Combustion of methane in fuel-rich mixtures

COMBUSTION AND FLAME 32, I 51 - I 61 (1978)

151

Combustion of Methane in Fuel-rich Mixtures D. B. OLSON and W. C. GARDINER. Jr. Department of Chembtry, University of Texas, Austin, Texas 78712

The combustion of C H 4 in fuel-rich, C H 4 1 0 2 / A r = 9/1190, mixtures was studied by infrared (IR) laser kinetic ab~rption spectroscopy behind incident shock waves with 1800 < T/K < 2700 at total densities of ~ I 2 x ! 0 - 6 tool cm - a . Computer simulations usin$ a 63-reaction mechanism were used to identify Ihe elementary reactions that determined the data parameters and to investWate the consequences ot varzous rate-constant assumptions. An experimental data base from the literature v,'as a l ~ used to test the mechanism and rate constants over a wide variety of conditions of temperature, pressure, and equivalence ratio Rate-constant expressions are suggested for CH 2 + CH 3 = C2H 4 + H and CH 3 + 0 2 = C H 2 0 + O H

INTRODUCTION The high-temperature combustion of methane has long been the subject of chemical investigations, but only in recent years have these begun to yield quantitative details about the reaction mechanism. Many parts of the mechanism and rate-constant set today remain only vaguely understood. The basic framework of the mechanism, however, seems to be clear, and we have recently shown by an evaluation of several published mechanisms and rateconstant sets that it is possible to simulate success. fully the results of a broad variety of experiments

Ill. The present report presents new experimental results obtained in a shock-tube study of fuel-rich methane combustion. In our experiments IR laserabsorption spectroscopy was used to record fuel concentration profiles at shock temperatures ranging within 1800-2700 K and densities of about 1.2 X 10- 6 mot cm - a . Computer simulations using a 63-reactiou mechanism were used to discover about which parts of the mechanism our results contained kinetic information. It was possible to achieve good agreement between our experiments and our computations by optimizing two rate-constant expressions. The reactions of CH 2, C2H 4, and C2H 2 were found to play an important role in the C1-4/O 2 system, especially at the higher Copyright ~ 1978 by The Combuslion Instilute Publ|shed by Fl~evier North-Holland. Inc.

temperatures and later times considered. We also performed simulations to test the final mechanism against a broad set of experimental results reported in the literature [2-8]. A mechanism and set of rate constants capable of accurately describing all of the experimental results considered were obtained.

EXPERIMENTAL The shock tube and laser-absorption apparatus have been clescnbed previously [9, IOI. Briefly, the transmitled intensity of a 2948 c m - I He-Ne laser beam through a 9.6 cm X 3.8 cm rectangular aluminum shock tube is measured using an lnSb pholovohaic detector and appropriate electronic circuitry. The laser consists of a Spectra-Physics 130C plasma tul~ mounted in a 31-cm cavity con. strutted from Burleigh optical ereclor set components and quartz spacer rods. The cavity mirrors both have 10-m radii of curvature, the o u t p u t mirror having 26% transmission. A piezoelectric translator-alignerholds the rear mirror and is used to position it for m a x i m u m ootput power before each experiment. This procedure helped to achieve laser operation with reproducible frequency from experiment to experiment, resulting in considerably reduced scatter in extinction coefficient OOIO-2180/78/0032-0151 $01 75

152

D. B. OLSON and W. C. GARDINER, Jr.

measurements. The plasma tube was operated at a current of 3.2 mA. Experimental records were recorded using a Biomation 802 transient recorder and displayed on a Tektronix RM31A oscilloscope using a type Z plug-in vertical amplifier. The time constant of the detector-electronics combination was such that the diameter of the laser beam in the shock tube (<~1.5 ram) determined the time resolution of the experiments. Gas mixtures were prepared manometrically in 25.rim a glass bulbs and allowed to mix at least 24 h before use. The CH4 and Oz were of Matheson research grade with stated purity greater than 99.99~. The Ar was Matheson prepurified grade with a stated purity of 99.998%. The experiments were done with a CHd/Oa/Ar = 9.2/I .!/89.7 mixture. Prescored aluminum diaphragms were pressure burst using H2-N2 driver gas mixtures. The shock tube had a combined leak and outgassing rate less than 0.2 Pa/h (<~2 X 10 - a torr/h) and was evacuated to less than 10 mPa (<~!0- 4 tort) before each experiment.

90

RESULTS Representative oscilloscope traces are shown in Fig. I. Prior to the arrival of the shock wave at the observation station, the signal was electronically clamped to a voltage level such that it remained within the full scale range of the transient recorder's vertical amplifier. This was necessary to achieve accurate DC response immediately after the large change in light transmission observed on shock heating the CH4, but it had no effect on the signal after shock passage. To relate the measured light transmission to species concentrations, it is necessary to know the extinction coefficient of all absorbing species. These extinction coefficients (base e) were calculated for CH4 horn the measured values of the light transmission immediately behind the shock front in these experiments. These CH 4 data are shown in Fig. 2, together with the results of simiiar experiments performed on Calla/At mixtures. The following expressions describe these data and

".._...~ (o}

I00

(b)

(c) 95

0

IO0 t/us

200

Fig. I. Representative laser-absorption oscilloscope traces for incident shock waves in a C H 4 / O 2 / A r = 9 . 2 / I . I / 8 9 . 7 m i x t u r e for: (a) T = 2 0 I O K , o = 1.1 x I O - e tool cm-a; (b) T = 2340 K, p = 1.2 x 10 - ~ tool c m - a ; (c) 7" = 2 5 5 0 K , o = 1.2 x 10 -41 tool c m - S T h e temperatures and densities given ate lhock front values c o m p u t e d from the shock velocity assuming vibrational relaxation but no chemical reaction. The signal prior to shock arrival (r = O) is electronically clamped to ensure accurate IX" response o f the transient recorder's amplifier after the large change in transmission which occurs on shock passage (typically from - 6 0 % to - 9 5 % transmission).

also our previously reported Call / and C21"ls extinction coefficients I 9 | . eCH4/cm2 tool - ! : 5.75 X lO s - 670T +O.275T "z - 3.80 X 10-ST ~ ~c2na/cm= tool - i = (I 72 ± 0.11) X I0 a +0.66T e c a n a / c m 2 mot-~ = (9.94 ± .42) X 104 - 19.92T ec2n4/cm 2 tool - l = (9.14 + .27) X IOa

METHANE COMBUSTION IN FUEL-RICH MIXTURES The computer program incorporated these expressions, and so the combined absorbance due to reactants, intermediates, and products was calcu. lated for comparison with the experimental data. Neither the Call4 nor the C a l l e absorption turned out to be significant in the analysis of the present data. The experimental transmission profdes (Fig. I) are smooth curves. Fitting c o m p u t e d transmission profiles to representative ones directly, for temperatures spanning the acce~ible range, would lead to a very awkward matching process, and more importandy to a nearly impossible task of reporting the sensitivity of computed profdes to assumptions about rate constants. The experimental records were therefore parameterized in the following manner to facilitate comparison wtth the computer simulations. The transmitted intensity, !, at I0 ~ , 20 ~ , 50 ~ , I 0 0 ~ , and 200 ps (laboratory time) was measured for each experiment. From these data, in addition to the full laser intensity, [o, the change in absorbance, ~ 4 f _ t, = In ( I o / I r ) - In ( l o / i t , ) , w a s c o m p u t e d for the four time intervals 10-20 ~ , 2 0 - 5 0 m , 2 0 - 1 0 0 ~ , and

o

,I O

O

O

O

0

0

O~

153 to o O

,,, ~No ~ o ¢

o

o

O

_ ~.t---

~

o

_t

2290 T/K

2000

A

t

*

2400

2600

Fig 3 The change m absorbance measured at tO-20 tss laboratory time as a function of temperature. The data are seen to decrease at the highest temperatures as a large part of the chemical reaction begin5 to occur prior to I0 u t The line represents the results of computer simulations using the mechanism and rateconstant tel of Table I.

100-200 ps. These data sets are shown in Figs. 3 - 6 . Each of the data sets is seen to exhibit a maximum. The decrease in change in absorbance observed at the higher temperatures results fronl most of the chemical reaction having occurred prior to the beginning o f the time interval. This maximum of the change in absorbance occurs at the higher temperatures for early time intervals and at progressively lower temperatures for later intervals. The results of numencal simulations using the mechanism and rate-constant set o f

0

~2

|0

o

o 0.5 a

t800

2200

2600

o° o

4

T/K F~. 2 Extinction coefficients (bate el for CH4(o), Call 2 (A), and Call 4 ( - - ) at functions of temperatune. The fit to the CH 4 data b a third-order polynomial; that to the C2I"I2 data is a linear least squares fit; and the dashed line represents the average extinction coefficient measured for C2H 4 [91.

o

O

0

OO O

2000

Z200

2400

Lq~

T/K Fig. 4.

Data and line as in Fi~. 3. for the tum¢ interval

D. B. OLSON and W. C. GARDINER, Jr.

154

o

used in the H2/O2/CO/CO a system I I 2], wherein a rapid and well-understood reaction system is slightly perturbed by the reaction(s)of interest. Here we have used what is essentially an "oxygencatalyzed-pyrolysis'" of methane to study the most important oxidation reactions. In Fig. 5 the acceleration of the change in the absorbance due to the effects o f the added oxygen is clearly seen as the difference between the data and the dashed line representing pyrolysis experiments [11]. The primary reaction zone is shown in the diagram to occur at lower temperatures for the oxygencontaining mixture, and the maximum slope of the fuel profile is also seen to be larger during this period when oxygen is present. We emphasize at this point that even a 63reaction mechanism need not be complete, and that some participating reactants and reactions may have been overlooked. The species CH and Cz are known from spectroscopic studies to be present in hydrocarbon flames; their omission here is based on our assumption that their concentrations and reaction rates are too small to affect the overall course of reaction. The species CH3 O and CH302 are undoubtedly important in lowtemperature CH4 oxidation, but we were not able to find any evidence that they play a role at flame temperatures I I I . To the best of our knowledge and belief all reactions and species known to be important have been included, but all conclusions from this study must still be qualified with the usual caveat of chemical kinetics that a revised

to

////

8 <

o

o

05 o

O

/ 2000

~t

__

l

l

2ZOO

i

A

2400

x

2600

T/K

I:~. 5. Data and solid line as m Fig. 3, for the time interval 20-100 us. The dashed line represents experimental results obtained from pyrolysis experiments in a CH4/Ar ~- 9.7/90.3 mixture [I II-

Table I are represented in each figure by a solid line. in Fig. 5 a dashed line is included to represent the results of earlier laser-absorption experiments [I I] on methane pyrolysis in a CH4/Ar = 9.7/90.3 mixture. DISCUSSION in this study we have used a modified chemical reactor shock-tube procedure, as was successfully

I0

oo o 0

0

o

!o, 0

°

1800

°

0

2000

2200

2400

2600

T/K I'ig. 6,

Data and line as in Fig. 3, for the time interval lO0-200#s.

METHANE

COMBUSTION

IN FUEL.RICH

155

MIXTURES TABLE I

Rate Constant~ Reaction

Ioglo A

Relerence

n

(1) CH 4 + M = CH 3 + H + M

17.67

0

46,900

19

(2) CH4 + H = CH 3 + H 2

14.86 7.07

0

7,600

19

2,1

3,840

13

3.1

1,010

38

(3) CH 4 + O = CH 3 • OH (4) CH 4 + OH ~ CH 3 • H 2 0 b

3.54

(5) CH 4 • C H 2 * C H 3 + C H 3 c

13.00

O

(6) C H 3 • M = C H

16.67

0

0 46,900

2•H+M

c'd

(7) CH3 • 0 2 * C H 2 0 + OH

I 1.84

0

4,530

(8) CH 3 • H

14.86

0

7,600

= C H 2 + H 2 e'e

thtx work

13.83

0

0

R

( i 0 ) CH 3 • OH = C H 2 0 • H 2

12.87

0

0

39

(11) CH 3 • C H 2--C2H 4 • H

13.30

0

0

(12) CH2 • CH 2 ~ C2H2 • H2

13.50

O

0

(13) CH2 +O2 - C H 2 0 + O (14) C H 2 0 • M = C H O • H • M

14.00

0

1,860

24

16.70

0

36,235

30

(15) C H 2 0 • H = C H O + H 2 (16) CH20 • O - CHO • OH

13.30

0

1.660

3O

13.70

0

(17) C H 2 0 • O H = C H O • H 2 0

15.70

0

2,300 6,540

41

(18) C H O • M ~ H • C O + M

14.47

0

7,4O0

30

119) CHO • 0 2 : 110 2 • CO

12.53

0

0

42

(9) CH 3 + O ' C H 2 0 + H

this work 4O

29

=CO•H 2

13.30

0

0

43

(21) CHO + O -" CO + OH

13.48

0

0

43

(22) CHO • OH * CO • H20

13.48

0

0

111.29

• 25.3

80,020

43 q

(20) C H O • H

(23) C2H e • M = CH 3 + C H 3 • M r (24) C2H 6 • H ~ C2H b • H 2

14.12

o

4,715

20

(25) C2H e • O - C2H 6 • OH

13.26

0

3,070

44

(26) C2H 8 ÷ OH = C2H ~ • H 2 0 I

13.80 14.74

0

1,810

45

(27) C2H e ÷ CH 3 ~ C2H 6 ÷ CH4 h

0

46

(28) C2H6+ M '= C2H 4 + H + M~

14.67

0

10,820 13,390

(29) C2H 6 • 0 2 = C2H 4 • HO 2

12.18

0

2,445

48

(30) C2H 5 ÷ H * CH3 + CHa

13.57

0

0

2O

(31) C 2 H 5 + H = C2H 4 • H 2

12.27

0

(32) C2H 4 • M - C 2 H

2•H 2+M (33) C2H 4 • M ,r C2H3 • H + M

17.32 17.41

0

0 39,810

49

0

48,600

49

(34) C2H 4 • H = C2H 3 • H 2

14.84

0

7,300

49

(35) C2H 4 + O = CH 3 • CHO (36) C2H 4 ÷ OH • CH$ • CH20

13.35

0

1,360

-"4

13.00

0

41

(37) C2H 3 + M =C2H 2 ÷ H • M (38) C2H 3 • H = C2H 2 + H2e

14.90 13.00

0

0 15,850

(39) C2H 2 + M ' C 2 H • H • M

16.62

0

(40) C2H 2 + H = C2H • H ~

0.89

(41) C2H2 + O-- CH2 +CO

13.72

0 3.2 0

0 53,850

20

50 9 51

250

17

1,860

24

D. B. OLSON and W. C. GARDINER, Jr.

156

TABLE I (continued1

Rate Constanta Reaction

Ioglo A

n

#

Reference

(42) C2H a + OH = CH3 +CO

12.08

0

250

(43) C2H a + Call a = C4H3 + IF

13.00

0

22,650

17

(44) C2H a • C2H -'- C4H 2 + H

(45) C~H2+ M * Call2+ H + ~

13.60 15.93

0 0

0 30,200

53 17

(46) C4H 2 + M ' C 4 H • H • M

17 54

0

40,260

17

13.23

0

24,210

54

17.08

-0.91

8,370

23

14.34

0

6.895

55

(47) (48) (49) (50)

H2•O a-OH+OH H•O 2"OH+O O•Ha*OH+H OH+H 2-HaO•H

J

52

13.72

0

3.270

56

=H20+O

13.74

0

3.520

56

(52) H + O a + M : ' H O 2 + M

15.40

0

0

57

(53) H • O H • M = H 2 0 + M

23.88

-2.6

0

58

(54) H 2 + M ' H + H + M

12.35

0.5

46,600

59

(551 O 2 + M = O + O + M

I 1,27

0.5

48.165

60

(56) CO • 0 2 ~' CO2 • O (57) C O + O H ~'CO2 + H k

11.08

0

17,615

61

12.60 13.45

0 0

4,025 - 2.285

56 63

(59) H a • HO 2 = H 2 0 • OH (60) H + H O 2 = O H + O H

11.86

0

9,410

64

14.40

0

960

64

(61) H • H O 2 =H 2 + O 2

13.40

0

350

64

(62) OH + HO 2 = H20 • O 2

13.70

0

500

64

(63) O • H O 2 = O H • O

13 70

0

500

64

(51) O H * O H

(58) C O + O + M

=CO2+M

2

a Rate constants in the form A x T~ e x p ( - O / T ) , in cm, tool, s, and K units. The reverse reaction rate constants were c o m p u t e d using J A N A F thermochemical data where possible and locally c o m p u t e d thermochemical data otherwise. b The 7~ factor m a y extrapolate the rate constant too high at higher temperatures, but is used here because this expression Igoes through the high-temperature data. c Estimate. No sensitivity to the rate of this reaction was observed. d Estimated to be equal to k l / l O . • Estimated to be equal to k 2 f This reaction is in the p r e u u r e - d e p e n d e n t falloff relpon of a untmolecular decompolution. This rate expression is from Olson et at. 191 for experiments over the range 1330 < T < 2500 K and 0.10 < P < 0.50 atm. Care must be taken that this rate-constant expression be used only for the pressure and temperature conditions for which it is valid. • This is a low-temperature value that agrees with the few high-temperature data. tt Strongly curved Arrhenius behavior is observed for this reaction. i This rate-constant expression was obtained by R R K calculations of the falloff from the experimental high-pressure limit expression of Glanzer and Troe [47 IJ Preliminary results. k See Baulch and Drytdale J62] for a review o f the literature on this reaction.

METHANE COMBUSTION IN FUEL-RICH MIXTURES interpretation may sooner or later be required as further mechanistic knowledge develops. Reference is made to the work of Olson and Gardiner [I] for the reasoning underlying the basic structure of the mechanism assumed. The mechanism and rate-constant set of Table I represent a slightly modified and extended version of those used in our earlier work [ ! ] . A more recent rate constant for 0 + CH4 = OH + CH a is now available [13l and was incorporated into the mechanism. The rates of CHa + Oa -- OH + CH20 and CH20 + M = CHO + H + M [reactions (7) and (14)], which as we pointed out earlier are not well established, were again critically evaluated and new values adopted. Six reactions describing the chemistry of CH2 were added to the mechanism, although only reactions (8), ( I l l and (13) were found to be significant for the conditions of our experiments. The other significant change in the mechanism concerns C2H 2 chemistry and involves the addition of reactions (39), (40), and (43) through (46). Also, recent values for the heat of formation of C2H [14, 15J are more than 50 kJ mol - t larger than the 1971 JANAF value [16]. We adopted for our calculations the Okabe and Dibeler [14} value of 531 ± 4 LI tool - s (127 4" I kcal t o o l - l ) . A few steps, such as reactions (56) and (58), are included in the mechanism, even though their rates are unimportant for the conditions of our experiments, in order that the same mechanism can be also tested for essentially different conditions. The results of the numerical simulations of the present experiments, shown in Figs. 3-6, are seen to match the data well. Slight discrepancies exist in the AAto-2o computations between 2100 K and 2300 K, where the simulations are somewhat lower than the data, and in the AAIoo_ao o simulations of 2300-2600 K, where the calculations give values too large. These errors are small, however, and the overall fit to the data is good. The A A l o o . a o o data, taken from the relatively slowly changing tail of the experimental records where the absorbance values are quite small, contain con. siderable scatter. Since most of the experimental errors are of fixed magnitude, when the logarithmic absorbance measurements become small the experimental scatter becomes larger.

157

The absorption due to C2H~ and C2H4, while included in the analysis, was found not to contribute significantly to the absorbance changes recorded in these experiments. At temperatures lower than those considered here their concentrations can build to much I'ugher levels, and their possible importance there must be considered. The C2H 2 contribution, on the other hand, was found to be significant at the higher temperatures and the later times of our experiments, requinng a more detailed C2H2 reaction sequence than was previously used. In Fig. 2 the extinction of C2H 2 is shovm to be extremely small, absorbing typically only about one part per thousand of the laser signal, but at 2600 K, for example, the calculated absorbances of CH 4 and C2H 2 are about equal at 200 ~s. It is possible that we could have removed the discrepancy in the high-temperature AA t oo-2oo calculations by adjusting the rates of some of the C2H 2 reactions. We chose not to do this, but to defer this possible adjustment to a later time and to more direct expenments on the C2H2 system itself [17l. An important question now is to determine to which elementary reactions our data are sensitive The results of a sensitivity study [18] for the AA2o.lo O data at three temperatures are presented in the pS graph of Fig. 7. Primary sensitivity is found to the pyrolysis reactions ( I ) and (30). and to the oxidation reactions (7) and (48). Addl. tional sensitivity is present for the CH 2 reactions (11) and (13) at the higher and lower temperatures, respectively. No significant sensitivities other than those shown in Fig. 7 were found. While it is obvious that errors in the value of k I (and kao ) would be significant over the whole temperature range, the Low-pressure limit rate con. stant for k I now seems to be well established l l 9 ] . The value of k_3o is not as well known, although the three kao measurements available [20-22] do agree well with one another, We ac. cepted the temperature-independent expression of Carmlleri et al. [2OI. The rate of reaction (48) may be considered to be fixed [?.3], leaving us with the rates of reactions (7), (11), and (13)as the less well determined, if not totally unknown, adjustable parameters. For the reaction of CH 2 with O 2 [reaction (13)], we used the rate constant

158

D. B. OLSON and W. C. GAP,DINER, Jr. PS (T*|IOOI() *GJI 0

GI

(T* 24001() *.0

.

"¢~I

•

gUI

( T ,2 ?00*( ) .

*¢~a

0o2

mEACTI0q

(0 (30)

P I

¢?) (48) (ul

2

I 3

1

115) (*¢) Ill

Fig. 7 Sensitwity o f the computed parameter AA 20-IOO to the a u u m e d rate constints for the ten most important reactions at three temperatures. The u'nsitivity

parameter is del-med [ I 81 as pS=

Iogto (~L420-t oo)/(a~420-too)

logt o ( ]/(mulliplier))

where AA'20..IOO refers to the result computed using the rate multiplier. Two bars

are presented for each reaction, the upper and lower bars corresponding respectively to the p$ values resulting when multipliers of 5 and I/5 are used A p$ = I would hmply a direct proportionality of the computed result to the rate multiplier, p$ = - I would imply an inverse proportionality; a value of pS near zero implies that the computed result is insensitive to changes in this rate. The calculated value of ,:LAao_IOO is seen to become more sensitive to the Call 4 and Call a chemistry with increating temperature.

cleaved from a study o f lean C2H2 flames by Peeters and Mahnen [24]. The rate constant o f reaction (I I) was varied to fit our data, especially at temperatures over 2200 K. where it¢ pS value is higher. A k i t value of 2 X IO t s cm s mol - n s - t was found to give the best match to the data. This result agrees quite well with the k i t value o f (3.0 ± 1.2) X IO t s cm s tool - t s - t reported by Pilling and Robertson [25], though lower by a factor o f three than that reported by Laufer and

was well established by methane oxidation data and that further consideration of the individual rate constants was in order. ArOtenius graphs o f the available data for the first two reactions are shown in Figs. 8 and 9. Experiments on CHaD decomposition are complicated by the rapid H-atom chain sequence H + C H a O = CHO + H 2

(15)

Bass [261.

CHO+M= H+CO+M,

(18)

In our earlier work [ I ] we showed that in methane combustion only the global rate of the CHs reaction sequence CH3 + Oa = C H a O + OH

(7)

CHaD + M = CHO + H + M

(]4)

CHO+M =CO+ H+M

(18)

rendering measurements of the primary decomposition reaction difficult. Consideration of the activation energies as reported in other works I 2 7 29I leads one to suspect that their rate constants do not represent simple elementary processes. We therefore accept for the present analysis the value o f k t 4 measured by Scbecker and .lost 130], with

METHANE

159

COMBUSTION IN FUEL-RICH M I X T U R E S

t2 "7 U3

~to u

v. 8

t 0.2

i 04

l 06

I

O8

I tO

Assigning error bounds to k~ and k t t is made difficult by the sensitivities to k n. k30, and k41l; adjustments to any of these would force reassessment of both k-z and ks t. It is reasonable to expect that little change in the values of k t or k4m in this temperature range will emerge from future work. As for kso, long-term laser-schlieren data on the pyrolysis rates of CH4, Carte. C2H4, and Call 2 [I 7] indicate that it is known to better than factor 2 in this temperature range. Considering the wide range of really coherent data on these reaction systems, we believe the present results to give k~ to within +-50% and k ! t to within a factor of 2.

tO~ K / T Fig. 8. Arrhenius graph forCH20 + M -CHO ÷ H + M: o Peeters and Mahnen 127l. tssumiag reaction products of CO + H2 ÷M; AGayetal. 128J; C3Bowman 129l : V Scheckel'and Jost 13OI the reservation that more experiments on the CHzO system are needed. To establish the rate of reaction (7) we then used, in addition to our own data, an experimental data base obtained from the publications of six other laboratories [2-8]. We found it possible to reproduce all of the data with an average deviation in the calculations which was less than in the experiments. The Table I mechanism and rateconstant set leads to an average pM value of 0.05 compared with the pM = 0.07 value of our earlier study [ I ]. The best fit to all the data was obtained when the rate constant for CH 3 + 0 2 was set to

SUMMARY Methane-concentration profiles dunng the combustion of very rich methane-oxygen mixtures in a shock tube were measured. These profiles, in addition to the results of six earlier studies, were analyzed by computer simulations using a 63reaction mechanism. Some details of the oxidation reactions of CHa and pyrolysis reactions of CH 2 were obtained. An overall excellent performance

\ 12 U3 I

kTlcm 3 mol -t s - t = 7.0 X tO st exp (-4530/T).

y,

This expression, presented in Fig. 9, is seen to be somewhat larger at 2000 K than the consensus values [6, 8, 31 ], which use activation energ/es of 12-14 kcal tool - s . When extrapolated to 1350 K, it does agree with the value reported by Clark et at. [32]. The lower activation energy of our express/on, however, may be more reasonable in view of the room temperature results. Variations in the value for k14 would require compensating changes in the k7 expression to keep the global methyl oxidation rate nearly the same, which is necessary i f one is to match the whole set of data.

._J

8

0

i

|

i

I

I

2

3

4

tO3 K / T Fig. 9 Arwhenius graph for the reaction CH 3 ÷ 0 2 = CH20 + OH: Q Washida and Bayes [33 I ; 0 Basco et al. 134J;aHoaze andWalsh [33]; XBaldwinetal. [361, upper and lower limits; o Clark et it [32]; A Seery and Bowman 137]; + Izod et is. [3lJ; OTsuboi q8[; @ Bowman 1291: VJachmaowski 16]; e Dean and K istiakowsky [ 2 t ; • this work.

160 o f this mechanism demonstrated.

D. B. O L S O N and W. C. G A R D I N E R , Jr. and rate-constant set was

Acknowledgment is made to the donors o f The Petroleum Research Fund, administered by the American Chemical Society. [or partial support o f this research. This research was also supported by the U.S. A r m y Research Office and the Robert A. Welch Foundation.

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