I
P. J. LUCCHESI,
B. L. TARMY, R. B. LONG, D. L. BAEDER, and J.
P. LONGWELL
Process Research Division, Esso Research and Engineering Co., Linden, N. J.
High Temperature Radiation Chemistry of Hydrocarbons An experimental study of the cracking of hydrocarbons initiated by nuclear radiation emphasizes effect of such process variables as temperature, feed composition, and phase. The effects of radiation intensity have been studied by comparing cobalt-60 radiation with the mixed radiation from the Brookhaven atomic reactor. Depending upon conditions, each variable can have important effects in radiation chemistry the radiation chemistry of hydrocarbons has been studied in some detail at relatively low temperatures (6, 8, 79, 24), corresponding studies have not been reported at high temperatures. This lack of data contrasts with the situation in photochemistry, where hydrocarbons have been studied over a wide temperature range (78). Data on high temperature efnear or at infects of radiation-i.e., cipient cracking conditions-are of general theoretical and great practical interest because they give insight into the possible utility of nuclear radiation for commercial processes.
ALTHOUGH
Experimental Radiation Sources. Most of the experiments reported were done in the cobalt-60 radiation laboratorv a t the Esso Research Center, Linden, N. J. (2). The radiation from the 3200-curie source is pure gamma radiation from cobalt-60 (1.17 and 1.33 m.e.v. per disintegration) and a small beta contribution (0.31 m.e.v. per disintegration), with a 5.26-year decay half life (76). The graphite-moderated reactor at Brookhaven National Laboratory was used as the source of high intensity, mixed pile radiation (4). One of the available experimental holes (W-45) was used for the experiments. Radiation Intensities and Dosimetry. The cobalt-60 source consists of a hollow cylinder of cobalt, 13.5 inches long and 3 inches in outside diameter (18/4 inches in inside diameter), encased in an aluminum shell. The source strength as of June 28, 1955, was 3130 curies.
The radiation intensities at various distances from the axis of the source were obtained by calculation using the standard “point source” and standard “pipe source” calculation (22), and by actual measurement. The dose ratedistance relationship was determined experimentally, iron(I1-111) dosimetry as described by Weiss (25). The experimental data agreed very well with the dose rate derived from the pipe source calculation. As expected, the pipe source calculation was better than the point source approximation a t smaller distances from the source axis. Having established the dosage (Rad) as a function of distance from the source, it was necessary to examine the uncertainties introduced by absorption of energy in the reactor materials which contain the experiment. The vapor phase radiocracking runs were done in a reactor consisting of a metal tube wound around the source and separated from it by insulation. A hydrocarbon vapor inside this reactor will clearly not be exposed to the same flux as would be seen by a ferrous sulfate dosimeter at that point. A good portion of the incident energy is absorbed by the material separating the gas from the cobalt60 source. The reactor inside the insulation may not be wound symmetrically with respect to the source, so that not all portions of the hidden reactor are at equal distances from the axis of the source. The shielding by the reactor material may be calculated (76). For example, if RM is the actual dose rate transmitted
PUMP
through a material in Rads per hour, and Ro is the dose rate transmitted if the material were replaced by vacuum,
For the reactor used, the following data apply: Material Insulation Carbon steel wall Aluminum space Stainless steel wall
PI PG G./Cc. x, Cm. G./Sq. Cm
0.1
2.5
0.25
7.9
0.71
5.6
2.7
0.48
1.3
7.9
0.46
3.6
Taking dll2 = 12.0 grams per sq. cm. a calculated dose rate was obtained for the hydrocarbon vapor inside the actual reactor. This calculation was then compared with an experimental measurement of dose rate, which uses cellophane dyes as dosimeters for gamma radiation. T h e method used in this work was adapted from the work of Henley and Richman (73) in which a dye-containing cellophane is exposed to gamma radiation and the increase in transparency is taken as a measure of the dosage. This increase in transparency was measured a t 6550 A., with a Beckman Model DU spectrophotometer. Figure 1 shows the transparency change induced in the dye by various total doses of cobalt-60 radiation, measured by iron(I1-111) dosimetry. This calibration was then used as a dosimeter for measuring the dosage at various
PRODUCT RECEl VER (I GAL.)
Equipment used for cobalt-60 flow studies of radiation-induced cracking is essentially the same as that used for pile studies VOL. 50, NO. 6
JUNE 1 9 5 8
879
500
r-7
as measured by this technique agreed within 20% with that calculated using Equation 1. The problem of pile dosimetry is far more complicated than that of cobalt-60 dosimetry. I n the experimental Brookhaven hole used for this work, the quoted fluxes are:
I
I
5
P 0
5
IO
15
20
25
% TRANSPARENCY INCREASE ( 6 5 5 0 A )
Figure 1. Calibration of dye-impregnated cellophane dosimeter is used to measure dosage inside reactor coil
positions inside the reactor coil, with the coil in position around the cobalt pipe. Experimentally, it was found that the dye decoloration for the same time exposure was a function of its position within the reactor coil. This distortion indicated a nonuniform geometry, in that the reactor coil was twisted within the insulation in such a way that some portions were farther removed from the cobalt-60 axis than others. The dose rate (as measured by dye decoloration) was then determined throughout the reactor volume and plotted against a distance from an arbitrary reference point in the coil. By taking the area under this calibration curve and dividing by the distance from the reference point, a space-average dose rate was obtained. This value was taken as the dosage delivered to the irradiated sample within the reactor. The dosage
ALUMINUM
1
/,
Thermal neutrons 4 . 8 X 10l2 Fast neutrons 1 . 7 x 1012 The reliability of the thermal flux was determined to be = t l 5 % on the basis of gold foil activation experiments. The gamma dosage rate quoted above was obtained by using the approximation that the Rad per hour dose rate due to pile gammas is proportional to the square root of the thermal neutron flux ( 4 ) . For the Brookhaven reactor this approximation is valid to about 25% and has been verified experimentally a t Brookhaven by calorimetric studies (4). After the slow neutron flux and, therefore, the gamma dose rate had been established, the total pile energy absorbed could be approximated if it was known what fraction of the total energy absorbed is due to pile gammas. Taking this fraction as 25%, as suggested by Calkins ( 5 ) , gives Pile energy absorbed = 4 (thermal neutron flux)' 2 (2) I t was now necessary to estimate the reliability of Equation 2 for the graphite-moderator Brookhaven pile. The conversion of n-hexadecane was studied in both the liquid and vapor phase, using pile and cobalt-60 gamma radiation. After the cobalt-60 dosimetry had been established to &25%, the gamma-induced conversion of n-hexadecane was determined and this yield, G, was used as a chemical dosimeter
I IN. LEAD SHIELD I N S.S. CAN
I
PREHEATER 20 FT OF 1/8 S C H . 8 0 304
s. s.
REACTOR 1/8 IN. SCH. z- 80 304 S.S. 56.5 FT. LONG
Table I. Composition of Industrial Mixtures Used in Radiation Cracking Studies Gas Oil Source South West Louisiana
Texas
Boiling Range, C. O
316-371
316-357 Composition, Wt. % Paraffins Cyclic saturates 1-ring 2-ring 3-ring 4-ring 5-ring Single ring aromatics Benzonaphthenes I-ring 2-ring Naphthalenes Acenaphthenes Acenaphthylenes Phenanthrenes Pyrenes Chrysenes Benzothiophenes Dibenzo thiophenes Naphthalenobenzothiophenes Sulfides
18.4
11.9
24.0 14.0 11.1 5.0 1.3 3.0
18.4 10.0 7.9 3.3 1.8 6.4
2.3 3.3 1.2 3.7 4.6 3.9 2.8 0.8 0.1 0.3
3.2 3.8 0.9 2.1 5.5 3.2 0.8 2.0 3.7 6.1
1.0 0.3
1.4 6.5
for measuring pile energy absorption. By measuring pile conversion, and estimating pile energy absorption from Equation 2, the G value for pile-induced conversion, G,, was obtained and compared with G. These values agreed within a factor of 2. Finally, Equation 2 was tested by a rigorous solution of the equations pertaining to a graphite-moderated pile (70, 20, 27). The result of the calculation showed that for the Brookhaven reactor, Equation 2 may be used to estimate energy absorption with twofold uncertainty. Materials. The materials used in this study were pure n-hexadecane, pure methylcyclohexane, and industrial gas oil mixtures. The methylcyclohexane (MCH) was Phillips pure grade material, and the n-hexadecane was ASTM material from Humphrey-Wilkinson, Inc. The two industrial mixtures were a South Louisiana and a West Texas gas oil. Their composition determined by mass spectrometric analysis, is given in Table I. Apparatus and Procedure. The equipment used for cobalt-60 work was essentially the same as that used for pile
CUTLET I
VOLU M E - 400 C. C. TH E R M O
INSULATION :- 3 IN. SUPER X 2 IN. MAGNESIA
~
WALL
ELECTRICAL WINDING ON OUTSIDE OF VESSEL Figure 2. Radiation-induced cracking with cobalt-60 source was studied in this reactor
880
INDUSTRIAL AND ENGINEERING CHEMISTRY
Figure 3. Radiation-induced cracking in-pile was studied in the Brookhaven atomic reactor
HYDROCARBON RADIATION I
studies. The reactors were somewhat different (Figures 2 and 3). Two types of batch reactor were used for the cobalt60 studies. One reactor, which fitted ,inside the center of the cobalt-60 pipe and was exposed to 106 Rad per hour, was a 150-cc. stainless steel bomb equipped with heaters, thermocouples, and insulation. The other reactor, a 500-cc. bomb, could be used near the outer surface of the source where the gamma intensity was about 105 Rad per hour. The reactor used for the cobalt-60 work (Figure 2) consisted of a reactor and preheater coil embedded in an aluminum block to maintain a uniform reactor temperature. The reactor was wound around a 6-inch pipe, in which the cobalt-60 source could be placed. The asymmetrical nature of the winding necessitated calculation of integrated dose rates. The preheater to the reactor coil was shielded with lead to minimize' radiocracking in the preheater. To protect the aluminum casing from melting, the cobalt-60 source was air-cooled during the high temperature runs. Radiation intensities available within the reactor were of the order of 2 X 105 Rad per hour. The flow reactor used for in-pile work (Figure 3) was a 11/4-inch aluminum pipe provided with a thermocouple well and lines for feed inlet and product outlet. Only the last 30 inches of the reactor were exposed to pile radiation, the remaining 20 feet being required to connect the radiation vessel to the auxiliary equipment outside the pile face. The reactor was encased in an electrically heated, stainless steel tubular furnace surrounded with insulation. The temperature of the furnace could be varied up to 540' C. and was measured by seven thermocouples connected to the outside auxiliary equipment. The procedure used for a run was as follows: All the equipment was flushed out with an organic solvent (Varsol) and nitrogen for 2 hours. The reactor and auxiliary lines were then filled with liquid feed and the actual run was begun when steady-state conditions were attained. The product from the reactor passed through a cold trap and a dry ice trap, in which most of the products were condensed. The noncondensable gas passed through a scrubber and was sampled, metered, and finally vented to the atmosphere. All runs were paired experiments with and without radiation; where a blank (thermal) contribution was observed, it was subtracted from the radiationinduced reaction to obtain the radiation yields. Therefore, radiation yields reported in this work refer only to radiation-induced conversion as obtained by difference between paired experiments, with and without radiation.
Table
II.
Conversion Data for Radiation-Induced Cracking of n-Hexadecane and Gas Oil Mixtures in Vapor Phase
Feed West Texas gas oil So. La. gas oil n-Hexadecane
Contact Time, Sec.
Conversion Level, Wt. %, without Radiation
% Conversion with Radiation
Temp.,
25 25 25 25 61 58
41.3 34.4 18.7 11.8 0 0
45.3 38.8 25.5 15,5 6.4 4.8
510 510 482 468 371 327
Analytical. The weights of liquids fed and collected in the cold and dry ice traps are subject to only negligible weighing error and were obtained with analytical balances. Volumes of noncondensable gas were measured to better than 1% accuracy with calibrated wet-test meters. The liquid , product was distilled with a 15-theoretical plate distillation column at a reflux ratio of 5 . The composition of the cuts was determined by a chromatographic technique which determines aromatics, saturates, and olefins to 5 1 % ; the composition of light gases was determined by mass spectrometry with a 95% confidence level (absolute) of 2~0.2%for all components except hydrogen, nitrogen and Cg. The 95% confidence level is f 0 . 5 % for these components. The instrumentation and calculation followed previous work (9, 75). The chromatographic technique (FIA) has been described (7). From the distillation and analysis of products, the amount of feed remaining after cracking could be measured for both radiation-induced cracking and the corresponding blank. After subtracting blank conversion, and estimating the energy absorbed, the G values are calculated as molecules of feed reacted per 100 e.v. absorbed. By assuming seven radicals made per 100 e.v., (24) radical yields, Y , are reported as G/7. Estimated Uncertainty. The largest error in the reported G values is felt to lie in the estimated energy absorption. For pile work, this estimate is considered reliable within a factor of 2. For cobalt-60 work, the energy absorption is considered good to 5 2 5 % . However, the reported cracking G values are so high that they are significantly different from normal even with a possible twofold error from dosimetry. The object of this work was to determine the radiation yield of hydrocarbon cracking at fairly low exposure. Therefore, the differences in conversion obtained with and without radiation were rather small despite the generally high radical yields. I t was necessary to design the experiments, so they could be treated statistically. All runs were paired, with and without radiation, and
O
c.
Radiation Source 03-60 CO-60 CO-60 CO-60
Pile Pile
the order in which paired runs were done was randomly varied-blank runs were not uniformly made before radiation runs, and vice versa-to reduce systematic errors as far as possible. All reported differences in conversion are greater than the material loss (material balance greater than 98%), and greater than the estimated error in determining conversion.
Results Higher cracking conversions were consistently obtained with radiation than with thermal blanks, for both pure and mixed feeds, at different levels of conversion and at different temperatures. This is illustrated in Table I1 for some high temperature, vapor phase data. The variables of interest in this work were temperature, phase, and radiation intensity (pile us. pure gamma). Generally speaking, for all materials studied, radiation increased the rate of cracking. Table 111. Products and Yields from Cobalt-60-Initiated and Thermally Initiated Cracking of a South Louisiana Gas Oil Mixture
Feed rate, 360 g./hr. Temperature, 510' C. Pressure, atmospheric Radiation dosage, Rad 900 0 Recovery, wt. %a 98.6 98.8 Conversion to cracked products, wt.% 38.8 34.4 Net difference, 4.4 wt. % converted per 900 Rad adsorbed , Com-
position
HZthrough C3 products, mole % Hz CH4
cz cs
4.3 28.8 40.3 26.6
4.5 28.7 39.2 27.6
CSthrough 220' C.
product, vol. % Aromatics 15.2 13.2 84.8 84.5 Olefins Saturates 2.5 220° C. through 315' C. product, vol. y* Aromatics 23.3 19.8 64.1 62.3 Olefins Saturates 12.6 17.9 a Difference between 100 and % recovery due t o coke formation. Material balance
..
99.5%.
VOL. 5 0 , NO. 6
JUNE 1958
881
Table IV. Composition of C1 to Cg Products from Pile Radiocracking of n-Hexadecane 327
L
W
a
CH4
cz c 3
C4 C6
Figure 4. Thermal and cobalt-60produced spectra of cracked products from methylcyclohexane are closely related 25-second exposure of methylcyclohexane at
4680
c.
The product compositions obtained thermally and with radiation were closely similar. Table I11 compares data obtained a t 510' C. from the cracking of a gas oil mixture initiated thermally and with cobalt-GO radiation. The question whether pure radiocracking results in the same product composition as pure thermal cracking is important. However, it is difficult to answer unequivocally by comparing thermal runs with runs in which cracking is initiated both thermally and by radiation. The products obtained in such paired runs invariably had a similar composition (Table 111). Howeverj as the difference in conversion between paired runs was small, it is more instructive to examine the data obtained from pure radiocracking of n-hexadecane.
BASED ON PILE STUDIES (EQ 20)
I30
140 I I T X I$
150
160
170
OK-'
Figure 5. At higher temperatures radiation yields are high. Radiation yields increase with increasing temperature
882
O
C. 500
Radiation Pile Pile None Composition, Mole %
I
i
Temperature, 371
23.9 60.0 11.2 4.0 0.5
31.1 55.1 12.2 1.2 0
19.2 47.2 21.8 8.3 3.2
At 371' and 327' C., n-hexadecane was decomposed by pile irradiation with a contact time that gave no measurable conversion thermally. In Table IV the composition of cracked products is compared with thermal data (12, 23) There is a close similarity between the distribution of decomposition products obtained by pure thermal cracking and pure radiocracking. An interesting effect becomes evident on comparing the cracking of n-hexadecane a t low temperatures with the results obtained a t cracking temperatures. For example, pile-induced cracking of n-hexadecane (liquid) a t 200' C. gives a hydrogen through CB product that is 97 mole % hydrogen. This is in sharp contrast to the 470' C. experiments, from which the corresponding hydrogen concentration is only 1 to 2 mole %. At an intermediate temperature of 370' C., the hydrogen through Cs product is 34 mole % hydrogen. Thus, on passing from the low temperature region to higher temperatures, where cracking is favored, the reaction changes from a nonchain process yielding gases rich in hydrogen to a long-chain reaction yielding gases that contain relatively little hydrogen. Because methylcyclohexane has never been studied with cobalt-60 gammas, and it represents a compound whose molecular structure is widely different from that of n-paraffins, the cracking pattern from pile irradiation of this compound was compared with that from thermal cracking. This compound, a t 468' C., gives cracking radiation yields (about IO4) indicative of long-chain reactions. I n Figure 4 the spectrum of light hydrocarbons obtained from methylcyclohexane is compared for the radiation-initiated and the thermally induced decomposition. For convenience, these yields are plotted as moles of product made for every 10 moles of material fed during the same time interval (25 seconds) with and without radiation. I t is evident from Figure 4 that the two decomposition spectra are closely related. A striking feature of radiocracking is that the radiation yields are extremely high a t high temperatures. No results are reported here for low temperature (below 200' C.) liquid phase cracking,
INDUSTRIAL AND ENGINEERING CHEMISTRY
a
as regardless of the feed studied and the radiation type used, these experiments gave low cracking yields. Under these conditions, the number of molecules of feed reacting to give cracked products was of the order 5 to 15 per 100 e.v. absorbed. The situation is different, however, a t higher temperatures, where the radiation yields are high. The yields, molecules decomposed per radical formed by radiation, are lo4 to 106 and increase with increasing temperature. As defined in this way, the yields are really radical yields, Y , and differ from ordinary G values in that they are the G value divided by the radicals made per 100 e.v. absorbed. The radical yields are plotted in Figure 5 us. the reciprocal of the absolute temperature. Data points are included for pile radiation (lower temperature data) and cobalt-60 radiation (higher temperature data). Liquid phase data for cobalt-60 work (n-hexadecane feed) are included for comparison with vapor phase work. Discussion At low temperatures, under conditions where nuclear radiation is the driving force for the cracking of hydrocarbons, low radiation yields are obtained and the cracked product is rich in hydrogen. The radiation-induced dehydrogenation of hydrocarbons a t low temperatures is well known (79). At higher temperatures, however, radiation tends to initiate a chain reaction. At high temperatures the cracked product distribution from radiocracking is the same as obtained thermally, the radical yields are extremely high and increase with increasing temperature, and there is a tendency for yields to decrease with increasing intensity of radiation, and to be lower in the condensed phase. Nuclear radiation gives ions, radicals, and excited species (ions or radicals) as the primary products of its interaction with matter. For a long-chain reaction, the actual nature of the initiation step might be expected to be less important than the subsequent chain propagation steps. While an unequivocal chain mechanism cannot be given for these reactions, it is instructive to ask whether the major results from this work could reasonably be reconciled with well established principles of value in ordinary chemistry. The similarity between products obtained in thermal and in radiocracking suggest that this should be the case. According to the Rice-Herzfeld mechanism for thermal cracking (77), the following free radical chain reactions could be written for a hydrocarbon M, with intermediate radicals denoted by R
M R
+
Rf
+M
+
. ..... RH
+ R'
(3) (4)
HYDROCARBON RADIATION R ’ + R 4- M’
(5)
2R’ + M ”
(6)
where M is the molecule decomposed, R and R’ are radicals made by radical decomposition and hydrogen abstraction reactions, respectively, and M denotes product molecules. The over-all activation energy for decomposition of n-hexadecane, ET, is taken as 6O/Kcal. per mole, following the work of Voge and Good (23). Where there is no thermal contribution to radio-cracking, as in the low temperature pile data for n-hexadecane (see Figure 5), the reported Yvalues are a direct measure of the chain length, L. These Y values are radiation yields expressed as molecules decomposed per radical formed by radiation. From Figure 5, the energy of activation, EL, is taken as 25 kcal. per mole. This value, EL,is reasonable from the low temperature pile data, and it is also reasonable for the activation energy of the chain-propagation steps in the Rice mechanism. The radiation initiation is assumed to be temperatureindependent and the mechanism given by Equations 3 to 6 is assumed to apply throughout the temperature range studied. For a long-chain reaction terminated by bimolecular recombination of like radicals, R‘, the following equations apply (7)
L =
1 k6 -( M ) ’ / 2 [ksks]”2
(7)
where L is the chain length of the reaction. The subscripts refer to Equations 3 to 6 of the mechanism, and the brackets ( ) denote concentrations. Now the rate of initiation is k 4 M ) for purely thermal initiation and I* for radiation initiation. The activation energy for recombination is assumed to be zero, and L is found to have an activation energy of 25 kcal. per mole from the pile data. Therefore, from the low temperature data. 1 5 k o e--2W00/RT L =Z*1/2
[keO]1/2
(8)
I n Equation 8, the superscripts O denote the pre-exponential term in the Arrhenius equation. Knowing L from the pile data at 371’ C. (no thermal contribution), and knowing the initiation rate for pile radiation, Equation 8 can be used to evaluate the ratio k5°/[k60]1/2. For p1I2= 106.5, the ratio is k6 Ikso]l12
= lol*
(9)
This result is in good qualitative agreement with the value calculated from the thermal mechanism. Thus, the theoretical frequency factor for the unimolecular Reaction 5 is 1018, and it is 10-10
for the bimolecular termination Reaction 6. The expected ratio, k50/[k6°]1/2is, therefore, 1O1*. Having justified the use of 25 kcal. per mole in Equation 8, one can now culate the rate at which the paraffin (nCl6H84) splits directly into radicals. This quantity, the primary rate of decomposition, is an important number that is rarely measured in the cracking literature. However, the use of radiation as an initiator gives an important additional tool with which this initiation rate can be measured: The rate of initiation is known for radiation, and the chain length can be measured under conditions where only radiation contributes to cracking. From these data, one can infer the activation energy, the ratio of frequency factors for propagation and termination and, finally, the rate of primary thermal decomposition. From the mechanism given it can be shown (78) that the cracking rate is proportional to k5 (k&k~)
[email protected], the over-all activation energy, ET, is given by
a-
ET
=
E6
+ Eiy
(10)
as the activation energy for termination is assumed to be zero. Ed is now the activation energy of the initiating primary split into radicals. Since ET E 60 25 kcal. per mole, and E5 = EL kcal. per mole, E; is about 70 kcal. per mole. The primary rate at about 500’ C. is then It,, =
1013 e-70 x 1.:/2
(MI
(11)
where 1013 is the pre-exponential term in the Arrhenius equation, and ( M ) the concentration of molecules in molecules per cc. For n-hexadecane the result is 3 X 101* molecules decomposed per cc. per second at about 500’ C. I t is now necessary to distinguish clearly between radiation yields and true “chain lengths” for the chain process. Radiation yields are a useful tool for gaining insight into the nature of the true chain reaction. However, in studying a reaction where there is a thermal back-ground component in addition to the radiation-induced process, it is necessary to examine the true chain length of the reaction as related to the measured radiation yield. The rate of a long-chain reaction, r, is governed by the propagation rate, and r = kp(R)
(12)
where r is the rate of disappearance of feed, k, the rate constant for propagation, and (R) the concentration of radicals. What is measured in this work is the rate, r*, the difference in rates obtained with and without radiation. These two independent experiments allow us to estimate the rate of thermal and of
radiation initiation. If the asterisk denotes the radiation portion of the chain, =
I*
k p (R)total
- k p (R)therrnal
(13)
Also; denoting initiation rates by I, and
(R)totsl =
(R)th =
(14)
[$]112
Combining equations gives r* p
=
k
4
m
2
1‘ +
-
[p 5]l/2
ply (15)
The term in brackets on the right side is denoted by A . The left side, corrected for the radical yield per 100 e.v., is the measured Y value in this discussion. Therefore, Y=-d
kP
(15’)
The true chain length, L, is defined by Equation 16.
Therefore,
Multiplying top and bottom of 17 by (I*)’/a and combining with 15’ gives
Denoting for convenience the term in brackets in Equation 18 by B, and the ratio A / B by C, the equations simplify to
Y = LC
(19)
Therefore, the extent to which measuring Y gives a true measure of L depends upon the value of C. C is composed entirely of terms in Iln/I*, the ratio of thermal to radiation initiation rates, and both rates can be estimated. C varies with the ratio of thermal to initiation rates as follows: C
Ith/I* 0 1 10
1
0.591 0.531 0.503
100
C is, therefore, about 0.5 at high ratios of thermal to radiation initiatic i rates. The equations derived above may now be used to calculate the Y values we should observe in the high temperature, cobalt-60 cracking studies. The intensities available from this gamma work were about 100-fold lower than available in the pile, and were such that Ith/I* corresponds to about 0.5 for the correction factor, C, based on the previously estimated It&. From Equations 17 and 19, substituting the values in 8 and 9, Equation 20 is obtained. VOL. 50, NO. 6
4
JUNE 1958
883
,
AS all the terms on the right side are available, Y may be estimated for the high temperature work with cobalt-60 initiation. I n Figure 5, the dashed line drawn at higher temperatures represents the calculated line for radical yields as a function of temperature. The good agreement between observed and calculated yields can be considered evidence of the postulated mechanism. Ignoring the possible effects of dose rate upon Ith, the variation of Y with temperature can be inferred from Equation 20. As the temperature coefficient of It&is greater than E L . a t very high temperatures (where Ith >> I*), Y should begin to decrease with increasing temperature. This region has not been reached in this work, but it is predicted from Equation 8, and for a Rice-Herzfeld mechanism of the type assumed. The temperature coefficient of the thermally initiated chain length will be the difference between the activation energy for propagation and one half the activation energy for initiation. This is predicted from the Rice-mechanism, (78) and evident from Equation 20. As one-half Ei > E L , the observed radical yields should begin to decrease at sufficiently high temperatures, and should decrease at a rate corresponding to a temperature coefficient of about 10 kcal. per mole. A very pronounced effect of phase is evident from Figure 5. The cracking radical yields, Y, are about 100-fold higher in the vapor than in the liquid phase, when compared for the same starting material a t comparable temperatures. A reasonable explanation for this inhibiting effect of phase is the “cage effect” postulated by Franck and Rabinowitch ( 7 7), which favors recombination of primary radicals in the solvent cage of a condensed phase. In the cracking literature, the question of chain length in hydrocarbon decomposition often comes up in connection with the effect of inhibitors on decomposition rate. Upon addition of radical traps such as NO, many hydrocarbon decomposition rates decrease and reach a limiting value, r m . The “chain length,” as measured by this technique ( 1 4 , is the ratio K of the over-all cracking rate (uninhibited) to fully inhibited rate. The true chain length, L, is the rate of the over-all free radical reaction rate to the rate of initiation, I t h . Boudart (3) has pointed out that K and L are related by
rate of cracking in the presence of a limiting concentration of inhibitor. Since I t h has been estimated in this work as roughly 3 X the ratio I t h / r m is small, of the order to 10-5. These considerations support the view that the “fully inhibited” thermal decomposition is still a free radical chain process. This limiting rate is sometimes considered to be due entirely to molecular reactions involving direct decomposition to products without intermediate radical chain reactions. However, Ith/r, is small; this means that the rate a t which the molecule splits into radicals is many orders of magnitude smaller than the rate at which it splits into molecules. I t seems more reasonable to invoke the other alternativethat the “fully inhibited” decomposition proceeds via free radical chain reactions.
X
Y
dose rate transmitted if material were replaced by vacuum = thickness of shielding material, cm. = molecules decomposed per radical made by radiation =
Acknowledgment
The authors wish to acknowledge the advice and encouragement of ,their colleagues a t the Esso Research and Engineering Co., and to express their appreciation to the company for permission to publish this information. They wish to thank M. Boudart and R. W. Houston for advice in preparation of this article. literature Cited
Nomenclature
The experimental value of K is usually about 10, but this can be reconciled with a large value of L, if the rate of initiation is much smaller than the
884
Ro
INDUSTRIAL A N D ENGINEERIN6 CHEMISTRY
correction factor product of density, p, and thickness, x for which dose rate in material is 1/2 Ro energy of activation for radical decomposition activation energy for primary decomposition of M into radicals energy of activation for radiocracking a t temperatures where there is no thermal contribution over-all activation energy for thermal decomposition radiation yield in molecules reacted per 100 e.v. adsorbed radiation initiation rate, radicals formed per cc. per second thermal initiation rate, radicals formed per cc. per second pre-exponential term in Arrhenius equation rate constants in units; molecules, cc., seconds rate constant for propagation of chain reaction rate constant for chain termination ratio of uninhibited to fully inhibited cracking rate chain lengths concentration of feed, molecules per cc. density of shielding material. grams per cc. rate of long-chain reaction rate of long-chain reaction due to radiation initiation only rate of thermal cracking reaction fully inhibited by S O radicals of different structure actual dose rate transmitted through a material, Rads per hour
(1) Am. SOC.Testing Materials, “Fluo-
rescence Indicator Adsorption,” Designation D 1319.
(2) Black, J. F., Kunc, J. F., Jr., Clark, G. B., Znt. J . A$@. Radiation and Isotopes, 1, (1957).
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