THERMAL CRACKING OF PROPANE Kinetics and Product Distributions A L F O N S G. B U E K E N S A N D G I L B E R T
F. F R O M E N T
Rijksuniuersiteit Gent, J. Plateaustraat 22, Gent, Belgium
The thermal cracking of propane was studied in a flow apparatus between 625' and 850' C. and a t atmospheric pressure. Fairly complete product distributions, including those for C4, C5, and Ca hydrocarbons, were established and a reaction scheme was deduced. The order of the propane decomposition was determiined by comparing experiments with different degrees of feed dilution and found to vary with conversion and temperature. When the rate was fitted by means of a first-order kinetic expression, the rate coefficient decreased with increasing conversion. This so-called "inhibition" was expressed mathematically by considering the rate coefficient to b e a hyperbolic function of conversion. The activation energy of the first-order rate coefficient increases with conversion. Finally, rate equations based on the radical nature of the process are discussed.
HE
main products of the thermal cracking of propane are
Tethylene and methane on one hand, propylene and hydro-
gen on the other. These products may be considered to be formed by two parallel decomposition reactions of propane. Ethane, butenes, butadiene, and aromatics are also formed. All these products are most important building blocks for the petrochemical industry, so that steam cracking of propane (or light naphtha) has become the major key process of this industry. The plant capacities are growing steadily. Plants producing 250,000 tons of ethylene per year are now in operation and bigger units are under way. The necessity of increasing the ratio of ethylene to propylene in the cracker effluent has led to increased severity in cracking conditions. T h e design of such units requires precise kinetic equations and detailed product distributions. T h e literature on propane cracking is rather extensive, but the majority of the published studies present a physicochemical character, concerned with the nature of the elementary radical steps from which the over-all process is built up. They are generally carried out under static conditions, a t temperatures below 650' C. and a t reduced pressure. Partial product distributions were published by Frey and collaborators (1928, 1933) and Steacie and Puddington (1938). Kinney and Crowley (1954) were mainly concerned with the formation of aromatics a t nearly complete propane conversion. Schutt (1 947) gives product distributions derived from industrial data. T h e most comprehensive product distributions were published in 1931 by Schneider and Frolich (1931) with analytical techniques which bear no comparison with present-day mass spectrographic and gas chromatographic techniques. T h e rate of propane cracking is generally expressed as: r = k exp( -j&)Cn
Some of the most representative kinetic data are summarized in Table I and represented in Figures 1 and 2. I n most studies the order was found to be 1, but Martin, Dzierzynski, and Niclause (1964) and Laidler, Sagert, and Wojciechowski (1962) found an order higher than 1. Table I shows considerable spread in activation energy and frequency factor. T h e absence of reliable kinetic data in the temperature
Table 1.
Literature Data Activation
Energy, Frequency Factor
Gal./
Temp. Range,
Authors Order Mole C. Paul and Marek (1934) 1 3.98 Y 10'6 74,850 550-650 Engel et al. (1957) ... 71,000 500-590 Martin et al. (1964) 1 .i l l .3 67,000 545-600 Laidler et al. (1962) 2 . 5 8 ' X l O I 4 67,100 530-670 ti.5 8.50 X 10'3 54,500 Steacie and Puddington (1938) 1 2.88 X 10la 63,300 551-602 ... ... 53.000 700-750 De Boodt (19621 Kershenbaurn ' (1967) 1 2.40 X 10" 52,100 800-1000
range encountered in industrial practice (650' to 825' C.) is striking. This work was undertaken to explain the inconsistencies and contradictions found in the literature. Experimental data were obtained in a flow apparatus for very wide ranges of temperatures and residence times, covering those encountered in industrial operation. From the product distribution a reaction scheme is derived. T h e over-all kinetic equation is established. Finally, radical mechanisms are discussed in an attempt to explain some of the observed facts. Apparatus
The apparatus is represented schematically in Figure 3. T h e flow rate of propane is measured by the calibrated capillary, C, and controlled by means of the valve, Kr. I n a certain number of experiments the propane was diluted with nitrogen. The flow rate of nitrogen was indicated by the flowmeter, r, and determined from the total flow rate measured by the wet-gas flowmeter and the analysis of the exit gases. T h e propane and nitrogen are mixed in a packed tube, D, before entering the tubular reactor, the upper part of which serves as a preheater. Upon leaving the reactor the gases are rapidly cooled, K , and analyzed in an on-line gas chromatograph. Their flow rate is measured in a wet-gas flowmeter, G . T h e reactor tube, 163 cm. long, is made of chromium steel (16% Cr, no nickel) and has an internal diameter of 4 mm. Short bends permit the insertion a t different heights of four VOL. 7
NO. 3
JULY 1 9 6 8
435
. 0
A a 9
DE BOODT PAUL STEACIE LAIDLER KERSCHENBAUM BUEKENS x a
log
30%
60% 90%
Ti [E :(set)-']
'90
900
1000
40 'I0
LOO
10.0
$ Figure 1 .
11,o
Arrhenius diagram
very thin thermocouples, Philips 2ABI 10, external diameter 1 mm., so that the temperature of the gas stream itself is measured. T h e geometry is such that the value measured is close to the mean cross-sectional temperature. T h e furnace is cylindrical and has a length of 160 cm. and an outside diameter of 36 cm. I t consists of two hinged half cylinders, made of fireproof concrete and surrounded by a steel casing. There are two sections: a preheat and a reaction section. The preheater is a metallic cylinder insulated by a mica sheet and wound with resistance wire. Its heating capacity is 3.5 kw. T h e reaction section (heating capacity 6 kw.) holds 12 vertical porcelain elements upon which resistance wire is wound a t a variable speed. Six of these elements have their maximum heating capacity on the top, the other six on the bottom. Both types alternate along the cylinder wall. Both series of six elements are separately connected and controlled. TO compensate for heat losses at the exit a radiant resistance wire with a heating capacity of 1.5 kw. is placed in the bottom of l&EC PROCESS DESIGN A N D DEVELOPMENT
lZ,O
(OK)-'
Integral valuer of rate coefficient,
436
= = x = x x
i
Table II.
Column Material
Silica gel Dimethylsulfolane on Celite 545 (60/100 mesh) Squalane on Chromosorb P ( 6 0 / 8 0 mesh)
Columns Used
Length, M.
Tzmp., C.
Products Anahred
2
25
Hz, 5 3 3 4 Carrier gas, NZ
12 8
40 100
From C1 to C4 All HC up to toluene
the cylinder. Variable transformers are built in the control circuits in order to attenuate the power input during operation. T h e temperatures are recorded by means of a Leeds & Northrup potentiometric recorder, Type G.
x
DEBOODT PAUL a LAIDLER o KERSCHENBAUM A STEACIE T
BUEKENS 8
KO
30%
1:x.
2 : : ~ 60% 3:x
8
90%
"C
99
1 Figure 2.
Arrhenius diagram
Point values of rate coefficient, k
Analysis
T h e reactor effluent stream was analyzed on a Wilkens Moduline 202 gas chromatograph with hot wire detector. T h e columns used are described in Table 11. The carrier gas was hydrogen, unless otherwise mentioned. The peak surfaces were measured by means of a mechanical integrator. Calibration factors determined for nitrogen, methane, ethane, ethylene, acetylene, propane, propylene, and benzene were in excellent agreement with those published by Rosie and Grob (1957). Experimental Results
The experiments covered the following range of variables : Temperature, 625' to 850' C. Pressure, atmospheric; maximum pressure, 1.3 atm. absolute.
Propane flow range, 0.4 to 10 moles per hour, and thus a residence time of 0.04 to 1 second and a Reynolds number of 8 to 200. Dilution factor, 6 (molar ratio of nitrogen to propane), 0 to 10. The analysis of the propane was as follows: propane 98.9 mole %, ethane 0.3 mole %, propylene 0.2 mole %,2-methylpropane 0.6 mole %, sulfur 10 p.p.m. Before a series of experiments the reactor surface was deactivated with CS2 at temperatures between 450' and 550' C. The material balance of the experiments checked within 1%. The results are presented in two ways: in conversion us. V/F, diagrams and in product distribution or selectivity diagrams. The diagrams of the first type are more directed toward a kinetic analysis, those of the second type toward a study of the reaction mechanism. VOL 7
NO. 3
JULY 1968
437
V(
Figure 3.
Figure 4. 438
Flow sheet of apparatus
Propane conversion vs. V / F ,
I&EC P R O C E S S D E S I G N A N D D E V E L O P M E N T
'
0
°
800°C
1
sx 50,
25
Figure
5. Total conversion of propane and conversion to primary products as a function of V / F , at 800" C.
Figure 4 shows t.he x us. V/F, curves for temperatures ranging from 625' to 850' C. Vis the equivalent reactor volume discussed in detail below. x represents the total propane conversion. Figure 3 shows, by way of example, the conversion us. V/F, curves for propane and the principal reaction products a t 800' C. T h e propylene curve goes through a maximum, resulting from the opposing effects of production and decomposition. Figures 6 and 7 show, by way of example, the product distributions as a function of the total propane conversion for two temperature ranges: 725' to 750' and 825' to 850' C. The temperature dependence is not very pronounced. Product Distribution
T h e primary products are methane, Primary Products,. ethylene, hydrogen, and propylene, which initially are formed in nearly equal molar quantities. Ethane is also partly a primary product, but it is produced in much smaller quantities. Table I11 gives the primary product distribution a t zero conversion for several temperature ranges. T h e selectivity with respect to a given product is defined below as the ratio of the number of moles of this product formed to 100 moles of propane decomposed. T h e hydrogen selectivity a t zero conversion was calculated from a hydrogen balance. The classical Rice rules for radical reactions (1934) would ethylene and 40% hydrogen predict at 600' C. 6057, methane
+
Table 111.
Primary Product Distribution at Zero Conversion
(Moles formed per 100 moles of propane cracked) 675/ 700°C.
Methane Ethylene Ethane Hydrogen Propylene
7.251 750" C.
47
48 0.7 52 52
775/
825/
8GUOC.
850OC.
49 50 1.4 51 49
48 50 3.2 53 47
47 49 1.1
52 51
+
propylene; at 800' C. 63 and 37%. Experimentally the proportion is practically 50 to 50 a t 800' C. I t follows from Table I11 that there is a slight trend in ethylene and propylene selectivity with temperature. These trends may be explained by the Rice rules, according to which the formation of n-propyl radicals requires 1.2 cal. per mole more than the formation of isopropyl radicals. Ethylene and methyl radicals are the decomposition products of n-propyl radicals; propylene and hydrogen radicals originate from isopropyl radicals. T h e temperature dependence of ethane selectivity is more pronounced. This may be explained by the growing importance of initiation and termination with temperature. T h e initiation can be represented by CaHs * CH3' VOL. 7
+ CzHs' NO. 3
JULY 1968
439
725-75Q.C
9 4
+
IO Figure 6.
Selectivity diagram for temperature range 725" to
The ethyl radicals may then form ethane. One possible termination reaction is the recombination of two methyl radicals 2CHsO
+
C2He
which also produces ethane. Figures 6 and 7 show how the selectivity for ethylene and methane increases with increasing conversion, while that for propylene and hydrogen decreases. T h e ethylene-propylene molar ratio rises from 1.0 a t zero conversion to 3.7 a t 85% and 6 a t 95% conversion. I n the technical literature the product distribution is often referred to the amount of ethylene produced. When propane is cracked to 90% conversion under industrial conditions, 33 kg. of propylene are produced per 100 kg. of ethylene (Burke and Miller, 1965). The figure obtained in this study is 36.6. For methane the figures are 61 and 62; for the secondary products, 7 and 7 (1.3-butadiene) and 4 and 3 (butenes). Secondary Products, T h e selectivities of the principal secondary products are shown in Figure 8. Acetylene, 440
I&EC PROCESS DESIGN A N D DEVELOPMENT
750" C.
methylacetylene, and propadiene (or allene) are dehydrogenation products of ethylene and propylene. The single curve drawn for these products is to be regarded as a mean curve, since the dehydrogenations are temperature-dependent. T h e rate of these reactions is lowered when the reactor wall is pretreated with CS2. At a conversion of 95% the selectivity for acetylene amounts to 1.8%-the equilibrium value-without, but only to 0.6% with pretreatment. The activation energies are estimated to be 90,000, 80,000, and 70,000 cal. per mole for acetylene, allene, and methylacetylene formation. T h e temperature effect on the 1-butene formation is undeniable. The selectivities go through a maximum for a propane conversion of 40 to 50%; below that conversion 1-butene is the most important secondary product. The decrease in selectivity beyond the conversion is probably due to isomerization into 2-butene and 2-methylpropene and also to dehydrogenation into 1,3-butadiene. There are several possibilities for the formation of 1-butene. One possibility is: 2C2H4 S CH&H2CH=CHz
(1)
*
801
-
825 850%
'
40
30
-
20 -
IO .
'.. T
. I
T
10
20
Figure 7.
30
.
40
x59.
ki2
C3Hb0 --t C4H3
(2)
where the allyl radicals are formed according to: C3Hrj
+ R"
-+
C3Hb"
-60
T T. ' T
70
. T
80
TT T
'ZH6,
90
1 0
Selectivity diagram for temperature range 825" to 850" C.
Several objections may be formulated against this reaction as the principal source of 1-butene. Indeed, the conversion to 1-butene is higher than the equilibrium conversion of Reaction 1. Furthermore, the selectivity for 1-butene increases with temperature, whereas the equilibrium conversion decreases with temperature. Finally, Reaction 1 was found by Krauze et al. (1935) to have an activation energy of 37,700 cal. per mole, considerably less than that for total propane decomposition. A comparison of selectivities at equal conversion for different temperatures indicates that the activation energy of 1-butene formation is approximately 15,000 cal. per mole higher than that of propane decomposition, which varies between 52,000 and 64,000 cal. per mole. For all these reasons, a more plausible way for the production of 1-butene is the recombination between methyl and allyl radicals: CH3"
_c
+ RH
(3)
Reaction 2 requires no activation energy. Therefore, the temperature dependence of the 1-butene formation has to be
traced back to the temperature dependence of the radical concentrations. When compared at the same inhibition level, these concentrations vary with temperature according to an Arrhenius-type relation, so that an activation energy may be used to characterize their temperature dependence. From the simulation of the cracking of propane on a digital computer a value of about 48,000 cal. per mole may be derived for the "activation energy" of the methyl radical, while that for the allyl radical must be between 20,000 and 30,000 cal. per mole (Buekens, 1967). I t follows that the apparent activation energy for 1-butene formation according to Reaction 2 must lie between 70,000 and 80,000 cal. per mole, in agreement with the experimental results. As mentioned above, 1-butene isomerizes partially into 2-methylpropene and 2-butene. The selectivity for 2-butene does not exceed 0.3%. 2-Methylpropene could not be separated completely from I-butene by gas chromatography. For propane conversions of 90 to 95% the amount of 2-methylpropene was estimated to represent some 40% of the sum of 1-butene and 2-methylpropene. The 1,3-butadiene selectivity, also represented in Figure 8, was found to be practically independent of temperature. If 1,3-butadiene were formed by dehydrogenation of 1-butene, the selectivity would decrease at high propane conversions, VOL. 7
NO. 3
JULY 1968
441
2.6
.
2.4
.
s 2.0
-
1.6
-
* t 2 tu W
-I
W
* 1.2 0.8.
~ H c /
Figure 8.
+ Hz
a conclusion set forward by Schneider and Frolich (1931). The Csand Cg hydrocarbons are mainly dienes and aromatics and are probably formed by condensation reactions of ethylene and propylene. The following products were identified : pentadiene, isoprene, methylpentadienes, cyclic dienes such as cyclopentadiene and probably cyclohexadiene; olefins such as I-pentene, 1-hexene, and 4-methyl-I-pentene; cyclic olefins such as cyclopentene and cyclohexene; and aromatics such as benzene and toluene. The formation of aromatics increases rapidly a t high conversions. I t is strongly dependent on wall effects. Reaction Scheme. To conclude this discussion of the product distribution, the following reaction scheme may be set u p :
CHI
+ CzH4
-
7
7
\
L
/
C3HS
4
Hz
Hz
+ CzHz
'/z(Hz -t G H s ) H z + CsHs
+
3
+ C3Hs * '/2(Hz + Ce"o)
T h e reactions of this scheme probably proceed over radicals almost entirely. An additional set of reactions is required to explain the formation of ethane and olefins: 442
CH
Selectivity diagram for secondary products
whereas the opposite is observed. I t is therefore likely that 1,3-butadiene is mainly formed according to: 2C2H4 + CHFCH-CH=CHZ
/
I&EC PROCESS DESIGN A N D DEVELOPMENT
2 CH3' CzHs' CH3'
C2&'
++ RC3H5' H
* CzHs 7
-{
I-butene
-
1
+ 2-butene +
J.
1,3-butadiene
+ Hz
2-methylpropene -+ I-pentene
+ C3H5'
C3H70+ C3H50
4-methyl-1-pentene l-hexene
Kinetic Study
Equivalent Reactor Volume. One of the main problems encountered in the derivation of rate equations for homogeneous gas-phase reactions from experiments in tubular flow reactors is the longitudinal temperature profile. Indeed, it is not possible to distinguish sharply between preheat and reaction sections as can be done in fixed-bed catalytic reactors. If the rate is to be determined a t a reference temperature, say TR, and if the reaction volume is counted from the point where TR is reached, an error is introduced by neglecting the conversion accomplished in the section below TR. A similar situation occurs at the outlet, where the conversion continues to some extent at a temperature lower than TR. To correct for this and to compare experimental data at the same reference temperature TR,use can be made of the equivalent reactor volume concept introduced by Hougen and Watson (1947). The equivalent reactor volume, V, is defined as that volume which, at reference temperature TR, would give the same conversion as the actual reactor, with its temperature profile. I t follows that TT
dV = - dV' ~ T R
(4)
and
Table IV.
LvLxp( - A ) d V t
V = exp(
625'
c.
-")
Conversion Order
RT R
T h e usefulness of this concept was discussed and demonstrated by Froment, Pijcke, and Goethals in their study of the thermal cracking of acetone (1961). T o be practical its utilization requires a good evaluation of the activation energy, E, prior to the knowledge of the rate coefficient, k. T h e experimental data of the present work were corrected by means for this concept, using a n estimated value of 50,000 cal. per mole for the activation energy. This value was sufficiently close to the final value obtained from an Arrhenius diagram to make iteration superfluous. I n some cases the true volume was reduced by a factor of 2. Determination of O r d e r a n d Rate Coefficient, I n this work it was attempted, as is usual in the study of cracking reactions, to describe the rate by a simple equation like r = kCn
(5)
When the differential method of analysis is applied, the rate is obtained as the slope of the tangent to the curves of x us. V/Fo. When the integral method of analysis is used, Rate Equation 5 has to be substituted in the continuity equation
F,dx = rdV and the resulting equation integrated. T h e data points x us. V/F, are then used to calculate k. I t was found using both methods of analysis that the rate coefficient decreases with increasing conversion, a t least for orders between 1 and 1.5. Using the terminology of the cracking literature the reaction is "inhibited by its reaction products or by intermediate species." Another way to put it is that Rate Equation 5 does not adequately describe the rate of the complex cracking phenomenon. Yet, in this section, the kinetic treatment is based upon Equation 5 , whose simplicity is attractive for practical purposes. Moreover, this treatment leads to considerable insight into more complex mechanisms. T h e variation of the rate coefficient, k, defined by Reaction 5 , with conversion necessitates a distinction between point and integral values. T h e differential method leads to point values; the integral method to integral values, E. I t also follows that the correct order of the reaction can be obtained only by comparison of data having the same level of inhibition, which is mainly determined by the relative rates of reaction of the chain-carrying radicals with propane and propylene. For this reason k/k,, the ratio of the point value of the rate coefficient a t conversion x to the point value at zero conversion, may be written:
k k,
k(R") (C3Hd
- k(Ro)(C3Hd + k"(Ro)(C3Hd
- E
Since the selectivity for propylene is almost independent of the pressure, the extent of inhibition is in first approximation determined by the conversion, so that Equation 6 is obtained:
0.022 1.36
Variation of Order 675' 700- 775' 825' c. C. 750" C. C. C. 0.058 0.067 . . . 0.238 0.412 1.21 1.14 1 0.99 0.96 650'
used in this work is based upon the integral method of analysis. The formulas used to calculate & for orders of 0.5, 1, 1.5, and 2 are given in the Appendix. I n these equations the expansion factor is taken to be 2 over the complete range of conversion, as observed experimentally. Figure 9 illustrates how the correct order is obtained from the intersection of two curves related to the experiments being compared. The semilogarithmic representation used leads to a sharper intersection. Table I V shows the mean values of the order a t several temperatures. Table IVdoes not make it possible to conclude unambiguously whether the order varies with conversion, with temperature, or with both. Indeed, the conversions used to determine the order at the higher temperatures are much higher than those a t the lower temperatures. I t has been shown, however, that the order decreases mainly with increasing conversion-Le., with increasing inhibition (Buekens 1967). First-Order Kinetics. I n the preceding section the order of the reaction, although not constant, was found to be close to 1. With a fixed value of 1 for the order it becomes possible to determine a n activation energy and a frequency factor for propane decomposition. When the first-order & values, determined by the integral method, are plotted in a n Arrhenius diagram (Figure l ) , a definite trend with respect to conversion is observed. T h e following activation energies and frequency factors are obtained: 30% conversion
130 =
2.33 X 10l2exp(
58,000
(second-')
60% conversion = 8.62 X lo1* exp
(--6yio)
(second-')
90% conversion
(--':io)
= 1.64 X 1013exp
(second-')
This shift in activation energy may explain the spread of the values reported in the literature, probably obtained a t different levels of inhibition. I t is of importance to present point values of the rate coefficient, too. Indeed, most of the k values reported in the literature are point values. Furthermore, if a relation is to be established between the over-all rate coefficient and the intimate nature of the reaction, point values are of more direct interest than integral values. Equation 6 suggests a hyperbolic law for the variation of point values k, with conversion:
k=-
Therefore, the determination of the order requires comparison of experiments carried out a t different ratios of nitrogen to propane but leading to the same conversion. T h e procedure
-T)
k0
1
+ ax
(7)
In Equation 7, a is a n empirical inhibition coefficient and k, is the value of k a t zero conversion and therefore a rather artificial quantity. Indeed, k should vary with conversion in the same way as the radical concentration. The latter goes through a maximum: I t increases as the reaction starts, but decreases VOL. 7
NO. 3 J U L Y 1 9 6 8
443
+:
+I
0
-1
-2
i 1
1/2 Figure 9. tR
v d-
(1
Determination of reaction order
kOCt(1 - x ) ax)(l x)
+
+
FO
V
-= FO
-a
2 In (1
- x) + 2x + - 2 In (1 - + x 2 X2
2)
(9) 444
Table V.
Temg ., O
c.
625 650 675 700 725 750 775 800 825
k,, a VI.
Temperature
kQ,
Sec. -1
a
0.0548 0.1819 0,3298 0.9452 1 ,7800 2.2140 4,0760 9.3580 13.9500
7.345 11.720 3.696 6.505 5.896 2.371 1.128 1.799 1.375
(8)
Upon integration and rearrangement, Equation 8 gives:
C,k,
3/2
= 675OC. V / F , = 7.86 x = 0.0253, dilution factor 6 = 0 V / F o = 13.50 x = 0.0259, dilution factor 6 = 6.43
afterward, as a result of the formation of allyl radicals. Such a maximum was observed experimentally a t the very low conversions which were measured in the temperature range 625’ to 675’ C. The hyperbolic law of Equation 7 does not consider the drop in k as zero conversion is approached, of course. T h e “initial value,’’ k,, and the inhibition coefficient, a, the constants of the empirical hyperbolic law describing the inhibition, were determined in the following way. When the expansion factor equaIs 2, the combination of Equation 7 with the continuity and rate equations leads to:
-dx- -
ORDER
I20
l & E C P R O C E S S DESIGN AND DEVELOPMENT
With an equation of this form k, and a may be calculated from a set of experimental x us. C,V/Fo values by linear regression. T h e results are shown in Table v. Figure 10 shows a k us. V/Fo or x curve and compares experimental and calculated E values at 775’ C. The calculated E values were obtained from:
I
rV/Fo.
k =-vJ ,
.v
7 7 5%
k d -
FLl
FO and the k values were related to V/Fo through Equations 7 and 9. I t follows from Figure 10 that the hyperbolic law (Equation 7 ) permits a n excellent description of the inhibition. I t is seen from Table V that the values of a are less in line a t the lower temperatures of 625' to 675' C. a is very sensitive to the spread on the data. T h e maximum in the k us. V/Fo curves also influences the results. From an Arrhenius diagram, the following temperature dependence is derived for a:
(2:3 ___
a = 3.01 X lO5exp
If a were exactly equal to the ratio kN/k', the temperature dependence would be less pronounced and amount to no more than 3000 cal. per mole. T h e value of 23,100 may be explained by the role played by the allyl radical, C ~ H S ' ,which becomes more effective as a chain carrier a t higher temperature. T h e following temperature dependence is found, by linear regression, for k,: k, = 4.10 X 10" exp
(- 'y:)
- (second-')
Figure 10. Comparison of experimental & values with those calculated from point values
I n 1934 Rice proposed the following sequence to describe the thermal cracking of propane under initial conditions:
I t now becomes possible to calculate point k values a t different conversions-e.g., 30, 60, and 90%. These values are plotted in a n Arrhenius diagram, as shown in Figure 2 . T h e following activation energies and frequency factors are found by linear regression: 30y0 conversion: k30
=
5.10 X 1OI2 exp
6OYc conversion : k60 =
1.98
x
loi3 exp
90% conversion: kgo = 3.84
x
1013 exp
(- 'y;) ~
(second-')
(- 6y:o) __
(- 6y:) ~
(second-')
With this system of reactions the rate of propane decomposition may be written:
(second-')
T h e point values are lower than the integral values, of course, while the activation energies are higher, as may be foreseen from the trend observed in Figure 1 . The activation energies given here are lower than those usually reported. No effect of heat transfer limitations may be involved: T h e thermocouples are inserted in the gas stream itself, not on the wall. However, De Boodt (1962) obtained a value of 53,300 cal. per mole in a flow apparatus of different construction than the one used in this study, while Kershenbaum and Martin (1967) came to an expression for the firstorder rate coefficient in the temperature range 800' to 1000' C. (Table I) which is in remarkable agreement with the equation given here for k,. Radical Mechanisms. T h e over-all order of propane decomposition depends upon the conversion and temperature. Values ranging from 1.3 to 1 were obtained. This clearly indicates that a simple power law like Equation 5 is not adequate for the description of the rate of propane decomposition under widely varying conditions. More satisfactory equations have to be based upon a more detailed consideration of the nature of the reaction.
where 0 = C1
I.' FO
The inaccessible radical concentrations may be eliminated from this expression with the help of the so-called steady-state approximation. According to this concept, introduced by Bodenstein, the radical concentration does not vary rapidly beyond the initial startup period. A balance on the production and consumption of CH3' and H' then leads to expressions for the concentrations of these radicals as a function of the propane concentration. After substitution of these expressions into Equation 10 the following rate law, which is of first-order with respect to propane, is obtained, provided no distinction is made between n- and isopropyl radicals and ki k3.
