Dichotomies in Catalytic Cracking - Industrial & Engineering Chemistry

Ind. Eng. Chem. Res. 1997, 36, 3323-3335

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Dichotomies in Catalytic Cracking Bohdan W. Wojciechowski† Chemical Engineering Department, Queen’s University, Kingston, Ontario, Canada K7L 3N6

This paper presents an explanation of why the quantification of the mechanism of catalytic cracking has eluded researchers for more than 60 years. The problem seems to lie in a set of dichotomiesspairs of related effectsswhich cause unanticipated changes in the parameter space within which catalytic cracking takes place. The consequences of these separate and overlapping effects are discussed below using our interpretation of catalytic cracking as a chain reaction. Quantitative expressions are derived on the basis of this postulate to describe the activity, selectivity, paraffin-to-olefin ratio, and volume expansion in catalytic cracking and to show how these quantities are affected by the presence of the dichotomies. 1. Introduction We propose that much of the confusion and ambiguity in catalytic cracking can be ascribed to the influence of pairs of related effects that influence the cracking reaction. These pairs, which we characterize as dichotomies, can interact in unexpected ways and lead to a confusing array of differing outcomes in seemingly similar investigations. We begin by identifying the dichotomies. None of the individual members of these pairs will come as a surprise; what casts a new light on the cracking reaction is a new-found focus on their linkagesson the everpresent and highly intertwined consequences of these dichotomies, whether they operate singly or in various combinations. Understanding of these consequences provides insights which are applicable to catalyst development, reactor design, and the interpretation of various aspects of cracking behavior. To provide these insights, the effects of the various dichotomies are interpreted using the recently-formulated chain mechanism of catalytic cracking (Zhao et al., 1993). This paper attempts to explain the wide range of observations reported since studies of catalytic cracking were first initiated. Sixy years of catalytic cracking literature would have to be cited in order to illustrate each and every historic twist and turn of catalytic cracking observations. Since our discussion addresses all that can be found in the existing literature on catalytic cracking, we have chosen instead to keep the list of citations to a minimum. 2. Dichotomies The dichotomies themselves are split into two quite different types, optional and consequential. 1. In optional (either/or, or mutually exclusive), for example, a surface site can be vacant or it can be occupied; an increase in one type requires a one-for-one decrease in the other. 2. In consequential (if this/then that), for example, as surface site density is decreased, the average strength of the remaining sites is increased; there is no general rule as to how strongly the two effects are related. 2.1. Thermal and Catalytic Reactions. The conversion of hydrocarbons at high temperature can proceed by these two distinct but intertwined mechanisms. All industrial catalytic cracking processes, and some laboratory investigations of catalytic cracking, are †

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subject to the simultaneous occurrence of both thermal and catalytic cracking. Both these conversion reactions proceed by chain mechanisms. 1. Gas phase pyrolysis proceeds by a free-radicalchain mechanism of a type first quantified and welldescribed some 50 years ago (Goldfinger et al., 1948). 2. Catalytic cracking proceeds by a more-recentlydescribed ion chain mechanism which takes place on the acid sites of the cracking catalyst (Zhao et al., 1993). The two mechanisms contribute in different measure to reactions of various molecular species. They differ in their contribution to product yields, depending on the temperature of the reaction and on a number of other contributing factors, some of which will be discussed below. The fact that the presence of this dichotomy is often ignored in otherwise careful experimental studies has hindered our ability to quantify the mechanism of catalytic cracking per se. Much literature and quite a few conclusions are muddied by ignoring the presence of the thermal component and therefore confusing its contribution with purely catalytic effects. One thermal reaction which is inseparable from catalytic processes is the thermal elimination of hydrogen and other small paraffins from carbenium ions. This process leads to a dehydrogenation or “hardening” of surface carbenium ions and thence to catalyst deactivation. This matter has been treated quantitatively in considerable detail in considerations of catalyst decay (Wojciechowski and Rice, 1996). 2.2. Disproportionation and Decomposition Reactions of Carbenium Ions. Surprisingly, most of the important processes (i.e. those that yield the major products) in catalytic cracking belong to one of only two types of reaction: (1) disproportionations, which consist of all processes involving the reaction of a molecule with a surface-resident ion, and (2) decompositions, which consist of all reactions which eliminate an olefin from a carbenium ion. 2.2.1. Disproportionations. The disproportionation reactions themselves present two potentially confusing dichotomies. The first is that disproportionation processes properly include both of the following: the protolysis of feed molecules by Brønsted acid protons and the disproportionation of feed molecules with a variety of carbenium ions which take the place of these protons during reaction. For purposes of understanding what we are about to describe, one must therefore think of acidic protons on Brønsted sites as carbenium ions of carbon number zero. A deeper level of dichotomy arises in the second of these disproportionationssin the disproportionations of © 1997 American Chemical Society

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feed molecules with carbenium ions. Such disproportionations can involve either the transfer of a carboncontaining moiety from the feed molecule to the surfaceresident ion or the transfer of a solitary hydride ion (a moiety of carbon number zero). In the latter case we have an example of true “hydrogen transfer”, while in the former we have an ion-molecule disproportionation, sometimes referred to as “dimerization cracking”. Both protolysis and dimerization cracking produce a paraffinic product. Thus, dimerization cracking results in the formation of “excess” paraffins, and in this way contributes to products which are commonly thought to result from “hydrogen transfer” (see mechanism in section 3). 2.2.2. Decompositions. Decompositions also have an internal dichotomy: (a) In one option, a decomposition can leave behind a proton to reconstitute a pristine Brønsted acid site and terminate the kinetic chain process. (b) In the other, decomposition involves β-cracking, leaving behind a smaller carbenium ion. This constitutes a chain transfer reaction in the overall mechanism of cracking. We see that, in a generalized view of decomposition events, both types of reactions belong to one set, with subtypes playing specialized roles in the overall process. Once again, in order to preserve generality, the proton must be considered a carbenium ion of carbon number zero. 2.3. Initiation and Propagation Reactions. The quantification of catalytic cracking in the form of wellordered chain mechanisms throws new light on the many confusing effects observed in this reaction. To see the consequences and cross-influences of the various dichotomies on the elementary steps in the chain mechanism of a cracking reaction, it is necessary to see the essential differences between the two major types of processes in a chain mechanism: initiation and propagation. These two, plus termination reactions, are present in all chain mechanisms, including catalytic cracking (see discussion of catalytic cracking kinetics in section 3). 2.3.1. Initiation Processes. In the catalytic cracking of paraffins, initiation involves the protolysis of a feed molecule by a Brønsted acid proton. The protolysis reactions are one type of disproportionation, as described in section 2.2.1. The initiation reactions differ from all other disproportionations in that they are first order in gas phase concentration and take place on pristine Brønsted acid sites. A generic initiation reaction for a paraffinic molecule is as follows:

CnH2n+2 + H+S- f CmH2m+2 + Cn-mH+2(n-m)+1SThis is a generalized protolysis reaction whose product paraffin can have m ranging from zero to n - 1. What this means is that, for the purposes of subsequent discussion, we must look upon product hydrogen as a paraffin with carbon number zero. The influences of the dichotomies on the rate of protolysis in any one set of circumstances are many. The most obvious is that, as acid strength increases, the rate of protolysis should increase as long as the number of pristine sites remains the same. However, it is rare if ever that this kind of unilateral change can be achieved; in most cases, stronger sites are obtained at the expense of fewer sites. Moreover, the relative rates of the alternative protolysis reactions will remain the same if and only if the increased acidity is obtained by generating a very special distribution of the stronger sites, one

that yields a product distribution which is the same as that obtained using the weaker set of pristine sites. In general, the site strength distribution will not be the same as before, nor will it assume the special form required to keep the ratios among the initiation rates (rates of reactions with differing values of m in the above equation) constant. These two features conspire to make sure that the relative probabilities of the various modes of the protolysis reaction change with all changes in average acid site strength. 2.3.2. Propagation Processes. In catalytic cracking, propagation reactions involve a disproportionation between gas phase molecules and surface-resident carbenium ions. These reactions belong to the set of disproportionation processes described in section 2.2.1, as do the initiation reactions. We see then that disproportionations are subject not only to the dichotomies already listed in section 2 but also to an additional dichotomy: two distinct and critical roles are played by disproportionation in the chain mechanism of the paraffin cracking reaction. The generic propagation reaction is of the form

CnH2n+2 + CmH+2m+1S- f Cm+xH2(m+x)+2 + Cn-xH+2(n-x)+1Swhere x can range from 0 to n - 1 but in all probability does not exceed n - 2. As was the case with the proton in the protolysis reactions, increased acid strength will result in more vigorous reactivity of the carbenium ions in the disproportionation reactions they undergo. In the case where x ) 0, the process is one of hydride abstraction or, as some might have it, a process of “hydrogen transfer”. If the surface carbenium ion which abstracts the hydride has time to rearrange before this disproportionation reaction takes place, isomeric forms of the products are formed. In particular, if the carbenium ion is an ion of the feed molecule (a parent carbenium ion) which has rearranged, the product of hydride transfer is an isomer of the feed. Since at low conversions the gas phase species reacting with the surface ions is most likely to be a feed molecule, this type of propagation replaces an isomerized parent carbenium ion with a new parent carbenium ion, making repeat cycles of isomerization reactions highly favored under initial conditions. Isomerization is therefore an integral part of the chain process and proceeds on the same sites as do the other disproportionation reactions. There is no need to invoke specialized “isomerization sites”. A less obvious fact is that propagation reactions are second order in the concentration of gas phase reactants. That arises because the concentration of carbenium ions is dependent on an equilibrium between gas phase species and the ions. The carbenium ions in turn react with another gas phase species, making 2 the overall order in gas phase concentration. At higher conversions this gas phase concentration effect is enhanced by the accumulation of olefin products, which tend to increase surface coverage by their corresponding ions and thereby enhance the probability of propagation reactions. One can expect that saturated products will be more prominent at higher conversions due to this effect alone, rather than to any hydrogen transfer from the coke on the catalyst surface. Notice that each initiation reaction and each propagation reaction consumes one molecule of feed and produces one paraffin product per molecule of feed con-

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verted (see the expression for Fpa in section 4, Kinetics Consequent on the Chain Mechanism Postulate). Therefore, the initial molar selectivity for paraffins must be equal to 1. This result is a necessary consequence of the fact that both of the feed conversion reactions of the catalytic cracking chain mechanism are disproportionation-type reactions. Notice also that since propagation reactions produce a molecule of paraffin each time a molecule of paraffin reactant is converted, the average molecular weight of the products of propatation alone is the same as that of the feed (see section 4.4). 2.4. Termination and β-Cracking Reactions. These two decomposition reactions have much more in common than is generally acknowledged in discussions of cracking mechanisms: they are the sole producers of olefins. 2.4.1. Termination. Only one kind of decomposition terminates the chain process on a given site: desorption. This takes place when a decomposition reaction returns a proton to the conjugate base on which the ion resides and releases a gas phase olefin. The structure of linear (i.e. nonbranching) chain reaction mechanisms requires that the total rate of these termination reactions is exactly equal to the total rate of initiation reactions as described in sections 2.3.1 and 4.3. Termination and initiation reactions are therefore irreversibly coupled in chain processes. If termination should lag behind the rate of initiation, the overall reaction would speed up until the two rates are equal. In the opposite case, the chain portion of the reaction would be self-extinguishing and only the initiation component would remain at steady state. Anything that changes the rate of termination causes exactly the same effect in the initiation reaction, however unexpected that may be, and vice versa. This can lead to much confusion, since the rate and Arrhenius parameters of the total rates of initiation and termination are the same, and reflect the parameters of the rate controlling processseither initiation or termination. There is no easy way to find out which. In view of this requirement of the chain mechanism operating in catalytic cracking, the initial molar selectivity for olefins (i.e. the probability of olefin formation), in the absence of β-cracking reactions, is going to be the same as the probability of initiation by protolysis. There is no contribution to olefin production from the propagation reactions. The termination reaction is therefore simply a type of decomposition which reconstitutes pristine Brøsted sites:

CnH+2n+1S- f CnH2n + H+SIf we define the kinetic chain length (KCL) as the ratio of the total rate of feed conversion to the total rate of initiation, we see that the paraffin-to-olefin (P/O) ratio in paraffin cracking should be equal to KCL. The KCL or P/O ratio can range from 1, for those reactions which have a high contribution to overall conversion by initiation processes and a low contribution by propagation, to very high values, for reactions in which conversion proceeds mostly by propagation reactions. In contrast, in the cracking of large molecules, where there exists a possibility of multiple cracking events in a single molecule of feed, the P/O ratio can be less than 1. 2.4.2. β-Cracking. The presence of chain transfer reactions, commonly called “β-cracking”, complicates the simple picture of olefin production presented thus far. These reactions are not important in most of the small molecules used in fundamental studies of catalytic

cracking. However, they play a significant role in the cracking of paraffins with a carbon number above 7 and therefore in the cracking of commercial feeds. The generic β-cracking process is as follows:

CnH+2n+1S- f CxH2x + Cn-xH+2(n-x)+1SThis produces an olefin without consuming a feed molecule and does not reconstitute an initiation site. This decomposition therefore forms “excess” olefins outside the initiation-propagation set of processes. The additional olefins produced in this way will decrease the P/O ratio, and their presence in a reaction disqualifies this ratio as a ready measure of the KCL. Notice that a chain transfer reaction or a desorptionsi.e. any decomposition reactionsdoes not consume a molecule of feed but will produce a molecule of product, or even several product molecules, if the original ion is large enough. It is therefore the decomposition reactions that are solely responsible for the increase in the number of molecules in the cracking reaction. The protolysis-desorption reaction couple corresponding to the initiation and termination of the chain process and β-cracking are jointly responsible for the observed reduction in the average molecular weight of products as compared to the feed. Propagation reactions can produce molecules which are smaller than the feed, but the average molecular weight of the products is the same as that of the feed. 2.5. Acid Strength Effects. Changes in the absolute value of the acid strength, even if the distribution of strengths were to remain unchanged, affect the kinetics and selectivity of the catalytic cracking reaction (see section 2.3.1). This is because the acid strength of the active sites affects the height of the energy barrier between reactants and the transition states, as is normal for catalytic sites. On the other hand acid strength does not change the energy difference between products and reactants. This too is normal in catalysis. The dichotomy in this case involves the fact that increasing acid strength connotes a decreasing strength of the conjugate base. 2.5.1. Increasing Acid Strength. Stronger acid sites will obviously accelerate all protolysis reactions. However, they may not speed up those protolysis reactions that require higher activation energies in such a way as to increase their relative contribution to the conversion. Generally, a change in average acid strength or a change in acid strength distribution will change the distribution of paraffinic products formed by protolysis, as well as the distribution of the various types of carbenium ions left behind on the surface. A surprising conclusion, which we will discuss below (see sections 2.5.2 and 2.6), is that the strongest sites tend to spend more of the time covered by carbenium ions and are therefore less available for protolysis. 2.5.2. Decreasing the Strength of Conjugate Bases. A much more subtle and underappreciated effect of an increase in acid strength is the simultaneous reduction in the strength of the conjugate bases on which the carbenium ions reside. This decrease in conjugate base strength will result in a reduction in the ability of the carbenium ions to decompose by β-cracking or desorption, and therefore to terminate chains, reconstitute pristine sites and produce olefins. One can also expect that the activation energy for the decomposition of ions residing on weaker bases will be greater. Simultaneously, weak bases will increase the reactivity of the carbenium ions (not just the proton, a zero-carbon-


number carbenium ion) in all disproportionation reactions, not just the protolysis reactions which are responsible for chain initiation on the acidic protons. The consequences of this strong-acid/weak-base dichotomy are profound. To begin, it results in a reduction in the rate of chain termination by desorption in relation to the rate of propagation. As we noted in previous discussion, in linear chain reactions the rate of termination is equal to the rate of initiation (see section 2.4). The slowing down of desorption means therefore that the rate of initiation is also slowed down. How can this be, on sites of increased acid strength? It can happen because the fraction of the surface covered by carbenium ions increases, due to lower desorption rates from the weak conjugate bases and a consequent increase in ion residence time on the surface. Since the total number of sites is fixed on any given catalyst, the number of pristine (unoccupied) sites is reduced. At the same time, the turnover number per protolysis site may be increased due to an increase in average acid strength. The two effects can combine to give a net reduction or an increase in the fraction of the overall conversion which is due to protolysis. In the terminology used to quantify chain processes, this means that a higher or lower value of the kinetic chain length (KCL) may be observed on catalysts with stronger sites. The effect of stronger sites on the P/O ratio is therefore also unpredictable in the general case. For example, decreases in acid strength have been observed to lead to lower KCL values (Zhao and Wojciechowski, 1993), i.e. to a higher contribution by protolysis to the total reaction products. This is contrary to any intuitive feeling that higher acid strength should lead to a higher contribution to overall conversion by the protolysis reactions. Supporting evidence for this comes from the observation that stronger sites often lead to a higher paraffin-to-olefin ratio and more coke. The higher P/O ratio is due to more conversion by propagation reactions, rather than by hydrogen transfer from coke. The higher coke make in such cases is due to a greater possibility of ion-ion interactions on a surface with higher coverage by ions and due to the increased ion residence times on the surface, which in turn is due to difficulties with desorption from the weak conjugate bases (see section 2.5.2 above). This effect will also enhance the probability of a thermal decomposition of an ion during its extended residence time on the surface. The higher P/O ratio under these circumstances is sometimes explained in terms of a hypothesized increase in a “hydrogen transfer” reaction, which saturates olefins, which in turn are deemed to be “missing” under this hypothesis. The necessary hydrogen is said to come from a “hardening” or dehydrogenation of the coke. Mass balances have shown that this explanation is impossible. The increased residence time of surface ions also leads to an increase in the possibility of ion isomerization or cyclization before a propagation reaction takes place. This will lead to more isomers of the feed and more aromatics being formed, but only if the following dichotomy does not interfere. 2.6. Site Coverage Effects. The dichotomy here is that coverage of the surface by carbenium ions has diametrically opposite effects on the two types of disproportionation processes responsible for feed conversion in catalytic cracking. As surface coverage is increased (1) the initiation reactions proceed on a smaller fraction of the original acid sites and so changes for initiation may be reduced (however, the turnover number for protolysis can increase at the same time

since the remaining protons may be more active); and (2) the propagation reactions are enhanced by the increased concentration of carbenium ions on the surface (this tends to increase the kinetic chain length in the mechanism, and changes in coverage will therefore lead to changes in selectivity; moreover, because the increased coverage, there are more chances for ion-ion disproportionation reactions to take place; this leads to faster coke formation and hence to faster deactivation). The site coverage and turnover number dichotomy are a major source of confusion on the way to understanding the behavior of catalytic cracking. Increased surface coverage may suggest that the overall reaction will slow down because initiation is slowed; however, this is not necessarily so. The observed change in rate and selectivity is a function of the catalyst, the reactant, and of the reaction conditions used. Moreover, the true nature of the effect can be masked by the effect of an increased rate of decay, unless care is taken to observe the initial rate of reaction, free of all decay. Notice that, on a given catalyst, higher surface coverage by carbenium ions normally occurs on the higher-acid-strength Brønsted sites. The most-acidic sites have the weakest conjugate bases and as a result are most likely to be covered by a hard-to-desorb carbenium ion. Thus, the pristine sites which are available for protolysis are usually (i.e. most of the time) not the strongest sites available on the catalyst. The effects of site coverage will be easiest to observe by varying reactant pressure. This should be done by changing the total reactant pressure, not by diluting the reactant. As we will see, diluents have the potential of altering the mechanism of cracking in unexpected ways (see section 2.8). 2.7. Acid Site Density Effects. Low site density on the catalyst surface is generally associated with wide separation between active sites. While it may be possible to formulate solid acid compositions where the active sites are grouped together in dense patches of weak sites, this is not the case for Si/Al molecular sieves where the aluminum atoms do not clump together. At the same time it is known that wide site dispersion results in stronger sites. Thus, site density and site strength constitute another dichotomy. 2.7.1. High Site Density. As site density decreases, the strength of the sites is increased. It can therefore be expected that Si/Al catalysts with a high site density will have weak sites and will tend to promote short kinetic chain lengths, low P/O ratios, and low rates of reaction. 2.7.2. Low Site Density. Low density is connected with high acidity. Strong sites in high Si/Al catalysts will form more paraffins, promote longer kinetic chain length, and give a higher P/O ratio. In general the overall rate of reaction should be increased on stronger sites. This is so because chain propagation processes are generally faster than the protolysis reactions and the fraction of total conversion due to propagation reactions is increased on stronger sites (see section 4.3). However, since stronger sites are obtained at the expense of site density, it will not be surprising if there is a maximum in the overall rate of reaction at some intermediate site density. It is interesting to note that, under this hypothesis, catalyst steaming can be used to reduce site density and increase site strength until an optimum in activity or P/O ratio is obtained. This principle is obviously compromised by the simultaneous desire to achieve maximum catalyst stability, leaving us with a catalyst which is probably less than optimum kinetically, but


may be preferred for other reasons. Efforts to achieve a stable catalyst which is closer to a kinetic or selectivity optimum must be behind much of the ongoing work in cracking catalyst development. 2.8. Diluent Effects. Dilution, in some cases mere contamination of the cracking feed, has unexpected effects on the rate and selectivity of a cracking reaction. It turns out that even a reduction in reactant pressure must generally lead to a change in cracking selectivity. The dichotomy described below is even more complicated than that and is related to two coexisting effects of diluents. (1) One effect arises from the simple reduction in feed concentration caused by the diluent. This effect is present with all diluents and whenever reactant partial pressure is decreased. Dilution reduces the rates of all reactions; however, it reduces the rates of decomposition reactions, which are first order in the gas phase concentration of reactants, to a lesser extent than disproportionation reactions, which are second order in gas phase concentration. Since initiation by protolysis (a disproportionation reaction: see section 2.2.1) is also first order in feed concentration, its rate is reduced to a lesser extent than those of chain propagation reactions. The overall effect is therefore to increase the chain length and the P/O ratio. The reason for this is as follows: the propagation reactions, all of which involve disproportionations between feed molecules and carbenium ions, are second order in gas phase concentration. Propagation rates will therefore be reduced to a greater extent than initiationdesorption or β-cracking, even though propagation reactions belong to the same type of reaction as initiation and are being affected by a perfectly inert diluent. In reactions where the KCL is large, the effects of an inert diluent on selectivity can be large. When the KCL is small, the inert diluent merely reduces the rate of overall reaction. These effects will be temperature dependent, as will be the value of the KCL, and can result in confusing observationsseven if the same molecule is studied under different reaction conditions. Since quite a few literature reports on cracking selectivity and activity involve experiments done in the presence of “inert” diluents used as “carriers” gases, much confusing information is to be found due to this effect alone. The same can be said about the not-sostandard MAT test where various amounts of carrier gas are commonly used. In fact, the extent of dilution is frequently not reported, although it is a factor in both the kinetics and the selectivity of cracking. The effects of a reduction in reactant pressure are exactly the same as those to be expected from the presence of “simple” or “inert” diluents. As we have seen above, these are not a simple reduction in the rate of reaction but can also involve changes in selectivity. (2) The other diluent effect is a “chemical” effect which influences site acidity on the catalyst framework. This takes place without any new products being formed or any evidence of the diluent undergoing a chemical reaction with the feed. The chemical effect of certain diluents seems to change the average acidity of the Brønsted sites without changing site density on the surface. In this way it differs from the effects of catalyst steaming and catalyst formulation as a means of changing site acidity. It seems that both increases and decreases of site acidity may have been observed in the presence of specific chemically active diluents. Oxides of carbon, for instance, seem to reduce acid strength, each in its own

way. The result is that, in their presence, reaction rates are reduced and the kinetic chain length is decreased (Zhao and Wojciechowski, 1993). A more interesting effect is that of steam, which seems to increase the acidity of the lattice-resident acid sites (Zhao and Wojciechowski, 1996a,b). The result is an increase in kinetic chain length, despite the contrary tendency to reduce the KCL by dilution alone (see effect 1 above). This chemical effect is so strong, and appears at such low steam dilutions, that it actually causes the overall rate to increase at low temperatures. At the same time, selectivity for paraffins is increased, particularly for paraffinic isomers of the feed. By extrapolation of this effect, one can visualize a temperature or a diluent which would make a cracking catalyst into an isomerization catalyst. Since steam is present in commercial catalyst crackers at levels sufficient to affect the product distribution, MAT tests may well have trouble reproducing industrial selectivities. Other minor “impurities” in the cracking mixture in a commercial operation, such as hydrogen sulfide, have not yet been studied as to their chemical dilution effect. The problem of reproducing the refinery performance of a given catalyst in a MAT test is therefore made difficult by the fact that a commercial cracker is operating in the presence of steam and various other impurities, some of which will certainly act as chemical diluents. To complicate matters, various chemical diluents may interact nonlinearly with each other to produce effects which are nonadditive. Moreover, these effects will depend on the composition of the feed, since some molecular types are more susceptible than others to these effects. The uncertainty here is a result of a lack of quantitative information on the consequences of the interactions which take place between molecular species during mixed feed cracking (see section 2.11). We note at this point that the effects of steam dilution and of dilution by other polar or polarizable diluents may be more uniform than we now know. Both the increases and decreases in catalyst activity due to dilution may well involve variants of the compensation effect which we will consider next. 2.9. Compensation Effect. This is a dichotomy which is well-known, found in many kinds of reactions, and often ignored. It involves a compensation between the size of the frequency factor and the activation energy. The effect has a deep fundamental justification involving the distribution of energy in reacting molecules and its consequences on the level of organization in the transition state. One variant of the compensation effect is evidenced when one examines the activation energies and frequency factors in a set of homologous reactions and finds that as activation is decreased, the frequency factor also decreases. This kind of compensation can be expected in catalytic cracking if changes in the acid strength of sites result in changes in the activation energy of reactions which take place on these studies. A homologous set of reactions in catalytic cracking consists therefore of any of the elementary reactions of the mechanism when it is observed on several catalysts whose sites have different acid strengths. There are therefore as many homologous sets of reactions as there are elementary processes in the reaction mechanism. It is to be expected that the compensation effect will vary in its particulars from reaction to reaction. As we have mentioned above, the most common form of this effect is when the activation energy is reduced in a homologous set of reactions and it is found that


the preexponential factor also decreases (see, for example, White (1990)). Taking this effect under consideration, we can reasonably expect that, for each of the elementary steps of the cracking mechanism, (1) when acid strength is increased, the activation energy of all the disproportionation reactions taking place on such sites is reduced and, (2) at the same time, the entropy of activation is decreased for the same reactions, with the result that the frequency factors are reduced. The result is that, on the stronger sites, the Arrhenius plot of each elementary disproportionation reaction rate constant will have a lower slope and a lower intercept at 1/T ) 0. Such Arrhenius lines can intersect within the region of reaction temperatures of practical interest. When they do, an isokinetic point arises at a temperature within the range under investigation. Rates at lower temperatures than the isokinetic temperature are higher than they were on the weaker sites, while those at higher temperatures are lower. Hence, the potential for confusion: stronger acid sites can result in lower reaction rates. This is so even for initial rates. The fact that each reaction has its own compensation effect, plus the presence of catalyst decay, will sow confusion unless the correct initial rates are used and one is prepared for changes in selectivity due to a variation in the compensation effect of each of the reactions, on top of the other effects one may have anticipated. 2.10. Pore Size Effects. There are a number of effects connected with catalyst pore size and pore size distribution. Much has been written on this subject, and we bring it up here in order to fill out the set of dichotomies under consideration. Small pores reduce the rate of reaction for bulky molecules, but at the same time they enhance the rates of secondary reactions of the less bulky products. Perhaps the best known effect due to pore size is the sieving effect of small pores. (1) Small and uniform pores act as molecular sieves by excluding large molecular species from access to the interior surface of the particle and thereby reducing their rates of conversion. The interior surface is where most of the active sites reside, and, by excluding large molecules from this region, molecular sieving forestalls the cracking of large molecules. In a mixed feed this means that only small or linear molecules may access the majority of the active sites. Such molecules are “cracked out” of the reacting mixture, leaving branched and other complex molecules largely untouched. (2) Small pores tend to enhance the secondary reactions of smaller molecules found in the products of cracking. They do this by admitting these molecules into the interior and then restricting their rates of diffusion out of the pore volume. It seems obvious that the size of the pores affects more than just the size of the molecules which can enter the interior of catalyst particles. Small pores must also encourage secondary reactions, in particular the reactions of olefinic products, because cracked products consist of smaller molecules than the feed. They also make possible the imposition of stearic constraints on the products formed by these secondary reactions, in this way displaying “shape selectivity” in the kind of products that are favored. In terms of their influence on the chain mechanism itself, small pores inhibit most bimolecular disproportionation reactions, in particular those between bulky carbenium ions and the feed, thereby shifting most of the conversion away from propagation to protolysis. β-cracking is also enhanced since it is a monomolecular

process. As a result, low P/O ratios can be expected when linear paraffins are cracked. Finally, bimolecular disproportionations between surface-resident ions are inhibited, reducing coke make and catalyst decay. Clearly, therefore, changes in pore size will affect kinetics and product selectivity independently and be superimposed on any changes in acid site strength or site density or any other parameter. 2.11. Feed Composition Effects. Catalytic cracking proceeds via a chain mechanism. We can therefore see that in mixed-feed cracking there is a potential for the disproportionation of every type of feed molecule with carbenium ions derived from any another molecule. The cracking process of mixed feeds is therefore very much dependent on the composition of the feed; one could call this a “polychotomy”. The consequences of this polychotomy on the rate of catalytic cracking have been quantified (Kemp and Wojciechowski, 1974). However, it is not clear how mixed feeds will behave with respect to selectivity (see effect 2 in section 2.8 and effect 2 in section 2.10 above). The presence of feed molecules which form stable carbenium ions will, for example, increase surface coverage. This can increase the KCL and perhaps the rate of the overall reaction, as well as enhancing paraffin and coke productionsbut only if the ionic species formed from such molecules react readily with the other constituents of the feed. If they do not, they may simply inhibit catalyst activity by covering active sites without facilitating a chain reaction. The presence of molecules which decompose or crack to yield hydrogen sulfide, or ammonia, or the oxides of carbon will influence the course of the reaction in still other ways: namely, by introducing the cross-influences which arise due to dilution by chemical diluents. Such effects may always remain difficult to quantify or correlate in any general way and are quite beyond our reach at present, given the small data base available to date on this subject. Much more systematic information needs to be gathered on the effects of various chemical diluents on various types of molecules. Nevertheless, we believe there is reason to expect that a blended feed composition can be designed to achieve specific purposes beyond the reach of presently available catalyst modification methods. The flexibility this offers can be enhanced by the purposeful addition or reduction of “chemical” impurities, diluents, or additives. These added flexibilities should contribute to the efficiency of commercial catalytic cracking, making the process more economical and efficient. 2.12. Effects Governing Catalyst Decay. There is a dichotomy in the process of catalyst decay which is due to the fact that coke can be formed both thermally and catalytically. The two processes are quite distinct kinetically and respond differently to changes in catalyst formulation and reaction conditions. (1) Thermal coke of the type we will consider is formed by the elimination of paraffins from carbenium ions. This process yields a gas phase paraffin and a surfaceresident olefin-ion. The process is complimentary to the process of β-cracking in which an olefin is eliminated from a carbenium ion. Coke formation by this process produces a small amount of excess paraffins and leaves behind the lessreactive olefins-ions. There is another type of thermal coke which is formed by the thermal decomposition of physically-adsorbed low-volatility components. Although the formation of this type of coke is very important in commercial operations, we will ignore it in the following discussion.


It is not formed by a process which is closely associated with the catalytic sites under discussion (see decay mechanism section 3). Its effect on catalyst activity is simply due to the mechanical blockage of surface sites by nondesorbable deposits. The effects of this type of coke are therefore connected with the physical properties of the catalyst; they have little to do with the catalytic properties, other than the obvious fact that sites are made unavailable by the deposited coke. This type of thermal coke is the result of a true “side reaction”, one which occurs in parallel with, and quite apart from, the catalytic reactions we are considering. Thermal elimination of saturated species from carbenium ions, which is connected to catalytic processes by virtue of the fact that it occurs exclusively on active sites, will be enhanced by high cracking temperatures and by long surface-residence times of carbenium ions. The long surface-residence times in turn are more likely in catalysts of high acid strength (see section 2.5.2). Coke made in this way is produced by a process which is first order in site density because each elimination event takes place in one carbenium ion, adsorbed on one active site. Thus, catalysts operated at high temperatures, or highly acidic catalysts, will tend to make more thermal coke and to decay rapidly by kinetics which are first order in site concentration. Another pyrolytic reaction of carbenium ions involves the thermal cracking of a carbenium ion to produce a gas phase free radical and a surface-resident radical ion. The gas phase free radical can initiate free radical chains of conversion reactions in the gas phase. If these contribute significantly to overall conversion, they can complicate the interpretation of catalytic cracking results. The radical ion in turn can add an olefin, eliminate an olefin, or abstract a radical (most likely a hydrogen atom) from a gas phase species and thereby become a normal carbenium ion, while transferring freeradical chain propagation to the gas phase by creating a free-radical chain-propagating species in the gas phase. There is little indication at this time that these free-radical processes contribute significantly to conversion or complicate the interpretation of catalytic cracking results based on the ionic mechanism alone. They may contribute to catalyst decay and coke make, in the same way that elimination reactions do: i.e. by a first order decay process. A different catalytic coke-making process can produce olefin ions via the initial formation of diions on the surface. (2) Catalytic coke is made by the disproportionation of adjacent carbenium ions. This produces an excess paraffin molecule and leaves behind a surface diion. The diion can desorb from one site, rejuvenating a pristine acid site and producing an olefin ion on the other side. Since olefin ions and diions will be in equilibrium, it is difficult to determine the origin of any given unsaturated ion of this type, i.e. whether it was formed by a thermal or catalytic reaction. However, in terms of the kinetics of coke formation and of catalyst decay, the two processes are significantly different. To begin, catalytic coke formation is more strongly dependent on site density. This is because, in order for two ions to disproportionate, they must be within reach of one another. Moreover, ion-ion disproportionations are second order processes in site concentration and one can expect that catalysts with high site densities and with large pores will make more of this type of coke and as a result will deactivate more rapidly.

The effects of acid strength on catalytic coke production and catalyst decay are difficult to foresee. As we discussed above (see section 2.5.2) strong sites connote a lower activation energy for disproportionations and a higher activation energy for decompositions. To these effects we must add the consequences and the compensation effect (see section 2.9) and the effects of site density variation (see section 2.7). The three effects are inextricably intertwined in all considerations of catalytic coke make, and since most of the coke made in the cracking of small molecules is catalytic coke, they are intertwined in catalyst decay. Consider the case where site density is reduced, say by steaming. This should reduce catalytic coke because the sites are more widely spaced and site density is reduced. At the same time, the carbenium ions are more active for disproportionation because they require a lower activation energy on the stronger sites. This brings in the compensation effect, which may produce a higher or lower rate constant for coke production at the temperature of the experiment (see section 2.9). Thus, the net effect of a small reduction in site density may be more or less coke make. At some point, however, site density must become so low that one can ignore all other effectssthere will be no adjacent carbenium ions which can react to make catalytic coke. Thermal coke will continue to form regardless of these considerations. The other way of changing site acidity arises when a chemical diluent, such as steam, increases acid strength without changing site density. In that case, the rate of catalytic coke production should go up, due to a reduction in the activation energy of disproportionation, but only if we neglect the compensation effect. However, if the compensation effect lowers the activation energy for coking as well as the frequency factor for the coking reaction, one can end up with a lower rate of coking in a given range of temperatures. This apparently is the case in 2-methylpentane cracking, where both coking and deactivation are slowed down while surface coverage is increased in the presence of steam (Zhao and Woiciechowski, 1996b). The reason for this is a dramatic decrease in the frequency factor for the cokemaking reaction. Why this is so is not clear at this point. 2.13. Quantification of the Effects of the Dichotomies. There is enough variability within the dichotomies listed above to allow a bewildering array of outcomes in any given experiment. In order to narrow the range of possible outcomes and to bring the issues into a focus, we must now resort to a more quantitiative treatment of the catalytic cracking mechanism. We can do this in general terms by examining the generic properties of the chain mechanisms which are present in this reaction. All chain mechanisms share certain properties: for example, the rate of initiation is equal to the rate of termination. Making use of these properties, we can write down equations of general validity for the process of catalytic cracking. We can then examine the effects of various dichotomies on the concentration terms and the rate constants in the expressions describing activity and selectivity in catalytic cracking. 3. Chain Mechanism of Cracking We will now quantify and discuss the effects of the above dichotomies by formulating the kinetics of catalytic cracking in terms of a chain process, using the cracking of 2-methylpentane as an example. This


reaction has been extensively studied on various catalysts under a variety of reaction conditions (Zhao et al., 1993, 1994; Zhao and Wojciechowski, 1993; Bamwenda et al., 1994, 1995). At low temperatures the cracking of 2-methylpentane is known to have a significant part of its conversion due to propagation reactions, while at higher temperatures, conversion proceeds mostly by protolysis. This allows us to see the chain mechanism as it approaches its two limits: pure protolysis and pure disproportionation. The construction of a chain mechanism is a wellunderstood procedure. One begins by identifying the initiation reactions. These must involve only the feed molecule and the available active sites. In catalytic cracking of 2-methylpentane the initiating reaction is the protolysis of feed molecules on pristine Brønsted acid sites. If we agree that such protolysis involves a carbonium ion as the transition state and that no isomerization can take place during this process, then the molecule of 2-methylpentane can be protolyzed in only five ways:

initiation (protolysis) C6H14 + H+S- f H2 + C6H+13SC6H14 + H+S- f CH4 + C5H+11SC6H14 + H+S- f C2H6 + C4H+9SC6H14 + H+S- f C3H8 + C3H+7SC6H14 + H S f C4H10 + C2H 5S + -

+

-

The carbenium ions thus formed can undergo disproportionation reactions with any gas phase molecule, desorb, or undergo an oligomerization with an olefin. If we restrict our considerations to initial conditions where conversion is low, there are few olefins present and decay is not significant, and we can eliminate all disproportionations except those with feed molecules. We therefore write

ions and the feed, but in studies using fully hydrogenated feed this process yields no recognizable products. In the following considerations we ignore the hydride transfer process unless it leads to the formation of isomers of the feed.

C6H14 + i-C6H+13S- f i-C6H14 + C6H+13Sisomerization (propagation) The other important chain processes are the decomposition reactions. Of these, the β-cracking reaction constitutes a chain transfer process. This process does not consume a molecule of feed; it produces an olefin, which enters the gas phase, and transfers the chain propagation role to a new carbenium ion on the surface.

C6H+13S- f C3H6 + C3H+7Sβ-cracking (chain transfer) To finalize the requirements for the quantification of this chain-reaction mechanism, we account for decompositions which produce olefins and reconstitute the pristine acid sites so that they can initiate new chains of reaction. These processes are commonly called “desorption”, a word which tends to hide the true nature of the reaction involved: a decomposition of a carbenium ion into a proton and an olefin.

CjH+2j+1S- f CjH2j + H+Stermination (desorption) Finally we come to a bothersome side reaction with little influence on the product distribution: the surface disproportionation of two adjacent carbenium ions. This event produces a paraffin which is additional to those produced in the chain processes. Fortunately, paraffin production by this route can usually be neglected due to the very small contribution by this source.

CjH+2j+1S- + CnH+2n+1S- f CkH2k+2 + Ci+n-kH2+2(i+n-k)S2-2 surface disproportionation (coke formation)

C6H14 + C2H+5S- f C4H10 + C4H+9S-

Such a process depends on site concentration to the second power. The diion thus formed can go on to grow to a triion and so on, or it can desorb from one of the two sites to release a pristine acid site, which can catalyze a subsequent initiation. The species left on the other site is an olefin ionsan unsaturated ionic species with enhanced possibilities of resonance stabilization and hence a lower tendency for desorption.

C6H14 + C2H+5S- f C5H12 + C3H+7S-

Ci+n-kH2+2(i+n-k)S2-2 f

propagation (disproportionation) C6H14 + C2H+5S- f C2H6 + C6H+13SC6H14 + C2H+5S- f C3H8 + C5H+11S-

C6H14 + C3H+7S- f C3H8 + C6H+13SC6H14 + C3H+7S- f C4H10 + C5H+11SC6H14 + C3H+7S- f C5H12 + C4H+9SC6H14 + C4H+9S- f C4H10 + C6H+13SC6H14 + C4H+9S- f C5H12 + C5H+11SC6H14 + C5H+11S- f C5H12 + C6H+13SPerhaps the most interesting disproportionation is the transfer of a hydride to an isomerized parent carbenium ion. Isotopic mixing studies will some day reveal how much reaction there is between unisomerized parent

Ci+n-kH+2(i+n-k)-1S- + H+Ssite rejuvenation (one-site desorption) The olefin ion can undergo a variety of rearrangements and reactions which lead to coke, paraffinic cyclics, aromatics, other minor products. It also seems that tying up the two sites in this way often leads to the deactivation of both sites and is the principal cause of catalyst decay in pure component cracking, including the cracking of 2-methylpentane. A second method of forming olefin ions which can then become site-poisoning diions is by thermal eliminationsa process which depends on the first power of site concentration and is also a chain transfer process, albeit one which transfers the chain propagating function to a rather inactive species.


CjH+2j+1S- f CkH2k+2 + Cj-kH+2(i-k)-1Sthermal elimination (surface decomposition) Cyclic products of catalytic cracking are the result of the desorption of olefin ions which have undergone monomolecular, internal cyclization. Cyclic unsaturates and aromatics are therefore formed if sequential thermal eliminations of one or more small paraffins, including hydrogen, take place before desorption occurs. Since olefin ions and diions are suspected of being much less readily desorbed than saturated ions, catalyst decay will in general depend on an order between first (decay due to thermal elimination to form olefin ions on single sites) and second (decay due to surface disproportionation of two adjacent ions to form a diion tying up two sites) in site concentration. In gas-oil cracking, where the carbenium ions tend to be large and therefore more susceptible to thermal cracking, the decay fucntion is indeed close to first order in site concentration. In cases where mechanical pore plugging by products is prominent, catalyst decay can be of a higher order than 2. This type of decay is not described by the above elementary processes (see discussion of “ion-ion interactions” in section 2.11). The order of the decay function in cases of pore blocking depends on the average number of sites blocked by a decay (blocking) event, and can be much greater than 2.

where

kp[CS] )

∑p ∑i kpi[CpS]

and [CS] is the total concentration of carbenium ions. This notation presumes that the propagation rate constants (kpi) can be represented by an average rate constant (kp) for each of the propagation reactions. Using this simplified notation for the total rate of feed conversion, we write

rt ) ri + rp ) k0[M][HS] + kp[M][CS] ) (k0[HS] + kp[CS])[M] We now note that the total surface ion concentration for classical carbenium ions [CS] and the protons [HS] can be written as fractions of the total active sites remaining on the surface [HS]0. θ denotes the fraction of all active acid sites which remain unpoisoned and are covered by classical carbenium ions.

θ ) [CS]/[HS]0 ) {[HS]0 - [HS]}/[HS]0 where [HS]0 is the concentration of all remaining active sites on the catalyst. Then, the fraction of sites available for protolysis is

1 - θ ) [HS]/[HS]0 4. Kinetics Consequent on the Chain Mechanism Postulate On examination of the above mechanism, it becomes clear that catalytic conversion of the feed proceeds exclusively via initiation (ri) and propagation (rp) reactions, both of which are disproportionations. We can therefore write the total rate of feed conversion (rt) as a sum of all processes involving these two kinds of reaction:

rt )

∑r0j + ∑rpi

where j and i are the indices for the possible processes of the initiation and propagation. According to the mechanism presented above, each of the rates of initiation is seen to be of the form

r0j ) k0j[M][HS] Each of the rates of propagation is of the form

rpi ) kpi[M][CpS] where p is the carbon number of the carbenium ion and i is the carbon number of the moiety transferred to it from the feed. The above sum of initiation rates can be written in simplified form as

ri ) k0[M][HS] where

k0 -

∑j k0j

For the sum of propagation reactions we can write

rp ) kp[M][CS]

Substituting in the rate equation for concentrations of surface species in terms of fraction of surface covered, we arrive at

rt ) (k0[1 - θ] + kp[θ])[M][HS]0 ) {k0 + (kp - k0)[θ]}[M][HS]0 We can also quantify the effects of catalyst decay using the time-on-stream decay function (Wojciechowski, 1974):

[HS]0 ) [HS]00 (1 + Gt)-N where the subscript 0 refers to the concentration of active sites still available at the time t during the reaction, while the subscript 00 refers to the concentration of acid sites capable of participating in the reaction which were present on the fresh catalyst, before it began to decay. This formulation follows strictly from a detailed consideration of the kinetics of surface disproportionation of adjacent ions following the mechanism describe above (Rice and Wojciechowski, 1991). For the initial stages of reaction, when the time-onstream (t) is close to zero and decay is not large enough to matter, we can neglect the effects of decay and write the expression for the initial rate of feed conversion as

rt ) (k0[1 - θ] + kp[θ])[M][HS]00 ) {k0 + (kp - k0)[θ]}[M][HS]00 This we will call the initial rate of reaction. Clearly, one can become enmeshed in semantics if one chooses to argue that, for this rate to be applicable, some conversion will have had to take place in order for θ to be nonzero and steady state to be established. We will leave such arguments aside, since in most cases steady state is established at very low conversions and in a very short time on stream. At these “initial” conditions the concentration of carbenium ions is at steady state with gas phase olefin concentrations, with the result that


[CS] is dependent on the first power of gas phase concentration via equilibria such as

O + HS / CS The concentration of ions on the surface is therefore governed by an equilibrium between the ions and the gas phase olefins,

[CS] ) Ke[O][HS] where O is an olefin in the gas phase. This leads to an expression relating the rate of overall conversion to olefin concentration:

rt ) (k0 + kpKe[O])[M][HS]0/(1 + Ke[O]) This expression shows that, in reactions where the chain propagation path is important (i.e. when k0 e kpKe[O]), an induction period will be observed as the concentration of olefins builds up from zero, and the function

kpKe[O]/(1 + Ke[O]) asymptotically approaches the value of kp. At the same time, the addition of an olefin to pure paraffin feed which is normally converted by a chain mechanism in which propagation steps play a significant role, will speed up the initial rate of reaction and minimize the induction period by forcing this function to approach the value of kp. In cases where k0 . kpKe[O], the presence of olefins will always slow down the reaction by reducing the number of available sites for protolysis. Thus, extraneous olefins can speed up or slow down the initial rate of reaction. A more detailed development of the rate of the overall reaction in terms of the chain mechanism presented above has been worked out and was used in the interpretation of experimental data (Zhao et al., 1993). However, for the purposes of our discussion, the development given above is correct, adequate and, we believe, more informative. 4.1. Consequences of the Chain Mechanism on Selectivity. The equations describing the rate of reaction give only a partial quantification of the characteristics of a cracking reaction. To fill out our set of useful equations, we note that the kinetic chain length (KCL) is defined as the rate of reactant conversion divided by the rate of initiation:

KCL ) rt/ri ) (ri + rp)/ri ) (k0[1 - θ] + kp[θ])/k0[1 - θ]

By substituting various expressions for the individual rates and for θ in the above expression for P/O, we arrive at

P/O ) (k0 + kpKe[O])/(k0 + kβKe[O]/[M]) In cases where initiation dominates the other terms, the P/O ratio will be one. In the other extreme, the P/O ratio will approach a value of kp/(kβ[M]) at high conversion. 4.2. Use of the RPPs To Quantify Other Details of the Chain Mechanism. More detailed information about the mechanism can be quantified using parameters we call reaction path probabilities (RPPs). These are defined as

xij ) rij /rt ) rij /

∑i ∑j rij ) rij /(ri + rp)

where j is the number of carbons in the moiety transferred to the surface species and i is the carbon number of the surface species itself and includes 0 for the protolysis reactions. In the case of the initiation and propagation reactions an RPP represents the probability that a molecule of feed will be converted by a given process. In the case of β-cracking we have also scaled the rate of each β-cracking process by dividing it by the sum (ri + rp) in order to put the β-cracking RPP values on the same basis as those for the other two processes. The effect of this is that an RPP for a β-cracking process gives the number of such events which take place per molecule of feed converted. In cases where a detailed calculation of the RPPs is possible using experimental data, various other features of the reaction can be calculated from the RPPs. For instance

Fpa ) (ri + rp)/(ri + rp) )

∑i ∑j Xij ) 1

where Fpa is the total molar selectivity for paraffins. The selectivity for olefins is

Fol ) (ri + rβ)/(ri + rp) )

∑j X0j + ∑i ∑j Xβij

The P/O ratio is therefore given by

P/O ) Fpa/Fol ) (ri + rp)/(ri + rβ) )

) 1 + (kp/k0)([θ]/[1 - θ]) ) 1 + (kp/k0)Ke[O]

∑j X0j + ∑i ∑j Xβij)

1/(

while the paraffin/olefin ratio (P/O) is

P/O ) (ri + rp)/(ri + rβ) ) rt/(ri + rβ) where

rβ )

∑p ∑j rβpj ) ∑p ∑j kβpj[CpS] ) kβ[CS]

Here we assume that the β-cracking constants can be represented by an average value kβ; p is the carbon number of the ion undergoing β-scission; while j is the carbon number of the olefin produced. We see at once that P/O is smaller than the KCL if the rate of β-cracking (rβ) is nonzero (see section 2.4.2).

where the sum of the βij RPPs extends over all β-cracking processes involving the breakup of ions of length i to give olefins of length j. The KCL is also available from the RPPs:

∑j X0j

KCL ) 1/

where the sum of the RPPs extends only over the protolysis reactions. We can also define various internal probabilities. For example, we can quantify the likelihood of a given bond being protolyzed (bond cracking probability, BCPi) by


defining this quantity as follows:

BCPi ) r0j /ri ) X0j /

∑j X0j

where the subscript 0j identifies a specific protolysis reaction. Other internal probabilities quantify the likelihood that a given ion will undergo a selected reaction. For example, the probability that an ion of carbon number i will abstract a hydride from the feed, rather than any other moiety, is

IAPi ) Xi0/

∑i Xij

and so on. 4.3. Volume Expansion. The cracking reaction is commonly thought of as being responsible for the formation of small molecules from large molecules. In fact the initiation and the propagation reactions can produce smaller molecules but, as described above, only at the expense of a molecule of feed consumed. Only the decomposition reactions (including desorption) lead to “excess” molecules being formed and hence to volume expansion as well as a reduction in average molecular size. We can quantify the volume expansion factor (Vex) by counting the number of molecules formed per reaction event and dividing this sum by the number of molecules of feed converted

Vex ) (ri + rd + rp + rβ)/(ri + rp) ) (2ri + rp + rβ)/(ri + rp) where rβ is the sum of the rates of the β-cracking processes and ri ) rd; i.e. the rate of initiation (ri) is equal to the rate of termination by desorption (rd) (see section 2.4.1). Using the previously derived relationship for P/O in paraffin cracking and the above equation, we have:

Vex) [(ri + rp) + (ri + rβ)]/(ri + rp) ) 1 + 1/(P/O) ) (1 +

∑X0j + ∑Xβij) ) 1 + Fol

Examination of the above the relationship shows that when the P/O ratio is 1, the volume of the products is twice the volume of the reactants: that is, a volume expansion of 100%. This is what we would expect if cracking produced two molecules of product per molecule of feed converted, for example in a reaction proceeding by protolysis alone. The same ratio can also be observed, by chance, under circumstances where β-cracking just compensates for the “extra” paraffins made by chain propagation. In most cases of purecomponent cracking the P/O ratio is greater than 1, leading to a Vex which is less than 2. Such a ratio indicates that there is a significant chain component present in the conversion reaction, in keeping with the discussion of the P/O ratio presented above. In gas-oil cracking on the other hand, Vex can be as high as 3. In that case the molar P/O ratio must be 1/2. This is to say that there are twice as many olefins as paraffins in the products. Such a low P/O ratio is indicative of sequential β-cracking of at least some of the carbenium ions. In the case of gas-oil cracking these may be the ions of long-chain paraffins or the ions of polyalkylated aromatics being sequentially dealkylated. One view of the P/O ) 1/2 value is that, on average, each feed molecule cracks twice, once by protolysis and once

by β-cracking. This will produce, after desorption of the residual ion, a paraffin and two olefins. A detailed understanding of the composition of a given gas oil will indicate the actual source of the excess olefins. Assessment of the volume expansion factor or the P/O ratio is not dependent on prior knowledge of the nature of the feed or of the catalyst. These and some other measures of the product properties can be obtained by experiment in systems where the feed is of arbitrary complexity. They can then be used to understand the global processes taking place in either pure component cracking or in mixed feed systems, such as gas-oil cracking. The conclusions being discussed are therefore applicable to industrial cracking operations. 4.4. Reduction in Average Molecular Weight due to Cracking. The corollary to volume expansion is a reduction in average molecular weight. Since the volume expansion factor Vex reflects an increase in the number of moles per unit mass of feed, its reciprocal (1/Vex) gives the factor by which average molecular weight is reduced. Thus, for Vex ) 3, as in our example, the average molecular weight of the product is a third of that of the feed.

MWprod/MWfeed ) 1/Vex ) (P/O)/(1 + (P/O)) ) rt/(rt + ri + rβ) We now can see that there will be no change in molecular weight due to propagation reactions alone since the volume expansion factor (Vex(propagation) ) rp/rp) is 1 for this process. For initiation plus desorption alone, that is, for the “classical β-cracking” process, the volume expansion (Vex(protolysis+desorption) ) (ri + rd)/ ri) is clearly 2, and the average molecular weight is halved. 5. Applications of the Kinetic Equations The above equations afford a variety of self-consistent views of the cracking reaction, ranging from detailed considerations of the contribution of individual elementary reactions, to more general overviews in terms of the total rates of selected types of reaction, to interpretations in terms of surface coverage. This makes it possible to consider the qualitative effects of reaction variables in reactions of arbitrary complexity, at times even where the detailed interpretation required to obtain the RPPs is not possible. If the RPPs are available, these and some additional equations allow us to quantify and examine the effects of the various dichotomies in great detail. In those cases where the RPPs can be obtained from experimental data, they can be used to calculate the BCPs and IAPs we have defined above. These quantities represent the options open to individual transition states and should be amenable to confirmation by ab initio calculations of the probabilities of each reaction path using MO or similar methods. To give an example, Table 1 reports a set of RPPs for the cracking of 2-methylpentane at various temperatures. The RPPs reported there can be used in the application of the above formulas and ideas. We will leave it to the reader to extract various quantities according to the above equations and to compare the results to other information they may have or to an intuitive understanding of the events involved. The availability of results across a temperature range also provides an opportunity to examine the relative activation energies and frequency factors between pairs of

3334 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 Table 1. Reaction Path Probabilities for 2-Methylpentane Cracking over USHY reaction path probabilitya for given temp (°C) reaction

RPP

400 °C

450 °C

500 °C

initiation initiation initiation initiation initiation total initiation propagation propagation propagation propagation propagation propagation total conversion β-cracking coking

X00 X01 X02 X03 X04 ∑iX0i X22 X23 X32 X41 X50 X60 ∑i∑jXij Xβ63 Xkc

0.0043 0.0145 0.0047 0.1801 0.0775 0.2811 0.0349 0.0245 0.0075 0.0321 0.0386 0.5712 0.9998 0.0019 0.0080

0.0248 0.0150 0.0046 0.2956 0.1007 0.4407 0.0213 0.0585 0.0148 0.0160 0.0212 0.4195 0.9994 0.0000 0.0074

0.0725 0.0167 0.0086 0.4248 0.1327 0.6553 0.0210 0.0737 0.0309 0.0000 0.0128 0.1658 0.9998 0.0338 0.0065

a

All RPP’s not listed here were found to be zero.

individual reactions by taking relative reaction path probabilities (RRPPs) such as

RRPPi/j ) X0i/X0j ) k0i/k0j ) (A0i/A0j) exp[-(E0i - E0j)] 6. Kinetic Consequences of the Dichotomies 6.1. Effect of Temperature on the Kinetics and Selectivity of Catalytic Cracking. The rate expression for total conversion is of a form which shows that if k0 . kp, then the maximum overall rate of conversion (k0[M][HS]00) will occur at zero coverage by carbenium ions (θ ) 0) and hence in the complete absence of propagation reactions. In that case, and in the absence of β-cracking, the P/O of the products will be 1. It will be lower than 1 if β-cracking is also present. Any carbenium ions which may be present and active in propagation reactions will reduce this maximum rate of total reaction until the lowest rate (kp[M][HS]00) is reached when θ ) 1 and the total product consists of paraffins, or paraffins diluted by any olefins which may be made by the β-cracking of the surface-resident ions. On a given real catalyst an intermediate value will arise, depending on the equilibrium between olefins in the gas phase and their carbenium ions on the surface. In practice k0 < kp in most of the known chain reactions at normal cracking temperatures. Thus, the maximum rate is obtained at full coverage by carbenium ions, while the minimum rate occurs at zero coverage. It is impossible, however, to change coverage without changing site strength, or the temperature of the reaction, so the extent of coverage and all that follows from its actual value is again a function of the molecule under investigation, of the catalyst, and of the reaction conditions. Considering the effect of temperature on coverage, we see that if the formation of carbenium ions from protons and olefins is an exothermic process, coverage by carbenium ions will decrease at higher temperatures. Thus, θ is smaller at high temperatures. Under the assumption that k0 < kp, this will mean that the rate is reduced from what it could have been if coverage had remained constant. At the same time, all rate constants increase with temperature. The observed change in the rate of total conversion will be the consequence of these two opposing tendencies. This will reduce the effect of temperature on the rate of the overall process and may

result in a non-Arrhenius behavior of the overall rate as a function of temperature; even a maximum rate over some range of temperatures is possible. The effect of temperature is somewhat clearer in its influence on the KCL. The activation energy for propagation reactions is normally smaller than that for the initiation (|Ep| < |E0|). Because activation energies have a negative sign in the exponential part of the rate constant, this means that the ratio kp/k0 has a negative temperature coefficient. This ratio is therefore smaller at high temperatures. At the same time, the ratio [θ]/[1 - θ] also decreases as coverage decreases with temperature. The two trends reinforce one another and lead to a rapid decrease in the KCL with increasing temperature. The P/O ratio will also decrease with increasing temperature, whether or not β-cracking is present. The presence of β-cracking enhances the rate of decrease in the P/O ratio with temperature. Since β-cracking tends to have a high activation energy, the rate of β-cracking increases rapidly with temperature. As a result, the denominator in the P/O equation increases even more rapidly than that in the KCL expression, and P/O will show a greater temperature sensitivity than the KCL. 6.2. Effect of Site Density and Strength on Catalytic Cracking. Confusion between cause and effect can also take a place when site density is varied. In Si/Al catalysts a change in site density brings with it a change in average acid site strength. Moreover, it probably changes the acid site strength distribution on the catalyst. Nevertheless, one can make sense of the expected behavior and offer some insights by using the kinetic and selectivity equations developed above. A reduction in the number of sites on the catalyst connotes a lower value of [HS]00. We see from the rate expression that this should lower the rate of conversion of the feed. However, a simultaneous increase in the acid strength of the remaining sites presumably lowers the activation energies of all the disproportionation reactions included in k0 and kp. These offsetting effects can result in an increase or a decrease in the overall rate, depending on how rapidly activation energies are decreased in comparison with the decrease in [HS]00. There are not enough data to address these effects in much detail, but it may be that there is a maximum in the rate of conversion at some intermediate site density. Contrary to what one might expect, it is the stronger sites on the catalyst which are preferentially covered with carbenium ions and hence less available for protolysis. This suggests that the KCL should be higher on a more acidic catalyst, as the [θ]/[1 - θ] ratio will increase with coverage. It remains to be seen if the ratio kp/k0 also increases on stronger sites. It may be that a maximum in the KCL, as well as in the P/O ratio, can occur at intermediate values of site density. There is no reason to believe, however, that any two of these maxima will occur at the same site density. Catalysts must therefore be tailored to achieve the most important optimum for a given purpose or an optimum combination of the various effects. This surely goes part way to explaining, in mechanistic terms, why so many catalyst formulations are available commercially and why so many are in fact necessary. 6.3. Effects of Diluents on the Activity and Selectivity of Catalytic Cracking. Diluents can have both a simple dilution effect and a “chemical” effect on catalytic cracking. The simple dilution effect is easy to understand. It results in a lower concentration of reactant in the gas phase (i.e. smaller [M] and [O]) and consequently a lower population of carbenium ions on


the surface. The result is that both initiation and propagation reactions are slowed down. But, as the rate expression for total conversion shows (see section 4), the rate of propagation is slowed down more because it depends on the value of θ which in turn depends on the gas phase concentration of olefins. Thus, the propagation term is second order in gas phase concentrations and decreases rapidly with decreases in partial pressure of the reactants. At the same time the rate of initiation is reduced much less as it actually benefits from the reduction in θ which appears in this term as (1 - θ), though the complete expression for initiation is also dependent on the first power of gas phase feed concentration. The upshot of this is that selectivity will change, even when the diluent is not adsorbed on the active sites of the surface, as long as there is a significant contribution to the total conversion by propagation reactions. The chemical diluents on the other hand can increase the overall rate of a cracking reaction as well as changing selectivity. They do this if they change the acid site distribution at low dilution ratios. Just how the acid site distribution is changed is not known, but diluents which change the rate of overall reaction up and down, beyond the effects caused by simple dilution, are known to exist (Zhao and Wojciechowski, 1996a,b). A diluent which lowers the acidity of the active sites will cause the activation energies E0 and Ep to increase and make the corresponding rate constants smaller. At the same time it will decrease θ so that reactions with k0 < kp are slowed down by both effects. The KCL may then decrease or increase depending on the effect of the lower site strength on kp/k0. The net result is not forseeable, but, in the case of 2-methylpentane cracking, KCL goes down in the presence of dilution by CO and CO2, perhaps due to such a decrease in site strength induced by the diluent. The chemical diluents hold more promise of excitement in cases where the diluent seems to increase site acidity at low diluent concentrations, conditions where the effect of simple dilution is negligible. In such a case, the value of [HS]00 remains essentially unchanged; θ goes up; the activation energies |E0| and |Ep| go down; and the frequency factors go down (see section 2.9, elementary step 2). Thus, we have the possibility that the rate of overall reaction can go up with a chemically active diluent in the low-temperature region and down in the high-temperature region. This is exactly what happens in the case of low-level steam dilution in the cracking of 2-methylpentane (Zhao and Wojciechowski, 1996a,b). 7. Conclusions The various reactions which constitute catalytic cracking are subject to a number of dichotomies. There are two kinds of dichotomies: “either/or” (optional) and “ifthis/then-that” (consequential). Both types force the cracking reaction to respond to changes in reaction conditions, or in catalyst formulation, in ways which may not agree with what one might expect. Moreover, changes in reaction conditions or catalyst formulation usually cause a change not only in the intended target process, say the rate of reaction, but also in associated

processes, for example selectivity. The result is that a change in process conditions can in fact yield a result which runs counter to that desired. Whether a given result comes about in a given reaction system is reactant- and reaction-condition dependent. To complicate matters even more, several dichotomies can combine to yield a bewildering array of effects which produce contradictory results, even in correctly-done studies of seemingly comparable reactions. For example, confusion can arise when different molecules are studied, because the kinetic chain lengths may be very different in isomers of a given compound, or when the same molecule is studied under different reaction conditions. The confusing effects of combined and overlapping dichotomies, especially when coupled with a lack of proper mass balances in the experimental work, are by themselves enough to explain the long period of murk in the quantification of catalytic cracking. It needs emphasizing that the quantitative arguments presented in the discussion of the effects of the dichotomies must be correct in general for the cracking of paraffins. This is so despite the fact that the formulas we develop are illustrated by an interpretation of the catalytic cracking of a specific paraffin in terms of a simple chain reaction. Even if one does not know the details of the reaction mechanism, the formulas derived above will correctly describe the behavior of product selectivities, etc., in Paraffin cracking. In effect, the formulas simply quantify atomic and overall mass balances from the point of view of chain mechanisms. Any other mechanism one may propose must yield products which are also in mass balance. Literature Cited Bamwenda, G. R.; Zhao, Y. X.; Wojciechowski, B. W. J. Catal. 1994, 148, 595. Bamwenda, G. R.; Zhao, Y. X.; Groton, W. A.; Wojciechowski, B. W. J. Catal. 1995, 157, 209. Goldfinger, P.; Letort, M.; Niclaus, M. Contribution a l’etude de la Structure Moleculaire. Victor Henri Commemorative Volume; 1948; p 283. Kemp, R. R. D.; Wojciechowski, B. W. Ind. Eng. Chem. Fundam. 1974, 13, 332. Rice, N. M.; Wojciechowski, B. W. Can. J. Chem. 1991, 69, 1100. White, M. G. Heterogeneous Catalysis; Prentice Hall International Series in the Physical and Chemical Sciences; Prentice Hall: Englewood Cliffs, NJ, 1990; p 216. Wojciechowski, B. W. Catal. Rev. 1974, 9 (1), 79. Wojciechowski, B. W.; Rice, N. M. ACS Symp. Ser. 1996, 64, 134. Zhao, Y. X.; Wojciechowski, B. W. J. Catal. 1993, 144, 377. Zhao, Y. X.; Wojciechowski, B. W. J. Catal. 1996a, 163, 365. Zhao, Y. X.; Wojciechowski, B. W. J. Catal. 1996b, 163, 374. Zhao, X. Y.; Bamwenda, G. R.; Groten, W. A.; Wojciechowski, B. W. J. Catal. 1993, 140, 243. Zhao, X. Y.; Bamwenda, G. R.; Wojciechowski, B. W. J. Catal. 1994, 146, 594.

Received for review October 11, 1996 Revised manuscript received January 28, 1997 Accepted April 12, 1997X IE960642O

X Abstract published in Advance ACS Abstracts, July 1, 1997.

Dichotomies in Catalytic Cracking - Industrial & Engineering Chemistry

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