Ind. Eng. Chem. Res. 1997, 36, 3427-3432
3427
Benzylation of Biphenyl with Benzyl Chloride over HY Zeolites: A Kinetic Model for Reaction and Catalyst Deactivation Paolo Beltrame* and Giovanni Zuretti Dipartimento di Chimica Fisica ed Elettrochimica, Universita` degli Studi di Milano, Via C. Golgi 19, I-20133 Milano, Italy
Two dealuminated HY zeolites were employed as catalysts for the Friedel-Crafts reaction of biphenyl with benzyl chloride in a slurry batch reactor, with solvents cyclopentane, cyclohexane, and methylcyclohexane, at temperature from 50 to 100 °C. Mainly benzylbiphenyl isomers (M), but also appreciable quantities of dibenzyl derivatives (D) were obtained and determined. Within the monobenzylated fraction, a para-selectivity of 65-70% at 60% conversion was reached. Magnetic stirring was found to be adequate for a chemically controlled reaction kinetics. Kinetic models, including equations for the process itself and for the catalyst deactivation, and applied on the basis of optimization procedures, were used to correlate the results. The model of choice was able to interpret runs carried out at different doses of catalyst and different initial concentrations of the benzylating agent. A solvent effect on the kinetics was evidenced. Deactivated catalysts were regenerated for a few reaction-regeneration cycles. Introduction
Experimental Section
Biphenyl and its derivatives are interesting for their high boiling point, thermal stability, and physicochemical properties. Since polychlorinated biphenyls (PCBs) had to be discarded for environmental reasons, interest was focused on other derivatives, useful in heat transfer and other applications, for instance as dye solvents (Thompson, 1992). Among these derivatives, also benzylbiphenyls have been considered (Ajimoto, 1974; Hino and Arata, 1981). The Friedel-Crafts reaction, typically employed for the synthesis of such compounds, used to be catalyzed by Brønsted or Lewis acids in liquid phase. However, in order to reduce plant corrosion and spent catalyst disposal problems, solid acid catalysts are of growing importance. In the particular case of benzylbiphenyls, catalysts such as montmorillonite and zeolites have been mentioned in the patent literature (Haase et al., 1991; Sakura et al., 1991) for their synthesis from biphenyl and benzyl chloride. In these laboratories, the kinetics of the reaction of biphenyl with benzyl chloride has been studied and preliminary results, obtained over a montmorillonite (K10) catalyst, have been presented (Beltrame et al., 1995). In the present work, dealuminated HY zeolites have been employed as catalysts for the same process. The reactions involved are the following:
Materials. Analytical grade products were used throughout (purity g99%). Dealuminated zeolites were Tosoh Corp. products: TSZ-360-HUD, pellets, bound with 25% clay, SiO2/Al2O3 bulk molar ratio ) 14, lot no. 781, was labeled HY360; TSZ-330-HUA, powder, SiO2/ Al2O3 molar ratio ) 6, lot no. C2-06-103, was labeled HY330. Solvents were dried by distillation and kept over 3A zeolite. Catalysts. Pellets of HY360 were crushed to particles mostly in the range 75-180 µm (ca. 5% b. A check on the peaks of the three isomers, by GC-MS (mass spectrometry) analysis, gave a molecular weight of 244. Isomer c was recognized as 4-benzylbiphenyl by comparison with a commercial sample; the latter was also employed to determine the calibration factor for the quantitative GC analysis, assumed valid for the other isomers too. Since in the literature (Haase et al, 1991; Sakura et al., 1991) the reported order of abundance is 4- > 3- > 2-benzylbiphenyl, the GC peaks a and b were assigned to the 3and the 2-isomer, respectively. The sum of the benzylbiphenyl isomers (M) was considered for the kinetic treatment. Several broad peaks in the gas chromatogram, with retention times from 18 to 26 min, were recognized as signals from dibenzylbiphenyl derivatives (D) by GCMS analysis: all peaks corresponded to a molecular weight of 334. The mixture obtained by a chromatographic separation on silica gel (eluent: n-hexane/ toluene, 9:1 (v/v)) was used to determine the calibration factor of D. Selectivities to M and D products were obtained as SM ) CM/(C°BzCl - CBzCl) and SD ) 2CD/(C°BzCl - CBzCl). The mass balance of the runs was satisfactory: for most runs, and for all those taken into account for kinetic interpretation, the sum of selectivities SM and SD was in the range 97-100%. Optimization Procedure. The sum of the squares of the deviations (δ) calculated from experimental data included, for each sample withdrawal, three molar concentration terms (CBzCl, CM, CD) and one term corresponding to the catalyst activity (a). Values of a/10 were employed instead of a-values, in order to manage numbers of similar order of magnitude. The computer program was based on the optimization routine OPTNOV (Buzzi Ferraris, 1968); each set of differential equations was integrated by a fourth-order Runge-Kutta numerical method (Carnahan et al., 1969). The objective function to be minimized was nt
F)
ns
∑ ∑ [(xexptl - xcalcd)i,j]2/(np - nk) i)1 j)1
were nt is the number of withdrawals, ns the number of variables considered, np the number of experimental data employed in the computations, and nk the number of parameters optimized, while the x-values refer to the terms CBzCl, CM, CD, and a/10. The standard error of
the estimate of the variables is σ ) F1/2; since F was in the range (4-36) × 10-6, σ was between 0.002 and 0.006. Results and Discussion The stability of benzyl chloride in contact with the catalysts was checked in blank runs under the reaction conditions (cyclohexane at 80 °C, methylcyclohexane at 100 °C) with C°BzCl = 0.1 mol/L, without biphenyl. With HY360 up to 20 g/L at 80 °C and up to 15 g/L at 100 °C, as well as with HY330 up to 15 g/L at 80 °C, only a slight decomposition of BzCl (from less than 1% up to 3%) was observed: it took place during the first 2 min of contact and did not increase during the next 5 h. In more severe conditions, i.e., with 39 g/L of HY360 at 100 °C or with 37 g/L of HY330 at 80 °C, the decomposition started immediately (50-80% during the first 2 min) and progressed to completion in 1-3 h. As a consequence of these blanks, kinetic runs were carried out keeping the catalyst dose under 13 g/L. Both catalysts were subject to deactivation during the reaction runs. An activity function (a), decreasing from 1 toward 0, was thus introduced into the equation of every kinetic model. Kinetic Runs Analysis of the reaction product gave in any case the three isomers of benzylbiphenyl (M), with a distribution depending on the catalyst, the solvent, and the reaction temperature. A summary of these results is given in Table 1. It can be appreciated that very little ortho isomer is produced, probably because of steric hindrance, and that the para/meta ratio is slightly decreasing with increasing reaction time (from y ) 30% to y ) 60%), giving evidence of a moderate catalyst activity in the isomerization of the para to the meta isomer. Catalyst HY360 is able to give around 65% of 4-benzylbiphenyl, while with catalyst HY330 this fraction can arrive at about 72%. Values of para-selectivity around 80% were previously reported in patents (Haase et al., 1991; Sakura et al., 1991). Besides benzylbiphenyl isomers, usually there was a mixture of dibenzyl derivatives, collectively labeled D. The amount of D at the end of a run depended on the extent of the reaction, i.e., the final fractional conversion yf. The selectivity SD,f was in the range 0-11% with yf < 40%, reached 13% with yf = 50-60%, and could be as high as 21% with yf > 90%, the rest of the product being M. Runs with conversion greater that 90% were not considered for kinetic interpretation.
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3429 Table 2. Runs on Catalyst HY360 at 80 °C, at Different Doses of Catalysta k1 (L/(min‚g))
ka (min-1)
106F
Solvent: Cyclohexane Eight runs, each with 10-12 samples. Ccat values around 5.2, 7.2, 10.4, and 12.8 g/L av of parameter values from single runs 0.00093 ( 0.00024 0.229 ( 0.072 overall calculation on the 8 runs (92 samples) 0.00097 0.232
from 5 to 35 26.5
Solvent: Methylcyclohexane Two runs, each with 10-12 samples. Ccat around 11 g/L av of parameter values from single runs 0.00046 ( 0.00003 0.202 ( 0.027 overall calculation on the 2 runs (22 samples) 0.00044 0.194 a
from 9 to 10 19.1
C°BIP ) ca. 0.4 mol/L; C°BzCl ) ca. 0.1 mol/L. Sum of selectivities ) 98-100%. Interpretation with model BIP3Y (k1 ) k2; N ) 2).
Table 3. Runs on Catalyst HY360, Solvent Cyclohexane, at 80 °C, at Different Concentrations of BzCla av of parameter values from single runs overall calculation on the 5 runs (48 samples)
k1 (L/(min‚g))
ka (min-1)
106F
0.00106 ( 0.00022 0.00103
0.289 ( 0.063 0.281
from 7 to 10 16.2
a C° BIP ) ca. 0.4 mol/L; Ccat ) ca. 10.4 g/L. Sum of selectivities ) 98-99%. Interpretation with model BIP3Y (k1 ) k2; N ) 2). Five runs, each with 7-12 samples. C°BzCl values of 0.04, 0.05, 0.07, 0.08, and 0.10 mol/L.
Kinetic runs were usually carried out with C°BzCl = 0.1 and C°BIP = 0.4 mol/L, in any case with an excess of biphenyl. Several kinetic models were tried in order to interpret the results, and one of them (BIP3Y, to be discussed later) was found satisfactory and was routinely employed. It is based on the following kinetic equations:
-dCBzCl/dt ) Ccata(k1CBIP + k2CM)
(1)
dCM/dt ) Ccata(k1CBIP - k2CM)
(2)
dCD/dt ) Ccatak2CM
(3)
-da/dt ) kaaN
(4)
As a four-parameter model, BIP3Y showed that k1 ) k2, approximately, and that N had values dependent on the catalyst but not on other reaction conditions (N ) ca. 2 for HY360; N ) ca. 1.5 for HY330). So it was used within this approximation, as a two-parameter model, the parameters (k1 and ka) being kinetic coefficients for the benzylation reaction and the catalyst deactivation, respectively. Because of the excess of biphenyl with respect to benzyl chloride, CBIP was taken as constant ()C°BIP). The results of a typical run are presented in Figure 1. Catalyst HY360 was examined first. A group of kinetic runs was carried out in cyclohexane at 80 °C, at different doses of catalyst from 5 to 13 g/L. As shown in Table 2, fairly well defined values of k1 and ka were obtained, independently of the level of Ccat, both by separately computing every run and averaging the results and by performing an overall calculation on the entire group of runs. Two runs in methylcyclohexane at the same temperature, also presented in Table 2, had lower values of the parameters, particulary of k1, showing that a solvent effect is present. Using the same catalyst, in cyclohexane at 80 °C, a group of runs was carried out at different initial concentrations of BzCl. The results are given in Table 3 and are not different, within experimental error, from those of the runs in cyclohexane presented in Table 2. Therefore the kinetic model proved able to interpret runs carried out by changing Ccat and C°BzCl. However, C°BIP had to be maintained at a value around 0.4 mol/ L, to prevent changes in the rate coefficients, probably because of a solvent effect. Figure 2 shows a comparison
Figure 1. Example of kinetic run: reaction SHY28 at 80 °C in cyclohexane, over HY360 (5.16 g/L), with C°BIP ) 0.408 mol/L. Curves are calculated within model BIP3Y, with k1 ) k2 ) 0.00084 L/(min‚g); ka ) 0.186 min-1, N ) 2.
of experimental and calculated values for the concentration of benzyl chloride during the group of runs from Table 3. Again with catalyst HY360 (Ccat from 5 to 13 g/L), a group of runs was carried out in methylcyclohexane, at 100 °C, and results are shown in Table 4. Also in this case, fairly well defined values of k1 and ka were obtained, independently of the level of Ccat. By separately computing every run and then averaging the results or by performing an overall calculation on the entire group of runs, similar results were obtained. Coefficient k1 is markedly increasing from 80 °C (Table 2) to 100 °C (Table 4); ka is also increasing, but to a lower extent. It should be noticed that at 100 °C methylcyclohexane is practically at its boiling point (as cyclohexane is at 80 °C) and it has been recently reported for a reaction similar to ours (cyclohexylation of naphthalene over HY zeolites) that the best results are obtained at the boiling points of the solvents (Mravec et al., 1996). The other catalyst (HY330) was used for runs at 80 °C in cyclohexane and at 50 °C in cyclopentane, all with C°BzCl = 0.1 and C°BIP = 0.4 mol/L, at different values of Ccat in the range 2-12 g/L, with the results shown in
3430 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 4. Runs on Catalyst HY360, Solvent Methylcyclohexane, at 100 °C, at Different Doses of Catalysta av of parameter values from single runs overall calculation on the 4 runs (50 samples)
k1 (L/(min‚g))
ka (min-1)
106F
0.00237 ( 0.00057 0.00253
0.322 ( 0.060 0.362
from 5 to 20 28.6
a C° BIP ) ca. 0.4 mol/L; C°BzCl ) ca. 0.1 mol/L. Sum of selectivities ) 97-98%. Interpretation with model BIP3Y (k1 ) k2; N ) 2). Four runs, each with 10-15 samples. Ccat values of 5.3, 7.4, 10.4, and 12.6 g/L.
Table 5. Runs on Catalyst HY330, Solvent Cyclohexane, at 80 °C, at Different Doses of Catalysta av of parameter values from single runs overall calculation on the 4 runs (46 samples)
k1 (L/(min‚g))
ka (min-1)
106F
0.00529 ( 0.00068 0.00510
0.666 ( 0.085 0.656
from 17 to 28 22.1
a C° BIP ) ca. 0.4 mol/L; C°BzCl ) ca. 0.1 mol/L. Sum of selectivities ) 98-99%. Interpretation with model BIP3Y (k1 ) k2; N ) 1.5). Four runs, each with 10-12 samples. Ccat values of 2.0, 6.9, 9.0, and 12.0 g/L.
Table 6. Runs on Catalyst HY330, Solvent Cyclopentane, at 50 °C, at Different Doses of Catalysta av of parameter values from single runs overall calculation on the 4 runs (48 samples)
k1 (L/(min‚g))
ka (min-1)
106F
0.00390 ( 0.00031 0.00390
0.531 ( 0.040 0.528
from 8 to 21 15.6
a C° BIP ) ca. 0.4 mol/L; C°BzCl ) ca. 0.1 mol/L. Sum of selectivities ) 99%. Interpretation with model BIP3Y (k1 ) k2; N ) 1.5). Four runs, each with 12 samples. Ccat values of 5.0, 7.0, 9.0, and 12.0 g/L.
Figure 2. Runs at 80 °C in cyclohexane, over HY360 (ca. 10.4 g/L), with C°BIP = 0.4 mol/L and different C°BzCl values. Curves of CBzCl vs t are calculated within model BIP3Y, with parameter values from an overall computation (Table 3).
Figure 3. Runs at 50 °C in cyclopentane, over HY330, with C°BIP = 0.4 mol/L and C°BzCl = 0.1 mol/L; the different Ccat values are shown. Curves of CM vs t are calculated within model BIP3Y, with parameters values from an overall computation (Table 6).
Table 5 for the former group and in Table 6 for the latter one. This catalyst proved more active and also more easily deactivated than HY360. Measurements with HY330 were actually rather difficult and results are to be considered as less reliable because the high rate would have required very frequent sample withdrawals, but in practice the frequency of one withdrawal every 2 min was the limit of our experimental method. Figure 3 shows a comparison of experimental and calculated values of CM for the runs in cyclopentane, with noticeable disagreement at short reaction times. The kinetic runs presented so far were carried out over fresh catalysts, under magnetic stirring at 825 rpm. The effectiveness of the stirrer was checked with runs using the same stirrer at different velocities or shifting to mechanical agitation. It was so found that the mechanical stirrer, which can be made to work at higher speed than the magnetic one, if actually used at high speed directs all the catalyst particles toward the surface of the liquid, worsening instead of improving the suspension and causing lower reaction rates; mag-
netic stirring is preferable, and a stirring rate around 600-800 rpm assures a good suspension (Figure 4). Attention was paid also to the problem of the catalyst deactivation. A regeneration was found possible, and Figure 5 shows that both catalysts resume a reasonable activity, as expressed by the k1 kinetic coefficient, during a few reaction-regeneration cycles, although there is also some irreversible deactivation. Discussion of the Kinetic Model Before model BIP3Y was accepted, several models were tried. The first ones were employed only on the basis of the measurement of the concentrations CBzCl, CM, and CD; catalyst activities were calculated but no experimental value was given. The features of the main models of this type can be so summarized: Model BIP2C: Pseudo-homogeneous reactions, with kinetics dependent on the product CBIP‚CBzCl for the first benzylation and on the product CM‚CBzCl for the second benzylation; a concentration-dependent deactivation (Corma et al., 1995; Sotelo et al., 1996), with the kinetic
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3431
optimization procedure. Within this different approach, the following models were mainly tested: Model BIP2Z: As for model BIP2A, apart from the use of “experimental” values of activity. Model BIP3Z: Reactions with Hougen-Watson kinetics, i.e., with terms such as
-
dCBzCl (kmCBIPCBzCl + kdCMCBzCl) ) Ccata dt (1 + K C )2 B
Figure 4. Runs at 100 °C in methylcyclohexane over HY360 (ca. 12.8 g/L), with C°BIP = 0.4 mol/L and C°BzCl = 0.1 mol/L, under different stirring conditions. Values of k1 were obtained for each run within model BIP3Y.
(5)
BzCl
where KB represents the adsorption coefficient of BzCl on the catalyst surface, deactivation as for BIP2A. Model BIP3X: as above, but with a linear rather than quadratic denominator in the Hougen-Watson equations. The interpretation based on model BIP2Z was good for a series of runs having different Ccat, at constant C°BzCl but not for a series involving different values of C°BzCl since at lower values of C°BzCl higher values of the benzylation kinetic parameters were found. This was evidence of a negative effect of benzyl chloride on the kinetics and suggested employing equations of the Hougen-Watson type. On the other hand, when using models BIP3Z and BIP3X, it was found that parameter KB was badly defined, being correlated with km and kd. Therefore model BIP3X was simplified under the assumption KBCBzCl >> 1, and model BIP3Y was obtained. This shows that model BIP3Y, which may seem to correspond to pseudohomogeneous reactions, derives actually from Hougen-Watson kinetics, with a strong adsorption of benzyl chloride giving rise to an apparent zero order with respect to this reactant. With this model, all runs could be reasonably interpreted. It can be pointed out that k1 ) km/KB and k2 ) kd/KB. An attempt was eventually made to interpret the runs with model BIP3Y but without using “experimental” catalyst activity values. The results were not very dissimilar from the ones given in the tables, but the dispersion of parameter values around their averages was larger, and values of k1 and ka appeared to be somewhat correlated. Conclusions
Figure 5. Comparison of runs over fresh or regenerated catalysts: HY360 at 100 °C in methylcyclohexane; HY330 at 80 °C in cyclohexane. Values of k1 were obtained for each run within model BIP3Y.
equation -da/dt ) kaaN(CM + 2CD), i.e., dependent on the sum of the benzyl groups in the reaction products. Model BIP2P: As above, but with deactivation depending only on CD. Model BIP4C: As with BIP2C, but with deactivation depending on CBzCl. Model BIP2A: Pseudo-homogeneous reactions, with kinetics as above; a deactivation independent of concentrations (Khang and Levenspiel, 1973), with a kinetic equation -da/dt ) kaaN. The interpretation of experimental data based on these models was not satisfactory; furthermore, some correlation was detected between reaction and deactivation parameters. The next step was the evaluation of “experimental” catalyst activities, by an approximate method (see Appendix), so as to use also these values, together with experimental CBzCl, CM, and CD, in the
Dealuminated HY zeolites proved to be useful catalysts, as far as para-selectivity within the monobenzylated fraction is concerned. Previous experiments with montmorillonite (K10) catalyst gave 50-60% of 4-benzylbiphenyl isomer, while selectivities of ca. 65% and ca. 72% could be reached with HY360 and HY330, respectively. Kinetic measurements could be made, with enough stirring to minimize diffusional limitations, and the model that better accommodated experimental data gave evidence of a strong adsorption of benzyl chloride on the catalysts. This might be a common phenomenon in the case of liquid mixtures of hydrocarbons with more polar compounds, in contact with zeolite catalysts; indeed for mixtures of benzaldehyde and o-xylene over the same catalyst here labeled HY360, we have recently found that benzaldehyde is quickly adsorbed in large amounts in the pores of the catalyst, before starting to react with xylene (Beltrame et al., 1996). The strong interaction of benzyl chloride with the catalyst surface brought complete decomposition of the compound, when heating was effected in the presence
3432 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
of large quantities of catalyst, but kinetic runs were carried out under conditions of good benzyl chloride stability. The catalysts deactivated during the reaction, HY330 more quickly than HY360; however, their regeneration was possible, with fairly good recovery, at least for a few reaction-regeneration cycles. The measured kinetic parameters were obviously found to depend on temperature: for both catalysts it was found that an increase of the reaction temperature, associated with an appropriate change of solvent (for HY360, from 80 °C in cyclohexane to 100 °C in methylcyclohexane; for HY330, from 50 °C in cyclopentane to 80 °C in cyclohexane), brings higher values of both reaction and deactivation coefficients, but the deactivation accelerates less than the reaction. Therefore, work at higher temperature seems advisable. Acknowledgment
C°BzCl C°BIPt1 ) k1Ccat y1
where t1 and y1 correspond to the first withdrawal; usually t1 ) 2 min. Substituting in eq 7, the formula for an,n+1 becomes
an,n+1 )
Nomenclature a ) catalyst activity (0 < a < 1) Ci ) molar concentration of i, mol/L Ccat ) weight concentration of catalyst, g/L F ) objective function in the optimization procedure k1, k2 ) rate coefficients in model BIP3Y, L/(min‚g) ka ) deactivation rate coefficient, min-1 KB )adsorption coefficient in models BIP3Z and BIP3X, L/mol km, kd ) rate coefficients in models BIP3Z and BIP3X, L2/ (mol‚min‚g) N ) reaction order in the deactivation rate equation t ) time, min x ) variable employed in the optimization procedure y ) fractional conversion of BzCl Subscripts f ) final n ) for the nth sample withdrawn Superscript ° ) at time zero
Appendix Catalyst Activity Evaluation. The rate of benzyl chloride disappearance, approximately evaluated as -∆CBzCl/∆t between two successive sample withdrawals, was employed to measure the “experimental” catalyst activity and its decrease during the run. In the case of kinetic model BIP3Y, with k1 ) k2, the kinetic equation for BzCl can be approximated, between the nth and the (n + 1)th withdrawal, as follows:
C°BzCl(yn+1 - yn) ) k1Ccatan,n+1(C°BIP + CM,n) (6) tn+1 - tn
an )
an-1,n + an,n+1 2
(10)
Literature Cited Ajimoto, K. Heating Medium Compositions with High Boiling Points. Jpn. Kokai 1974, 74,104,890 (Oct 03, 1974); Chem. Abstr. 1975, 82, 125044. Beltrame, P.; Carniti, P.; Franchi, A.; Zuretti, G. Benzylation of Biphenyl over Solid Acid Catalysts. Proceeding of the 18th National Congress; Societa` Chimica Italiana: Milano, 1995; Poster CI-P24. Beltrame, P.; Gerardini, G.; Zuretti, G. Condensation of Benzaldehyde with o-Xylene over a Solid Acid Catalyst. Gazz. Chim. Ital. 1996, 126, 815. Bertolacini, R. J. Acidity Distributions in Cracking Catalysts. Anal. Chem. 1963, 35, 599. Buzzi Ferraris, G. Automatic Optimum Seeking Method. Ing. Chim. Ital. 1968, 4, 171. Carnahan, B.; Luther, H. A.; Wilkes, J. O. The Approximation of the Solution of Ordinary Differential Equations. In Applied Numerical Methods; Wiley: New York, 1969; p 361. Corma, A.; Gonza`lez-Alfaro, V.; Orchille`s, A. V. Catalytic Cracking of Alkenes on MCM-22 Zeolite. Comparison with ZSM-5 and beta Zeolite and its Possibility as an FCC Cracking Additive. Appl. Catal. A 1995, 129, 203. Haase, J.; Hillner, K.; Brueggemann, W.; Momm, G. p-Benzylbiphenyl. Eur. Pat. Appl. 1991, EP 431,265 (Jun 12, 1991); Chem. Abstr. 1991, 115, 49053. Hino, M.; Arata, K. The Synthesis of Thermally Stable Oils by the Benzylation of Biphenyl with Benzyl Chloride Catalyzed by Iron(III) Oxide. Bull. Chem. Soc. Jpn. 1981, 54, 311. Khang, S. J.; Levenspiel, O. The Suitability of an nth-Order Rate Form to Represent Deactivating Catalyst Pellets. Ind. Eng. Chem. Fundam. 1973, 12, 185. Mravec, D.; Michvocı´k, M.; Hronec, M.; Moreau, P.; A. Finiels, A.; Geneste, P. Cyclohexylation of Naphthalene over Unmodified HY Zeolite. Catal. Lett. 1996, 38, 267. Sakura, K.; Takeuchi, H.; Furumoto, M. Manufacture of Benzylbiphenyls. Jpn. Kokai Tokkyo Koho 1991, JP 91,170,442 (Jul 24, 1991); Chem. Abstr. 1991, 115, 279572. Sotelo, J. L.; Uguina, M. A.; Valverde, J. L.; Serrano, D. P. Deactivation Kinetics of Toluene Alkylation with Methanol over Magnesium-Modified ZSM-5. Ind. Eng. Chem. Res. 1996, 35, 1300. Thompson, Q. E. Biphenyl and Terphenyls. Kirk-Othmer Encyclopedia of Chemical Technology, 4th ed.; Wiley: New York, 1992; Vol. 4, p 223.
Received for review February 24, 1997 Revised manuscript received May 5, 1997 Accepted May 5, 1997X IE970170T
(7) Abstract published in Advance ACS Abstracts, July 1, 1997. X
Assuming a0,1 ) 1, one obtains
(9)
The instantaneous activity value at time tn can eventually be obtained as
where an,n+1 represents the catalyst activity in the interval under consideration. Therefore
yn+1 - yn C°BzCl k1Ccat (tn+1 - tn)(C°BIP + CM,n)
yn+1 - yn t1 C°BIP C°BIP + CM,n tn+1 - tn y1
apart from a0, which is taken as unity.
This work was supported by Consiglio Nazionale delle Ricerche (C.N.R., Roma) within the “Progetto Strategico Tecnologie Chimiche Innovative”. Tosoh Corp. is thanked for the catalyst samples.
an,n+1 )
(8)
