Ind. Eng. Chem. Res. 1993,32, 2495-2499
2496
Selective Aromatization of C3- and C4-Paraffins over Modified Encilite Catalysts. 2. Kinetics of n-Butane Aromatization A p u r b a K.Jana and Musti S. Rao' Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208 016, U.P.,India The kinetics of the aromatization of n-butane over Zn-encilite catalyst was studied in a fixed bed reactor under steady-state conditions at atmospheric pressure and in the temperature range of 480-540 "C. The experimental data were analyzed, and a dual-site mechanism was proposed. Six rate equations of the Langmuir-Hinshelwood type were tested. T h e unknown parameters in the rate equations were estimated by a nonlinear regression method. A kinetic equation for n-butane aromatization is proposed. 1. Introduction
The catalytic conversion of lower alkanes and alkenes into more valuable products such as benzene, toluene, and xylenes (BTX) has received considerable attention in literature in the recent past. The literature on the aromatization of Ca- and Cr-paraffins has been extensively reviewed in part 1of this series (Jana and Rao, 1993). In most of the previous studies the acidic catalysts employed contain platinum or transition group metals and the emphasis has been on the study of the effect of metals and acid sites on the yield of aromatics. Some studies were also carried out on the mechanisms of the aromatization reaction over metal-incorporated zeolites (Kitagawa et al., 1986;Maggiore et al., 1991;Schulz et al., 1991). However, limited investigations exist on the reaction kinetics and the value of apparent activation energy (Mole et al., 1985). Only recently Le Van Mao et al. (1991) reported the kinetics of n-butane aromatization over ZSM-5 and Gaincorporated ZSM-5. Since only limited kinetic data on n-butane aromatization are available, it appears appropriate to study the kinetics in more detail. In part 1 of this series the catalytic activity of Zn-encilite in the aromatization of propane and n-butane has been studied by a comparative study of the yields of BTX using propane and n-butane as feeds. It was found that n-butane had a better activity and selectivity to BTX than propane. The results indicated that the activity and the Selectivity were directed by the acidity and Zn loading on the catalyst. The objectives of the present investigation were (a) to study the kinetics of n-butane aromatization over Znencilite catalysts, (b) to derive a kinetic model based on the reaction mechanism, and (c) to estimate the unknown parameters in the kinetic model. 2. Experimental Study The reaction has been studied over Zn-exchanged encilite catalyst with a surface area of 419 m2 gl.The details of the catalyst preparation and characterization were given in part 1of this series. All experiments were performed in a fixed bed, tubular reactor under differential conditions. Details of the experimental setup and catalyst pretreatment procedure were reported in part 1 of this series. The products were analyzed by using two gas chromatographs, viz., a NUCON gas chromatograph and a Hewlett-Packard 5890A gas chromatograph. The details of the analytical procedures were also reported in part 1 of this series. The reaction products detected in reasonable
* To whom correspondence should be addressed.
quantities were benzene, toluene, and xylenes. Very small amounts of methane, propane, and butene were also observed in the product stream. The experiments were carried out under steady state at atmospheric pressure at four temperature levels of 480, 500, 520, and 540 "C, respectively. The n-butane concentration in the feed was varied from 4 to 24 %. The feed stream contains n-butane with nitrogen as diluent. 3. Kinetic Analysis
(a) Reaction Scheme. In our earlier study (part 1of this series) it was observed that butene was found as an intermediate in n-butane aromatization. It was well known that the dehydrogenation of n-butane to butene is a reversible reaction. Butene may form due to cracking of an oligomer formed from butene as described by Engelene et al. (1985). Hence it can be proposed that the formation of BTX from n-butane is a consecutive reaction, and both steps are reversible. The reaction may be represented as follows:
B+O'-A (1) where B, 0, and A represent n-butane, butene, and BTX, respectively. The dehydrogenation of n-butane to butene and the aromatization of butene to BTX are considered to take place on different active sites, viz., B and r. The existence of two different types of sites in Zn-encilite catalyst has been confirmed by our earlier investigation (Jana and Rao, 1993). (b) Kinetic Models. Since the catalyst is a pure crystalline material, and the active sites are exchanged Zn2+ ions and protonic in nature, they are expected to be energetically uniform. The Langmuir adsorption isotherms were assumed to hold good. The LangmuirHinshelwood model (Hougen and Watson, 1947) can be proposed for the above reaction scheme. In the development of a plausible Langmuir-Hinshelwood reaction mechanism, a distinction was made between active sites u, which are protonic sites responsible for dehydrogenation of n-butane to butene, and sites r , which are responsible for aromatization. In the development of the kinetic models it was assumed that any of the following steps could be rate controlling: (i) the adsorption of the reactant or intermediate, (ii) the surface reaction of the adsorbed species, and (iii) the desorption of the intermediates or products. The mechanism of the above proposed reaction scheme is given below: (A) For the dehydrogenation of n-butane to butene on the u sites,
0 1993 American Chemical Society QSS0-5005/93/2632-2495~Q4.QQ~Q
2496 Ind. Eng. Chem. Res., Vol. 32,No. 11, 1993
where CB, and CO, represent the concentrations of the adsorbed n-butane and butene, respectively, on the u sites and C, represents the concentration of the vacant u sites. (B) For the aromatization of butene to aromatics on the 7 sites,
and Himmelblau, 1988;Arora, 1989)for implementing the above procedure. The method was implemented on a Hewlett-Packard 9000 Series 800 computer system. The Davidon-Fletcher-Powell method uses an approximate Hessian instead of an actual one. Therefore, secondorder derivatives of the least-squares objective function with respect to parameters need not be provided. Use of the DFP method provides faster convergence and is also robust. Calculation of confidence intervals is based on the t-test as recommended by Froment and Bischoff (1990). It involves only first-order derivatives of the model equation with respect to parameters. Therefore, it does not depend on what optimization method is used as long as the optimization method provides converged estimates. Model discrimination was done using the lack-of-fit F-test. For acceptable models, the estimated reaction rate constants and adsorption/desorption equilibrium constants should be positive. The discrimination among rival models was done by using the Bayes’ theorem. 4. Results and Discussion
k4 CAT Ar + A + r ; K , =(3) k6 PAC? where Co, and CA?represent the concentrations of the adsorbed butene andaromatics, respectively, on the 7 sites and C, represents the concentration of the vacant r sites. In all cases, the reverse reaction was accounted for, assuming the applicability of microscopic reversibility. The surface reaction of butene aromatization was also considered to be a reversible one. Taking the above proposed reaction mechanism as a basis, a set of six different rate expressionswas developed, assuming each elementary step to be rate determining. As the product stream contains a very small amount of butene, we express the rate of n-butene depletion in terms of the partial pressures of the major components, namely, n-butane and BTX. The rate equations for the above proposed mechanisms are given in Table I. (c) Parameter Estimation and Model Discrimination. For differential reactor operation, observed rates were computed from the conversions as follows: robs
=
FAX
(4)
where AX and (WIF)represent conversion and contact time, respectively. The rates as computed by eq 4 were used for the verification of the derived rate equations. The number of parameters for each model was seven. In order to reduce the number of parameters and to avoid numerical problems in analyzing each rate equation, some parameters were clubbed together as shown in Table I. The rate equations are nonlinear with respect to the unknown parameters. In order to evaluate these unknown parameters, a nonlinear regression analysis has been carried out. The residual sum of squares (RSS) given by
where n is the total number of experiments a t any given temperature, has been minimized. The calculated rate from a given model (Ricd)is a function of the unknown parameters. RiexPis the corresponding experimental rate. The Davidon-Fletcher-Powell (DFP) method of unconstrained minimization has been used (Fox, 1971;Edgar
All kinetic runs were carried out under conditions where interparticle and intraparticle diffusion effects were negligible. In order to check the importance of external diffusional resistances, experiments were conducted by varying the feed rate, keeping WIF constant. From the results, the feed rate at which interparticle diffusional resistances were negligible was found. To test the intraparticle diffusional limitation, experiments were carried out a t constant WIF with the particle size varied in each run. The results were used to find the particle size range at which the intraparticle diffusional resistances are negligible. The experiments for intraparticle diffusion limitations shows only the absence of diffusion in micropores. As the channel dimensions of Zn-encilite are comparable with the kinetic diameters of hydrocarbon molecules like benzene, toluene, and xylenes, a micropore diffusional effect cannot be ruled out. Hence, the kinetic parameters presented here include the diffusional effects, if any. The heat-transfer resistances also play an important role in heterogeneous reactions. Although the aromatization reaction sequence involves some steps that are exothermic, the dehydrogenations and cracking reactions are endothermic in nature. Since a large excess of nitrogen is used in the feed gas (75% or more), and since in the kinetic experiments the conversion is less than l o % , it is reasonable to neglect the thermal resistances. The activity and selectivity of the Zn-encilite catalyst were tested for the n-butane aromatization, and the results are presented in Figure 1. It is obvious from the figure that the total conversionand the BTX selectivity remained essentially constant even after a 3-h time on stream. The catalyst did not show any sign of deactivation during this period. The experiments were carried out under a differential mode of operation of the reactor. The experimental conditions and the responses of the experiments are given elsewhere (Jana, 1993). The values of the concentrations used in the parameter estimation of the models were the average values of the inlet and outlet concentrations of each component. The difference between the inlet and outlet concentrations ranged up to lo%, substantiating the differential operation of the reactor. With these values, all six models have been tested. The parameters were estimated for models 1-6 using data at each temperature separately, using the aforementioned technique. The
Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 2497 Table I. Rate Equations for Various Rate-Controlling Steps no. of rate equation
rate-controlling step
rate equations
1
2
3
4
6
1
IUU
On the basis of the F-test it is difficult to discriminate between models 5 and 6 having very close RSS values. In model 6, the clubbed parameter Kle is negative at all temperature except at 540 O C . Further discrimination was achieved using the Bayes theorem (Boxand Hill, 1967; Prasad and Rao, 1977; Roth, 1965, which states that the posterior probability of a model is given by
P(AJ W I A J P(A,/B)=
OL 0
I
1.o
I
2.0
I
3.0
P r o c e s s t i m e , hr
Figure 1. Activity and selectivity of n-butane to BTX over ZnFeedgas: 16%n-butaneandrestnitrogen. encilitecataly~tat50~C. W/F= 0.8 ph-mol-1. 0,Conversion; 0 , BTX selectivity.
values of the parameters and the residual sum of squares (RSS)for models 1-6 are given in Table 11. We have tested the model adequacy for all six models from the "lack-of-fit" s u m of squares and the "pure error" sum of squares as described by Froment and Bischoff (1990). Pure error sum of squares has been calculated from the four replicated experiments at 480 "C. The standard F-test for model adequacy was based on the value of the ratio of F d (which is the ratio of the variance of the lack-of-fit sum of squares to the variance of the pure error sum of squares) to that of Ftab (which is the corresponding tabulated value) with the corresponding degrees of freedom in the numerator and denominator and desired level of confidence. Table I11 lists the values of Fc,dFt.b for all models at 480, 500, 520, and 540 "C. The tabulated F-values are used a t the 95% confidence level. Models 1-4 are found to be not appropriate due to lack of fit ( F J Ftab >> 1). On the other hand, models 5 and 6 seem to be competing.
(6)
where Ai (i = 1,...,r ) denotes the ith model, B denotes the data, P(Ai)denotes the prior probability of the ith model, and P(B/Aj) denotes the likelihood of the ith model. A knowledge of the prior probabilities for various models is required. If there is no information regarding the prior probabilities, equal probabilities for all the models are assigned. A knowledge of the error structure is required for calculating the likelihood. Once the observations and design matrix are substituted into the expression for the probability density function (PDF), the resulting expression, which is a function of the parameters and variance, is called the likelihood. By use of the estimated parameters of Table 11, the likelihoods are calculated. Equal prior probabilities were assigned to both models 5 and 6 and the posterior probabilities were calculated at four different temperatures (480,500,520, and 540 "C)on the basis of the results of 10 experiments at each temperature. The values of prior as well as posterior probabilities for models 5 and 6 are shown in Table IV. From the values of the posterior probabilities after 10 experimental runs, it is evident that model 5 is superior to model 6 at all temperatures. Table V lists the values of the kinetic parameters and adsorption constants of model 5 at four different temperatures. Parameters were estimated at the 95% confidence level. It is obvious from Table V that with an increase in temperature the kinetic constant, the equilibrium constant, and the adsorption constant increase, whereas the value of the clubbed constant decreases. The activation energy and the frequency factor had been
2498 Ind. Eng. Chem. Res., Vol. 32, No. 11, 1993 Table 11. Values of Parameters and RSS for Models 1-6 temp, OC model 1 model 2 model 3 480 kl’ = 1.116 k2‘ = 0.269 k3’ = 0.906 K1 4.178 K12 1.249 K I = 1.513 KQ= 6.668 K11 = 1.993 K8 = 13.269 Klo = -1.153 K1 = 2.628
RSS = 2.9 X 10-4
RSS = 1.2 X 104
RSS = 1.3 X 1W
500
kl’ = 1.443 K I = 1.414 Ks = 9.8880
kd = 0.210 K1 = 6.362 Kg = 9.508 Klo = -12.454
k3’ = 0.449 K12 = 3.146 K11 = 4.593 K1= -0.227
520
540
RSS = 1.1X 106
RSS = 2.4 X 10-6
RSS = 6.2 X 10-6
kl’
= 1.757 K7 = 1.467 Ke = 6.073
kd = 0.461 K1 = 3.599 Kg 5.408 Klo = -6.687
= 1.723 Klz = 0.998 K11 1.486 K1 = 0.732
RSS = 1.8 X 106
RSS = 1.2 X 106
RSS = 1.5 X 106
k< = 2.360 K I = 1.497 Ke = 5.028
k2‘ = 0.336 K1 5.817 Kg = 8.848 Klo = -16.88
= 0.781 K12 2.921 K11 4.402 K1 = -1.565
RSS = 3.1 X 106
RSS = 1.3 X 106
RSS = 2.5 X 10-5
k3’
k3‘
model 4 k4’ = 1.251 K13 = 1.665 K14 = 1.333 Klg 2.009 K6 = 2.942 RSS = 2.9 X 10-6 k4‘ = 0.809 K13 = 1.655 K14 = 2.279 K15 = 11.177 K6 7.859 RSS = 9.3 X 1W k4‘ = 0.838 Ki3 1.988 Kid = 2.871 K1g = 9.911 K6 = 4.580 RSS = 1.5 X 106 k4’ = 1.726 K13 1.159 K14 = 1.657 Klg = 27.480 K6 = 0.830 RSS = 1.9 X 106
model 5 kgl = 0.152 K16 = 10.481 Kg = 0.119 K6 = 9.198
model 6 k6’ = 0.123 Ki7 = 93.85 Kl8 -19.4 Kig = 13.6
RSS = 3.6 X leg RSS = 1.2 X 10-1 kg’ = 0.244 K16 = 8.869 Kg = 0.290 K6 7.809
k6’ = 0.208 K I T= 75.51 Klg = -8.36 K1g = 13.84
RSS = 1.5 X 10-8
RSS = 1.4 X 10-7
kg’ = 0.409 Kl6 = 7.057 Kg 0.581 K6 = 7.010
k6’ K17 Kie Kig
RSS = 1.3 X 10-8
RSS = 5.2 X 10-8
kg’ = 0.655 Kl6 = 5.982 K5 = 0.87 Ke = 6.006
k6’ = 0.571 Kii = 37.87 Kip, = 0.561 Kig = 10.64
RSS = 2.0 X 10-8
RSS = 5.7 X 10-8
0.351 = 51.60 = -0.40 = 11.90
Table 111. Ratios of calculated F-values to Tabulated F-values of Models 1-6 temp,OC model1 model2 model3 model4 model5 model6 27.36 74.76 00.02 24.99 02.57 480 53.87 50.72 132.68 238.73 00.27 02.98 500 196.57 01.07 520 329.25 269.65 322.08 391.80 00.23 00.39 01.17 540 568.65 280.67 532.42 480.44
Table IV. Posterior Probabilities of Models 5 and 6 temp, OC 480 500 520 540
prior probabilities of both models 0.5 0.5 0.5 0.5
posterior probabilities of model 5 model 6 1.0 0.0 1.0 0.0 1.0 0.0 1.0 0.0
Table V. Ninety-Five Percent Confidence Limits of Parameters in Model 5 teF8, 480 500 520 540
kS’, mol/(gh)
0.152 f 0.003 0.244 f 0.005 0.409 f 0.006 0.655 f 0.014
Kls, atm-1 10.481 f 0.403 8.869 0.285 7.057 f 0.134 5.982 0.135
*
K5 0.117 f 0.099 0.290 f 0.259
0.581 f 0.358 0.870 f 0.688
Ke, atm-1 9.198 f 4.559 7.809 f 3.643 7.010 f 1.991 6.006 f 2.157
evaluated from the rate constants by using Arrhenius relationship k = ko exp(-EIRT). Figure 2 shows an Arrhenius plot of In kg/versus 1/T. The activation energy calculated from the slope is 121 kJ/mol. The apparent activation energy for the aromatization of n-butane to aromatics is 100 kJ/mol as reported by Le Van Mao et al. (19911, using ZSM-5 and gallium-incorporated ZSM-5, which is comparable to our present study. From the above results it is evident that the surface reaction of the adsorbed butene is the rate-controlling step. The surface reaction in the aromatization step involves several steps, viz., oligomerization, cyclization, dehydrogenation, and dealkylation, in order to form specific products like benzene, toluene, and xylenes. 5. Conclusions
A systematic kinetic study on n-butane aromatization over Zn-encilite catalyst has been made. Kinetic data were obtained by employinga fixed bed differential reactor
-1.4-
1.30
1.22
1.34
1 lo3 T Figure 2. Temperature dependence of the logarithm of the rate constant of n-butane aromatization.
at temperatures in the range 480-540 “C at atmospheric pressure. From the product distribution pattern a reaction mechanism has been proposed for the title reaction. The rate equations for this mechanism were derived on the basis of Langmuir-Hinshelwood models with dual site mechanism. The unknown parameters in the rate equations were estimated using a nonlinear regression algorithm. The proposed reaction mechanism was confirmed by a trend shown by the kinetic constants with temperature. The kinetic model which best fit our experimental data is given by (7)
The calculated activation energy for the aromatization of n-butane to BTX is 121 kJ/mol, which is comparable to the value reported by Le Van Mao et al. (1991). The values of the adsorption constants are not available in the literature.
Ind. Eng. Chem. Res., Vol. 32,No. 11,1993 2499
Nomenclature A = benzene, toluene, and xylenes B = n-butane k[ = reaction rate constant of the ith rate-controlling step K1 = n-butane adsorption equilibrium constant, atm-1 Kz = thermodynamic equilibrium constant for n-butane dehydrogenation Ks = butene adsorption equilibriumconstant on u sites, atm-l K4= butene adsorption equilibrium constant on T sites, atm-l Ka = thermodynamic equilibrium constant for butene aromatization Ke = BTX adsorption equilibrium constant, atm-l n = total number of experiments at any given temperature 0 = butene P(AJ = prior probability of the ith model P(BIAJ = likelihood for the ith model Pi = partial pressures of the ith component, atm r = number of models rB = rate of reaction of n-butane, mol/(g.h) WIF = contact time, h X = conversion of n-butane u = acid sites on Zn-encilite catalyst 7 = Zn2+ site on Zn-encilite catalyst Literature Cited Arora. J. S. Introduction to Optimum Design; - . McGraw-Hik New York, 1989; pp 327-330. Box, G. E. P.; Hill, W. J. Discrimination Among Mechanistic Models. Technometrics 1967, 9 (1). 57-71. Edgar,T. F.;Himmelblau,D. M. Optimization of ChemicalProcesses; McGraw-Hik New York, 1988, Chapter 6. Engelene, C. W. R.;Wolthuizen, J. P.; Van Hoof, J. H. C. Reactions of Propane over a Bifunctional Pt/H-ZSM-5 Catalysts. Appl. Catal. 1986,19,153-163.
Fox, R. L. Optimization Methods For Engineering Design; Addison-Wesley: Reading, MA, 1971. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design, 2nd ed.; W h y : New York, 1990, pp 94-98. Hougen, 0. A.; Watson, K. M. Chemical Process Principles; Wiley: New York, 1947; Vol. 111. Jaua,A. K. Studiea on SelectiveAromatizationof C r and C4- Paraffii Over Modified Encilite Catalysts. Ph.D. Thesis, Indian Institute of Technology, Kanpur, India, 1993. Jana, A. K.; Rao, M. S. SelectiveAromatization of Ca and C4 P a r a f f i i over Modified Encilite Catalysts. 1. Qualitative Study. Znd.Eng. Chem. Res. 1993,32,1046-1052. Kitagawa, H.; Sendoda, Y.; Ono, Y.Transformation of Propane into Aromatic Hydrocarbons over ZSM-5Zeolites. J. Catal. 1986,101, 12-18. Le Van Mao, R.;Yao, J. Kinetic Study of n-Butane Aromatization on ZSM-5 and Gallium Bearing ZSMd Catalyets. Appl. Catal. 1991, 79,77-87. Maggiore, R.; Scire, 5.;Galvagno, S.; Crisafdi, C.; Toscano, G. Influence of Iridium, Rhenium and Lanthanum on Propane AromatizationoverPlatinum/ZSM-5Catalysta.Appl. Catal. 1991, 79, 29-40. Mole, T.; Anderson, J. R.;Creer, G. The Reaction of Propane over ZSM-CZn Zeolite Catalysts. Appl. Catal. 1986,17,141-154. Praead, K. B. S.; Rao,M. S. Use of Expected Likelihood in Sequential Model Discriminationin Multirespom Systems. Chem.Eng. Sci. 1977,32, 1411-1418. Roth, P. M. Design of Experiments for Discriminating Among Rival Models. Ph.D. Thesis, Princeton University, Princeton, NJ, 1965. Schulz, P.; Baerns, M. Aromatization of Ethane over Gallium Promoted H-ZSM-5 Catalysts. Appl. Catal. 1991, 78,15-29.
Received for review February 23, 1993 Revised manuscript received June 4, 1993 Accepted June 16, 1993. Abstract published in Advance ACS Abstracts, September 1, 1993.
