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A flame structure study of lean propaneoxygen flames diluted with argon
COMBUSTION AND FLAME 46: 177-190 (1982)
177
A Flame Structure Study of Lean Propane-Oxygen Flames Diluted with Argon S. J. COOK and R. F. SIMMONS The University of Manchester Institute of Science and Technology, Manchester, England
Temperature and composition profiles have been obtained through a series of fiat flames containing between 1.23 and 1.38 mol% C3H s, in which the ratio [02] : [Ar] was kept constant at 15 : 85. These profiles have been analysed in terms of the continuity equations for mass, energy, and individual species to obtain the heat release and reaction rates as a function of distance through the flame, and hence information about the reactions which control the propagation of the flame. it is concluded that the heat release in the early part of the flame is controlled by the rate of the reaction: OH + C a l l 8 = H 2 0 + C a l l 7. The subsequent steps in the oxidation are discussed in the light of known rate constant data for the likely reactions and it is shown that the initial steps in the mechanism can be considered as an oxygen-induced decomposition of the propane. Chain branching is unimportant below 1000K, but above this temperature [H] and [OH] rise rapidly, reaching their maximum values in the range 1300-1400K (final flame temperatures in the range 1500-1600K). In all cases, the maximum [H] was reached at a slightly lower temperature than the maximum for [OH], and it is shown that quasi-equilibrium between H, O, and OH can only exist in the region where the radical concentrations are decaying to their equilibrium levels. The fate of the oxygen atoms produced in the branching reaction H+O2=OH+O is considered, and it is concluded that the predominant removal process is O + H 2 0 = 2OH
INTRODUCTION There have been a number of detailed structural studies of flat methane-oxygen flames [1, 2] and these have yielded useful information about the individual reactions which are important in such flames. In many ways, however, methane is not a typical hydrocarbon fuel, particularly in its oxidation characteristics, and thus it is surprising that there has been no detailed mechanistic analysis for a more typical fuel such as propane. Friedman and Burke [3] have studied the heat release rate Copyright © 1982 by The Combustion Institute Published bY Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY ! 0017
through a lean propane-air flame burning at low pressure (0.06 atm) and Fristrom and Westenberg [4] have reported the results of a detailed structure study of an approximately stoichiometric propaneair flame burning at 0.25 atm on a conical burner. Some more detailed information has been presented by Simmons et al. [5, 6], but these latter papers are primarily concerned with the effect of hydrogen bromide and tetraethyl lead, respectively, on the propagation of the flame. The present paper is concerned with a detailed study of lean flames burning at atmospehric pressure in the absence of any additive. Temperature
0010-2180/82/05177+ 14502.75
178 and composition profiles are presented for a series of lean flames diluted with argon, and the results are used to discuss the important rate-controlling reactions in the various parts of the flame. EXPERIMENTAL
Details of the burner, thermocouple, and microprobe have been given elsewhere [5]. The thermocouple (0.0025-cm-diam Pt/Pt-Rh coated with silica [7]) was traversed slowly (,--0.5 mm min-1) through the flame by a small electric motor and the output from the thermocouple was fed to a potentiometric recorder. A second thermocouple bead was positioned in the flame where the temperature rises steeply, and approximately linearly with distance, to detect any movement of the flame during the traverse, and the change in temperature from the second thermocouple was used to apply a temperature correction to the recorded temperature profile. It should be noted that in the region of maximum temperature gradient the temperature increased by ~ 10K in 0.05 mm, a comparable distance to the typical diameter of the thermocouple beads (< 0.04 mm), and that the corrected profiles for a given flame were very reproducible and did not vary with the direction in which the traverse was made. This gave added confidence that the temperature profiles were reliable, but as an added precaution a number of traverses were made in each direction with each flame, so that they could be averaged. The quartz microprobes had an orifice diameter <20 p, so that the disturbance to the gas flow upstream of the probe tip was restricted to a distance of 0,05--0.1 mm; under these conditions any aerodynamic effect of introducing the probe into the flame is minimal [8]. The sample from the microprobe was fed to the continuous sampling system of an MS 10 mass spectrometer, and this was designed so that viscous flow was maintained and the major part of the sample was pumped away through a bypass line. Thus the composition of the sample entering the mass spectrometer was identical to that of the original sample and the analysis was made almost instantaneously. These concentration measurements were made on a point-to-point basis through the flame at very
S.J. COOK and R. F. SIMMONS close intervals, the position of the tip of the probe being noted for each determination in relation to the temperature profile by the use of a thermocouple arranged at the side of the probe. Both the temperature and the composition profiles were obtained in terms of an absolute distance through the flame by noting the position of the thermocouple bead, in relation to the schlieren plane of the flame, at the beginning and end of each traverse. The experimental profiles were analyzed in terms of the continuity equations for mass, energy, and species which apply to a flat flame [7]. These give the rate of heat release Q as Q = d(2 d T / d z ) / d z
- povoCp(dT/dz),
where P0 is the density and Vo the average flow velocity of the initial mixture at the schlieren plane, 2 is the thermal conductivity and ~'p the average specific heat of the mixture at temperature T, while z is the distance coordinate through the flame. For the purposes of these calculations t~p and 2 were obtained from the values of oxygen and argon alone, using the mixing formula given by Brokaw [9], since these components comprise >98% of the initial mixture. The variation in these values with temperature was represented by a polynomial in T so that the values for the given temperature could be used in the computation. The species conservation equation leads to the following expression for the rate of reaction R i of species i: R i = (pOVO/Mi)(dG i/dz),
where M~ is the molecular weight of species i and G~ its mass flux fraction. The latter is given by G, = ( M , X J E M i X , ) [ ( v + V~)/v] = NiMi(v + Vi)/PoVo,
where v is the flow velocity, Vi the diffusion velocity, and N i the concentration of species i. In this analysis it has been assumed that the stream/tube area ratio is unity, since all measurements have been made with the schlieren plane as the reference level for PoVo and chemical reaction was essentially
STRUCTURE OF LEAN PROPANE-OXYGEN FLAMES complete within 2-3 mm. Since p = pK/I/RT, where /('/is the average molecular weight of the mixture, the flow velocity v was obtained directly from the temperature profile and the continuity equation for mass (pv=PoVo). The diffusion velocities were obtained by Fick's law using binary diffusion coefficients for the various species in argon, since the latter always comprised > 80% of the mixture. These binary diffusion coefficients were calculated using the Lennard-Jones potential [10]. The experimental data gave a series of values for T and X~ at 0.1-mm intervals through the flame and a computer program was used to calculate the various quantities required in the analysis [6]. The profile extended over a minimum distance of 5 mm and thus at least 50 values of each quantity were used in the analysis of each flame. The first stage in this analysis was to apply a radiation correction to the measured temperatures using the equation derived by Kaskan [11]. The appropriate value of the thermal conductivity was obtained from the polynomial expression in T used in the subsequent analysis of the temperature profile (see earlier) and the variation in the emissivity of the thermocouple wire with temperature was also taken into account. This was done by using the data of Bradley [12] for the emissivity of 0.005-cm-diam silica-coated platinum wire to derive the necessary polynomial expression in T. The magnitude of the radiation correction increased with temperature, but for an observed temperature of 1400K the correction was only about 70K, and the maximum correction in the hottest flames was only ~ 120K. The corrected final flame temperature was always within _ 15K of the calculated adiabatic flame temperature and this gave added confidence in the reliability of the values.
RES[~.LTS Temperature Profiles Figure 1 shows the results from a typical thermocouple traverse. The output from the fixed thermocouple shows some drift occurred in the position of the flame front (in an upward direction)
179
during the traverse, since its recorded temperature is slightly higher at the beginning than at the end of the traverse; as the moving thermocouple approaches the reaction zone of the flame the temperature of the fixed thermocouple falls, indicating an upward movement of the flame. Presumably the main reaction zone is being repelled by the upward moving thermocouple wire, so that the traversing thermocouple has moved less distance through the flame than it has with respect to the burner and, to correct the profile for this movement, the distance coordinate must be moved upstream correspondingly. The corrected profile (also shown in Fig. l) was obtained using the slope of the temperature profile through the flame, i.e. dT/dz at the reference level, and the change in temperature indicated by the reference thermocouple to derive the distance correction. Temperature profiles were obtained for a series of flames containing between 1.23 and 1.38 molY/o Calls, in which the ratio [O2]:[Ar ] was 15:85, and Fig. 2 shows two typical profiles for the rate of heat release Q. Below the schlieren plane (taken as the zero for the distance coordinate) there is very little chemical reaction and the temperature rise is solely due to heat conduction back from the hotter parts of the flame. Q then rises very rapidly to a maximum and falls back to zero as the final equilibrium composition in the flame is attained. Increasing the initial concentation of propane has two effects; the overall thickness of the flame decreases and Qmax increases, but although the latter occurs earlier in the flame on a distance basis it is reached at a higher temperature (see Table 1). The integrated heat release h in the postflame zone, i.e., when Q had fallen back to zero, was always 98.5-100% of the expected value, which gives a check on the internal consistency of the calculations. Figure 3 shows the variation in Qmax with mixture composition, together with the values reported earlier [5]. The present values are not only more consistent from flame to flame but they are generally higher, and this can be attributed to the correction for movement of the flame during the traverse of the thermocouple. Although Qm,~ increases steadily with the initial concentration of propane, the value of h at this level is remarkably
180
S.J. COOK and R. F. SIMMONS i
|
II
I
I
1500
4) Im
I000
QQQIBQtQ~OQaQa~IQ~
Q
t~ 4) Q.
4)
I--
/
S
500
'
,/
'
-2
!
0 Distance
I
2 /ram
Fig. 1. Comparison of experimental and corrected temperature profiles through a flat propane-oxygen-argon flame. - - , experimental profile; - - - , corrected profile; ---, temperature of reference level in flame.
constant at 48 _+3~, which is identical to the value reported by Friedman and Burke [3]. With the leaner flames a plot of In Q against 1/T gives a good straight line, as shown in Fig. 4. These data cover a distance of nearly 2 mm and temperatures from 480 to 1100K, and it is surprising that an Arrhenius relation should be followed over such a wide range; the associated activation energy is 5 kcal tool- 1. Figure 4 also shows that with a richer flame the plot is slightly curved; but even so, the two sets of data superimpose remarkedly well, and this
is the case when data for a number of different flames are plotted together. The simplest interpretation of this observation is that the rate of heat release in the early part of the flame is primarily controlled by a single reaction step with an activation energy of 5 kcal mol- t.
CompositionPrordes The composition profiles confirm that there is little consumption of propane before the schlieren plane
STRUCTURE OF LEAN PROPANE-OXYGEN FLAMES
181
1
20
o
15
0
0
0
•,..
5
-2
0
2
O i s t a rice, z l
4
mm
Fig. 2. Typical heat release profiles. Composition of flame: A, 1.26 tool% C3H8; % 1.39 mol% Call 8.
is reached, and the slight decrease which does occur is due almost entirely to diffusion. As the flame reactions begin, however, Xc3n8 decreases rapidly and Xco passes through a maximum as expected [4] (see Fig. 5). Propane is consumed both earlier and more rapidly as the initial concentration of propane is increased, which is in accord with the profiles for Q, and the maximum value of Xco is
also higher and occurs earlier. A check on the conservation of carbon atoms showed a deviation between + 10~ and - 3 ~ through most of the flame, but rising to a maximum of + 18~ in the region where Xc3us was falling rapidly. In this region, however, the diffusion velocity of propane is very high, so that even a slight overestimate of this value gives a positive deviation in the carbon
182
S. J. COOK and R. F. SIMMONS TABLE 1 Effect of Initial Mixture Composition on the Temperature at Which Qmax and Maximum Reaction Rates Are Reached Temperature/K at Rmax
CaH8/mol% 1.28 1.30 1.35 1.38
Qmax
-RcaH 8
-Ro 2
RCO
-Rco
RCO 2
1130 1235 1250 1300
1105 1165 1160 1185
1320 1210 1280 1370
1155 1115 1160 1185
1325 1285 1325 1400
1360 1260 1355 1360
balance. Even so, the observed deviations are not sufficiently large to effect any of the conclusions from this work. The typical reaction rate profiles given in Fig. 6 show that as the rate of consumption of propane increases there is a corresponding increase in the rate of formation of carbon monoxide, and both rates reach their maximum value at the same temperatures (l160K). At this level, the rate of removal of oxygen is still rising rapidly and it reaches its maximum value at 1280K, while the consumption of carbon monoxide and formation of carbon dioxide reach their maximum rates a little later (at 1325 and 1355K, respectively). In this region of the flame a temperature difference of 50K corresponds to a spatial separation ot~only 0.1 mm, but Table 1 shows that the same separation is observed in the other flames as well. Table 2 summarizes these maximum rates as a function of initial mixture composition, and there is a steady increase with increasing initial concentration of propane. In the vicinity of the maximum value of --Rc3H8 the ratio (Rco+Rco)/-Rc3Hs has a value of 3.1_+0.3 and the maximum values of -Rco and Rco2 are normally equal (RcojRco=l.0-+O.1). These simple checks give added confidence that the analysis of the experimental data is essentially correct: OH+CO=CO2 +H,
(1)
H+O2=OH+O.
(2)
The conversion of carbon monoxide to carbon dioxide is known [13] to occur by reaction (I), and
the rate constant for this reaction is well established [14]. At a given temperature in the flame Rco2=k,[OH][CO], and hence the experimental values of R c o 2 a n d Xco appropriate to that temperature can be used to calculate X on. Similarly, once X c3~ s has fallen to a very low level, the only important removal process for oxygen is reaction (2), so that the experimental values of - R o 2 and Xo2 can be combined with the known [14] value of k 2 at that temperature to calculate X H. The typical profiles shown in Fig. 7 were obtained in this way, and it will be seen that the radical concentrations do not begin to rise rapidly until the temperature reaches 1200K. X o , is at least an order of magnitude greater than X n, as expected for a lean flame, but X Hreaches its maximum value slightly before X o.. DISCUSSION The experimental results show that there is no significant consumption of propane below 700K and its maximum rate of removal occurs between 1150 and 1200K. The most likely removal process is reaction with hydroxyl radicals: .~ n-Call7 + H 2 0 OH + C3Ha. ~ i'C3H7 + H:O.
(3p) (3s)
The apparent activation energy for the rate of heat release in the early part of the flame eliminates reaction with H or HO2 as major removal pro-
STRUCTURE OF LEAN PROPANE-OXYGEN FLAMES
a
183
e
.
20
15 T I
E U R
t~
I0
A
E 0
&
&
&
5
I
I
I
1.25
1.30
1-35
Mole
per
cent
C3H8
Fig. 3. Variation in the maximum rate of heat release with initial concentration of propane: O, present work;A, values obtained earlier [4].
184
S.J. COOK and R. F. SIMMONS
!
I
I
2
i.
0
0 f-
0
-I I
I
I
1.0
1.5
2-0
103KIT Fig. 4. Variation of In Q and In (Q/XcaHR) with lIT in the early part of the flame: o, e, In Q; A, , In (Q/XcaHs). Composition of flames: e, •, 1.28 mol% Calls; o, A, 1.35 mol% C3H8.
STRUCTURE O F LEAN PROPANE-OXYGEN FLAMES
185
•
|
16
x
12
c O m
O ¢9
i ~t
8
O
4
-2
0 Distance,
2 zlmm
Fig. 5. Typical composition profiles: A, I03XC3Hs; E~, e, 103Xco; ~, 4 Open symbols: 1.38 mol% C3H8. Full symbols: 1.28 mol% C3H8.
×
102Xco 2.
i
186
S . J . C O O K and R. F. SIMMONS
u)
4
I
E m
0
E 2
Xl" I
0 w
om
0 tO tJ t~
-2
-4
0
I Distance,
2 z /
mm
Fig. 6. Typical reaction rate profiles: :x, C3H8 ; ~7, 02: ®, CO; o, CO 2. Initial concentration of propane: 1.35 tool% Call a.
TABLE 2 Variation in Maximum Reaction Rates with Initial Mixture Composition Maximum reaction rate/lO--4 mol cm--a s--1 Calla/tool% 1.28 1.30 1.35 1.38
-Rc3H 8
-Ro 2
0.95 1.09 1.20 1.50
1.95 2.02 2.70 3.20
RCO 2.52 3.14 2.70 3.20
-Rco
RCO 2
2.42 3.20 4.00 4.60
2.20 3.48 3.20 4.30
STRUCTURE OF LEAN PROPANE-OXYGEN FLAMES II
187
w
5 I t
t t I
I
| | I I 1 1 I t t t t
1.5
4
t
3
t t t
m
t
O
t I t
I'O
X
I t
O
-I-
-IX
2
I I
O m 0"5
1200
Temperature/K
1400
Fig. 7. Variation in X H and XOH with temperature in the flame: G, H; A, OH. - - - , quasi-equilibrium values for X O. Initial concentration of propane: 1.35 mol% Call s.
cesses, since these reactions have activation energies of 8.8 and 18.0 kcal mol- 1, respectively [151. In contrast, reactions (3p) and (3s) have activation energies [,151 of only 1.7 and 0.9 kcal mol- 1, which are well below the 5 kcal tool- 1 obtained from the rate of heat release. If this is controlled solely by the rate of reactions (3p) and (3s), Qocka['OH]['CaHs],
so that a plot of In (Q/[-C3H8])against 1/T should give a straight line if [OH] remains constant. Figure 4 shows that this is obtained in the early part of the flame and the activation energy (2-3 kcal tool- 1) is quite close to the overall value expected for reactions (3p) and (3s). The data in Fig. 8 are perhaps even more convincing. This shows profiles for X OHobtained from R co 2(discussed earlier) and from - R c 3 u s using the experimenta! values for
188
S.J. COOK and R. F. SIMMONS
-3 -i-
O X
o~ O m
-4
-5
/
!
!
IOOO
|
14OO TemperaturelK
Fig. 8. Variation in In XOH with temperature in the flame: ®, from -Rc3H8 and XC3H8; e, from RCO2 and XCO. Initial concentration of propane: 1.35 mo]% C3H8.
Xc3H8 and the known [15] values of k3p and k3s. These cover different parts of the flame, but where they overlap they are in excellent agreement. The rates of formation of n-propyl and i-propyl radicals will be approximately equal, since kap~ k 3~ in the temperature range of interest [15] and these radicals will either undergo reaction with oxygen to give the conjugate olefln or undergo unimolecular decomposition. In the case of the i-propyl radical these two paths are kinetically equivalent in the early part of the flame, since propylene is formed in
both reactions and the hydrogen atom formed in reaction (5) will react predominently by reaction (7) below 1000K. The known rate constants [15] for reactions (4) and (6) show that even at 750K reaction (6) is about four times faster than reaction (4) under flame conditions and its importance will increase with increasing temperature since it has the higher activation energy. Fristrom et al. [16] detected propylene, ethylene, ethane, acetylene, and methane as intermediates in a stoichiometric propane--air flame burning at 0.25 atm, which can
STRUCTURE OF LEAN PROPANE-OXYGEN FLAMES be taken as general support for the preceding discussion about the fate of the propyl radicals, but their analytical procedure was such that there was a time lag of 3-5 min between taking the sample and making the analysis. It seems clear, therefore, that the initial stages of the oxidation can be considered as an oxygen-induced decomposition of the fuel: C3H7+ O 2 = C 3 H 6 + H O 2 ,
(4)
n-C3H7 =C3H6 + H,
(5)
i-C3H ~---C2H++CH 3,
(6)
H+O2+M=HO2+M.
(7)
The main features of the subsequent oxidation are also fairly clear. The propylene and ethylene will be removed by reaction such as OH + C2H 4 = CH 3 + HCHO,
(8)
while the methyl radicals formed in reactions (6) and (8) can react with molecular oxygen to give formaldehyde (detected as an intermediate in the early part of the flame I17]) or with oxygen atoms diffusing back from the hotter parts of the flame. Calculations by Dixon-Lewis [18] show that recombination of methyl radicals to give ethane can occur in a methane-air flame and presumably the same reaction can occur in the present propane flame. Methane can be formed by H atom abstraction from a hydrocarbon species by the methyl radical and acetylene by the degradative oxidation of ethylene. The main route, however, must be the oxidation steps as these lead rapidly to the formation of carbon monoxide and the regeneration of chain centers, as required for a chain reaction: OH + C O = C O 2 + H ,
(1)
H + 0 2 --- OH + O,
(2)
O + H 2 0 = 2OH.
(9)
The subsequent conversion of carbon monoxide to carbon dioxide, which occurs by reaction (I),is important from quite early in the flame, as shown
189
by Fig. 5. The major part of this conversion, however, occurs at temperatures above 1000K, and at about this temperature the branching reaction (2) begins to be important. Up to this temperature any hydrogen atoms present will react predominently by reaction (7) or with propane, but above 1000K reaction (2) is of increasing importance as the temperature rises [6]. The oxygen atoms formed in reaction (2) are unlikely to react with propane, since Xc3as has fallen to a low value by this level in the flame, and the only alternatives that can be envisaged are reaction with methyl radicals and reaction (9). The latter has the added advantage that reactions (1), (2), and (9) constitute a branching cycle of reactions that produce three OH radicals for every OH which enters the cycle. Thus there can be a very rapid increase in radical concentration above 1000K as found experimentally. It should be noted that in the absence of any reaction of oxygen atoms, reactions (1) and (2) only form a straight chain, and that the rate controlling process in this branching cycle is reaction (9) and not reaction (2); the lifetime of the oxygen atom is about an order of magnitude greater than the lifetime of the hydrogen atom. The analysis of the present results also leads to two other conclusions. The first of these concerns the assumption made by a number of workers that a quasicquilibrium exists between the radical species. If this is the case, a profile for X o can be calculated from the known values of X ,, X o2, X o,, and the equilibrium constant for reaction (2). Figure 7 shows that this only leads to a sensible result in the region of the flame where the radical concentrations are decaying to their final equilibrium values. The second concerns the role of the HO 2 radical in the mechanism below 1000K. The net result of the mechanism is to convert the reactive OH radical into an HO 2 radical, which must regenerate an OH radical unless the reaction in this region of the flame is maintained solely by diffusion of this species from the hotter parts of the flame. This seems most unlikely. Reaction with propane can bc rejected since this will be far too slow even at 1000K, as will the decomposition of hydrogen peroxide [14] formed in the reaction
HO 2+HO 2--H202+O2.
(10)
190
S.J. COOK and R. F. SIMMONS
The most likely way in which HO 2 radicals regenerate OH is by the quadratic branching reaction (11): H+HO2=2OH.
(11)
Estimates of the probable [HO2] below 1000K show that reaction (11) should be able to compete with reaction (7) in this region. The authors wish to thank The Associated Octel Company Jbr financial support during the course of this work. REFERENCES 1. Fristrom, R. M., and Westenberg, A. A., J. Phys. Chem. 65:591 (1961). 2. Peeters, J., and Mahnen, G., Fourteenth Symposium (International} on Combustion, The Combustion Institute, 1973, p. 133. 3. Friedman, R., and Burke, E.,J. Chem. Phys. 22:824 (1954). 4. Fristrom, R. M., and Westenberg, A. A., Combust. Flame 1:217 (1957). 5. Pownall, C., and Simmons, R. F., Thirteenth Symposium (International} on Combustion, The Combustion Institute, 1975, p. 585.
6. Cooke, S. J., and Simmons, R. F., Seventeenth Symposium (International} on Combustion, The Combustion Institute, 1979, p. 891. 7. Fristrom, R. M., and Westenberg, A. A., Flame Structure, McGraw-Hill,New York, 1965. 8. Westenber$, A. A., Raezer, S. D., and Fristrom, R. M., Combust. Flame 1:467 (1957). 9. Brokaw, R. S.,Ind. Eng. Chem. 47:2398 (1955). 10. Hirshfelder, J. O., Curtiss, C. F., and Bird, R. B., The Molecular Theory of Gases and Liquids, John Wiley, New York, 1954. 11. Kaskan, W. E., Sixth Symposium (International) on Combustion, Reinhold, 1957, p. 134. 12. Bradley, D.,Brit. J. AppL Phys. 17:1155 (1966). 13. Freidman, R. M., and Cyphers, J. A., £ Chem. Phys. 23:1875 (1955). 14. Baulch, D. L., Drysdale, D. D., Horne, D. G., and Lloyd, A. C., Evaluated Kinetic Data for High TemperatureReactions, Butterworths, London, 1972. 15. Walker, R. W., Reaction Kinetics L The Chemical Society, 1975, p. 161. 16. Fristrom, R. M., Prescott, R., and Grunfelder, C., Combust. Flame 1:102 (1957). 17. Pownall, C., Ph.D. Thesis, University of Manchester, 1971. 18. Dixon-Lewis, G., private communication.
Received 19 March 1981; revised 5 August 1981
177
A Flame Structure Study of Lean Propane-Oxygen Flames Diluted with Argon S. J. COOK and R. F. SIMMONS The University of Manchester Institute of Science and Technology, Manchester, England
Temperature and composition profiles have been obtained through a series of fiat flames containing between 1.23 and 1.38 mol% C3H s, in which the ratio [02] : [Ar] was kept constant at 15 : 85. These profiles have been analysed in terms of the continuity equations for mass, energy, and individual species to obtain the heat release and reaction rates as a function of distance through the flame, and hence information about the reactions which control the propagation of the flame. it is concluded that the heat release in the early part of the flame is controlled by the rate of the reaction: OH + C a l l 8 = H 2 0 + C a l l 7. The subsequent steps in the oxidation are discussed in the light of known rate constant data for the likely reactions and it is shown that the initial steps in the mechanism can be considered as an oxygen-induced decomposition of the propane. Chain branching is unimportant below 1000K, but above this temperature [H] and [OH] rise rapidly, reaching their maximum values in the range 1300-1400K (final flame temperatures in the range 1500-1600K). In all cases, the maximum [H] was reached at a slightly lower temperature than the maximum for [OH], and it is shown that quasi-equilibrium between H, O, and OH can only exist in the region where the radical concentrations are decaying to their equilibrium levels. The fate of the oxygen atoms produced in the branching reaction H+O2=OH+O is considered, and it is concluded that the predominant removal process is O + H 2 0 = 2OH
INTRODUCTION There have been a number of detailed structural studies of flat methane-oxygen flames [1, 2] and these have yielded useful information about the individual reactions which are important in such flames. In many ways, however, methane is not a typical hydrocarbon fuel, particularly in its oxidation characteristics, and thus it is surprising that there has been no detailed mechanistic analysis for a more typical fuel such as propane. Friedman and Burke [3] have studied the heat release rate Copyright © 1982 by The Combustion Institute Published bY Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY ! 0017
through a lean propane-air flame burning at low pressure (0.06 atm) and Fristrom and Westenberg [4] have reported the results of a detailed structure study of an approximately stoichiometric propaneair flame burning at 0.25 atm on a conical burner. Some more detailed information has been presented by Simmons et al. [5, 6], but these latter papers are primarily concerned with the effect of hydrogen bromide and tetraethyl lead, respectively, on the propagation of the flame. The present paper is concerned with a detailed study of lean flames burning at atmospehric pressure in the absence of any additive. Temperature
0010-2180/82/05177+ 14502.75
178 and composition profiles are presented for a series of lean flames diluted with argon, and the results are used to discuss the important rate-controlling reactions in the various parts of the flame. EXPERIMENTAL
Details of the burner, thermocouple, and microprobe have been given elsewhere [5]. The thermocouple (0.0025-cm-diam Pt/Pt-Rh coated with silica [7]) was traversed slowly (,--0.5 mm min-1) through the flame by a small electric motor and the output from the thermocouple was fed to a potentiometric recorder. A second thermocouple bead was positioned in the flame where the temperature rises steeply, and approximately linearly with distance, to detect any movement of the flame during the traverse, and the change in temperature from the second thermocouple was used to apply a temperature correction to the recorded temperature profile. It should be noted that in the region of maximum temperature gradient the temperature increased by ~ 10K in 0.05 mm, a comparable distance to the typical diameter of the thermocouple beads (< 0.04 mm), and that the corrected profiles for a given flame were very reproducible and did not vary with the direction in which the traverse was made. This gave added confidence that the temperature profiles were reliable, but as an added precaution a number of traverses were made in each direction with each flame, so that they could be averaged. The quartz microprobes had an orifice diameter <20 p, so that the disturbance to the gas flow upstream of the probe tip was restricted to a distance of 0,05--0.1 mm; under these conditions any aerodynamic effect of introducing the probe into the flame is minimal [8]. The sample from the microprobe was fed to the continuous sampling system of an MS 10 mass spectrometer, and this was designed so that viscous flow was maintained and the major part of the sample was pumped away through a bypass line. Thus the composition of the sample entering the mass spectrometer was identical to that of the original sample and the analysis was made almost instantaneously. These concentration measurements were made on a point-to-point basis through the flame at very
S.J. COOK and R. F. SIMMONS close intervals, the position of the tip of the probe being noted for each determination in relation to the temperature profile by the use of a thermocouple arranged at the side of the probe. Both the temperature and the composition profiles were obtained in terms of an absolute distance through the flame by noting the position of the thermocouple bead, in relation to the schlieren plane of the flame, at the beginning and end of each traverse. The experimental profiles were analyzed in terms of the continuity equations for mass, energy, and species which apply to a flat flame [7]. These give the rate of heat release Q as Q = d(2 d T / d z ) / d z
- povoCp(dT/dz),
where P0 is the density and Vo the average flow velocity of the initial mixture at the schlieren plane, 2 is the thermal conductivity and ~'p the average specific heat of the mixture at temperature T, while z is the distance coordinate through the flame. For the purposes of these calculations t~p and 2 were obtained from the values of oxygen and argon alone, using the mixing formula given by Brokaw [9], since these components comprise >98% of the initial mixture. The variation in these values with temperature was represented by a polynomial in T so that the values for the given temperature could be used in the computation. The species conservation equation leads to the following expression for the rate of reaction R i of species i: R i = (pOVO/Mi)(dG i/dz),
where M~ is the molecular weight of species i and G~ its mass flux fraction. The latter is given by G, = ( M , X J E M i X , ) [ ( v + V~)/v] = NiMi(v + Vi)/PoVo,
where v is the flow velocity, Vi the diffusion velocity, and N i the concentration of species i. In this analysis it has been assumed that the stream/tube area ratio is unity, since all measurements have been made with the schlieren plane as the reference level for PoVo and chemical reaction was essentially
STRUCTURE OF LEAN PROPANE-OXYGEN FLAMES complete within 2-3 mm. Since p = pK/I/RT, where /('/is the average molecular weight of the mixture, the flow velocity v was obtained directly from the temperature profile and the continuity equation for mass (pv=PoVo). The diffusion velocities were obtained by Fick's law using binary diffusion coefficients for the various species in argon, since the latter always comprised > 80% of the mixture. These binary diffusion coefficients were calculated using the Lennard-Jones potential [10]. The experimental data gave a series of values for T and X~ at 0.1-mm intervals through the flame and a computer program was used to calculate the various quantities required in the analysis [6]. The profile extended over a minimum distance of 5 mm and thus at least 50 values of each quantity were used in the analysis of each flame. The first stage in this analysis was to apply a radiation correction to the measured temperatures using the equation derived by Kaskan [11]. The appropriate value of the thermal conductivity was obtained from the polynomial expression in T used in the subsequent analysis of the temperature profile (see earlier) and the variation in the emissivity of the thermocouple wire with temperature was also taken into account. This was done by using the data of Bradley [12] for the emissivity of 0.005-cm-diam silica-coated platinum wire to derive the necessary polynomial expression in T. The magnitude of the radiation correction increased with temperature, but for an observed temperature of 1400K the correction was only about 70K, and the maximum correction in the hottest flames was only ~ 120K. The corrected final flame temperature was always within _ 15K of the calculated adiabatic flame temperature and this gave added confidence in the reliability of the values.
RES[~.LTS Temperature Profiles Figure 1 shows the results from a typical thermocouple traverse. The output from the fixed thermocouple shows some drift occurred in the position of the flame front (in an upward direction)
179
during the traverse, since its recorded temperature is slightly higher at the beginning than at the end of the traverse; as the moving thermocouple approaches the reaction zone of the flame the temperature of the fixed thermocouple falls, indicating an upward movement of the flame. Presumably the main reaction zone is being repelled by the upward moving thermocouple wire, so that the traversing thermocouple has moved less distance through the flame than it has with respect to the burner and, to correct the profile for this movement, the distance coordinate must be moved upstream correspondingly. The corrected profile (also shown in Fig. l) was obtained using the slope of the temperature profile through the flame, i.e. dT/dz at the reference level, and the change in temperature indicated by the reference thermocouple to derive the distance correction. Temperature profiles were obtained for a series of flames containing between 1.23 and 1.38 molY/o Calls, in which the ratio [O2]:[Ar ] was 15:85, and Fig. 2 shows two typical profiles for the rate of heat release Q. Below the schlieren plane (taken as the zero for the distance coordinate) there is very little chemical reaction and the temperature rise is solely due to heat conduction back from the hotter parts of the flame. Q then rises very rapidly to a maximum and falls back to zero as the final equilibrium composition in the flame is attained. Increasing the initial concentation of propane has two effects; the overall thickness of the flame decreases and Qmax increases, but although the latter occurs earlier in the flame on a distance basis it is reached at a higher temperature (see Table 1). The integrated heat release h in the postflame zone, i.e., when Q had fallen back to zero, was always 98.5-100% of the expected value, which gives a check on the internal consistency of the calculations. Figure 3 shows the variation in Qmax with mixture composition, together with the values reported earlier [5]. The present values are not only more consistent from flame to flame but they are generally higher, and this can be attributed to the correction for movement of the flame during the traverse of the thermocouple. Although Qm,~ increases steadily with the initial concentration of propane, the value of h at this level is remarkably
180
S.J. COOK and R. F. SIMMONS i
|
II
I
I
1500
4) Im
I000
QQQIBQtQ~OQaQa~IQ~
Q
t~ 4) Q.
4)
I--
/
S
500
'
,/
'
-2
!
0 Distance
I
2 /ram
Fig. 1. Comparison of experimental and corrected temperature profiles through a flat propane-oxygen-argon flame. - - , experimental profile; - - - , corrected profile; ---, temperature of reference level in flame.
constant at 48 _+3~, which is identical to the value reported by Friedman and Burke [3]. With the leaner flames a plot of In Q against 1/T gives a good straight line, as shown in Fig. 4. These data cover a distance of nearly 2 mm and temperatures from 480 to 1100K, and it is surprising that an Arrhenius relation should be followed over such a wide range; the associated activation energy is 5 kcal tool- 1. Figure 4 also shows that with a richer flame the plot is slightly curved; but even so, the two sets of data superimpose remarkedly well, and this
is the case when data for a number of different flames are plotted together. The simplest interpretation of this observation is that the rate of heat release in the early part of the flame is primarily controlled by a single reaction step with an activation energy of 5 kcal mol- t.
CompositionPrordes The composition profiles confirm that there is little consumption of propane before the schlieren plane
STRUCTURE OF LEAN PROPANE-OXYGEN FLAMES
181
1
20
o
15
0
0
0
•,..
5
-2
0
2
O i s t a rice, z l
4
mm
Fig. 2. Typical heat release profiles. Composition of flame: A, 1.26 tool% C3H8; % 1.39 mol% Call 8.
is reached, and the slight decrease which does occur is due almost entirely to diffusion. As the flame reactions begin, however, Xc3n8 decreases rapidly and Xco passes through a maximum as expected [4] (see Fig. 5). Propane is consumed both earlier and more rapidly as the initial concentration of propane is increased, which is in accord with the profiles for Q, and the maximum value of Xco is
also higher and occurs earlier. A check on the conservation of carbon atoms showed a deviation between + 10~ and - 3 ~ through most of the flame, but rising to a maximum of + 18~ in the region where Xc3us was falling rapidly. In this region, however, the diffusion velocity of propane is very high, so that even a slight overestimate of this value gives a positive deviation in the carbon
182
S. J. COOK and R. F. SIMMONS TABLE 1 Effect of Initial Mixture Composition on the Temperature at Which Qmax and Maximum Reaction Rates Are Reached Temperature/K at Rmax
CaH8/mol% 1.28 1.30 1.35 1.38
Qmax
-RcaH 8
-Ro 2
RCO
-Rco
RCO 2
1130 1235 1250 1300
1105 1165 1160 1185
1320 1210 1280 1370
1155 1115 1160 1185
1325 1285 1325 1400
1360 1260 1355 1360
balance. Even so, the observed deviations are not sufficiently large to effect any of the conclusions from this work. The typical reaction rate profiles given in Fig. 6 show that as the rate of consumption of propane increases there is a corresponding increase in the rate of formation of carbon monoxide, and both rates reach their maximum value at the same temperatures (l160K). At this level, the rate of removal of oxygen is still rising rapidly and it reaches its maximum value at 1280K, while the consumption of carbon monoxide and formation of carbon dioxide reach their maximum rates a little later (at 1325 and 1355K, respectively). In this region of the flame a temperature difference of 50K corresponds to a spatial separation ot~only 0.1 mm, but Table 1 shows that the same separation is observed in the other flames as well. Table 2 summarizes these maximum rates as a function of initial mixture composition, and there is a steady increase with increasing initial concentration of propane. In the vicinity of the maximum value of --Rc3H8 the ratio (Rco+Rco)/-Rc3Hs has a value of 3.1_+0.3 and the maximum values of -Rco and Rco2 are normally equal (RcojRco=l.0-+O.1). These simple checks give added confidence that the analysis of the experimental data is essentially correct: OH+CO=CO2 +H,
(1)
H+O2=OH+O.
(2)
The conversion of carbon monoxide to carbon dioxide is known [13] to occur by reaction (I), and
the rate constant for this reaction is well established [14]. At a given temperature in the flame Rco2=k,[OH][CO], and hence the experimental values of R c o 2 a n d Xco appropriate to that temperature can be used to calculate X on. Similarly, once X c3~ s has fallen to a very low level, the only important removal process for oxygen is reaction (2), so that the experimental values of - R o 2 and Xo2 can be combined with the known [14] value of k 2 at that temperature to calculate X H. The typical profiles shown in Fig. 7 were obtained in this way, and it will be seen that the radical concentrations do not begin to rise rapidly until the temperature reaches 1200K. X o , is at least an order of magnitude greater than X n, as expected for a lean flame, but X Hreaches its maximum value slightly before X o.. DISCUSSION The experimental results show that there is no significant consumption of propane below 700K and its maximum rate of removal occurs between 1150 and 1200K. The most likely removal process is reaction with hydroxyl radicals: .~ n-Call7 + H 2 0 OH + C3Ha. ~ i'C3H7 + H:O.
(3p) (3s)
The apparent activation energy for the rate of heat release in the early part of the flame eliminates reaction with H or HO2 as major removal pro-
STRUCTURE OF LEAN PROPANE-OXYGEN FLAMES
a
183
e
.
20
15 T I
E U R
t~
I0
A
E 0
&
&
&
5
I
I
I
1.25
1.30
1-35
Mole
per
cent
C3H8
Fig. 3. Variation in the maximum rate of heat release with initial concentration of propane: O, present work;A, values obtained earlier [4].
184
S.J. COOK and R. F. SIMMONS
!
I
I
2
i.
0
0 f-
0
-I I
I
I
1.0
1.5
2-0
103KIT Fig. 4. Variation of In Q and In (Q/XcaHR) with lIT in the early part of the flame: o, e, In Q; A, , In (Q/XcaHs). Composition of flames: e, •, 1.28 mol% Calls; o, A, 1.35 mol% C3H8.
STRUCTURE O F LEAN PROPANE-OXYGEN FLAMES
185
•
|
16
x
12
c O m
O ¢9
i ~t
8
O
4
-2
0 Distance,
2 zlmm
Fig. 5. Typical composition profiles: A, I03XC3Hs; E~, e, 103Xco; ~, 4 Open symbols: 1.38 mol% C3H8. Full symbols: 1.28 mol% C3H8.
×
102Xco 2.
i
186
S . J . C O O K and R. F. SIMMONS
u)
4
I
E m
0
E 2
Xl" I
0 w
om
0 tO tJ t~
-2
-4
0
I Distance,
2 z /
mm
Fig. 6. Typical reaction rate profiles: :x, C3H8 ; ~7, 02: ®, CO; o, CO 2. Initial concentration of propane: 1.35 tool% Call a.
TABLE 2 Variation in Maximum Reaction Rates with Initial Mixture Composition Maximum reaction rate/lO--4 mol cm--a s--1 Calla/tool% 1.28 1.30 1.35 1.38
-Rc3H 8
-Ro 2
0.95 1.09 1.20 1.50
1.95 2.02 2.70 3.20
RCO 2.52 3.14 2.70 3.20
-Rco
RCO 2
2.42 3.20 4.00 4.60
2.20 3.48 3.20 4.30
STRUCTURE OF LEAN PROPANE-OXYGEN FLAMES II
187
w
5 I t
t t I
I
| | I I 1 1 I t t t t
1.5
4
t
3
t t t
m
t
O
t I t
I'O
X
I t
O
-I-
-IX
2
I I
O m 0"5
1200
Temperature/K
1400
Fig. 7. Variation in X H and XOH with temperature in the flame: G, H; A, OH. - - - , quasi-equilibrium values for X O. Initial concentration of propane: 1.35 mol% Call s.
cesses, since these reactions have activation energies of 8.8 and 18.0 kcal mol- 1, respectively [151. In contrast, reactions (3p) and (3s) have activation energies [,151 of only 1.7 and 0.9 kcal mol- 1, which are well below the 5 kcal tool- 1 obtained from the rate of heat release. If this is controlled solely by the rate of reactions (3p) and (3s), Qocka['OH]['CaHs],
so that a plot of In (Q/[-C3H8])against 1/T should give a straight line if [OH] remains constant. Figure 4 shows that this is obtained in the early part of the flame and the activation energy (2-3 kcal tool- 1) is quite close to the overall value expected for reactions (3p) and (3s). The data in Fig. 8 are perhaps even more convincing. This shows profiles for X OHobtained from R co 2(discussed earlier) and from - R c 3 u s using the experimenta! values for
188
S.J. COOK and R. F. SIMMONS
-3 -i-
O X
o~ O m
-4
-5
/
!
!
IOOO
|
14OO TemperaturelK
Fig. 8. Variation in In XOH with temperature in the flame: ®, from -Rc3H8 and XC3H8; e, from RCO2 and XCO. Initial concentration of propane: 1.35 mo]% C3H8.
Xc3H8 and the known [15] values of k3p and k3s. These cover different parts of the flame, but where they overlap they are in excellent agreement. The rates of formation of n-propyl and i-propyl radicals will be approximately equal, since kap~ k 3~ in the temperature range of interest [15] and these radicals will either undergo reaction with oxygen to give the conjugate olefln or undergo unimolecular decomposition. In the case of the i-propyl radical these two paths are kinetically equivalent in the early part of the flame, since propylene is formed in
both reactions and the hydrogen atom formed in reaction (5) will react predominently by reaction (7) below 1000K. The known rate constants [15] for reactions (4) and (6) show that even at 750K reaction (6) is about four times faster than reaction (4) under flame conditions and its importance will increase with increasing temperature since it has the higher activation energy. Fristrom et al. [16] detected propylene, ethylene, ethane, acetylene, and methane as intermediates in a stoichiometric propane--air flame burning at 0.25 atm, which can
STRUCTURE OF LEAN PROPANE-OXYGEN FLAMES be taken as general support for the preceding discussion about the fate of the propyl radicals, but their analytical procedure was such that there was a time lag of 3-5 min between taking the sample and making the analysis. It seems clear, therefore, that the initial stages of the oxidation can be considered as an oxygen-induced decomposition of the fuel: C3H7+ O 2 = C 3 H 6 + H O 2 ,
(4)
n-C3H7 =C3H6 + H,
(5)
i-C3H ~---C2H++CH 3,
(6)
H+O2+M=HO2+M.
(7)
The main features of the subsequent oxidation are also fairly clear. The propylene and ethylene will be removed by reaction such as OH + C2H 4 = CH 3 + HCHO,
(8)
while the methyl radicals formed in reactions (6) and (8) can react with molecular oxygen to give formaldehyde (detected as an intermediate in the early part of the flame I17]) or with oxygen atoms diffusing back from the hotter parts of the flame. Calculations by Dixon-Lewis [18] show that recombination of methyl radicals to give ethane can occur in a methane-air flame and presumably the same reaction can occur in the present propane flame. Methane can be formed by H atom abstraction from a hydrocarbon species by the methyl radical and acetylene by the degradative oxidation of ethylene. The main route, however, must be the oxidation steps as these lead rapidly to the formation of carbon monoxide and the regeneration of chain centers, as required for a chain reaction: OH + C O = C O 2 + H ,
(1)
H + 0 2 --- OH + O,
(2)
O + H 2 0 = 2OH.
(9)
The subsequent conversion of carbon monoxide to carbon dioxide, which occurs by reaction (I),is important from quite early in the flame, as shown
189
by Fig. 5. The major part of this conversion, however, occurs at temperatures above 1000K, and at about this temperature the branching reaction (2) begins to be important. Up to this temperature any hydrogen atoms present will react predominently by reaction (7) or with propane, but above 1000K reaction (2) is of increasing importance as the temperature rises [6]. The oxygen atoms formed in reaction (2) are unlikely to react with propane, since Xc3as has fallen to a low value by this level in the flame, and the only alternatives that can be envisaged are reaction with methyl radicals and reaction (9). The latter has the added advantage that reactions (1), (2), and (9) constitute a branching cycle of reactions that produce three OH radicals for every OH which enters the cycle. Thus there can be a very rapid increase in radical concentration above 1000K as found experimentally. It should be noted that in the absence of any reaction of oxygen atoms, reactions (1) and (2) only form a straight chain, and that the rate controlling process in this branching cycle is reaction (9) and not reaction (2); the lifetime of the oxygen atom is about an order of magnitude greater than the lifetime of the hydrogen atom. The analysis of the present results also leads to two other conclusions. The first of these concerns the assumption made by a number of workers that a quasicquilibrium exists between the radical species. If this is the case, a profile for X o can be calculated from the known values of X ,, X o2, X o,, and the equilibrium constant for reaction (2). Figure 7 shows that this only leads to a sensible result in the region of the flame where the radical concentrations are decaying to their final equilibrium values. The second concerns the role of the HO 2 radical in the mechanism below 1000K. The net result of the mechanism is to convert the reactive OH radical into an HO 2 radical, which must regenerate an OH radical unless the reaction in this region of the flame is maintained solely by diffusion of this species from the hotter parts of the flame. This seems most unlikely. Reaction with propane can bc rejected since this will be far too slow even at 1000K, as will the decomposition of hydrogen peroxide [14] formed in the reaction
HO 2+HO 2--H202+O2.
(10)
190
S.J. COOK and R. F. SIMMONS
The most likely way in which HO 2 radicals regenerate OH is by the quadratic branching reaction (11): H+HO2=2OH.
(11)
Estimates of the probable [HO2] below 1000K show that reaction (11) should be able to compete with reaction (7) in this region. The authors wish to thank The Associated Octel Company Jbr financial support during the course of this work. REFERENCES 1. Fristrom, R. M., and Westenberg, A. A., J. Phys. Chem. 65:591 (1961). 2. Peeters, J., and Mahnen, G., Fourteenth Symposium (International} on Combustion, The Combustion Institute, 1973, p. 133. 3. Friedman, R., and Burke, E.,J. Chem. Phys. 22:824 (1954). 4. Fristrom, R. M., and Westenberg, A. A., Combust. Flame 1:217 (1957). 5. Pownall, C., and Simmons, R. F., Thirteenth Symposium (International} on Combustion, The Combustion Institute, 1975, p. 585.
6. Cooke, S. J., and Simmons, R. F., Seventeenth Symposium (International} on Combustion, The Combustion Institute, 1979, p. 891. 7. Fristrom, R. M., and Westenberg, A. A., Flame Structure, McGraw-Hill,New York, 1965. 8. Westenber$, A. A., Raezer, S. D., and Fristrom, R. M., Combust. Flame 1:467 (1957). 9. Brokaw, R. S.,Ind. Eng. Chem. 47:2398 (1955). 10. Hirshfelder, J. O., Curtiss, C. F., and Bird, R. B., The Molecular Theory of Gases and Liquids, John Wiley, New York, 1954. 11. Kaskan, W. E., Sixth Symposium (International) on Combustion, Reinhold, 1957, p. 134. 12. Bradley, D.,Brit. J. AppL Phys. 17:1155 (1966). 13. Freidman, R. M., and Cyphers, J. A., £ Chem. Phys. 23:1875 (1955). 14. Baulch, D. L., Drysdale, D. D., Horne, D. G., and Lloyd, A. C., Evaluated Kinetic Data for High TemperatureReactions, Butterworths, London, 1972. 15. Walker, R. W., Reaction Kinetics L The Chemical Society, 1975, p. 161. 16. Fristrom, R. M., Prescott, R., and Grunfelder, C., Combust. Flame 1:102 (1957). 17. Pownall, C., Ph.D. Thesis, University of Manchester, 1971. 18. Dixon-Lewis, G., private communication.
Received 19 March 1981; revised 5 August 1981