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Ind. Eng. Chem. Res. 2004, 43, 4080-4086
On the Modeling of the Kinetics of the Selective Deactivation of Catalysts. Application to the Fluidized Catalytic Cracking Process Jose´ Corella† Faculty of Chemistry, Chemical Engineering Department, University Complutense of Madrid, 28040 Madrid, Spain
The deactivation of a solid catalyst may affect in different ways each reaction taking place in a complex network. This creates a variation with time on stream of the product distribution at the reactor exit. To handle data from this common situation, a selective deactivation kinetic model fits the data much better than a nonselective one. Selective deactivation kinetic models are scarcely used because they are often complex and difficult to handle. They also introduce more deactivation kinetic parameters than the nonselective models. Nevertheless, selective deactivation kinetic models are a refinement and are a step forward in the modeling of deactivation kinetics. They might also improve the existing macrokinetic models for commercial reactors. In this paper, several new concepts and ideas are given relating to selective deactivation kinetic models. These concepts are applied to the kinetics of the deactivation of commercial fluidized catalytic cracking catalysts with commercial feedstocks. It is also proven how the kinetics of cracking of the feedstock (heavy oils) is much more affected by the catalyst deactivation than the cracking of the gasoline. A discussion of the results is included. Introduction: A General Discussion on the Selective Deactivation Kinetic Models It is well-known how the deactivation of a solid catalyst not only affects the conversion of the reactants but also may affect the product distribution. A large number of papers have been published on the variation of the product distribution with the time on stream (t) because of the deactivation of the catalyst. These papers were reviewed in 1988 by Corella et al.1 The basic reason of the variation of the product distribution is that the deactivation of the catalyst may affect each one of the reactions existing in a network in different ways. This creates a different variation with time on stream of the yield to each product at the reactor exit. The kinetics of the variation of the product distribution by the catalyst deactivation can be fitted, in principle, by two different models: the selective and the nonselective deactivation kinetic models. If the symbols aj, kj, and rj are used for the activity of the catalyst, kinetic constant, and reaction rate, respectively, of the jth reaction in a network, in a nonselective deactivation model, all of the kinetic constants (kj) or reaction rates (rj) are multiplied by only one and the same activity or deactivation function. That is to say, in this model a1 ) a2 ) a3 ) ... ) aj ) a. On the other hand, in a selective deactivation kinetic model, each kj or rj is multiplied by a different activity (aj) or deactivation function. Therefore, in the selective deactivation kinetic model, a1 * a2 * a3 * .... Work by some pioneers using a different deactivation function, or at least mentioning it, for each reaction in a network is described in refs 2-8. Nevertheless, it is believed that the first rigorous or general model for the kinetics of the selective deactivation model was presented by Corella and Asu´a in 1982.9 For a reaction network under catalyst deactivation, the rate †
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of each reaction was proposed as
(rj)t ) rj aj
(1)
where (rj)t and rj are the rates of the jth reaction at time t (or at Cc or Cp) and at t ) 0, respectively, and aj is the activity of the catalyst with respect to the said jth reaction at time t (or at Cc or Cp). aj has to refer to each elementary reaction in the network and not to a given component, reactant, species, or lump because the overall rate of appearance or disappearance of the component is determined by different elementary reactions (all reactions in which that component, reactant, species, or lump is present), which the catalyst deactivation may affect in a different manner. In some situations, such as (1) when the reactor is differential, (2) when the deactivation is in parallelseries, as discussed in ref 10, or (3) when the composition of the reactant mixture in the catalyst is constant with time, eq 1 can be simplified to
(kj)t ) kj aj
(2)
According to this equation, the catalyst activity with respect to the jth reaction of the network is given by the ratio between the rate constants of such reactions at time t, (kj)t, and at zero time, kj. Equation 1 or 2 has to be used together with a kinetic equation that relates aj with the variables of the process (pi and T) and with the time on stream (t), or with Cc or Cp, such as
-daj,q /dt ) ψj,q(pi,T,aj,q)
(3)
where aj,q is the catalyst activity for the jth reaction in the active sites of qth strength and ψj,q is the so-called function of deactivation. Their structure for different mechanisms of deactivation can be found in, for example, refs 11-13.
10.1021/ie040033d CCC: $27.50 © 2004 American Chemical Society Published on Web 05/21/2004
Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004 4081
Equation 3 may be too complex and is usually used in a simplified form. Depending on the simplification adopted, a different level of confidence or of fidelity to the real mechanism of deactivation is obtained. Assuming, for instance, that all of the active sites have the same strength (homogeneous surface), for the particular case of deactivation by coke in parallel-series [as takes place in the fluidized catalytic cracking (FCC) process], eq 3 may be simplified (even in the case of an integral or nondifferential reactor) to
-daj /dt ) ψj(T,feedstock composition)ajdj
(4)
which, for dj ) 1 and (aj)0 ) 1, becomes
aj ) e-ψjt
(5)
and, for dj * 1, becomes
aj ) [1 + (dj - 1)ψjt]-1/(dj-1)
(6)
equations that correspond to the “level of confidence III” as described by Corella et al.10 For a given catalyst, feedstock, and temperature, these equations have two parameters of deactivation: dj and ψj. dj is the order of deactivation of the catalyst with respect to the jth reaction. For easier mechanisms of deactivation, dj is given9,13 by
dj )
mj + hj - 1 mj
(7)
mj and hj are the number of active sites involved in the controlling steps of the mechanisms of the jth reaction and of the catalyst deactivation for that reaction, respectively.9,13 Because mj and hj may be different for each reaction in the network, dj may be different from one reaction to another. If dj is different for some, if not all, reactions in the network, aj may also be different for each reaction. A selective deactivation then appears as a likely situation. A selective deactivation kinetic model would then be the most reasonable and advisable one to be used in nonsimple reaction networks under some catalyst deactivation. However, this is not the case in real life because selective deactivation kinetic models are very seldom used. Two reasons, at least, may be given to explain why realistic selective deactivation kinetic models are very scarcely used. The first reason is that these models are usually very poorly understood and often difficult to apply because one needs to know, as a starting point, the variation of all kj in the network with t (or with Cc or Cp), which sometimes does not occur. The second reason is the overparametrization that they introduce. For example, in the FCC process there are from the first Weekman 3-lump model3 and models with 4 (ref 14, for instance), 5 (ref 15), 6 (ref 16), 10 (ref 17), and 12 (refs 18 and 19) lumps to models based on 297 species,20 on continuous mixtures, or on compositional models,21 or, under a different approach, on distributions of acid site strengths.22 The 6-lump model, for example, introduces 12 kj (ref 16) to which it would be necessary to add 12 different ψj and 12 dj if the catalyst were to affect each reaction in the network in a different way. A fully selective deactivation modeling would introduce 24 deactivation parameters. On the
other hand, a model for the catalytic cracking reactor, “riser” in this process, of a FCC unit needs to introduce a lot of hydrodynamic parameters (refs 15, 19, 23, and 31, for example) and heats of reaction together with the kinetic parameters. In the case of a 6-lump model, 12 kinetic parameters concerning the cracking reactions together with 24 concerning the catalyst deactivation would have to be introduced. This clearly appears as an enormous overparametrization that has to be “rationalized”. Two of the easiest and often used simplifications or approaches, in the model of a riser or of a whole FCC unit, are to consider all of the cracking and deactivation kinetic equations as being of the first order, which is not scientifically correct when lumps are used (refs 10 and 24, for example), and that there is only one deactivation function, ψ, for all reactions in the network. These two assumptions generate relatively manageable and easy to solve macrokinetic models that are the models mostly used today; they usually provide an acceptable description of the product distribution. Therefore, because selective deactivation kinetic models generate some overparametrization, nonselective (only one ψ used) and first-order deactivation kinetics based models are today the most commonly used, even though they may contain disguised kinetics25 and may not be scientifically correct. Although some scientific and advanced refinements may not be used nowadays in macrokinetic models for industrial reactors, these refinements still provide small improvements that might be used in the future. With this line of argument and with this idea in mind, this paper tries to shed some light on the modeling of the kinetics of the selective deactivation of catalysts. It will demonstrate how this kind of deactivation is the one that appears in the catalytic cracking of heavy oil fractions (the FCC process). Selective Deactivation Kinetic Model Applied to the FCC Process Oil companies have to test periodically the cracking behavior of new feedstocks and of new commercial catalysts. For this purpose, they use advanced MAT tests and/or pilot plants. The comparison of the results is generally based on graphs of yields (yi) to different products (i) versus the conversion (XA) of the feedstock (A). Consider the following reaction scheme that might be a part of a more complex reaction network:
with
-rA ≡ dXA/dτ ) (k1)t(1 - XA)2 + (k3)t(1 - XA)2 ) [k1a1 + k3a3](1 - XA)2 (9) rG ≡ dyG/dτ ) (k1)t(1 - X)2 - (k2)tyG ) k1a1(1 - XA)2 - k2a2yG (10) where A ) heavy feedstock to crack, G ) gasoline, yG ) yield to gasoline, and τ ) space time (of A).
4082 Ind. Eng. Chem. Res., Vol. 43, No. 15, 2004
If a nonselective deactivation model (a1 ) a2 ) a3) is used, eqs 9 and 10 provide
dyG k1 k2 yG ) dXA kA kA (1 - X )2 A
(11)
kA ) k1 + k3
(12)
where
When yG vs XA was plotted for a given catalyst, feedstock, and temperature, only one curve would then be obtained because k1/kA and k2/kA do not depend on the time on stream (t). The slope at the origin of the yG-XA curve (as at XA ) 0 and yG ) 0) leads to
( ) dyG dXA
(≡selectivity of the catalyst toward
XA)0
gasoline at XA ) 0) )
k1 (13) kA
The slope of the yG-XA curve at XA ) 0 enables the calculation of the selectivity for gasoline, k1/kA, for a given feedstock-catalyst-temperature system, which is an interesting datum in the FCC process. When a selective deactivation model is considered, eqs 9 and 10 lead to
k1a1 k2a2 yG dyG ) (14) dXA k1a1 + k3a3 k1a1 + k3a3 (1 - X )2 A This equation relates to the yield of gasoline with the conversion for a given time on stream (effect on a1, a2, and a3) and for a given catalyst-temperature-feedstock (which have an effect on k1, k2, and k3 and on ψ1, ψ2, and ψ3 and, in turn, on a1, a2, and a3). The k1a1/... and k2a2/... ratios appearing in eq 14 may have a different value for each time on stream (t). Different yG-XA curves will be obtained at different values of t. Therefore, the variation of the yield to gasoline, or to any other product, with t (or with Cc) is well explained by a selective deactivation kinetic model. With this model, the slope at XA ) 0 of the yG-XA curves is, from eq 14:
( ) dyG dXA
XA)0
)
k1a1 k1a1 + k3a3
(
