Influence of coke formation on the conversion of hydrocarbons

Applied Catalysis A: General 202 (2000) 65–80

Influence of coke formation on the conversion of hydrocarbons II. i-Butene on HY-zeolites M.-F. Reyniers a , Y. Tang b , G.B. Marin a,∗ a

Laboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium b Department of Chemistry, Fudan University, Shangai 200433, PR China Received 6 September 1999; received in revised form 9 January 2000; accepted 14 January 2000

Abstract The influence of coke formation on the conversion of i-butene was investigated on a series of HY-zeolites differing by the number of framework and extra framework Al (EFAL) atoms per unit cell. The reactions were carried out at 723 K, an inlet partial pressure of i-butene of 1 kPa and a total pressure of 105 kPa, in a recycle electro-balance reactor, operating gradientlessly under high conversion, with on-line gas chromatographic analysis of the effluent. Coke formation not only leads to pore blockage but also to reactions involving coke molecules that cause changes in the activity and the selectivity of the catalysts. Even in the presence of important pore blockage, the occurrence of these reactions can result in an increased activity of the catalyst. In the absence of EFAL, the conversion rate is found to decrease with coke content for H+ /u.c.<29, while for H+ /u.c.≥29, the conversion rate of i-butene initially increases with increasing coke content until pore blockage becomes dominant. Up to 2 wt.% of coke, and in the absence of EFAL, the influence of coke formation on the formation rate of n-butenes is positive for catalysts with H+ /u.c.≥25, while it is negative for H+ /u.c.<25. On all catalysts, the rate of the dimerization-␤-scission path decreases with coke content. Except for the zeolite with H+ /u.c.=6, the rate of hydride transfer and of coke formation are positively influenced by coke formation. The rate of hydride transfer parallels the rate of coke formation. To explain the influence of coke formation on the reaction rates, a reaction mechanism involving coke molecules is proposed. © 2000 Elsevier Science B.V. All rights reserved. Keywords: HY-zeolites; i-Butene; Coke formation

1. Introduction Catalytic cracking of heavy oil fractions is an important process in the refining industry. An industrial cracking catalyst usually contains a USY zeolite as the active component. As a side reaction, however, heavy secondary products, so-called coke, are formed ∗ Corresponding author. Tel.: +32-9-2644517; fax: +32-9-2644999. E-mail address: [email protected] (G.B. Marin)

leading to catalyst deactivation. Generally, the deactivation of zeolites by coke formation is attributed to two effects: coke can cover irreversibly the active sites thereby poisoning them and/or coke can block the access of the reactant to the active sites [1–4]. Catalyst deactivation by site coverage and pore blockage, and in particular the modeling aspects have been investigated thoroughly by Froment et al. [5–9]. Pore blockage being a physical phenomenon, it is clear that its deactivating effect is identical for all the catalyzed reactions. There are indications, however, that the deactivation

0926-860X/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 6 - 8 6 0 X ( 0 0 ) 0 0 4 5 1 - 8

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by site coverage is not identical for all the reactions involved in catalytic cracking [6,10–12]. Different requirements in acid strength of the active site could be one of the reasons for these differences [13–16]. The objective of this study is two-fold. Firstly, to obtain a deeper insight into the changes induced by coke formation on the importance of the various reaction types occurring in catalytic cracking i.e. hydride transfer, isomerization, ␤-scission. Also secondly, to evaluate how these changes differ from one zeolite to another within the same zeolite family. The determination of the effect of coke on the various reaction types by analyzing the influence of coke formation on the product distribution is not straightforward, especially when using a complex feed. Usually, the deactivating effect of coke is described by means of a deactivation function 8 that, by definition, corresponds to a single reaction [5–9] and not to the net formation rate of a component. Each reaction path occurring in the reaction network involves several elementary steps. Furthermore, several reaction paths can give rise to the same product that itself can be engaged in secondary reactions. Therefore, the effect of coke formation on the product distribution during conversion of a model component was investigated. Isobutene was chosen as a model component for two reasons. Firstly, i-butene is an important coke precursor on acid catalysts [1–3] and secondly, the relative simplicity of the reaction network involved in i-butene conversion allows a qualitative evaluation of the influence of coke formation on the various reaction types involved without requiring a detailed kinetic analysis. As described by Beirnaert et al. [11], the electrobalance technique combined with on-line GC-analysis allows coupling of the catalyst activity and selectivity with the coke content of the catalyst. Both the conversion reactions and the coking reactions can then be studied as a function of both the reaction conditions and the coke content. Therefore, experiments were carried out in a recycle electro-balance reactor operating gradientlessly under high conversion, with on-line gas chromatographic analysis of the effluent. The evaluation of the influence of the acid properties of the catalyst on the deactivating effect of coke formation was focused on catalysts that contain no extra frame work Al (EFAL). Therefore, a series of HY-zeolites was prepared by dealumination with ammonium hexafluorosilicate to avoid the formation

of extra framework Al (EFAL) [17]. Two deep-bed steamed Y-zeolites containing EFAL were also considered in this study.

2. Experimental 2.1. Catalyst preparation The original NH4 Y zeolite powder used in this study was obtained from UOP and is referred to as Y-62. Four silicon-enriched Y zeolites with a Si/Al ratio of 3.6, 4.9, 6.5 and 8 (referred to as SiY-4, SiY-5, SiY-7 and SiY-8, respectively) were prepared by reacting Y-62 with a controlled amount of (NH4 )2 SiF6 solution at pH=6 and 343 K, as described in [17,18]. Samples of two USY’s, containing both non-structural and tetrahedral Al, were obtained from UOP (LZY-20) and from IFP (Z-427). 2.2. Catalyst characterization All samples were characterized by chemical analysis (bulk Si/Al and Na-content), 27 Al and 29 Si MAS NMR (framework Si/Al ratio and extra framework Al content). The 29 Si MAS NMR spectra were recorded on a Bruker AMX 300 spectrometer. The chemical shift reference was tetramethylsilane (TMS). A pulse length of 5 ␮s, a recycle time of 10 s and 5000 accumulations were applied. The 27 Al MAS NMR spectra were recorded on a Bruker MSL-400 spectrometer. The chemical shift reference used was Al(NO3 )3 . A pulse length of 0.61 ␮s, a recycle time of 0.1 s and 3000 accumulations were used. The surface area and pore volume were determined by analyzing N2 adsorption at 77 K in a conventional volumetric apparatus (Micrometrics ASAP 2000) after 7 h degassing at 623 K. The percentage of pore blockage was obtained from:   100V (1) % Pore blockage = 100 − V0 − Vc with V the pore volume of the coked catalyst, V0 the micro pore volume of the fresh catalyst, Vc , the volume occupied by coke, calculated from a coke density of 1.2 cm3 /g and (V0 −Vc ) the micro pore volume accessible if coke deposition is considered to take place by

M.-F. Reyniers et al. / Applied Catalysis A: General 202 (2000) 65–80

pore filling only without rending inaccessible a fraction of the pore network [19]. XRD diffractograms were recorded with a Siemens D5000 diffractometer using Cu K␣ radiation. The relative crystallinity of the samples was determined by comparing the sum of peak heights at 2θ=15.7, 20.4, 23.8, 27.2 and 31.5◦ with that for Y-62. The acidity of the samples (100 mg) was characterized by temperature programmed desorption of ammonia using an Altamira AMI-1 apparatus equipped with a thermal conductivity detector (TCD). Samples were preheated for 3 h at 773 K in a He flow (40 ml/min). Ammonia adsorption was carried out at 393 K (He: 40 ml/min, NH3 : 5 ml/min) for 30 min. After flushing of the samples in a He flow (40 ml/min) at 393 K, the temperature was raised at a rate of 10 K/min. 2.3. Isobutene conversion The reactions were carried out at 723 K in a recycle reactor equipped with an electro-balance and on-line gas chromatographic analysis of the effluent. The reactor was operated gradientlessly, allowing to obtain data at relatively high conversion. The coke content (Cc ) of the catalyst was measured continuously, enabling a direct coupling of the catalyst activity and the product distribution with the coke formation on the catalyst. Prior to the introduction of the feed, the catalyst samples (W=8–100 mg; particle diameter=0.25– 0.5 mm) were pretreated in situ under nitrogen at 773 K during 1 h. The inlet partial pressure of i-butene was kept at 1 kPa, the total pressure in the reactor was 105 kPa. The space time, W/F0 , was varied between 10.5 and 105 kg s/mol. Dimethylether was added as internal standard to the effluent enabling the analysis of the effluent on an absolute basis. All data reported in this paper stem from experiments performed with the carbon balance closing within 2% and pertain to an i-butene conversion of 23%. Upon the introduction of the feed into the reactor, the pretreatment gases are gradually displaced by the feed. In the initial period of a deactivation experiment, transient effects, such as adsorption of hydrocarbons, pressure stabilization, drag forces on the catalyst basket etc., disturb the measurement of the coking curve. It was observed that, if the reactor pressure is kept constant, these transient effects are extinguished

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after 1–5 min. After this period, the mass changes measured are due solely to coke deposition. However, the actual amount of coke at this moment is not known, since the initial amount of coke deposited is unknown. This requires an independent measurement of the total amount of coke deposited. Therefore, at the end of a deactivation experiment, the catalyst is exposed to pretreatment conditions again. The mass difference between the fresh and the coked catalyst then gives the total amount of coke deposited. The experimental accuracy on the coking curve thus determined is 0.15 mg. Formation rates (mol formed/kg cat s) were calculated from GC-analysis of the effluent. Selectivities (mol formed/mol i-butene converted) were calculated as the ratio of the formation rates (mol formed/kg cat s) to the rate of i-butene conversion. The coke content (wt.%) of the catalyst is measured directly. Derivation of the coke content with respect to time gives the coking rate (g coke formed/kg cat s). Coke selectivity is expressed as g coke formed/100 g i-butene converted. Values for the fresh catalyst were obtained by extrapolation to Cc =0 wt.%. A detailed description of the methodology used for the interpretation of information obtained from deactivation experiments in a recycle electro-balance reactor was given earlier [11]. At constant inlet conditions, the conversion changes during a deactivation experiment since the catalyst activity changes upon coke formation. Therefore, the formation rates measured during a single deactivation experiment under constant inlet conditions are influenced simultaneously by the change in concentration of the reactants and by coke formation. To distinguish between the influence of coke formation and that of conversion on the kinetics of the main reactions and of the coke formation, a series of experiments at constant inlet hydrocarbon pressure but at different space times were performed. Interpolation at a given conversion level then permits to obtain formation rates, as a function of the coke content, at constant conversion. Based on the formation rates, determined at X=23%, the rates of three global reactions, i.e. the overall reaction, the dimerization-␤-scission path and the coke formation, and of two elementary reactions, i.e. hydride transfer and isomerization, were estimated as follows. Since propene was found to be more stable than pentenes under the conditions used in this study,

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the rate of formation of C3 -hydrocarbons was taken as a measure of the rate of dimerization-␤-scission path. Although hydride transfer reactions can produce a broad spectrum of paraffins, the rate of formation of i-butane is selected as a measure for the rate of hydride transfer reactions, since i-butane is the most important paraffin present in the reaction mixture. The isomerization rate was obtained from the rate of formation of n-butenes. The coking rate is calculated from the measured amount of coke deposited.

Table 1 Chemical composition of the catalysts H+ /u.c. Na/u.c. Si/Al framea Si/Al bulk AlIV /AlTot. b Y-62 SiY-4 SiY-5 SiY-7 SiY-8 LZY-20c Z-427d

41.4 35.2 28.9 25.4 20.5 6.2 32.5

15.1 6.5 3.6 0.2 0.8 0.0 0.0

2.4 3.6 4.9 6.5 8.0 30.0 4.9

2.6 3.6 5.9 7.7 8.8 2.7 3.3

100 100 100 100 100 35 60

a

From 29 Si MAS NMR. From 27 Al MAS NMR. c Provided by UOP. d Provided by IFP. b

roverall reaction = −Risobutene

(2)

rdim.-␤-sciss. = Rpropene + Rpropane

(3)

3. Results

rhydride transfer = Risobutane

(4)

3.1. Catalyst characterization

risomerization = Rn-butenes

(5)

rcoke = Rcoke

(6)

The chemical composition and the characteristics of the catalysts are given in Tables 1 and 2. The framework Si/Al ratios were calculated from 29 Si MAS NMR according to the formula of Klinowski et al. [20]. The Si/Al ratio for the SiY samples as determined by 29 Si MAS NMR is in good agreement with the values obtained from chemical analysis. 27 Al NMR confirmed the absence of EFAL in the SiY samples. The 27 Al NMR spectrum of LZY-20 and of Z-427 indicate that these samples contain non-structural Al and that both octahedral Al (sharp signal at δ=0 ppm, AlO ) and penta-coordinated Al (broad signal at δ=30–40 ppm, AlP ) are present. LZY-20 contains as much as 66% EFAL (AlO =28%, AlP =38%). Z-427 contains 40% EFAL (AlO =17%, AlP =23%). Except for LZY-20, the BET-surface area of all samples is

The deactivation function, 8i , for the reaction types considered was calculated from: 8i =

ri ri,o

(7)

with ri , the rate of reaction i on the coked catalyst and ri ,o , the rate of reaction i on the fresh catalyst. To estimate the contribution of the different reaction types to the overall activity of the catalyst, a reaction type selectivity is defined as the ratio of the rate of the reaction type considered to the conversion rate.

Table 2 Characteristics of the catalysts NH3 (mmol/g)

Y-62 SiY-4 SiY-5 SiY-7 SiY-8 LZY-20 Z-427

3.49 3.04 2.49 2.19 1.77 0.99 2.82

Crystal (%)

100 100 100 98 95 78 100

Surface area (m2 /g)

739 720 664 672 671 481 700

Pore volume Total (ml/g)

Micro (ml/g)

Meso (ml/g)

0.38 0.39 0.36 0.36 0.37 0.35 0.42

0.34 0.30 0.28 0.29 0.28 0.19 0.29

0.04 0.09 0.08 0.07 0.09 0.16 0.13

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about 700 m2 /g and the micro pore volume is about 0.3 cm3 /g, confirming the high crystallinity of these samples. The higher meso pore volume of LZY-20 and of Z-427 results from the steam treatment in the preparation of the catalysts. 3.2. Acid properties Table 1 shows that upon dealumination of Y-62, the total ammonia adsorption capacity of the catalysts decreases. Fig. 1 indicates that the amount of ammonia desorbing at T>648 K increases, reaching a maximum value at Al/(Si+Al)=0.15 or 29 H+ /u.c., while the amount of ammonia desorbing in the temperature range 393–523 K gradually decreases. Upon dealumination of Y-62, the total number of acid sites and the number of weak acid sites decreases, while the number of strong acid sites increases reaching a maximum at about 29 H+ /u.c. The acidity of zeolites depends on their Al content and their acid properties can be explained on the basis of the concept of ‘Next Nearest Neighbors Al’ (NNN Al) as introduced by Pine et al. [21]. In zeolites, the Al atoms are distributed randomly within the constraints of Lowenstein’s rule that requires that no AlO4 –AlO4 bonds are formed. Thus, each Al is bounded by an oxygen bridge to Si and its acid strength is influenced by the inductive effect exerted by the Al atoms present from the second layer of tetrahedra onwards, i.e. by its next nearest neighbors. The strongest acid sites are associated with isolated AlO4 -tetrahedra (0 NNN Al).

Fig. 1. Amounts of ammonia desorbed between 393 and 523 K, at : 393 K648 K; T>648 K and at T>723 K ( : T>723 K. Hollow symbols: contains EFAL).

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Both experimental observations and statistical calculations indicate that the maximum number of 0 NNN Al occurs at Al/(Si+Al)=0.146 or at about 28 Al atoms per unit cell [17,22,23]. Z-427, containing 40% EFAL, has a higher number of strong acid sites, than would be expected on the basis of its framework Al content only (Fig. 1). The presence of EFAL can strongly influence the acid properties of Y-zeolites [24]. It has been proposed that cationic EFAL species, such as Al(OH)2+ , can withdraw electron density from nearby Brønsted acid sites, causing an enhancement in the strength of these sites [17,25]. In addition, EFAL can act as a Lewis acid site influencing the catalyst activity [26]. 3.3. Isobutene conversion network Table 3 shows the product selectivities on Y-62 at different coke content. On all catalysts and at all coke contents, the main reaction products are n-butene, propene, i-butane, i-pentene and n-pentene. No C8 -paraffins or olefins were detected in the effluent. Minor amounts of aromatics up to C9 were formed. Clearly, under the conditions used, the main types of reaction are isomerization, hydride transfer and dimerization followed by ␤-scission. Depending on the type of the catalyst and on the reaction conditions, the skeletal isomerization of butenes might follow a monomolecular or a bimolecular mechanism. The monomolecular mechanism involves the formation of a very unstable primary carbenium ion although a protonated cyclopropane (pcp) intermediate can also be involved. The bimolecular mechanism occurs via three successive steps: dimerization and skeletal isomerization of the dimers followed by ␤-scission. Despite extensive experimental studies of the skeletal isomerization of butenes, the problem of which mechanism is prevailing, or is solely operating, is still a topic of debate [27–34]. Therefore, both mechanisms are considered in the reaction network, presented in Fig. 2, that is proposed to account for the product distribution observed during conversion of i-butene on the investigated catalysts. According to this reaction scheme, dimerization␤-scission should produce equal amounts of P PC3 and C5 . However, it was observed that C5 < C3 , indicating that secondary cracking reactions are more likely to occur with the larger C5 -carbenium ions [35].

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Table 3 Product selectivities on Y-62 at different coke content (X=23%) Coke content (wt.%) Selectivity (mol%) Methane Ethene Ethane Propene Propane n-Butane i-Butane n-Butene i-Pentane n-Pentane n-Pentene i-Pentene Toluene Xylene C9 -aromatics Coke (g/100 g) P C P 1 − C2 P C3 C P 4 C P 5 Aromatics C P3 /C3 P C P 5 / P C5 C3 / C5

0

2.7

5

10.3

15.3

17.6

0.2 0.6 0.0 16.3 0.1 0.2 5.2 77.1 0.2 0.0 3.4 8.7 0.3 1.2 0.9 0.7

0.4 0.7 0.1 13.2 0.1 0.5 18.1 60.7 0.6 0.0 2.5 6.5 0.3 1.1 1.1 4.8

0.4 0.7 0.1 13.3 0.1 0.7 25.7 51.5 0.7 0.0 2.5 6.4 0.3 1.2 1.2 7.7

1.0 1.1 0.1 11.1 0.2 0.9 31.8 42.1 0.8 0.1 1.8 4.7 0.3 1.2 0.9 9.8

1.3 1.2 0.1 11.1 0.2 1.1 31.1 43.5 0.5 0.1 1.7 4.6 0.2 1.0 0.8 10.1

2.8 1.9 0.1 10.6 0.4 2.2 26.1 50.3 0.4 0.1 1.4 3.6 0.3 1.1 0.5 10.5

0.8 16.4 82.4 12.4 2.4 0.004 0.02 1.3

1.2 13.4 79.8 9.7 2.6 0.006 0.07 1.4

1.2 13.4 77.9 9.7 2.5 0.011 0.08 1.4

2.2 11.3 74.7 7.3 2.3 0.015 0.14 1.5

2.6 11.3 75.6 7.0 2.1 0.018 0.10 1.6

4.9 11.0 78.7 5.6 1.9 0.040 0.11 2.0

Moreover, further alkylation reactions to produce aromatics and coke proceed faster with pentenes than with propene as can be expected from the larger inductive effect exerted by the longer alkyl chain in pentenes. Representative plots of coke content versus time for a series of deactivation experiments on Y-62 at varying space time are presented in Fig. 3. On Y-62, as well as on all the other catalysts, the influence of conversion on coke formation could be neglected for initial conversions <35%. At initial conversions >35%, the rate of coke formation decreases with increasing conversion. Fig. 3 also illustrates the autocatalytic effect of coke on coke formation. Coke formation on zeolites can be considered as a nucleation-growth process. As shown by Figueiredo et al. [36] and Moljord et al. [37], at 723 K, coke formation is related to entrapment of sterically bulky secondary products in the zeolite cages. As shown in Fig. 2, in the conversion of i-butene on HY-zeolites, the formation of the first coke molecules occurs from successive reactions of olefins, i.e. alkylation, hydride

transfer and cyclization reactions, that become trapped in the zeolite cages. Once these first molecules are formed, further alkylation, hydride transfer and cyclization reactions then transform them into high molecular weight unsaturated compounds with a highly aromatic character [1]. The decrease of the coking rate at X>35%, indicates that i-butene is more active in coke formation than its reaction products. At X<35%, i-butene is the main gas phase component. 3.4. Effect of coke content Fig. 4 shows the micro pore volume and the percentage of pore blockage as a function of coke content for Y-62. Under the conditions used in this study, deactivation by pore blockage can be expected to become important from Cc >5 wt.%. 3.4.1. On the overall conversion Fig. 5 presents the deactivation function 8 for the overall conversion on the investigated catalysts.

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Fig. 2. Reaction scheme for the conversion of i-butene.

Fig. 3. Coke content as a function of time for a series of deactivation experiments at constant inlet partial pressure of i-butene with different space times on Y-62 ( : W/F0 =105 kg s/mol, X=35%; : W/F0 =73 kg s/mol, X=33%; : W/F0 =42 kg s/mol, X=26%; : W/F0 =10.5 kg s/mol, X=9%).

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Fig. 4. Micro pore volume ( coke content for Y-62.

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) and % pore blockage (

) vs.

Clearly, the effect of coke on the conversion rate can be positive or negative depending on the coke content and on the acid properties of the catalyst. In the absence of EFAL, for H+ /u.c.<29, the conversion rate decreases with increasing coke content, while for H+ /u.c.≥29, the conversion rate of i-butene initially increases with increasing coke content, reaching a maximum value. The increase is most pronounced for Y-62. For Y-62, with 41 H+ /u.c., the maximum value of the conversion rate is 25% higher than on the fresh catalyst and is reached at Cc =10 wt.%. However, as can be seen from Fig. 4, at Cc =10 wt.%, 25% of the volume of the coked Y-62 is inaccessible for gas phase molecules.

Fig. 5. Deactivation function 8 for the overall conversion of i-butene as a function of coke content on the investigated catalysts ( : 41 H+ /u.c.; : 35 H+ /u.c.; : : 25 H+ /u.c.; : 21 H+ /u.c.; 29 H+ /u.c.; : 6 H+ /u.c.+EFAL; : 33 H+ /u.c.+EFAL).

The coke content corresponding with the maximum value of the conversion rate decreases with decreasing H+ /u.c. For SiY-4 and SiY-5, with respectively 35 and 29 H+ /u.c., the maximum value in the conversion rate is 8%, respectively 5%, higher than on the fresh catalyst and is reached at Cc =2 and 0.9 wt.%, respectively. The above observations clearly indicate that coke intervenes in one or more of the reactions contributing to the conversion of i-butene. On LZY-20 and on Z-427, both containing EFAL, the rate of conversion of i-butene decreases with coke content, the decrease being most pronounced for LZY-20. 3.4.2. On dimerization-β-scission Fig. 6A presents the deactivation function 8 for the dimerization-␤-scission path on the investigated catalysts. On all catalysts, the rate of the dimerization-␤-scission path decreases with increasing coke content. In the absence of EFAL, for H+ /u.c.≤35, the influence of the number of acid sites per unit cell is less pronounced. The deactivating effect of coke on the dimerization␤-scission path drastically increases in the presence of EFAL as can be seen by comparing 8 for SiY-4 (35 H+ /u.c.) and for Z-427 (33 H+ /u.c.). 3.4.3. On isomerization Fig. 6B shows the deactivation function 8 for the isomerization reaction on the investigated catalysts. The influence of coke formation on the isomerization activity of the catalyst can be positive or negative depending on the coke content and on the acid properties of the catalyst. In the absence of EFAL, up to Cc =2 wt.%, the isomerization rate remains practically constant for catalysts with H+ /u.c.≥25 and then decreases at Cc >2 wt.%. On Y-62, with 41 H+ /u.c., the isomerization rate remains practically constant even up to Cc =5 wt.%, although 15% of the volume of the coked zeolite is inaccessible for gas phase molecules as can be seen from Fig. 4. Consequently, the constant activity for isomerization measured on the coked catalysts actually implies a positive influence of coke formation on the rate of formation of n-butenes. For H+ /u.c.<25, the isomerization rate initially increases with coke content.

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Fig. 6. Deactivation function 8 for the dimerization-␤-scission path (a), for the isomerization (b), for the hydride transfer reaction (c) and for coke formation (d) as a function of coke content on the investigated catalysts ( : 41 H+ /u.c.; : 35 H+ /u.c.; : 29 H+ /u.c.; : 25 H+ /u.c.; : 21 H+ /u.c.; : 6 H+ /u.c.+EFAL; : 33 H+ /u.c.+EFAL).

The effect of EFAL on the influence of coke formation on the isomerization activity is not unequivocal. At Cc =1 wt.%, the rate of isomerization on LZY-20 is 55% lower than on the fresh catalyst, while on Z-427, it increases with 8%. The maximum isomerization rate on Z-427 is 10% higher than on the fresh catalyst and is reached at Cc =3 wt.%. 3.4.4. On hydride transfer Fig. 6C presents the deactivation function 8 for the hydride transfer reaction on the investigated catalysts. In the absence of EFAL, the hydride transfer activity of the catalysts increases with increasing coke content reaching a maximum value. The coke content corresponding with the maximum value of the rate of hydride transfer as well as the maximum value itself decrease with decreasing H+ /u.c. For Y-62 and SiY-8, with respectively 41 and 21 H+ /u.c., the maximum value in the hydride transfer rate is 670%, respectively

50%, higher than on the fresh catalyst and is reached at Cc =10 and 5 wt.%, respectively. These observations clearly indicate that coke formation has a positive influence on the hydride transfer reaction, the influence being more pronounced with increasing H+ /u.c. As for the influence of coke on the rate of isomerization, the effect of EFAL on the rate of hydride transfer is not unequivocal. On LZY-20, the rate of hydride transfer decreases, while on Z-427 it increases, reaching a maximum at Cc =1 wt.%. 3.4.5. On coke formation Fig. 6D presents the deactivation function 8 for the coke formation on the investigated catalysts. In the absence of EFAL, the rate of coke formation increases with coke content reaching a maximum value. The coke content corresponding with the maximum value in the rate of coke formation as well as the maximum value itself decrease with decreasing H+ /u.c. For Y-62

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Fig. 7. Rate of hydride transfer and coke formation as a function of coke content on Y-62 (left) and on Z-427 (right).

and SiY-8, with respectively 41 and 21 H+ /u.c., the maximum value in the coke formation rate is 1670%, respectively 120%, higher than on the fresh catalyst and is reached at Cc =10 and 5 wt.%, respectively. The higher the number of H+ /u.c., the more pronounced the effect of coke. Also, these observations clearly illustrate the autocatalytic effect of coke formation. Again, the effect of EFAL on the influence of coke on the rate of coke formation is not unequivocal. On LZY-20, the rate of coke formation decreases while on Z-427 it increases with content, reaching a maximum value at Cc =1 wt.%. On all catalysts, it was found that the rate of hydride transfer parallels the rate of coke formation. In Fig. 7, this is illustrated for Y-62 and for Z-427. The observed

Fig. 8. Selectivity on the fresh catalysts as a function of H+ /u.c. (䉬: Dimerization-␤-scission; 䊏: Hydride transfer; 䉱: Isomerization; ×: Cokes. Hollow symbols: contains EFAL).

correlation between coke formation and hydride transfer indicates that they are intertwined processes and confirms the importance of hydride transfer reactions in coke formation [1]. A strong correlation between the rate of hydride transfer in n-hexane conversion and the amount of coke formed in micro-activity tests with a standardized vacuum gas oil on commercial FCC catalysts has been reported by Brait et al. [12]. 3.5. Product selectivities: effects of acid properties and of coke content In Fig. 8 the selectivities for the main types of reaction are shown as a function of H+ /u.c. for the fresh catalysts. Since the influence of coke depends on the reaction type considered, it is clear that these selectivities also changes with coke content. Figs. 9 and 10 highlight these changes. As can be seen in Figs. 9 and 10, the effects of the acid properties on the selectivities do depend on the coke content of the catalyst. 3.5.1. Fresh catalysts On all catalysts, except on Z-427, the main reaction type is isomerization followed by hydride transfer and dimerization-␤-scission. With decreasing number of H+ /u.c., the selectivity of isomerization gradually decreases while the selectivity of dimerization-␤-scission, hydrogen transfer and coke formation increases. Dimerization-␤-scission, hydride transfer and coke formation seem to be more favored than the isomerization reaction by the increase in the number of the strong acid sites. These observations suggest that the need for strong acid sites increases in the series isomerization, dimerization-␤-scission,

M.-F. Reyniers et al. / Applied Catalysis A: General 202 (2000) 65–80

Fig. 9. Selectivity for isomerization as a function of coke content on the investigated catalysts. a: : 41 H+ /u.c.; : 29 H+ /u.c. b: : 25 H+ /u.c.; : 21 H+ /u.c.; : 6 H+ /u.c.+EFAL; : 33 H+ /u.c.+EFAL.

hydride transfer. In this series, as compared to the sequence presented by Wojciechowski and Corma [38], i.e. isomerization, hydride transfer, alkylation, cracking, the order of hydride transfer and dimerization is reversed. This can probably be related to the fact that i-butene, which is the main gas phase component, is easily alkylated due to the inductive effect exerted by the two methyl groups. The present observations are in agreement with the finding that the highest selectivity towards skeletal isomerization during n-butene conversion is found on the weakest acid catalysts as reported in [33,39,40]. On Z-427, the selectivity for dimerization-␤-scission is highest. The selectivity for hydride transfer is practically the same as that for isomerization. The selectivity for dimerization-␤-scission, hydride transfer and coke formation are higher than would be expected

75

: 35 H+ /u.c.;

on the basis of the number of H+ /u.c., while the selectivity for isomerization is lower. For high values of H+ /u.c., the presence of EFAL seems to promote dimerization-␤-scission, hydride transfer and coke formation at the expense of isomerization. LZY-20, the other investigated catalyst containing EFAL, shows the same picture as the catalysts without EFAL. The difference in behavior between LZY-20 and Z-427 is in accordance with the findings of Wang et al. [25] who reported that for Al/u.c.<15, the presence of EFAL has no marked influence on the reaction rates. 3.5.2. Coked catalysts Up to Cc =3 wt.%, the same order of relative importance as on the fresh catalysts is observed. As expected from the positive influence of coke on the rate of hydride transfer, at Cc >5 wt.% hydride transfer becomes

Fig. 10. Selectivity for hydride transfer as a function of coke content on the investigated catalysts. a: : 41 H+ /u.c.; : 29 H+ /u.c. b: : 25 H+ /u.c.; : 21 H+ /u.c.; : 6 H+ /u.c.+EFAL; : 33 H+ /u.c.+EFAL.

: 35 H+ /u.c.;

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more important than the dimerization-␤-scission path. Fig. 9 presents the selectivity for isomerization as a function of coke content for the investigated catalysts. Fig. 9a shows that in the absence of EFAL, the selectivity for isomerization decreases with increasing coke content for H+ /u.c.>25, while Fig. 9b shows that for H+ /u.c.<25, a maximum in the relative importance of isomerization is observed at Cc =1 wt.%. The influence of the number of H+ /u.c. becomes less pronounced at higher coke content. On LZY-20, the selectivity for isomerization increases with coke content, while on Z-427 it remains practically constant up to Cc =3 wt.% and then increases with coke content. As expected, the selectivity for coke formation parallels the selectivity for hydride transfer on all catalysts. Fig. 10 shows that the relative importance of hydride transfer increases with increasing coke content. At higher coke content, the influence of the acid properties on the relative importance of hydride transfer and coke formation becomes less pronounced. At Cc >5 wt.%, in the absence of EFAL, the selectivity for hydride transfer and coke formation is practically the same on all catalysts.

4. Discussion Usually, the effect of coke formation on the catalyst activity is described in terms of two mechanisms: site coverage and pore blockage [1–3,6–9,41]. The pore blockage is caused by coke growing from a precursor covering an active site [41]. From Fig. 4, it is clear that, under the conditions used in this study, pore blockage by coke deposition will be important at Cc >5 wt.%. The observation that coke molecules are not inert with regard to the formation of cracked products is at variance with the general ideas concerning coke formation and deactivation commonly used in modeling coke formation and its deactivating effect. This holds in particular with respect to the identification of site coverage and deactivation. Therefore, to avoid confusion, the notion of site coverage will not be used. However, in view of the highly unsaturated nature of coke molecules, competitive chemisorption between reactant and coke molecules obviously will occur.

Table 4 Summary of the observed influences of coke formation on the reaction rates on the investigated catalysts at X=23% Overall conversiona Isomerizationa

Dimerization-␤-scission Hydride transfer Coke formation a

H+ /u.c.≥29 H+ /u.c.<29 H+ /u.c.≥25, Cc ≤2 wt.% H+ /u.c.>25, Cc >2 wt.% H+ /u.c.<25 All catalysts H+ /u.c.>6 H+ /u.c.>6

Positive Negative Positive Negative Negative Negative Positive Positive

In the absence of EFAL.

The present observations, summarized in Table 4, clearly indicate that the influence of coke formation can be positive or negative depending on the reaction type considered, on the coke content and on the acid properties of the catalyst. Under the conditions used in this study, coke formation has a positive influence on the overall conversion, on the formation of n-butenes, on hydride transfer and on coke formation, while its influence on dimerization-␤-scission is negative. To explain these observations, a reaction mechanism for the conversion of i-butene involving coke molecules as intermediates, as shown in Fig. 11, is proposed. The close relation between the rate of hydride transfer and the rate of coke formation, see Fig. 7, implies that hydride transfer reactions are important in the formation of products retained on the catalyst. The increase in the rate of hydride transfer with coke content, Fig. 6C, demonstrates that coke molecules act as a hydride source, i.e. as a reactant, in hydride transfer reactions. Thus, coke molecules have the ability to act as a hydride source and to successfully compete with gas phase components for hydride transfer to surface carbenium ions. As coke molecules are highly unsaturated compounds with an aromatic character [1,2], the corresponding coke carbenium ions are highly delocalized and the activation energy for their formation can be expected to be relatively low. Consequently, in the presence of coke formation, hydride transfer reactions involved in the formation of coke molecules (Fig. 11, path A) will occur in competition with the hydride transfer reactions that already occurred on the fresh catalyst (Fig. 11, path B, vide infra). For the same reason, alkylation of coke molecules with surface carbenium ions can be expected to occur easily (Fig. 11, paths D and F). Furthermore, coke carbenium ions can interact with i-butene since a

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Fig. 11. Reaction mechanism for hydride transfer and n-butenes formation in the presence of coke formation.

stable tertiary carbenium ion is formed (Fig. 11, path C). The resulting alkylated coke carbenium ion can, after rearrangement, undergo ␤-scission thereby producing n-butenes or it can contribute to further coke growth. Hence, coke formation ultimately not only leads to pore blockage but also to the occurrence of reactions that greatly influence the activity and selectivity of the catalyst. Even in the presence of significant pore blockage, the occurrence of these reactions can result in an increased activity of the catalyst. Consequently, a fundamental description of the influence of coke formation on the activity and selectivity of a catalyst requires a fundamental kinetic description of coke formation, taking into account the involvement of coke molecules in the formation of cracked products. The positive influence of coke formation on hydride transfer reactions can be traced back to the chemical structure of the coke molecules and is related to the potential of coke molecules to form highly delocalized and hence stable carbenium ions. Clearly, this effect is related to the aromatization of the coke molecules and has an autocatalytic nature. Hydride

transfer can be expected to occur more easily in the series C–H, C=C–C–H, C=C–C=C–H, ∅–CH since the stability of the resulting carbenium ions increases in the same series [42]. In the quantum-mechanical picture, as presented in [43–46], this would amount to a lower energy of the transition state in the series secondary>tertiary>allyl>di-allyl>benzyl. This can be illustrated as follows:

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The observed influence of the chemical structure on the hydride donor capacity, however, also raise the question as to the involvement of alkenes in the hydride transfer reactions occurring in the bimolecular cracking mechanism.

Usually, only paraffins, cycloparaffins, long-chain olefins and cyclo-olefins e.g. cyclopentene, cyclohexene, are considered as a hydride source in this mechanism [47–50]. Alkenes can act both as hydride acceptor, via the corresponding carbenium ion, and as hydride donor. Transfer of an allylic hydride to surface carbenium ions generates a stable delocalized allylic carbenium ion (Fig. 11, path B). The finding that no di-olefins are observed in the product stream, see Table 3, can then probably be related to the fact that di-olefins, since they are more easily alkylated than mono-olefins, are very active in coke formation. In the present case of i-butene conversion, a high surface concentration of t-butyl carbenium ions can be expected. Moreover, i-butene, is present in high concentrations at the investigated conversion. Both factors will facilitate hydride transfer reaction from i-butene to surface t-butyl carbenium ions. The allylic carbenium ion thus formed can, after hydride shift, give rise to the very stable non-classical cyclopropylmethyl carbenium ion that can undergo further isomerization to n-butenes [42]. It could also contribute to a monomolecular isomerization of i-butene without the involvement of unstable primary carbenium ions. Schematically, this can be represented as follows:

The observed increase of the positive effect of coke formation on the rate of hydride transfer with increasing number of acid sites, as presented in Fig. 6C, implies that hydride transfer from coke molecules can also occur to carbenium ions adsorbed on weaker acid sites. Therefore, it is suggested that the increase in the conversion rate with increasing coke content observed on catalysts with H+ /u.c.≥29 can be related to their acid strength distribution. On the fresh Y-62 with 41 H+ /u.c., for instance, hydride transfer will proceed mainly on the stronger acid sites, present in relatively low amounts. In the presence of coke formation, however, hydride transfer reactions with growing coke molecules can also occur on weaker acid sites, present in far larger amounts than the strong acid sites in Y-62 (Fig. 1). In the presence of coke formation, the involvement of the weaker acid sites in hydride transfer reactions more than compensates for the effect of pore blockage resulting in higher conversion rates on Y-62. On Y-62 containing 15 wt.% coke and with 50% of the catalyst volume blocked by coke (Fig. 4), the activity for conversion of i-butene is the same as that of the fresh catalyst (Fig. 5). On SiY-7 with 25 H+ /u.c., the number of weak acid sites is far lower and their contribution in hydride transfer reactions in the presence of coke can no longer compensate for the effects of pore blockage. The positive influence of coke formation on the formation of n-butenes, Fig. 6B, is related to the interaction of coke carbenium ions, formed by hydride transfer from coke molecules to surface carbenium ions (Fig. 11, path A), with i-butene (Fig. 11, path C). Subsequent isomerization and ␤-scission then leads to the formation of n-butenes. Similar views concerning the involvement of coke in the skeletal isomerization of n-butene on zeolites can be found in [27–30]. Alkylation of the alkylated coke carbenium ion (Fig. 11, path C), leading to further coke growth or,

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after rearrangement and ␤-scission, to the formation of n-butenes, occurs in competition with deprotonation. The observed increase in the relative importance of the formation of n-butenes with coke content on catalysts with H+ /u.c.<25, Fig. 9, indicates that on strong acid sites alkylation is favored over deprotonation. Clearly, on strong acid sites the equilibrium coefficient for protonation/deprotonation is higher than on weaker sites. As can be seen from Fig. 6D, the influence of coke formation on coke formation is far more pronounced than on the formation of n-butenes although accumulation of coke clearly also involves alkylation of coke molecules. Alkylation of coke carbenium ions with i-butene produces a tertiary carbenium ion (Fig. 11, path C), while alkylation of coke molecules with surface t-butyl carbenium ions (Fig. 11, path D) produce a more stable delocalized coke carbenium ion. Therefore, it can be expected that the latter route will be predominant in coke growth. The negative influence of coke formation on the dimerization-␤-scission path, Fig. 6A, could then also be related to the predominant interaction of t-butyl carbenium ions with coke molecules (Fig. 11, path D) as compared to their involvement with i-butene leading to dimerization (Fig. 11, path E). This can lead to a decreased concentration of octyl carbenium ions on the catalyst surface. Moreover, octyl carbenium ions can also interact with coke molecules (Fig. 11, path F). Further, octyl carbenium ions can also be involved in hydride transfer reactions with coke molecules (not indicated in Fig. 11). These effects can contribute to a decreased selectivity for dimerization-␤-scission.

on the acid properties of the catalyst. 3. Under the conditions used in this study, reactions involving coke molecules contribute to the rates of formation of n-butenes, of hydride transfer and of coke formation. 4. A fundamental description of the influence of coke formation on the activity and selectivity of a cracking catalyst requires that the involvement of coke molecules in the conversion reactions is explicitly accounted for in the reaction network. 5. The involvement of coke in the conversion reactions is related to the chemical structure of the coke molecules. Hence, coke content is not the only required variable to describe catalyst activity and selectivity. The potential of coke molecules to form highly delocalized stable coke carbenium ions rather than the coke content constitutes a crucial link between catalyst activity and coke. 6. The low activation energy of hydride transfer from coke molecules to surface carbenium ions implies that hydride transfer from coke molecules can also occur to carbenium ions adsorbed on weaker acid sites.

5. Conclusions

References

The following main conclusions can be drawn: 1. The formation of coke not only leads to pore blockage but also to the occurrence of reactions that cause a significant change in the activity and the selectivity of the investigated catalysts. Even in the presence of important pore blockage, the occurrence of these reactions can lead to an increased activity of the catalyst. 2. The influence of coke formation on the reaction rates can be positive or negative depending on the reaction type considered, on the coke content and

Acknowledgements The authors wish to thank P. Grobet (Katholieke Universiteit Leuven) for the NMR work and S. Lacombe (l’Institut Français du Pétrole) for kindly providing a sample of Z-427. Y. Tang gratefully acknowledges support from the Fudan University, Shangai and the Universiteit Gent.

[1] [2] [3] [4]

[5]

[6] [7] [8]

M. Guisnet, P. Magnoux, Appl. Catal. 54 (1989) 1. M. Guisnet, P. Magnoux, Stud. Surf. Sci. Catal. 88 (1994) 53. M. Guisnet, P. Magnoux, Catal. Today 36 (1997) 477. P.D. Hopkins, J.T. Miller, B.L. Meyers, G.J. Ray, R.T. Rogonski, M.A. Kuehne, H.H. Kung, Appl. Catal. A: General 136 (1996) 29. G.F. Froment, in: J.L. Figuerido (Ed.), Progress in Catalyst Deactivation, NATO Advanced Study Institute Series-E54, Nijhoff, The Hague, 1982. I.-S. Nam, G.F. Froment, J. Catal. 108 (1987) 271. A.O.E. Beyne, G.F. Froment, Chem. Eng. Sci. 45 (1990) 2089. G.F. Froment, J. De Meyer, E. Derouane, J. Catal. 124 (1990) 391.

80

M.-F. Reyniers et al. / Applied Catalysis A: General 202 (2000) 65–80

[9] G.F. Froment, in: C.H. Bartholomew, J.B. Butt (Eds.), Catalyst Deactivation 1991, Elsevier, Amsterdam, 1992. [10] C. Bourdillon, C. Gueguen, M. Guisnet, Appl. Catal. 61 (1993) 123. [11] H. Beirnaert, R. Vermeulen, G.F. Froment, Stud. Surf. Sci. Catal. 88 (1994) 97. [12] A. Brait, K. Seshan, H. Weinstabl, A. Ecker, J.A. Lercher, Appl. Catal. A: General 169 (1998) 315. [13] A. Corma, F. Mocholi, V. Orchilles, G.S. Koermer, R.J. Madon, Appl. Catal. A: General 67 (1991) 307. [14] A. Corma, J.B. Monton, A.V. Orchillés, Ind. Eng. Chem. Res. Dev. 23 (1984) 404. [15] D. Barthomeuf, Mat. Chem. Phys. 17 (1987) 49. [16] K.A. Das, B.W. Wojciechowski, Chem. Eng. Sci. 48 (1993) 1041. [17] Z. Gao, Y. Tang, Zeolites 8 (1988) 232. [18] G.W. Skeels, D.W. Breck, in: D. Olson, A. Bisio (Eds.), Proceedings of the International Zeolite Conference, Butterworths, Guildford, 1984, p. 87. [19] A. de Lucas, P. Canizares, A. Durán, A. Carrero, Appl. Catal. A: General 156 (1997) 299. [20] J. Klinowski, S. Ramdas, J.H. Thomas, C.A. Fyfe, J.S. Hartman, J. Chem. Soc., Faraday Trans. 78 (1982) 1025. [21] L.A. Pine, P.J. Mahler, W.A. Wachter, J. Catal. 85 (1984) 466. [22] D. Barthomeuf, J. Phys. Chem. 97 (1993) 10092. [23] Z. Gao, Y. Tang, Z. Yugin, Appl. Catal. 56 (1989) 83. [24] A. Corma, Chem. Rev. 95 (1995) 559. [25] Q.L. Wang, G. Giannetto, M. Guisnet, J. Catal. 130 (1991) 471. [26] V.Y. Kissin, J. Catal. 163 (1996) 50. [27] K. de Jong, H. Mooiweer, J. Buglass, P. Maarsen, Stud. Surf. Sci. Catal. 111 (1997) 127. [28] P. Andy, N.S. Gnep, M. Guisnet, E. Benazzi, C. Travers, J. Catal. 173 (1998) 322. [29] M. Guisnet, P. Andy, N.S. Gnep, C. Travers, E. Benazzi, Ind. Eng. Chem. Res. 37 (1998) 300. ˇ [30] J. Cejka, B. Wichterlová, P. Sarv, Appl. Catal. A: General 179 (1999) 217.

[31] M. Guisnet, P. Andy, S.P. Gnep, E. Benazzi, C. Travers, J. Catal. 158 (1996) 551. [32] J. Houžviˇcka, O. Diefenbach, V. Ponec, J. Catal. 164 (1996) 288. [33] J. Houžviˇcka, J.G. Nienhuis, V. Ponec, Appl. Catal. A: General 174 (1999) 207. [34] J. Houžviˇcka, S. Hansildaar, J.G. Nienhuis, V. Ponec, Appl. Catal. A: General 176 (1999) 83. [35] J.S. Buchanan, J.G. Santiesteban, W.O. Haag, J. Catal. 158 (1996) 279. [36] J.L. Figueiredo, M.L. Pinto, J.J. Orfao, Appl. Catal. 104 (1993) 1. [37] K. Moljord, P. Magnoux, M. Guisnet, Appl. Catal. A: General 122 (1995) 21. [38] B.W. Wojciechowski, A. Corma, Catalytic cracking: catalysts, chemistry and kinetics, in: Chemical Industries, Vol. 25, Marcel Dekker, New York, 1986. [39] M.A. Asensi, A. Corma, A. Martinez, M. Derewinski, J. Krysciak, S.S. Tamhankar, Appl. Catal. A: General 174 (1998) 163. ˇ [40] B. Wichterlová, N. Žilkova, E. Uvarova, J. Cejka, P. Sarv, C. Paganini, J.A. Lercher, Appl. Catal. A: General 182 (1999). [41] J.W. Beeckman, G.F. Froment, Chem. Eng. Sci. 33 (1980) 805. [42] G.A. Olah, J. Am. Chem. Soc. 94 (1972) 808. [43] A.M. Rigby, G.J. Kramer, R.A. van Santen, J. Catal. 170 (1997) 1. [44] V.B. Kazansky, M.V. Frash, R.A. Van Santen, Appl. Catal. A: General 146 (1996) 225. [45] P. Sinclair, A. de Vries, P. Sherwood, C. Catlow, R.A. van Santen, J. Chem. Soc., Faraday Trans. 94 (1998) 3401. [46] M. Boronat, P. Viruela, A. Corma, J. Phys. Chem. A 102 (1998) 982. [47] A. Corma, Appl. Catal. A: General 47 (1989) 125. [48] W.C. Cheng, K. Rajagopalan, J. Catal. 119 (1989) 2354. [49] J.R. Anderson, Y.-F. Chang, R.J. Western, J. Catal. 118 (1989) 466. [50] B. Mercier Des Rochettes, C. Marcilly, C. Gueguen, J. Bousquet, Appl. Catal. A: General 58 (1990) 35.