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A shock-tube investigation of the ignition of lean methane and n-butane mixtures with oxygen
A SHOCK-TUBE INVESTIGATION OF THE IGNITION OF LEAN M E T H A N E A N D n-BUTANE MIXTURES WITH OXYGEN R. hi. R. HIGGIN AND ALAN WILLIAMS
Department of Fuel Science, The University of Leeds, Leeds, England An investigation has been made of the ignition of shock-heated mixtm'es of methane and oxygen highly diluted with argon. The shocked-gas temperatures and pressures covered the ranges 1800~ to 2500~ and 200 to 300 Torr, respectively. The ignition delays were inversely proportional to the oxygen eoneentration and a plot of log~0(t,[O2]) against inverse temperature yielded an apparent activation energy of 32 keal mole t. The addition of trace amounts (,f n-butane greatly reduced the ignition-delay times. A theoretical model has been used to study lhe ignition mechanism which utilizes the numerical integration of the reaction-rate expressions, lleasonable agreement with experimental data can be achieved if the major initiation reaction is the first-order dissociation of methane. The only oxidation reaction of the methyl radical is its bimoleetdar reaction with oxygen and, to achieve reasonable agreement with experiment, this mu.,t be assigT~eda value of about 0.8 X 10TM ema mole-t see-l at 1875~
Introduction
Experimental
A considerable number of investigations, both experimental and theoretical, have been made of the combustion of hydrogen and carbon monoxide in shock-heated gases. In contrast to this, hydrocarbons have received much less attention because of their complexity although some publications have dealt with the simpler hydrocarbons, particularly methane?-8 The high-temperature ignition and combustion of methane is an especially interesting ease because there already is available considerable information about its oxidation mechanism at moderate temperatures and in flames?-~2 Despite this, little information is available concerning two areas important to ignition kinetics, namely, the initiation reactions and the oxidation reactions of the me/,hyl radical. The problem of n-butane eombustion is even more complex and few high-temperature combustion investigations have been attempted. However, it is well known that the higher normal alkanes are nmch more reactive and exhibit much smaller ignition delays than methane. In this paper, data is presented for ignitiondelay times (induction-period times) for mixtures of methane alone or in a mixture with n-butane. To aid the interpretation of the results, a theoretical ignition model has been used.
The shock tube and associated apparatus were of conventional design. The shock tube was 3.3 em i.d. The driver and low-pressure sections were 120 and 230 em long, respectively, wit.h a dump tank at the end of the driven section. The lowpressure section could be evacuated to ca. 10.4 Torr by an oil diffusion pump. The diaphragm material used was 0.001 to 0.003-in. thick Melinex (I.C.I. Ltd.) and the driver gas was helium. Shock-velocity measurements were made by means of five deposited platinum heat-transfer gauges ~a that operated transistor trigger amplifiers?4 The output of the amplifiers could be presented on an oscilloscope, together with tinting marks, or could operate a digital timer. At the central detector position, two sapphire windows masked to a l-ram slit width were mounted on opposite sides of the tube. For the emission experiments, a monochromator (Hilger and Watts D285) was used to observe the ultraviolet radiation of OH radicals at 3067 ~. due to the 2Z+--"lI transition, a band-pass of 3064 to 3070 .~ being allowed. The light intensity was measured by a photomultiplier and the signal was presented on a Tektronix 545B oscilloscope. For OH absorption measurements, a bismuth-discharge lamp excited by a 2450-MHz discharge in argon was used. Pressure measurements of the shocked
579
580
DECOMPOSITION AND EXPLOSION
eC
'
,
I00
~sec
time FIG. 1. Hydroxyl emission curves for: (a) 2% methane, S ~ oxygen, 90% argon, T2 = 1925~ (b) 1.53c/~methane, 0.22% n-butane, 8.23% oxygen, 90~ argon, T._~ = 1680~ (c) same mixture, T2 = 1780~ gases were made by means of a 610L Kistler transducer and a charge amplifier. It was assumed that the gas behind the shock wave was in complete thermodynamic equilibrium and that complete vibrational equilibration was attained. The shock front underwent a slight attenuation (2.0% to 3.5% per meter) and the mean temperature and pressure of the shocked gases during the induction period were calculated from the shock velocity and mixture enthalpies by means of an iteration procedure. The temperature error may be about + 4 0 ~ for the lower end and about ::L60~ near the upper end of the temperature range covered. 5Ieasurements of the pressure profiles behind the shock front are consistent with these estimates.
Experimental Results The induction times for the appearance of hydroxyl emission from a number of methaneoxygen mixtures diluted with 90 mole % argon have been studied in the range of conditions 1800~ T0_< 2500~ and 200_< P2_< 300 Torr. The form of a typical emission spectrum from such a shock heated methane-oxygen mixture is shown in Fig. l ( a ) . The emission signal did not occur until after a defnite induction time, but it then rose rapidly to a sharp maximum value (11) followed by an approximately exponential
decay to a level (I.,) of about 0.5 to 0.6 the nlaximum value for a period of 50-200 ~sec, it then fell to zero. The ignition-delay time was defined as the time for the emission intensity to rise to 0.05I, so as to eliminate errors due to light reflection. These emission-iuduction times proved to be a sensitive means of detecting the onset of reaction. Comparison with data obtained using hydroxyl absorption measurements showed that the detection threshold corresponded to a hydroxyl concentration of about 1 X 10-9 moles cm-3. The hydroxyl emission-induction times obtained in this way and corrected to gas times by multiplication with the density ratio are given in [Fig. 2 for equivalence ratios of 2 to 0.25. The equivalence ratio is the fuel-to-oxygenratio divided by the stoichiometricratio. The induction times were approximately inversely proportional to the oxygen concentration. The slopes of these plots correspondto an apparent activation energy of 30 4-3 kcal mole-k Most previous investigators have presented methane-oxygen ignition data in the form of a plot of log (&EO2~) as a function of inverse temperature. The present experimental data are plotted in this way in Fig. 3 together with the results obtained in other investigations. This parameter gives a reasonable correlation of the data, although a parameter of
the form log (t,.EO23mECI-h-]1-m), where m - - 0.8 to 0.9, is also consistent with the experimental data. The temperature dependence of the plot in F i g 3 corresponds to an apparent activation energy of 32 4- 4 kcal mole-L This is similar to
3.0
u 2.5
I
~"2oI
m
i
i
i
4
5
6
104/T
FIG. 2. Plot of log,0& against 1/7' for mixtures of 90% argon and 10% (methane 4- oxygen) with the following equivalence ratios: A 2, (D 1, 9 0.5, [] 0.25.
SHOCK-HEATED MIXTURES estimates given by Kistiakowsky and Richards 2 (E = 33 keal mole-1) and Soloukhin s (E = 33 kcal mole-l), although Asaba et al. a and Miyama and Takeyama 4 obtained values of 20.6 and 21.5 kcal mole-1, respectively. Glass et al. 7 used the parameter
581
9 ,a
2.5
/ ( D
i/1
-q
loglo (ro,_,-l'/2EAr]i/2&)
2.0
and found an apparent activation energy of 56 kcal for methane-oxygen results at 2000 ~ 2300~ If our results are plotted in this form, we find a poor correlation and a much lower apparent activation energy of 30 kcal mole-~. Measurements were made of the magnitude of the hydroxyl emission in the reaction zone (I1) and in the past combustion zone (I=). I t was observed that these did not vary much with temperature; in the case of a mixture with an equivalence ratio of 0.5, the temperature dependence for both quantities corresponded to an apparent activation energy of only 5 keal mole-~. Ignition of Mixtt~res of Methane and Oxygen with Added n-Butane The addition of small amounts of n-butane to methane-oxygen mixtures had a very marked effect on the ignition-delay times. In addition, hydroxyl emission also occurred in the pre-ignition region while the main combustion zone was
-8
o -9 E
0
/
1.5 9
i
4
5 104/T ~
6
FIG. 4. Plot of log,& against 1/T for the following mixtures: (a) 2% methane, 8Co oxygen, 90% argon; (b) 1.94/C7c.methane, 0.02c{ n-butane, 8.04.% oxygen, 90% argon; (c) 1.87% methane, 0.05c~ n-butane, 8.08% oxygen, 90(i~ argon; (d) 1.53~ methane, 0.22% n-butane, S.23% oxygen, 90% argon; (e) 0.715c n-butane, 9.29c'c oxygen, 90% argon. These nfixtures all have an equivalence ratio of 0.5.
characterized by a further, more-marked enfission as shown in Figs. l ( b ) and 1 (e). The ignition delay was defined as the time taken until this second emission occurred. The mixtures used had an equivalenee ratio of 0.5 and, for these, plots of log ti against reciprocal temperature produced straight lines with apparent activation energies of 28 to 32 kcal mole-1 as shown in Fig. 4. The addition of 1% n-butane reduced the ignition delay by a factor of 3, 5% n-butane reduced it hy a factor of 6, while 10% n-butane reduced it by a factor of 10.
TheoreticalModelof Methane-Oxygen Ignition
g'-,o
5
6
7
8
9
I0
I 04/T OK Fro. 3. PIo! of logl01,[Odagainst 1/T for methaneoxygen mixtures. 1, t~ef. 3; 2, Flef. 4; 3, Ref. 8; 4, 1Ref. 2; 5, this work.
A mathematical model has been used to provide information about the kinetics and mechanism leading to ignition. In this, a number of reactionrates expressions, together with the equations for conservation of mass, energy, and momentum, were numerically integrated by means of a digital computer. The differential equations used for reaction, rate, temperature, etc., were those given in Ref. 15. The thermoehemieal quantities required for each species were computed over the required range of temperature by means of a polynomial equation, the coefficients used being taken h'om
582
D E C O M P O S I T I O N A N D EXPLOSION TABLE I Reactions used in the theoretical model Rate expression (mole, em, see, units)
Reaction
(2) (4) (5) (7) (8) (9) (10)
(11) (12) (13) (14) (15) (16)
CH4 = CH~ + H CH~ -t- O_~ = CIt:O q- OH CH3 q- O = CH20 + H CH~O + Oil = tt_~O + II + CO CH4 + OH = It~O + CII3 H + O 2 = OH + O CH4 + O = CH~ + OH CH4 + H = CHa -t- H.~ CO + OH = CO~ + H O + H2 = OH + H OH -~- H.~ = H~O q- H OH + OH = H20 + O H + O t I + M = H20 q - M
Ref.
Varied, see Table II Varied, see Table II k5 = 1.9 X 1013 k7 = 3.12 X 1014 exp(-4240/RT) k8 = 7.24 X 10 ~3 exp(-5810/RT) k~ = 2.53 • 10" exp(-16790/RT) kl0 = 3.2 • 1013 exp(-7950/RT) kH = 4.14 • 1013exp(--11610/RT) ~'12 = 6.63 • 1011 exp(--1030/RT) kl3 = 1.27 N 1013 exp(--9400/RT) kl~ = 3.68 • 101~ exp(-5490/RT) ~5 = 8.6 N 10 ~ exp(-1000/RT) kl~ = 5.4 • 1015
Ref. 16. Other data was taken from the J A N A F TablesJ 7 The net rates of the chemical reactions were derived from the species concentrations and the forward and reverse rate constants, these latter quantities being calculated from the appropriate equilibrium constants. T h e reverse rates were not included for Reactions (2) and (7) but the error introduced is small. F o r the recombination reaction, the rate constant for argon was assumed for all third-body species. The species equations and five shock equations were integrated simultaneously with distance as the independent variable means of a R u n g a K u t t a - M e r s o n procedure.
Choice of Chemicals Reactions and Kineth's The system chosen for theoretical investigation was a lean m e t h a n e - o x y g e n mixture with an equivalence ratio of 0.5, diluted with 90% argon. The temperature of the unreacted shocked gas was 1875~ and the pressure 212.8 Torr. The experimental ignition delay time in this case was 467 #see. The number of reactions involved in the combustion of methane is quite considerable. Consequently, a very much simplified model has been used in this exploratory study to obtain information about the relative importance of various reaction steps. The chemical reaction scheme and the rate expressions used are given in Table I. The reaction scheme involved twelve species and was largely based on the scheme used by DeGroat and A b b o t t 18 for the supersonic combustion of methane, although a number of
12 25 25 25 25 25 25 25 25 25 26
modifications have been made to suit the particular circumstances considered here. These are of major importance and are discussed further now.
Initiation Reactions Three reactions are possible: CH4 -I- 02 -- CH3 -t- H02 AH1875~ ---- 55.4 kcal mole -1
(1)
CH4 = CH3 -t- H AHlsTa~ -= 105.7 kcal mole -1 O._,+ M = 2 0 .
(2)
-t- M
A/II875~ = 121.9 kcal mole~1.
(3)
Reaction (1) is the most important step in lowtemperature oxidation, but at higher temperatures, both Reactions (1) and (2) are involved as suggested by Skinner and R u e h w e i n ) Reaction (3) contributes significantly only at very much higher temperatures. Unfortunately, little data is available for kl, but the expression kl = 4 X 1011 X exp (--55,000/RT) cm 3 mole -1 see-1 has been theoretically derived by D e n i s o v J 9 The lmblished experimental data for the first-order
SHOCK-ItEATED MIXTURES decomposition of methane have been sunmmrized by the expression
553
Reactions of For,laid(hyde Formaldehyde may react with all the free radicals present, thus,
k,_ = 4 X 1014exp (-103,000/RT)sec -1 by Palmer and Hirt? ~ Thus, at temperatures above 1500 ~ to 1600~ the rate of Reaction (2) is much greater than that of Reaction (1) provided that the methane decomposition reaction is truly first-order. If this is so, under the experimental conditions used here, then there is no need to include the hydroperoxyl species in the reaction scheme.
Reactions of Methyl Radicals Methyl radicals may be oxidized by the reactions
tt q- CH..,O = RH -4- CHO, followed by many possible reaetion.~ of the formyl radical. To reduce the mm~ber of possible reactions, two simplifying a~sumptions have been made. First, the only radiual taking part in thi~ reaction was assulned to be hydroxyl. This is a reasonable approximation since hydroxyl concentrations are higher than H or O, al~d it is also the fastest reaction. Second, the formyl radicals produced by this exothermic reaction (AII~:~ h; = --43.68 kcal mole-a) were assumed to ,lecuml),,,e very rapidly. CHO= COq-H
E=
23kcalmole -l (Ref. 25).
CH~ q- O2 = CH20 q- OH AHlST~~ = --51.3_kcal mole-1
(4)
CH3 q- O = CHaO = CH20 q- H aHlsT~~ = -- 66.94 kcaI mole-I
(5)
Thus, the over-all reaction of formaldehyde and hydroxyl was approxitnated 1)\- the followit~ sequence '. OH-f- CH~O = H,O q- H if- CO.
(7)
CH3 -ff O.2 = c g a o -ff O
AIIls75~ = + 3 2 kcal mole-L
(6)
The bimolecular reaction between methyl radicals and oxygen molecules [Reaction (4)-] has been established at lower temperatures ~-~ and it may be reasonably assumed to be of importance in the present system. However, there is little kinetic data available for this reaction at the temperature of interest and there is considerable variation in the results reported at lower temperatures? -~The bimolecular reaction between methyl radicals and oxygen atoms has been suggested by Fenimore ~2 as the sole methyl oxidation reaction in certain methane-oxygen flames. This reaction has therefore been included in the scheme. Fenimore ~2 did not indicate the fate of the methoxyl radical but it has been assumed here to undergo unimoleeular dissociation to formaldehyde and hydrogen atom. The third reaction [-tleaction (6)~ will have a rather high activation energy ( E ~ 3 2 keal mole-1) and can only be of importance at much higher temperatures, 2a and was therefore not included in this scheme. Dimerization reactions of methyl radicals as well as other methyl association reactions occur extensively in the oxidation of methane-rich mixtures? Calculations showed that, under the conditions used here, these reactions are relatively unimportant in the pre-ignition period.
Results. Influence of Kinetic Parameters
Using the method and chemical reaction scheme outlined, it was possible to obtain a set of calculated profiles representing the build-up of free radicals and other intermediates in the pre-ignition period, together with information on temperature, pressure, ere. The more important results of a typical computation are shown in Fig. 5. The profiles obtained are very dependent upon the particular choice of rate expressions. Fortunately, a critical completion of data is available for some of the more important reactions, 2~ and this data was accepted as a starting point and attention was concentrated on the influence of the parameters k2 and k4. The kinetic data used is listed in Table I, while the variations in k., and ],'4 are given in Table II. In all the cases studied, the radical concentrations rose rapidly in a complex manner from initial zero value at zero time at the shock front to values of about 10-~~ to 10-I2 mole cm-a. Thereafter, the increase in concentrations of the species followed approximately an exponential form until their values were about 10-9 mole em-3. At this point, eonsumption of the reactants rapidly increased, resulting in a temperature rise, and this resulted in a further acceleration in the build-up of radical concentrations.
584
DECOMPOSITION AND EXPLOSION
-8
'E - I 0 0
s
u-12
2200
0
o
K
o~ 0
-14
2000
I00
200 time ~ s r
FIG. 5. Computed pre-ignition composition profiles and temperature plotted against time for Run 6. It was observed in all cases that the formaldehyde concentration was at a maximum at the point where the temperature and reactant consumption rapidly rose, and that thereafter it decreased. The hydroxyl concentration at this point was about 1 X 10-9 nmle cin-3 and since this is in accordance with the experimental criterion of ignition delay then the time at which this concentration was attained was taken as the ignition delay time. The values obtained in this way for various assumed values for k2 and k4 are given in Table II.
For Runs 1 to 4, the value given by Palmer and Hirt 2~ for k2 F = 4 X 1014exp (--103,000/RT) sec-13 was assumed and the ignition delay was computed for various values of k4, the object being to bring the computed ignition delay roughly in agreement with the experimental value of 467 ~sec. The ignition times so obtained are given in Table II. Second, a value of k4 = 1 X 10n cm3 mole-1 sec-~ at 1875~ was assumed, and the influence of variations in k2 was investigated (Runs 3, 5, and 6). Over the limited range studied, the
TABLE II Computed ignition-delay times for various kinetic assumptions Run No.
k.,.
1
4 X 1014exp(--lO3,0OO/RT) 4 X 1014exp(--lO3,0OO/RT) 4 X 1014exp(--lO3,0OO/RT) 4 X 10TM exp(--lO3,0OO/RT) 2 X 1014exp(-103,000/RT) 1 X 1014exp(-lO3,0OO/RT) 2 X 1014exp(-lO3,0OO/RT)
2
3 4 5 6 7 8
1 . 3 X 10 ~4 exp(-lO3,0OO/RT)
kd1875~ 4 2 1 1 1
>< 1011 X 101' X 1011 X 10TM X 1011 1 X 1011 1 >< 101~ 8 X 109
Calc. ti(~sec) 72 106 131 261 170 231 350 460
Experimental value 467
SHOCK-ItEATED MIX~I UtlES ignition delay followed the apl)roximate relationship ti c~ --ln ~. It is significant to note that the effect of doubling k~ is virtually the same as that of doubling h4. Finally, in Runs 4 and 7, k4 was fixed at i X 10 ~~enr~ mole-~ see-~, and values of/~2 were tried to obtain reasonable agreement with the experimental ignition delay time. In order to assess the relative contributions of the two methyl radical oxidation reactions [ ( 4 ) and (5)], the value of ka was reduced by a factor of 103 in one run. This made only a small difference to the computed profiles and the ignition delay was only 5% different to the run that ineluded k5 at the value given in Table I. It was concluded that Reaction (5) played only a minor role but, nevertheless, it was included in all the computations reported here. A number of runs were made to test the sensitivity of the calculated ignition-delay times to errors in the assumed reaction-rate parameters for some of the more important reactions. The effect of halving kt~, the rate constant of the reaction H -t- 0~ = OH ~- O, was to increase the ignition-delay time by 11%. The effect of halving ks, the rate constant of the (major) methane consumption reaction with hydrox)q, was to decrease the ignition delay by 9%. This effect presumably results from the replacement of a reactive hydroxyl radical by a less-reactive methyl radical. Halving kLo, the rate constant for the sole carbon monoxide oxidation reaction, did not change the ignition-delay time.
Discussion The only detailed analyses of the ignition mechanism in shock-heated lean methane-oxygen mixtures are by Asaba et al. 3 and an extension of this work by Miyama and Takeyama. 4 In the latter analysis, it was assumed that, during the induction period, species such as OH, CH._,O, etc., are quasi-steady-state intermediates and that the principal chain carrier is the CH~ radical. They included Reaction (4) in their mechanism, but not Reaction (9). The)- deduced that both hydroxyl and methyl concentrations rose exponentially and were able to derive the relationship /c4[Oe]t~ = eonst. That is, a plot of log ( t f 0 2 ] ) against l I T should be a straight line, with its slope giving the value of E4. Experimentally, they obtained values of 20.6 (Ref. 3) and 21.5 kcal mole-1 (Ref. 4). However, from the computed concentration profiles in all the eases studied here, it was clear that the quasi-steady-state assumption does not strictly hold. Furthernmre, Bradley 27 has obtained analytical expressions for the ignition-delay time for various types of chain-branching reactions. He was able to show
585
that, in the case of a simple direct chain-branching reaction, a relationship of the type t~ cc {/q[-O.,]}-~ would apply. Obviously, in the methane-oxygen system, a much more complex state of affairs exists and a simple expression of this type cammt hold. However, experimentally, the relationship log ti[-O._,]against 1/T does appear to hold, but it must be concluded that its temperature dependence (E = 32 kcal mole-1 in this work) does not correspond to any single reaction step and that this equation does not indicate the role of oxygen or methane in the induction-period reactions. Indeed, the present results suggest that the activation energy of the initiation reaction plays an important part in determining temperature dependence of the ignition delay as well as its absolute magnitude. The use of the present mathematical model seems to be a promising method of investigating the interrelation of the various reaction steps. At present, detailed discussion is premature, but the following points can be made. The Initiation Reaction
In previous work on methane-oxygen ignition it was generally assumed that initiation occurs via the bimolecular reaction of methane with oxygen. However, in the particular experimental conditions used here, the computed data was consistent with the experimental ignitiondelay time if the initiation reaction were largely the simple first-order dissociation of methane. This raises a problem concerning the collisionat activation of the methane molecule, but this has been discussed by Kondratiev, 28 who pointed out that the rate constant for the second-order decomposition CH4+Ar=
CHs+H+Ar
is given by k2' = 1021exp ( - - E / R T ) em 3 mole-1 sec-1 with an accuracy to within a power of 10. Consequently, at reasonably high pressures, the thermal dissociation of methane obeys a strict first-order law. At the lower experimentM pressures considered here, and using the argument advanced by Kondratiev, ~ it still seems probable that first-order dissociation of methane does occur. However, the conditions must be near that of the second-order fall-off region and a small fall-off in rate must occur. Furthermore, it must be stressed that, at very low pressures or at high oxygen concentrations, or in very lean mixtures, the bimolecular reaction of methane with oxygen can be an important competitor with the methane-dissociation reaction. In fact, preliminary runs in which the oxygen concentration has been
586
DECOMPOSITION AND EXPLOSION
12 "iu oll
E ~E
~10 O
o
t
9
V
\
J
A
2&r
3
Fro. 6. Arrhenius plot for Ct{a + O2. Q This work; 9 Ref. 29; A Ref. 30; [] Ref. 31; 9 Ref. 32; I Ref. 33; 9 Ref. 34; V Ref. 35; - - - Ref. 36. greatly increased indicate that the experimental dependence of log ti[02] against inverse temperature can only be reproduced if the bimolecular reaction of methane and oxygen [Reaction (1)] is included in the reaction scheme.
The Reactions of Methyl Radicals and Oxygen Molecules If the first-order decomposition of methane is the predominant initiation step, then, from the published data on the rate of this reaction, it is possible to estimate k4. This value is dependent upon the accuracy of the e:~erimentally determined ignition delay, on the accuracy to which k2 is known, on the validity of the chemical model and on the total resultant effect of the errors in the other rate expressions used. If the value given by Pahner and Hirt 2~ for k2 ~4 X l0 '4 X exp (--103,000/RT) sec-~] is accepted, then the value of k4 required to give agreement between comlmted and experimental ignition delays is estimated to be about 1 X 109 cm a mole- t sec-1 at 1875~ However, Pahner and Hirt 2~ obtained their value for ke by combining their experimental data with previously reported shock-tube work on methane pyrolysis--this latter data being interpreted on the basis of first-order kinetics and on the assumption of a chain length of 2. This probably suggests that the over-all rate expression given by them is an upl)er limit and, indeed, their own experimental results were expressed in the form k2 = 1.26 X 10 t4 exp (-- 101,000/RT) see-l; this expression is equivalent at 1875~ to k._,= 2 X 10~4exp (--103,000/RT) sec-k The mean
estimate of/~4is thus obtained using the expression k4 = 4 X 10+14 exp (--103,000/RT) combined with an estimated pressure fall-off factor of 3; this leads to a value of about 109"9~-1cm a mole- l sec-1 at 1875~ The value obtained for k4 provides a method of checking the validity of the theoretical model and the accuracy of the other data used, since it should be in reasonable agreement with the published estimates of/ca. McMillan and Calvert -~2 have summarized the data available up to 1965 (Refs. 29 to 34) and these are plotted in Fig. 6 together with the present value. More recently, Baldwin et alY have tentatively suggested the value of 5.8 X 10-s cm a mole-1 sec-1 at 500~ while Barnard and Cohen a6 have been able to explain their methyl oxidation results at 400~ on the basis that k4 = 2 X 10t2exp (--25,000/RT) cm a mole-~ s e c t. These latter estimates are significantly smaller than the earlier values of k4. However, despite the wide variations in the published data, the present value seems to be in reasonable agreement with previous estimates of k4, although obviously much further work is required in this direction.
The Effect of Added n-Butane to Methane-Oxygen Ignition The reduction in ignition delay can be interpreted in terms of the ease of dissociation of n-butane by C - - C bond fission compared with the initiation reactions of methane that involve breaking a C - - H bond. n-Butane decomposes unimolecularly, thus, n-C4Hm = C..,H5q- C2H~, = CHa q- CaHv,
(17) (18)
followed by CaH7 -- C',H4 q- CHa,
etc.
There is some uncertainty concerning rate expressions, but a recent value a~ for Reaction (18) of k18 = 10*agexp (--69,500/RT) will be used here to illustrate the more rapid initiation rate. The ratio of the rates of radical production in a mixture of methane -k 1% n-butane/oxygen mixture to the equivalent methane/oxygen mixture is given by
{/~_['CH4] --[- k,s[-n-C4H,o-] }/k:~.ECH,-]. At 1875~ this ratio is about 20 and if the relationship ti o: --ln(rate of initiation) holds good, then the ratio of ignition delays should be about 4. This is of course quite approximate,
SHOCK-ItEATED MIXTURES since it does not take into account the relative reaction efficiencies of the different radicals, but nevertheless it is in agreement with the experimental ratio of 3.
16. 17.
ACKNOWLEDGMENTS
18.
The authors thank Mrs. V. I. Higgin for assistance with the computer programming and D. J. Battyre, T. Boddington, and G. Dixon-Lewis for useful discussions. One of us (R.M.R.H.) is grateful to S.R.C. for the award of a Research Studentship.
19. 20.
REFERENCES
22.
1. SXIXNER, G+ B. AND RUEHRWEIN, 1)~. A.: J. Phys. Chem. 63, 1736 (1959). 2. KISTIAKOWSKY, G. B. AND I~ICHARDS, L. W.: J. Chem. Phys. 36, 1707 (1962). 3. ASABA, T., YONEDA, K., KAKIHARA, K., AND HIKITA, T.: Ninth Symposi~ml (Intevm+tional) on Combustion, p. 193, Academic Press, 1963. 4. Ms H. AND TAKE'I'AMA, T.: J. Chem. Phys. 38, 37 (1965). 5. ~*OEVODSKY, V. AND SOLOUKHIN, R. I.: Dokl. Akad. Nauk SSSR 161, 1118 (1965). 6. DovE, J. E. AND ~IouLTON, ]). McL.: Proc. Roy. Soc. A283, 216 (1965). 7. GLASS, G. P., KISTIAKOWSKY,G. B., MICHAEL, J. V., A~'I) NIKI, H.: Tenth Symposium (International) on Combustion, p. 513, The Combustion Institute, 1965. 8. SOLOUKHIN, R. I.: Eleventh Symposium (International) on Combustion, p. 671, The Combustion Institute, 1967. 9. ENIKOLOPYAN,N. S.: Seventh Symposium (International) on Combustion, p. 157, Butterworth, 1959. 10. ~INKOFF, G. J. AND TIPPER, C. F. It.: Chemistry of Combustion Reactions, p. 151, Butterworths, 1962. 11. FRISTROM, R. M. AND WESTENBERG, A. A.: Flame Structure, McGraw-IIill, 1965. 12. FENIMORE, C+ P.: Chemistry of Premixed Flames, p. 43, Pergamon, 1964. 13. GAYDON, A. G. AND HURLE, I. R.: The Shock Tube in High Temperature Chemical Physics, Chapman and Ilall, 1968. 14. SmLLIN6, M. J.: N.P.L. Aero Note 1050, October 1966. 15. SOTTER, J. G.: Tenth Symposium (International)
23.
21.
24. 25. 26.
27. 28.
29. 30. 31. 32. 33. 34.
35.
36. 37.
587
on Combustion, p. 1405, The Combustion Institute, 1965. WILL~A.~IS,M.: NAVWEPS l~eport 7609, 1961. J A N A F Thermoehemical Tables, Dow Chemical Company. DEGROAT, J. J. AXD ABBOTT, M. J.: AIAA J. 3, 381 (1965). DENISOV, E. T.: Russ. J. Phys. Chem. 38, 2 (1964). PALMER, H. B. AND I]IRT, T. J.: J. Phys. Chem. 67, 709 (1963). HOARE, D. E. ~,XD PEACOCK, G. B.: Proc. Roy. Soe. A201, 85 (1966). MCMILLAN G. R. AND CALVERT, J. G.: Oxidation Combust. Rev. 1, 102 (1965). FABIAN, D. J. AND BRYCE, W. A.: Seventh Symposi+lm (International) on Comb~Lslion, p. 150, Butterworths, 1959. GRIFFITHS, J. F. AXD SKIRROW, G.: Oxidati(m Combust. Rev. 3, 57 (1968). SCHOFIEH), K.: Planet. Space Sci. 15, 6+I3 (1967). GETZINGER, R. W.: Eleventh Symposium (Irdernational) on Comb~slio~b p. 117, The Combustion Institute, 1967. BRADLEY, Z. N.: Trans. Faraday Soc. 63, 2945 (1967). KONDRIATIEV, V. N.: Tenth Symposbot~ (Ddernational) on Combustion, p. 319, The Combustion It,stitute, 1965. CHRISTIE, M. J.: Proe. Roy. Soc+ A2.}4, 411 (1958). HEICKLEN, J. AND JOHNSTON, H. S.: J. Anl. Chem. Soc. 83, 4030 (1962). WENGER, F. AND KUTSCHKE, K. O.: Can. J. Chem. 37, 1546 (1959). SLEEPY, W. C. AND CALVERT, J. G.: J. Am. Chem. Soc. 8l, 769 (1959). INGOLD, K. V..aND BRYCE, \V. A.: J. Chem. Phys. 24, 360 (1956). AVRAMENKO, K. I. AND PONTNIKOV, L. ~1.: Izv. Akad. Nauk SSSll, Otd. Khim. Nattk 1960, 1921. BALDWIN, R. R., N(mms, A. C., AND WALKI'~R, R. W.: Eleve~lh Symposium (International) on Combustion, p. 889, The Combustion Institute, 1967. BAR~ARD,J. A. AND COHEN, A.: Trans. Faraday Soc. 64, 396 (1968). ItALSTEAD, M. P. AND QVIN, C. P.: Trans. Faraday Soc. 64, 103 (1968).
COMMENTS T. Takeyama, T o k y o R a y o n Co., Ltd., Kamakura, Japan. I imagine that you have simply assigned a value of 10-9 mole/cc of the groundstate OH concentration to the detection threshold of O H emission.
Did you check the effect of shifting this value (say, to 10-1~) on the reaction-rate constants you obtained?
A. Williams. The value of 10-9 mole/cc of
58,q
I)ECOMP(),qITION AND EXPLOSION
ground-state OII concentrt/tion for the detection threshold is based on an exl)erimental comparison of OIt emission and absorption as described in the paper. Since the ()[l concentration changes so rapidly at the poi~/t of ignition, the rate constant derived is insensitive to errors here.
H. B. Palmer, Pennsylvania State University, University Park, Penna. The work on CH4 decomposition by Hirt and myself was, regrettably, limited to a total pressure condition of about 1 atm. Shock-tube studies available at the time seemed to indicate little if any dependence of the rate upon total pressure, so we reported an apparent first-order rate constant for the initial step that should be accurate at total pressures near 1 atm in systems not having very high CH4 concentration. The estimate by Higgin and Williams of the reduction in the effective firstorder rate constant at their somewhat lower pressures seems quite reasonable. I know of no published experiments providing firm information on the total pressure dependence; however, a welcome contribution on this matter apparently will be forthcoming from the group at Gottingen. I t should be mentioned that one still cannot state what the first step in CHt decomposition is, and at this stage in the history of chemical kinetics, that seems almost incredible. One difficulty is that the decomposition quickly becomes very complicated. We now know, for example, that one cannot expect to obtain information on the homogeneous reaction from conventional flow--or static-system experiments2 One must turn to methods, such as shock tubes, that avoid complications presented by nucleation. REFERENCE 1. PALMER, H. B., LAHAYE, J., AND HOt', K. C.: J. Phys. Chem. 72, 348 (1968).
A. Williams. As pointed out by Palmer, there is no reliable experimental data available on methane decomposition at low pressures. We therefore calculated the fall-off in rate on tile basis of the theoretically derived data of D. W. Placzek, B. S. Rabinovitch and G. Z. Whitten [J. Chem. Phys. 43, 4071 (1965)].
H. B. Palmer. In fitting our low-temperature CH4 decomposition data to shock-tube results, Hirt and I assumed that the reaction was close enough to the high-pressure limit that errors would be small. I t now seems possible that the facts that our experiments were at about 1-atm pressure and the shock-tube work was at about 5 atm may have led to a fortuitous cancellation
of errors. I have made crude estimates of the low (k0) and high (kc,) pressure rate constants over the range, 1250~176 on the assmnption that the high-pressure activation energy must be about 102-105 kcal. The results "trc k0 = 1017"aexp (--87.5 kcal/RT) cm3/mole see, k~o = 1015~exp (-- 104 kcal/RT) see-1. The latter is very close to our reported result. These rate constants seem rather reasonable but, of course, are not reliable. I t is nevertheless interesting that they indicate that k~ (1250~ 1.7k (exp, 1 atm) and k~ (1667~ ~---2k (exp, 5 atm). I t is also interesting that k~ is virtually identical to the expression reported by Kondratiev at the Tenth Symposium, based upon rapid compression studies at an effective pressure of about 20 arm.
D. J. Seery, United Aircraft Research Laboratories, East Hartford, Conn. Bowman and I have been carrying out experimental and analytical studies of methane oxidation for several years. Some of our results have already been reported. 1 In the experimental studies, the progress of the reaction behind reflected shock waves in hydrocarbon/oxygen/argon mixtures is followed using spectroscopic and pressure-measuring techniques. Our experimental studies of methane oxidation indicate that the reaction passes through two phases--a first (induction) phase characterized by a slow increase in pressure and OH emission, followed by a second (rapid-reaction) phase characterized by a rapid increase in pressure and OH emission and absorption. It is convenient to characterize the oxidation reaction by an induction time, ~'i, defined as the time between shock heating of the gas mixture and the onset of the rapid-reaction phase. This definition is to be preferred over one based on an initial increase in pressure or emission, since r~ then would depend upon the sensitivity of the measuring system. In our experiments, low-level OH emission is observed immediately behind the shock wave (Ref. l a ) . Our induction-time measurements, together with those of Skinner and Ruehrwein, 2 were correlated with initial 02 and CH4 concentration and temperature in Fig. 1, and the expression log40ri(O2)02(CH4)0 -~ was found to fit the experimental data best. This complex dependence of r upon initial O~ and CH4 concentration indicates that the kinetics of the induction period are complex and that no single reaction is rate
SI[OCK-IIEATED MIXTURES
5g,q
TEMPERATURE, T - ~ 10
-9
-
18OO I i 1
1600 ]
I
I
1400 I
,
'
I
(MOLE %)
10 -lO _
CH4
0 2
Ar
P
8.0
16.0
4.0
x
3.0
60.0
40.0
Lx 9 9
5.0 2.0 0.5 0.5 0.2
33.3 16.7 4.8 4.8 2.0
13.3 16.7 19.1 19.1 20.0
80.0 0 53.4 66.6 76.2 76.2 78.0
5 t 6 / 3.4 1.7 1.7 3.4 3.4
o
T
-j--
DATA F R O M REF 2
X X
CALCULATED
.,r
d
T ....
(ATM)
+
v
12OO
,
o
A
C~ x
10 -n _
0
"1U
v
o
% o
o~
10 -12 _
/ 10 -13
10 -14 0.50
J
I 0.60
J
I 0.70
,
I 0.80
10 3/T (~ Figure 1 controlling. In the analytical studies, temperature, pressure, and concentration profiles are calculated for a proposed reaction mechanism using a computer pl'ogranl that numerically integrates the system of reaction-kinetic and state equations. An appropriate mechanism for the reaction can be obtained from high-temperature flame studies. A detailed discussion of the technique as applied to the oxidation of methane is presented in Ref. la. As Higgin and Williams have noted, the lmo
major areas of uncertainty in such a mechanism are the initiation reactions and the methyl radical oxidation reaction~. The greater part of our analytical study was directed toward determining the appropriate reactions in these two areas. Two initiation reactions are generally suggested for methane oxidation: CH~--~ CH3 q- H, CIt~ q- 02---+ CII~ q- It02.
(la) (lb)
590
DECOMPOSITION AND EXPLOSION
In agreement with Higgin and Williams, our studies indicate that the appropriate initiation step for the bigh-temper-~ture regio~ (> 1500~ is Reaction (la). The initiation reactioll is important only in the initial portion of the induction period. Once the branching reactions become important, Reaction (la) can be neglected. The mechanism for the oxidation of CH3 to CO is somewhat uncertain, although it is generally felt that the oxidation proceeds via
and k4 = 5 -4- 5 X 1013 cm3/mole sec in the temperature range 1700%2000~ One uncertainty yet to be resolved is the fact that the calculated temperature dependence of T is larger than the experimental temperature dependence. Our studies indicate that this difference can probably be attributed to the initiation step.
CHa --~ 02--+ H2CO "~- OH,
(2a)
REFERENCES
CH3 --F O --+ H2CO --~ H,
(2b)
1. (a) SEERY, D. J, AND BOWMAN,C. T.: A Paper presented at the 154th National Meeting of the American Chemical Society (Division of Fuel Chemistry), Chicago, Ill., Sept. 1967; (b) BOWMAN, C. T. AND SEERY, D. J.: Combust. Flame (in press). 2. SKINNER, G. B. AND RUEHRWEIN, R. A. : J. Phys. Chem. 63, 1736 (1959).
H~CO + OH--~ HCO + H.~O,
(3)
HCO -~- OH--+ CO ~- H20.
(4)
Parametric studies of the rate constants for Reactions (2a)-(4) indicate that, during the induction period, Reaction (2b) can be neglected in comparison with (2a) if k2a/k2b > 10-5. Furthermore, if ks > 10k2a, then steps (2a) and (3) can be combined, C H 3 ~ 02--~ HCO-t- H20,
(2c)
with only a slight effect on the calculated induction times. The rates constants for Reactions (2c) and (4) that provided the best agreement between calculated and measured induction times were found to be k2c = 1 ! 3 X 1012em3/mole sec
A. Williams. It is very interesting to hear that similar conclusions have been reached by other workers concerning the basic features of methane ignition. However, certain differences arise in the over-all reaction scheme used for the reaction of methyl radicals and oxygen molecules. This seems to indicate that numerical integration techniques of this type can successfully indicate the major steps involved in ignition processes, but that it does not give a unique indication of the secondary reactions involved. The experimental induction-time measurements given in the paper can be correlated by means of the function log ['O230:rCH4~o--~ However, other functions of this form also can be used to satisfactorily correlate the results.
Department of Fuel Science, The University of Leeds, Leeds, England An investigation has been made of the ignition of shock-heated mixtm'es of methane and oxygen highly diluted with argon. The shocked-gas temperatures and pressures covered the ranges 1800~ to 2500~ and 200 to 300 Torr, respectively. The ignition delays were inversely proportional to the oxygen eoneentration and a plot of log~0(t,[O2]) against inverse temperature yielded an apparent activation energy of 32 keal mole t. The addition of trace amounts (,f n-butane greatly reduced the ignition-delay times. A theoretical model has been used to study lhe ignition mechanism which utilizes the numerical integration of the reaction-rate expressions, lleasonable agreement with experimental data can be achieved if the major initiation reaction is the first-order dissociation of methane. The only oxidation reaction of the methyl radical is its bimoleetdar reaction with oxygen and, to achieve reasonable agreement with experiment, this mu.,t be assigT~eda value of about 0.8 X 10TM ema mole-t see-l at 1875~
Introduction
Experimental
A considerable number of investigations, both experimental and theoretical, have been made of the combustion of hydrogen and carbon monoxide in shock-heated gases. In contrast to this, hydrocarbons have received much less attention because of their complexity although some publications have dealt with the simpler hydrocarbons, particularly methane?-8 The high-temperature ignition and combustion of methane is an especially interesting ease because there already is available considerable information about its oxidation mechanism at moderate temperatures and in flames?-~2 Despite this, little information is available concerning two areas important to ignition kinetics, namely, the initiation reactions and the oxidation reactions of the me/,hyl radical. The problem of n-butane eombustion is even more complex and few high-temperature combustion investigations have been attempted. However, it is well known that the higher normal alkanes are nmch more reactive and exhibit much smaller ignition delays than methane. In this paper, data is presented for ignitiondelay times (induction-period times) for mixtures of methane alone or in a mixture with n-butane. To aid the interpretation of the results, a theoretical ignition model has been used.
The shock tube and associated apparatus were of conventional design. The shock tube was 3.3 em i.d. The driver and low-pressure sections were 120 and 230 em long, respectively, wit.h a dump tank at the end of the driven section. The lowpressure section could be evacuated to ca. 10.4 Torr by an oil diffusion pump. The diaphragm material used was 0.001 to 0.003-in. thick Melinex (I.C.I. Ltd.) and the driver gas was helium. Shock-velocity measurements were made by means of five deposited platinum heat-transfer gauges ~a that operated transistor trigger amplifiers?4 The output of the amplifiers could be presented on an oscilloscope, together with tinting marks, or could operate a digital timer. At the central detector position, two sapphire windows masked to a l-ram slit width were mounted on opposite sides of the tube. For the emission experiments, a monochromator (Hilger and Watts D285) was used to observe the ultraviolet radiation of OH radicals at 3067 ~. due to the 2Z+--"lI transition, a band-pass of 3064 to 3070 .~ being allowed. The light intensity was measured by a photomultiplier and the signal was presented on a Tektronix 545B oscilloscope. For OH absorption measurements, a bismuth-discharge lamp excited by a 2450-MHz discharge in argon was used. Pressure measurements of the shocked
579
580
DECOMPOSITION AND EXPLOSION
eC
'
,
I00
~sec
time FIG. 1. Hydroxyl emission curves for: (a) 2% methane, S ~ oxygen, 90% argon, T2 = 1925~ (b) 1.53c/~methane, 0.22% n-butane, 8.23% oxygen, 90~ argon, T._~ = 1680~ (c) same mixture, T2 = 1780~ gases were made by means of a 610L Kistler transducer and a charge amplifier. It was assumed that the gas behind the shock wave was in complete thermodynamic equilibrium and that complete vibrational equilibration was attained. The shock front underwent a slight attenuation (2.0% to 3.5% per meter) and the mean temperature and pressure of the shocked gases during the induction period were calculated from the shock velocity and mixture enthalpies by means of an iteration procedure. The temperature error may be about + 4 0 ~ for the lower end and about ::L60~ near the upper end of the temperature range covered. 5Ieasurements of the pressure profiles behind the shock front are consistent with these estimates.
Experimental Results The induction times for the appearance of hydroxyl emission from a number of methaneoxygen mixtures diluted with 90 mole % argon have been studied in the range of conditions 1800~ T0_< 2500~ and 200_< P2_< 300 Torr. The form of a typical emission spectrum from such a shock heated methane-oxygen mixture is shown in Fig. l ( a ) . The emission signal did not occur until after a defnite induction time, but it then rose rapidly to a sharp maximum value (11) followed by an approximately exponential
decay to a level (I.,) of about 0.5 to 0.6 the nlaximum value for a period of 50-200 ~sec, it then fell to zero. The ignition-delay time was defined as the time for the emission intensity to rise to 0.05I, so as to eliminate errors due to light reflection. These emission-iuduction times proved to be a sensitive means of detecting the onset of reaction. Comparison with data obtained using hydroxyl absorption measurements showed that the detection threshold corresponded to a hydroxyl concentration of about 1 X 10-9 moles cm-3. The hydroxyl emission-induction times obtained in this way and corrected to gas times by multiplication with the density ratio are given in [Fig. 2 for equivalence ratios of 2 to 0.25. The equivalence ratio is the fuel-to-oxygenratio divided by the stoichiometricratio. The induction times were approximately inversely proportional to the oxygen concentration. The slopes of these plots correspondto an apparent activation energy of 30 4-3 kcal mole-k Most previous investigators have presented methane-oxygen ignition data in the form of a plot of log (&EO2~) as a function of inverse temperature. The present experimental data are plotted in this way in Fig. 3 together with the results obtained in other investigations. This parameter gives a reasonable correlation of the data, although a parameter of
the form log (t,.EO23mECI-h-]1-m), where m - - 0.8 to 0.9, is also consistent with the experimental data. The temperature dependence of the plot in F i g 3 corresponds to an apparent activation energy of 32 4- 4 kcal mole-L This is similar to
3.0
u 2.5
I
~"2oI
m
i
i
i
4
5
6
104/T
FIG. 2. Plot of log,0& against 1/7' for mixtures of 90% argon and 10% (methane 4- oxygen) with the following equivalence ratios: A 2, (D 1, 9 0.5, [] 0.25.
SHOCK-HEATED MIXTURES estimates given by Kistiakowsky and Richards 2 (E = 33 keal mole-1) and Soloukhin s (E = 33 kcal mole-l), although Asaba et al. a and Miyama and Takeyama 4 obtained values of 20.6 and 21.5 kcal mole-1, respectively. Glass et al. 7 used the parameter
581
9 ,a
2.5
/ ( D
i/1
-q
loglo (ro,_,-l'/2EAr]i/2&)
2.0
and found an apparent activation energy of 56 kcal for methane-oxygen results at 2000 ~ 2300~ If our results are plotted in this form, we find a poor correlation and a much lower apparent activation energy of 30 kcal mole-~. Measurements were made of the magnitude of the hydroxyl emission in the reaction zone (I1) and in the past combustion zone (I=). I t was observed that these did not vary much with temperature; in the case of a mixture with an equivalence ratio of 0.5, the temperature dependence for both quantities corresponded to an apparent activation energy of only 5 keal mole-~. Ignition of Mixtt~res of Methane and Oxygen with Added n-Butane The addition of small amounts of n-butane to methane-oxygen mixtures had a very marked effect on the ignition-delay times. In addition, hydroxyl emission also occurred in the pre-ignition region while the main combustion zone was
-8
o -9 E
0
/
1.5 9
i
4
5 104/T ~
6
FIG. 4. Plot of log,& against 1/T for the following mixtures: (a) 2% methane, 8Co oxygen, 90% argon; (b) 1.94/C7c.methane, 0.02c{ n-butane, 8.04.% oxygen, 90% argon; (c) 1.87% methane, 0.05c~ n-butane, 8.08% oxygen, 90(i~ argon; (d) 1.53~ methane, 0.22% n-butane, S.23% oxygen, 90% argon; (e) 0.715c n-butane, 9.29c'c oxygen, 90% argon. These nfixtures all have an equivalence ratio of 0.5.
characterized by a further, more-marked enfission as shown in Figs. l ( b ) and 1 (e). The ignition delay was defined as the time taken until this second emission occurred. The mixtures used had an equivalenee ratio of 0.5 and, for these, plots of log ti against reciprocal temperature produced straight lines with apparent activation energies of 28 to 32 kcal mole-1 as shown in Fig. 4. The addition of 1% n-butane reduced the ignition delay by a factor of 3, 5% n-butane reduced it hy a factor of 6, while 10% n-butane reduced it by a factor of 10.
TheoreticalModelof Methane-Oxygen Ignition
g'-,o
5
6
7
8
9
I0
I 04/T OK Fro. 3. PIo! of logl01,[Odagainst 1/T for methaneoxygen mixtures. 1, t~ef. 3; 2, Flef. 4; 3, Ref. 8; 4, 1Ref. 2; 5, this work.
A mathematical model has been used to provide information about the kinetics and mechanism leading to ignition. In this, a number of reactionrates expressions, together with the equations for conservation of mass, energy, and momentum, were numerically integrated by means of a digital computer. The differential equations used for reaction, rate, temperature, etc., were those given in Ref. 15. The thermoehemieal quantities required for each species were computed over the required range of temperature by means of a polynomial equation, the coefficients used being taken h'om
582
D E C O M P O S I T I O N A N D EXPLOSION TABLE I Reactions used in the theoretical model Rate expression (mole, em, see, units)
Reaction
(2) (4) (5) (7) (8) (9) (10)
(11) (12) (13) (14) (15) (16)
CH4 = CH~ + H CH~ -t- O_~ = CIt:O q- OH CH3 q- O = CH20 + H CH~O + Oil = tt_~O + II + CO CH4 + OH = It~O + CII3 H + O 2 = OH + O CH4 + O = CH~ + OH CH4 + H = CHa -t- H.~ CO + OH = CO~ + H O + H2 = OH + H OH -~- H.~ = H~O q- H OH + OH = H20 + O H + O t I + M = H20 q - M
Ref.
Varied, see Table II Varied, see Table II k5 = 1.9 X 1013 k7 = 3.12 X 1014 exp(-4240/RT) k8 = 7.24 X 10 ~3 exp(-5810/RT) k~ = 2.53 • 10" exp(-16790/RT) kl0 = 3.2 • 1013 exp(-7950/RT) kH = 4.14 • 1013exp(--11610/RT) ~'12 = 6.63 • 1011 exp(--1030/RT) kl3 = 1.27 N 1013 exp(--9400/RT) kl~ = 3.68 • 101~ exp(-5490/RT) ~5 = 8.6 N 10 ~ exp(-1000/RT) kl~ = 5.4 • 1015
Ref. 16. Other data was taken from the J A N A F TablesJ 7 The net rates of the chemical reactions were derived from the species concentrations and the forward and reverse rate constants, these latter quantities being calculated from the appropriate equilibrium constants. T h e reverse rates were not included for Reactions (2) and (7) but the error introduced is small. F o r the recombination reaction, the rate constant for argon was assumed for all third-body species. The species equations and five shock equations were integrated simultaneously with distance as the independent variable means of a R u n g a K u t t a - M e r s o n procedure.
Choice of Chemicals Reactions and Kineth's The system chosen for theoretical investigation was a lean m e t h a n e - o x y g e n mixture with an equivalence ratio of 0.5, diluted with 90% argon. The temperature of the unreacted shocked gas was 1875~ and the pressure 212.8 Torr. The experimental ignition delay time in this case was 467 #see. The number of reactions involved in the combustion of methane is quite considerable. Consequently, a very much simplified model has been used in this exploratory study to obtain information about the relative importance of various reaction steps. The chemical reaction scheme and the rate expressions used are given in Table I. The reaction scheme involved twelve species and was largely based on the scheme used by DeGroat and A b b o t t 18 for the supersonic combustion of methane, although a number of
12 25 25 25 25 25 25 25 25 25 26
modifications have been made to suit the particular circumstances considered here. These are of major importance and are discussed further now.
Initiation Reactions Three reactions are possible: CH4 -I- 02 -- CH3 -t- H02 AH1875~ ---- 55.4 kcal mole -1
(1)
CH4 = CH3 -t- H AHlsTa~ -= 105.7 kcal mole -1 O._,+ M = 2 0 .
(2)
-t- M
A/II875~ = 121.9 kcal mole~1.
(3)
Reaction (1) is the most important step in lowtemperature oxidation, but at higher temperatures, both Reactions (1) and (2) are involved as suggested by Skinner and R u e h w e i n ) Reaction (3) contributes significantly only at very much higher temperatures. Unfortunately, little data is available for kl, but the expression kl = 4 X 1011 X exp (--55,000/RT) cm 3 mole -1 see-1 has been theoretically derived by D e n i s o v J 9 The lmblished experimental data for the first-order
SHOCK-ItEATED MIXTURES decomposition of methane have been sunmmrized by the expression
553
Reactions of For,laid(hyde Formaldehyde may react with all the free radicals present, thus,
k,_ = 4 X 1014exp (-103,000/RT)sec -1 by Palmer and Hirt? ~ Thus, at temperatures above 1500 ~ to 1600~ the rate of Reaction (2) is much greater than that of Reaction (1) provided that the methane decomposition reaction is truly first-order. If this is so, under the experimental conditions used here, then there is no need to include the hydroperoxyl species in the reaction scheme.
Reactions of Methyl Radicals Methyl radicals may be oxidized by the reactions
tt q- CH..,O = RH -4- CHO, followed by many possible reaetion.~ of the formyl radical. To reduce the mm~ber of possible reactions, two simplifying a~sumptions have been made. First, the only radiual taking part in thi~ reaction was assulned to be hydroxyl. This is a reasonable approximation since hydroxyl concentrations are higher than H or O, al~d it is also the fastest reaction. Second, the formyl radicals produced by this exothermic reaction (AII~:~ h; = --43.68 kcal mole-a) were assumed to ,lecuml),,,e very rapidly. CHO= COq-H
E=
23kcalmole -l (Ref. 25).
CH~ q- O2 = CH20 q- OH AHlST~~ = --51.3_kcal mole-1
(4)
CH3 q- O = CHaO = CH20 q- H aHlsT~~ = -- 66.94 kcaI mole-I
(5)
Thus, the over-all reaction of formaldehyde and hydroxyl was approxitnated 1)\- the followit~ sequence '. OH-f- CH~O = H,O q- H if- CO.
(7)
CH3 -ff O.2 = c g a o -ff O
AIIls75~ = + 3 2 kcal mole-L
(6)
The bimolecular reaction between methyl radicals and oxygen molecules [Reaction (4)-] has been established at lower temperatures ~-~ and it may be reasonably assumed to be of importance in the present system. However, there is little kinetic data available for this reaction at the temperature of interest and there is considerable variation in the results reported at lower temperatures? -~The bimolecular reaction between methyl radicals and oxygen atoms has been suggested by Fenimore ~2 as the sole methyl oxidation reaction in certain methane-oxygen flames. This reaction has therefore been included in the scheme. Fenimore ~2 did not indicate the fate of the methoxyl radical but it has been assumed here to undergo unimoleeular dissociation to formaldehyde and hydrogen atom. The third reaction [-tleaction (6)~ will have a rather high activation energy ( E ~ 3 2 keal mole-1) and can only be of importance at much higher temperatures, 2a and was therefore not included in this scheme. Dimerization reactions of methyl radicals as well as other methyl association reactions occur extensively in the oxidation of methane-rich mixtures? Calculations showed that, under the conditions used here, these reactions are relatively unimportant in the pre-ignition period.
Results. Influence of Kinetic Parameters
Using the method and chemical reaction scheme outlined, it was possible to obtain a set of calculated profiles representing the build-up of free radicals and other intermediates in the pre-ignition period, together with information on temperature, pressure, ere. The more important results of a typical computation are shown in Fig. 5. The profiles obtained are very dependent upon the particular choice of rate expressions. Fortunately, a critical completion of data is available for some of the more important reactions, 2~ and this data was accepted as a starting point and attention was concentrated on the influence of the parameters k2 and k4. The kinetic data used is listed in Table I, while the variations in k., and ],'4 are given in Table II. In all the cases studied, the radical concentrations rose rapidly in a complex manner from initial zero value at zero time at the shock front to values of about 10-~~ to 10-I2 mole cm-a. Thereafter, the increase in concentrations of the species followed approximately an exponential form until their values were about 10-9 mole em-3. At this point, eonsumption of the reactants rapidly increased, resulting in a temperature rise, and this resulted in a further acceleration in the build-up of radical concentrations.
584
DECOMPOSITION AND EXPLOSION
-8
'E - I 0 0
s
u-12
2200
0
o
K
o~ 0
-14
2000
I00
200 time ~ s r
FIG. 5. Computed pre-ignition composition profiles and temperature plotted against time for Run 6. It was observed in all cases that the formaldehyde concentration was at a maximum at the point where the temperature and reactant consumption rapidly rose, and that thereafter it decreased. The hydroxyl concentration at this point was about 1 X 10-9 nmle cin-3 and since this is in accordance with the experimental criterion of ignition delay then the time at which this concentration was attained was taken as the ignition delay time. The values obtained in this way for various assumed values for k2 and k4 are given in Table II.
For Runs 1 to 4, the value given by Palmer and Hirt 2~ for k2 F = 4 X 1014exp (--103,000/RT) sec-13 was assumed and the ignition delay was computed for various values of k4, the object being to bring the computed ignition delay roughly in agreement with the experimental value of 467 ~sec. The ignition times so obtained are given in Table II. Second, a value of k4 = 1 X 10n cm3 mole-1 sec-~ at 1875~ was assumed, and the influence of variations in k2 was investigated (Runs 3, 5, and 6). Over the limited range studied, the
TABLE II Computed ignition-delay times for various kinetic assumptions Run No.
k.,.
1
4 X 1014exp(--lO3,0OO/RT) 4 X 1014exp(--lO3,0OO/RT) 4 X 1014exp(--lO3,0OO/RT) 4 X 10TM exp(--lO3,0OO/RT) 2 X 1014exp(-103,000/RT) 1 X 1014exp(-lO3,0OO/RT) 2 X 1014exp(-lO3,0OO/RT)
2
3 4 5 6 7 8
1 . 3 X 10 ~4 exp(-lO3,0OO/RT)
kd1875~ 4 2 1 1 1
>< 1011 X 101' X 1011 X 10TM X 1011 1 X 1011 1 >< 101~ 8 X 109
Calc. ti(~sec) 72 106 131 261 170 231 350 460
Experimental value 467
SHOCK-ItEATED MIX~I UtlES ignition delay followed the apl)roximate relationship ti c~ --ln ~. It is significant to note that the effect of doubling k~ is virtually the same as that of doubling h4. Finally, in Runs 4 and 7, k4 was fixed at i X 10 ~~enr~ mole-~ see-~, and values of/~2 were tried to obtain reasonable agreement with the experimental ignition delay time. In order to assess the relative contributions of the two methyl radical oxidation reactions [ ( 4 ) and (5)], the value of ka was reduced by a factor of 103 in one run. This made only a small difference to the computed profiles and the ignition delay was only 5% different to the run that ineluded k5 at the value given in Table I. It was concluded that Reaction (5) played only a minor role but, nevertheless, it was included in all the computations reported here. A number of runs were made to test the sensitivity of the calculated ignition-delay times to errors in the assumed reaction-rate parameters for some of the more important reactions. The effect of halving kt~, the rate constant of the reaction H -t- 0~ = OH ~- O, was to increase the ignition-delay time by 11%. The effect of halving ks, the rate constant of the (major) methane consumption reaction with hydrox)q, was to decrease the ignition delay by 9%. This effect presumably results from the replacement of a reactive hydroxyl radical by a less-reactive methyl radical. Halving kLo, the rate constant for the sole carbon monoxide oxidation reaction, did not change the ignition-delay time.
Discussion The only detailed analyses of the ignition mechanism in shock-heated lean methane-oxygen mixtures are by Asaba et al. 3 and an extension of this work by Miyama and Takeyama. 4 In the latter analysis, it was assumed that, during the induction period, species such as OH, CH._,O, etc., are quasi-steady-state intermediates and that the principal chain carrier is the CH~ radical. They included Reaction (4) in their mechanism, but not Reaction (9). The)- deduced that both hydroxyl and methyl concentrations rose exponentially and were able to derive the relationship /c4[Oe]t~ = eonst. That is, a plot of log ( t f 0 2 ] ) against l I T should be a straight line, with its slope giving the value of E4. Experimentally, they obtained values of 20.6 (Ref. 3) and 21.5 kcal mole-1 (Ref. 4). However, from the computed concentration profiles in all the eases studied here, it was clear that the quasi-steady-state assumption does not strictly hold. Furthernmre, Bradley 27 has obtained analytical expressions for the ignition-delay time for various types of chain-branching reactions. He was able to show
585
that, in the case of a simple direct chain-branching reaction, a relationship of the type t~ cc {/q[-O.,]}-~ would apply. Obviously, in the methane-oxygen system, a much more complex state of affairs exists and a simple expression of this type cammt hold. However, experimentally, the relationship log ti[-O._,]against 1/T does appear to hold, but it must be concluded that its temperature dependence (E = 32 kcal mole-1 in this work) does not correspond to any single reaction step and that this equation does not indicate the role of oxygen or methane in the induction-period reactions. Indeed, the present results suggest that the activation energy of the initiation reaction plays an important part in determining temperature dependence of the ignition delay as well as its absolute magnitude. The use of the present mathematical model seems to be a promising method of investigating the interrelation of the various reaction steps. At present, detailed discussion is premature, but the following points can be made. The Initiation Reaction
In previous work on methane-oxygen ignition it was generally assumed that initiation occurs via the bimolecular reaction of methane with oxygen. However, in the particular experimental conditions used here, the computed data was consistent with the experimental ignitiondelay time if the initiation reaction were largely the simple first-order dissociation of methane. This raises a problem concerning the collisionat activation of the methane molecule, but this has been discussed by Kondratiev, 28 who pointed out that the rate constant for the second-order decomposition CH4+Ar=
CHs+H+Ar
is given by k2' = 1021exp ( - - E / R T ) em 3 mole-1 sec-1 with an accuracy to within a power of 10. Consequently, at reasonably high pressures, the thermal dissociation of methane obeys a strict first-order law. At the lower experimentM pressures considered here, and using the argument advanced by Kondratiev, ~ it still seems probable that first-order dissociation of methane does occur. However, the conditions must be near that of the second-order fall-off region and a small fall-off in rate must occur. Furthermore, it must be stressed that, at very low pressures or at high oxygen concentrations, or in very lean mixtures, the bimolecular reaction of methane with oxygen can be an important competitor with the methane-dissociation reaction. In fact, preliminary runs in which the oxygen concentration has been
586
DECOMPOSITION AND EXPLOSION
12 "iu oll
E ~E
~10 O
o
t
9
V
\
J
A
2&r
3
Fro. 6. Arrhenius plot for Ct{a + O2. Q This work; 9 Ref. 29; A Ref. 30; [] Ref. 31; 9 Ref. 32; I Ref. 33; 9 Ref. 34; V Ref. 35; - - - Ref. 36. greatly increased indicate that the experimental dependence of log ti[02] against inverse temperature can only be reproduced if the bimolecular reaction of methane and oxygen [Reaction (1)] is included in the reaction scheme.
The Reactions of Methyl Radicals and Oxygen Molecules If the first-order decomposition of methane is the predominant initiation step, then, from the published data on the rate of this reaction, it is possible to estimate k4. This value is dependent upon the accuracy of the e:~erimentally determined ignition delay, on the accuracy to which k2 is known, on the validity of the chemical model and on the total resultant effect of the errors in the other rate expressions used. If the value given by Pahner and Hirt 2~ for k2 ~4 X l0 '4 X exp (--103,000/RT) sec-~] is accepted, then the value of k4 required to give agreement between comlmted and experimental ignition delays is estimated to be about 1 X 109 cm a mole- t sec-1 at 1875~ However, Pahner and Hirt 2~ obtained their value for ke by combining their experimental data with previously reported shock-tube work on methane pyrolysis--this latter data being interpreted on the basis of first-order kinetics and on the assumption of a chain length of 2. This probably suggests that the over-all rate expression given by them is an upl)er limit and, indeed, their own experimental results were expressed in the form k2 = 1.26 X 10 t4 exp (-- 101,000/RT) see-l; this expression is equivalent at 1875~ to k._,= 2 X 10~4exp (--103,000/RT) sec-k The mean
estimate of/~4is thus obtained using the expression k4 = 4 X 10+14 exp (--103,000/RT) combined with an estimated pressure fall-off factor of 3; this leads to a value of about 109"9~-1cm a mole- l sec-1 at 1875~ The value obtained for k4 provides a method of checking the validity of the theoretical model and the accuracy of the other data used, since it should be in reasonable agreement with the published estimates of/ca. McMillan and Calvert -~2 have summarized the data available up to 1965 (Refs. 29 to 34) and these are plotted in Fig. 6 together with the present value. More recently, Baldwin et alY have tentatively suggested the value of 5.8 X 10-s cm a mole-1 sec-1 at 500~ while Barnard and Cohen a6 have been able to explain their methyl oxidation results at 400~ on the basis that k4 = 2 X 10t2exp (--25,000/RT) cm a mole-~ s e c t. These latter estimates are significantly smaller than the earlier values of k4. However, despite the wide variations in the published data, the present value seems to be in reasonable agreement with previous estimates of k4, although obviously much further work is required in this direction.
The Effect of Added n-Butane to Methane-Oxygen Ignition The reduction in ignition delay can be interpreted in terms of the ease of dissociation of n-butane by C - - C bond fission compared with the initiation reactions of methane that involve breaking a C - - H bond. n-Butane decomposes unimolecularly, thus, n-C4Hm = C..,H5q- C2H~, = CHa q- CaHv,
(17) (18)
followed by CaH7 -- C',H4 q- CHa,
etc.
There is some uncertainty concerning rate expressions, but a recent value a~ for Reaction (18) of k18 = 10*agexp (--69,500/RT) will be used here to illustrate the more rapid initiation rate. The ratio of the rates of radical production in a mixture of methane -k 1% n-butane/oxygen mixture to the equivalent methane/oxygen mixture is given by
{/~_['CH4] --[- k,s[-n-C4H,o-] }/k:~.ECH,-]. At 1875~ this ratio is about 20 and if the relationship ti o: --ln(rate of initiation) holds good, then the ratio of ignition delays should be about 4. This is of course quite approximate,
SHOCK-ItEATED MIXTURES since it does not take into account the relative reaction efficiencies of the different radicals, but nevertheless it is in agreement with the experimental ratio of 3.
16. 17.
ACKNOWLEDGMENTS
18.
The authors thank Mrs. V. I. Higgin for assistance with the computer programming and D. J. Battyre, T. Boddington, and G. Dixon-Lewis for useful discussions. One of us (R.M.R.H.) is grateful to S.R.C. for the award of a Research Studentship.
19. 20.
REFERENCES
22.
1. SXIXNER, G+ B. AND RUEHRWEIN, 1)~. A.: J. Phys. Chem. 63, 1736 (1959). 2. KISTIAKOWSKY, G. B. AND I~ICHARDS, L. W.: J. Chem. Phys. 36, 1707 (1962). 3. ASABA, T., YONEDA, K., KAKIHARA, K., AND HIKITA, T.: Ninth Symposi~ml (Intevm+tional) on Combustion, p. 193, Academic Press, 1963. 4. Ms H. AND TAKE'I'AMA, T.: J. Chem. Phys. 38, 37 (1965). 5. ~*OEVODSKY, V. AND SOLOUKHIN, R. I.: Dokl. Akad. Nauk SSSR 161, 1118 (1965). 6. DovE, J. E. AND ~IouLTON, ]). McL.: Proc. Roy. Soc. A283, 216 (1965). 7. GLASS, G. P., KISTIAKOWSKY,G. B., MICHAEL, J. V., A~'I) NIKI, H.: Tenth Symposium (International) on Combustion, p. 513, The Combustion Institute, 1965. 8. SOLOUKHIN, R. I.: Eleventh Symposium (International) on Combustion, p. 671, The Combustion Institute, 1967. 9. ENIKOLOPYAN,N. S.: Seventh Symposium (International) on Combustion, p. 157, Butterworth, 1959. 10. ~INKOFF, G. J. AND TIPPER, C. F. It.: Chemistry of Combustion Reactions, p. 151, Butterworths, 1962. 11. FRISTROM, R. M. AND WESTENBERG, A. A.: Flame Structure, McGraw-IIill, 1965. 12. FENIMORE, C+ P.: Chemistry of Premixed Flames, p. 43, Pergamon, 1964. 13. GAYDON, A. G. AND HURLE, I. R.: The Shock Tube in High Temperature Chemical Physics, Chapman and Ilall, 1968. 14. SmLLIN6, M. J.: N.P.L. Aero Note 1050, October 1966. 15. SOTTER, J. G.: Tenth Symposium (International)
23.
21.
24. 25. 26.
27. 28.
29. 30. 31. 32. 33. 34.
35.
36. 37.
587
on Combustion, p. 1405, The Combustion Institute, 1965. WILL~A.~IS,M.: NAVWEPS l~eport 7609, 1961. J A N A F Thermoehemical Tables, Dow Chemical Company. DEGROAT, J. J. AXD ABBOTT, M. J.: AIAA J. 3, 381 (1965). DENISOV, E. T.: Russ. J. Phys. Chem. 38, 2 (1964). PALMER, H. B. AND I]IRT, T. J.: J. Phys. Chem. 67, 709 (1963). HOARE, D. E. ~,XD PEACOCK, G. B.: Proc. Roy. Soe. A201, 85 (1966). MCMILLAN G. R. AND CALVERT, J. G.: Oxidation Combust. Rev. 1, 102 (1965). FABIAN, D. J. AND BRYCE, W. A.: Seventh Symposi+lm (International) on Comb~Lslion, p. 150, Butterworths, 1959. GRIFFITHS, J. F. AXD SKIRROW, G.: Oxidati(m Combust. Rev. 3, 57 (1968). SCHOFIEH), K.: Planet. Space Sci. 15, 6+I3 (1967). GETZINGER, R. W.: Eleventh Symposium (Irdernational) on Comb~slio~b p. 117, The Combustion Institute, 1967. BRADLEY, Z. N.: Trans. Faraday Soc. 63, 2945 (1967). KONDRIATIEV, V. N.: Tenth Symposbot~ (Ddernational) on Combustion, p. 319, The Combustion It,stitute, 1965. CHRISTIE, M. J.: Proe. Roy. Soc+ A2.}4, 411 (1958). HEICKLEN, J. AND JOHNSTON, H. S.: J. Anl. Chem. Soc. 83, 4030 (1962). WENGER, F. AND KUTSCHKE, K. O.: Can. J. Chem. 37, 1546 (1959). SLEEPY, W. C. AND CALVERT, J. G.: J. Am. Chem. Soc. 8l, 769 (1959). INGOLD, K. V..aND BRYCE, \V. A.: J. Chem. Phys. 24, 360 (1956). AVRAMENKO, K. I. AND PONTNIKOV, L. ~1.: Izv. Akad. Nauk SSSll, Otd. Khim. Nattk 1960, 1921. BALDWIN, R. R., N(mms, A. C., AND WALKI'~R, R. W.: Eleve~lh Symposium (International) on Combustion, p. 889, The Combustion Institute, 1967. BAR~ARD,J. A. AND COHEN, A.: Trans. Faraday Soc. 64, 396 (1968). ItALSTEAD, M. P. AND QVIN, C. P.: Trans. Faraday Soc. 64, 103 (1968).
COMMENTS T. Takeyama, T o k y o R a y o n Co., Ltd., Kamakura, Japan. I imagine that you have simply assigned a value of 10-9 mole/cc of the groundstate OH concentration to the detection threshold of O H emission.
Did you check the effect of shifting this value (say, to 10-1~) on the reaction-rate constants you obtained?
A. Williams. The value of 10-9 mole/cc of
58,q
I)ECOMP(),qITION AND EXPLOSION
ground-state OII concentrt/tion for the detection threshold is based on an exl)erimental comparison of OIt emission and absorption as described in the paper. Since the ()[l concentration changes so rapidly at the poi~/t of ignition, the rate constant derived is insensitive to errors here.
H. B. Palmer, Pennsylvania State University, University Park, Penna. The work on CH4 decomposition by Hirt and myself was, regrettably, limited to a total pressure condition of about 1 atm. Shock-tube studies available at the time seemed to indicate little if any dependence of the rate upon total pressure, so we reported an apparent first-order rate constant for the initial step that should be accurate at total pressures near 1 atm in systems not having very high CH4 concentration. The estimate by Higgin and Williams of the reduction in the effective firstorder rate constant at their somewhat lower pressures seems quite reasonable. I know of no published experiments providing firm information on the total pressure dependence; however, a welcome contribution on this matter apparently will be forthcoming from the group at Gottingen. I t should be mentioned that one still cannot state what the first step in CHt decomposition is, and at this stage in the history of chemical kinetics, that seems almost incredible. One difficulty is that the decomposition quickly becomes very complicated. We now know, for example, that one cannot expect to obtain information on the homogeneous reaction from conventional flow--or static-system experiments2 One must turn to methods, such as shock tubes, that avoid complications presented by nucleation. REFERENCE 1. PALMER, H. B., LAHAYE, J., AND HOt', K. C.: J. Phys. Chem. 72, 348 (1968).
A. Williams. As pointed out by Palmer, there is no reliable experimental data available on methane decomposition at low pressures. We therefore calculated the fall-off in rate on tile basis of the theoretically derived data of D. W. Placzek, B. S. Rabinovitch and G. Z. Whitten [J. Chem. Phys. 43, 4071 (1965)].
H. B. Palmer. In fitting our low-temperature CH4 decomposition data to shock-tube results, Hirt and I assumed that the reaction was close enough to the high-pressure limit that errors would be small. I t now seems possible that the facts that our experiments were at about 1-atm pressure and the shock-tube work was at about 5 atm may have led to a fortuitous cancellation
of errors. I have made crude estimates of the low (k0) and high (kc,) pressure rate constants over the range, 1250~176 on the assmnption that the high-pressure activation energy must be about 102-105 kcal. The results "trc k0 = 1017"aexp (--87.5 kcal/RT) cm3/mole see, k~o = 1015~exp (-- 104 kcal/RT) see-1. The latter is very close to our reported result. These rate constants seem rather reasonable but, of course, are not reliable. I t is nevertheless interesting that they indicate that k~ (1250~ 1.7k (exp, 1 atm) and k~ (1667~ ~---2k (exp, 5 atm). I t is also interesting that k~ is virtually identical to the expression reported by Kondratiev at the Tenth Symposium, based upon rapid compression studies at an effective pressure of about 20 arm.
D. J. Seery, United Aircraft Research Laboratories, East Hartford, Conn. Bowman and I have been carrying out experimental and analytical studies of methane oxidation for several years. Some of our results have already been reported. 1 In the experimental studies, the progress of the reaction behind reflected shock waves in hydrocarbon/oxygen/argon mixtures is followed using spectroscopic and pressure-measuring techniques. Our experimental studies of methane oxidation indicate that the reaction passes through two phases--a first (induction) phase characterized by a slow increase in pressure and OH emission, followed by a second (rapid-reaction) phase characterized by a rapid increase in pressure and OH emission and absorption. It is convenient to characterize the oxidation reaction by an induction time, ~'i, defined as the time between shock heating of the gas mixture and the onset of the rapid-reaction phase. This definition is to be preferred over one based on an initial increase in pressure or emission, since r~ then would depend upon the sensitivity of the measuring system. In our experiments, low-level OH emission is observed immediately behind the shock wave (Ref. l a ) . Our induction-time measurements, together with those of Skinner and Ruehrwein, 2 were correlated with initial 02 and CH4 concentration and temperature in Fig. 1, and the expression log40ri(O2)02(CH4)0 -~ was found to fit the experimental data best. This complex dependence of r upon initial O~ and CH4 concentration indicates that the kinetics of the induction period are complex and that no single reaction is rate
SI[OCK-IIEATED MIXTURES
5g,q
TEMPERATURE, T - ~ 10
-9
-
18OO I i 1
1600 ]
I
I
1400 I
,
'
I
(MOLE %)
10 -lO _
CH4
0 2
Ar
P
8.0
16.0
4.0
x
3.0
60.0
40.0
Lx 9 9
5.0 2.0 0.5 0.5 0.2
33.3 16.7 4.8 4.8 2.0
13.3 16.7 19.1 19.1 20.0
80.0 0 53.4 66.6 76.2 76.2 78.0
5 t 6 / 3.4 1.7 1.7 3.4 3.4
o
T
-j--
DATA F R O M REF 2
X X
CALCULATED
.,r
d
T ....
(ATM)
+
v
12OO
,
o
A
C~ x
10 -n _
0
"1U
v
o
% o
o~
10 -12 _
/ 10 -13
10 -14 0.50
J
I 0.60
J
I 0.70
,
I 0.80
10 3/T (~ Figure 1 controlling. In the analytical studies, temperature, pressure, and concentration profiles are calculated for a proposed reaction mechanism using a computer pl'ogranl that numerically integrates the system of reaction-kinetic and state equations. An appropriate mechanism for the reaction can be obtained from high-temperature flame studies. A detailed discussion of the technique as applied to the oxidation of methane is presented in Ref. la. As Higgin and Williams have noted, the lmo
major areas of uncertainty in such a mechanism are the initiation reactions and the methyl radical oxidation reaction~. The greater part of our analytical study was directed toward determining the appropriate reactions in these two areas. Two initiation reactions are generally suggested for methane oxidation: CH~--~ CH3 q- H, CIt~ q- 02---+ CII~ q- It02.
(la) (lb)
590
DECOMPOSITION AND EXPLOSION
In agreement with Higgin and Williams, our studies indicate that the appropriate initiation step for the bigh-temper-~ture regio~ (> 1500~ is Reaction (la). The initiation reactioll is important only in the initial portion of the induction period. Once the branching reactions become important, Reaction (la) can be neglected. The mechanism for the oxidation of CH3 to CO is somewhat uncertain, although it is generally felt that the oxidation proceeds via
and k4 = 5 -4- 5 X 1013 cm3/mole sec in the temperature range 1700%2000~ One uncertainty yet to be resolved is the fact that the calculated temperature dependence of T is larger than the experimental temperature dependence. Our studies indicate that this difference can probably be attributed to the initiation step.
CHa --~ 02--+ H2CO "~- OH,
(2a)
REFERENCES
CH3 --F O --+ H2CO --~ H,
(2b)
1. (a) SEERY, D. J, AND BOWMAN,C. T.: A Paper presented at the 154th National Meeting of the American Chemical Society (Division of Fuel Chemistry), Chicago, Ill., Sept. 1967; (b) BOWMAN, C. T. AND SEERY, D. J.: Combust. Flame (in press). 2. SKINNER, G. B. AND RUEHRWEIN, R. A. : J. Phys. Chem. 63, 1736 (1959).
H~CO + OH--~ HCO + H.~O,
(3)
HCO -~- OH--+ CO ~- H20.
(4)
Parametric studies of the rate constants for Reactions (2a)-(4) indicate that, during the induction period, Reaction (2b) can be neglected in comparison with (2a) if k2a/k2b > 10-5. Furthermore, if ks > 10k2a, then steps (2a) and (3) can be combined, C H 3 ~ 02--~ HCO-t- H20,
(2c)
with only a slight effect on the calculated induction times. The rates constants for Reactions (2c) and (4) that provided the best agreement between calculated and measured induction times were found to be k2c = 1 ! 3 X 1012em3/mole sec
A. Williams. It is very interesting to hear that similar conclusions have been reached by other workers concerning the basic features of methane ignition. However, certain differences arise in the over-all reaction scheme used for the reaction of methyl radicals and oxygen molecules. This seems to indicate that numerical integration techniques of this type can successfully indicate the major steps involved in ignition processes, but that it does not give a unique indication of the secondary reactions involved. The experimental induction-time measurements given in the paper can be correlated by means of the function log ['O230:rCH4~o--~ However, other functions of this form also can be used to satisfactorily correlate the results.