Rate-Contro(Jing Path for Catalytic Butane Dehydrogenation John Happel and Richard S. Atkins' Department of Chemical Engineering, New York Cniversity, Bronx, N . Y . 10.463
In an experimental study of the nature of the rate-controlling steps in the dehydrogenation of butane to butenes and the reverse hydrogenation reaction over a commercial chromia-alumina catalyst, runs were made in a differential continuous flow reactor containing 40 grams of pelleted catalyst. 14C-tagged butane and 1 -butene were used as tracers to follow independently the unidirectional rates, while the over-all reaction was simultaneously observed. The system was studied over a range of ratios of forward to reverse reaction rates from 0.02 to 10; an apparent stoichiometric number close to unity was observed. Chemisorption or desorption of hydrogen is not a rate-controlling step, or very high apparent stoichiometric numbers would have been observed using I4C as a tracer. One or more rate-controlling steps exist in the elementary reactions involving transformation of the dehydrocarbon skeleton.
THE
PURPOSE of this study was to establish the nature of the rate-controlling step or steps in the catalytic dehydrogenation of butane and the correspoiiding hydrogenation of butenes. A commercial chromia on alumina catalyst' was used. The present study is part of a continuing investigation of studies attempting bo place the structure of catalytic rate expressions on a firm fundamental basis. Yang and Hougen (1950) noted that mathematical expressions for rate equations derived on the basis of the principles developed by Hougen and Watson (1943) indicate t,hat rates may be often expressed by a combina.tion of three terms, the kinetic term, the potential t,erm, arid the adsorption term, arranged as follows:
__V = (kinetic term) (potential term)
(1)
(ailsorpt'ion t,erm) Our research program started with an experimental study similar to the pioneer work of Dodd and Watson (1946) on butane dehydrogenation. We determined rates of dehydrogenation and hydrogenation reactions among the Cq hydrocarbons using a chromia-alumiria catalyst. The results of this work, reported by Happel et al. (1966), were correlated on the basis of coiiventiotial H'ougen and Watson models, assuming :t single rate-controlling :step, and a surface of uniform, noninteracting sites. Rate equations for both butane and butene dehydrogenation took the same forin, corresponding to a mechanism which ~voultlinvolve dissociation of the reacting species into activated complexes with two carbon atoms (corresponding to x stoichiometric number of 2 for the ratecotitrolling step). However, subsequent studies by Okarnoto et al. (1967) indicated that such a mechanism is not likely. Other possible esplanai ioiis of the correlation obtained were that hydrogen atom transfer might be the rate-controlling step, the catalyst surface might be nonuniform, or a single rate-controlling step may not exist. Preliminary studies using were initiated by ,ltkins and Happel (1968) to resolve some of these problems. Present address, Shell Chemical Co., Yew York, S . Y.
The present investigation, concluding this work, is based on theories employing the stoichiometric number concept as applied to reactions where more tha.n one rate-controlling step may exist. This concept,, originated by Horiuti (1957), has been discussed by Hallpel (1967) for cases where a single rate-controlling step esists :ind for more complicated cases, using the concept of reaction paths int,roduced by Happel (1968). The stoichiometric number is defined for each elementary step which comprises an over-ttll reaction: the number of times that the step takes place for each occurrence of the over-all reaction. JT'hen a single rate-coritrolling step exists, it, is possible to relate the stoichiometric number of this step to the thermodynamic equilibrium constant and the speed of the forward and reverse reactions. If a more complicnted reaction occurs in a single reactiou path and the stoichiometric number of each step is the same, it is still possible to relate selected forward and reverse reaction rates to thermodynamics in somewhat the same way as for the case of a single rate-controlling step--e.g., Equatioii 4. The concept of forward and reverse reaction rates requires some explanation, since they are not uniquely fixed wit'hout specifying a reaction path. The rate of ai1 over-all reaction, characterized by a single chemical equation, may be identified with the conversion of each atomic species involved. Transfer of atomic species proceeds through a number of paths, each consist,ing of a single unbroken series of mechanistic steps whereby a given atomic species can move from :i chosen reactant, to a chosen product or the reverse. Each path corresponds to a given fraction of the total atomic transport' for the atomic species selected. The atomic velocity in a given path divided by this fraction will give the over-all reaction velocity (expressed as atoms per unit time). In turn, if this quant,ity is divided by the number of atoms of the chosen type which are transferred for a single occurrence of the reaction, we obtain the over-all reaction velocity expressed as occurrences per unit time. Usually a chemical reaction is written so that the smallest coefficient of participating molecules is unity and the reaction rate may then be expressed as moles per unit time in t,erms of conversion of components with a coefficient, of unit,-. I t is, of course, not possible to VOL. 9 NO. 1 FEBRUARY 1970
I&EC FUNDAMENTALS
11
identify rates in two or more paths of atomic transfer which initiate and terminate in a single molecular species, or for the portion of a path which splits and later recombines. While the molecular species change from reactants t o products, the atomic species remain the same and their rates can be measured in either the forward or reverse direct'ion by isotopic tracing. The division of the forward and reverse atomic velocities by the factors discussed above will give unidirectional forward and reverse rates characteristic of the chosen path. These rates will be the same for a given path, regardless of the atomic species employed for their determination. They will be different for each separate path but always characterized by the relationship
V
=
V + (P) - V - (PI
(2)
where V is the over-all reaction velocity and V+(p)represents unidirectional over-all velocities for path p . Such unidirectional forward atomic velocities can be measured by conducting experiments in a differential flow reactor fed with a mixture containing all species involved as both reactants and products. The atomic unidirectional rate in each path may be determined by appropriat,e isotopic t'ransfer measurements. If an atomic species can be chosen which is confined to a single path, the forward velocity in that path may be determined in a simple manner by marking the reactant species and leaving the product species unrnarked. This study represents an attempt' to determine whether butane dehydrogenation can be characterized in this fashion as regards the path iiivolving the carbon skeleton. I n the case of butane dehydrogenation, the over-all reaction involved may be written CIHIO
C A
+ Hz
(3)
Under the conditions of our experiments isomerization among the but'enes was many times faster than t'he hydrogenation and dehydrogenation rates and equilibrium among them was attained rapidly. I t was thus possible to treat C4H8as if it were a single species in so far as the determination of stoichiometric number was involved. The apparent stoichiometric number is calculated from the relationship v =
- AG/RT
v+
ln-
(4)
V-
where
D AG
= apparent stoichiometric number = Gibbs free eiiergy change a t reaction conditions R = gas coiist'ant' T = absolute temperature V+, - = forward and reverse rates of reaction (using carbon as a tracer) The forward and reverse reaction rates refer to the transfer of a chosen atomic species, in this case carbon. They must be obtained a t the same conditions of temperature, pressure, and concentration of species involved. The most accurate method is to determine them simultaneously during the same experiment. I n the present instance radioactive carbon was employed as a tracer. Only one of the hydrocarbons was tagged in any experiment. The unidirectional rates were determined 011 the hasi5 of radioactive gain by the notitagged hydrocarbon. The overall rate of reaction was independently determined by the change in butane conceiitratioii from feed to product sniiiplei. 12
l&EC FUNDAMENTALS
VOL. 9 NO. 1 FEBRUARY 1970
Since only a small conversion (less than 3%) occurred in the reactor, it was not necessary to have information on kinetics to determine reaction rates as in the caSe of an integral reactor. The Gibbs free eiiergy change for the over-all reaction was calculated from reaction conditions using average reactor component concentrations and values for the equilibrium constant computed from X.P.I. Project 44 tables assembled by Rossini (Rossini et nl., 1953). Obtaining a constant stoichiometric number for a range of conditions is equivalent to showing that a system conforms to a reaction rate expression, derivable from Equation 4. For our present system this expression reduces to
where IJ is an undetermined function of pressure, temperature, and composition, The right-hand expression in brackets in Equation 5 may be identified with the so-called "potential term" iri Equation 1. S o t all coinplex reactions can be described by such a relat'ionahip (Happel, 1968). Therefore experimental demonstration of its existence for a given reaction system is important as a basis for identifying a precise analytical rate expression regardless of the mechanism involved. Furthermore, the establishment of a constant stoichiometric number with a numerical value equal to either an integer or rational fract'ion lends weight to the hypothesis that a rate-controlling step or steps is associated with the path traced by t,he marked atomic species. Experimental Procedure
The n-butane and 1-butene uere C.P grade purchased from the JIatheson Co. The l-butene-l-14C and n-butane-lI4C 1%ere supplied by the Nuclear Equipment and Chemical Corp. These radioactive materials TI ere diluted by Matheson and furnished to us in small cylinders a t a radioactivity of 0.5 me per 200 grams. The apparatus was a continuous-flow differential reactor. Reactants a e r e metered into the system through calibrated rotameters. Feed gas leaving the rotameter section passed through a preheater in ~ h i c hit n a s heated to within 50" to 100°C below reactor temperature. The reactor tube containing the catalyst bed is diagrainmed in Figure 1. The catalyst bed was 3l/2 inches high and contained 40 grams of catalyst. Catalyst employed \\as Type ,150 supplied by the Houdry Process Corp., containing 20% chromia (Cr20,) on alumma. It was i n the form of pellets 1/8 inch in diameter and 1/4 inch i n length. The wrfdce area a a s determined to be 55 sq meter\ per gram. The 1/4-inch 0.d. stain1e.s steel tubing used to support the catalyst basket served as an a u a l thermocouple M ell, M hich contained blx thermocouples evenly spaced along the length of the catalyst basket Feed gas to the resctor mas sampled through a port a t the top of the catalyst bed. Product gas was sampled from a port just beneath the bed. Both the feed and product ports alqo served a3 pressure taps The reactor tube n as encloqed 111 an electricallv heated aluminum bronze block furnace, uhich served as a heat smk for the reactor. I t i temperature was controlled by n proportional temperature controller. Prior to making an e\periment the catal: 5t 1- pretreated to ensure that the catalyst nil1 be a t the iaine level of actlvlty for each e\periment. I'ietreatmeiit consist5 in buriilng all
118'' O D TUBE S A M P L E IUNE
\fl
I
L .I
o
. ?MARKED n. BUTANE - LARKED I-BUTENE
W k
4 la I
114'' O.D. T U B E
j
iI
Ln Figure 3.
Butane dehydrogenation
A
-4
VI
0
- CI'YARKED
II-BUTANE
CI'HARKED
I-BUTENE
-
-3
Figure 1.
rG C
COLUMN
Reactor assembly
mm
ROTAMETERS -4
Ln
Figure 4.
FLOW
CkRRIER
LEAD
G0.S
@
SAMPLE INJECTION PORT
@
HIGH VOLTAGE POWER SUPPLY
COUNTER SHIELDING EXHAUST LINE
-FUEAMPLIFIER
@AMPLIFIER
@
7
DECADE
@ LINEAR- LOG
SCALER
0 - 1 MV RECORDER
RbTEMETER
Figure 2.
Analysis system
coke off the catalyst a t 525OC. The system is then purged with nitrogen, followed by a %hour treatment with hydrogen at 525°C. Feed and product gas samples are automatically withdrawn, using an electr Lc system which activates withdrawal of mercury from sample bulbs. Gas samples are analyzed using a standard gas chromatograph and P-ray proportional detector. Figure 2 is a diagram of the analysis system. The detector is similar to that described by Wolfgang and Rowland (1958). The column for the gas chromatograph was packed with an inert material saturated with ethyl mslonate. I n all samples hydrogen and major hydrocarbon components were determined separately, using a nitrogen carrier gas in the chromatograph. A second analysis was made for hydrocarbons aiid radioactivity. I n this case helium was used as the carrier gas in the chromatography and roughly half as much methane as helium was used as a quench in the proportional detector. The peaks for all hydrocarbons from C1 to Cq were obtained. Counts associated with each peak were determined separately. Total activity associated with a gas fraction was obtained by subtracting the integrated counts before the peak from those after it, making, allowance for background activity. Typical background activity was 60 to 100 counts, and a
+-
Butene hydrogenation
typical sample-integrated count ranged from 500 t'o 5000 counts. I t was established that both the amounts of CI to C1 hydrocarbons obtained and their radioactivity could be neglected in calculating reaction rates. T o coiifirni the reliability of the determiiiat'ion of radioactivity by the proportional counter, in several runs each component fraction leaving the chroniatogra1)h was also dissolved separately iii a known amount of toluene. The radioactivity of the toluene solutions was measured by a liquid scintillation counter (Model Viiilux 11, Suclear Chicago Corp.). Satisfactory sgreenieiit n-as obtained. The scintillation counter is more accurate, but other experimental errors in the determinatioii of stoichiometric number were such that this additional accuracy was not necessary in the present study. Several determinations of stoichiometric number were also made with catalyst crushed aiid screened to 14 to 20 mesh t'o determine whether heat transfer or diffusional effects would iiifluence the result obtained. S o effect on observed value of stoichiometric number could be detected. Results
Calculated results are given in Figures 3 and 4. Further details are giveu in *Itkins' (1967) thesis. The system was studied over a range of ratios of fortTard to reverse rates of reaction from 0.02 to 10. AIllruns were made a t atmospheric pressure. Temperatures varied from 390" to 56OOC. The Gibbs free energy change associated with this wide range of operating conditions on both sides of equilibrium varied from -3150 to $4450 calj(gram inole). Figure 3 is a plot of the butane dehydrogenation results. The stoichiometric iiuinber is the slope of a line passing through the origin. In this case the best, value for ii is 0.94 i 0.28. Similarly, Figure 4 is a plot of the data for butene hydrogenation. I n this case the apparent stoichiometric number is 1.14 i 0.35. VOL. 9 N O . 1 FEBRUARY 1970
I&EC FUNDAMENTALS
13
The results indicate that one or more rate-controlling steps exist in a single path of elementary reactions iiivolviiig transformation of the hydrocarbon skeleton and with stoichiometric numbers of unity. It appears that adsorption or desorption involving hydrogen alone is not a rate-controlling step, or very high apparent stoichiometric iiunibers 15 ould have been obtained. Therefore, if these processes appear in the mechanism, they must be very fast. Experiments conducted very close to equilibrium will suffer inaccuracies in fixing the apparent stoichiometric number due to difficulty in exactly measuring temperature, with consequent uncertainty in determining AG. At the other extreme, measurements far from equilibrium finally become inaccurate because of errors 111 radioactivity measurement. Best accuracy should be attained a t intermediate values of V,/V,, although, as is apparent from examination of Figures 3 and 4, scatter seems about the same over the range ttudied. A method used to increase the experimental accuracy was to measure the smaller unidirectional reaction rate directly. Thus in the dehydrogenation experiments radioactive 1butene was the most satisfactory tracer because the rate of hydrogenation of butenes, 1% hich is small, is measured directly rather than by difference. In the case of hydrogenation eyperiments n-butane was the better tracer. I n the case of butene hydrogenation some experiments were also conducted using traced 1-butene to confirm the validity of using Equation 2 . Discussion
The determination of an apparent stoichiometric number of unity using 14C as a tracer furnishes much useful iiiformation regarding the necessary form of the rate equation and also supplies restrictions regarding the rate-controlling steps in the mechanism of the butane dehydrogenation reaction. It is possible to speculate as to mechanisms consistent with these findings, although the mechanism itself must be supported by other considerations as well. Thuc, a plausible mechanism for the dehydrogenation of paraffins on chromia was proposed by Donden (1965), involving dissociative adsorption on a single pite, immediately follolved by formation of a *-complex a t the same site. For hydrogenation of olefins, similar mechanisms were propoqed by Halpern (1966) and Burwell (1966). Studies by Horiuti and 1Iiyahara (1968) on ethylene hydrogenation, by Hiroto et al. (1969) on propene hydrogenation, and by . h e n o m i y a (1961) on butene hydrogenation indicate that these reactions follow an associative mechanism which involves a half-hydrogenated species. From this viewpoint we may write a tentative sequence as: u -* 1 C~HIO 1 C4HlOl
+
I1 C4H10l
+1
0-1
1-2
C4H9l
+ HI
U-2
for individual mechanistic steps. The stoichiometric number for each step in this sequence is unity. Prelimiiiary experiments have been conducted in which 1butene mixed with deuterium reacted under conditions similar to those employed in the present study (Koehler and Happel, 1969). Very rapid exchange of deuterium occurs with the hydrogen of the butene, although the rate of deuteration of butene is about the same as the rate of hydrogenation of 1butene. Similar experiments conducted with mixtures of butane and hydrogen shmv very slow exchange with deuterium. Thus it appears that steps I11 to V are rapid, assuming that this exchange involves the same mechanism as the dehydrogenation sequence. Experimentation is now in progress on the rate of chemisorption of n-butane on the catalyst to determine whether this might be a rate-controlling step. I t is also possible that step I1 does not exist but C4H101is directly dehydrogenated in one step Ci"o1z
CJLl
+ Hz
(7)
If C4H91is involved, there will be a split in the hydrogen transfer path from butane to molecular hydrogen. Neither the present work or the earlier investigation by Happel et al. (1966) is able to assign sufficiently accurate values for the constants appearing in the kinetic and denominator terms of Equation l to ensure unequivocal identification of the rate model for over-all kinetics. Further work is now in progress to attempt to accomplish this, especially to determine whether the prefactor # in Equation 5 can be represented qatiqfactorily by a single-term algebraic expression, as would be the case for a uniform surface. literature Cited
Amenomiya, Yoshimitsu, J . Res. Inst. Catalysis, Hokkaido Univ. 9, 1 (1961). Atkins, R. S . , doctoral thesis, School of Engineering and Science, New York UniverTity, 1967. Atkins, R. S., Happel, John, IV, International Congress on Catalysis, ~Ioscow,unpublished, 1968. Burwell, R. L., Jr., Chem. Eng. S e w s 44, 58 ( h g . 22, 1966). Dodd, R. H., Watson, K. hI., Trans. Am. Inst. Chem. Eng. 42, 263 (1946). I)owden, I). A , , Endeavour 24 (92), 69 (1965) Halpern, Jack, Chem. Eng. S e w s 44, 68 (Oct. 31, 1966). Happel, John, Chem. Eng. Progr. Symp. Ser. 63 (72), 31 (1967). Happel, John, J . RPS.Inst. Catalysis, Hokkaido Cniv. 16, 305 (1968). Happel, John, Blanck, Hillard, Hamill, T. D., IND.ESG.CHEY. FUND.\MEXT.\I,S 5 , 289 (1966). Hiroto, Kozo, Yoshidn, Soritetsu, Teratani, Shousuke, Kitavama, Toyoki, J . Catalysis 13, 306 (1969). Horiuti, Juro, Advan. Catalysis 9, 339 (1957). Horiuti, Juro, XIiyahara, Koshiro, National Standard Reference Data Sei-., Sational Bureau of Standards 13 (1968). Hougen, 0. A., Watson, K. lI.,Znd. Eng. Chcm. 35,:29 (1943). Koehler, George, Happel, John, unpublished investigation, 1IQGQ I/"I.
Okamoto, Yoshiyuki, Happel, John, Koyama, Hiroaki, Bull. Chcm. SOC.Japan 40, 2333 (1967). Rosqini, F. D., Pitzer, K. S., Arnett, R. L., Braun, R . ll.,Pimental, G. C., "Selected Values of Physical and Thermodynamic Properties of Hvdrocarbons and Related Compounds," Carnegie Prew, Pittsburgh, Pa., 19.53. Wolfgang, Richard, Rowland, F. S.,Anal. Chem. 30, 903 (19*58). Yang, K . H., Hougen, 0 . h.,Chem. Eng. Progr. 46, 146 (1950). RECEIVED for review February 7, 1969 A 4 ~November ~ ~ 12,:1969~
where 1 represents sites on the catalyst surface ut which adsorption occurs. The rates vii represent reaction velocities
14
ILEC FUNDAMENTALS
VOL. 9 NO. 1 FEBRUARY 1970
Work supported in part by the Petroleum Rmearch Fund administered by the hmerican Chemical Society and the Sational Science Foundation.
~
~
