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MALCOLM A. WEISS, ROBERT J. LANG, and JOHN P. LONGWELL Esso Research and Engineering Co., P.O. Box 12 1, Linden, N. J.
Combustion Rates in Spherical Reactors Effects of Inlet Temperature and Fuel Type Prediction of activation energy is confirmed as this follow-up extends earlier work to higher inlet temperatures and to 11 other fuels I
A N EARLIER discussion (7) presented data on combustion rates in insulated spherical reactors. A homogeneous mixture of iso-octane (2,2,4trimethylpentane) and air was injected through a small perforated ball a t the center of a spherical reactor into a concentric reaction space. Combustion occurred continuously in this reaction space, while the gases were vigorously stirred by the incoming jets. Products of combustion were exhausted through holes in the outer spherical walls of the reaction zone. These walls consisted of insulating firebrick to minimize heat losses. Because of the vigorous stirring in the reaction space, it was found useful to assume that the reactor was completely stirred-that the time of mixing of fresh material into the reacting gases was small compared to the time of reaction. If this assumption is true, rates of combustion are limited by the chemical kinetics of reaction between fuel and oxygen. Assuming an extremely simple reaction, quasikinetic constants were derived for the iso-octane-air system; the apparent over-all activation energy of the reaction was about 42,000 calories. This number was determined by trial as the value best matching the observed blowout data to the blowouts predicted by the simple reaction scheme. I n these earlier experiments, reaction temperature was yaried by varying fuel concentration (thus varying flame temperature). The inlet mixture temperature was held constant a t about 400' K. Another way to vary reaction temperature is to vary the inlet mixture
temperature as a check on the earlier activation energy. A second objective was to test fuels other than iso-octane; of interest were both fuel evaluation per se and the attempt to shed light on the combustion mechanism by interpreting the variation of combustion rates with fuel structure.
temperature a t any given fuel concentration. An apparent activation energy obtained by varying reaction temperature in this way would be independent of the activation energy obtained by varying reaction temperature via fuel concentration. Therefore, the first objective in this present work was to vary the inlet
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Figure 1.
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2 5 IO 20 50 REACTOR LOADING AT BLOWOUT, N/VP'.*
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Blowouts of iso-octane-air mixtures at high inlet temperatures
Comparison with values predicted from earlier low inlet temperature data
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4 Figure 2. Blowouts of nonaromatic hydrocarbons
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Reference curve for iro-octane
0.P > 0.8 atm. B.
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I]. Intermediate P
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Experiments at High Inlet Temperatures
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4 6 810 MOLES AIR/SECOND
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Table I.
Pressure
Air Rate (-V), Gram Moles/Sec. 1.589 1.447 1.010 0.970 1.157 1 274 0.977 1.165 1.576 1.015 1.434 1.160 1.579 1.540 0.977 1.489 1.173 1.268 1.149 0.959 1.274 1.579 1.160 1.121 1.156 1.013 1.157 1.534 1.440 1 589 1.151 0.959 1.157 0.966 1.271 1.151 1.012 1.436 1.528
( P ) ,h t m . 0.329 0.602 0.346 0.551 0.349 0.471 0.351 0.375 0.352 0.476 0.462 0.354 0.360 0.400 0.397 0.386 0.398 0.467 0.401 0.349 0.370 0.401 0.398 0.401 0.402 0.445 0.404 0.410 0.400 0.410 0.411 0.402 0.378 0.412 0.424 0.371 0.443 0.324 0.257 0.448 0.450 0.330 0.451 0.382 0.451 0.349 0.454 0.279 0.454 0.294 0.457 0.276 0.457 0.302 0.460 0.376 0.470 0.354 0.312 0.489 0.498 0.271 0.498 0.212 0.501 0.275 0.220 0.501 0.294 0.501 0.283 0.504 0.236 0.507 0.303 0.510 0.292 0.516 Adjusted t o Toe = 866OK. (1100"F.); V = 0.236liter I
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Lean Blowouts of Iso-octane-Air Mixtures at High Inlet Temperatures
Equivalence Ratio
a
~~~~
40
INDUSTRIAL AND ENGINEERING CHEMISTRY
Effective
Inlet Temp. (Toe), O K.
Adjusteda
878 874 868 878 892 898 876 883 843 872 889 880 872 892 876 887 872 889 884 884 879 866 879 917 884 876 883 891 869 858 885 883 885 877 869 890 876 877 892
15.3 16.7 16.3 22.2 15.6 17.6 20.0 24.4 30.6 27.9 31.7 23.8 27.2 29.2 28.6 28.7 27.5 28.1 33.3 42.1 36.9 38.0 30.6 35.4 40.1 41.0 38.1 32.7 38.9 61.6 46.3 60.6 45.1 58.7 47.5 41.6 54.0 49.5 51.7
s/V P ' J
Apparatus. The apparatus used was similar to That described previously. All of the tests at high inlet temperatures were performed in a 3-inch inside diameter (5-inch outside diameter) insulated reactor. Premixed and preheated air and iso-octane were injected through 102 holes 0.047 inch in diameter in a central ball 1 inch in outside diameter. fed by inlet tubes 5/la outside diameter. This reactor design was designated 3f and the reaction volume was about 0.24 liter. T o preheat air to a high inlet temperature, a small furnace was constructed of a refractorylined, 50-gallon oil drum containing about 40 feet of coiled, stainless steel, 3/,-inch pipe. I t was fired by premixed propane-air injected through a perforated distributor cap mounted in the bottom of the drum below the coil. Outlet air temperature was controlled by varying the firing fuel-air ratio and the air flow to the coil. Thirty nine runs were made, obtaining the lean blowouts of iso-octane-air mixtures. Measured inlet temperatures for these runs averaged 885' K. (1 134' F.). As a precaution against prereaction in the hot air stream, the isooctane was prevaporized and injected into the air stream just before the inlet tubes entered the reactor. Total exposure of iso-octane to hot air (at about 1100' F.) before entering the reaction zone probably did not exceed 0.5 millisecond. This time compares to reaction time ranging from about 1 to 0.4 millisecond at temperatures of about 2400' to 3100' F., respectively. Results. The blowout results are plotted in Figure 1 as the equivalence ratio a t blowout against the reactor loading, the air rate (A', gram moles of air per second) divided by reaction volume ( V , liters) and pressure ( P , atmospheres) to the 1.8 power. This is the loading group that best correlated the earlier results. All data are plotted as adjusted (using a n activation energy of 42.000 calories) to a n effective inlet temperature (Toe)of 1100' F. (866' K.). The effective inlet temperature for each run (Table I) is equal to the measured inlet temperature less an approximate correction due to heat losses through the insulating walls. This correction
S PH E R I C A L R E A C T O RS-COMBUSTI ON R A T E S ranged from 1' to 8' K. (averaging 5' K.) and was computed as in the previous work. For comparison, the mean curve through the earlier data a t an inlet temperature of 260' F. (400' K.) is also included in Figure 1. Using this curve and the original activation energy of 42,000 calories, blowout data at 1100' F. should have fallen on the dashed curve shown. Two additional dashed curves in Figure 1 predict location of the blowout data if the activation energy were 45 or 48 kcal. Flame temperatures used in this prediction are listed in Table 11. (The method of calculation was the same as in the earlier work, assuming that incomplete combustion results in carbon monoxide only; no iso-octane remains under any circumstances. In Table 11, no dissociation corrections were made. None of the experimental data included temperatures high enough for dissociation to be important.) O n the average, the 45-kcal. curve best fits the data, although there is some indication that the slope of the best curve through the data is slightly greater than the slope of the 45-kcal. curve. This value is a good check on the 42-kcal. value previously estimated from only the low inlet temperature data. One important aspect to determining the activation energy by changing inlet temperature is the activation energy's insensitivity to nontemperature parameters in the reaction rate equation. For example, the over-all reaction order of 1.8 would have to be in error by about 0.5 to cause a 1-kcal. error in activation energy (assuming a constant proportion between fuel and oxygen exponents in the reaction rate equation); the fuel exponent (assumed to be 0.8, with the oxygen exponent at l.O), would have to be in error by about 0.4 to cause a 3-kcal. error in activation energy (assuming a constant over-all reaction order). Therefore, regardless
Table 111.
Table 11.
Equivalence Ratio
ea = 0.7
at
a
e
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K.
€=os
at To, K.
800
900
800
900
1231 1358 1480 1597 1709
1324 1450 1572 1688 1800
1327 1483 1632 1774 1909
1420
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E
at To,OK. 800
= 1.0
at To, I 0.8atm. H.
11.
P < 0.4 atm. Intermediate P
of the residual gases with a n oxygen analyzer. I n the entire test sequence, the reaction pressure ranged from an upper limit of about 1 atm. to a lower limit of about 0.1 atm. However, for any given fuel, no serious attempt was made to vary air rate and pressure independently over a wide range; this variation would be required to determine the over-all reaction order for each fuel. Results. I n Figures 2: 3, 4, and 5: the results for the fuels tested are plotted. Again, the lean blowout equivalence ratio is shown as a function of the loading group N/VP1.*. For each fuel, a best smooth curve has been drawn through all the points on this plot. T h e dotted curve is the best average for iso-octane results previously reported ( 7 ) and is a convenient reference when considering the relative reactivity of each fuel. Summarized values from these smooth curves are listed in Table I11 and the original data are in Table IV. Effective inlet temperatures were, again, the measured inlet temperatures corrected for heat losses. When the effective temperature was not 400’ K., the value of AV/VP’,* was adjusted using a n activa-
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tion energy of 42.000 calories. Although 42,000 calories is clearly not the best activation energy to use for each of these fuels, the adjustments were small and the errors caused by using 42,000 are probably negligible, except possibly for hydrogen. In each figure, the points are pressure coded. Completely shaded squares are experimental values a t pressures lower than 0.4 atm. ; open squares are pressures greater than 0.8 atm., and half-shaded squares are intermediate pressures. Plotting the data against a loading group in which the pressure exponent is 1.8 implicitly assumes an over-all reacrion order of 1.8. If this 1.8 were seriously in error, some stratification of the pressure-coded points should show upfor example, completely shaded points would tend to lie above the best smcoth curve and completely open points beloir it, if a better pressure exponent were greater than 1.8. (This would occur where there is some overlap in pressure range-points from more than one pressure group falling a t or near the same loading factor.) However, for no fuel (with enough data for overlap) is such a stratification apparent. There-
INDUSTRIAL AND ENGINEERING CHEMISTRY
fore, for the pressure ranges tested, the over-all reaction order for each fuel should not be greatly different from 1.8. Results for nonaromatic hydrocarbons are shown in Figure 2. LVithin experimental error, the reactivities were about as expected. T h e flame temperatures of heptane are very slightly higher than the flame temperatures of isooctane, and its burning rate seems slightly faster. T h e ratio of the observed rate to the rate that would be calculated for iso-octane if iso-octane gave the same flame temperature as heptane is about 1.2, as shown in the last column of Table V. (Table V tabulates this kind of comparison for all the fuels tested a t the arbitrarily chosen equivalence ratio of 0.6, except at 0.4.for hydrogen.) T h e low carbonh>-drogen ratio of methane causes its flame temperature to be loiver than isooctane. I t is thus predicted and observed, that on the average, methane burns more slowly than iso-octane. (.kt an equivalence ratio of 0.6, where the Table V comparisons are made, methane burns atypically faster than iso-octane.) T h e high flame temperatures of dicyclopentadiene cause the predicted rate to be about 50y0 faster than isooctane, but the observed rate was only 20yo faster at 0.6 equivalence ratio. Therefore the over-all ratio of observed ro predicted burning rate for dicyclopentadiene was about 0.8. Five volume per cent of a n “ignition promoter,’’ n-propyl nitrate, was added to iso-octane, but it had no effect on burning rate and would have no effect on flame temperature. Therefore, for these four nonaromatic hydrocarbon fuels, the observed blowout rates matched predicted rates within about 20%again excepting the point comparison chosen for methane and possibly richer dicyclopentadiene mixtures. A 207, mismatch is not considered greater than the probable experimental error. Somewhat greater deviations were found in burning aromatic hydrocarbons (Figure 3). Benzene’s 90c76 higher burning rate compares with a predicted rate only 50% higher (Table V). For equivalence ratios exceeding 0.8, benzene’s advantage drops abruptly; there is no explanation for this behavior and it should be confirmed over a wider range of operating conditions. Although toluene and x)-lene have flame temperatures about equal to benzene? their reactivities are much lower and are only about 60 to ’0% of‘ predicted values. One can speciilate that methyl groups on the benzene ring form a n intermediate which inhibits combustion and offsets an expected advantage due to higher flame temperatures. T h e flame temperatures of Tetralin are intermediate between those of iso-octane and benzene, and, on the average, the reactivity is also
S PH ERIC AL R E A C T 0 RS-COMBU S T I 0 N RATES intermediate; it is about 1.3 times as great as would be predicted bv its flame temperature advantage over isooctane. Tetralin is somewhat difficult to evaporate completely, but, once mixed homogeneously, it burns rapidly and with no luminosity. Summing up then, the aromatic fuels tested vary by u p to about 40% from corrected iso-octane predictions. Still greater variations are found in burning the nonhydrocarbons of Figures 4 and 5. T h e nonhydrocarbons exaggerate differences that would result from flame temperature differences. Thus isopropyl chloride blows out a t only 40y0 of the iso-octane rate rather than the predicted 70%, whereas propylene oxide blows out a t 3307, rather than the predicted 170%. Possibly inhibition by the halogen accounts for isopropyl chloride's poor burning, while easy
Table V.
ISOPROPYL
0
CHLORIDE
,.0.6 PROPYLENE OXIDE
Figure 4.
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Blowouts of nonhydrocarbons Reference curve for iso-octane ah. atm. Intermediate P
0.P > 0.8 D. P < 0.4 11.
Comparison of Blowout Data with Predictions from Flame Temperature Effects Relative Blowout Rate Temp., K." Observedb Predicted"
Observed/ Fuel predictedd Iso-octane reference (1.00) (1.00) 1616 (1.00) Heptane 1.2 1.1 1620 1.0 1.1 Methane 1.5 0.8 1580 Dicyclopentadiene 1.2 0.8 1680 1.5 5% %-Propyl nitrate in isooctane 1.0 1.0 1.0 (1620) Benzene 1.9 1.3 1680 1.5 1.1 1.5 0.7 Toluene (1680) 0.8 0.6 Xylene (1680) 1.5 Tetralin 1.6 1.2 1.3 1640 0.4 0.6 Isopropyl chloride 1560 0.7 3.3 2.0 Propylene oxide 1700 1.7 200 6 30 Hydrogen 1800 a Temperatures estimated t o nearest 10' K for homogeneous inlet mixture at 400' K. burning to 90% 0 2 consumption efficiency. Unburned material is CO only, except for Hz fuel ,411 values at equlvalence ratio of 0 6 except for hydrogen, all hydrogen comparisons at equivalence ratio of 0 4 wheie iso-octane gives 1262' K Toluene and xyleiie flame tempeiatures assumed equal to benzene; propyl nitrate mixture assumed equal to iso-octane Observed ratio of NIVP' t o value for iso-octane at blowout with equivalence ratlo of 0 6 (except Hz) Ratio predicted if iso-octane flame temperature were equal to fuel tested Rounded values from 3-figure calculations ~
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CARBON
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Figure 6. Comparison of carbon monoxide and consumable oxygen contents of combustion gases
attack on the strained ring may account for propylene oxide's fast burning. I n any case, these fuels demonstrate that fuel structure is of particular importance in burning nonhydrocarbons and that no single effect as simple as flame temperature can account for all the differences among fuel combustion rates. Both lean and rich blowouts of hydrogen are shown in Figure 5 . Although there was no doubt that hydrogen would burn very rapidly, it was of interest to have a quantitative comparison with iso-octane. Hydrogen can provide a convenient standard of reference for other very reactive, but possibly more exotic, fuels. Comparing the extrapolated data at an equivalence ratio of 0.4, the blowout loading for hydrogen is about 200 times greater than that for iso-octane. An equal or higher ratio exists for rich mixtures. Flame temperature differences alone would account for only a sixfold increase over iso-octane. I t is likely that a fuel like hydrogen which differs so greatly in reactivity from iso-octane also has different kinetic constants. Thus. the over-all reaction order seems to be near 1.8. but the individual orders of reaction of fuel and oxidant may well be different from the values of 0.8 and 1.0 estimated for iso-octane and oxygen, respectively. There are not enough data to determine a hydrogen activation energy or collision factor with confidence. and these constants too may vary from the values reported for iso-octane. If the activation energy for hydrogen were lo^ er than for iso-octane, one would expect a lower combustion efficiency (for hydro-
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gen compared to iso-octane) a t a given reaction temperature. However, combustion efficiencies have not yet been measured. All the data demonstrate that there are chemical effects as well as temperature effects on reaction rates observed in a well-stirred reactor. These chemical effects may not be the same as those observed under other conditions. Thus, heptane has an octane number of 0 and iso-octane has an octane number of 100, but both burn a t the same rate (within experimental error) here. The low temperature oxidation reactions important in determining octane number seem unimportant in a stirred reactor. Thermal fragmentation of the fuel molecule is not critical; although the thermal cracking rate a t 1000" F. for iso-octane is about 100 times greater than for benzene. benzene's burning rate here is about 30YG faster than the temperaturecorrected iso-octane burning rate. Both Tetralin and benzene burn about 30% faster than (corrected) heptane, but both have longer ignition delays than heptane when injected into air streams at 1500' to 1800" F. In addition, 570 of ethyl nitrate added to kerosine cuts ignition delays about in half, but addition of 5% n-propyl nitrate to iso-octane did not affect burning rates in the spherical reactor. Therefore, the reactions important to ignition delay phenomena are not important here. In general, hydrocarbons show a greater variation in behavior due to structure during reactions that take place (or begin) at low temperature than they show in a high temperature stirred reactor.
INDUSTRIAL AND ENGINEERING CHEMISTRY
During some tests with benzene. Tetralin, and methane, oxygen and carbon monoxide were determined in the gases from the sampling probe before the gases were passed through the combustion furnace. The difference in oxygen content before and after the furnace is the percentage of consumable oxygen-Le.. the amount of oxygen that will combine with any gases not burned completely before passing through the furnace. By comparing the consumable oxygen with the carbon monoxide present, it was found that carbon monoxide accounts for most or all of the combustibles present. The total amount of other combustible species was usually small-within experimental scatter (Figure 6). Most of the gas samples were withdrawn near the blowout equivalence ratio; the data are for random equivalence ratios, pressures, and mass flows. Perfect correspondence between oxygen and carbon monoxide contents would cause a point to fall on the 45" line shown. Although there is data scatter, all points fall reasonably near the line. The earlier tests with iso-octane ( I ) showed that, for leaner than stoichiometric mixtures, carbon monoxide accounted for about all of the combustion inefficiency observed. Conclusions
Experiments using homogeneous mixtures entering a spherical reactor a t about 1100' F. confirm that the overall apparent activation energy for the combustion of iso-octane in air is 42 to 45 kcal. With fuels other than isooctane, differences in reactivity tend to agree qualitatively with differences in flame temperature. However, the differences usually cannot be accounted for quantitatively by these temperature differences; the effect of fuel structure on burning rate was less important for the hydrocarbons tested than for the nonhydrocarbons. Scattered gas samples showed that carbon monoxide was the only major product of incomplete combustion while burning homogeneous lean mixtures of benzene or Tetralin. Acknowledgment
The Ivork reported was done under contract with the Bureau of Ordnance, Department of the Navy, as part of a program in cooperation with the Applied Physics Laboratory, The Johns Hopkins University. The bureau's permission to publish these results is gratefully acknowledged. literature Cited (1) Longwell, J. P., Weiss, M. A,, IND. ENG.CHEM.47, 1634 (1955).
RECEIVED for review March 23, 1957 ACCEPTEDJune 6 , 1957
