Correlation of Data with Severity Factor
The product distribution of hydrocarbons depend in a complex manner on the temperature and the residence time of the process. Except for the very simple hydrocarbons a n accurate mechanism of cracking is still not known. To overcome this difficulty, yields of products from cracking furnaces have usually been correlated by a severity factor (Linden and Peck, 1955; White, et al., 1970). The severity factor can be defined mathematically as S = TP
(3)
where T is a characteristic temperature and T the residence time. To correlate the data of this study, T was taken as the equivalent reactor temperature in degrees centigrade and T as the residence time, in seconds, based on the equivalent reactor temperature. The value of m which gave the best fit for all the products was 0.06. Figures 5 and 6 show the variation of some of the major products with the severity factor. However, Figure 6 shows that the slope of the curve for 2butene decreases and it shows a maximum, Le., a t high severity. The rate of cracking of 2-butene becomes competitive with the rate of formation and a t higher severities the rate of cracking would eventually predominate and the yields of 2-butane would decrease with severity. Except for hydrogen, the other products would follow the same trend although the severity a t which the maximum is reached would be different for different hydrocarbons. Conclusions
The following conclusions can be made from the present study. (1) The rate constant for overall decomposition of 2pentene over the temperature range 670-725’ has a frequency factor 8.77 X 10” sec-1 and an activation energy of 53.4 kcal/mol. (2) Rice’s theory does not predict well the product distribution for the cracking of 2-pentene.
(3) The severity function, S = TTO*O~, where T is in “C, can be used to correlate the variation of production distribution for the cracking of 2-pentene. Nomenclature
A E k m
S X
= = = = = =
frequencyfactor activation energy firsborder rate constant exponent in severity correlation severityfactor conversion
GREEKLETTERS T = residence time Y = moles product per mole of pentene cracked literature Cited
Crynes, B. L., Albright, L. F., Ind. Eng. Chem., Process Des. Develop., 8 , 25 (1969).
Fabuss, B. M., Smith, J. O., Lait, R. I., Borsanyi, A. S.,Satterfield, C. N., Ind. Eng. Chem., Proc. Design Develop., 1 , 293 (1962).
Gorin, E., Oblad, A. G., Schmuck, R. F., Znd. Eng. Chem., 38, 1187 (1946l. --, \ - -
Hepp, H. J., Frey, F. E., Znd. Eng. Chem., 41,827 (1949). Hurd, C. C., Goodyear, G. H., Goldsby, A. R., J . Amer. Chem. SOC.,58, 235 (1936).
Kunzru, D., Ph.D. Thesis, University of Pittsburgh, 1972. Kunzru, I)., Shah, Y. T., Stuart, E. B., Ind. Eng. Chem., Process Des. Develop., 1 1 , 605 (1972).
Linden, H. R., Peck, R. E., Ind. Eng. Chem., 47,2470 (1955). Magaril, R. S., Advan. Chem. Ser., No. 97, 110 (1970). RIarschner, R. F., Znd. Eng. Chem.,30,554 (1938). Norris, J. F., Reuter, R., J . Amer. Chem. SOC.,49, 2626 (1927). Pease, R. N., Morton, J. R., J . Amer. Chem. Soc., 55,3197 (1933). Rice, R. O., Rice, K. K., “The Aliphatic Free Radical,” Johns Hopkins Press, Baltimore, Md., 1935. Sakai, T., Soma, K., Sasaki, Y., Tominaga, H., Kunugi, T., Advan. Chem. Ser., No. 97, 68 (1970).
Szabo, Z. G., “Advances in the Kinetics of Homogeneous Gas Reactions,” Methuen, London, 1964. White, L. R., Davis, H. G., Keller, G. E., Rife, R. S., paper presented at the 63rd AIChE Meeting, Chicago, Ill., Nov 1970. RECEIVED for review September 25, 1972 ACCEPTEDFebruary 16, 1973 The financial support from Gulf Educational Fund is appreciated.
Thermal Cracking of Hydrocarbon Mixtures. Mixtures of Octane-Nonane and Nonane-2-Pentene Yatish T. Shah,* Edward B. Stuart, and Deepak Kunzru Chemical and Petroleum Engineering Department, University of Pittsburgh, Piitsburgh, Pennsylvania 15213
A l t h o u g h we now have a n extensive literature on thermal cracking of pure hydrocarbons, we are still unable to design an industrial naphtha cracking reactor. One of the main reasons for this is that the existing theories as well as experiments on the subject have seldom examined a mixture of hydrocarbons in a systematic way. Specifically, the existing literature fails to answer the question: can we use our present knowledge of cracking of pure hydrocarbons and analyze the cracking of multicomponent mixtures? Or do the hydrocarbons interact during mixture cracking? This paper takes a step toward the analysis of this question. I n this paper we make an attempt to systematically understand thermal cracking of binary hydrocarbon mixtures. 344 Ind.
Eng. Chem. Process Des. Develop., Vol.
12, No. 3, 1973
We examine two mixtures, namely, octane-nonane and 2pentene-nonane. The mixture octane-nonane was closen because octane and nonane are the two largest carbon number alkanes present in a significant amount in light naphtha. Moreover, if one does not find a significant interaction in cracking of this mixture, then it would strongly suggest that the lower member of the series would also behave the same way. This is because the smaller alkanes are less reactive and also they would crack to give fewer species of free radicals, thus reducing the possibility of an interaction. The mixture of 2-pentene and nonane was chosen to evaluate interaction effects between an aliphatic and an olefinic compound during thermal cracking. 2-Pentene is the lowest
This paper reports an experimental study on thermal cracking of two hydrocarbon mixtures, namely, octanenonane and ;!-pentene-nonane, in a laboratory scale flow reactor. The reactor was operated between 650 and 7 2 5 " and at atmospheric pressure. The residence time of the mixtures was varied from 0.1 to 2 sec. The experimental results indicated that cracking of nonane is essentially unaffected by the presence of octane. Thle cracking of nonane is, however, significantly affected by the presence of 2-pentene. The paper presents an empirical relationship for the predictions of product distribution of octane-nonane mixture crackling from the available data on pure component cracking at the same pressure, temperature, and residence time conditions. Finally, the severity correlation outlined earlier by Kunzru, et a/., for cracking of n-nonane and 2-pentene was found to be applicable for cracking of octane-nonane and 2-pentenenonane mixtures.
olefinic compound pre5,ent in feed naphtha in liquid form. Furthermore, the range of temperatures under which it cracks significantly is similar to the cracking temperature range for n-nonane. Thus, one can compare the data of mixture cracking with tHe ones for pure components under similar temperature and residence time conditions. Previous Work
Literature data on the pyrolysis of hydrocarbon mixtures is very limited. In order to increase 1-butene yields Robinson and Weger (1971) pyrolyzed propylene-propane mixtures a t temperatures near 1100' and 1 msec reaction time in a quartz annular flow reactor. The reaction conditions employed in their study were unconventional (as compared to conditions used in industrial cracking units) in order to produce significant amounts of 1-butene. KO 1-butene was formed when propane was pyrolyzed by itself and only very small amounts when propylene was pyrolyzed separately. However, when propane-propylene were copyrolyzed a sixfold increase in prop) lene selectivity (moles of 1-butene formed per mole of propylene decomposed) resulted. They did not report the effect on the yields of other products in the copyrolysis. I s part of a study on ethylene pyrolysis, Kunugi and coworker,j (1969) pyrolyzed ethylene-ethane mixtures at 770" and found the product distribution in the presence of ethane to be substantially the same as that of ethylene itself a t the same conversion. Barabanov and Mukhina (1962) studied the pyrolysis of ethane-propane mixtures a t atmospheric pressure and temperatures of 750 and 800'. At 750', the rate of decomposition of propane in ethane-propane mixtures was higher than the rate of decomposition of propane alone but there was no effect on the rate constant of propane a t 800'. On the other hand, a t 750' ethane in ethane-propane mixtures cracked a t the same rate as pure ethane, whereas a t 800' and identical residence times, the conversion of ethane in ethane-propane mixtures was lower than in the pyrolysis of pure ethane. They found that the yield of ethylene in the pyrolysis of ethane-propane mixtures could be calculated by using the rule of additivity, L e . . from its yield in the pyrolysis of ethane and propane separately. The yields of the other pyrolysis products could not be calculated according to this rule of additivity. The actual yields of methane and the CCfraction were higher and those of propylene and hydrogen (at 750') were lower than those calculated from the rule of additivity. Rice and Polly (1938) reported that the presence of propylene retarded the rate of decomposition of propane and butane. They put forth the explanation that propylene inhibited the rate by reacting with the free radicals forming an allyl radical and a saturated paraffiri. According to them the allyl radical
thus formed rcacted with itself to form diallyl. Product yields and activation energies were not measured. Eshevskaya (1940) found that diisobutane, normal butene, and ethylene exerted no noticeable retarding effect on the cracking of isooctane a t atmospheric pressure but that isobutene, propylene, butadiene, cyclohexene, and isoprene reduced the decomposition velocity of isooctane. She also measured the effect of butadiene on the rate of cracking and the product yields of normal octane. At a 10 mol % concentration of butadiene in normal octane, the conversion a t 552' and a residence time of 7.4 sec reduced from 17.5 to 10.2%. The effect on the product distribution was negligible. She explained the phenomena on a mechanism based on the assumption that active radicals were combined by molecules of unsaturated hydrocarbons forming radicals of low activity. The combination of active radicals with the formation of inactive radicals was regarded as a rupture of the chain. Most of the studies on the copyrolysis of hydrocarbons have concentrated on the determination of rate a t one temperature and very few activation energies and product distribution have been reported. Invariably the workers have assumed that the retarding component was not decomposed itself. Moreover, no data on the copyrolysis of two large hydrocarbons are available. Experimental Section
The experimental details for this study are the same as ones described by Kunzru, et al. (1972, 1973). The precautions for removal of possible catalytic effect of stainless steel reactor described by Kunzru, et al. (1972, 1973), were also taken in the present study. For the reasons discussed by Kunzru, et al. (1972, 1973), the catalytic effect of stainless steel wall on the overall product distribution and the kinetic data of the present study is believed to be very small. The data were generated in stainless steel wall reactor because they are more representative of industrial operations. A more detailed description of the experimental aspects of this study is also given by Kunzru (1972). Cracking of Octane-Nonane Mixtures
To study the interaction between octane and nonane, three different octane-nonane mixtures (25, 52, and 75 w t OCtane) were cracked a t 650, 670, 700, and 725'. Residence times were varied from 0.1 to 2 sec, the lowest residence times being realized a t the highest temperatures. High conversions a t 725' could not be achieved because of the clogging of the reactor with carbon deposits formed in the run. Overall Kinetics
The order of the reaction was determined in the same manner as mentioned earlier (Kunzru, et al., 1972, 1973). Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973 345
Table 1.
Order of the Reaction for Octane-Nonane Mixtures Octane
Nonane Mixture comporition, wt
r, oc
25
1.16 1.23
725 670 100
52
I
4
1.2 1.2
I
I
Octane
25
52
75
1.15 1.22
1.1 1.2
1.06 1.15
1.02 1.17
1.03 1.13
I
I
I
% OCTANE 100 25 52 7s 6 5 0 ~ 670.f 8 0 0 0
e o o a
-
80
700%
A A A A
-
z i 60 0 VI a W >
"
40
20
0 0
04
08
12
16
20
24
28
32
T, SECONDS
Figure 1 . Conversion of octane vs. r for pure octane and octane-nonane mixtures 100, '
85O.C
80
670.C 700.C
725.C
a@ i 60
-I
X OCi4NE 100 25 52 75
e o o a
8 0 0 0
P
> 40
20
0 04
08
12
16
20
24
28
3.2
r, SECONDS Figure 2. Conversion of nonane vs. r for pure nonane and octane-nonane mixtures
The values determined a t 670 and 725' for the three mixtures are listed in Table I. As can be seen from Table I, there was no significant effect on the order with a change in the composition of the hydrocarbon feed. In all cases, the order increases with decrease in temperature. This effect was the same as the ones observed in the cracking of pure octane and nonane. Rate Constant
The variation of octane and nonane conversion in the copyrolysis of the various mixtures is shown in Figures 1 and 2, respectively. First, the mixture with approximately equal parts of octane and nonane was studied. Then, to see the effect when one of the components was in excess, mixtures with weight ratio of octane to nonane of 3:l and 1:3 were studied. I n order to evaluate any effect on the kinetics, the individual conversions of octane and nonane, rather than the overall percentage decomposition of the feed were calculated. In calculating octane conversions, the amount of octane pro346
1.01 1.11
duced by the cracking of nonane was neglected. In nonane cracking, for the range of experimental conditions studied, the highest amount of octane formed was 1.2 mo1/100 mol of nonane cracked. The amounts of octane produced in nonane cracking had the maximum effect on the conversion when nonane was in excess, Le., the mixture in which the weight per cent octane was 25. However, this maximum error was approximately 2% so that neglecting the amounts of octane formed had a negligible effect on the calculated conversion. From Figures 1 and 2, it is clear that there was no effect on the conversions obtained in the copyrolysis as compared to the conversions of the pure hydrocarbons. For identical experimental conditions the percentage decompositions for octane and nonane in the copyrolysis of the three mixtures a t all temperature levels and residence times were within k3% of the values found in the cracking of pure octane and nonane. Since the conversions for each component a t any temperature could be represented by a single curve, individual activation energies and frequency factors for the different mixtures were not calculated for the cracking of octane-nonane mixtures. Product Distribution
W
0
Nonane
A A A A
+ 000
0"
E
% octane
75
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
The products formed in the cracking of octane-nonane mixtures were very similar to the products formed in the cracking of pure octane and pure nonane. No new products were formed. The gas weight per cent values obtained were between those obtained for pure octane and pure nonane. The variation of gas weight per cent with conversion for one mixture (52.0wt % of octane) is shown in Figure 3. The conversions in Figure 3 are overall percentage decomposition calculated on the total feed. At a conversion of 50%, whereas the gas weight per cent obtained in octane and nonane cracking was 42.5 and 39.2,respectively, the gas weight per cent for this mixture was 42.0. Gas weight per cent values a t different concentrations and conversions follow a similar trend. A detailed product analysis of some typical runs a t 670' is shown in Table 11. At high percentage conversions, only about 90% of the total products could be individually determined. As one may expect, under the investigated experimental conditions ethylene is the major product a t all temperatures and constitutes about 30 mol % of the products. The amounts of Hz and CrC3 hydrocarbons increase with increasing conversion while those of Cg and higher decrease. This result is reasonable because a t large residence times the larger paraffins and olefins produced in the cracking decompose a t a faster rate than the lower hydrocarbons, thereby increasing the yield of the lower members of the series. The variations in the amounts of hydrogen, methane, ethylene, propylene, ethane, and hexene with residence time a t a typical temperature of 700' and a feed concentration of 52% octane are illustrated in Figure 4. Over the range of experimental conditions studied, except for hexene, the
Table II. Product Distribution in Octane-Nonane Cracking at 670" 25 25 52 52 75 Wt % octane 0.4 1.6 0.35 1.66 0.25 Residence time, sec 17.5 40.2 12.3 38.7 17.4 Octane conversion, % 44.0 9.2 15.2 20.0 41.5 Nonane conversion, % ' 97.5 98.7 98.4 98.4 97.0 Material balance, YO 1.9 5.2 2.1 5.1 2.1 Unidentified material, % ' Mo1/100 mol cracked 27.8 20.2 29.5 20.7 25.1 H2 52.2 77.5 49.5 78.7 55.5 CH4 123.1 93.5 122.0 90.2 98.2 C2H4 34.2 32.0 35.0 32.0 31.7 CzHs 45.1 45.5 33.2 31.2 36.1 CaHa 5.2 4.1 6.0 4.5 4.9 CaHs 25.1 17.5 21.7 16.2 15.7 1-CdHs 7.9 2.4 2.8 8.3 8.0 ca10 4.3 9.0 9.5 8.0 3.1 l-CaHio 0.75 0.3 0.2 0.8 0.8 C5H12 4.7 8.2 9.0 7.7 4.1 l-CaH12 0.5 2.5 1.7 3.3 0.9 C&l4 2.1 2.1 3.5 5.6 7.2 I-c~Hia 0.5 0.4 0.7 0.9 1.06 C,&a 0.7 1.3 1.7 2.0 3.2 l-C8Hle 1.2 Benzene 1.3 0.04 0.4 0.4
75 2.13 49.8
50.0 97.4 4.4 28.2 83.2 125.2 36.0 47.5 4.9 27.5 2.0 2.5 0.2 3.0 1.0 1.3 0.15 0.2 1.3
,.
LL 0 W v)
80-
d =
. 0
0
W -
a Y V
a
0
20
40
60
80
100
0 0 E
40
-
Y v)
OVERALL CONVERSION %
Figure 3. Gas weight per cent vs. overall conversion of feed (52.0 wt % octane)
amount of all components shown in Figure 4 increased with an increase in nonane conversion. The variations in moles of Cs-Cs hydrocarbons with nonane conversion were similar to the one for hexene. The percentage of unidentified material varied from 1.2% a t low conversions to approximately 8.0% a t 70% conversion. Thje amounts of carbon formed (as measured from the material balance) were slightly increased a t high temperatures. For instance, the material balance for octane a t 725' and a residence time of 0.21 sec was 97.7% a t the same temperature a,nd a residence time of 0.25 sec, i t was 98.1yo.for nonane, whereas for 52 wt % octane feed, at 725' and a residence time of 0.26 sec the material balance decreased to 95.1%. However, the increase in carbon formation was not large enough to have any noticeable effect on the yields of the products. Discussion of Results
From an analysis of all the runs for the different reactant mixtures, it was concluded that the product selectivities (mol produced/100 mol cracked) from the cracking of mixtures could be predicted from a knowledge of the product
4
H2'
n
-0
.4
.E
1.2
1.6
2.0
RESIDENCE T I N E , S E C O N D S
Figure 4. Product selectivity vs. residence time in cracking of octane-nonane mixture (52.0 wt octane)
%
selectivities of the individual components, i.e., octane and nonane. The produce selectivities could be simply calculated by the following equation mol of any product/100 mol of mixture cracked = (mol produced/100 mol of octane cracked) X mol % of octane in feed (mol produced/100 mol of nonane cracked) X mol % of nonane feed (1)
+
Table I11 shows the amounts of products predicted and measured experimentally a t 700" and a residence time of 0.28 sec for 52.0 wt % octane feed. Since this mixture was not cracked a t this particular residence time, the values were obtained by interpolating between 0.23 and 0.4 sec. As can be seen from Table 111, the products smaller than Ce can be predicted with an accuracy of *5%. The percentage errors are larger for the higher hydrocarbons but this is due to the fact that Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
347
1
I
I
I
0.6
0.8
Table 111. Calculated and Measured Product Distribution for Octane-Nonane Mixture. Mol produced/lOO mol cracked Calcd from Exptl eq 1
Component
28.2 29.4 58.2 59.3 C2H4 101.5 102.0 CzHe 32.2 32.1 C3& 38.0 37.8 5.3 4.7 C3Ha 1-CdHab 18.7 17.6 C4Hio0 6.6 6.7 1-CsHio 7.6 7.4 0.7 0.7 C5HlZ 1-CeHiz 7.9 8.2 1.6 1.4 CeH14 1-C~Hi4 3.8 4.5 0.6 0.55 C'lHlfi 1-CSHlfi 1.6 1.5 Benzene 0.4 0.4 a Wt % octane = 52.0; temperature = 700'; mol % octane = 54.7; residence time = 0.28 sec. The possible isobutene was not measured separately. The possible isobutane was not measured separately. Hz
CH,
30 2
0 In
Y p:
g 0 "
20
X PENTENE 100 50 670.C 0 700.C Q
+
725.C
0
.2
.4
.6
A
I
I
,
.8
1.0
1.2
I
0
A 1.4
T,SECONOS
Figure 5. Conversion of 2-pentene vs. 7 for pure 2-pentane and 2-pentene-nonane mixtures
their amounts are so small so that any variation has a very large effect on the percentage error. The products for the various mixtures and experimental conditions could also be predicted with a similar accuracy. From the above results it is obvious that under the experimental conditions investigated, octane and nonane do not interact. The results can be explained by the fact that the large octyl and nonyl radicals have a half-life in the order of microseconds, whereas the half-life of the ethyl and methyl radicals is in the order of milliseconds (Rice and Rice, 1935). Hence, these large radicals decompose before they get a chance to react with other free radicals. When they decompose, radicals which are common to both octane and nonane are formed. Thus, no new radicals are formed. Moreover, since the product distribution of octane and nonane are similar, the concentration of the radicals produced would also be very similar, thus having no effect on the kinetics or the product distribution. Cracking of 2-Pentene-Nonane Mixture
To study the effect of 2-pentene in the cracking of n-nonane, a mixture with equal parts by weight of pentene and nonane 348 Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
-0
0.2
0.4 r,SECONDS
Figure 6. Conversion of nonane vs. residence time for 2pentene-nonane mixture
was cracked at 670, 700, and 725'. Residence times were varied from 0.16 to 0.59 sec. Kinetics of Cracking
The variation of pentene and nonane conversion with residence time for pentene-nonane copyrolysis is shown in Figures 5 and 6, respectively. As in the cracking of octane-nonane mixtures, individual conversions of pentene and nonane, rather than the overall decomposition of the feed, has been plotted in these figures. Material balances were 99.7% a t 7.0% conversion but decreased to 97.2% a t the highest conversion. As in the earlier runs, some unidentified material was present in all the runs. Since 2-pentene was not a product of nonane cracking and nonane not a product of 2-pentene cracking, conversions could be calculated in a straightforward manner. Figure 5 shows that, for a particular residence time and temperature, pentene conversion in pentene-nonane cracking was essentially the same as the conversion obtained in the cracking of 2-pentene. However, comparing Figures 6 and 2, it can be seen that for a particular residence time and temperature, the conversion of nonane in pentene-nonane cracking was not the same as the conversion obtained in the cracking of pure nonane. A similar reduction in the conversion of nonane in nonane-pentene cracking was observed for all the experimental runs a t the three different temperatures. The order of the reaction was assumed to be one. For the first-order reaction A
+ vB
(2)
it can be shown that
kr
= v In
1 -1-x
(v
- l)X
(3)
The rate constants for the inhibited decomposition of nonane were calculated using eq 2. The mol of product formed per 1 mol of nonane cracked were assumed to be the same as that for pure nonane cracking a t the same temperature and conversion. Since the compressibility factors for the mixture varied from 0.99 to 0.993, the residence time, 7,was calculated by assuming the ideal gas law, Figure 7 shows the variations of the right-hand side of eq 3 for the inhibited decomposition of nonane a t the three different temperatures. The values of the rate constants are also listed in Figure 7. Compared to the rate constant obtained for pure nonane cracking (Kunzru, et al., 1972), the inhibited rate constant a t 725' was found to be 34.0% lower. The Arrhenius plot of the rate constants for the inhibited decomposition of nonane is shown in Figure 8.
Table IV. Temperature, OC Residence time, ziec Pentene conversion, % Nonane conversion, % Material balance, % Unidentified material, % Mo1/100 moles ciracked H2 CH4 CzH4 C2H6 CsHa CsHs 1-CdHs 2-C4Hs C4H10 C4Hs 1-CsHio cSH12 1-ceH12 C8H14 1-C7Hia C7Hl6 l-C~Bl6 Benzene a Wt yopentene = 50.0.
r
Product Distribution in Pentene-Nonane Cracking. 670 670 700 700 0.59 0.58 0.18 0.21 32.7 13.5 7.2 17.2 35.2 15.3 7.1 16.9 97.2 98.5 99.7 99.0 2.0 4.2 1.9 1.5
i
670'C ke0.37 tee-'
A i'0O.C
0.8
k.1.02 ,re-'
8 725.C k:2.25
23.1 49.2 50.4 17.7 21.9 0.6 6.8 13.0 6.0 3.2 3.4 0.3 4.6 1.6 2.0 0.2 1.2 0.3
21.2 47.6 48.4 16.4 19.8 0.4 5.9 11.9 7.1 2.5 4.2 0.4 5.2 1.9 2.6 0.4 1.5 0
arb1
24.7 50.2 56.4 18.8 22.8 0.9 6.8 12.1 5.1 4.0 3.4 0.2 3.8 1.1 1.7
26.0 56.2 60.2 21.2 24.6 1.1 8.3 13.7 4.2 5.5 2.5 0.1 2.9 0.9 1.3 0.1 0.6 0.4
0.3 1.0 0.08
1.2
I
I
1
725 0.16 19.4 25.1 97.4 2.8
725 0.21 26.3 30.1 97.9 3.5
24.8 51.5 55.7 18.9 22.9 0.4 6.9 12.0 5.0 5.4 3.0 0.1 3.3 0.5 1.3 0.2 0.8 0.7
25.5 53.5 58.4 20.9 24.4 0.2 7.1 12.1 4.7 6.0 2.9 0.1 3.0 0.5 1.2 0.2 0.7 1.0
I
I
I
A: 3.54 x lor4 sec-' E = 64.5 h colr/g-mole
0.2
0
0.2
0.4
0.6
0.8
0.10
-0.8
-
T, SECONDS I
Figure 7. Deterrninati'on of overall decomposition rate of nonane in 2-pentene-111onanemixtures
1.0
1.02
1.04
1.06
1.08
1.10
Lx1$.K-l T
The frequency factor and the activation energy of the inhibited decomposition were 3.54 X 1014 sec-' and 64.5 kcal/ mol, respectively. As is to be expected, the activation energy for the inhibited decomposition was higher than the activation energy for the uninhibited decomposition of nonane. Product Distribution
The main products in pentene-nonane cracking were hydrogen, methane, ethylene, ethane, propylene, 1- and 2butene, and l13-butadiene. Small amounts of C6-Cs olefins and paraffins were also formed. Methane and ethylene were the dominant products and constituted approximately 25 mol % each of the reaction products. The typical product distribution is listed in Table I1 and the variations of some of the products with residence time are shown in Figure 9. At 700°, the methane selectivity increased by 11.9% and ethylene selectivity by 6.87; as the residence time increased from 0.18 to 0.59 sec. Just as in the cracking of nonane, the seleetivity of the olefins and paraffins larger than C4 decreased
Figure 8. Determination of activation energy for nonane cracking in 2-pentene-nonane mixture
with an increase in the residence time. Yo new products, Le., products which were neither formed in nonane cracking nor in pentene cracking, were formed in the copyrolysis of the pentene-nonane mixture. Discussion of Results
The already complex phenomenon of nonane cracking is further complicated when pentene is added. Both pentene and nonane crack as well as interact with each other. Any explanation put forwardoof the reactions occurring in the system would have to account for the fact that the conversion of pentene remains virtually unaffected whereas the conversion or the rate constant of nonane decreases. The product distribution which would result if eq 1, with mole per cent pentene substituted for mole per cent octane, is used t o calculate the Ind. Eng. Chem. Process Des. Develop., Vol. 1 2, No. 3, 1973
349
~~
Table V. Calculated and Measured Product Distribution for Pentene-Nonane Mixtures
Component
Moll100 mol of product Colcd from Exptl eq 1
25.7 27.4 52.4 63.3 CH4 CZH4 57.7 47.8 ( 3 3 6 20.4 15.4 CaHe 23.7 22.3 1.1 2.3 CsHs 1-C4Hsb 7.7 5.8 2-C4H,3 12.4 21.0 1,3-C& 4.5 10.3 c4HlOc 4.9 3.0 1-caio 3.0 3.1 0.2 0.3 CsHn 3.2 3.8 1-CaHiz 1.0 0.14 ca14 1-G&4 1.5 3.1 0.2 0.2 c7&6 1-CsHis 0.7 1.2 Benzene 0.15 0.1 a Wt. % pentene = 50.0; temperature = 700'; mol % pentene = 65.0. b The possible isobutene was not measured separately. 0 The possible isobutane was not measured separately.
H2
product distribution is shown in Table V. Table V also shows the amounts of the different products predicted and measured experimentally a t 700" and a residence time of 0.28 sec. Since the pentene-nonane mixture was not cracked a t this particular residence time, the values were obtained by interpolating between 0.21 and 0.35 sec. The results of this table indicate that the predicted amounts of methane, 2-butene, and 1,3butadiene are higher, whereas the predicted amounts of ethane and ethylene are lower, than the experimentally measured values. Compare to pure nonane cracking, the new radicals or molecules most likely to be present in appreciable quantities in pentene-nonane cracking are C5H10, C5H9, 1,3-C4&, and 2-CdHs. It follows that one of these radicals or molecules most likely causes the inhibition. Eshevskaya (1940) observed butadiene to reduce the rate of cracking of octane. The butadiene can react with the CgHls radical forming a radical of low activity thus rupturing the chain. This would explain the lower yields of butadiene but not the increased yield of ethylene and ethane. One possibility is that the large radical is formed when butadiene reacts with CQH19 and it decomposes to give ethylene and ethane. The 2-butene formed in the cracking of 2-pentene could stop the propagation of the chains, thus inhibiting the decomposition, by the reaction CaH19 f 2-C4&
+
CgHa
+ 2-C4H,
the resulting unsaturated radical being stabilized by resonance and not acting as a chain-carrier itself. The 2-CdHs amounts are about 50y0 of the predicted amounts strongly indicating that the 2-butene is reacting with the free radicals. Since butadiene and 2-butene are the products of 2-pentene cracking, their interaction with the CQHlg free radical would not affect the rate of 2-pentene cracking. The 2-pentene radicals forming nonane and can also react with the CQH~Q C& radicals CsHi9 f 2-CaHio + CQHZO f ~-C~HQ where 2-CJ39 would be stabilized by resonance and not act 350 Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
70
-
8
60
" X
u 0
50 a
I-
x
k
40
w Y)
r:
. "
30
0
W
a
2 a
20
0
v)
W 2
p
10
0
0
0.2
0.4 R6 ?,SECONDS
0.8
3
Figure 9. Product selectivity vs. residence time in 2-pentenenonane mixture
as a chain carrier and thus the reverse reaction would not be favored. This again would not have any effect on the rate of 2-pentene cracking. The inhibited cracking of 2-pentene-nonane mixtures is a complex phenomenon and the above steps, although giving an explanation for most of the observed results, do not have any quantitative justification. These radicals and molecules (C5Hl0, GHs, 1,3-C4&, and 2-CdHs) can also react with the other large free radicals present in the nonane cracking. Further quantitative explanations cannot be made without the values of the activation energies and frequency factors of these free-radical reactions. Correlations of Experimental Data by Severity Factor
The product distribution of hydrocarbon cracking is quite commonly correlated with a severity factor (Kunzru, et al., 1972). I n the present study this type of correlation was applied to both octane-nonane and pentene-nonane mixtures. The results indicate that for both the mixtures severity factor S = T ~ 0 . 0 6 ,where T is in "C (or S = T ~ 0 . 0 2 7 ,where T i s in OK), used earlier (Kunzru, et aZ., 1972, 1973) was found to be applicable to the product distributions of the mixture cracking. The details of these results are described by Kunzru (1972). Conclusions
(I) For octane-nonane mixture, the order of overall cracking is essentially independent of mixture composition. The conversions of octane and nonane in the copyrolysis are found to be essentially the same as ones of the pure hydrocarbons. The product selectivities for octane-nonane mixture can be calculated using eq 1 of the present paper. (11) The conversion of nonane in pentene-nonane cracking was not the same as the conversions obtained in the cracking of pure nonane a t the same temperature and residence time. The activation energy for nonane decomposition in nonanepentene mixtures was higher than the activation energy for pure nonane decomposition. Equation 1 does not apply well to the predictions of product distributions of 2-pentenenonane cracking. (111) The product distributions of both octane-nonane and 2-pentene-nonane mixtures can be correlated with where Tis in degrees centigrade. severity factor S = TTO.~,
Nomenclature
A E
= = k = m = S =
frequency factor activation energy firsborder rate constant exponent in severity correlation severity factor
GREEKLETTERS = residence time Y = mol of product pler mol of pentene cracked
T
literature Cited
Barabanov, N. L., Muk.hina, T. N., Petrol. Chem. USSR,1,227 (1962).
Eshevska a M. P., Refiner, 19, 264 (1940). Kunugi, Sakai, T., Soma, K., Sasak, Y., Ind. Eng. Chem., Fundam., 8, 374 (1969). Kunzru, D., Ph.D. Thesis, University of Pittsburgh, 1972. Kunzru, D., Shah, Y. T., Stuart, E. B., Ind. Eng. Chem., Process Design Develop., 11,605 (1972). Kunzru, D., Shah, Y. T., Stuart, E. B., Ind. Eng. Chem., Process Design Develop., 12, 339 (1973). Rice, F. O., Polly, 0. L., J . Chem. Phys., 6, 273 (1938). Rice, F. O., Rice, K. K., “The Aliphatic Free Radicals,” Johns Hopkins Press, Baltimore, Md., 1935, p 91-107. Robinson, K. K., Weger, E., Ind. Eng. C i a . , Fundam., 10, 198 (1971). RECEIVED for review September 28, 1972 ACCEPTEDFebruary 26, 1973 The financial help by Gulf Educational Fund is appreciated.
5,:
Mass Transfer in a n Agitated Vessel Brahmi D. Prasher and George B. Wills* Chemictzl Engineering Department, Virginia Polytechnic Znstitute and State University, Blacksburg, Virginia 24061
The applicability of Lamont’s eddy cell model to gas-liquid transfer in turbulent flow in an agitated vessel is examined. According to this model the very small scales of turbulent motion in the equilibrium range are considered to be! controlling the mass transfer process. Gas-liquid absorption data in an agitated vessel indicate that the rate of surface renewal in the expression for the mass transport coefficient is predictable on the basis of the easily measured hydrodynamic quantities, viz., the rate of energy dissipation and the liquid kinematic viscosity, as predicted by the Lamont model.
v a r i o u s models have been offered to predict mass transfer around gas-liquid interfaces. Most of the models proposed so far are based on the concept of a rigid interface or an interface where some sort of surface renewal occurs through the displacement of liquid a t the interface or a combination of these concepts. Surface renewal theories presented so far have received greater acceptance for free surface mass transfer. However, in the case of most of these models, whether those based on the concept of a rigid interface (e.g., Lewis and Whitman, 1924), or those based on the concept of surface renewal (e.g., Higbie, 1935; Danckwerts, 1951; Kishinevsky, 1955, 1956) or those based on the modified film-penetration theories (e.g., Dobbins 1956; Marchello and Toor, 1963; Toor and Marchello, 1958, Harriott, 1962), the hydrodynamic parameters in them cannot yet be determined without recourse to observations of mass transfer rates. Certainly, if a theoretical basis for determining any of these hydrodynamic parameters in terms of easily measured hydrodynamic quantities could be found, then the value of the model would be infinitely increased. I n recent years there have been a number of attempts to relate mass transfer coefficients with the conditions of agitation in stirred vessels in both gas-liquid and solid-liquid systems. I n the case of solid-liquid mass transfer, a number of workers (Calderbank, 1961; Harriott, 1962; Keey, 1966; Sykes and Gomezplata, 1967; Nienow, 1969; Miller, 1971; Levins, 1972; Levich, 1962; Middleman, 1965) have tried to explain the mechanics of particle-liquid mass transfer by in-
voking Kolmogorov’s theory of local isotropic turbulence, though some of them found that some additional parameters . approaches based on this are necessary to predict k ~ All theory of local isotropy make the implicit assumption that equal power input per unit mass is the right method to be used in mixer scale-up. As regards to gas-liquid transfer in agitated vessels, the results of the investigation of the dependency of the mass transfer coefficient on the conditions of agitation are so unclear that further investigations in this direction are necessary. Calderbank’s data (1961) indicate that the liquid-phase mass transfer coefficient in gas-liquid transfer is independent of agitation intensity. Hyman (1962) also reported that the mass transfer coefficient is relatively constant, even a t high rates of shear; Davies, et al. (1964), studied gas absorption rates in exceedingly clean water in a stirred cell and found that the mass transfer rates are dependent on the agitation intensities. Yoshida (1963) working with different types of impellers also found that the mass transfer coefficients in agitated vessels are dependent on the agitation intensity. It is the purpose of this paper to examine whether the energy input in a gas-liquid system in agitated vessels affect the liquid side mass transfer coefficient and also to examine if any model can be used to predict the mass transfer coefficients on the basis of easily measurable hydrodynamic quantities. Eddy Cell Model
Calderbank (1961) working with particle-liquid transfer in Ind. Eng. Chem. Process Des. Develop,, Vol. 12, No. 3, 1973
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