Reduction of the Combustion Mechanism of Hydrogen, CHEMIA I PIROTECHNIKA, Chemia i Pirotechnika

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Combustion, Explosion, and Shock Waves, Vol. 37, No. 1, pp. 1{3, 2001
Reduction of the Combustion Mechanism of Hydrogen
V. G. Matveev
1
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
known [1]. The maximum complete mechanism of
combustion is known for a set of particles H
2
, O
2
,
OH, H, O, HO
2
, H
2
O, and H
2
O
2
[2, 3] (see Table 1);
the role of individual reactions and the limits of ig-
nition are analyzed (see the review in [4]). A rather
extensive scheme of 42 reactions was used in [5] for
comparison with the experiment. However, the direct
use of the parameters recommended in [4] or [6] does
not allow one to describe the limits of ignition [1] or
the kinetics of hydrogen oxidation [7]: one has to t
some parameters. In the present work, a set of pro-
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):
The reverse reaction rates were calculated from ther-
modynamic constants of equilibrium [9]. The rates
of heterogeneous reactions k
h
[1/sec] were calculated
using Semenov's formula [10] for a spherical vessel:
k
h
=
4
d
2
D
T
T
0
1:75
p
0
p
:
(1)
Here d [cm] is the vessel diameter, D is the diu-
sivity (D = 0:34 cm
2
/sec for OH, 1.43 cm
2
/sec for
H, 0.36 cm
2
/sec for O, and 0.198 cm
2
/sec for HO
2
),
T and p are the experimental values of temperature
and pressure, respectively, and T
0
and p
0
are the tem-
perature and pressure under normal conditions. The
1. H
2
+ O
2
! 2OH,
2. H
2
+ OH ! H
2
O + H,
3. O
2
+ H ! OH + O,
4. H
2
+ O ! OH + H,
8. H + OH + M ! H
2
O + M,
11. O
2
+ H + M ! HO
2
+ M,
16. H + HO
2
! 2OH,
32. H ! wall.
This scheme was used in the inverse problem by the
method of the fastest descent using the algorithm
proposed in [8] to determine the direct reaction rates.
Fig. 1. Kinetic curves for oxidation of hydrogen of a
stoichiometric H
2
+ O
2
mixture: the points refer to the
experimental data of [7] for initial pressures of 7.4, 7.1,
6.8, 6.4, and 6.1 torr; the solid curves refer to the calcu-
lation by the maximum mechanism (see the parameters
in Table 1).
1
Institute of Problems of Chemical Physics
in Chernogolovka, Russian Academy of Sciences,
Chernogolovka 142432.
0010-5082/01/3701-001 $25.00
c
2001
Plenum Publishing Corporation
1
2
Matveev
TABLE 1
Maximum Scheme, Mechanism, and Parameters
Reactions
A
+
n
+
E
+
A
n
E
1. H
2
+ O
2
! 2OH
2:81 10
10
0
38.90
6:24 10
8
0
20.38
2. H
2
+ OH ! H
2
O + H
8:65 10
10
0
5.4
3:21 10
11
0
20.82
3. O
2
+ H ! OH + O
4:42 10
11
0
17.60
2:20 10
10
0
0.98
4. H
2
+ O ! OH + H
7:07 10
7
1
8.95
3:15 10
8
1
7.05
5. H
2
O + O ! 2OH
8:00 10
10
0
18.80
9:63 10
9
0
1.47
6. H + H + M ! H
2
+ M
2:00 10
8
0
0
2:20 10
16
1
103.26
7. O + O + M ! O
2
+ M
4:53 10
8
0
0.53
4:37 10
17
1
118.50
8. H + OH + M ! H
2
O + M
1:27 10
16
2
0
1:81 10
16
0
118.20
9. OH + OH + M ! H
2
O
2
+ M
9:10 10
8
0
0
9:53 10
15
0
51.06
10. OH + O + M ! HO
2
+ M
8:50 10
10
0
6.69
1:11 10
17
0
73.50
11. H + O
2
+ M ! HO
2
+ M
3:78 10
9
0 1:89
2:48 10
14
0
48.30
12. H
2
+ HO
2
! H
2
O
2
+ H
9:50 10
8
0
21.80
3:38 10
9
0
4.15
13. H
2
+ HO
2
! H
2
O + OH
1:50 10
8
0
24.80
9:71 10
5
0.5
77.94
14. H
2
O + HO
2
! H
2
O
2
+ OH
4:00 10
10
0
34.00
3:83 10
10
0
4.08
15. HO
2
+ HO
2
! H
2
O
2
+ O
2
4:00 10
9
0
0
1:11 10
9
0.5
41.70
16. H + HO
2
! OH + OH
8:90 10
9
0
2.58
4:28 10
8
0
37.13
17. H + HO
2
! H
2
O + O
2:00 10
10
0
3.58
7:99 10
9
0
58.62
18. H + HO
2
! H
2
+ O
2
5:00 10
9
0
1.20
1:08 10
10
0
54.27
19. O + HO
2
! OH + O
2
6:00 10
10
0
0
5:86 10
10
0
51.17
20. H + H
2
O
2
! H
2
O + OH
1:30 10
12
0
11.90
6:52 10
11
0
79.53
21. O + H
2
O
2
! OH + HO
2
4:00 10
10
0
1.30
5:02 10
10
0
13.89
22. H
2
+ O
2
! H
2
O + O
8:00 10
10
0
57.62
4:00 10
10
0
61.28
23. H
2
+ O
2
+ M ! H
2
O
2
+ M
5:00 10
6
0
21.90
1:16 10
12
0
54.44
24. OH + M ! O + H + M
4:00 10
13
0
105.3
6:31 10
8
0
3.94
25. HO
2
+ OH ! H
2
O + O
2
3:00 10
10
0
0.6
8:75 10
9
0.5
69.97
26. H
2
+ O + M ! H
2
O + M
5:00 10
8
0
0
1:17 10
14
0
116.78
27. H
2
O + O + M ! H
2
O
2
+ M
9:00 10
7
0
13.00
1:13 10
14
0
46.73
28. H
2
O
2
+ O ! H
2
O + O
2
2:00 10
8
0
29.00
2:01 10
8
0
113.24
29. H
2
O
2
+ H
2
! 2H
2
O
2:00 10
10
0
22.00
3:72 10
9
0
105.06
30. HO
2
+ H + M ! H
2
O
2
+ M
3:00 10
8
0
1.50
1:51 10
14
0
87.11
31. OH + wall ! OH
s
30.4
0
0
0.1
0
0
32. H + wall ! H
s
10:5 0
0
0.1
0
0
33. O + wall ! O
s
29.5
0
0
0.1
0
0
34. HO
2
+ wall ! HO
2s
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 sucient for process description:
within the range of pressures of 1{200 torr and tem-
peratures of 400{600
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
H
2
+ O
2
: the curves refer to calculations by the max-
imum mechanism (1) (see the parameters in Table 1),
reduced mechanism M-I (2), and reduced mechanism
M-II (3); the points refer to the experimental data of [1].
1. B. Lewis and G. Von Elbe, Combustion, Flames, and
Explosions of Gases, Academic Press, New York{
London (1961).
2. V. I. Dimitrov and V. V. Azatyan, \Maximum kinetic
mechanism of oxidation of H
2
," in: Problems of Gas
Dynamics, Inst. Theor. Appl. Mech., Sib. Div., Acad.
of Sci. of the USSR, Novosibirsk (1975), pp. 69{73.
3. V. I. Dimitrov, \The maximum kinetic mechanism
rate constants in the H
2
{ O
2
mixtures," React. Ki-
netic Catal. Lett., 7, No. 1, 81{86 (1977).
4. V. I. Dimitrov, Simple Kinetics [in Russian], Nauka,
Novosibirsk (1982).
5. U. Maas and S. B. Pope, \Simplifying chemical ki-
netics: Intrinsic low-dimensional manifolds in com-
position space," Combust. Flame, 88, No. 2, 239{264
(1992).
6. D. L. Baulch, C. J. Cobos, et al., \Summary table of
evaluated kinetic data for combustion modeling: Sup-
plement 1," Combust. Flame, 98, No. 1, 59 (1994).
7. A. A. Kovalski, in: Phys. Z. Sow., 4, 723 (1933).
8. E. F. Brin and B. V. Pavlov, \The use of one mod-
ication of the gradient method for seeking an ex-
tremum for evaluating kinetic parameters," Kinet.
Katal., 16, No. 1, 233 (1975).
9. V. P. Glushko (ed.), Thermodynamic Properties of
Individual Substances [in Russian], Vol. 1, Izd. Akad.
Nauk SSSR, Moscow (1962).
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and Reaction Capability [in Russian], Izd. Akad. Nauk
SSSR, Moscow (1958).
values of these rates were 20 times greater than those
obtained in solving the inverse problem. Therefore,
in determining the limits of ignition, the rates of het-
erogeneous reactions were calculated by formula (1)
with a factor of 1/20.
The rates obtained diered from those recom-
mended in [4, 6] by no more than a factor of 3. Us-
ing these rates in the maximum scheme (see Table 1)
allowed us to describe the kinetic curves of hydrogen
combustion [7] (Fig. 1) and to reach good agreement
with experimental data for the rst and second lim-
its of ignition (see curve 1 in Fig. 2). These rates
were used in thermodynamic analysis. Eliminating
all reactions whose thermodynamic fraction
2
at an
arbitrary time from the reaction beginning to an al-
most equilibrium state is less than 0.01, a reduced
mechanism M-I was obtained; this mechanism con-
sists of 11 reversible reactions, namely, Nos. 1, 2, 3,
4, 11, 16, 18, 31, 32, 33, and 34 (see curve 2 in Fig. 2).
Some change in the limits of ignition is observed. The
mechanism M-II was obtained by rejecting reaction
Nos. 18 and 33 whose fractions are the smallest from
these 11 reactions. In calculations based on the mech-
anism M-II, a signicant deviation of the upper limit
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 (dG
i
=dt) to the variation rate of
the Gibbs free energy in all reactions (
P
i
dG
i
=dt) of this
mechanism [4].
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