ꢀ
•
The sensitivity of the Hidaka et al.’s targets to k7b,
k21a, and k21b is very small (which explains the small
GRI-Mech 3.0; – – –, Model LW; ------, Model 0; –··–, Model
1; ——, Model 2.

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
409
Figure 8 Logarithmic response sensitivities of the half-decay time t1/2 of O2 concentration computed for the experimental
conditions of Fig. 7 with Model 0. Only values above 0.05 are shown.
differences between the predictions of Models 0 and 1
for the conditions of Fig. 7).
Comparison of the sensitivity spectra shown in
Figs. 5 and 8 indicates that the optimization variables
common to our experimental data and those of Hidaka
et al. [24] are k22, k24a, and k24b. As was shown in the
Melius [41] and included into their kinetic mechanism
with a rate coefficient of 5.0 × 1013 cm3 mol−1
s
−1. It
was modified in a later study [79] to a significantly
lower value, 2.0 × 1012 e−503/T cm3 mol−1
s
−1. In
light of these facts, we added k27 to the optimization
variables.
previous section, the sensitivity of our targets to k24a
,
and k24b is only marginal. This leaves k22 as the only
optimization variable common to the both data sets.
Having examined the behavior of k22 under the con-
ditions of our experiments (Cases XXVIII–XXXIX in
Table IV), we now focus on the analysis of the Hidaka
et al.’s data.
In addition to the chosen rate coefficients, we in-
cluded the enthalpies of formation ꢀf H2◦98 of C3H2,
i-C4H3, and n-C4H3 as optimization variable because
of the large uncertainties in the thermodynamic data of
these species. A screening sensitivity analysis showed
that with a decrease in the enthalpy of formation of
C3H2 the influence of reaction
Optimization Results
The results of several optimization runs are summa-
rized in Table VI. Case HI corresponds to the base
mechanism, Model 0. Case HII is an unconstrained
optimization run. It resulted in a simultaneous twofold
decrease in rate coefficients k24a and k24b and hence
in the total rate coefficient of reaction (24). Model 0
employs k24 taken from the multichannel RRKM cal-
culations of Mebel et al. [120] which are in excel-
lent agreement with consensus experimental values at
temperatures below 1000 K (see, e.g., Knyazev and
Slagle [121]). On this basis, a twofold reduction in
k24 is unacceptable. Fixing k24a and k24b at the Model
0 expressions (Case HIII) produced approximately
the same quality of fit to experimental data as Case
HII. Therefore, the rate coefficients of reactions (24a)
C3H2 + O2 → HCCO + H + CO
(27)
increases. Reaction (27) was proposed by Miller and

410
EITENEER AND FRENKLACH
Table VI Results of Model Optimization Against Hidaka et al.’s Targets in Table V
Optimization Variablesa
Objective
Function
ꢁ
Reaction Rate Coefficients
Species Enthalpies, ꢀh
Case
A22
A24a
A24b
A25
A26
A27
C3H2
0
i-C4H3
n-C4H3
HI
HII
HIII
HIV
HV
HVI
HVII
HVIII
HIX
1
1
1
0.58
1
1
2.19
2.41
1
4.00
0.13
0
0
3.53
3.00+
1.81
0.50
3.00+
0.33
5.00
5.00
4.00
3.00
3.16
0.76
0.83
0.94
0.72
0
5.00
2.50
2.50
2.50
0.080
0.090
0.093
0.096
0.091
0.110
0.111
0.099
0.100
0.095
0.115
0.133
0.148
0.153
0.116
0.132
0.223
0.996
0.325
0.108
−
−
−
−
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.13
0.13
0.13
0.25
0.18
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.50
1.00
0.25
0.25
0.25
0.25
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
1.84
1.84
1.94
2.24
2.36
2.02
2.05
1.96
1
2.59
0.33
−
−
−
1
2.73
0.33
−
−
−
1
1
1
1
2.60
0.33
0.33
0.33
0.33
5.00
2.50
−
−
−
3.00+
3.00+
2.93
0
0
0
0
0
4.00
2.00
2.40
3.00
2.50
2.50
0
0
0
0
0
−
0
0
−
4.00
−
−
HX
HXI
1
2.93
0.33
0
1.14
0.77
2.34
2.95
3.33
3.36
0
0
0
0
0
−
−
1
1
1
1
1
1
1
1
2.78
0.33
0.33
0.33
0.33
0.50
0.33
0.33
1.00
4.00
3.00
4.00
3.00
−
−
−
HXII
HXIII
HXIV
HXV
HXVI
HXVII
HXVIII
HXIX
HXX
HXXI
1.50+
1.50+
1.50+
1.50+
2.66
3.00+
2.50+
2.50+
3.00+
3.00+
3.00+
3.00+
1.00
−
−
−
−
−
−
−
−
−
3.00
−
−
−
0
0
0
0
0
−
3.00+
3.00+
3.00+
1.50+
1.50+
−
1
1
1
0.33
0.33
0.33
−
3.00+
3.00+
−
4.00
1.97
2.00
−
−
−
a Entry designations are as follows. For A22 through A26, 1 indicates that the corresponding rate coefficient was fixed at the Model 0
expression. For A27 the numbers listed are multiplication factors to the Pauwels et al.’s expression [79]. For species enthalpies, 0 indicates that
G3
◦
the corresponding standard enthalpy of formation was fixed at the G3 result, ꢀf
H
= 127.4, 116, and 126.2 kcal mol−1 for C3H2, i-C4H3,
298
G3
◦
and n-C4H3, respectively, and for the nonzero entries ꢀf H2◦98 = ꢀf
H
− ꢀh (kcal mol−1). Numerical entry followed by the + (in superscript)
298
or − (in subscript) sign indicates that the optimization variable reached the upper or lower boundary of the optimization range, respectively.
Underlined numerical entry indicates that the value was fixed during the optimization.
and (24b) were not included into further optimization
runs.
CONCLUSIONS
The rest of the runs in Table VI report the results of
various constrained optimizations, looking for a suit-
able compromise between the kinetic and thermody-
namic changes required to reconcile the model and
Hidaka et al.’s targets. Cases HIV–HXI show that the
optimized values of k22 were about twice higher than
the initial, Model 0 value. Comparing these optimiza-
tion runs to Cases XXVIII–XXXIX in Table IV, those
testing k22 on our targets, shows opposite trends. As a
compromise, we chose a multiplier of 1.50 for A22.
After an additional series of optimization runs,
testing further constraints (Cases HXII–HXXI), we
selected the Case HXXI as the best current com-
promise for the Hidaka et al.’s targets. It combines
acceptable (see below) kinetic and thermodynamic
changes with a relatively low value of ꢁHXXI = 0.108,
not far removed from the unconstrained minimum of
ꢁHII = 0.080.
On the basis of the present analysis of our and Hidaka
et al.’s experimental data along with the assessment of
uncertainties in the pertinent thermochemical data, our
choice for the best current parameter set is a combina-
tion of the results from Case XXXVIII in Table IV and
Case HXXI in Table VI. This parameter set is sum-
marized in Table VII and the corresponding reaction
model is designated as Model 2. Many aspects of the
parameter changes were addressed in the previous sec-
tions, while discussing the results of and motivation for
the performed optimization runs. The most noteworthy
of these changes are as follows:
•
Model 2 makes a compromise to the branching
ratio of reaction (21), increasing it from 0.33 in
Model1to0.4, closertoanaverageliteraturevalue
of 0.66 used in GRI-Mech 3.0.

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
411
Table VII Best Current Parameter Set
Model Parameter
Parameter Valuesa
Source/Action
k6
C2H2 + M → H2CC: + M
2.45 × 1015 T −0.64 e−25010/T
[25]
k[25]/3
[46]
fit, Fig. 3
fit, Fig. 4
k7b
k8a
k9
H2CC: + O2 → CH2 + CO2
HCCO + O2 → OH + 2CO
C2H + H2 → H + C2H2
3.3 × 1012
4.2 × 1010 e−430/T
4.45 × 106T 2.22 e−461/T
1.94 × 1013T 0.238 e37/T
1.25 × 107 T 2.0 e−956/T
8.1 × 106 T 2.0 e−956/T
5.06 × 107 T 2.0 e−7046/T
5.8 × 1012 e−755/T
k10
k21a
k21b
k22
k23
k24a
k24b
k25
k26
k27
C2H + C2H2 → H + C4H2
O + C2H2 → CO + CH2
O + C2H2 → H + HCCO
OH + C2H2 → C2H + H2O
CH2 + O2 → 2H + CO2
kGRI-Mech 3.0 × 1.8
kGRI-Mech 3.0 × 0.60
k[122] × 1.5
GRI-Mech 3.0
[120]
C2H3 + O2 → O + CH2CHO
C2H3 + O2 → HCO + CH2O
C4H2 + H → i-C4H3
3.03 × 1011 T 0.3 e5.5/T
4.58 × 1016 T −1.4 e−511/T
3.3 × 1030 T −4.92 e−5435/T
1.33 × 1013
[120]
k[47] × 3
C3H3 + OH → C2H3 + HCO
C3H2 + O2 → HCCO + H + CO
k[47]/3
1.25 × 1011 e−503/T
k[79] × 0.0625
ꢀf H2◦98(C3H2)
123.4
114.0
124.2
See text
See text
See text
ꢀf H2◦98 (i-C4H3)
ꢀf H2◦98 (n-C4H3)
a Units are cm3 mol−1 s−1 for rate coefficients and kcal mol−1 for enthalpies of formation.
•
The pre-exponential factor of k22 is increased by
50% from Miller and Melius’ recommendation
[122]. All optimization cases for the Hidaka et al.’s
targets show a persistent upward trend for this rate
coefficient, either reaching the upper boundary
when constrained or doubling its value when left
free (Table VI). On the other hand, Cases XXVIII–
XXXIX in Table IV show that increasing k22 de-
teriorates the quality of fit for our own targets:
raising it by factors of 1.5 and 2 increases the
objective function by 25 and 50%, respectively,
from Case XIX. Our choice of a 50% increase in
k22 is a compromise between the two trends; we
consider it to be feasible in light of the scatter in
reported experimental data on this reaction (see,
e.g., Baulch et al. [101]).
the midst of estimates [17] based on recent experi-
mental values for c-C3H2 [74,77] and quantum ab
initio calculations of the difference between C3H2
and c-C3H2 [41,75,82,85–89].
•
•
Rate coefficient k26 of Model 0 is an estimated
value [47] and hence a factor of 3 decrease in k26
is not prohibitive.
The decrease of k27 by a factor of 16 from Ref.
[79] is the largest change suggested by Model 2.
It follows a definite trend seen in our optimiza-
tion runs (Table IV). The reduction can be ratio-
nalized considering the 1,3-diradical structure of
C3H2 and is consistent with the increased stability
of C3H2 radical. Also, k27 in Model 2 is closer in
magnitude to the experimental result of 3.0 × 1010
e−1443/T cm3 mol−1 s−1 reported [37] for reaction
C3H3 + O2 → HCO + CH2CO.
Figure 9 Observed and calculated species profiles. Top
panel: Relative C2H2 concentration in a 4.0% C2H2–2.0%
O2–Ar mixture at T0 = 1343 K and C0 = 13.4 mol m−3
.
Bottom panel: CO concentration in a 4.0% C2H2–2.0% O2–
Ar mixture at T0 = 1292 K and C0 = 13.0 mol m−3
. , ex-
•
•
The Model 2 value for the enthalpy of formation
of C3H2, ꢀf H2◦98(C3H2) = 123.4 kcal mol−1, is in
periment (Hidaka et al. [24]); – – –, Model LW; ------, Model
0; ——, Model 2.

412
EITENEER AND FRENKLACH
and 10. This is not to say that Model 2 is the best pos-
sible model. On the contrary, we use language “best
current” to qualify the result of the present modeling
effort, emphasizing the transient nature of the process
of derivation of reaction models we advocate in gen-
eral [23,99] and practice in the present study. The abil-
ity to reconcile the two sets of experimental data, ours
and Hidaka et al.’s, did not come “easy” but required
some difficult and possibly problematic choices. Model
2 represents our best assessment of the current data
and their associate uncertainties. It is a noteworthy fea-
ture of the employed numerical procedure that pos-
sible tradeoffs are expressed in rigorous quantitative
terms. One can create a different best current model
by changing optimization constraints, either as a re-
sult of personal preferences or by adding new data as
they become available (for instance, an anonymous Re-
viewer suggested decreasing k24a based on very recent
reports [123,124]). The present recommendation, sum-
marized in Table VII, is offered in expectation that the
development of acetylene combustion mechanism will
continue, with inclusion of larger data sets and broader
participation of the community in the process.
BIBLIOGRAPHY
1. Glassman, I. Combustion; Academic Press: Orlando,
FL, 1996.
Figure 10 Observed and calculated CO emission profiles at
4.24 ꢀm. Top panel: 1.0% C2H2–2.5% O2–Ar, T0 = 1221 K,
C0 = 14.5 mol m−3. Middle panel: 1.0% C2H2–5.0% O2–
Ar, T0 = 1214 K, C0 = 14.5 mol m−3. Bottom panel: 2.0%
2. Turns, S. R. An Introduction to Combustion: Concepts
and Applications; McGraw-Hill: New York, 2000.
3. Spear, K. E.; Dismukes, J. P. (Eds.) Synthetic Diamond:
Emerging CVD Science and Technology; Wiley: New
York, 1994.
4. Frenklach, M.; Ebert, L. B. J Phys Chem 1988, 92, 561.
5. Richter, H.; Grieco, W. J.; Howard, J. B. Combust
Flame 1999, 119, 1.
C2H2–2.5% O2–Ar, T0 = 1179 K, C0 = 14.3 mol m−3
. ,
•
experiment (Hidaka et al. [24]); – - –, Model H; – – –, Model
LW; ------, Model 0; ——, Model 2.
6. Frenklach, M.; Feigelson, E. In From Stardust to Plan-
etesimals; Pendleton, Y. J.; Tielens, A. G. G. M. (Eds.);
Astronomical Society of the Pacific: San Francisco,
1997; p. 107.
7. Palmer, H. B.; Cullis, C. F. In Chemistry and Physics
of Carbon; Walker, P. L. (Ed.); Marcel Dekker: New
York, 1965; p. 265.
8. Haynes, B. S.; Wagner, H. G. Prog Energy Combust
Sci 1981, 7, 229.
9. Frenklach, M. Phys Chem Chem Phys 2002, 4, 2028.
10. Varatharajan, B.; Williams, F. A. Combust Flame 2001,
125, 624.
•
The optimization results for the enthalpies of
formation of i-C4H3 and n-C4H3 radicals, ob-
tained in fitting the reaction model against the
Hidaka et al.’s targets, exhibit a definite down-
ward trend. The Model 2 choices are within the
current range of reported estimates [16,20,21,24,
25,41,47,56,95–98], with a difference of about
10 kcal mol−1 between the two isomers, the mid-
dle grounds among recent theoretical predictions
[98].
11. Charlston-Goch, D.; Chadwick, B. L.; Morrison,
R. J. S.; Campisi, A.; Thomsen, D. D.; Laurendeau,
N. M. Combust Flame 2001, 125, 729.
12. Yuan, T.; Wang, C.; Yu, C.-L.; Frenklach, M.;
Rabinowitz, M. J Phys Chem 1991, 95, 1258.
13. Yu, C.-L.; Wang, C.; Frenklach, M. J Phys Chem 1995,
99, 14377.
Model 2 fits our experimental targets almost as good
as Model 1 (see bottom panel of Fig. 2), with rela-
tive errors of +25/−20%, over the entire temperature
range studied. At the same time, contrary to Model 1,
Model 2 also reproduces closely the experimental data
of Hidaka et al. [24], as demonstrated in Figs. 7, 9,

EXPERIMENTAL AND MODELING STUDY OF SHOCK-TUBE OXIDATION OF ACETYLENE
413
14. Eiteneer, B.; Yu, C.-L.; Goldenberg, M.; Frenklach, M.
J Phys Chem 1998, 102, 5196.
43. Bozzelli, J. W.; Dean, A. M. J Phys Chem 1993, 97,
4427.
15. Colket, M. B.; Seery, D. J.; Palmer, H. B. Combust
Flame 1989, 75, 343.
16. Colket, M. B.; Seery, D. J.; Palmer, H. B. Combust
Flame 1991, 84, 434.
44. Baulch, D. L.; Cobos, C. J.; Cox, R. A.; Frank, P.;
Hayman, G.; Just, T.; Kerr, J. A.; Murrells, T.; Pilling,
M. J.; Troe, J.; Walker, R. W.; Warnatz, J. J Phys Chem
Ref Data 1994, 23, 847.
17. Eiteneer, B. N. PhD Thesis, University of California at
Berkeley, 2000.
18. Gardiner, W. C., Jr.; Walker, B. F.; Wakefield, C. B. In
Shock Waves in Chemistry; Lifshitz, A. (Ed.); Dekker:
New York, 1981; p. 319.
45. Frenklach, M.; Wang, H. In Soot Formation in Com-
bustion: Mechanisms and Models; Bockhorn, H. (Ed.);
Springer-Verlag: Berlin, 1994; p. 165.
46. Hidaka, Y.;Kimura, K.;Hattori, K.;Okuno, T. Combust
Flame 1996, 106, 155.
19. McBride, B. J.; Gordon, S.; Reno, M. A. NASA TM-
4513, 1993.
47. Wang, H.; Frenklach, M. Combust Flame 1997, 110,
173.
20. Burcat, A.; McBride, B. J. Technion TAE 697, 1993.
21. Burcat, A. http://garfield.chem.elte.hu/Burcat/burcat.
html.
48. Wodtke, A. M.; Lee, Y. T. J Phys Chem 1985, 89, 4744.
49. Green, P. G.; Kinsey, J. L.; Field, R. W. J Chem Phys
1989, 91, 5160.
22. Eiteneer, B.; Frenklach, M. J Phys Chem 2000, 104,
9797.
50. Segall, J.; Lavi, R.; Wen, Y.; Wittig, C. J Phys Chem
1989, 93, 7287.
23. Smith, G. P.; Golden, D. M.; Frenklach, M.; Moriarty,
N. W.; Eiteneer, B.; Goldenberg, M.; Bowman, C. T.;
Hanson, R.; Song, S.; Gardiner, W. C.; Lissianski, V.;
Qin, Z. http://http://www.me.berkeley.edu/gri mech/.
24. Hidaka, Y.; Hattori, K.; Okuno, T.; Inami, K.; Abe, T.
Combust Flame 1996, 107, 401.
25. Laskin, A.; Wang, H. Chem Phys Lett 1999, 303, 43.
26. Colket, M. B.; Naegeli, D. W.; Glassman, I. Int J Chem
Kinet 1975, 7, 223.
51. Ervin, K. M.; Gronert, S.; Barlow, S. E.; Gilles, M. K.;
Harrison, A. G.; Bierbaum, V. M.; DePuy, C. H.;
Lineberger, W. C.; Ellison, G. B. J Am Chem Soc 1990,
112, 5750.
52. Habibollahzadeh, D.; Murray, J. S.; Grodzicki, M.;
Seminario, J. M.; Politzer, P. Int J Quantum Chem 1992,
42, 267.
53. Mordaunt, D. H.; Ashfold, M. N. R. J Chem Phys 1994,
101, 2630.
27. Tanzawa, T.; Gardiner, W. C., Jr. Combust Flame 1980,
39, 241.
54. Partridge, H.; Bauschlicher, C. W., Jr. J Chem Phys
1995, 103, 10589.
28. Miller, J. A.; Mitchell, R. E.; Smooke, M. D.; Kee, R. J.
Proc Combust Inst 1982, 19, 181.
55. Peterson, K. A.; Dunning, T. H., Jr. J Chem Phys 1997,
106, 4119.
29. Warnatz, J.; Bockhorn, H.; Moser, A.; Wenz, H. Proc
Combust Inst 1983, 19, 841.
56. Kiefer, J. H.; Von Drasek, W. A. Int J Chem Kinet 1990,
22, 747.
30. Warnatz, J. In Combustion Chemistry; Gardiner,
W. C., Jr. (Ed.); Springer-Verlag: New York, 1984;
p. 197.
31. Perry, R. A. Combust Flame 1984, 58, 221.
32. Scherzer, K.; Claus, P.; Karwath, M. Z Phys Chem
1985, 266, 321.
33. Tsang, W.; Hampson, R. F. J Phys Chem Ref Data 1986,
15, 1087.
34. Frank, P.; Bhaskaran, K. A.; Just, T. Proc Combust Inst
1986, 21, 885.
35. Wu, C. H.; Singh, H. J.; Kern, R. D. Int J Chem Kinet
1987, 19, 975.
36. Dean, A. M.; Westmoreland, P. R. Int J Chem Kinet
1987, 19, 207.
37. Slagle, I. R.; Gutman, D. Proc Combust Inst 1988, 22,
875.
38. Miller, J. A.; Bowman, C. T. Prog Energy Combust Sci
1989, 15, 287.
57. Gardiner, W. C.; Walker, B. F. J Chem Phys 1968, 48,
5279.
58. Jachimowski, C. J. Combust Flame 1977, 29, 55.
59. Duran, R. P.; Amorebieta, V. T.; Colussi, A. J. J Phys
Chem 1988, 92, 636.
60. Kiefer, J. H.; Sidhu, S. S.; Kern, R. D.; Xie, K.; Chen,
H.; Harding, L. B. Combust Sci Technol 1992, 82, 101.
61. Gallo, M. M.; Hamilton, T. P.; Schaefer, H. F., III, J Am
Chem Soc 1990, 112, 8714.
62. Jones, I. T. N.; Bayes, K. D. Proc R Soc London Ser A
1973, 335, 547.
63. Peeters, J.; Schaekers, M.; Vinckier, C. J Phys Chem
1986, 90, 6552.
64. Farhat, S. K.; Morter, C. L.; Glass, G. P. J Phys Chem
1993, 12789.
65. Stephens, J. W.; Hall, J. L.; Solka, H.; Yan, W.-B.; Curl,
R. F.; Glass, G. P. J Phys Chem 1987, 91, 5740.
66. Lander, D. R.; Unfried, K. G.; Glass, G. P.; Curl, R. F.
J Phys Chem 1990, 94, 7759.
67. Koshi, M.; Nishida, N.; Matsui, H. J Phys Chem 1992,
96, 5875.
39. Kern, R. D.; Xie, K.; Chen, H.; Kiefer, J. H. Proc Com-
bust Inst 1990, 23, 69.
40. Tsang, W. J Phys Chem Ref Data 1991, 20, 221.
41. Miller, J. A.; Melius, C. F. Combust Flame 1992, 91,
21.
68. Koshi, M.; Fukuda, K.; Kamiya, K.; Matsui, H. J Phys
Chem 1992, 96, 9839.
42. Wang, H. Ph. D. Thesis, Pennsylvania State University,
1992.
69. Opansky, B. J.; Leone, S. R. J Phys Chem 1996, 100,
19904.

414
EITENEER AND FRENKLACH
70. Peeters, J.; Van Look, H.; Ceursters, B. J Phys Chem
1996, 100, 15124.
97. Cioslowski, J.; Liu, G.; Moncrieff, D. J Phys Chem A
1999, 103, 11465.
71. Kruse, T.; Roth, P. J Phys Chem A 1997, 101, 2138.
72. Shin, K. S.; Michael, J. V. J Phys Chem 1991, 95, 5864.
73. Pedersen, J. O. P.; Opansky, B. J.; Leone, S. R. J Phys
Chem 1993, 97, 6822.
98. Krokidis, X.; Moriarty, N. W.; Lester, W. A., Jr.;
Frenklach, M. Int J Chem Kinet 2001, 33, 808.
99. Frenklach, M.; Wang, H.; Rabinowitz, M. J. Prog En-
ergy Combust Sci 1992, 18, 47.
74. Clauberg, H.; Minsek, D. W.; Chen, P. J Am Chem Soc
1992, 114, 99.
75. Jonas, V.; Bohme, M.; Frenking, G. J Phys Chem 1992,
96, 1640.
76. Herges, R.; Mebel, A. J Am Chem Soc 1994, 116, 8229.
77. Chyall, L. J.; Squires, A. A. Int J Mass Spectrom Ion
Proc 1995, 150, 257.
78. Kern, R. D.; Chen, H.; Kiefer, J. H.; Mudipalli, P. S.
Combust Flame 1995, 100, 177.
100. Yu, C.-L.; Frenklach, M.; Masten, D. A.; Hanson,
R. K.; Bowman, C. T. J Phys Chem 1994, 98, 4770.
101. Baulch, D. L.;Cobos, C. J.;Cox, R. A.;Esser, C.;Frank,
P.; Just, T.; Kerr, J. A.; Pilling, M. J.; Troe, J.; Walker,
R. W.; Warnatz, J. J Phys Chem Ref Data 1992, 21,
411.
102. Sullivan, J. O.; Warneck, P. J Phys Chem 1965, 69,
1749.
103. Niki, H. J Chem Phys 1967, 47, 3102.
104. Brown, J. M.; Thrush, B. A. Trans Faraday Soc 1967,
63, 630.
79. Pauwels, J.-F.; Volponi, J. V.; Miller, J. A. Combust Sci
Technol 1995, 110/111, 249.
80. Robinson, M. S.; Polak, M. L.; Bierbaum, V. M.;
DePuy, C. H.; Lineberger, W. C. J Am Chem Soc 1995,
117, 6766.
105. James, G. S.; Glass, G. P. J Chem Phys 1969, 50, 2268.
106. Hoyermann, K.; Wagner, H. G.; Wolfrum, J. Z Phys
Chem 1969, 63, 193.
81. Miller, J. A.; Volponi, J. V.; Pauwels, J.-F. Combust
Flame 1996, 105, 451.
107. Westenberg, A. A.; deHaas, N. J Phys Chem 1969, 73,
1181.
82. Takahashi, J.; Yamashita, K. J Chem Phys 1996, 104,
6613.
83. Jackson, W. M.; Mebel, A. M.; Lin, S. H.; Lee, Y. T. J
Phys Chem A 1997, 101, 6638.
84. Kiefer, J. H.; Mudipalli, P. S.; Sidhu, S. S.; Kern, R. D.;
Jursic, B. S.; Xie, K.; Chen, H. J Phys Chem A 1997,
101, 4057.
108. Stuhl, F.; Niki, H. J Chem Phys 1971, 55, 3954.
109. Peeters, J.; Mahnen, G. Proc Combust Inst 1973, 14,
133.
110. Vandooren, J.; Van Tiggelen, P. J. Proc Combust Inst
1977, 16, 1133.
111. Westenberg, A. A.; deHaas, N. J Chem Phys 1977, 66,
4900.
85. Ochsenfeld, C.; Kaiser, R. I.; Lee, Y. T.; Suits, A. G. J
Chem Phys 1997, 106, 4141.
112. Aleksandrov, E. N.; Arutyunov, V. S.; Kozlov, S. N.
Kinet Katal 1981, 22, 391.
86. Seburg, R. A.; Patterson, E. V.; Stanton, J. F.;
McMahon, R. J. J Am Chem Soc 1997, 119, 5847.
87. Guadagnini, R.;Schatz, G. C.;Walch, S. P. JPhysChem
A 1998, 102, 5857.
113. Lohr, R.; Roth, P. Ber Bunsen-Ges Phys Chem 1981,
85, 153.
114. Homann, K. H.; Wellmann, C. Ber Bunsen-Ges Phys
Chem 1983, 87, 527.
88. Mebel, A. M.; Jackson, W. M.; Chang, A. H. H.; Lin,
S. H. J Am Chem Soc 1998, 120, 5751.
89. Vereecken, L.; Pierloot, K.; Peeters, J. J Chem Phys
1998, 108, 1068.
90. Vereecken, L.; Peeters, J. J Phys Chem A 1999, 103,
5523.
115. Mahmud, K.; Fontijn, A. J Phys Chem 1987, 91, 1918.
116. Russell, J. J.; Senkan, S. M.; Seetula, J. A.; Gutman,
D. Proc Combust Inst 1988, 22, 1007.
117. Bohn, B.; Stuhl, F. J Phys Chem 1990, 94, 8010.
118. Michael, J. V.; Wagner, A. F. J Phys Chem 1990, 94,
2453.
91. Seburg, R. A.; DePinto, J. T.; Patterson, E. V.;
McMahon, R. J. J Am Chem Soc 1995, 117, 835.
92. Boullart, W.; Devriendt, K.; Borms, R.; Peeters, J. J
Phys Chem 1996, 100, 998.
119. Harding, L. B.; Wagner, A. F. J Phys Chem 1986, 90,
2974.
120. Mebel, A. M.; Diau, E. W. G.; Lin, M. C.; Morokuma,
K. J Am Chem Soc 1996, 118, 9759.
93. Deyerl, H.-J.; Fischer, I.; Chen, P. J Chem Phys 1999,
111, 3441.
121. Knyazev, V. D.; Slagle, I. R. J Phys Chem 1995, 99,
2247.
94. Moriarty, N. W.; Eiteneer, B. Personal communication,
1990.
122. Miller, J. A.; Melius, C. F. Proc Combust Inst 1988, 22,
1031.
95. Melius, C. F. http://www.ca.sandia.gov/HiTemp-
Thermo/.
96. Kee, R. J.; Rupley, F. M.; Miller, J. A. SAND89-8009B
UC-706, Sandia Laboratories, 1993.
123. Qin, Z.; Lissianski, V. V.; Yang, H.; Gardiner, W. C.;
Davis, S.; Wang, H. Proc Combust Inst 2000, 28, 1663.
124. Carriere, T.; Westmoreland, P. R. Proc Combust Inst;
(in press).