Ind. Eng. Chem. Res. 1990, 29, 499-502 Null, H. R.; Johnson, H. F. Drop Formation in Liquid-Liquid Systems from Single Nozzles. AZChE J . 1958, 4 , 273-281. Rao, E. V. L. N.; Kumar, R.; Kuloor, N. R. Drop Formation Studies in Liquid-Liquid Systems. Chem. Eng. Sci. 1966, 21, 867-880. Scheele, G. F.; Meister, B. J. Drop Formation at Low Velocities in Liquid-Liquid Systems-Part 1. Prediction of Drop Volume. AIChE J. 1958, 14,9-15. Siemes, W. Zur Entstehung von Tropfendispersionen an Siebboden bei der Solventextraktion. Chem. Ing. Tech. 1956,28, 727-731. Skelland, A. H. P. Diffusional Mass Transfer; Wiley Interscience: New York, 1974; reprint ed. with revisions, Krieger, FL., 1985. Skelland, A. H. P.; Huang, Y.-F. Effects of Surface Active Agents on Fall Velocities of Drops. Can. J . Chem. Eng. 1977, 55, 24G245. Skelland, A. H. P.; Raval, V. K. Drop Size in Power Law Non-Newtonian Systems. Can. J . Chem. Eng. 1972,50, 41-44. Skelland, A. H. P.; Vasti, N. C. Effects of Interaction between Circulating or Oscillating Droplets on Drop Formation, Free Fall, and Mass Transfer. Can. J . Chem. Eng. 1985, 63, 390-398.
499
Skelland, A. H. P.; Walker, P. G. The Effects of Surface Active Agents on Jet Breakup in Liquid-Liquid Systems. Can. J . Chem. Eng. 1989,67, 762-770. Skelland, A. H. P.; Wellek, R. M. Resistance to Mass Transfer Inside Droplets. AZChE J . 1964, 10, 491-496. Skelland, A. H. P.; Woo, S.; Ramsay, G. G. Effects of Surface-Active Agents on Drop Size, Terminal Velocity, and Droplet Oscillation in Liquid-Liquid Systems. Znd. Eng. Chem. Res. 1987, 26, 907-911. Slaymaker, E. A. Effects of Surface Active Agents on Drop Size in Liquid-Liquid Systems. M.S. Dissertation, Georgia Institute of Technology, Atlanta, GA, 1985. Ueyama, K. Size of Drops Formed a t the End of Single Nozzles. Kagaku Kogaku 1957,21, 766-774. Received f o r review October 13, 1989 Accepted October 30, 1989
COMMUNICATIONS Pyrolysis Kinetics for Long-chain n -Alkylbenzenes: Experimental and Mechanistic Modeling Results We developed a reaction model for the pyrolysis of long-chain n-alkylbenzenes in order to determine the influence of the alkyl chain length on the pyrolysis kinetics. The model, which has as its basis the previously deduced free-radical reaction mechanism for alkylbenzene pyrolysis, incorporates the effect of the alkyl chain length on the reaction path degeneracy for the hydrogen-abstraction steps. The kinetics predicted by the reaction model for pyrolyses at 400 " C and an initial reactant concentration of 1.3 M were in good accord with experimentally determined pseudo-first-order rate constants for seven different n-alkylbenzenes having aliphatic substituents ranging from butyl (C,) to pentadecyl (C16). Long-chain n-alkylbenzenes are the simplest chemical models of the alkyl aromatic moieties that exist in heavy crude oils, kerogen, and coal. The pyrolysis of n-alkylbenzenes, then, can provide insight to the thermal reactions that occur during the upgrading and conversion of such complex materials. These factors motivated numerous previous pyrolyses of long-chain n-alkylbenzenes (Mushrush and Hazlett, 1984; Blouri et al., 1985; Savage and Klein, 1987a,b;Billaud et al., 1988), and these studies have resolved the governing thermal reaction pathways, kinetics, and mechanisms. The pyrolysis pathways and free-radical mechanism previously deduced are general and describe the thermal reactions of any long-chain n-alkylbenzene. The pyrolysis kinetics, on the other hand, are compound specific. Note, however, that, in complex materials such as heavy oils, kerogen, asphaltenes, or coal, aliphatic chains with a distribution of lengths substitute the periphery of aromatic rings (Calkins, 1984; Nelson, 1987; Rovere et al., 1989; Speight, 1989; McGowan et al., 1989; Strausz, 1989). Therefore, this lack of generality in the kinetics of n-alkylbenzene pyrolysis can limit the application of the model compound data in mathematical models of the thermal reactions of the complex materials. To overcome this limitation, one could experimentally determine the pyrolysis kinetics for compounds with different chain lengths by pyrolyzing every alkylbenzene containing a chain length of interest. An alternate approach, however, would be to develop a general, mechanistically grounded relationship OSSS-5SS5/90/2629-0499$02.50/0
between the kinetics and the length of the alkyl substituent. This latter approach, which eliminates the need for an extensive experimental program, was previously employed by Savage and Klein (1989a). These investigators postulated that the pseudo-first-order rate constant for alkylbenzene disappearance should, to a first approximation, scale with the square root of the alkyl chain length. Their arguments were based on the form of the mathematical expression for the first-order rate constant for a single Rice-Herzfeld (1934) chain reaction and the expected influence of the alkyl chain length on the reaction path degeneracy for the kinetics of the individual elementary steps in the chain reaction. The sparse kinetics data that were available provided limited confirmation of their postulated relationship. Recently, however, advances have been made in confirming the mechanism for and in modeling the pyrolysis of long-chain n-alkylbenzenes (Savage, 1990; Savage and Klein, 1989b). These advances now permit development of a more fundamental model for determining the influence of the alkyl chain length on the pyrolysis kinetics. This paper describes the new model, presents the model predictions, and then provides experimental verification of the model results. Reaction Model Previous pyrolyses of long-chain n-alkylbenzenes showed that there were two pairs of major products (Le., toluene plus an N - 1 carbon atom alkene and styrene plus an N 0 1990 American Chemical Society
500 Ind. Eng. Chem. Res., Vol. 29, No. 3, 1990 H
23
Table 11. Rate Constant Estimates k k at 400 "C," (in Fig. 1) s-' or l/(mol.s) RPDb I 2.35 X 1 T 1.58 X loa 1 11 4.54 x 102 2 12 2.27 x 103 2 13 4.54 X 10' 2N - 3 21 1.96 x 104 2 22 1.27 x 105 2 23 1.96 X lo4 2N - 3 31 1.96 x 104 2 32 1.27 x 105 2 33 1.96 X lo4 2N - 3 '12 3.29 x 104 2 '13 4.75 X lo3 2N - 3 '2 1 2.25 X lo2 2 '23 2.25 X 10' 2N - 3 '31 4.75 x 101 2 '32 3.29 x 104 2 c11 4.10 X lo5 1 #Z 6.24 X lo2 1 113 1.50 x 104 2
[Inititition)
effective k , s'l or l/(mol.s) 2.35 X lo-? 1.58 X loa 9.08 X loz 4.54 x 103 4.54 X 102(2N- 3 ) 3.92 x 104 2.54 x 105 1.96 X 104(2N- 3) 3.92 x 104 2.54 x 1.96 X 6.58 x 4.75 X 4.50 X 2.25 X 9.50 x 6.58
105 104(2N- 3) 104 10"(2N - 3) lo2
102(2N103
X lo4
4.10 x lo" 6.24 X 10" 3.00 x I O 4
"From Savage (1990). *Reaction path degeneracy, N = alkyl chain length. Table I. Chemical Identity of Species in Figure 1 p1 benzyl radical p, y-alkylbenzene radical p2 n-alkyl radical pz a-alkylbenzene radical & other non-p radicals p3 other alkylbenzene radicals &H toluene Q1 1-alkene &H n-alkane Qz styrene &H minor products Q3 minor products
alkane, where N is the alkyl chain length) and numerous minor products. The total product spectrum, therefore, could be conveniently apportioned into three product lumps. The presence of only three unique product lumps suggested that the elementary reaction steps in the governing free-radical mechanism could be organized as three parallel chains (Savage and Klein, 1989b). Figure 1 displays the key steps in this reaction mechanism, and Table I provides the chemical identity of each of the species in Figure 1. Following standard notation, we denote p radicals as those that propagate the chain reaction exclusively via bimolecular steps and y radicals as those that participate in unimolecular propagation steps. Savage and Klein (1989b) used the mechanism of Figure 1 and invoked the long-chain and pseudo-steady-state approximations to derive a closed-form, analytical rate expression for substrate disappearance. Equation 1 gives the pseudo-first-order rate constant that results from their derivation. The subscripts i and j , which denote the species involved in a particular reaction step, can be equal to 1, 2, or 3: - 2 carbon atom
' ' ')!(!!!
k1
k =
+ k,F1 + k3F2
where k, = k,,
F1 =
212231
+ k , , + k,, + 232(z12
K)
and 2, = k$(? + k :/R + 213) + 223)
and F2 =
z13
+ Z23F1
+ 232 Equation 1 can be used to determine the pyrolysis kinetics 221z32
+ 231(221
231
for any long-chain n-alkylbenzene by determining reliable estimates for the effective rate constants for all of the elementary steps in Figure 1. This, in turn, requires estimates of the intrinsic kinetics for each step and a determination of the effect of the alkyl chain length on the rate of each individual reaction step. To fulfill the former requirement, we note that Savage (1990) provides estimated values (at 400 "C)for all of the necessary rate constants. These estimates of the intrinsic kinetics, listed in Table 11, combined with the mechanism of Figure 1 to yield a quantitative correlation of the experimentally observed kinetics and product yields from pentadecylbenzene pyrolysis (Savage, 1990). This earlier confirmation of the rate constant values led us to use the same estimates in the present work. To fulfill the latter requirement, we now examine the effect of the alkyl chain length on the rate of each class of reaction depicted in Figure 1. For example, the initiation step, homolytic dissociation of the weak bond between the 01 and p aliphatic carbons, should proceed at a rate that is essentially independent of the number of carbon atoms in the aliphatic substituent provided this number is large (e.g., greater than four). Likewise, the p-scission steps, which for all long-chain n-alkylbenzenes involve decomposition of the same types of y radicals, are expected to be largely independent of the alkyl chain length. Termination steps show little variation in their rate constants (Benson, 1976); thus, these reactions were also taken to be independent of the aliphatic substituent. Unlike the initiation, p-scission, and termination steps, however, hydrogen-abstraction steps, the only remaining class of reactions, are affected by the alkyl chain length. This is because the number of abstractable hydrogen atoms increases with the alkyl chain length, and this factor influences the rate of the third chain reaction depicted in the central column of Figure 1. Therefore, as the number of carbon atoms in the n-alkyl substituent increases, we expect the net rate of hydrogen abstraction, and hence the apparent reaction rate, to increase as well. To summarize the foregoing arguments, the alkyl chain length should have the largest influence on the rates of the hydrogenabstraction reactions and an essentially negligible effect on the rates of the initiation, ,&scission, and termination reactions. These are good approximations for long-chain n-alkylbenzenes, but they become poorer as the chain
Ind. Eng. Chem. Res., Vol. 29, No. 3, 1990 501 length decreases, and the terminal methyl group plays a more dominant role in the kinetics of the elementary steps. The discussion above indicates that one can account for the effect of the alkyl chain length on the apparent pyrolysis kinetics by multiplying the intrinsic rate constants for the hydrogen-abstraction steps, which are on a per hydrogen atom basis, by the number of abstractable hydrogen atoms. Doing so determines the effective rate constant values that can be used in eq 1. Thus, by accounting for this alkyl-substituent-dependentreaction path degeneracy (RPD) in the hydrogen-abstraction steps, one can determine the effect of the alkyl chain length on the pyrolysis kinetics for an alkylbenzene using eq 1. Table I1 lists the reaction path degeneracy for each elementary step and the resulting effective rate constant values that were used in eq 1. The reaction path degeneracy for the hydrogen-abstraction steps is simply the number of abstractable hydrogen atoms, and for the p-scission steps, it is the number of scissile C-C bonds p to the radical center.
Experimental Section The compounds included in the experimental phase of this study were n-butyl-, n-hexyl-, n-octyl-, n-decyl-, ndodecyl-, n-tetradecyl-, and n-pentadecylbenzene. All compounds were obtained in high purity (typically > 98%) from commercial vendors and used as received. The alkylbenzenes were pyrolyzed at 400 "C for 60 min in stainless steel, batch, tubing-bomb microreactors fashioned from a single Swagelok port connector and two caps. The reactor volume was approximately 0.6 cm3. A stock solution comprising the n-alkylbenzene and biphenyl (an inert internal standard) in a benzene solvent was prepared so that the substrate concentration in the reactor would be 1.3 mol/L. The reactors were loaded with an aliquot of the stock solution, purged with argon, closed, and immersed in a preheated, isothermal, fluidized sand bath for 60 min. The time required to heat the reactors from room temperature to 400 "C was short compared to the 60-min batch holding time. Upon removal from the sand bath, the reactors were rapidly cooled by immersing them in cold water. The cooled reactors were then opened, and their contents were removed and analyzed chromatographically. All analyses employed a Hewlett-Packard Model 5890 gas chromatograph operated in the split injection mode and equipped with a 50-m HP-5 capillary column. Sample constituents were observed by using a flame ionization detector (FID), and the peak areas were electronically integrated. The substrate conversion, X , was calculated by using the integrated peak areas for the substrate and biphenyl (the internal standard) and an experimentally determined FID response factor. A minimum of three pyrolyses was run for each compound, and the average conversion was used in eq 2 to calculate the pseudofirst-order rate constant, k: In (1 - X ) 12 (min-') = 60 min Model and Experimental Results Figure 2, which depicts the variation of the pseudofirst-order rate constant a t 400 "C with the number of carbon atoms in the n-alkyl substituent, provides a summary of the experimental and model results. The curve consisting of a large number of small rectangles was calculated from eq l using the effective rate constant values in Table 11. The larger circles in Figure 2 are the average experimental rate constants calculated from eq 2, and the
h
0 . 0 1 5 ~ I
f
I 0.013-
\
c y
0.011
i'
a: w n 0.009; a: 0 i
2
0.003-
'
in LL 0.001
1--7---T4 0
4
8
12
16
20
24
28
ALKYL CHAIN LENGTH
Figure 2. Model and experimental results from n-alkylbenzene pyrolyses at 400 "C and 1.3 M: effect of alkyl chain length on kinetics.
vertical lines denote the 95% confidence limits. Inspection of the experimental results and the model predictions displayed on Figure 2 reveals that they are in good agreement. This reasonable accord between the experiments and the mechanistically based reaction model provides a measure of confidence in the model and the rate constant estimates used as parameters. This, in turn, suggests that one could use the reaction model to examine the influence of other parameters (e.g., substrate concentration) on the pyrolysis kinetics or on the selectivities to the different lumped reaction products. The data in Figure 2 also permit evaluation of the scaling factor suggested previously by Savage and Klein (1989a). The pseudo-first-order rate constant calculated from the reaction model increases by a factor of 3.3 as the length of the aliphatic substituent increases from C4 to CZ5when the substrate concentration is 1.3 M. If the square root of the alkyl chain length were used as the scaling factor, however, the rate constant would increase by a factor of 2.5 over this interval. Thus, the approximate relationship suggested by Savage and Klein (1989a) is rather close to the one calculated from the more complete reaction model for pyrolyses at 1.3 M. The depature of the results of the present reaction model from those obtained using the more approximate relationship arises from the basis of the present model being the more complete, but complex, mechanism in Figure 1 rather than the simpler model of a single Rice-Herzfeld (1934) chain reaction with a single, dominant termination step.
Conclusions The pyrolysis kinetics for long-chain (i.e., >4 carbon atoms) n-alkylbenzenes can be reliably correlated by using the closed-form analytical rate expression (i.e., eq 1) derived from the governing reaction mechanism (i.e., Figure 1). This example shows that resolving the reaction mechanism from experiments with one model compound (e.g., n-pentadecylbenzene) can permit the generalization of the model compound results to other members of that class of model compounds (e.g., alkylbenzenes) via the development of mechanistically based reaction models. Thus, it is apparent that mechanistic models can be a powerful complement to experiments when probing the reactions of complex, heavy hydrocarbon-containing materials such as heavy oils or coal. Acknowledgment This work was supported by the Shell Faculty Career Initiation Fund.
Ind. Eng. Chem. Res. 1990, 29, 502-504
502
Nomenclature Fi, F , = dimensionless parameters defined in eq 1 k = pseudo-first-order rate constant, s-l k I = initiation rate constant, s-l k,, = rate constant for hydrogen abstraction at position j by fii, 1/(mol-s) k’iJ = rate constant for hydrogen abstraction a t position j by ij(moi.sj
kT = termination rate constant, l/(mol-s) k , = @-scission rate constant for ki,s-l = number of carbon atoms in alkyl chain = reactant concentration, mol/L X = reactant conversion Z!, = paramet.er defined in eq 1, l/(mol.s) Registry No. n-Butylbenzene, 104-51-8; n-hexylbenzene, 107-7-16-3;n-octylbenzene, 2189-60-8;n-decylbenzene, 104-72-3; n-dodecylbenzene, 123-01-3; n-tetradecylbenzene. 1459-10-5: n-pentadecylbenzene, 21 31-18-2. i\
X
Literature Cited Benson, S.W. Thermochemical Kinetics, 2nd ed.; John Wiley 6r Sons: New York, 1976. Billaud, F.; Chaverot, P.; Berthelin, M.; Freund, E. Thermal Decomposition of Aromatics Substituted by a Long Aliphatic Chain. Ind. Eng. Chem. Res. 1988,27, 1529. Blouri, B.; Hamdan, F.; Herault, D. Mild Cracking of High-Molecular-Weight Hvdrocarbons. Ind. Eng. Chem. Process Des. Dec. 1985, 24, 30. Calkins, W. H. Coal Flash Pyrolysis 3. An Analytical Method for Polvmethvlene Moieties in Coal. Fuel 1984, 63, 1125. McGowan, C. W.; Stanton, B. J.; Morris, R. M. A. Comparison of the Organic Mataerialin the Green River Formation and the Chattanooga Shale. Prepr. Pap.-Am. Chem. Soc., Dio. Pet. Chem. 1989, 34, 48. Mushrush, G. W.; Hazlett, R. N. Pyrolysis of Organic Compounds Containing Long Unbranched Alkyl Groups. Ind. E m . Chem. Fundum. 1984; 23, 288.
Nelson, P. F. Chemically Bound n-alkyl Groups in Coal. Fuel 1987, 66, 1264. Rice, F. 0.;Herzfeld, K. F. The Thermal Decomposition of Organic Compounds from the Standpoint of Free Radicals VI. The 1934,56, mechanism of some chain reactions. J . Am. Chem. SOC. 284.
Rovere, C. E.; Ellis, J.; Crisp, P. T. Determination of Polynuclear Aromatic Hydrocarbons in Shale Oils by Low Pressure Liquid Chromatography. Fuel 1989, 68, 249. Savage, P. E. Pyrolysis of a Binary Mixture of Complex Hydrocarbons: Reaction Modeling. Chem. Eng. Sci. 1990, in press. Savage, P. E.; Klein, M. T. Discrimination Between Molecular and Free-Radical Models of 1-Phenyldodecane Pyrolysis. Ind. Eng. Chem. Res. 1987a, 26, 374. Savage, P. E.; Klein, M. T. Asphaltene Reaction Pathways. 2. Pyrolysis of n-Pentadecylbenzene. Ind. Eng. Chem. Res. 1987b, 26, 488. Savage, P. E.; Klein, M. T. Asphaltene Reaction Pathways. 5. Chemical and Mathematical Modeling. Chem. Eng. Sci. 1989a, 44, 393. Savage, P. E.; Klein, M. T. Kinetics of Coupled Reactions: Lumping Pentadecylbenzene Pyrolysis into Three Parallel Chains. Chem. Eng. Sei. 198913, 44, 985. Speight, J. G. Latest Thoughts on the Molecular Nature of Petroleum Asphaltenes. Prepr. Pup.-Am. Chem. Soc., Diu. Pet. Chem. 1989, 34, 321. Strausz, 0. P. Structural Features of Athabasca Bitumen Related to Upgrading Performance. Prepr. Pap.-Am. Chem. Soc., Diu. Pet. (‘hem. 1989, 34, 395. *Corresponding author. P h i l l i p E. Savage,* David J. Korotney Department of Chemxal Engineering University of Michigan Ann Arbor, Michigan 48109-2136 Received for review July 13, 1989 Revised manuscript received November 17, 1989 Accepted December 11, 1989
Separation of Xylene Isomers on Silicalite in Supercritical and Gaseous Carbon Dioxide An experimental study of the separation of an equal amount of p - and m-xylenes on silicalite using carbon dioxide as the carrier was performed. The results showed that the operations in the gaseous phase of carbon dioxide offered a better separation efficiency over those at supercritical conditions. The effects of temperature, pressure, and flow rate on the effectiveness of separation were also examined. It was found that, for a pulse of’ 1.0 cm3 of xylene isomers and 39.5 g of silicalite, the tnost appropriate o p e r a t i n g conditions were temperature around 358 K, pressure of 47.6 atm, and flow rate of 15.0 cm3,/min. Xylene isomers a r e i m p o r t a n t industrial raw materials, which usually come from naphtha crackers and reformers. Because their close boiling points, it is difficult t o separate t h e m b y distillation. In industrial practice, t h e separation is usually achieved b y the a d s o r p t i o n method u n d e r liquid-phase or gas-phase operation. Several p a t e n t s dealing w i t h t h i s m e t h o d a r e available (Neuzil and Grove, 1971; Rosback, 1976; Neuzil and Korous, 1977; Maas and Visser, 1982; Fishkill and Esters, 1984). W i t h t h i s m e t h o d , t h e desorbent is generally required, and p-diethylbenzene, isopropylbenzene, propylbenzene, and toluene are t h e most c o m m o n l y e m p l o y e d desorbents ( L u and L e e , 1987; R u t h v e n , 1984; Santecesaria e t al., 1982; S e k o et al., 1979; S t o r t i et al., 1985). If d e s o r b e n t c a n be avoided, t h e separation cost should obviously be reduced. S i n c e the solubilities of p- and m-xylenes in c a r b o n dioxide a r e q u i t e high at relatively high pressures (Chao et ai.. 1980; Francis. 1954), separating
0888-5885/90/2629-0502$02.50/0
xylene isomers o n molecular sieves in supercritical or gaseous c a r b o n dioxide seems to be possible. Under t h i s condition, the functions of carbon dioxide m a y be not only the carrier but also the d e s o r b e n t . The objective of this communication is t o s t u d y this possibility. The operating temperature, pressure, and flow rate were varied to observe their effects o n separation.
Experimental Section Cylindrical silicalite pellets of 0.16-cm d i a m e t e r and 0.62-cm length were used as the adsorbent which contain t h e binder of A1203 a b o u t 2 0 % . Before use, these pellets were activated b y h e a t i n g at 873 K for about 24 h in a nitrogen environment. T h e sample was then cooled t o a m b i e n t temperature, and approximately 39.5 g of sample was weighed and packed i n t o a stainless steel 316 column of 2.12-cm i.d. and 25-cm length, which is shown as the packed bed in Figure 1. In order t o m a k e the flowing fluid 9,1990 American Chemical Society
