Combustion, Explosion, and Shock Waves, Vol. 37, No. 1, pp. 1 3, 2001
Reduction of the Combustion Mechanism of Hydrogen
V. G. Matveev1 UDC 541.124 + 534.222
Translated from Fizika Goreniya i Vzryva, Vol. 37, No. 1, pp. 3 5, January February, 2001.
Original article submitted April 9, 1997; revision submitted June 17, 1999.
A set of programs for thermodynamic analysis of a complex chemical reaction is
developed. Based on the maximum complete scheme of hydrogen combustion, reduced
mechanisms that describe available experimental data are found.
The reaction of hydrogen oxidation is rather well The reverse reaction rates were calculated from ther-
known [1]. The maximum complete mechanism of modynamic constants of equilibrium [9]. The rates
combustion is known for a set of particles H2, O2, of heterogeneous reactions kh [1/sec] were calculated
OH, H, O, HO2, H2O, and H2O2 [2, 3] (see Table 1); using Semenov s formula [10] for a spherical vessel:
the role of individual reactions and the limits of ig- 1.75
4Ą T p0
kh = D . (1)
nition are analyzed (see the review in [4]). A rather
d2 T0 p
extensive scheme of 42 reactions was used in [5] for
Here d [cm] is the vessel diameter, D is the diffu-
comparison with the experiment. However, the direct
sivity (D = 0.34 cm2/sec for OH, 1.43 cm2/sec for
use of the parameters recommended in [4] or [6] does
H, 0.36 cm2/sec for O, and 0.198 cm2/sec for HO2),
not allow one to describe the limits of ignition [1] or
T and p are the experimental values of temperature
the kinetics of hydrogen oxidation [7]: one has to fit
and pressure, respectively, and T0 and p0 are the tem-
some parameters. In the present work, a set of pro-
perature and pressure under normal conditions. The
grams was developed for deriving a reduced mecha-
nism by the method of thermodynamic analysis [4].
For the test conditions of [7], a rather simple
scheme was obtained from the maximum complete
mechanism (see Table 1):
1. H2 + O2 - 2OH,
2. H2 + OH �! H2O + H,
3. O2 + H �! OH + O,
4. H2 + O �! OH + H,
8. H + OH + M - H2O + M,
11. O2 + H + M - HO2 + M,
16. H + HO2 - 2OH,
32. H - wall.
This scheme was used in the inverse problem by the
Fig. 1. Kinetic curves for oxidation of hydrogen of a
method of the fastest descent using the algorithm
stoichiometric H2 + O2 mixture: the points refer to the
proposed in [8] to determine the direct reaction rates.
experimental data of [7] for initial pressures of 7.4, 7.1,
1
6.8, 6.4, and 6.1 torr; the solid curves refer to the calcu-
Institute of Problems of Chemical Physics
lation by the maximum mechanism (see the parameters
in Chernogolovka, Russian Academy of Sciences,
in Table 1).
Chernogolovka 142432.
0010-5082/01/3701-001 $25.00 � 2001 Plenum Publishing Corporation 1
2 Matveev
TABLE 1
Maximum Scheme, Mechanism, and Parameters
Reactions A+ n+ E+ A- n- E-
1. H2 + O2 �! 2OH 2.81 � 1010 " 0 38.90 6.24 � 108 0 20.38
2. H2 + OH �! H2O + H 8.65 � 1010 " 0 5.4 3.21 � 1011 0 20.82
3. O2 + H �! OH + O 4.42 � 1011 " 0 17.60 2.20 � 1010 0 0.98
4. H2 + O �! OH + H 7.07 � 107 " 1 8.95 3.15 � 108 1 7.05
5. H2O + O �! 2OH 8.00 � 1010 0 18.80 9.63 � 109 0 1.47
6. H + H + M �! H2 + M 2.00 � 108 0 0 2.20 � 1016 -1 103.26
7. O + O + M �! O2 + M 4.53 � 108 0 0.53 4.37 � 1017 -1 118.50
8. H + OH + M �! H2O + M 1.27 � 1016 " -2 0 1.81 � 1016 0 118.20
9. OH + OH + M �! H2O2 + M 9.10 � 108 0 0 9.53 � 1015 0 51.06
10. OH + O + M �! HO2 + M 8.50 � 1010 0 6.69 1.11 � 1017 0 73.50
11. H + O2 + M �! HO2 + M 3.78 � 109 " 0 -1.89 2.48 � 1014 0 48.30
12. H2 + HO2 �! H2O2 + H 9.50 � 108 0 21.80 3.38 � 109 0 4.15
13. H2 + HO2 �! H2O + OH 1.50 � 108 0 24.80 9.71 � 105 0.5 77.94
14. H2O + HO2 �! H2O2 + OH 4.00 � 1010 0 34.00 3.83 � 1010 0 4.08
15. HO2 + HO2 �! H2O2 + O2 4.00 � 109 0 0 1.11 � 109 0.5 41.70
16. H + HO2 �! OH + OH 8.90 � 109 0 2.58 4.28 � 108 0 37.13
17. H + HO2 �! H2O + O 2.00 � 1010 0 3.58 7.99 � 109 0 58.62
18. H + HO2 �! H2 + O2 5.00 � 109 0 1.20 1.08 � 1010 0 54.27
19. O + HO2 �! OH + O2 6.00 � 1010 0 0 5.86 � 1010 0 51.17
20. H + H2O2 �! H2O + OH 1.30 � 1012 0 11.90 6.52 � 1011 0 79.53
21. O + H2O2 �! OH + HO2 4.00 � 1010 " 0 1.30 5.02 � 1010 0 13.89
22. H2 + O2 �! H2O + O 8.00 � 1010 0 57.62 4.00 � 1010 0 61.28
23. H2 + O2 + M �! H2O2 + M 5.00 � 106 0 21.90 1.16 � 1012 0 54.44
24. OH + M �! O + H + M 4.00 � 1013 0 105.3 6.31 � 108 0 3.94
25. HO2 + OH �! H2O + O2 3.00 � 1010 0 0.6 8.75 � 109 0.5 69.97
26. H2 + O + M �! H2O + M 5.00 � 108 0 0 1.17 � 1014 0 116.78
27. H2O + O + M �! H2O2 + M 9.00 � 107 0 13.00 1.13 � 1014 0 46.73
28. H2O2 + O �! H2O + O2 2.00 � 108 0 29.00 2.01 � 108 0 113.24
29. H2O2 + H2 �! 2H2O 2.00 � 1010 0 22.00 3.72 � 109 0 105.06
30. HO2 + H + M �! H2O2 + M 3.00 � 108 0 1.50 1.51 � 1014 0 87.11
31. OH + wall �! OHs 30.4 0 0 0.1 0 0
32. H + wall �! Hs 10.5 " 0 0 0.1 0 0
33. O + wall �! Os 29.5 0 0 0.1 0 0
34. HO2 + wall �! HO2s 46.4 0 0 0.1 0 0
Notes. A is the preexponent measured in (liters/mole)/sec for bimolecular reactions and in (liters/mole)2/sec for trimolec-
ular reactions, n is the power index of temperature, and E is the activation energy measured in kcal/mole; the superscripts
plus and minus indicate the parameters for the direct and reverse reactions, respectively; the asterisk indicates preexponents
obtained in the present work.
Reduction of the Combustion Mechanism of Hydrogen 3
the mechanism, whereas the accuracy of the reduced
mechanism remains sufficient for process description:
within the range of pressures of 1 200 torr and tem-
peratures of 400 600ć%C, the mechanism M-I almost
coincides with the maximum mechanism; the ther-
modynamic fraction characterizes the importance of
a reaction during the entire process.
The author is grateful to A. N. Ivanova and
B. L. Tarnopolskii for the programs for calculating
the kinetics of chemical reactions and critical condi-
tions and for fruitful discussions of the work.
This work was supported by the International
Science and Technology Center (Grant No. 124).
REFERENCES
Fig. 2. Limits of ignition of a stoichiometric mixture
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is observed for p > 10 torr (see curve 3 in Fig. 2).
Thus, it is shown in the present work that the
use of thermodynamic analysis allows reduction of
2
The thermodynamic fraction of a reaction is determined
as the ratio of the variation rate of the Gibbs free en-
ergy in the ith reaction (dGi/dt) to the variation rate of
the Gibbs free energy in all reactions ( dGi/dt) of this
i
mechanism [4].