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Ind. Eng. C h e m . Res. 1991,30, 71-82 Marquardt, D. W. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. SOC.Znd. Appl. Math. 1963, 11, 43 1-44 1.
Mazanec, T. J. On the Mechanism of Higher Alcohol Formation Over Metal Oxide Catalysts. I. A Rationale for Branching in the Synthesis of Higher Alcohols from Syngas. J. Catal. 1986, 98, 115-125.
Natta, G.; Colombo, U.; Pasquon, I. Higher Alcohols. in Catalysis; Emmett, P. H.. Ed.; Reinhold New York, 1957; Vol. 5, Chapter 3, pp 131-174. Nunan. J. G.: Klier. K.: Youne. C. W.: Himelfarb. P. B.: Herman. R. G. Promotion of Methanobynthesis over CujZnO Catalysts' by Doping with Caesium. J. Chem. Soc., Chem. Commun. 1986, 193-195.
Nunan, J. G.; Bogdan, C. E.; Klier, K.; Smith, K. J.; Young, C. W.; Herman, R. G. Methanol and Cz Oxygenate Synthesis over Cesium Doped Cu/ZnO and Cu/ZnO/AlZO3 Catalysts: A Study of Selectivity and 13C Incorporation Patterns. J . Catal. 1988, 213,
Promoted Copper/Zinc Oxide Catalysts. Can. J. Chem. Eng. 1983,61, 40-45.
Smith, K. J.; Anderson, R. B. A Chain Growth Scheme for the Higher Alcohols Synthesis. J. Catal. 1984,85, 428-436. Smith, K. J.; Young, C. W.; Herman, R. G.; Klier, K. Reaction Kinetics of the Higher Alcohol and Oxygenate Synthesis over Cesium Doped Cu/ZnO Catalysta. Znd. Eng. Chem. Res. 1990, to be submitted. Tronconi, E.; Ferlazzo, N.; Forzatti, P.; Pasquon, I. Synthesis of Alcohols from Carbon Oxides and Hydrogen. 4. Lumped Kinetics for the Higher Alcohol Synthesis Over a Zn-Cr-K Oxide Catalyst. Znd. Eng. Chem. Res. 1987, 26, 2122-2129. Vedage, G. A,; Himelfarb, P. B.; Simmons, G. W.; Klier, J. AlkaliPromoted Copper-Zinc Oxide Catalysts for Low Alcohol Synthesis. ACS Symp. Ser. 1985,279, 295-312. Young, C. W. Effect of Cesium on Alcohol Synthesis, Water-Gas Shift Reaction, and Ester Hydrogenolysis over Copper-Zinc Oxide Catalysts. Ph.D. Dissertation, Lehigh University, Bethlehem, PA, 1987.
410-433.
Nunan, J. G.; Bogdan, C. E.; Klier, K.; Smith, K. J.; Young, C. W.; Herman, R. G. Higher Alcohol and Oxygenate Synthesis over Cesium-Doped Cu/ZnO Catalysts. J. Catal. 1989,116,195-221. Silver, R. G.; Tseng, S. C.; Ekerdt, J. G. Isosynthesis Mechanisms Over Zirconium Dioxide. Prepr. Pap.-Am. Chem. Soc., Diu. Fuel Chem. 1986,32 (3), 11-16. Smith, K. J.; Anderson, R. B. The Higher Alcohol Synthesis Over
Young, C. W.; Herman, R. G.; Klier, K. Probing the Mechanism and the Reactive Intermediates that Undergo Chain Growth Reactions during Higher Alcohol Synthesis over Cesium-Doped Cu/ZnO Catalysts. In preparation, 1990. Receiued f o r review February 20,1990 Accepted August 8,1990
Analysis of Zeolite Catalyst Deactivation during Catalytic Cracking Reactions Sebastian C. Reyes* E r r o n Research and Engineering Company, Annandale, New Jersey 08801
L. E. Scriven Chemical Engineering Department, University of Minnesota, Minneapolis, Minnesota 55455
Catalyst deactivation during cracking reactions is analyzed in terms of the physical, chemical, and transport processes taking place within zeolite crystals. Special attention is given to the interactions of zeolite morphology and the wide range of components present in a typical cracking feed. By analyzing the functional form of activity decays, obtained via a detailed model of adsorption, diffusion, and reaction, it is possible to identify three regimes of deactivation. These can be classified as dynamical, chemical, and structural. They dominate the shape of the activity decay curves at short, intermediate, and longer times, and are related to competitive adsorption, site coverage, and pore blockage phenomena, respectively. The model predicts the correct activity patterns under a wide variety of reaction conditions, closely mimics those observed experimentally, and spans those obtained from available empirical correlations.
Introduction A basic observation about heterogeneous reacting systems that suffer from coke formation is the continuous decrease in catalyst activity. Whether or not the activity of the catalyst can be partially or totally restored by some regenerative process, this phenomenon is likely to have an impact on the overall economy of the process. This is particularly the case when catalyst activity is lost over short periods of time, as is often observed in various processes where hydrocarbons are present in the reaction mixture. Catalytic processes where carbonaceous materials are deposited onto the catalytic surfaces are numerous. The present work focuses attention on the cracking of hydrocarbons over zeolite catalysts, which is a challenging example of coke-formingreactions where the activity of the catalyst decreases by orders of magnitude in very short times. For typical riser-reactor operation the deactivation
* To whom correspondence should be addressed.
time is of the order of seconds (Venuto and Habib, 1978). Accordingly, the incorporation of the appropriate deactivation mechanisms becomes an essential element in a process model description because the time scale for catalyst deactivation is comparable to the time scale in which the reactions occur. The cracking of hydrocarbons over zeolite catalysts combines deactivation processes in both the crystalline and amorphous componentsof the catalyst. In order to provide the necessary heat-transfer and mechanical properties required during commercial operation, the catalyst particles (40-60 pm) are manufactured by embedding small zeolite crystals (1-3 pm) within amorphous silica-alumina matrices. Crystalline and amorphous materials are two somewhat extreme catalyst structures in which most heterogeneous catalytic processes are carried out. The present work is restricted to the analysis of deactivation in the crystalline component of cracking catalysts. The aim of the present study is then to use mathematical modeling to gain a fundamental understanding of the interactions of physical, chemical, and transport processes
0888.58851 91/ 2630-0071$02.50/0 0 - 1991 American Chemical Societv
72 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 1
I
I
I
1
(1): Dynamical
(2): Chemical (3): Structural
1
-
(1): Exponential (2): Hyperbolic (3): Power Law
-
-
-
3
I
0 0
I
I
I
1
1
2
3
4
5
Time, t ( 8 )
Figure 2. Activity decays as predicted by exponential, hyperbolic, and power-law relations.
laid down on the catalyst (W,) could be satisfactorily correlated with the catalyst residence time ( t )by means of a simple power-law behavior of the form W , = botbl
(1)
where bo and bl are appropriate fitted constants. Over the years, Voorhies's work gained increasing support as evidenced by the number of investigators that have reported a good agreement between (1) and experimentally measured coke deposition rates (e.g., Rudershausen and Watson, 1954; Prater and Lago, 1956; Wilson and Den Herder, 1958; Andrews, 1959; Butt et al., 1975). Some deviations from Voorhies's correlation have also been observed. For example, whereas Eberly et al. (1966) noted that coke formation was also dependent on space velocities through the reactor, other investigators have observed an initially rapid coke formation followed by a slower saturation period (e.g., Ozawa and Bischoff, 1968; Butt et al., 1975; Bilbao et al., 1985). In order to describe quantitatively the cracking of hydrocarbons it was necessary to provide a working expression for evaluating the observed activity decays. Since coke on catalyst was the source of the activity losses, Voorhies's correlation became instrumental. Thus, as shown in (2), it was first proposed that the actual rate constant k , could be obtained by multiplying a decay function B by the intrinsic rate constant ki (Szepe and Levenspiel, 1970). That is k, = O(t)ki (2) Then, by using Voorhies's correlation, and assuming that 8 ( t ) was inversely proportional to W,to some power q, it was found that B(t) =
C0t-C'
(3)
The above power-law relation has been extensively used to describe activity decays in cracking reactions over zeolite catalysts (e.g., Nace 1969,1970;Weekman and Nace, 1970; Nace et al., 1971; Voltz et al., 1972; Pryor and Young, 1984). However, as shown in (4) and (51, it has also been e ( t ) = eTAt 8(t)
=
1 1 + gt
(4) (5)
proposed that exponential and hyperbolic decay functions are sometimes more appropriate to describe certain ranges of decay (e.g., Weekman, 1968 1969; Weekman and Nace, 1970; Nace et al., 1971; Paraskos et al., 1976; Shah et al.,
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 73 1977; Jacobs et al., 1976). Figure 2 compares activity decays predicted by (3)-(5), the appropriate constants having been chosen to give a 10-fold decrease in catalyst activity over a period of 5 s. In particular, for (3), a normalizing condition of unit activity at time (nearly) zero (1/100 s) has been used. From this figure it is apparent that the functional form of the activity decay influences the predicted results, particularly regarding conversion levels at short times. A common feature of these empirical decay functions is that catalyst activity is described only in terms of the catalyst residence time. On the basis of this assumption, Wojciechowski (1968) proposed the socalled “time-on-stream”theory of catalyst,deactivation, in which the catalyst is taken as deactivating simply as a result of being on-stream. He proposed the following differential form to describe the rate of decay of active sites (5’) during coking reactions:
where h is a constant and d is the deactivation order. Clearly, depending on the value of d, this equation can give rise to linear, power-law, exponential, and hyperbolic decays. Wojciechowski and co-workers have extensively used (6) to describe activity decays in various coke-forming reactions (Campbelland Wojciechowski, 1971a,b; Best and Wojciechowski, 1973; Pachovsky et al., 1973a,b; Pachovsky and Wojciechowski, 1978; Yeh and Wojciechiowski, 1978; Viner and Wojciechowski, 1982). Corella and co-workers (Corella and Asua, 1981, 1982a,b; Corella et al., 1981) have also analyzed catalyst activity decays during cracking reactions, giving particular emphasis to the role of concentration-dependent deactivation as well as to the nonuniformity of acidic strengths of the active sites. They have derived numerous formulations describing activity as a function of time, acidic strength of active sites, and deactivation order for various coke-formingmechanisms. A somewhat different approach has been proposed by Froment and co-workers (Froment and Bischoff, 1961, 1962; Froment, 1980), who have emphasized that the activity decays should be expressed in terms of the true deactivation variable, which is coke on catalyst and not catalyst residence time, the usual choice. This has also been discussed more recently by Corella and Monzon (1988). By analyzing various reaction mechanisms, DePauw and Froment (1975) proposed a number of deactivation functions correlating catalyst activity with the concentration of coke on catalyst. The expressions for these activity decays are similar to those of (3)-(5), where concentration of coke instead of time appears in the equations. Both DePauw and Froment (1975) and Dumez and Froment (1976) observed that exponential forms adequately described catalyst deactivation in pentane isomerization on a platinum reforming catalyst and in l-butene dehydrogenation on a chromia-alumina catalyst, respectively. By using Froment and Bischoff s approach, Lin et al. (1983) and Hatcher (1985) have also shown that exponential functions adequately described experimental activity data for cumene cracking on a lanthanum-exchanged zeolite catalyst. Similarly, in studying the kinetics of coking for various C6 hydrocarbons in a platinum on alumina reforming catalyst, Cooper and Trimm (1980) observed linear and hyperbolic relationships between activity and coke content on the catalyst. It is convenient at this point to summarize some of the features of the semiempirical functions that have been used until now to describe catalyst activity during coke-forming reactions. The chief attraction of these decay functions is that they are simple to use. One of the major disad-
vantages is that a single function is usually not sufficient to describe the entire range of decay. This is apparent from Nace’s data for cracking of n-hexadecane (Nace, 1969) and cracking of gas-oil (Nace, 1970) over zeolite catalysts, where the activity shows an initially rapid decrease followed by a relatively slower decay. Changes in the functional form of the deactivation curve have been more recently discussed by Corella et al. (1985) on the basis of their analysis of cracking of gas-oil in two commercial zeolite catalysts. By using an equation of the form (6), they concluded that these changes could be explained in terms of a change in the deactivation order with time on-stream. By analyzing their data, they found deactivation orders of 3, 2, and 1 for short, intermediate, and large times, respectively. They also noted similar trends when they analyzed data from Blanding (1953) and Paraskos et al. (1976). A second disadvantage of empirical deactivation functions relates to the fact that the most adequate functional form cannot be selected a priori. This becomes a serious problem when kinetics are to be unraveled from experimental data. The problem is that the kinetic constants are likely to depend on the particular decay function that is chosen to describe catalyst deactivation. This aspect has been clearly illustrated by Absil et al. (1984), who analyzed data of cumene disproportionation over a commercial hydrocracking catalyst. Even though they found that hyperbolic and exponential decays gave a good representation of the experimental data, the resulting kinetic parameters were found to be significantly different. In a subsequent paper, Corella et al. (1986) analyzed the data by Absil et al. (1984) in terms of coke formation mechanisms that lead to Langmuir-Hinshelwood equations. Their conclusion was that the data could be fitted by two different mechanisms: (a) two types of active sites or (b) noninteger deactivation order equal to 1.5. From this discussion it may be concluded that, up to the present, activity decays during coking reactions cannot be adequately described. It is apparent that the semiempirical decay functions generally do not capture the essence of the mechanisms of deactivation. The basic assumption that catalyst activity can be correlated only in terms of the time on-stream or the concentration of coke on catalyst can be a drastic oversimplification. As discussed in the next section, it seems clear that the complex physical, chemical, and transport phenomena taking place within the catalyst particles play significant roles in the mechanisms of catalyst deactivation.
Nature and Role of Coke Deposits It is well-known that accumulation of coke on the catalytic surfaces has the adverse effect of decreasing catalyst activity. Although “coke” molecules are poorly defined compounds, it is known that they exhibit low hydrogen content and behave as solidlike deposits that remain irreversibly attached to the catalytic surfaces. There seems to be general agreement that coke formation proceeds primarily through intermediate aromatic structures of increasing size and complexity (Appleby et al., 1962). It is accepted that coke formation involves initial adsorption of highly unsaturated hydrocarbons followed by condensation and hydrogen elimination reactions (Eberly et al., 1966). The latter reactions can proceed by olefins interacting with absorbed condensed-ring aromatics to form paraffins and hydrogen-deficient coke. Because these coke deposits may grow to form stacking complexes of dimensions comparable to the size of pores, the activity of the catalyst may not be proportional solely to the remaining fraction of active sites. It may be a more complex function
74 Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991
that accounts also for the influences of internal structural changes. Continuous coke buildup on the pore surfaces is likely to reduce local diffusivities, thus reducing catalyst activity and possible leading the selectivity problems. Ultimately, a more dramatic impact on activity is caused by pore blockage, which not only lengthens the diffusion paths through the pore structure but also renders active sites inaccessible for reaction. There are a number of experimental investigations that have detected pore blockage and increasing diffusional resistances during coke-forming reactions. For example, in an early experimental study, Ramser and Hill (1958) presented evidence that a fraction of pores in a silicaalumina cracking catalyst became sealed off by coke deposition. They noticed that the decrease in pore volume during coking was twice the volume of coke deposited. In a similar study, Levinter et al. (1967) demonstrated that pore plugging was responsible for significant decreases in pore volume during cracking reactions of hydrocarbons. Suga et al. (1967) reported a gradual decrease in effective diffusivity with coke content on catalyst. Butt et al. (1975) and Butt (1976) reported that effective diffusivities during cumene cracking on a commercial H-mordenite decreased more than a factor of 2 during the coking process and were nonlinearly related to the amount of coke on catalyst. By using scanning electron microscopy they observed eignificant pore blockage near the outer surface of the catalyst, whereas no coke was found toward the particle interior-a particularly noteworthy finding. From these experimental studies the conclusion is that the influence of coke accumulation must be taken into account when analyzing catalyst deactivation. From a modeling point of view, it is necessary to distinguish among those molecules that form a monolayer and those that form a multilayer or deeper deposit. Whereas the first are responsible for site coverage deactivation, the second reduce activity by transforming the internal structure of the catalyst. Coke buildup within the pore cavities not only decreases diffusion rates but also renders active sites inaccessible for reaction. Diffusivity and accessibility changes can be estimated by making use of the concepts of percolation theory. The use of this theory as a suitable technique for quantifying diffusion and accessibility in changing pore structures is discussed in the next section.
Pore Blockage Phenomena One of the earliest mathematical models analyzing the performance of fouled catalyst pellets is due to Masamune and Smith (1966) and Sagara et al. (1967). Their model described the evolution of catalyst effectiveness (active surface area) as a function of time for three typical fouling processes. A basic assumption in their model, which may not apply to typical coking reactions, is the absence of pore plugging. Beeckman and Froment (1979,1980) have also investigated catalyst deactivation mechanisms by correctly emphasizing that, besides site coverage, the accessibility of active sites is reduced by pore blockage. They have developed relationships to estimate the accessibility of active sites as a function of coke content for various model pore space representations, ranging from single pores to networks of interconnected pores of different size. Since they have been primarily concerned with activity decays in amorphous catalysts, whose internal structure is highly disordered, realistically representing pore space connectivity is a serious obstacle in their studies. Moreover, although pore blockage also reduces the diffusion rates within the pore structure, they have made no attempt to describe the changes in diffusivity with coke content, a dependence that is also strongly correlated with the con-
Uncoked Catalyst
20% Coke
3OYo Coke
40% Coke
Figure 3. Schematic representation of deactivation by pore blockage in a square lattice.
nectivity of the changing pore structure. For more information on the latter subject, the reader is referred to the work by Mo and Wei (1986). Beeckman and Froment’s description of pore blockage can be improved and formalized by using the concepts of percolation theory, a theory that provides a natural framework for describing diffusivity and accessibility properties of randomly disordered structures. The present section outlines some of the concepts of percolation theory that are relevant to the description of diffusion and accessibility in a catalyst particle whose internal structure is changing due to coking reactions. Some of these concepts have already been discussed by Sahimi and Tsotsis (1985) in the context of deactivation by pore blockage. Specifically, the useful quantities are defined as follows: d ( t ) = fraction of the initial pore volume that is occupied by coke deposits at time t. E ( t ) = ratio of diffusivity a t a coke loading 4 ( t ) to the diffusivity value for uncoked catalyst. P ( t ) = fraction of the initial active sites that remain accessible for reaction a t time t. The objective of the present section is to illustrate the use of percolation concepts in characterizing the effective diffusion rates ( E )and accessibility of active sites ( P ) as functions of coke content on the catalyst. It bears emphasizing that the above quantities are locally defined within the particle. That is, it is assumed that the locale is small compared to the particle volume, yet large compared to the submicroscopic pore system. Figure 3 illustrates the role of structural deactivation in a square latice where continuous coke buildup is shown to affect both E and P. As is likely to be the case in actual reaction conditions, coke accumulation is taken here to occur preferentially near the outer edge of the catalyst. When the concentration of coke is 20%, E decreases as a consequence of the tortuous paths generated through the sample.
Ind. Eng. Chem. Res., Vol. 30, No. 1, 1991 75 However, at this low concentration of coke, P remains unity because all the unblocked sites are still accessible from the outer surface. As the concentration of coke increases to 30%, E continues to fall because the open pathways become increasingly tortuous. A t this concentration of coke, P also starts to decrease because some sites have become blocked by coke deposits. Ultimately, when the concentration of coke is high (40% in this example) the interior sites became isolated because complete plugging of the outer surface has occurred. At this point, E and P are reduced to zero, and therefore the catalyst becomes deactivated. As will be shown later, the conclusions drawn here for a two-dimensional network are also valid in three-dimensional structures. Broadbent and Hammersley (1957) and their successors developed percolation concepts to evaluate connectivity and transport properties in networks. Although the theory was developed to apply to the limit of systems of unbounded extent, the development has been found to apply well to (large) real systems. By adopting the terminology of gas diffusion in porous structures, two fundamental concepts of percolation theory can be summarized as (1) no mass transport is possible if the porosity of the pore structure is smaller than a nonzero threshold value X,, called the percolation threshold, and (2) the notion of percolation probability P, which is defined as the likelihood that there is a connected path for mass transport across the sample. The concept of percolation threshold is highly significant for deactivation phenomena because it determines the critical porosity at which most of the pore space becomes completely isolated. Percolation probability, on the other hand, allows the fraction of the initial active sites that remain accessible for reaction to be evaluated. From the work of Broadbent and Hammersley (1957) it follows that if X < X,, then E and P vanish identically. That is, below X , the pore space remains as disconnected clusters. However, as X rises, a continuous region of pores is generated when X reaches X,. A t this point E and P undergo a sharp transition from zero to some finite value as a consequence of the connected path generated through the sample. As X continues to rise past X , , more pores are incorporated into the accessible region by two mechanisms: (1) by joining dead-end pores and (2) by forming bonds between isolated pore clusters and the accessible collection of pores. The rate of increase of this region with X is proportional to the degree of connectivity of the pore structure because the more ramified the structure is the faster the rate at which either of the above mechanisms can take place. Thus, in order to characterize the pore structure, it is convenient to split the porosity into the porosity XI that exists as isolated pores, and that which is accessible, the porosity X A :
x
= XI + X*
(7) By using this relation, it follows that the fraction of the initial pore volume that is occupied by coke deposits and the fraction of the initial active sites that remain accessible for reaction are simply given by f$ = 1 - x / x , (8)
P = XA/X (9) where X o is the initial porosity of the sample. The pore structure can be further characterized by splittin the accessible pore space into the backbone fraction X % and the dead-end fraction X D : XA = XB + XD (10) This relation is useful for understanding diffusion within
Figure 4. Schematic representations of cubic and Voronoi tessellations.
the pore structure. The backbone fraction corresponds to the largest connected region through which mass transport is possible across the sample, i.e., the accessible region minus its dead ends. It should be noticed that even though XB is active in transport it still contains tortuous paths that further decrease the diffusion rates through the pore structure. Therefore, in general, the ratio of diffusivity in partially coked to that in uncoked catalyst is less than (or at most equal to) the fraction of pores that remain in the backbone of pore space connected to the outside of the catalyst:
E
