On high-temperature oxidation of methane

25 ON

HIGH-TEMPERATURE

OXIDATION

OF

METHANE

G. I. K O Z L O V INTRODUCTION T h e solution of m a n y problems related to the inflammability a n d b u r n i n g of gases, as well as to the calculation of the more complex combustion p h e n o m e n a , requires knowledge of the overall kinetic equation, owing to the fact t h a t the process of heat liberation is related to the overall reaction rate. These equations are interesting in connection with the present-day engineering t r e n d of employing forced conditions of b u r n i n g in highspeed gas flows. So far, however, the only field in which some clarity has been achieved with regard to the kinetic relationships of the process is the h i g h - t e m p e r a t u r e oxidation of c a r b o n monoxide. As to other gases, h y d r o c a r b o n s included, extensive material has a c c u m u l a t e d in the literature on the kinetic regularities of low t e m p e r a t u r e (300 to 600~ oxidation, b u t these relationships c a n n o t be extrapolated into the regions of higher temperatures. This p a p e r will deal with a n experimental derivation of the overall kinetic e q u a t i o n of the high t e m p e r a t u r e (700 to 1,100~ oxidation of m e t h a n e . T h e investigation of c a r b o n monoxide b u r n i n g involved was of auxiliary interest a n d was carried out, first, for the purpose of testing the experimental procedure, i n a s m u c h as the principal kinetic characteristics of this process are already known from the l i t e r a t u r O -6 a n d are considered, besides, in other papers of this SymposiumV-9; secondly, because a n i m p o r t a n t factor in the oxidation of m e t h a n e is the oxidation of the c a r b o n monoxide formed d u r i n g the oxidation of m e t h a n O ~ a n d thirdly, because of the a m b i g u i t y of available data on the absolute values of the rate of oxidation of c a r b o n m o n o x i d e a n d its t e m p e r a t u r e d e p e n d e n c e in the above-indicated t e m p e r a t u r e range. EXPERIMENTAL

PROCEDURE

A d y n a m i c procedure was employed. A gas-air mixture of definite composition was saturated with water v a p o u r at room temperature. T h e n it passed t h r o u g h a coil immersed in melting ice to condense the excess moisture. T h u s , on leaving the cooler the concentration of w a t e r v a p o u r in the mixture corresponded to the c o n c e n t r a t i o n of saturated water v a p o u r at 0~ namely, 0.6 per

cent by volume. This was checked for all rates of the mixture by passing a m e a s u r e d volume of the mixture over phosphorus pentoxide a n d then d e t e r m i n i n g the moisture c o n t e n t gravimetrically. F r o m the cooler the mixture passed into a threesection q u a r t z reaction vessel (reactor). T h e first section the gas entered served as the pre-heater a n d h a d a n i n d e p e n d e n t electric heater. Here, d e p e n d i n g on the conditions of the experiment, the mixture was h e a t e d to a t e m p e r a t u r e between 500 a n d 800~ t h a t is a b o u t 200 or 300~ below the t e m p e r a t u r e of the reaction. I n the second section, the ante-reactor, w h i c h was a q u a r t z tube 1.5 m m in d i a m e t e r a n d 60 m m long a n d equipped with a n i n d e p e n d e n t electric heater, the mixture was h e a t e d rapidly to the t e m p e r a t u r e of the reaction. T h e t e m p e r a t u r e of the walls of the ante-reactor was m a i n t a i n e d at a level h i g h enough to ensure t h a t the reacting m i x t u r e should enter the first p r o b e of the reactor at the t e m p e r a t u r e of the reaction. T h e t h i r d section, the reaction section, was m a d e of 2.0 m m q u a r t z t u b i n g a n d consisted of four probes t h r o u g h which the gas passed to be analysed. I n addition, these probes served as ducts t h r o u g h w h i c h thermocouples were inserted into the reactor to measure the t e m p e r a t u r e of the reacting mixture. I n the" published literature the general opinion is that quartz is inert to the h i g h - t e m p e r a t u r e oxidation of m e t h a n e a n d c a r b o n monoxide. T h e use of a reactor of small d i a m e t e r ensured a large surfaceto-volume ratio in the reactor, m a k i n g it possible to conduct the process isothermically right u p to temperatures of the order of 1,100~ A constant t e m p e r a t u r e was tested by means of seven p l a t i n u m - p l a t i n o - r h o d i u m thermocouples m a d e of 0.15 m m wire. T h e beads of the four inner thermocouples were glazed with a thin layer of porcelain to avoid catalysis. T h e three outer thermoeouples were inserted u n d e r a h e a t isolating layer so t h a t they should measure the t e m p e r a t u r e of the outer wall over the length of the reaction section. T h e reactor h a d a compensation-type p l a t i n u m electric winding b y m e a n s of w h i c h the t e m p e r a t u r e of the reaction section could be regulated. T h e length of the reaction zone in the experiments with this reactor, which in the following will be referred to as reactor A, varied from 107 to 160 m m d e p e n d i n g on the section 142

H I G H - T E M P E R A T U R E O X I D A T I O N OF METHANE selected, between the probes of which the process would proceed isothermically. O w i n g to the h i g h - t e m p e r a t u r e g r a d i e n t along the probes (about 100~ per 1 m m ) the gas samples were frozen almost instantly. T h e cooled reaction products were analysed by means of two type G I P - 5 infra-red absorption gas analysers selectively sensitive to CO 2 a n d CO respectively. I n the experiments with m e t h a n e , carried out with the same apparatus, other reactors were used which will be referred to in the following as reactors B a n d C. R e a c t o r B h a d a n i n n e r d i a m e t e r of 1 m m a n d two probes with i n n e r diameters of 0.5 ram, t h r o u g h w h i c h the gas passed to be analysed. Isothermic conditions were controlled by means of two inner thermocouples inserted t h r o u g h special side tubes a n d three outer thermocouples. T h e length of the reaction zone was 75 ram. R e a c t o r C was m a d e of 5.0 m m q u a r t z tubing, the length of the reaction zone being 297 mm. I t h a d two probes, one on each side, similar to those o f reactor A, t h r o u g h which the gas passed on its way to be analysed. Isothermic conditions were controlled by m e a n s of three i n n e r thermocouples, two of t h e m stationary, inserted t h r o u g h the probes, a n d one sliding thermocouple capable of m o v i n g over the entire length of the reaction zone. I f the deviation of the t e m p e r a t u r e from its m e a n value over the length of the reaction zone did not exceed 4- 5~ the t e m p e r a t u r e field was considered as satisfactory.

where K 0 is the specific rate c o n s t a n t o f overall reaction; P0 is the density of gas at s.t.p. (g/cm a) ; T o is the initial t e m p e r a t u r e of the mixture, 273~ /~ is the molecular weight of gas at s.t.p. (g/cma); E is the activation energy of overall reaction (cal/mole); R is the gas constant (cal/mole~ a n d T is the absolute t e m p e r a t u r e (~ As the oxygen c o n c e n t r a t i o n in o u r experiments was over 5 per cent, the d a t a were treated according to equation 2. Neglecting the change in concentration of the oxygen, i n t e g r a t i o n of e q u a t i o n 2 gives

log Cr _

where

r

Determination of absolute rates of high-temperature oxidation of carbon monoxide

d[COJ dt--=

K ?~17615 ~

for

]

[COJ[O2J[H~O]~

[02] < 0.05

Z/nT (1)

and d[CO] dt

K~176

//w

r = 1"04. 1012 [CO][02]~176 T2.5

e_32,000/RT

(4)

,T!

[02] > 0-05

In (1 -- n')

where r is the reaction rate (sec-~); n" is ([COl0 -- [ C O ] ) / [ C O ] 0 , degree of b u r n i n g out; l is the length of reaction zone (cm) ; a n d w is the rate of flow in reactor (cm/sec). T h e change in t e m p e r a t u r e u n d e r the l o g a r i t h m sign m a y be neglected. T h e n , plotting the results of t r e a t m e n t of the experimental d a t a as log qV versus l/T, we find the value of the overall kinetic parameters E a n d K 0 by the conventional m e t h o d from the slope of the straight line. T h e experiments were carried in reactor A. T h e concentration of c a r b o n m o n o x i d e in the C O - a i r mixture varied from 2 to 6 p e r cent. Simultaneously, the initial c o n c e n t r a t i o n of oxygen in the m i x t u r e varied insignificantly a n d could be considered to equal 20 p e r cent in all experiments. T h e reaction t e m p e r a t u r e in the experiments r a n g e d from 600 to l, 100~ It was established t h a t the rate of flow does not affect the reaction rate, a n d therefore in the experiments this p a r a m e t e r was varied in such a way as to make the difference in concentration of c a r b o n m o n o x i d e in the samples r a n g e from 0.7 to 1.5 per cent. T h e results of t r e a t m e n t of the e x p e r i m e n t a l data are shown in Figure 1. W i t h i n the t e m p e r a ture range 750-1,100~ the activation energy was found to e q u a l 32,000 cal/mole. A t lower temperatures the activation energy rises insignificantly up to a value of 35,000 cal/mole. T h e results of these experiments are well described b y the following kinetic e q u a t i o n

Po To~ l s [CO] [O2]~176 for

2 log e

I~T ]

EXPERIMENTAL RESULTS, TREATMENT AND ANALYSIS

It has been established 1-4, 0-s, t h a t in the case of lean mixtures of carbon m o n o x i d e a n d oxygen the overall order of the reaction w i t h respect to c a r b o n monoxide equals 1-0. T h e overall order of the reaction with respect to w a t e r v a p o u r equals0-5. T h e order of the r e a c t i o n w i t h respect to oxygen equals 1.0 a n d 0.25 respectively for mixtures containing over a n d u n d e r 5.0 per cent oxygen. O n the basis of these d a t a the kinetic e q u a t i o n of the overall reaction of oxidation of c a r b o n m o n o x i d e m a y be written as follows

l o g [Ko(0-05)0 75

(2)

I n Figure 2 the absolute rate values o b t a i n e d by us for the overall reaction of oxidation of c a r b o n 143

M E C H A N I S M OF COMBUSTION REACTIONS large discrepancy are not clear so far, a n d special experiments will h a v e to be m a d e to find t h e m out. Thus, the absolute values o b t a i n e d b y us experimentally a n d the t e m p e r a t u r e dependence of the overall rate of oxidation of c a r b o n monoxide is in general a g r e e m e n t with the calculated and experimental d a t a found in the literature.

monoxide are c o m p a r e d with the d a t a of other authors. Besides corrections related to various water v a p o u r content in mixtures were not introduced. A t t e n t i o n is d r a w n to the good agreement of our d a t a as concerns absolute reaction rates with the values d e t e r m i n e d b y Zeldovich a n d SemenovZ, 3 o b t a i n e d by c o m p u t a tion on the basis of the t r e a t m e n t of the d a t a of various authors on the n o r m a l velocity of flame propagation. Besides this our d a t a are in good a g r e e m e n t with the results of c o m p u t a t i o n of the kinetics of c a r b o n monoxide carried out by T s u k h a n o v a s. However, as can be seen from Figure 2, the activation energy calculated by h e r for the overall reaction is somewhat lower t h a n the d a t a of other authors. O u r d a t a agree also with the calculations of Sobolev v w h o d e t e r m i n e d the kinetic relationships of the combustion of c a r b o n monoxide proceeding from m e a s u r e m e n t s of n o r m a l velocities a n d flame temperatures; a n d also with other experimental data 9. R e g a r d i n g the experiments of K a r z h a v i n a 4, there is a certain indefiniteness in h e r experiments, as is known, with respect to the rate of flow in the reaction section, a n d therefore in Figure 2 the d a t a o b t a i n e d by h e r are represented calculated for the greatest a n d smallest possible flow rates u n d e r 3.C

,I ,!

~~

,

o

\

-1-0

\ 5

7

9

11

13

1o/T

u~

~ k E = 35,000

91.0

9 0 850

lO.O

11.o

I

I

2500 1800 1300

I

950

i

750

I

550

T'C

Determination of overall kinetic equation of hightemperature oxidation of methane

1.c

8"0

I

Figure 2. Comparisonof data of various authors on temperature dependence of carbon monoxide oxidation. Q--Chukhanov; ID(~Karzhavina ; (D--Solovyova; /k V--Sobolev ; | ; O--Zeldovich and Semenov; . . . . Tsukhanova; @--Friedman and Cyphers

o

1100

~ 2.0 1,0

i

2'C

710

I

-2.0

cal/mole

6"0

,o'~",."4

~0

1

\

"x,j~

5.0

~/T

6;0 T~

Figure 1. Temperature dependence of overall rate of carbon monoxide oxidation the conditions of h e r experiments. O u r d a t a (see Figure 2) fall within the region b o u n d e d b y these limit curves. M e n t i o n should be m a d e of the considerable divergence, almost two orders between our data, on absolute values, a n d the d a t a o b t a i n e d in the t e m p e r a t u r e range 600-750~ by Chukhanov s a n d t h a t in the region just b e h i n d the flame front by Sobolev 7. T h e reasons for such a

T h e r e are m a n y papers in the literature devoted to elucidation of the m e c h a n i s m a n d kinetic relationships of the oxidation of m e t h a n e at temperatures below 750~ w h e n the walls of the reaction vessels influence the kinetics, a n d the rate of reaction permits the use of static methods for investigation. We know of only one p a p e r 1~ in which the kinetics of oxidation of m e t h a n e was investigated in the region of 1,000~ The authors of t h a t p a p e r gave n o general kinetic equation b u t their p a p e r contains a great deal of information concerning the specific features of the course of the reaction, as well as the concentrations of intermediates. I t follows from their paper, first, t h a t the oxidation of m e t h a n e takes place, as it were, in two stages----oxidation of the m e t h a n e to c a r b o n m o n o x i d e a n d combustion of the latter; secondly, in the course of the oxidation 144

H I G H - T E M P E R A T U R E O X I D A T I O N OF M E T H A N E of m e t h a n e the concentration of the chief intermediate, formaldehyde, is stationary a n d insignificant; thirdly, the concentrations of the other intermediates are also small; fourthly, m e t h a n e retards its own oxidation to c a r b o n m o n o x i d e ; a n d finally, m e t h a n e retards the oxidation of the c a r b o n monoxide formed d u r i n g its oxidation, especially effectively in the initial stage of oxidation of the methane. T a k i n g the a b o v e into

1.0- o~

(Oz)-~ 2 0 %

in experiments involving reaction t e m p e r a t u r e between 900 a n d 1,100~ we m a d e use of reactor B. I n contradistinction to reference 11 there was evidently no activation of the walls in time in o u r experiments. This is b o r n e out b y the fact that the process was stationary a n d by the good reproducibility of the experiments. T h e reaction rates, as in the experiments with c a r b o n monoxide, were virtually i n d e p e n d e n t of the rate of flow in the reactor. Assuming t h a t the overall rate of oxidation of m e t h a n e c a n be a p p r o x i m a t e d by the following function

~PoTo~ n+m r = Ko -~] [CHa]n[Oe]me-E/Rr 0s

;070"c7

02

-2 ~

-O'5 -1.o~ o

9700C

~'-

----.-.-..z.._.~ B70*C I ..-.- ~

780"C

~

740"C 725"(2

/

-2.0 -2"5

~;

930 "C ]

-1'5

, E tou '(5

~" /

"Q

-3.0 -35

-;2"0

'

1!0

-1"5

2!0

-10

5!0

10"0

log (ell4)

where n is the overall order of reaction w i t h respect to fuel; a n d m is the overall order of reaction with respect to oxygen. T h e task was to d e t e r m i n e the values of the kinetic p a r a m e t e r s K0, n, m, E. Determination of n - - I n the experiments for d e t e r m i n i n g the order of the reaction with respect to m e t h a n e the oxygen c o n c e n t r a t i o n in the mixture was kept constant a n d e q u a l to 20 per cent in all cases. Several series of tests were r u n at various temperatures r a n g i n g from 700 to 1,070~ T h e m e t h a n e c o n c e n t r a t i o n in all series was varied between 1-0 a n d 10-0 per cent, the reaction rate in some of the series being d e t e r m i n e d for only three m e t h a n e concentrations, n a m e l y 1, 5 a n d 10 per cent. T h e results are s h o w n in Figure 3, a n e x a m i n a t i o n of w h i c h suggests t h a t the d e p e n d e n c e of the reaction rate on the m e t h a n e concentration

*/,(CH4)'

Figure 3. Dependence of reaction rate on methane concentration in mixtures at various temperatures

0"5

account, a n d also owing to the fact t h a t we did not u n d e r t a k e to establish the m e c h a n i s m of oxidation of m e t h a n e , b u t just to d e t e r m i n e the overall rate of oxidation of m e t h a n e to C O a n d of combustion of the latter, the reaction products were analysed only for C O a n d C O 2. T h e reaction rate was calculated from the difference b e t w e e n the concentrations of C O a n d C O z in the probes according to the formula

0"0

~ o

-0"5

~

-o--o--

-1"0 700

r = _ d [ C H , ] _ d ( [ C O ] + [C02] ) dt dt A ( [ C O ] + [CO2] ) At

(6)

-

800

900

1000

l"~

Figure 4. Variation of order of reaction with respect to methane with the temperature

4 Q T A ( [ C O ] § [CO2] ) ~d21To

(5) w h e r e Q is the rate of flow of mixture (cm3/sec); a n d d is the inner d i a m e t e r of reactor (cm). I n the t e m p e r a t u r e r a n g e 700-900~ the experiments were carried o u t in reactor C, b u t at h i g h e r temperatures it was impossible to m a i n t a i n isothermal conditions in this reactor. Therefore,

is linear in each series, the slope varying with the temperature. Figure 4 gives the t e m p e r a t u r e dependence of the order of the reaction with respect to m e t h a n e . Over the t e m p e r a t u r e range 700 to 930~ it varies almost according to a rectilinear law from 0.65 to -- 0.5. W i t h t e m p e r a t u r e s of 930~ a n d higher, u p to 1,070~ the order of the reaction with respect to m e t h a n e remains constant a n d equal to n = -- 0.5. 145

M E C H A N I S M OF COMBUSTION REACTIONS T o determine the possible influence of the effective oxygen concentration in mixtures rich in oxygen on the order of the reaction w i t h respect to m e t h a n e , a series of experiments was m a d e with mixtures containing 30 per cent oxygen. Figure 5 shows the dependence of the rate of m e t h a n e oxidation on the m e t h a n e concentration for effective oxygen concentrations of 18 a n d 30 p e r cent, obtained at 1,030~ T h e lines h a v e identical slopes, showing that the oxygen c o n c e n t r a t i o n does not influence the order of the reaction with respect to m e t h a n e at this temperature. Determination of m - - E x p e r i m e n t s for d e t e r m i n i n g the order of the reaction with respect to oxygen were carried out at temperatures of 740~ 970~ a n d 1,030~ T h e effective m e t h a n e c o n c e n t r a t i o n in the experiments a t 740~ was kept e q u a l to 4-5 per cent. T h e effective oxygen concentration was varied from 7 to 50 per cent. T h e results of these experiments, represented in Figure 6a, are well expressed by a straight line corresponding to m = 2.0, illustrating the great influence of the oxygen concentration on the rate of reaction. Similar d a t a obtained at 970~ for a n effective m e t h a n e concentration of 4 p e r cent a n d oxygen concentrations ranging from 10 to 30 per cent indicate a reaction order with respect to oxygen of 1.5. T h e value m = 1.5 remains i n v a r i a b l e at higher temperatures as well, as c a n be seen by e x a m i n i n g Figure 6b, where the d e p e n d e n c e of the rate of oxidation of m e t h a n e on oxygen concentrations between I0 a n d 30 p e r cent at 1,030~ is represented for effective m e t h a n e c o n c e n t r a t i o n of 3 a n d 8 per cent. Besides, the fact t h a t the lines

-1.5

i

T=?40~

(a)

are parallel indicates t h a t the m e t h a n e concentration does not affect the order of the reaction with respect to oxygen at these temperatures. Determination of K o and E T o d e t e r m i n e the t e m p e r a t u r e d e p e n d e n c e of the rate of m e t h a n e oxidation the concentrations of m e t h a n e a n d

[

T:1030"C

1.0

~e.

" ~

n:-O "50

0'5

i 30O/o 02

'lS~ Oz -2.0 I 1.0

-1.5 I 2.0

-1-0 L og (C H 4)

I

I 5.0 (CH4)

/~

(b)

T=1030~ 3%Cy

1.0

-2.0

~

:e

oo~-2-5

-3'5

~0-5

-1.5

-2.0

-1.0 I

5'0

I

-0.5 [

I

iog(O2) I

~

oxygen in the mixture were kept constant. T h e effective oxygen concentration equalled 20 per cent in all experiments. T h e t e m p e r a t u r e r a n g e d from 700 to 1,120~ Figure 7 demonstrates the t e m p e r a t u r e dependences of the rate of m e t h a n e oxidation for effective m e t h a n e concentrations of 1, 5 a n d 10 p e r cent. However, the curves reflect

(CH4) =4"5~176 /

/

I

Figure 5. Dependenceof reaction rate on methane concentration at T = 1,030~

|

-3"0

T 10.0

I

10.0 20'0 30"040"0 (02)%

/8~

0

~

m:1.5

).5 -1.5

-1.0

-0"5

I

I

5"0

I

I

I

I

I

10"0 20"0 30.04o.05O-O(02)%

Figure 6. Dependenceof reaction rate on concentration of oxygen in mixture 146

I

tog(O2)

H I G H - T E M P E R A T U R E O X I D A T I O N OF METHANE not only the action of the A r r h e n i u s d e p e n d e n c e of the reaction rate on the t e m p e r a t u r e b u t also a weaker t e m p e r a t u r e d e p e n d e n c e of the reaction orders with respect to m e t h a n e a n d oxygen. T h e influence of the latter factors could h a v e been excluded in order to d e t e r m i n e the value of the activation energy over the entire r a n g e of temperatures studied, but this would h a r d l y h a v e 10 * - (CH 4 ) =0'01~(0z)=0"LK o. (CH4 ) ='0.05~(0z) =0-19 9 - (CH 4 ) =0"10; (02) =0-2C

\

~- -10 o~

-2"0

-3.0 7"0 ,

9-0

8"0 ,

,

r

i

i ~ 110010501000 950 900 8 5 0

104/T

10-C ~

0

, 750

700

T~ i

the large difference between the rates of m e t h a n e oxidation a n d of c a r b o n m o n o x i d e oxidation at the temperatures employed. Estimations of the rate of this process showed t h a t after the r e t a r d i n g influence of m e t h a n e h a d disappeared the rate of oxidation of the c a r b o n m o n o x i d e formed from the m e t h a n e was close to the rate of oxidation of ordinary c a r b o n monoxide. A comparison of the rates of the overall reactions of m e t h a n e oxidation a n d c a r b o n monoxide oxidation, presented in Figure 9 for 5 per cent mixtures of these gases with air, shows that a p p r o x i m a t e l y u p to 1,500~ the overall rate of b u r n i n g of m e t h a n e is limited by the reaction of its oxidation, while at higher temperatures the b u r n i n g of c a r b o n monoxide should become the limiting factor, provided, of course, that the extrapolation of relationships 4 a n d 7 into the region of higher t e m p e r a t u r e s is correct. T h e kinetic relationships o b t a i n e d for m e t h a n e oxidation are in a g r e e m e n t with the experimental data of Burgoyne a n d Hirsh a~ However, our kinetic equation 7 does not agree with the kinetic e q u a t i o n proposed by Norrish 15 on the basis of a theoretical e x a m i n a t i o n of the possible m e c h a n i s m of m e t h a n e oxidation, employed b y B a r t h o l o m O 6 a n d Sandri x3 in their calculations of the normal rate of flame propagation.

Figure 7. Temperaturedependence of overall rate of oxidation of methane to carbon monoxide

I

been advisable as we do not know the value of the reaction rate constant over the t e m p e r a t u r e r a n g e 700-900~ I t has b e e n shown above t h a t the values of n a n d m are constant at t e m p e r a t u r e s between 930 a n d 1,120~ T h e m e a n value of the activation energy for effective m e t h a n e concentrations from 1 to 10 per cent in the mixture over this t e m p e r a t u r e range equals a p p r o x i m a t e l y 60,000 cal/mole on the basis of Figure 8. Accordingly, the following overall kinetic equation c a n be written for the overall reaction rate of m e t h a n e oxidation to c a r b o n monoxide within the temp e r a t u r e r a n g e 930-1,120~ 4' = 7 "108 [CH4]

0"5[02]l5e-60'OOO/RT

o - ( C H 4 ) --0"05 ; ( 0 ~ =0-19

1.4

\

9 - { C H 4) --'0.10 ; (0z)=0.20

"~

1.2

I-0

~

O"8

,\

c. 0-6 o

E=60000

0"4

o ca|/mote

0-2

0

(7)

-0.2

T b e i n g the reaction rate (mole/cm 3 sec). I t is evident t h a t to u n d e r s t a n d the combustion of m e t h a n e to its end products we must h a v e d a t a on the process of combustion of c a r b o n m o n o x i d e w h i c h forms according to relationship 7. For this purpose we a t t e m p t e d to d e t e r m i n e experimentally the rate of oxidation of the c a r b o n m o n o x i d e formed d u r i n g the oxidation of m e t h a n e w h e n the r e t a r d i n g action of the latter disappears. However, in these experiments, the c a r b o n monoxide would ignite, as a rule, before the m e t h a n e h a d disapp e a r e d completely, this a p p a r e n t l y being d u e to

9 - ( C H 4) ='0.01 ; (Oz)=0.20

1.6

6"8 I

'7"0 !

1150

7"4

7"2 I

7(3 I

1 1 0 0 1050

7"8

8"0

8"2

8"4. 10='/T

I

I

I I

1000

950

900T~

Figure 8. Temperaturedependence of reaction rate constant T h e good a g r e e m e n t o b t a i n e d by Sandri between the calculated values of the n o r m a l rate of flame p r o p a g a t i o n a n d the e x p e r i m e n t a l values for mixtures containing 8 a n d 9.5 p e r cent m e t h a n e in air c a n n o t serve as a n evidence of the correctness of Norrish's mechanism. A t all events G a y d o n 17 came to the conclusion on the basis of 147

M E C H A N I S M OF COMBUSTION REACTIONS spectroscopic measurements t h a t the i n n e r cone of the m e t h a n e flame contains no atomic oxygen, which is the basic active particle in the m e c h a n i s m suggested by Norrish. CALCULATION OF ABSOLUTE VALUES OF NORMAL RATE OF FLAME PROPAGATION IN CH4-AIR MIXTURES As the t e m p e r a t u r e conditions of the abovedescribed experiments are close to those in the flame front near the lower limit of flame propagation, the relationships o b t a i n e d m a y serve as a starting point for establishing the m e c h a n i s m of chain reactions taking place in the m e t h a n e flame, if the overall kinetics d e t e r m i n e d by us are actually realized in the flame front. T h e latter idea can be verified at present only indirectly by a calculation (based on the kinetic equations obtained above) of the absolute values of the n o r m a l rate of flame p r o p a g a t i o n i n C H 4 - a i r mixtures. Such a calculation was carried out on the basis of the theory developed bY Zeldovich, 2-0

'

'

(H20)

=

-3.0

\

3.0

4.0

2,700

5-0 t

7.0

6.0 I

8.0 F

1,900 1,500

1,100

164/T I

ToC

Figure 9. Compar#on of overall rates of decomposition of methane to carbon monoxide (equation 2) and of oxidation of latter (equation 1) calculated by equations 7 and 4 .for concentrations [CH4] -- [CO] = 0.05; [02] ~ 0"2; [HzO] = 0"1 Frank-Kamenetskii a n d Semenov3,1~. T h e following expression was employed in calculating the n o r m a l velocity of flame p r o p a g a t i o n 1 U--po(Tm--

L2Jro ~PP'qCdTJ F

To)

s

2

2

200 10"0 - - - -

,,"

i k

I 6

8

10

12

14

4

Figure 10. Comparison of calculated curve with experimental data of various authors for dependence of u on CH 4 concentration in methane-air mixtures. (~--Coward and Har dweU; C)--Egerton ; ID---Hartman ; ~ - - J a n ; | ; @--Klingman ; O--Andreyer ; x--calculated

o -2.0

-5.0

D 30 0

~

0-1

-4.0

Loo / ~,w~ i 4

(CO)= (CH4)= 0"05 (02)= 0-2

- 1.0

'-' 50 0

0 x/

,~ ,Tnvln$(CHt,)-0.5(O 1"0-~'~='" .... T ;~)1.5l- SO.O00 R--7--

~

E

9

0.25 ',u .,.,,,,0.5' 32,000 Q) 4) = 1.04 x 1012 (C0)(O2)T2.5',n:~U,' 1- RT

0~

heat conductivity of gas (cal/cm sec~ ; C~ is the specific heat of gas at constant pressure (cal/g~ ; a n d q is the t h e r m a l effect of reaction (cal/mole). This expression was o b t a i n e d b y neglecting thermal diffusion a n d on the assumption that similarity exists between the t e m p e r a t u r e and concentration fields. This formula m a y be considered sufficiently accurate, according to estimates m a d e by Sandri is, the error in the value of the n o r m a l rate of flame

q89

where u is the n o r m a l rate of flame p r o p a g a t i o n (cm/sec); T,+ is the t e m p e r a t u r e at which r function reaches m a x i m u m (~ 7"i is the t e m p e r a t u r e of reaction products (~ 2 is the 148

p r o p a g a t i o n calculated a c c o r d i n g to formula 8 does not exceed 5 per cent in comparison with the m e t h o d of exact n u m e r i c a l integration. T h e absolute values of the n o r m a l rate of flame p r o p a g a t i o n in m e t h a n e - a i r mixtures were calculated according to formula 8 by graphical integration. It was assumed t h a t the overall combustion rate of m e t h a n e is limited by its oxidation to c a r b o n monoxide, a n d therefore the overall kinetic e q u a t i o n 7 o b t a i n e d in this p a p e r was employed as the source of heat. However, the calculation m e t with a difficulty in connection with the fact that, as it follows from e q u a t i o n 7, the value of the reaction rate tends towards infinity as the effective m e t h a n e concentration drops to 0. Therefore we were obliged to 'cut off' the source at very small effective m e t h a n e concentrations in the m i x t u r e (concentrations of the order of 0.05 per cent); this, however, could hardly produce a n y substantial error in calculating u. O n the other h a n d , it is quite clear that kinetic e q u a t i o n 7 c a n h a r d l y be true for very low m e t h a n e concentrations in the mixture. I n Figure 11 the calculated curve is c o m p a r e d with the experimental d a t a of various authors

H I G H - T E M P E R A T U R E O X I D A T I O N OF METHANE (3) It has been shown that the overall rate o~ methane combustion is most probably limited approximately up to 1,500~ by the oxidation of methane to carbon monoxide, whereas at higher temperatures the limiting factor must be the combustion of the carbon monoxide formed from the methane; provided that the extrapolation of the above determined kinetic equations of methane oxidation and carbon monoxide oxidation is correct. (4) T h e absolute values of the normal rate of flame propagation calculated on the basis of the Zeldovich-Frank-Kamenetskii-Semenov theory, with the aid of the overall kinetic equation of methane oxidation obtained in this paper, agrees well with experiment in the vicinity of the lower limit of flame propagation.

who measured u in methane-air mixtures. It can be seen from Figure 11 that the calculated curve agrees rather well with experimental results up to methane concentrations of approximately 8 per cent in the mixture. For methane concentrations exceeding 8 per cent the calculated curve deviates from the experimental ones. Especial note should be made of the surprisingly good agreement between the calculated values of u at the lower limit of flame propagation with the precision experimental data of Egerton and T h a b e t 14 (see Figure 11) obtained with a flat burner. CONCLUSIONS Analysis of the results of this study suggests the following conclusions : (1) The additional information obtained by direct experiment on the absolute values and

o

The author wishes to express his special thanks to Professor L. N. Khitrin for valuable advice and continued interest in this work.

/

10

9

REFERENCES

Zh. fiz. Khim., Mosk. 25, Part 5 (1951) 2 ZELDOVICH, Y. B. and SEMENOV, N. N. J. Exp. teor. Phys., Moscow 10, Part 10 (1940) 3 SEMENOV, N. N. Adv. phys. Sci., Moscow 24, Part 4 (1940) 4 KARZHAWNA, N. A. Zh. fiz. Khim., Mosk. 19, Part 10 (1945) 5 CHUKHANOV, Z. F. Zh. tekn. Fiz., Mosk. 8, Part 2 (1938) 6 FRIEDMAN, R. and CYPHERS, J. J. chem. Phys. 25, No. 3 (1956) 7 SOBOLEV, G. K . High Temperature Oxidation and Burning qf Carbon Monoxide. This volume, Paper No. 57 s TSUKHANOVA, O. A. Calculation of the Overall Reaction Kinetics .for Carbon Monoxide with Oxygen and Methane with Oxygen. To be published 9 KHITRIN, L. N. and SOLOVYOVA, L. S. Homogeneous-Heterogeneous Combustion of Carbon Monoxide m Narrow Tubes (Channels). This volume, Paper No. 74 10 BURGOYNE,J . H. and HIRSH, H. Proc. Roy. Soc. A 227 (1954) 73 n KOVALSKY,A. A., SADOVmKOV, P. Y. and CmRKOV, N. M. Zh. fiz. Khim., Mosk. 4, Part I (1938) x2 ZELDOVmH, Y. B. and FRANK-KAMENETSKII, D. A. Zh. fiz. Khim., Mosk. 12, Part 1 (1938) 18 SANDRX, R. Canad. J. Chem. 34, No. 3 (1956) la EGERTON, SIR ALFRED and THABET, S. K. Proc. Roy. Soc. A 2 2 8 (1955) 1174 15 NORRISH, R. G. W. Proc. Roy. Soc. A 150 (1936) 36 16 BARTHOLOMI~, E., DREYER, H. J. and LESEMAN, K . J . Z . Elektrochem. 54 (1950) 246 17 GAYDON, A. G. Trans. Faraday. Soc. 42 (1946) 295 1 BARSKY, G. A. and ZELDOVICH, Y. B.

7 m

6

l !

4 t ! 5.0 5'4 5.8

62

%CH 4

Figure II. Comparison of calculated values of u with experimentaldata of Egerton and Thabet : | . . . . . calculated temperature dependence of the reaction rate of the high-temperature oxidation of carbon monoxide agrees on the whole with the material available in the literature. The temperature dependence of the rate of carbon monoxide oxidation at temperatures between 750 and 1,100~ corresponds to an activation energy of 32,000 cal/mole. (2) The overall kinetic equation of hightemperature methane oxidation to carbon monoxide has been determined. For the temperature range 930-1,120~ it has the following form r = 7"108 [CH4] ~ T

e 6O,OOOtRT

At temperatures below 930~ the values of the kinetic parameters vary with the temperature.

149