Kinetics of the lsobutane-lsobutene-Hydrogen System Using Tracers John Happel,* Kenneth Kamholz, Dennis Walsh, and Vincent Strangio Department of Chemical Engineering, New York University, Bronx, N.Y. 10453
The mechanism of the isobutane-isobutene-hydrogen system over a commercial chromia-alumina catalyst was studied in a differential reactor, using both radioactive carbon 14C and deuterium D. It was established b y 14C experiments that hydrogen adsorption and desorption are at equilibrium. Experiments with deuterium showed that chemisorption of isobutane to produce the half-hydrogenated adsorber species i s the ratecontrolling step in the kinetics. Transformation of this species to produce chemisorbed isobutene is much faster, and the desorption of isobutene is close to equilibrium. Kinetic data were correlated on the basis of this information for a temperature range from 650 to 763°K. Activation energies were obtained for the constants appearing in the rate equation.
T h e r e are many studies reported for the important reactions involving hydrocarbon hydrogenation and dehydrogenation. However, those in which both reactions are studied with the same catalyst are rare. Still rarer are studies in which labeled atoms are used to determine unidirectional rather than overall reaction rates. The additional information afforded by such a procedure is useful for correct identification of rate models. The present study employing both 14Cand D for this purpose uses a commercial chromia-alumina catalyst.
" i-C4Hio = i-C4Hs
+ i-C4H101 + I S CCdHgE + HI i-C4H91+ 1 & i-C&l + HI i-C4Hsl *i-C4Hs + 1 2H1 Hzl + 1
1
(1)
u c4
-
1
A 16
1
t'-4
A 1: +6
1
1: -5
6
Hzl
- uH-62 + 1
Here 1 denotes a site for chemisorption on the catalyst. Symbols i-C&01, i-C4H91,i-C4H81,Hzl, and HI refer to adsorbed species. The stoichiometric number represents the number of times each of the individual steps occurs for each occurrence of the overall reaction. Interpretation of data by means of tracers involves the grouping of the individual vhz. For this purpose several relationships are useful (Happel, 1972). The overall forward velocity of atomic species through a series of steps will depend on the path of steps taken from a reactant to a product, but in general
V
=
V+lV+Z
V+lV+2V+3
v-1v-2'
.q n - l )
V+1V+2'
' ' v+(n-l)V+n
vn
(3)
and
1
U-3
5
v+1
+
I
u -?
4
V-lV-zUa
Finally from thermodynamics and transition state theory, the following relationship is obtained
?.?I
GC~HIO 1 =+= u-I i-C4H101
3
-+-+-+... V-lYZ
(5)
Stoichiometric no., v
Elementary reaction
2
1 VI
+ Hz may be written
Step no.
1
where 8 , designate velocities taken through steps 1, 2, . . . , n in the forward and backward directions. These velocities are further related to step velocities as follows. V+lA.. .!n =
g+l,z,. . .,n -
V-LZ,. . .,n =
v+t
-
v-5
(2)
Theory
Interpretation of l4C transfer data by means of these relationships is straightforward, since carbon transfer occurs only in a single path involving mechanistic steps 1, 2, 3, and 4. Transfer of any terminal species is conveniently defined as dnei/d0, atoms transferred to the species per unit time. The superscript i denotes the species to which transfer occurs, whereas the subscript e denotes the element transferred. This rate is measurable by tracing techniques for each species involved in a reaction. In the case of 14Ctransfer
Here zeirefers to the fraction of atomic species e in the species i, in this case the fraction of l4C in i-C4H10and i-C4H8, respectively. Experiments in which 14C tracing occurs enable (V+1,*13,4/V-1,2,3,4) to be determined. If these values are subInd. Eng. Chem. Fundam., Vol. 12, No. 3, 1973
263
Table 1. Run no.
85-1 85-2 853 90-1 90-2 90-3 96-1 96-2 96-3 108-1 108-2 108-3 111-1 111-2 111-3 112-1 112-2 112-3 113-1 113-2 113-3 115-1 115-2 1153 130-1 130-2 130-3 131-1 131-2 131-3 R R 9-1 RR 9-2 R R 9-3 RR 10-1 R R 10-2 RR 10-3 RR 12-1 RR 12-2 RR 12-3 RR 13-1 RR 13-2 R R 13-3 RR 14-1 RR 14-2 RR 14-3
Temp.,
O K
703 700 699 727 727 726 723 723 723 723 723 723 727 727 727 723 723 723 723 723 723 723 723 723 790 790 790 790 790 790 760 759 759 762 760 759 770 769 769 767 764 764 770 767 766
IiobuGne
0.557 0.557 0.556 0.545 0.542 0.546 0.811 0.810 0.809 0.240 0.241 0.240 0.473 0.477 0.476 0.320 0.320 0.320 0.625 0.625 0.625 0.870 0.869 0.866 0.532 0.532 0.530 0.0669 0.0672 0.0671 0.164
0.166 0.167 0.162 0.162 0 162 0.140 0.140 0 140 0.140 0.140 0.140 0.163 0.163 0.164
14C Tracer
Results V+1,2,8.4
Partial pressure, atm lsabutene
Hydrogen
0.225 0.225 0.226 0.0387 0.0385 0.0387 0.0648 0.0657 0.0654 0.736 0.739 0.735 0.0590 0.0590 0.0593 0.480 0.479 0.480 0.181 0.181 0.181 0.0815 0.0813 0.0810 0.0805 0.0803 0.0800 0.878 0.878 0.877 0.728 0.726 0.726 0.146 0.146 0.146 0.411 0.411 0.411 0.421 0.421 0.421 0.426 0.426 0.426
0.231 0.231 0.231 0.490 0.493 0.489 0.194 0.194 0.195 0.0512 0.0473 0.0516 0.491 0.487 0.488 0.200 0.201 0.200 0.194 0.194 0.194 0.048 0.050 0.0529 0.396 0.396 0.399 0.0783 0.0777 0.0789 0.495 0.494 0.493 0.485 0.485 0.485 0.481 0.481 0.481 0.135 0.135 0.135 0.838 0.838 0.838
y-i,z,a,a
0.1199 0.1235 0.1402 0.720 0.712 Q ,745 1.318 1.339 1.300 0.1652 0.1355 0.1368 0.387 0.398 0.381 0.0719 0.0951 0.0518 0.321 0.390 0.382 4.52 4.49 4.36 1.916 1.960 2.05 0.1011 0.1214 0.0980 0.0451 0.0441 0.0394 0.0875 0.0812 0.1176 0.1059 0.1058 0.1078 0.1728 0.1531 0.1974 0.0594 0.0676 0.0619
exp( -AG/Rtl
0.1248 0.1182 0.1170 0.712 0.708 0.691 1.396 1.376 1.370 0.1377 0.1487 0.1366 0.400 0.406 0.403 0.0690 0.0716 0.0720 0.385 0.387 0.384 4.81 4.65 4.37 2.003 1.999 1.986 0.1169 0.1181 0.1164 0.0276 0.0276 0.0276 0.1327 0.1327 0.1327 0.0573 0.0573 0.0573 0.1588 0.1588 0.1588 0.0337 0.0337 0.0337
V+s,a V-686
1.04 0.96 0.83 0.99 0.99 0.93 1.06 1.03 1.05 0.84 1.10 1.00 1.03 1.02 1.06 0.96 0.75 1.39 1.20 0.99 1.01 1.06 1.03 1.oo 1.05 1.02 0.97 1.16 0.97 1.19 0.61 0.63 0.70 1.52 1.63 1.13 0.54 0.54 0.47 0.92 1.04 0.80 0.57 0.50 0.54
A further theoretical development involving deuterium transfer may be based on this finding. Material balances assuming no isotopic kinetic effects may be written for the first two steps of the proposed mechanism as follows.
stituted into eq 6, we obtain
The left-hand side of eq 8 may be readily evaluated from thermodynamic data. In this case exp ( - AG/R T) = KpPi-C&o
P H P i-C4Ha
(9)
The equilibrium constant K , as determined experimentally (Happel and Mezaki, 1973) differs substantially from that available in thermodynamic tables. Experiments conducted by Kamholz (1970) and reported in this paper indicate that exp(--GIRT) = V+1,2,3,4/ V-'r2f3s4to a very close approximation. I n that case, the steps involving hydrogen are close to equilibrium and V + 5 * 6 / V= 6f6 1. 264 Ind. Eng. Chem. Fundarn., Vol. 12, No. 3, 1973
Eliminating the surface concentration
Z
D
~ we- obtain ~ ~
~
~
~
~
+
From eq 3 and 4 Y+lsZ= (v+Iv+z)/(v-I v+2) and V-'g2 = ( v ~ l v ~ z ) / ( v ~ l V + Z ) and substitution of these into eq 12 yields
+
Table II. D Tracing Results
- dnDi-C4HL0
- --
D-2
d6
+
1OZD2'-C4HlOV +l , Z - v-1,2(9ZDi-C4HP~ Z D ~ ' ) (13) Additional deuterium balances for the assumed mechanism may be written (14)
zD i-CaHd
- ~ D ~ ' v - 3 (17)
~ + 3
Since V+5v6/V-536 1, these velocities are very large. Therefore Z D ~ ' Z D ~ and * eq 16 can be eliminated. The four equations, (13), (14), (15), and (17), contain fiveunknowns, namely v+1,2, v + ~ u, + ~ ,z ~ , and Z~D ~ ' The . - fifth equation ~ ~ required ~ to determine the five unknowns is furnished by writing eq 6 in the form
=
exp(--GIRT)
Run no. D-3
D-4
Temperature, OK 693 652 765 Total pressure, atm 1.055 1.018 1.055 Partial pressure, atm Isobutane 0.553 0,610 0.437 Isobutene 0.224 0.119 0.264 Hydrogen 0.278 0.289 0.354 ~ ~ ~ - C 4 fraction ~ l a , D 0.00436 0.00489 0.00495 0.0178 0.0410 ~ D ~ . ~ fraction 4 ~ s , D 0.00262 Z D ~ fraction ~ , D 0.1038 0.2000 0.1376 d n ~ ~ - ~ ~ atoms ~ l ~ / ofd e , D/(hr) (g of catalyst) 0.00208 0.00417 0.00849 d n ~ ' - ~ ~ ~ atoms ~ / d Oof, (g of catalyst 0.01759 0,0225 0.0466 dnDHz/dO,atoms of D/(hr)(g of catalyst -0.01807 -0.0238 -0.0616 V , moles of i-C4H10 reacted/(hr)(g of catalyst) -0.00413 -0.00397 -0,00443 ESP( - AG/R T ) 0.0773 0.0392 0,3072 v+ 1, Z/V- 1 * * 11.7 19.7 2.75 ~v+3jv-3 ~ 0.97 0.95 0.98 1.14 1 31 1.13 v+4/v- 4 V+5,6/V- 5 , 6 (assumed) 1.00 1.00 1.00
=
Algebraic solution of these equations is cumbersome. They can by simple manipulation be reduced via simultaneous equations which are readily solved by a numerical iterative procedure, as discussed by Kalsh (1972). Thus by l4C and D tracing it is possible to narroFv down the choice of possible rate-determining steps. Further elucidation of the mechanism is provided by conventional modeling of the system using kinetic data for the overall reaction. Experimental Procedure
Isobutane and isobutene were CP grade purchased from the Matheson Co. The radioactive species employed were 2rnethylpropane-l-'4C and 2-methyl prop-l-ene-2-l4C which were obtained from Suclear Chemical Corp. These radioactive materials were diluted with, respectively, isobutane and isobutene by lfatheson and supplied to us a t an activity of 0.5 mCi/200 g. The apparatus was a continuous-flow differential reactor, previously described by Happel and dtkins (1970). The catalyst employed was Type A50 supplied by the Houdry Process Corp., containing nominally 20% chromia. It was supplied in cylindrical pellets which were crushed to 14-20 meah size before use. Surface area was determined to be 55 m2/g. Prior to making an esperiment, the catalyst was pretreated to ensure the same level of activity for each experiment. Pretreatment consists in burning all coke (if any) off the catalyst at about 525"C, followed by a nitrogen purge and a 2-111treatment of hydrogen at the temperature of the run. Gas samples are analyzed using a standard gas chromatograph system. All hydrocarbons were separated by the chromatograph, and individual fractions were collected. In the case of runs containiiig radioactive l4C, the fractions were dissolved in a fluorescent toluene-based solution and analyzed
by liquid scintillation counting as described by Kamholz (1970). ;Inalysis for hydrogen was accomplished by comparing the pressure in a sample before and after freezing out the hydrocarbons with liquid nitrogen. In the case of deuterium tracing, fractions were collected for mass spectrometric analysis as described by Walsh (1972). The scintillation counter employed was a Unilux I1 manufactured by the Nuclear Chicago Corp. Typical background activity was about 30 countsjmin. Sample counts ran from about twice the background rate to as much as 1000 times the background rate. Deuterium analysis was accomplished by means of a Consolidated Electrodynamics hIodel21-103C mass spectrometer. Results
Results for I4C tracing are summarized in Table I. Temperature was varied from 699 to 790OK. The system was studied over a range of forward to reverse rates from 0.05 to 4.5. The first 30 runs (Kamholz, 1970) were made close to atmospheric pressure arid for the most part at relatively lower temperatures. The value of V+jt6/V-j'6 for these runs is 1.09 f 0.10. The remaining 15 runs (Walsh, 1972) (with prefixes RR to run numbers) were a t higher temperatures and a t different pressures. Results of these run3 show more scatter, with V+56/V-5,6values of 0.81 i 0.29. Taken together all forty-five runs give V+5$6/V-5s6= 1.00 0.26. These results confirm earlier data of Happel and Atkins (1970) for hydrogenation and dehydrogenation in the system n-butane-nbutenes-hydrogen. These results indicate that one or more rate-controlling steps esist in the single path of elementary reactions involving transformation of the hydrocarbon skeleton. Steps involving hydrogen alone appear to be close to equilibrium. A further restriction of the choice of rate-controlling steps was possible by deuterium tracing (Walsh, 1972). Table I1
*
Ind. Eng. Chem. Fundam., Vol. 12, No. 3, 1973
265
gives the results of three runs, which were treated following = 1.00 using eq 13, 14, 15, the assumption that V+5,6/V-6,6 and 17. ZD' values in Table I1 were taken as arithmetic averages of inlet and outlet Z D ~ ' S .It is clear that (V+lpz/V-l**) exerts by far the most important influence on the overall rate. Step 3, the transformation of the half-hydrogenated species (i-C4H91)to chemisorbed isobutene (GCdHsl) appears to be very close to equilibrium. Step 4, the chemisorption and desorption of isobutene, is perhaps not completely a t equilibrium. Thus the rate of the overall reaction is controlled by the rates of either or both steps 1 and 2, the chemisorption of isobutane and its dissociation into the half-hydrogenated species. This conclusion does not depend on the assumption of any specific type of adsorption theory or surface kinetics and should be useful both for modeling the behavior of chromiaalumina catalysts or serving as a basis of comparison with the mechanism of other catalysts. A comprehensive study of the overall kinetics for this system was conducted (Walsh, 1972). Isobutane dehydrogenation was studied a t pressures ranging from 0.30 to 1.7 atm and temperatures ranging from 646 to 768°K. Most experiments were conducted a t 652 f 8'K and 763 f 5°K. A few additional runs were performed a t temperatures within the range. I n all cases it was possible to operate a t differential conversion with 99% selectivity. A total of 84 dehydrogenation runs were made. Hydrogenation experiments were performed to investigate the rates of the reverse reaction. Isobutene hydrogenation experiments were conducted a t 650 + 7°K and 767 + 8'K, a t total reactor pressures ranging from 0.3 to 1.4 atm. At each total reactor pressure the ratios of isobutene to hydrogen studied were 3 : 1, 1: 1, 1:3. In all cases, it was possible to operate a t differential conversion with 99% selectivity. h few additional runs were performed a t various average temperatures and a t random isobutene to hydrogen ratios. A total of 75 hydrogenation runs were performed. To complete the complement of kinetic data necessary for the development of a rate model two types of intermediate data were obtained for the isobutane-isobutene-hydrogen system: data on the hydrogenation of isobutene in the presence of isobutane and data on the dehydrogenation of isobutane in the presence of isobutene and hydrogen. These in7°K and a t 765 f termediate data were obtained a t 651 7°K. 4 total of 72 such runs were performed. I n addition, earlier data (Kamholz, 1970) following the same procedure but all a t a temperature of 723 + 8°K were used. A total of 160 such runs were performed. A total of 340 of these runs were used for kinetic modeling calculations. These data were correlated using a nonlinear regression computer routine to minimize the following objective function
*
[
robsd
o.f. = i=l
- Tcdod *
robsd
1
Various power functions and Langmuir-Hinshelwood type models were employed. The most satisfactory correlation was obtained with a Langmuir-Hinshelwood model following the mechanism outlined in eq 1, with a single rate-controlling step, the chemisorption of isobutane (step 1) with other mechanistic steps a t equilibrium. In addition, it was found that no improvement in correlation was possible by including terms involving more than the equilibrium adsorption constants for steps 4, K4 = (P(-C4Ha)(Ci)/(CC4Hai) and for step 6, K6 = ( P H 2 ) ( C i ) / C H 2 $ ) . K 4 and K6 are the equilibrium constants for the corresponding reaction steps given by eq 266 Ind. Eng. Chem. Fundam., Vol. 12, No. 3, 1973
1, and C l , C 1 - ~ , ~and l o l CH2i refer to the concentration of free sites, chemisorbed isobutane, and chemisorbed hydrogen, respectively. The Langmuir-Hinshelwood model thus assumes the form
with kl =
)(,,,,,
1.818 X lo3 exp - -
x
(mole)/(hr) (g of catalyst) (atm)
K4 = 4.63 X lo4 exp Ke
=
2.33 X lo6 exp
((-
ly;)atm __ 2__ iy)atm
The overall equilibrium constant K,, is given by
K,,
= 1.408 X lo7 exp
The average deviation for the entire 340 point data set used + 12.7%. No systematic deviation was observed when data were segregated according t o temperature or concentration. Discussion
The significance of the constants kl, K 4 ,and K6 with regard to their relationship to the mechanistic steps appearing in eq 1 may, of course, be questioned, but it is believed that they have more than purely empirical value. From a purely empirical modeling standpoint, eq 20 does in fact yield the best correlation. Computations included two-term prefactor models, dual site mechanism models in which the adsorption denominator or denominators were squared, and models involving various interaction terms in the adsorption denominator. Two-term models were found to reduce to those involving a single term. Fairly complex forms of the single term model were tested. I t was observed that interaction terms of the form K ~ , - C , Hwhen ~ ~ Hadded ~ to the adsorption denominator did not improve the correlation. The resulting value for K was so small as to completely obscure its contribution. J17hen a second-order iteration term was used to replace one or both of the first-order adsorption denominator terms, the resulting average deviation was from 7 to 20% larger than that from eq 20. Single-term models in which the square root of the partial pressure of hydrogen was used in the adsorption denominator term (indicating hydrogen dissociation) yielded average deviations from 5 to 13% greater than eq 20. Exponential terms such as e--KpzC4H~ were placed on the thereby renumerator of eq 20 as a multiplier of k l 4 ~the a adsorption denominator. It placing the term K p z - ~ in was thought that this might indicate whether the Langmuir form properly described adsorption. S o observable advantage was gained by the use of the exponential and, in fact, it increased the average deviation to 3-6y0 greater than eq 20. When the denominator of eq 20 was squared, as would be the case for a dual-site mechanism, the deviations increased from 5 to 12% above those from eq 20. This is important be-
cause it represents the model which would be obtained if step 2 were rate controlling. Thus the model which is obtained empirically is in agreement with the restrictions imposed by the 14C and D tracing results. This lends weight to its additional theoretical significance and therefore to the possibility of extrapolation as well as utility in establishing further details of the mechanism of this reaction. Earlier studies in our laboratory (Happel, et al., 1970) on the n-butane-n-butenes-hydrogen system have indicated that the kinetic prefactor, the left-hand factor on the right side of eq 20 designating the forward overall velocity V+1,2,3,4, is complicated and involves the sum of a t least two terms. The complexity of this prefactor opens the question of whether such a two-term factor is characteristic of hydrocarbon dehydrogenation-hydrogenation reactions using chromia-alumina catalyst or whether in the particular case of the nbutane-n-butenes-hydrogen system a more elaborate form is required due to simultaneous reactions involving the three n-butenes. One approach to this question is the present study in which no isomeric forms of either isobutane or isobutene exist and the catalyst is inactive toward skeletal isomerization. The present system has the further advantage that isobutene will not dehydrogenate, whereas the n-butenes form 1,3-butadiene. Equation 20 is far simpler than the form required for the n-butane-n-butenes-hydrogen system, which indicates that the simultaneous reactions are responsible for the more complicated behavior rather than the properties of the catalyst itself. The present study does not confirm the necessity for a squared denominator term in the kinetic prefactor which seems to correlate data on the n-butane-n-butenes-hydrogen system best (Carra and Forni, 1971). Such a squared denominator corresponds to a dual site mechanism for the rate-controlling step, such as for example, step 2 in eq 1. The recombination of hydrogen atoms before desorption, step 5, which is required for hydrogen partial pressure to appear to the first power, rather than as the square root, is somewhat unconventional. Some of our previous studies (Happel and Atkins, 1970) have interpreted tracer data in terms of the apparent stoichiometric number, which in the case of isobutane dehydrogenation is given by
- AG/RT
This number vc would obviously become larger than unity if V+5,6/V-5,6 > 1 as shown in eq 8. It seems more appropriate to calculate V+6,6/V-s,6directly from eq 8 as
T/'-1.2,3,4
Use of the apparent stoichiometric number (eq 21) to indicate the extent to which the path 1,2,3,4 is rate determining will be less sensitive than calculation of V+'~6/V-5,6 (using eq 22) because the former involves taking logarithms of the numerator and denominator of the same fraction as employed in eq 22. Conclusions
The use of l4C and D enables a considerable restriction to be made of the choice of appropriate mechanisms for the dehydrogenation of isobutane over chromia-alumina catalyst. The possibilities from a choice of a number of mechanistic steps are narrowed down to chemisorption of isobutane without dissociation together with a surface reaction in which chemisorbed isobutane is dissociated into the half-hydrogenated species and adsorbed hydrogen atoms or alternatively a step involving dissociative adsorption of isobutane to form the half-hydrogenated species in a single step. Based on further studies of overall kinetics, it is concluded that chemisorption of molecular isobutane is the rate-controlling step. Though this conclusion is weaker, since it is based on the assumption of Langmuir-Hinshelwood kinetics, nevertheless the final rate equation seems not only to be consistent with the tracer results but to be the best empirical representation of the data obtained. Acknowledgment
This work was supported in part by a National Science Foundation grant to Kenneth Kamholz and a National Science Foundation Fellowship awarded to Dennis Walsh. Assistance was also obtained by a grant from the North Atlantic Treaty Organization. literature Cited
Carra, S., Forni, L., Catal. Rev. 5, 159 (1971). Happel, J., Catal. Rev.6 , 221 (1972). 9, 11 (1970). Happel, J., Atkins, R. S., IND.ENG.CHEM.,FUNDAM. Happel, J., Mezaki, R., J. Chem. Eng. Data, 18, 152 (1973). Happel, J., Mezaki, R., Hnatow, hI. A,, Advan. Chem. Ser. No. 97, 92 (1970). Kamholz, K., doctoral thesis, School of Engineering and Science, New York University, 1970. Walsh, D. E., doctoral thesis, School of Engineering and Science, New York University, 1972. RECEIVED for review March 31, 1971 RESUBMITTED April 19, 1973 ACCEPTEDMay 2, 1973 Presented at the 2nd North American Meeting of the Catalysis Society, Houston, Texas, February 1971.
Ind. Eng. Chem. Fundam., Vol. 12, No. 3, 1973
267
