Deactivation Kinetics of Toluene Alkylation with Methanol over

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Ind. Eng. Chem. Res. 1996, 35, 1300-1306

Deactivation Kinetics of Toluene Alkylation with Methanol over Magnesium-Modified ZSM-5 Jose L. Sotelo,* Maria A. Uguina, Jose L. Valverde, and David P. Serrano Chemical Engineering Department, Faculty of Chemistry, Complutense University of Madrid, 28040 Madrid, Spain

The deactivation kinetics of toluene alkylation with methanol over a Mg-modified ZSM-5 catalyst has been studied. A kinetic model taking into account both the deactivation of the main and the secondary reactions and the influence of the intracrystalline diffusion has been developed. The best fit of the experimental data has been obtained assuming that gaseous hydrocarbons, formed mainly by ethylene, are the coke precursors. The secondary reactions of p-xylene dealkylation, toluene disproportionation, and external p-xylene isomerization deactivate faster than the main reaction, probably due to differences in the strength of the acid sites over which they take place. The paraselectivity corresponding to the primary product decreases with the time on stream as a consequence of the pore blockage by coke, which attenuates the diffusional control of the internal xylene isomerization. Methanol dehydration is the reaction least affected by coke. Introduction The selective preparation of p-xylene by alkylation of toluene with methanol has potential interest as an alternative route to the conventional separation of the xylene isomer by adsorption (Parex process) or to its synthesis by toluene disproportionation. Methylation of toluene is usually carried out over acid zeolites, specifically ZSM-5 zeolite, due to the possibility of directing the reaction toward the selective formation of the most valuable xylene isomer (p-xylene) by modification of the zeolite with several agents (Young et al., 1982; Cavallaro et al., 1987). The high paraselectivity exhibited by modified ZSM-5 zeolites has been assigned to three possible effects caused by the modifier agents: (a) decrease of the intracrystalline diffusion rate, which favors the presence of p-xylene in the product just outside the zeolite channels (primary product) (Wei, 1982; Olson and Haag, 1984); (b) deactivation or removal of the acid sites located on the external zeolite surface which prevents the primary product isomerization toward m- and o-xylene (Fraenkel, 1990; Uguina et al., 1992; Sotelo et al., 1994b); (c) decrease of the overall acid strength which favors the main reaction compared to p-xylene isomerization (Kim et al., 1991, 1992). Toluene alkylation with methanol, like whatever reaction carried out over acid catalysts, is accompanied by the formation of a coke deposit on the zeolite which causes its progressive deactivation. Two major modes of zeolite deactivation by coke deposition have been proposed: site coverage and pore blockage, the deactivating effect of coke being more pronounced when deactivation is due to the latter (Guisnet and Magnoux, 1989). In contrast with other zeolites, ZSM-5 shows a higher resistance to deactivation, which has been related to the absence of large cavities in the pore structure and to its low acid site concentration (Guisnet and Magnoux, 1989; Bibby et al., 1992). Coke formation on the catalyst may produce variations in the ZSM-5 shape selectivity in addition to those caused by the modifier agent, which could lead to * To whom correspondence should be addressed. FAX: 341-3944114. E-mail: [email protected].

0888-5885/96/2635-1300$12.00/0

changes in the xylene distribution observed in the effluent. The literature on the deactivation of this industrially important reaction is scarce (Ducarme and Ve´drine, 1985; Hashimoto et al., 1988; Rao et al., 1991; Sotelo et al., 1994a), and no works have been found dealing with the deactivation kinetics of toluene alkylation with methanol over modified ZSM-5 catalysts. Rao et al. (1991) have studied the deactivation of toluene alkylation with methanol over unmodified ZSM-5, concluding that both toluene and methanol are the coke precursors. However, these authors take into account only the effect of coke deposition on the activity of the main reaction, whereas secondary reactions such as methanol dehydration to yield ethylene, xylene dealkylation and isomerization, and toluene disproportionation are not included in the kinetic analysis. In a previous work (Sotelo et al., 1993), we have studied the kinetics of toluene alkylation with methanol on both unmodified and Mg-modified ZSM-5. The kinetic model developed takes into account not only the main toluene alkylation reaction but also the presence of secondary reactions, diffusional effects, and the influence of the nonselective acid sites located on the external surface of the zeolite crystals. Subsequently, we have qualitatively studied the deactivation of this catalyst due to coke deposition, relating the changes observed in the reaction parameters along the time on stream to the nature and location of the coke species (Sotelo et al., 1994a). It has been observed that the shape selectivity of the Mg-modified ZSM-5 is decreased by the coke deposition within the zeolite channels, as denoted by the lower paraselectivity corresponding to the primary product of the coked samples compared to the fresh catalyst. This phenomenon has been related to a variation in the mode of coke deposition along the time on stream: initially coking takes place mainly by pore filling, whereas, at higher times on stream, pore blockage becomes predominant, leading to a decrease of the effective diffusional pathway length. Taking into account these conclusions, the aim of the present paper is the development of a kinetic model for the deactivation of toluene alkylation with methanol over a Mg-modified ZSM-5 catalyst, including the presence of secondary reactions. In addition, the effect of the intracrystalline diffusion on the deactivation kinet© 1996 American Chemical Society

Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1301

ics has been established from the conclusions previously obtained by Khang and Levenspiel (1973) about the influence of the diffusion rate on the deactivation order for different coking mechanisms: parallel, series, sideby-side, and independent. Experimental Section ZSM-5 zeolite was synthesized by hydrothermal crystallization using ethanol as the template, according to the procedure earlier reported (Costa et al., 1987). The product was 100% crystalline (determined by XRD) with a SiO2/Al2O3 mole ratio of 58 and an average crystal size of 5.4 µm (measured by laser granulometry and being in good agreement with the size observed by SEM). The as-synthesized zeolite was exchanged to the acid form with aqueous HCl, bound with 35 wt % of montmorillonite, and modified by impregnation with magnesium acetate, yielding a catalyst with a 1.1 wt % Mg content. Toluene alkylation with methanol was carried out at atmospheric pressure in a fixed-bed continuous downflow reactor working under integral conditions. The composition of the reactor effluent at different times on stream was determined by GC analysis, using 5% SP1200/S bentone 34 on Supelcoport and Porapak Q columns for the liquid and gaseous products, respectively. Detailed descriptions of the catalyst preparation and characterization, as well as of the experimental apparatus, have been reported in earlier works (Sotelo et al., 1993, 1994a). Results and Discussion The deactivation of toluene alkylation with methanol over the Mg-modified ZSM-5 catalyst has been studied, taking into account the results obtained in 24 experiments carried out by varying the temperature (460540 °C), the space time (5.4-27.0 g h/mol, referred to the toluene feed rate), and the toluene/methanol mole ratio (1-4). For each experiment, time on stream was varied in the range 0-6 h. The effects of the external mass-transfer limitations and of the diffusion through the binder matrix on the overall process rate were determined to be negligible in previous experiments. According to a previous kinetic study (Sotelo et al., 1993), the system can be described at zero time on stream with the following reactions: Intrinsic rates

Observed rates

r1 ) k1pTpM

(r1)obs ) r1η1

(1)

1 M f GH + W 2 (3) Toluene disproportionation

r2 ) k2pM2

(r2)obs ) r2

(2)

1 1 T f B + (p-X) 2 2 (4) p-Xylene dealkylation

r3 ) k3pT

(r3)obs ) r3η3

(3)

1 p-X f T + GH 2 (5) External p-xylene isomerization

r4 ) k4pp-X

(r4)obs ) r4η4

(4)

r5 ) k5pp-X

(r5)obs ) r5

(5)

Main Reaction (1) Toluene alkylation T + M f p-X + W Secondary reactions (2) Methanol dehydration

1 p-X f (m-X + o-X) 2

Figure 1. Variation of the reaction parameters with the time on stream (W/FTo ) 16.2 g h/mol; Tol/MeOH ) 2; T ) 500 °C).

Reactions 1, 3, and 4 occur mainly within the zeolite pore system; hence, an effectiveness factor for each one (η1, η3, and η4) was defined in order to relate the intrinsic and observed reaction rates. Methanol dehydration yielding gaseous hydrocarbons (GH) proceeds in a similar way, although due to the small size of the methanol molecule, we considered the corresponding effectiveness factor to be 1. On the contrary, p-xylene isomerization takes place only on the external surface of the zeolite, being unnecessary to define an effectiveness factor for this reaction. Thus, the paraselectivity corresponding to the primary product of the fresh Mgmodified ZSM-5 is 100%, calculated by extrapolating at zero space time. Therefore, the m- and o-xylene finally observed in the effluent are formed by p-xylene isomerization over the acid sites located on the external zeolite surface. Effect of the Time on Stream. Figure 1 shows the evolution of toluene and methanol conversions and paraselectivity with the time on stream for one of the experiments, with similar trends being observed in all of them. As expected, toluene conversion decays with the time on stream whereas methanol is completely converted during the first 3 h of reaction. Thereafter, methanol conversion undergoes a decline. Simultaneously, a maximum of paraselectivity along the time on stream is observed. The deactivation is favored at lower space times and toluene/methanol ratios and at higher temperatures. The faster loss of catalytic activity at lower toluene/methanol ratios suggests a relationship between the catalyst deactivation and the presence of methanol or other products formed by its dehydration in the reaction mixture. The position of the paraselectivity maximum (see Table 1) is affected by the reaction conditions in the same manner as the catalytic activity. It is shifted toward lower times on stream at lower space times and toluene/methanol ratios and at higher temperatures. The maximum of paraselectivity is clearly related to the deactivation rate, in all cases being observed around the time on stream in which toluene conversion undergoes the fastest decline and methanol conversion starts decreasing below 100%. Deactivation Kinetic Model. The model here proposed has been developed by taking into account the

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Table 1. Position and Value of the Paraselectivity Maximum at Different Reaction Conditions W/FTo (g h/mol)

T (°C)

Tol/MeOH

(Ps)max (%)

tmax (h)

5.4 10.8 16.2 21.6 16.2 16.2 16.2

500 500 500 500 460 540 500

2 2 2 2 2 2 1

93 86 84 82 86 87 85

0.5 2.5 3.2 4.5 4.0 3.0 1.0

deactivation kinetics of both main and secondary reactions. For each reaction, the activity is defined as:

aj(t) )

rj(t) rj(0)

(6)

rj(t) and rj(0) being the rate of the reaction j at any time t and at zero time, respectively, both measured for the same composition of the reaction mixture. The variation of the activity with the time on stream has been described by the deactivation equation proposed by Corella and Asuá (1982):

-daj/dt ) Ψj(pi,T) ajdj

(7)

where dj is the order of deactivation and Ψj(pi,T) the deactivation function which includes the influence of the operation conditions. Khang and Levenspiel (1973) have performed a theoretical study about the interaction between pore diffusion resistance and reaction kinetics for a deactivating catalyst pellet. They concluded that the order of deactivation observed may be influenced by the diffusional resistance. This effect depends on the mechanism of coupling between the coking and the main reaction: (i) Parallel deactivation. When the reactant decomposes to produce coke, the order of deactivation depends on the Thiele modulus, shifting from 1 to 3 as diffusional resistance increases. (ii) Series deactivation. The order of deactivation is insensitive to the magnitude of the Thiele modulus and close to unity when coke is formed directly from one of the reaction products. (iii) Independent deactivation. When deactivation is originated by both reactant and product, a first-order deactivation is observed. (iv) Side-by-side deactivation. When some impurity in the feed causes the loss of activity, the order of deactivation is close to unity, being insensitive to the magnitude of the Thiele modulus. According to these conclusions, we have developed several deactivation models, assuming that the coke precursor is methanol (M), gaseous hydrocarbons (GH), toluene (T), or the different combinations among them. In all cases, a strong control of the intracrystalline diffusion was assumed. Benzene and xylenes were not considered as likely coke precursors, taking into account the conclusions of a previous work on the deactivation kinetics of paraselective toluene disproportionation over a Mg- and Si-modified ZSM-5 catalyst (Uguina et al., 1994). The deactivation function has been described by the expression:

Ψj(pi,T) ) kjdPc

(8)

Figure 2. Block diagram of the computer program used to fit the experimental data and the deactivation models. Table 2. Fitting of the Deactivation Kinetic Models model

coke precursor

d1

d2

d3

d4

d5

Φ (eq 11)

(%)

1 2 3 4 5 6 7

M T GH M + GH T+M T + GH M + T + GH

3 3 1 3 3 3 3

3 1 1 1 3 1 1

1 3 1 1 3 3 3

1 1 1 1 1 1 1

1 1 1 1 1 1 1

38.0 88.2 19.6 39.4 108.7 105.1 62.8

12.7 12.9 8.5 12.7 13.3 13.3 12.8

Pc being the partial pressure of the coke precursor and kjd the deactivation kinetic constant of the reaction j. Combining eqs 7 and 8:

-d[(aj)obs]/dt ) kjdPc(aj)obsdj

(9)

The integration of this expression yields the activity of each reaction. According to eq 6, the reaction rates at any time t can be evaluated from the activities by means of:

(rj)obs(t) ) [(rj)obs(0)][(aj)obs(t)]

(10)

The deactivation orders of the five reactions considered for the different models checked are given in Table 2. Figure 2 shows the block diagram for the procedure used to fit the models and the experimental results, whereas the mathematical models are described in detail in the appendix. It involves two numerical integrations: one with respect to the time on stream to calculate the activities and the other with respect to the space time to determine the mole fractions of the different compounds in the reaction product. The fit between the experimental data and the deactivation models has been performed by combining a fourth-order Runge-Kutta method to carry out the numerical integrations with a nonlinear regression method based on Marquardt’s algorithm to estimate the parameters of the model (Marquardt, 1963). These parameters were

Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1303

calculated by minimizing the objective function: n

Φ)

m

∑∑

k)1i)1

{

} {

[(yi)cal - (yi)obs]2 (yi)obs2

+

k

n

∑

k)1

}

[(Ps)cal - (Ps)obs]2 (Ps)obs2

(11)

k

Besides the mole fraction of the different compounds, paraselectivity has been included in the objective function in order to get a better prediction of the paraselectivity maxima experimentally observed. The discrimination among the models has been based on the values of the objective function and the significance of the parameters (determined by means of a t-student test). If the deactivation models are compared on the basis of the coke precursor (Table 2), the best fit of the experimental data is clearly obtained when gaseous hydrocarbons are assumed to be the coke precursor (model 3). The average error in the reproduction of the experimental values obtained with this model is 8.5%. The conclusion drawn from the deactivation kinetic analysis about the behavior of the gaseous hydrocarbons as coke precursors is consistent with the findings previously pointed out in this paper, taking into account the qualitative influence of the toluene/methanol ratio on the deactivation rate. According to them, methanol or products formed by its dehydration are directly related to the coke formation. Methanol dehydration yields in a first step dimethyl ether and through a second dehydration leads to gaseous olefins, mainly ethylene (Chang, 1983). In fact, this compound is the major component present in the gaseous hydrocarbon fraction; hence, it is probably the main cause of the coke formation during the reaction. This conclusion agrees well with the results obtained in an earlier work (Uguina et al., 1993), which showed that olefins present a higher tendency than aromatic hydrocarbons for coke formation over ZSM-5 zeolite. The apparently anomalous behavior observed for the deactivation of p-xylene isomerization is remarkable. For all the checked models, the preexponential factor calculated for the deactivation kinetic constant of this reaction has a negative value; i.e., its activity increases with the time on stream instead of being negatively affected by the coke deposition. Nevertheless, this behavior can be explained by taking into account that in this system coke deposition leads to an important blockage of the zeolite pores. As concluded in a previous work (Sotelo et al., 1994a), pore blockage by coke species causes a part of the internal zeolite volume to become inaccesible to the reacting aromatic molecules, decreasing the length of the effective diffusional pathway and, hence, attenuating the diffusion control on the internal xylene isomerization rate. As a consequence, paraselectivity of the primary product in the coked Mgmodified ZSM-5 decreases below the value of 100% corresponding to the uncoked catalyst, whereas it has been considered constant in the deactivation kinetic models. This assumption was valid for the fresh catalyst, but, as coke deposition progresses, the primary product is formed not only by p-xylene but also by oand m-xylene. The proportion of the last two isomers in the primary product increases with the time on stream, leading to an apparent enhancement of the external p-xylene isomerization activity.

Figure 3. Variation of the activity of the main and the secondary reactions with the time on stream (W/FTo ) 16.2 g h/mol; Tol/MeOH ) 2; T ) 500 °C). Table 3. Kinetic Parameters of the Modified Model 3 parameter

preexponential factor (h-1)

activation energy (kJ/mol)

k1d k2d k3d k4d k5d

24.23 0.585 45.35 464.80 104.10

30.6 12.5 17.9 27.2 23.9

Φ (eq 11) ) 19.7 (%) ) 8.7

In order to check this hypothesis, the kinetic model 3 has been modified considering that the paraselectivity of the primary product decreases with the time on stream. Thereby, as described in the appendix, the equations for the xylene formation rates have been modified including the primary product paraselectivity at a certain time on stream (Pso(t)). To avoid increasing the number of adjustable parameters of the model, Pso(t) has been estimated directly from the experimental data by extrapolating at space time approaching zero the paraselectivities obtained at different times on stream and for the three temperatures investigated. The results so obtained have been fitted to linear functions of the time on stream (see the appendix). Table 3 summarizes the kinetic parameters and the results of the fitting obtained with model 3 after including the above-mentioned modifications. It is remarkable that, although the values of the objective function and the average relative error of the fitting are just slightly changed, the deactivation constant of the external p-xylene isomerization has turned out positive; i.e., the modified model predicts that the activity of this reaction decreases with the time on stream. These results confirm the earlier assumptions and show that the modifications introduced in model 3 have allowed the variation of the diffusional control on the internal xylene isomerization to be isolated from the evolution of the external p-xylene activity with the time on stream. Figure 3 shows the evolution of the activities of the different reactions included in the kinetic analysis with the time on stream for one of the experiments according to the modified model 3. The following order of deac-

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tivation rates is derived from this figure, being valid for the rest of the experiments: p-xylene dealkylation > toluene disproportionation > external p-xylene isomerization > toluene methylation > methanol dehydration According to different authors (Aneke et al., 1979; Meshram, 1987; Uguina et al., 1991), dealkylation reactions of alkylaromatics over zeolites take place on stronger acid sites than those active in toluene disproportionation. In the same way, Vinek and Lercher (1991), using ZSM-5 zeolite as catalyst, have concluded that toluene disproportionation requires stronger acid sites than toluene alkylation with methanol. This finding has been later confirmed by Kim et al. (1992), who compared the acidity requirements of toluene disproportionation and ethylbenzene alkylation with ethanol over different ZSM-5 samples modified with boron oxide and coke, as well as over several metallosilicate zeolites with MFI structure. They concluded that toluene disproportionation proceeds over stronger acid sites than p-ethyltoluene isomerization, whereas this last reaction requires acid sites of higher strength than toluene alkylation. Taking into account these results, it seems that in the system here studied there is a relationship between the deactivation rate and the acid strength required by every reaction. The stronger the acid sites which are necessary to catalyze one reaction, the faster this is deactivated by coke deposition. This correlation suggests that the deactivation by coke occurs preferentially on the strongest acid sites of the zeolite. A similar conclusion was obtained in a previous work (Uguina et al., 1994) when comparing the deactivation rate of p-xylene dealkylation and toluene disproportionation over a Si-Mg-modified ZSM-5 catalyst. Nevertheless, the diffusional constraints associated with the pore blockage by coke species must also be taken into account to explain the loss of activity. The effect of the pore blockage is supposed to be more pronounced for reactions involving large molecules as reactants, products, or intermediates. Thus, the deactivation of toluene disproportionation in the present work is faster than that observed in the absence of methanol and gaseous olefins (Uguina et al., 1994), which could be due not only to the preferential coke deposition on the strongest acid sites but also to the effect of the pore blockage, since this reaction involves the participation of two toluene molecules in an intermediate step. Finally, methanol dehydration is the least affected reaction by coke deposition, with its activity slowly decreasing with the time on stream (Figure 3). The weak acidity required for this reaction and the small size of the methanol molecules are probably the reasons of its slow deactivation. As is seen in Table 3, the activation energies of the deactivation constants are lower than those previously calculated for the kinetic constant at zero time, being in agreement with the results reported in similar works (Rao et al., 1991; Uguina et al., 1994). Finally, as is observed in Figure 4, the toluene and p-xylene mole fractions predicted by the selected kinetic model fit well the experimental results. Conclusions A kinetic model for the deactivation of the toluene alkylation with methanol over a Mg-modified ZSM-5 catalyst has been developed by taking into account the presence of secondary reactions and the effect of the intracrystalline diffusion.

Figure 4. Comparison between experimental and predicted mole fractions of toluene and p-xylene at different space times (Tol/ MeOH ) 2; T ) 500 °C).

The best fit of the experimental data is obtained when gaseous hydrocarbons (mainly formed by ethylene) are assumed to be the coke precursor. Coke deposition affects in a different way the activity of the reactions included in the kinetic analysis. The deactivation rate seems to be directly related to the acid strength required for the active sites involved in every reaction. Thus, p-xylene dealkylation is deactivated faster than toluene disproportionation, with this one faster than the external p-xylene isomerization and the latter faster than the main reaction of toluene alkylation with methanol. These results suggest that the deactivation by coke deposition takes place preferentially on the stronger acid sites of the zeolite. Methanol dehydration is the reaction less affected by coke deposition, with its activity being slowly decreased along the time on stream. The paraselectivity corresponding to the primary product decreases below 100% for times on stream longer than 1 h. This effect arises from a lower diffusional control of the internal xylene isomerization due to the partial blockage of the ZSM-5 pores by coke species, which decreases the effective length of the diffusion pathway. Acknowledgment Financial support from DGICYT (Direccioń General de Investigacioń Cientı´fica y Tećnica, Ministry of Education, Spain), Project PB 90-240, is gratefully acknowledged. Nomenclature aj(t) ) activity of the reaction j dj ) order of deactivation of the reaction j kj ) kinetic constant of the reaction j kjd ) deactivation kinetic constant of the reaction j (h-1) m ) number of components n ) number of experiments Pc ) partial pressure of the coke precursor (atm) Ps ) paraselectivity Pso ) paraselectivity of the primary product pi ) partial pressure of component i (atm) rj ) rate of the reaction j (mol/g h) (rj)obs ) observed rate of the reaction j (mol/g h)

Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 1305 T ) reaction temperature (°C) Tol/MeOH ) toluene/methanol mole ratio t ) time on stream (h) W/FTo ) space time (g h/mol, referred to the toluene feed rate) (yi)obs ) experimental mole fraction of component i (yi)cal ) predicted mole fraction of component i

The formation rate of each species at any time t is related to the reaction rates through the stoichiometry:

RT(t) )

d[yT(t)] d(W/FTo)

) -(r1)obs(t) - (r3)obs(t) + (r4)obs(t) (22)

Greek Letters ) average relative error Φ ) objective function defined by eq 11 ηj ) effectiveness factor of reaction j Ψ ) deactivation function

RM(t) )

d[yM(t)]

) -(r1)obs(t) - r2(t)

d(W/FTo)

(23)

Compounds B ) benzene GH ) gaseous hydrocarbons M ) methanol o-X ) o-xylene m-X ) m-xylene p-X ) p-xylene T ) toluene W ) water

Rp-X(t) )

d[yp-X(t)] d(W/FTo)

1 ) (r1)obs(t) + (r3)obs(t) 2 (r4)obs(t) - r5(t) (24)

Rm-X+o-X(t) )

d[ym-X+o-X(t)]

Appendix The block diagram of the computer program used to calculate the evolution along the time on stream of the product distribution predicted by the different deactivation models is shown in Figure 2. Starting from the initial value of the model parameters, the activity of each reaction is calculated by the integration of eq 9 with respect to the time on stream:

d[(a1)obs(t)] ) k1dPc[(a1)obs(t)]d1 dt

-

-

(13)


(14)


(15)

d[a5(t)] ) k5dPc[a5(t)]d5 dt

(16)

-

The reaction rates at any time t are calculated from the activities according to eq 10:

[(r1)obs(t)] ) [(r1)obs(0)][(a1)obs(t)]

(17)

[r2(t)] ) [r2(0)][a2(t)]

(18)

[(r3)obs(t)] ) [(r3)obs(0)][(a3)obs(t)]

(19)

[(r4)obs(t)] ) [(r4)obs(0)][(a4)obs(t)]

(20)

[r5(t)] ) [r5(0)][a5(t)]

RW(t) )

(12)

d[a2(t)] ) k2dPc[a2(t)]d2 dt

-

RB(t) )

RGH(t) )

d(W/FTo)

d[yB(t)]

d(W/FTo)

(26)

) (r1)obs(t) + r2(t)

(27)

d[yGH(t)]

1 1 ) r2(t) + (r4)obs(t) 2 2 d(W/FTo)

(28)

The molar fraction of the different species at any time, temperature, and space time is obtained by integration of eqs 22-28 with respect to the space time. By comparison between the predicted and the experimental product distribution and application of a regression method based on Marquardt’s algorithm, a new value of the model parameters is determined, the calculations being repeated until the objective function of the fitting (eq 11) is no longer improved. When the paraselectivity of the primary product is considered to vary with the time on stream, eqs 24 and 25 are replaced by:

Rp-X(t) )

d[yp-X(t)] d(W/FTo)

Rm-X+o-X(t) )

) (r1)obs(t)

d[ym-X+o-X(t)] d(W/FTo)

Pso(t) 1 + (r3)obs(t) 100 2 (r4)obs(t) - r5(t) (24b)

) r5(t) +

(21)

where (r1)obs(0), r2(0), (r3)obs(0), (r4)obs(0), and r5(0) are given by the kinetic model at zero time (eqs 1-5), determined in a previous work (Sotelo et al., 1993).

(25)

1 ) (r3)obs(t) 2

d(W/FTo)

d[yW(t)]

) r5(t)

(r1)obs(t)

[100 - Pso(t)] (25b) 100

where Pso(t) is related to the time on stream through

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the following empirical expressions:

te1h

T ) 460, 500, 540 °C; Pso(t) ) 100% (29) t>1h T ) 460 °C; Pso(t) ) 100 - 5.76t

(30)

T ) 500 °C; Pso(t) ) 100 - 6.40t

(31)

T ) 540 °C; Pso(t) ) 100 - 7.20t

(32)

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Received for review January 26, 1995 Revised manuscript received October 31, 1995 Accepted December 28, 1995X IE9500836 X Abstract published in Advance ACS Abstracts, February 15, 1996.

Deactivation Kinetics of Toluene Alkylation with Methanol over

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