Westbrook et al.
zone is due significantly to the mobility of hydrogen atoms. Free radical (H, 0, OH) concentrations are about an order of magnitude above local equilibrium values in the reaction zone. Because of diffusion, superequilibrium is even more pronounced in the lean and rich wings. Partial equilibrium is found to be an excellent approximation for H, 0, and OH in the reaction zone; it breaks down, however, in the wings, where reaction is essentially frozen. Because of the large 0 and OH concentrations in the flame, a mechanism involving H02 as an intermediate is found to be the dominant one by which oxygen is chemically transformed in the flame.
References and Notes
(13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27)
(1) S.P. Burke aml T. E. W. Schumann, Id. Eng. Chsm., 29?998 (1928). (2) J. A. Fay, J . Aero. Sci., 21, 681 (1954).
(28)
(3) H. C. Hottel and W. R. Hawthorne, Symp. Combust. Flame Explos. Phenom., 3rd, 254 (1949). (4) A. Goldburg and S. I.Cheng, Combust. Flame, 9, 259 (1965). (5) R. E. Mitchell, Sc.D Thesis, MIT, 1975. (6) P. A. Libby and C. Economos, Int. J . Heat Mass Transfer, 6, 113 (1963). (7) R. B. Edelman et al, Symp. (Int.) Combust. [Proc.], Uth, 399 (1973). (8) F. A. Williams, Ann. Rev. Fluid Mech., 3, 171 (1971). (9) J. F. Clarke, Proc. R. Soc., Ser. A , 307, 283 (1968). (10) T. M. Liu and P. A. Libby, Combust. Sci. Techno/., 2, 131 (1970). (11) N. Peters, Int. J. Heat Mass Transfer, 19, 385 (1976). (12) R. J. Kee and J. A. Miller, AIAA Paper No. 77-639, AIAA Third Computational Fluid Dynamics Conference, Albuquerque, N. Mex.,
(29) (30) (3 1) (32)
(33) (34) (35)
June 27-28, 1977 (AIAA J., in press). R. A. Svehla, NASA Technical Report R-132 (1962). J. H. Pohl, Masters Thesis, MIT, 1973. S . Gordon and B. J. McBride, NASA SP-273 (1971). C. J. Jachimowski and W. M. Houghton, Combust. Flame, 17, 25 (1971). W. C. Gardiner, Jr., et al., Symp. (Int.) Combust. [Proc.], 74th, 61 (1973). G. L. Schott, Combust. Flame, 21, 357 (1973). D. L. Baulch, D. D. Drysdale, and D. G. Horne, Symp. (Int.) Combust. [Proc.], 7 4 7 , 107 (1973). D. Gutman et al., J . Chem. Phys., 47, 4400 (1967). N. J. Friswell and M. M. Sutton, Chem. Phys. Lett., 15, 108 (1972). M. J. Day, K. Thompson, and G. Dixon-Lewis, Symp. (Int.) Combust., [Proc.], W h , 47 (1973). G. Dixon-Lewis, J. B. Greenburg, and F. A. Goldsworthy, Symp. (Int.) Combust. [Proc.], 15th, 717 (1975). W. T. Rawlins and W. C. Gardiner, Jr., J . Chem. Phys., 60, 4676 (1974). A. L. Myerson and W. S.Watt, J . Chem. Phys., 49, 475 (1968). W. S. Watt and A. L. Myerson, J . Chem. Phys., 51, 1638 (1969). J. B. Homer and I. R. Hurle, Proc. R. Sac. London, Ser. A , 314, 585 (1970). D.L. Baulch et al., Department of Physical Chemistry, Leeds, Engbnd, Reports No. 3 and 4 (1969). I. M. Campbell and B. A. Thrush, Trans. Faraday Soc., 64, 1265 (1968). E. Krause, New York University Report NYU-AA-66-57, June 1966. N. N. Yanenko, "The Method of Fractional Steps", Springer-Verlag, New York, N.Y., 1971. A. C. Hindmarsh, "Linear Multistep Methods for Ordinary Differential Equations: Method Formulations, Stability, and the Methods of Nordsieck and Gear", Lawrence Livermore Laboratory, UCRL-51186, Mar 20, 1972. G. Dixon-Lewis, Proc. R . Soc., Ser. A , 317, 235-263 (1970). R. E. Mitchell, L. A. Clomburg, and A. F. Sarofim, Combust. Flame, to be submitted. Reaction numbers refer to Table I.
A Numerical Model of Chemical Kinetics of Combustion in a Turbulent Flow Reactort C. K. Westbrook," J. Creighton, C. Lund, Lawrence Livermore Laboratory, University of California, Livermore, California 94550
and F. L. Dryer Guggenheim Laboratories, Princeton University, Princeton, New Jersey 08540 (Received May 5, 1977) Publication costs assisted by Lawrence Livermore Laboratory
Calculations with a numerical model incorporatingdetailed chemical kinetics,hydrodynamic motion, and energy transport in a turbulent flow reactor have been compared with experimental results of Dryer and Glassman. A reaction mechanism, including 19 chemical species and 56 reactions, for the reaction of dilute moist carbon monoxide in air and of dilute methane in air was established for the temperature range 1000-1350 K. €402 and HzOzwere found to be important in the mechanism for both carbon monoxide and methane oxidation, and CH20,CH30, C2Hs,and C2H4were found to be important in methane oxidation. Important steps in the reaction mechanisms have been identified, and optimal values for some key reaction rates have been determined. The branching ratio between reaction 3, H + O2 = OH i- 0, and reaction 17, H + O2 + M = HOz + M, was found to be important in determining the length of the induction period in each experiment. At 1100 K the value determined for hI7was 2.6 X 1015 cm6/(mo125). Decomposition reaction 7 for HCO, HCO + M = H + CO M, was found to play a key role in methane oxidation, providing the major path for production of carbon monoxide. At 1100K, k7 was found to be 2.4 x 1O1O cm3/(mols). Even though the reaction studied was extremely oxygen rich, recombination of methyl radicals and subsequent oxidation of the ethane thus formed was found to provide a major route for methyl radical destruction. The assumption that plug flow conditions prevail in the turbulent flow reactor was examined and found to be valid under most practical conditions.
+
Introduction In systems such " engines and gas turbines, it has been recognized that quench regions may extend to temperatures Of 'This work was performed under the auspices ofthe u.s.Energy Research and Development Administration, Contract No. W-7405Eng-48. The Journal of Physical Chemistry, Voi. 8 1, No. 25, 1977
K and are responsible for major emissions of unburned and partially oxidated fuel. Furthermore, it has been noted that several key elementary oxidation reactions appear to exhibit significant non-Arrhenius behavior at the>se temperatures. Thus, for both practical and theoretical reasons, the determination of reaction mechanisms and elementary rates in the intermediate temperature range is receiving new interest.
A Numerical Model of a Turbulent Flow Reactor
TABLE I Flow reactor inlet conditions Model 1 Temperature, K 1 0 2 8 Velocity, cm/s 1 1 3 3 Pressure, atm 1 0 2 ,
%
H,,5%
co, % co,, % CH,, %
20.51 2.48 1.233 0.135
Model 2 1097 672
1 24.01 0.0037 0.0376 0.5078
2543
Model 3 1142 1298
1 20.08 0.0145 0.0023 0.0807 0.8041
The turbulent flow reactor technique developed at Princeton University2 has been one of the more frequently employed experimental methods for obtaining such data. Several publi~ationsl*~-~ have appeared in which flow reactor results have been used to conceptually determine kinetic mechanisms and overall or global rate expressions for oxidation and pyrolysis reactions. The use of steady state assumptions6t7has also led to computation of elementary reaction data. However, it has never been attempted to justify either the mechanism chosen nor the validity of the steady state assumption other than by qualitative arguments. A numerical approach would appear to offer a more appropriate means of substantiating such arguments as well as a method of increasing the yield of important reaction data from turbulent flow reactor experiments. In fact, the turbulent flow reactor concept itself has a number of interesting features which make it an attractive and relevant subject for numerical modeling purposes.
Experimental Section The experimental system consists of a cylindrical quartz duct with a conical quartz inlet section. The main duct is 1m long and has a diameter of 10 cm. A hot inert carrier gas (nitrogen) flowing at 9.0-15.0 m / s enters the reactor through a heated cylindrical inlet section in which uniform turbulence is established and in which oxygen and water vapor may be added. The Reynolds number of the flow is of the order of lo5. At the 2.5-cm diameter position in the conical inlet, a gasified fuel enters normal to the flow through four diametrically opposed 1-mm jets. Rapid mixing of the fuel with the seeded carrier flow results from the turbulence, and by properly adjusting the reactant and carrier flow rates as well as the carrier inlet temperature, a zone of chemical reaction can be produced which extends over the entire length of the reactor. The reactor itself is enclosed in a resistance heated, large thermal inertia oven so that the reactor wall temperature can be matched to the initial inert carrier gas temperature. Thus, the reaction zone can be treated as nearly adiabatic. Reacting samples are withdrawn at up to 20 locations along the center line of the reactor using a gas quenched water-cooled probe extended axially from the reactor exit. Temperature is simultaneously measured a t the sampling location by a quartz-coated platinum-platinum-rhodium thermocouple. Quenched samples are later analyzed using temperature programmed gas chromatography. Further details of the experimental technique are described elsewhere.2 However, the turbulent flow reactor itself was constructed to approximate the following assumptions: (1) steady reaction zone (2) negligible longitudinal diffusion of mass or energy (3) negligible radial diffusion of mass (4) adiabatic wall (5) constant pressure, ideal gas system (6) no effect of turbulence on chemical kinetic mean quantities The effort described here is a first approach to the problem
with the intent of validating several ofthe above experimental assumptions. The paper describes a numerical examination of experiments on carbon monoxide and methane oxidation reported earlier by Dryer2and by Dryer and Glassman.’ Detailed kinetic mechanisms for these reactions were developed and in themselves point to several new and interesting features with regard to these reactions in the temperature range 1100-1400 K. Initial conditions from the three sets of experimental data are summarized in Table I.
Modeling Techniques
T w separate ~ modeling procedures were used in the current study. However, both assume that (1)conditions are essentidly one-dimensional and steady; (2) turbulent mixing is sufficiently rapid that all conditions are radially uniform over a cross section at any axial location; (3) well-defined average parameters exist at every point in the reaction zone; (4)the effects of turbulent fluctuations on chemical kinetic reaction rates are negligible. Dryer2used cylindrical reaction ducts with different diameters and found no change in the experimentally determined concentration profiles, indicating that wall effects were unimportant and that radial concentration and temperature variations were small. As a result, wall effects and radial diffusion of chemical species were neglected in the numerical modeling. For a small number of initial calculations, a one-dimensional, time-dependent formulation of the coupled chemical kinetic and hydrodynamic equations was used to validate the plug flow and steady state assumptions. Details of this model are described elsewhere.8 On the basis of the results of this work, subsequent calculations were performed using a zero-dimensional chemical kinetic thermodynamic model. In each approach, the equations for the time evolution of each chemical species and the local temperature are written as a set of coupled differential equations. In the one-dimensional model, the method of lines is used to convert the coupled partial differential equations to a system of ordinary differential equations. For each chemical species i, the time rate of change in the concentration ci is written dci/dt = P i ( ~ j-) Li
+ D(c~)
(1) where Pi(c,) is the chemical production rate of species i (which will depend on the concentrations of all other species cj), Li is the chemical loss rate, and D(ci) includes diffusional transport effects, if any. The reaction rates which are included in Pi(cj) and Li are written in modified Arrhenius form
R = 1 0 A P exp(-E/RT)
(11) Reverse reaction rates are derived from the forward reaction rates and the reaction equilibrium constants, all expressed in the form shown in eq 11. For each species ci all of the reactions which produce species i are included in P;(cj) and all reactions destroying species i are included in Li. At constant pressure, the total enthalpy is written
d/dt(Ccihi) 1 = D(h)
(111)
where hi is the specific enthalpy for the ith species and is a function of temperature, evaluated from the specific heat for species i, Cp, by
The
Cpi are
evaluated using a fifth order polynomial in The Journal of Physlcal Chemistry, Vol. 8 1, No. 25, 1977
Westbrook et al.
2544
TABLE 11: Rate Constants [ k = A P e x p ( - E J R T ) ] in em3,mol, K Units
No. 1
2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Reaction
log A
n
HCO t O H = CO t H,O OH t C O = CO, t H HtO,=OH+O H, t O = O H + H 0 t H , O = OH t OH H t H,O= OH t H, HCO t M = H + CO t M 0 t H t M = OH t M OtOtM=O, t M H, t M = H + H t M 0, t H, = OH t OH H,OtM=HtOHtM CO t 0 t M = CO, t M co t 0, = co, t 0 HCO t H = CO t H, HCO t O = CO t OH H t O , tM=HO, t M OtOHtM=HO, t M HO, t O = 0, t OH HCO t 0, = CO t HO, HtHO,=OHtOH H t HO, = IT, t 0, OH t HO, = H,O t 0, HO, t HO, = H,O, t 0, H,O, t M = OH t OH t M H t H,O, = HO, t H, CO t HO, = CO, t OH H,O, A O H = H,O t HO,
14.0 7.18 14.34 10.26 13.83 13.97 14.16 16.00 15.70 14.34 14.90 16.34 15.77 11.50 14.30 14.00 15.22 17.00 13.70 12.52 14.40 13.40 13.70 13.00 17.08 12.23 14.00 13.00
0 1.3 0 1 0 0
temperature, fit to data from the JANAF thermochemical table,g and accurate to within 0.1% over the temperature range 298-3000 K. When diffusive effects, represented generally in eq I11 by D ( h ) , are negligible, the flow is isenthalpic. Equations I and I11 are solved simultaneously by means of a first-order implicit (i.e., backward) difference scheme. Convergence of the difference equations is achieved by means of a multidimensional Newton iteration algorithm. The experimental results of Dryer and Glassmanl for carbon monoxide and methane oxidation are reported in the form of temperature and stable species concentrations as functions of the axial distance from injection. Concentrations of CO and C02 are given for CO oxidation, and CH4, CO, COz, CzH4,and CzHsfor CHI oxidation. Mixing and some pyrolysis and oxidation occur in the conical inlet section as described by Dryer,2 with the result that it is difficult to translate axial distances into absolute time values through the plug flow relations. To determine proper relative concentrations of radical and other intermediate species at the point where the experimental data are first quoted, a number of induction period models were formulated. The approximate residence time in the mixing region was used, together with the experimental concentration measurements, to give reasonable initial conditions for these calculations (see Table I). We assume that the entire flow is adiabatic, so there are no wall heat losses. Although in the experimental configuration the reactor walls are heated to the inflow gas temperature, there can be small heat losses,2 and the computed temperatures may therefore be somewhat higher than the measured values. A refined model could empirically account for heat losses or the temperature measurements themselves could be used as input data. Concentration and temperature profiles are generated for each set of mechanism parameters and the validity of both the reactor model and the chosen kinetics are evaluated by the qualitative and quantitative agreement with experimental data. Elementary reaction rates within the model can be varied individually, within quoted limits of experimental uncertainty, to improve that agreement. Both forward and reverse rates are varied simultaneously, The Journal of Physical Chemistry, Vu/. 81, No. 25, 1977
0 0 - 0.25
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
E,, kcal 0 -0.765 16.79 8.9 18.36 20.37 19.0 0 0 96.0 44.7 105.1 4.10 37.6 0 0 -1.00 0 1.0 7.00 1.90 0.70 1.00 1.00 45.50 3.78 23.00 1.80
Ref 18 25 26 13 13 13 27 28 29 13 29 13 30 31 32 32 13 33 11 This work 13 . 13 11 11
13 13 10 13
so that the rates are still related by the equilibrium constant. In the present cases, computed profiles were found to be sensitive to variations in the rates of only a limited number of the many reactions included in the mechanisms, greatly simplifying this optimization process. Verification of Diffusional Properties A series of calculations for the oxidation of carbon monoxide and methane were performed using the onedimensional hydrodynamics, detailed chemical kinetic, flow reactor model. In these calculations, each spatial point in the entire reactor was represented by a value for temperature and each chemical species. All of these quantities were advanced simultaneously over each time step, including all spatial coupling terms. For each such analytical experiment a total turbulent diffusivity was assumed. This variable sets an upper limit to diffusion relative to the mean convection through the flow reactor. For each chosen diffusivity, the model was adjusted, using important reaction rates, to give the best agreement with the experimental data. In all cases where assumed diffusion effects were appreciable, it was found that the rates of well-documented reactions, particularly reactions 2 and OH t C O = CO, t H
(2)
HtO,=OHtO
(3)
3 (see Table 11), required values well outside the ranges of experimental uncertainty in order to approximate flow reactor experimental results. Even in these cases, many qualitative features of the concentration profiles disagreed with measured data. We will show subsequently that if axial diffusion is assumed to be negligible, it is possible to reproduce the experimental results using accepted values for all reaction rates. As a result of these calculations, an estimate of the upper limit to the effect which axial diffusion can produce in the flow reactor was made. This estimate is that longitudinal diffusion of chemical species and energy is at most 1%of the total transport. Carbon Monoxide Oxidation The oxidation of carbon monoxide was examined, primarily because its reaction mechanism is simpler than,
2545
A Numerical Model of a Turbulent Flow Reactor q 0 0
I I?
I,o E-02
0
10
&I
0
3
0
l-
a
5a
0
0
0
0
0
1 ,OB
0
E
0
0 0
E-03 5.0
W t-
0 0
I .06
0
0 0
E.03
0
I 04
O B O O O O O n n ,
w
w
POSIT ION
POSl T ION
0
0 0
0 0 0
0 0
E - : 3 0 1 0 0 0 0
,
,
J
W
0 0 0
-
-7
m
POS I T I ON FLOW REACTOR NUMERICAL MODEL
Figure 1. Comparison between experimental and computed temperature and concentration profiles for moist carbon monoxide oxidation, using the preliminary reaction mechanism. Experimental data are represented by open circles. Concentrations are shown in mole fractlons, temperature in Kelvin.
and is a subset of, that for hydrocarbon oxidation. Reaction rates and the relative importance of different trace species in the CO-HZ-O2 mechanism can be verified for flow reactor conditions; these can then be incorporated without further modification into the reaction mechanism for more complex fuels (methane in this case). This procedure considerably simplifies the analysis of the methane reaction mechanism. Temperature, CO concentration, and C 0 2concentration profiles were computed using reactions 1-16 from Table I1 and were compared with the experimental data. Reaction rate data were used as quoted, without modification. Initial agreement between the experimental and computed results was poor, as illustrated in Figure 1. The optimization procedure described earlier failed to improve the agreement between the two sets of data. It was found that in order to get even a qualitative comparison between computed and experimental results, many reaction rates for reactions 1-16 had to be assigned values well outside accepted limits. The CO oxidation mechanism was enlarged through the addition of reactions 17-28 from Table 11, including reactions involving HOz and H20z. The agreement with experiment improved immediately, and it was possible to accurately reproduce all of the measured quantities with all reaction rates within accepted ranges. In Figure 2 the temperature, CO mole fraction, and COz mole fraction
from the numerical model are plotted, together with the experimental data. In Figure 3 mole fractions of the important intermediate species are plotted. Most of the carbon monoxide is consumed by reaction 2. Therefore, the rate of consumption of CO is controlled GO t O H = C O , + H (2) directly by the availability of OH radicals. The primary source of OH during most of the oxidation is reaction 3.
H + 0, = O H + 0
(3)
Thus the inclusion of reaction 17 provides an alternate H+O, +M=RO, t M (17) path for H and O2 reactants a t the expense of reaction 3. Addition of reaction 17 to the reaction mechanism directly reduces the production rates for OH and 0 radicals. Since most of the 0 atoms produced by reaction 3 go on to react with H 2 0 via 0 + H,O= OH t OH (5) inclusion of reaction 17 significantly reduces the OH production rate in several ways. The first numerical model, without reactions 17-28, gives OH concentrations higher by nearly a factor of 10 than the levels in the second model with the additional reactions. The H 0 2 in the second mechanism acts as a reservoir, slowly releasing OH which The Journal of Physical Chemistry, Vol. 81, No. 25, 1977
2546
Westbrook et al.
I
,
i
I
I
.)
F L W R E A C T C R N U M i R i C A L MOClEL
Figure 2. Comparison between experimental and computed temperature and concentration profiles for moist carbon monoxide oxidation, using the complete reaction mechanism. Experimental data are represented by open circles. Concentrations are shown in mole fractions, temperature in Kelvin.
can then oxidize the CO. This significantly slows the overall oxidation rate for CO. As noted earlier, most of the CO oxidation takes place through reaction 2. Reaction 27 has been suggested as an CO + HO, = CO, + OH (27) alternate oxidation path, but with the quoted reaction rate for reaction 27,'O the ratio [H02]/[OH] would have to be nearly 100 for reaction 27 to be important. The present calculations indicate (Figure 3) that [H02]/[OH] < 1 / 2 over most of the flow reactor and less than 1%of the CO oxidation occurs by reaction 27. Thus the primary function of H02 rests not in its ability to oxidize CO but in its role in regulating the availability of OH. This conclusion would not be modified by the use of other correlations which have been presented in the literature for reaction 27.11J2 Since the reactions of HOz with other species determine in part the overall oxidation rate of CO, it is interesting to note those reactions which contribute to the rate of HOP consumption. Reactions 19, 23, and 21 contribute in the
+ 0 = 0, + OH HO, + O H = H,O t 0, HO, + H = OH t OH HO,
(19)
proportions of approximately 6:3:1, respectively. Reaction 24 is found to be not important, using the rate given by The Journal of Physical Chemistry, Vol. 8 1,
No. 25, 1977
HO, t HO, = H,O, i- 0 ,
(24)
Lloyd;" however, the uncertainty in the rate of this reaction is quite large,'l and a significant upward reevaluation of this rate might result in a large contribution of reaction 24 to the HOz consumption rate. The H atom concentration profile does not appear in Figure 3. Although H atoms are being produced rapidly, primarily by reaction 2, the high reactivity of the H atoms, principally through reactions 3 and 17, consumes them just as rapidly. Throughout most of the flow reactor the mole fraction of H atoms is slightly lower than the mole fraction of H202. A series of calculations was performed in which the sensitivity of the concentration profiles to variations in individual reaction rates was examined. It was found that, through its role in producing HO, and slowing OH production, reaction 17 has a strong effect on all of the concentration profiles. This has permitted us to determine its rate k17 with some degree of precision. Taking into account quoted uncertainties in other important reaction rate expressions we find best agreement for h17 = 2.6 X 1015 at 1100 K. This agrees well with the results of other authors.13 The estimated uncertainty for this rate, determined computationally, is f20%. There are three important conclusions to be drawn from the CO oxidation calculations. First, at the temperatures characteristic of flow reactor, HO, and Hz02must be
2547
A Numerical Model of a Turbulent Flow Reactor FLOW REACTOR NUMERICAL MODEL 4.5
3.5
3 0
Z
-0 c 0 G K iL
2.5
LU 2.0
x 1 5
E-05 I
.o
E-06
5 0
0 0
-
- 0
Iu
m
m
LD
r.
m
Y
PO51 T I
ON
Figure 3. Computed concentration profiles of important intermediate species in moist carbon monoxide oxidation, using the complete reaction mechanism.
included in any reaction mechanism in which CO is being oxidized. These conditions will prevail in the oxidation of all hydrocarbon fuels; it is clear that HOz and HzOz will also be important in the methane oxidation mechanism. In addition, we have taken advantage of the sensitivity of the computed results to variations in the rate of reaction 17 to assign it a specific value at flow reactor temperatures. Finally, we have established that the reaction mechanism defined by reactions 1-28 in Table I1 is sufficient to describe lean CO oxidation a t flow reactor temperatures, while the mechanism defined by reactions 1-16 is not adequate. The reactions involving HCO, reactions 1,7, 15, 16, and 20, were originally included to see if any appreciable amount of HCO could be formed. Under the lean conditions being studied, these reactions played no significant role in the mechanism for CO oxidation and could be omitted in the CO oxidation calculations. Some of the recombination reactions, reactions 8, 9, and 10, also were relatively unimportant and could be omitted with no appreciable effect on the computed concentration and temperature profiles. Although these recombination reactions play an important role in establishing chemical equilibrium, residence times in the flow reactor are much too short for them to be of any importance in the present context.
next. The previously determined CO oxidation mechanism was augmented by the addition of the chemical species and reactions shown in Table 111. Reactions 29-48 include most of the methane oxidation mechanisms proposed by a number of other authors.14J5 In addition, reactions 49-56 include a mechanism for the formation and oxidation of ethane. Methyl radical recombination and the ethane-ethene chain of reactions were included for two related reasons. First, the experimental data showed appreciable amounts of C2HGand CsH4 in methane oxidation studies, and in calculations in which reactions 49-56 were not included, methyl concentrations were higher than expected. Second, as noted earlier by Dryer,l estimates of the rate for reaction 56 indicated that recombination would be a significant
Methane Oxidation Methane oxidation experimental data from the flow reactor studies of Dryer and Glassmanl were examined
C,H,
CH,
+ CH,
= C,H,
(56)
consumption mechanism for methyl radicals. The mechanism for formation of ethene is relatively complete and reaction rate estimates are reasonably well defined. However, the mechanism for oxidation of ethene is currently not well understood. While the rate and products of reaction 50 have been experimentally deterC,H,
+ 0 = HCO + CH,
(50)
mined, much less is known about reaction 50a. Reaction
+ OH
-f
products
(50a)
50a is generally considered to be an addition reaction yielding CzH40H by ruling out abstraction and substiThe Journal of Physical Chemistry, Vol. 81, No. 25, 1977
2548
Westbrook et al.
TABLE 111: Rate Constants [ k = A T n e x p ( - E , l R T ) ] in c m 3 ,mol, K Units No. 29 30 31 32 33 34 35 36 31 38 39 40 41 42 43 44 45 46 41 48 49 50 51 52 53 54 55 56
Reaction CH, t M = C H , + H t M CH, t H = CH, t H, CH, t O H = CH, t H,O CH, t 0 = CH, t OH CH; t HO, = CH,O + OH CH,O t M = HCO t H t M CH,O t O H = HCO t H,O CH,O t H = HCO t H, CH,O t O = HCO t OH CH, t OH = CH,O t H, CH, t O = C H , O t H CH, t O,= CH, 0 t 0 CH,O t CH, = HCO t CH, HCO t CH, = CH, t CO CH,O t M = CH,O t H t M HCO t HO, = CH,O t 0, CH,O t 0, = CH,O t HO, CH, t HO, = CH, t 0, CH, t HO, = CH, t H,O, CH,O t HO, = HCO t H,O, C,H, t CH, = C,H, t CH, C,H, t 0 = CH, t HCO C,H, = C,H, t H C,H, t H = C,H, t H, C,H, t 0, = C,H, t HO, C,H, t OH = C,H, t H,O C,H, t O = C,H, t OH CH, t CH, =C,H,
log A
11.30 14.10 12.50 13.30 13.30 16.70 14.70 13.10 13.70 12.60 14.10 13.40 10.00 11.50 13.70 14.00 12.00 12.00 13.30 12.00 -0.26 13.50 13.58 14.12 12.50 13.05 13.40 13.00
, 20
@ I
n 0
Ea, kcal
Ref
88.40 11.90 3.17 9.20 0.00 72.00 6.30 3.76 4.60 0.00 2.00 29.00 6.00 0.00 21.00 3.00 6.00 0.40 18.00 8.00 8.28 19.40 38.00 9.37 5.00 2.45 6.36 0.00
34 35 21 36 23 22 14 32 14 31 24 38 39 39 38 40 41 42 42 11 43 44 45 46 47 21 48 49
0
0 0 0 0
0 0 0
0 0 0 0.5 0.5 0 0 0
0
0 0 4 0 0 0 0 0 0 0
3
IE
3 i-
Q
3
K l 16
c)
w
2.
CL
E
E1
!Li
E-03
I 12
0
.-
0
N O
w
m
w
POSIT I ON
POSl T ION
5.
5.
4
a
Li
3.
r\J
f
3.
I
0 0
e. 2.
E-03 I.
E-03 I
O
0.
.-
LD
NYP
m
0
POSITION
._ w:
Lo
m
PO5 IT ION FLOW
REACTOR NUMERICAL MODEL
Figure 4. Comparison between experimental and computed temperature and concentration profiles for lean methane oxidation at 1097 K. Experimental data are represented by open circles. Concentrations are shown in mole fractions, temperature in Kelvin. The Journal of Physical Chemistry, Vol. 87, No. 25, 1977
2549
A Numerical Model of a Turbulent Flow Reactor FLOW REACTOR NUMERICAL MODEL
D
-
- 0
rL
m
W
In
r
rn
w
POSIT I 3 N Figure 5. Comparison between experimental and computed concentration profiles for CPHBand C2H4in lean methane oxidation at 1097 K. Experimental data are represented by open circles (CpH4)and triangles (C,H,). Concentrations are shown in mole fractions.
tution on the basis of energetics. The negative activation energy found by G r e i n e P supports this conclusion. No higher temperature data or product confirmation on this reaction currently exist. However, it is clear from available data on reaction 50a and the ratio [OH]/[O] that both reactions 50 and 50a are equally competitive for ethene under reactor conditions. If reaction 50a is assumed to be additive, little is known about the mechanism which finally yields oxidation products from C2H40H. Possible intermediate products relevant to the mechanism already formulated might be CH3, CHzO, and HCO. One might choose the reaction C,H, t OH = CH,O
+ CH,
as a means of estimating the effects of reaction 50a.17350 However, as a first approach, we have chosen to account for the reactions of ethene by adjusting upward the measured rate for reaction 50. Because of these uncertainties and the approximations used, we have also neglected radical-radical reactions between CzH5 and other radicals as being considerably less important than reactions of C2H5with stable species. In any case, it is very clear that methyl radical recombination and the subsequent oxidation of ethane plays an important role in the oxidation mechanism of methyl radicals. In the current numerical model, roughly half of the methyl radicals are directly oxidized, while the remainder proceed through the oxidation route afforded by methyl radical recombination. With regard to the direct oxidation of methyl radicals, several authors"JQ have used the reaction
CH,
+ 0, = HCO t
H,O
(40a)
This reaction path, which bypasses reactions of CH30 and CHzO, was examined numerically, using the reaction rate suggested by Bowman,ls and was found to produce very poor agreement with experiment. Since reaction 40a is probably not an elementary reaction, it is likely that the sequence of elementary reactions it replaces (e.g., reactions 33,45, and 35) proceeds much more slowly at flow reactor temperatures than at the shock tube temperatures for which reaction 40a was proposed. A comparison between experimental and calculated results is shown in Figures 4 and 5, including concentration and temperature profiles. The agreement is good with respect to CH4, CO, and C 0 2 behavior. The computed temperatures are higher than the experimental values by about 5-10 K. A majority of this small difference can be explained by heat losses to the reactor wall, as discussed earlier. The computed C2H6 level is higher than the experimental data by a factor of about 2, although the spatial dependence agrees quite well. The computed CzH4level is in closer agreement with experiment but is also somewhat higher and reaches its maximum slightly earlier than does the experimental data. It is believed that departure of computed results in the early and late sections of the oxidation are caused by inadequacy of the ethene oxidation model. Measurements of additional species of Dryer and Glassman,' including methanol and acetylene, suggest the reaction mechanism may eventually require additional consideration of these species. The Journal of Physical Chemistry. Vol. 8 1, No. 25, 1977
2550
Westbrook et al. FLOW REACTOR NUMERICAL MODEL
0 Q
CT k
i
(
w
A
0
t 3
2
E-05 I
O 0
-
-4
hl
m
f
0
r
u)
m
POS I T I ON Flgure 6. Computed concentration profiles of important intermediate species in lean methane oxidation at 1097 K.
If reactions 49-56 are not included, the rate of the major CO oxidation reaction, reaction 2, must be adjusted C o t OH=CO, t H
(2)
downward by at least 50% in order to achieve results comparable with the experiment. Even then, the computed temperature in the first 40 cm of the reaction zone is considerably higher than shown in Figure 4. This behavior, in addition to the computed rate of reaction 56 and the experimental evidence of the presence of considerable amounts of C2H6 and C2H4, demonstrate conclusively the importance of C2Hs, C2H5, and C2H4 in the oxidation mechanism for methane. The concentrations of some radical and other intermediate species are plotted in Figure 6. From these curves we can describe the important steps in the methane oxidation as the reactants pass through the flow reactor. The first stable intermediate, CH20, is formed quite rapidly, reaching a maximum mole fraction of approximately 7 X (70 ppm) at about 25 cm. The conversion of methane t o formaldehyde is supported by a relatively constant concentration of methyl radicals. Methyl quickly reaches a state of chemical balance, in which it is formed principally by the reactions CH, t O H = CH, t H,O CH, t O = CH, t OH
(31) (32)
and consumed by the reactions CH, t CH, = C , H , CH, t HO, = CH,O t OH CH, t 0 = CH,O t H The Journal of Physical Chemistry, Vol. 81, No. 25, 1977
(56) (33)
(39)
Reactions 31 and 32 produce CH3 in the ratio of approximately 4:l. In light of the fact that reaction 31 is the dominant mechanism for methyl radical production, the rate of this reaction was further examined. The rate determined by Zellner and Steinert,20k31 = 3.47 X 103P.0s, exp(-lOlO/T) cm3/mol s, was substituted. At 1100 K the Zellner and Steinert value is more than five times the Greiner21rate used in most of these calculations. The net loss rate for CH4 was found to be insensitive to changes of this magnitude in the rate of reaction 31, largely because until the methane has been totally consumed, reaction 31 is also the major loss term of OH. Therefore, use of the Zellner and Steinert rate consumes OH faster than does the Greiner rate, with the result that the locally balanced OH concentration is lower for the first 50 cm of the reactor than in Figure 6. However, once the CH4 has disappeared the OH level quickly returns to the higher value of Figure 6. Sizable variations in the rates of reactions 29, 30, 32, and 47 similarly have little effect on the methane disappearance rate. The CH30 formed by reaction 33 reacts rapidly with 0 2 (reaction 45) to produce formaldehyde. Between 15 and CH,O
+ 0, = CH,O t
HO,
(45)
50 cm, the region in which CH3 is chemically balanced, the average branching ratio between reactions 33 and 56 is very close to unity. Beyond approximately 45 cm reaction 39 also provides a substantial fraction of the total methyl destruction. Reaction 39 owes its increased importance to the rapid rise after 45 cm in oxygen atom concentration. During the first 45 cm most of the 0 and OH are produced by reaction 3 and are immediately consumed by reactions
2551
A Numerical Model of a Turbulent Flow Reactor
1
Cr
3
c
l
2
1.25
W
a E
W tI .20
E103 1.15
._
f
Nu0
0
w
m
W
0
.-
w
POSIT ION
W
1110
m
POSIT ION
I
8.
6
rL
0 0 -
E-03
2.
r'1 I
1
9
6.
I
0 3
5
E-03 \
2.
n
-
0
4.
0
0. f
m
W
0
3
-
ID
1 1 1 0
rn
POSITION
POSITION FLOW REACTOR NUMERICAL MODEL
Figure 7. Comparison between experimental and computed temperature and concentration profiles for lean methane oxidation at 1142 K. Experimental data are represented by open circles. Concentrations are shown in mole fractions, temperature in Kelvin.
(3)
H+O,=OH+O
with CH4, CH3, CzH6, and CzH4. Once most of these species have been destroyed, 0 and OH concentrations rise rapidly and are available for oxidation of CH20 and then Hz and CO. The rapid increase in 0 and OH concentrations is also primarily responsible for the rapid oxidation of CzH6 and CzH4 after 45 cm as shown in Figure 5 . There are two branches for the products of CH3 + H 0 2 CH,
+
HO, = CH,O t OH
CH, t HO, = CH,
+ 0,
(33) (46)
At flow reactor temperatures, reaction 33 appears to be 20 times faster than reaction 46, so that reaction 46, which is the only significant mechanism for re-forming CH4, has no noticeable effect on the methane loss rate. Reaction 34, the dissociation reaction for formaldehyde, CH,O t M = HCO t H
+M
(34)
was discussed by Bowman,14 who pointed out the large differences in the literature for the apparent activation energy for this reaction. It is interesting to note that in these calculations, reaction 34, using either the rate from Schecker and JostZ2or that given by Bowman,14 is never important, contributing less than 1% of the CHzO formation or loss rate. Bowman14 found that this reaction was important in richer mixtures and a t higher temperatures. However, the large activation energy of this re-
action reduces its importance at flow reactor temperatures. Both methyl radical oxidation paths, that through ethane and ethene, and that through formaldehyde, eventually produce formyl radicals and then CO. The two principal reactions producing CO are HCO + 0, = CO + HO, HCO t M = H + CO t M
(20)
(7)
The rate used for reaction 20 was based on that of Bowman14 and is considerably lower than the rate proposed by C01ket.~~ The latter value is similar to the rate suggested by Peeters and MahnenZ4at 1600 K. Use of the higher rate in the flow reactor resulted in extremely poor comparison with experimental data. Our computational results suggest a value for hzo= 1.35 X 10l1 cm3/mol s at 1100 K. The apparent activation energy of 7 kcal/mol used in this model is intermediate between the value of 1.6 kcal/mol proposed by C01ket~~ and that of Bowman,14 14.3 kcal/mol. This reaction appears to be important a t flow reactor temperatures, and further experimental data on its rate would be valuable. Reaction 20 and reaction 7 each provide approximately half of the CO formation rate in this model. Reaction 7 has been shown to be important at higher temperatures as well as Bowman.14 The calculated concentration and temperature profiles were sensitive to variations in the rates of both reaction 7 and reaction 20. In addition to the rate quoted for reaction 20, we determined the rate for reaction 7 at 1100 K as k7 The Journal of Physical Chemistv, Vol. 81, No. 25, 1977
2552
Westbrook et al. FLOW R E A C T O R NUMERICAL MODEL 3 3
a 5
z
-
2 c
0 t
0 Q
a: I 1 5 J_1
1
0 E E 04
0
E-C5 5 0
0 0
-
- 0
rL
m
m
ID
P
rn
A !
POSI T I ON Flgure 8. Comparison between experimental and computed concentration profiles for C2H6 and C2H4in lean methane oxMation at 1142 K. Experimental data are represented by open circles (C2H,) and triangles (C&).
Concentrations are shown in mole fractions.
= 2.4 X 1O1O cm3/mol s. An estimate of the uncertainty in these rates can be made on the basis of a series of calculations and is approximately &50% for both reaction rates. Once the methane, formaldehyde, ethane, and ethene have been converted to CO, H2,and other species including HOz and HzOz, the remainder of the oxidation follows much the same path as described earlier for the CO oxidation. However, the Hz levels in the methane oxidation are of course much higher than in the case of moist CO oxidation. The Hz molecule concentration (Figure 6) reaches a maximum of approximately 80 ppm between 40 and 50 cm from the entrance of the flow reactor. The H atom concentration is not included in Figure 6 for the same reasons noted in the discussion of CO oxidation. Reactions producing and consuming H atoms maintain them at a concentration slightly below the H202concentration. The reaction mechanism and elementary reaction rates developed for the methane oxidation study above were finally applied to another methane oxidation experimental study reported by Dryer and G1assman.l These additional data are characterized by a higher initial temperature (1142 K) and a slightly richer fuel mixture. As a result, the oxidation is faster and is confined to a narrower spatial region than in the lower temperature case. In Figures 7 and 8 we plot the temperature and concentration profiles obtained from the numerical model, together with the experimental data points. Additional important radical and stable intermediate species concentrations are plotted in Figure 9. The temperature and major concentration The Journal of Physlcal Chemistry, Val. 81, No. 25, 1977
profiles agree reasonably well with the experimental data and indicate that the present mechanism still describes most of the properties of the methane oxidation. The agreement is not as close as in the leaner, lower temperature model. In particular, the carbon monoxide concentration has a peak computed value nearly twice that of the measured result, although the spatial location of that peak agrees well with the experiment. In addition, the computed methane disappearance rate is somewhat too large between 35 and 60 cm. The qualitative features of the intermediate chemical species in Figure 9 are quite similar to those for the leaner model in Figure 6. A fairly broad CHzO peak is followed by a sharper H2 peak, which is centered at about the same spatial location as the CO peak. The CO and H2 are then consumed by the 0 and OH which can be seen to rise sharply in the richer model at a distance of approximately 30 cm from the injector. All of these concentration peaks are narrower than in the previous experiment, reflecting the substantially shorter reaction time of the higher temperature mixture. The most significant qualitative difference between the richer case profiles in Figure 9 and the leaner model profiles in Figure 6 is in the relative heights of the Hzand CHzO peaks. The cause for this difference is due to the methyl destruction mechanism. As noted earlier, the methyl recombination rate depends quadratically on the methyl concentration, while the methyl oxidation rate depends linearly on methyl concentration. In the richer model the methyl concentration is approximately twice that in the earlier model. As a result, a larger fraction of the methyl is consumed by
2553
A Numerical Model of a Turbulent Flow Reactor FLOW EEACTOR NUMERICAL MODEL 3 0
H2
2 5
2 0
Z
-
0
I
F 0
\
\
Q
LT iL
1.5
W
i 0
r
E-04
I O
E-05 5 0
n v1
LD
,
PO5 I T I O N Figure 9, Computed concentration profiles of important intermediate species in lean methane oxidation at 1142 K.
ethane formation and less by formaldehyde formation. Since both mechanisms eventually produce H2,the relative heights of these curves are a measure of the relative importance of the two methyl destruction mechanismb. It appears clear that in the richer model ethane and ethene oxidation play a larger part than in the leaner case. Improvements in the oxidation mechanism for these species must be made to improve the agreement between computed and experimental data. However, the present mechanism is able to treat most of the important features of both methane oxidation experiments. In Table IV we present the maximum concentrations for a number of species in the two methane oxidation calculations, together with similar data quoted by Dryer and G1assman.l The trends in the species concentrations are predicted in most cases by the numerical model, with the major discrepances occurring for C2H6and CzH4,as expected.
Conc1usi on
A reaction mechanism for the oxidation of carbon monoxide and of methane has been developed for the temperature range 1000-1350 K. This mechanism, embodied in a numerical model for chemical kinetics, hydrodynamic motion, and energy transport, has been used to interpret experimental results in a turbulent flow reactor. The mechanism presented has been able to interpret all of the experimentally determined features of carbon monoxide oxidation and most of the important features of methane oxidation. The present study demonstrates conclusively that at intermediate temperature ranges, typical of the turbulent
TABLE IV: Maximum Concentration (ppm) Computed models 0.5% CH,-air
To =
1097K 80 70 140 110 15 13 20 3500
0.8%
CH,-air
To =
1142K 280 100 300 220 50 14 30 6000
2 : : ; 0.5% CH,-air
To =
1200K
300 100 60 40 1
3200
flow reactor, it is necessary to include a large number of chemical species and reactions in the oxidation mechanism. A number of these species, particularly H02,H20z,CH20, CH30, C2He,and C2H4,are not commonly included in high temperature reaction mechanisms for these fuels. Their roles in the intermediate temperature range are extremely important in predicting intermediate species concentrations and overall fuel oxidation rates. As a result, thiL study shows that these species must be included in combustion models which intend to predict certain pollutant formation rates in practical combustion systems. The importance and, under some conditions, dominance of the methyl recombination reaction in the methane oxidation mechanism has been demonstrated. As the importance of ethane formation increases, ethahe oxidation to ethene and the eventual oxidation of ethene also become increasingly important. We have shown how calculations The Journal of Physical Chemistry, Vol. 8 I, No. 25, 1977
2554
with different fuel-air equivalence ratios point out the shortcomings of the present ethene oxidation mechanism, indicating an area in which further development is needed. Calculations including energy and species diffusion in the axial direction, coupled to the chemical kinetics rate equations, demonstrated that axial diffusion is negligible in comparison with the bulk fluid flow through the flow reactor. The sensitivity of the computed results to changes in selected elementary reaction rates has been used to determine estimated values for some of these reaction rates. In addition, the ability of this model to reproduce a variety of independent experiments, each including several measured quantities, is a significant demonstration of the essential validity and accuracy of the reaction mechanism and rates incorporated into the numerical model.
References and Notes (1) F. L. Dryer and I. Glassman, Fourteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1973. (2) F. L. Dryer, Ph.D. Thesis, Princeton University, Department of Aerospace and Mechanical Sciences, March, 1972. (3) I.Eberstein and I.Glassman, Tenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1965. (4) R. F. Sawyer and I. Glassman, Eleventh International Symposium on Cornbustion, The Combustion Institute, Pittsburgh, Pa., 1967. (5) R. F. Sawyer and I. Glassman, Twelfth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1969. (6) M. B. Colket, D. W. Naegeli, and I. Glassman, Sixteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1977. (7) R. Cohen, F'h.D. Thesis, Princeton University, Department of Aerospace and Mechanical Sciences, in preparation. (8) C. K. Westbrook, "A Generalized ICE Method for Chemically Reactive Flows in Combustion Systems", University of California Lawrence Livermore Laboratory Report UCRL-78915, 1976. (9) JANAF Thermochemical Tables, Dow Chemical Company, Midland, Mich., 1974. (10) R. R. Baldwin, R. W. Walker, and S. J. Webster, Combust. Flame, 15, 167 (1970). (11) A. C. Lloyd, Int. J . Chem. Kinet., 6, 169 (1974). (12) I.A. Vardanyan, G. A. Sachyan, and A. B. Nalbandyan, Int. J. Chem. Kinet., 7, 23 (1975). (13) D. L. Baulch, D. D. Drysdale, D. G. Horne, and A. C. Lloyd, "Evaluated Kinetic Data for High Temperature Reactions", Vol. 1, Butterworths, London, 1973. (14) C. T. Bowman, Fifteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1975. (15) M. Koshi, H. Ando, M. Oya, and T. Asaba, Fifteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1975. (16) N. R. Greiner, J . Chem. fhys., 53, 1284 (1970). (17) S. C. Sorenson, P. S. Myers, and 0. A. Uyehara, Thirteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1971.
The Journal of Physical Chemistry, Vol. 8 1, No. 25, 1977
Westbrook et ai.
(18) C. T. Bowman, Combust. Sci. Techno/., 2, 161 (1970). (19) B. R. Bowman, D. T. Pratt, and C. T. Crowe, Fourteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1973. (20) R. Zeilner and W. Steinert, Int. J . Chem. Kinet., 8, 397 (1976). (21) N. R. Greiner, J. Chem. fhys., 53, 1070 (1970). (22) H. G. Schecker and W. Jost, Ber. Bunsenges. fhys. Chem., 73, 521 (1969). (23) M. D. Colket, Ph.D. Thesis, Princeton University, Department of Aerospace and Mechanical Sciences, Dec, 1975. (24) J. Peeters, and G. Mahnen, Fourteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1973. (25) D. L. Baulch and D. D. Drysdale, Combust. Name, 23, 215 (1974). (26) D. L. Baulch, D. D. Drysdale, and D. G. Horne, Fourteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1973. (27) S. W. Benson and H. E. O'Neal, Natl. Bur. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 21 (1970). (28) G. Moretti, AIAA J., 3, 223 (1965). (29) D. R. Jenkins, V. S. Yumlu, and D. B. Spaiding, Eleventh International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1967. (30) R. Simonaltis and J. Heicklen, J . Chem. fhys., 56, 2004 (1972). (31) W. C. Gardiner, M. McFarland, K. Morinaga, T. Takeyama, and B. F. Walker, J . Phys. Chem., 75, 1504 (1971). (32) A. A. Westenberg and N. de b a s , J. fhys. Chem., 76, 2213 (1972). (33) G. S. Bahn, fyrodynamics, 2, 315 (1965). (34) R. Hartig, J. Troe, and H. G. Wagner, Thirteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1971. (35) R. R. Baldwin, D. E. Hopkins, A. C. Norris, and R. W. Walker, Combust. Flame, 15, 33 (1970). (36) J. T. Herron, Int. J. Chem. Kinet., 1, 527 (1969). (37) C. P. Fenimore, Twelfth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1969. (38) T. A. Brabbs and R. S. Brokaw, Fifteenth International Symposium on Combustlon, The Combustion Institute, Pittsburgh, Pa., 1975. (39) R. Tunder, S. Mayer, E. Cook, and L. Schieler, Aerospace Corp. Report TR- 100 1 (9210-02)-1 (AD8 13485). (40) R. R. Baldwin and R. W. Walker, Fourteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1973. (41) V. S. Engleman, "Survey and Evaluation of Kinetic Data on Reactions in Methane/Air Combustion", EPA Report EPA-600/2-76-003, Jan 1976. (42) G. B. Skinner, A. LifshZz, K. Scheller, and A. Burcat, J. Chem. fhys. 56, 3853 (1972). (43) T. C. Clark and J. E. Dove, Can. J . Chem., 51, 2147 (1973). (44) D. D. Davis, R. E. Huie, J. T. Herron, M. J. Kurylo, and W. Braun, J . Chem. Phys., 56, 4868 (1972). (45) M. C. Lin and M. H. Back, Can. J . Chem., 44, 2357 (1966). (46) P. Camillerl, R. M. Marshall, and J. H. Purnell, J. Chem. Soc., Faraday Trans. 7 , 70, 1434 (1974). (47) D. F. Cooke and A. Williams, Thirteenth International Symposium on Combustion, The Combustion Institute, Pittsburgh, Pa., 1971. (48) J. T. Herron and R. E. Huie, J. fhys. Chem. Ref. Data, 2, 467 (1973). (49) P. D. Pacey, Chem. fhys. Lett., 23, 394 (1973). (50) D. B. Olson and W. C. Gardiner, J . fhys. Chem., paper to appear in this issue. (51) Reference to a company or product name does not imply approval or recommendation of the product by the University of California or the US. Energy Research and Development Administration to the exclusion of others that may be suitable.
