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A one-parameter model of catalyst deactivation for FCC modelling
OWX-2SO9/93 S6.00 + 0.00 0 1993 Psrgamon Press Ltd
A ONE-PARAMETER MODEL OF CATALYST DEACTIVATION FOR FCC MODELLING A. K. DAS Indian Oil Corporation, R&D Center,Faridabad,India and B. W. WOJCIECHOWSKI’ Departmentof Chemical Engineering, Queen’s University, Kingston, Ontario, Canada K7L 3N6
(First receiued20 November 1991; accepted for publicationin revised form 19 May 1992) Abstract-A one-parametermodel of catalyst deactivation, based on the distribution of acid site strengths, is proposed.The model describes the deactivation rate as a function of time-on-stream (TOS) and accounts for the very fast initial rate of decay observed in commercial FCC. All of the model parameters are temperature-invariant and are shown to apply to feeds and catalysts not too different from the base case. The proposed model can be used to generate the catalyst deactivation profile at very short times-on-stream (TOS < 6 s) from experimental data obtained at relatively large TOS (> 30 s). Tbe same data is fitted using two forms of the TOS decay function. An examination of the resultant parameters indicates that decay in the first few seconds of TOS, is of a high kinetic order. Subsequently, the catalyst decays by processes which remove active sites by reactions of a lower order, one which is probably related to the chemical mechanism of catalyst poisoning. It is this change in kinetics which will not allow a valid extrapolation to short on stream times when the conventional TOS function, 0 = (1 + Gc)-~, is applied to data at t > 30 s.
INTRODUCHON
Deactivation of cracking catalysts is of primary concern in the laboratory, the pilot plant and, most importantly, in commercial cracking reactors. Though there are various causes of cracking catalyst deactivation, the present work deals with that deactivation due to fouling by coke. A review of published deactivation data shows large variations (Corella et al., 1985) in the observed rate of deactivation with time-on-stream (TOS). Moreover, a high kinetic order for the deactivation reaction is reported at very short TOS (Corella et al., 1985). This very rapid initial rate of decay at low TOS is an important phenomenon of major commercial interest. The problem is made more serious as the rate of decay observed at the long times,on-stream normally studied in the laboratory, cannot be safely used to simulate commercial FCC operation where much shorter times-on-stream are encountered. Furthermore, Wojciechowski and Corma (1986) have shown that both the activity and selectivity obtained in laboratory fixed-bed reactors is distorted by the time-averaging of catalyst decay. A decay expression based on a satisfactory model of catalyst decay which accurately describes the first few seconds of TOS on the basis of the more readily obtainable laboratory decay data at longer TOS, would be very useful since it would allow the use of easily obtained laboratory data to predict the behaviour of commercial units. It is clear from titration and TPD studies that surface heterogeneity is a common phenomenon in cracking catalysts [see for example Mikhail and ‘Author to whom correspondence should be addressed
Robens (1983)]. Use of an overall decay function in such situations has been occasionally reported to fail to simulate experimental data (Onal and Butt, 1980; Bakshi and Gavalas, 1975).To overcome this, Butt et al. (1978) and Corella and Menendez (1986) have proposed the use of the acid strength distribution to describe surface heterogeneity and proceeded to derive decay functions from this. The work of Butt et al. (1978) mostly concerns the separability of the decay function based on an empirical activity distribution. Corella and Menendez (1986), in turn, showed how surface. heterogeneity can account for the change of the decay rate with TOS. Their model contains four unknowns: the acid strength distribution, 5, sensitivity of the activation energy to acid strength, as expressed by yt and ya, and the decay constant I&,. In that work, the parameters are found to be dependent on temperature and, thus, cannot be readily used to simulate the behaviour of the near-adiabatic conditions encountered in commercial riser reactors. More important is the fact that there are many unknowns in the model which must be evaluated for each new feed, temperature and catalyst system. The evaluation of each set of model constants demands that accurate deactivation data be obtained for both short and long times-on-stream. This is not an easy matter in practice. In a more recent development, Rice and Wojciechowski (1991) proposed a very different model of decay based on the inhibition caused by the accumulation of less and less reactive surface species. They have shown that in the cases where such inhibition is offset to some extent by the occasional restoration of the site activity to its pristine condition, as by a
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A. K.
1042
DAS
and B. W. WOJCIECHOWSKI
hydrogen transfer followed by desorption, two distinct episodes of decay can be distinguished. The first rapid decay, characterized by a high decay order if the TOS function is applied, is due to the rapid establishment of quasi steady-state coverage of the pristine active sites by hydrocarbon species of lower activity than the original pristine sites. These lower activity sites, based on adsorbed carbenium ions, proceed to decay more slowly as their average activity level continues to decrease with TOS. It is this second stage of decay which is commonly observed in the laboratory. In this paper we develop an equation which attempts to model both stages of decay from observations made only on the second stage of decay. The model we describe below is based on premises similar to those of Corella and Menendez (1986) but contains only one unknown parameter: Four other parameters which appear in our model are insensitive to a reasonably wide range of changes in feed and catalyst properties. More importantly, none of our parameters varies with temperature, thereby making the modelling of commercial semi-adiabatic conditions much easier. THE KINETIC
where nr is the concentration of active sites in the range q to q + dq. (9) The rate of feed conversion is taken to obey the rate expression Y‘J,=o = k&G.
(3)
It is important to note that in a homologous series of cracking reactions, the order m will vary with feed composition, temperature and catalyst. Pachovsky and Wojciechowski (1971) have shown how to use such an approach to take account of the effects of refractoriness. The method of accounting for system heterogeneity is based on the theoretical work of Kemp and Wojciechowski (1974). With these assumptions, eq. (1) can be rewritten as Yq = (k,p%,
(4)
where a, is the activity of sites with energy q. Assuming the activation energy for a cracking reaction to vary linearly with the heat of chemisorption of the active site, we can write
MODEL
Catalytic cracking is a very complex process. The introduction of surface heterogeneity makes it even more difficult to treat the problem systematically. Some of the assumptions which help in making the problem trackable were made by Corella and Menendez (1986) and will be used here to develop our expressions for catalyst decay. We assume that:
(1) The catalyst is monofunctional and diffusion free.
(2) Heterogeneity exists in the activity of the catalytic sites. (3) Catalyst deactivation is somehow connected with coke. (4) We will consider only the main reaction: Feed + Product + Coke so that coke is a primary product of the reaction. (5) Decay is assumed to be non-selective. (6) Each active site is characterized by its acid strength 4. (7) Separable decay for each individual site is applicable so that the rate on each site can be written as Yr = (r,lt=o)(o,)
(1)
where y4 is the rate and a4 is the activity on sites of strength q. (8) The overall reaction rate is the summation of rates on all sites
k, = k0 exp (-
E, - B&/R T
(5)
where k, is a temperature- and acid-strength-independent frequency factor. This assumption presupposes that the strength of chemisorption on a site does not affect the configuration and, hence, the entropy of the transition state. The only effect of site strength is to change the energy required to cause reaction. Individual active sites may decay by first- or higherorder processes. Studies of pure components have generally shown orders around two, while mixed feeds show decay orders ranging from one up to more than two (Wojciechowski and Corma, 1986).The equations we develop here are based on first-order decay as a function of site concentration. Thus, as = exp (-
kdp t).
(6)
We believe that the change of k,, with temperature and acid strength is not as simple as that assumed by Corella et al. in their model (1985). As found by Pachovsky and Wojciechowski, k,, does not follow an Arrhenius relationship. Corella et al. (1985) have also shown that the activation energy for deactivation (&) changes with acid strength. At the same time, it was shown by many authors [e.g. Moscou and Mone (1973)] that strong sites are responsible for more coke than weak sites (Barthomeuf, 1979). In short, temperature and acid strength both have complex influences on the deactivation constant. For this reason, we assume that both the pre-exponential factor and the activation energy of deactivation increase with increasing site strength. To explain our assumption, we first look at the proposed mechanism of coke formation in gas oil cracking.
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One-parametermodel of catalystdeactivationfor FCC modelling MECHANISM
OF COKE FORMATION
amount and nature of the total coke formed during catalytic cracking is dependent on the type of feed, the nature and strength of active sites and on the reaction conditions. There is little general agreement in various reports on coke formation but a few points are clear.
rate constant for such a system is represented by
The
(1) Olefins and poly-aromatics are the primary contributors to coke formation.
(2) Cracking, condensation, cyclization, hydrogen
transfer and &hydrogenation are all steps leading to coke formation. (3) The higher the acid strength of the site, the lower the activation energy for conversion and the lower the coking activation energy. In other words, at higher temperatures strong sites tend to produce less coke (Blue and Engle, 1951; Walsh and Rollman, 1977). (4) As shown by Langner (1981), coke formation occurs by two distinctly different paths. (0 By tde formation of non-diffus& high molecular weight hydrocarbons. This phenomenon dominates at low temperatures or on weak sites where the probability of /3 scission is low. The coke formed by this path contains more saturates and its deactivation efficacy appears to be rather low perhaps because these species can take part in chain processes. (ii) At high temperature or on sites with strong acidity, most coke precursors desorb from the site very rapidly. Some of these precursors, nonetheless, dehydrogenate or fuse together to produce “aromatic coke”. If this occurs, the coke precursors lose their ability to promote reaction via the chain mechanism and gradually lead to a loss of activity by a process of increasing inhibition. The “inhibition” picture of decay suggests that some or most sites initially acquire carbenium ions whose activity to conversion is lower than that of the pristine sites. This is responsible for the initial phase of rapid decay. Subsequently, these carbenium ions change into less and less active forms thereby causing the second, slower phase of catalyst decay normally observed in laboratory studies. The dual coking mechanism illustrates the fact that the absolute amount of coke cannot be correlated with catalyst deactivation in any general way. Both the amount and nature of coke must be considered. (5) In a homologous series of reactions like those associated with coke formation, the free-energy change, AG, often remains almost constant for different reactants. This compensation effect occurs when both the frequency factor and the activation energy change so that an increase in one is echoed by an increase in the other. The
k = k,exp(ASjR
- AH/RT)
(7)
where AS and AH are the changes in entropy and enthalpy of the system. In the case of compensation, both AS and AH change in the same direction as reactants in a homologous series are changed. We will assume that both follow a linear relation with 4. Therefore, we write the deactivation constant kdq as k, = k,,exp(B,q/R)exp(-
&q/RT)
(8)
where B1 and & are two constants of proportionality and k,, is a site-independent pre-exponential term. Equation (8) can be rewritten as k, = k,,exp(-
Bzq/RCl/T-
IlGl)
(9)
where & = T,B,. The activity of the catalyst at any time t is defined as rate of reaction at time t - ~ rate of reaction at t = 0 and, hence,
a=
a = Y/YO
(10)
4ln n,~. dq I ;:
(11)
s ga
n,y,o dq
Equation (11) is our defining equation for catalyst activity. THE SITE DISTRlBUTlON
Butt et al. (1978) have examined expressions for various acid strength distributions. Corella and Menendez (1986) have applied these distributions and found that a Gaussian distribution fits the measured FCC catalyst strength distribution very well with u = 4000 kcal/mol in eq. (12). This was confirmed by the work of Pratt (1982). A Gaussian-type distribution will, therefore, be used here: n,=n,exp[-
l/2(4-F’2)1].
Equation (11) can now be rewritten as
a=
*In “.Y~o ar dq I ‘O ‘I”. n.y.0 dq Im
(12)
A. K. DAS and B. W.
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WOJC~ECHOWSKI
and substituting from the above we have
cqm%e*p(+
Bd,qlRT)exp(- kdot)exp{(- B2qIWC11T- l/Gl)dq
%
exp(&alRT)da
where fi,, = n&t,-, In the normalized form,
J0
n,=exp[-
iiRexp(y,l/RT)dA
1/2rq)s]
(14)
(13 Yk =
A4m
- da/dt = k,a”.
Yd= ,&a Equation (13) is not as simple as one might like and would be of little use if it were not for the fact that we find we can correlate a range of systems using only one parameter, kdO_ It is worthwhile to compare eq. (13) with the model 3 equation of Corella and Menendez (1986) where the activity is given as 1 c
ii,‘W’(&/R~)exP
chain cracking. If we assume that the concentration of carbenium ions is constant on the reacting surface with TOS and conversion, then we can write the decay equation as
[(-
kd,~)exP(~dA/RT)l
a
(13’) using a notation similar to that of eq. (13). We note that all the terms of eqs (13) and (13’) are the same except for the term for the activation energy of decay. Physically, this difference is critical and is best understood by considering the temperature sensitivity of eq. (13). In decay governed by eq. (13’), the deactivation rate will decrease with an increase in site strength whereas the reverse is predicted by eq. (13). In fact, experimental data presented by Corella et al. (1985) confirm that the deactivation rate increases rapidly with an increase in site strength. This happens in our model for T> To. To see the mechanistic behaviour which lies behind the semi-empirical form of eq. (13), we turn to the TOS formulation. The standard “sudden death” TOS description of decay is based on the assumption that activity is directly proportional to the total number of all active sites. The loss of activity is then directly proportional to the loss of sites by some agent formed in the cracking reaction. This agent is a portion of “coke” and is made from precursor species which are indistinguishable from carbenium ions involved in
(19)
The value of n is 1 for cases where one site is lost per deactivating event, 2 if a two-site mechanism is involved or > 2 if pore blockage is the agent of deactivation. We can also write eq. (19) as - da/dt = k,a + k,a2 + kdam.
(20)
If n is a free parameter in eq. (20), we might as well return to eq. (19X integrate and obtain u = (1 + Gt)-N
(21)
where G = k,(n -
1)
(22)
N = l/(n-
1).
(23)
Equation (20) can also be derived by considering a decay mechanism, a gradual inhibition of active sites with possible reactivation, as put forward by Rice and Wojciechowski (1991). As shown there, occasional reactivation of active sites will lead to a change in the slope of the activity-time curve to produce two regions of catalyst decay. Both regions can be represented by functions of the type given by eq. (21), each with its own parameters, or by the detailed formulas presented by Rice and Wojciechowski or, it turns out, by eq. (13). We see the relationship between eq. (13) and the inhibition-dependent decay model to be as follows. Both models visualize rapid initial loss of activity; eq. (13) attributes this to the rapid loss of a small population of strong active sites. Thereafter, the decay proceeds more slowly in an exponential or hyperbolic fashion according to the form of the acid strength distribution of the remaining active sites. The inhibition model does not assume a preexisting distribution of activities and the inclusion of such a distribution will not change the predictions of the model. Instead, it assumes that the total activity of a catalyst consists of that due to pristine sites plus that due to
One-parameter model of catalyst deactivation various adsorbed carbenium ions which propagate “chain cracking”. The pristine sites are more active than the carbenium ions and it is the covering of these pristine sites by carbenium ions which is responsible for the initial rapid loss of activity. The subsequent, slower loss of activity is due to the chemical changes in the population of adsorbed carbenium ions. With time, this population becomes less reactive in the chain cracking process and in the limit completely poisons the pristine sites. The result is loss of activity due to a gradual inhibition of sites rather than “sudden death”. The generalized TOS decay function (Pachovsky et al., 1973) assumes that all processes in eq. (20) are active and the experimental value of n will reveal which is most important. In fact, most pure hydrocarbons on Si /Al, LaY and HY show values of n = 2 (Abbot and Wojciechowski, 1987). Cracking on HZSM-5, however, shows n % 2 suggesting that pore blockage is the decay mechanism for this catalyst (Fukase and Wojciechowski, 1988). In the following, we will investigate the fit of eqs (18)-(20) with n = 3, for catalyst decay data obtained from Corella and Menendez (1986). NUMERICAL
COMPUTATION
Equation (13) must be solved in order to obtain the activity vs time relationship. It contains five unknowns: 5, yL, yd, T, and k,,. If we have a suitable measure of the acid strength distribution of the catalyst, 5 may be calculated independently. The other four unknowns, or all five if t is unknown, are obtained from a least-squares fit of experimental data. The most important step in this is the computation of the integral which contains ill-behaved functions. The Gauss-Chebychev method used by Corella and Menendez (1986), seems to be the best method of integration in this case, with other methods giving poor results. A non-linear Marquardt method was used to find the best fit to experimental data. The experimental data themselves have been taken from Corella and Menendez (1986) and Corella et al. (1985). The sum of squares of residuals was minimized in computing the optimum parameters. The models based on eqs (19) and (20) are much simpler to use and require no special precautions. EXPERIMENTAL
DATA
activity function given by eq. (13) was fitted for four unknowns yk, yd, To and k,, using < and the initial values from Corella et al. (1985). To was taken to lie somewhere in the range of temperatures used for cracking since decay has been found to increase or to decrease with temperature depending on the system (Wojciechowski and Corma, 1986) suggesting that the change from positive to negative dependence lies in the range of experimental temperatures. Therefore, only yd, y, and k,,, were varied to fit the a vs I curve in Fig. 1. Because the data was hard to read from the published figures (Corella et al., 1985), the ‘experiThe
for FCC modelling
1045
t. min --) Fig. 1. Activity vs TOS for catalyst MZ-7P and gas oil GOII at 520°C. Solid line shows fit obtained using eq. (13) to data Points from the work of Corella et al. (1985). The parameters used are reported in Table 1.
mental” data was calculated using eqs (47) and (48) of the above-mentioned paper to produce the a vs t curves at various temperatures. We note that a significant difference exists in the final (I vs t curves depending on whether model 3 or model 5 is used [eqs (21)-(23) or eqs (47) and (48)] in the reference. To obtain all other data, experimental points were read from original data in Fig 8 of Corella et al. (1985). The values tabulated for various model constants in the source (Table 1, Corella and Menendez, 1986) did not seem to fit these data. We realize that these are not entirely satisfactory procedures as in obtaining the parameters of our model, in some cases we are attempting to fit the function of model 3 proposed by Corella et al. (1985) while, in evaluating other experimental data, we are dependent on digitization of graphical data. Any statistical evaluation of our fit is of little, if any, use in this case. RESULTS
Experimental data obtained on the MZ-7P catalyst using GO-II at 520°C were fitted by eq. (13) to obtain ya, yr, To and kdo. Figure 1 shows that our model fits the data very well. That is to say, our model behaves exactly the same as Coreila’s model 3. Once the parameters were obtained for this catalyst, feed and temperature, we find that eq. (13) can be used to fit the a vs t behaviour for other reported reaction temperatures for this feed. Figure 2 shows the fit of calculated and experimental activity at various times on stream for the same system at 480, 500 and 540°C. The parameters used are those shown in Table 1. Only the temperature was changed. Models based on eqs (19) and (20) had to be fitted separately to each data set as the parameters are temperature-dependent. Parametric sensitioity
Since the mechanism of coke formation is almost the same in all cracking reactions irrespective of feed,
1046
A. K. DAS and B. W. WOICIECHOWSKI
CAT. OIL: x A . -
M27P GOII 4E%o*c 500°C 540°C
t
t
a
a
0
I.,
0
I
I
I
I
I
I
I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 0.1 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9
1 I
t,min-
t. min --) Fig. 2. Effect of temperature on 509°C and (0) 540°C. The gas oil is MZ-7P. Only the temperature has The parameters remain as for Fig.
activity.
(x) 480-C,
(4)
GO-II and the catalyst is
been changed in eq. (13). 1. Points represent data
from Corella et al. (1985).
Fig. 3. Effect of the decay constant kdoon the morphology of activity curves. Curves l-4 correspond to kro = 0.00462 0.011, 0.023 and 0.090 min-‘, respectively. All other parameters are the same as shown in Table 1 for GO-II on MZ-
7P.
we may suppose that yd and T, should not change with the system. There is a suggestion of this in the work of Corella and Menendez (1986), where ya remained constant for various feeds and catalysts. A priori knowledge of catalyst strength distribution can, in principle, be used to estimate the value of {, which is independent of the temperature. Therefore, only k,, and yr may be expected to change. The effect of kdo on the a vs t curve is shown in Fig. 3, keeping all other parameters constant. Figure 4 shows the effect of yk on a vs t. We see that the sensitivity of the activity to site strength, as measured by y,,, is small. Comparing Figs 3 and 4, it is clear that the behaviour of the a vs t is similar for variations in yk and k,,, at least in the neighbourhood of values examined here. This means
1.0 0.9 0.8 0.7 0.6 t a
0.5 0.4 0.3 0.2 0.1
0 0 0.1 0.2 0.3
that kd,, can serve as the one and only parameter which needs to be adjusted to fit data for various feed,
temperature and catalyst combinations.
Table
Eq. (13) model
‘All parameters
0.5
0.6
0.7
0.8
0.9
Fig. 4. Effect of the reactivity parameter yI = /3kqmon the morphology of activity curves. Curves 1-3 correspond to yt
E&t offeed and catalyst Having established the values of <, yh, Y,,and T,, we can fit a variety of experimental a vs t curves obtained with different catalysts and feeds using k,, as a parameter. This is illustrated in Fig. 5, where the a vs t curves for two different feeds and catalysts have been fitted by changing k,, only. The experimental data for these systems was also obtained from the work of Corella et al. (1986).
Conditions
0.4
t. mine
= 2.5, 7.5 and 12.5 kcal/mol. respectively.All other parameters are as in Table 1 for GO-II on MZ-7P.
Site selective decay In eq. (13), the fast decay at time = 0 and the reduction of the decay rate with TOS can be understood to be the result of different rates of decay for active sites of different acid strengths. Figure 6 represents the contribution to the instantaneous activity
1. Values of model parameters’
Feed Catalyst
GO-II MZ-6s
GO-II MZ-7P
ys(kcaI/mol) y (kcal/mol) 5 To (K) kdo(min-‘)
25.0 7.5 0.165 481.0 O-0332
25.0 7.5 0.165 481.0 0.0462
are temperature-invariant.
GO-AV MDZ-7P
2% 01165 481.0 0.023
One-parameter model of catalyst deactivation for FCC modelling
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0.9 1.0 t.
min --+
Fig. 5. Fitting of systems consisting of various feeds and
catalysts. Curve 1 is for GO-AV on MDZ-7P at 520°C using k,, ; 0.0332 min-I. Curve 2 is for GO-II on MZ-6S ai 520°C using kdo = 0.023 min- ‘. All other parameters are the same as for GO-II on MZ-7P at 520°C in Fig. 1 and Table 1.
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of various active sites with changing TOS. Initially, almost 60% of the activity is contributed by the strong sites, but within 2 s, about 50% of the strong sites are decayed. After 30 s, most of the activity comes from medium and weak sites. Interestingly, a similar conclusion is reached by starting with an entirely different decay mechanism; the gradual inhibition of sites by a less and less efficient chain process, as proposed by Rice and Wojciechowski (1991). They have shown that a catalyst with a homogeneous initial surface will also show such a behaviour, as pristine sites on the framework are at first rapidly reduced in activity by the attachment of carbenium ions. This phase is followed by a slower reduction of activity of the adsorbed cations due to reactions such as dehydrogenation and cyclization. Although the two models differ from one another in detail, they lead to similar conclusions and the model proposed here seems to offer a more readily applicable formula. DEXXJSSION
I
1.01
0.9 0.8
0.6
t
0.5
a
0.4 0.3 0.2 0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fig. 6. The contribution of sites of various strengths to the total activitv as TOS increases.At t = 0 much of the activitv is due to strbng sitesas shown by curve 1. As TOS inere.a& to
t = 0.03, 0.10 and 0.30 min the distribution
of surviving active sites shifts to lower strengths and narrows.
Table 2. Multiple Cotiditions
Fed
site decay model constants
GO-II MZ-7P 520
GO-II MZ-7P 540
GO-AV MZ-7P 540
42.3 0.8 1 34.39 2.23
57.23 0.78 44.7 2.28
67.1 0.78 52.4 2.28
29.15
0.75 12.5 25.0
0.70 12.0 47.0
0.70 12.5 62.0
0.75
GO-II
MZ-7P Catalyst Temperature (“C) 500 Hyperbolic decay constants [eq. (21)]
Multiple
decay
(W
N kd (min-‘) m k, (min-‘) k, @in-‘)
constants rw.
G @in-‘)
n =
31
k, (min-‘)
In the heterogeneous model of catalyst decay, the sole adjustable parameter kdOhas been made to account for all the effects caused by changing feed and catalyst. In that sense, it is a “lumped” parameter and despite the obvious advantages of this approach to decay rate modelling, we can extract little mechanistic interpretation from the variation of k,,. The TOS model is more cumbersome in that all its parameters are temperature-dependent. Nevertheless, they can also be more informative as to the nature of the processes occurring on the surface. For example, Table 2 shows that the TOS exponent N and, hence, n, the order of the decay, is fairly constant over the range of systems studied. The “lumped” orders of the decay in the various systems are grouped near 2.30, indicating that similar mechanisms are responsible for catalyst decay in all the systems and that some higherorder (> 2) decay process is present; presumably pore blocking. When we attempt to break down the TOS expression into its constituent terms, as per eq. (20), we must assume the value of n, the number of sites lost per average pore blocking event. No quantitative information exists on this matter and we have chosen
0.77 22.7 2.29
8.5 15.0
GO-II MZ-6s 520 47.3 0.73 34.77 2.36 0.75 11.5 24.0
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A. K. DAS and B. W. WOJCIECHOWSKI
n = 3. With this assumption, a satisfactory fit is obtained with the rate constants for first- (= k, ), second(= k,) and third-order (= k,) terms as shown in Table 2. We now consider the relative magnitudes of k,, k2 and k,. Clearly, the higher the order of a reaction, the more rapidly its rate decreases with the extent of reaction. In a mechanism where three parallel reactions of order 1, 2 and 3 are present, the high-order reaction will be significant early on in the process only if it has a large initial rate constant. We see, therefore, that, in all three systems, third-order decay will dominate the loss of activity in the initial stages of the reaction. We interpret this as indicative of pore plugging being the dominant form of decay in the first few moments on stream. This is followed by secondorder decay, as is found for most pure components. This second-order decay dominates throughout most of the test period and weighs heavily on the observed average order. Finally, at long times-on-stream, firstorder decay takes over as site density is depleted to the point where few site pairs are available. The temperature effect on rate constants k, and k, is small or zero. This we take to indicate that decay which proceeds by a chemical process on the catalytically active sites requires essentially no activation energy. It simply seems to be a stochastic process governed by chance “malignant” reactions of coke precursors. The k, value, the one that accounts for pore blocking, has a strong temperature dependence. This suggests that pore blocking involves a free radical, uncatalyzed surface reaction dependent on normal free-radical activation processes. Differences between the catalysts are also reflected in the values of the ks. MZdS has larger pores than MZ-7P, and we see that, whereas k, and k, are similar for the two, k3 is smaller by a factor of two on the large pore catalyst. We conclude that small pores are easier to block. Work on HZSM-5 confirms this very clearly (Fukase and Wojciechowski, 1988). Finally, the gas oil GO-AV is much lighter than GO-II, and we see that pore blocking by this feed is much reduced while k, and k, are not affected as strongly. In summary, all three models describe decay adequately. The heterogeneous model is clearly the one which requires the least number of parameters but requires complex calculation procedures and the establishment of four semi-fixed parameters. The standard TOS model is simple to fit and requires two parameters. It may fail at very short times-on-stream if the initial decay is very rapid and data is gathered from very short to very long timeson-stream. For that reason, it cannot be used for riser cracker simulation if the decay parameters were obtained at long times-on-stream. The detailed TOS model requires three parameters, gives an adequate fit and reveals a wealth of mechanistic information. It is to he preferred for research purposes in gas oil cracking but requires data from short times-onstream to obtain parameters valid for short on-stream times.
We propose that the model described by eq. (13) is the most convenient for predicting that behaviout at commercially important short TOS while only requiring data obtained from conventional MAT or fixed-bed type experiments. This useful capability comes from the fact that the “constant” parameters 5, y,,, yk and To are largely responsible for the shape of the curve at short TOS while kdo, which determines the rate of decay on some absolute scale can be obtained from data at longer TOS. CONCLUSIONS
The heterogeneous model developed here is based on the assumption of a distribution of activities on a cracking catalyst. Its advantage over similar models in the literature (Corella et al., 1985; Butt et al., 1978) is that it allows activities of a range of catalyst-feedstock systems to be modelled using only one variable parameter kdo. Temperature effects are accounted for by simply using the appropriate absolute temperature in the equations. This is an attractive property for the simulation of commercial cracking operations which do not take place at isothermal conditions. Computational difficulties are readily overcome by the use of computers, whereas considerable experimental difficulty is avoided by being able to model the near-adiabatic operation of a riser cracker, without the need to establish model parameters at a variety of temperatures, at short times-onstream. Although the number of parameters in this model is larger than in model 3 of Corella et al. (1985), we found that for purposes of commercial interest yr, y,, and To remain almost constant. < is obtained from experimental data on acid strength distribution. Thus, only k,, remains as an unknown to be determined by experiment. Therefore, in a situation where the feedstock, catalyst and process conditions are not much different from some initial base case (whose parameters are known) it is possible to determine k,, even from long TOS data and to use eq.113) to predict short TOS decay kinetics. The detailed TOS model is less useful for reactor simulation as it requires three temperature-dependent constants. It is, on the other hand, more informative regarding the nature of the decay process. Both approaches seem to fit experimental data adequately. Acknowledgements-Thiswork was supported by the financial aid from UNIDO and iointlv oraanized bv Indian Oil Corporation, Faridabad, India “and- Queen’sv University, Kingston, Ontario, Canada. We thank Dr. S. Ghosh of Indian Oil for his valuable suggestions at the beginningof this work. NOTATION a
E G k&
KY
activity of sites activation energy for the conversion decay parameter in the TOS decay function rate constant for decay of sites of strength q rate constant for conversion on sites of strength q
One-parameter m
model of catalyst deactivation
exponent in the rate expression for conversion
N
decay
n
exponent in the rate expression for decay number of sites of strength between q and q
a,
+
PA 4 Greek A
Y
e
exponent
in the TOS
decay
function
4
partial pressure of reactant A acid strength of site letters
proportionality constant describing the dependence of activation energy on site strength rate of conversion fraction of sites remaining active at a given TOS REFERENCES
Abbot, J. and Wojciechowski, B. W.. 1987, Kinetics of reaction of C, olefins on HY zeolite.. J. Coral. lO& 346-35s. Bakshi, K. R. and Gavalas, G. R., 1975, Effects of nonseparable kinetics in alcohol dehydration over poisoned silica-alumina. A.1.Ch.E. J. 21, 494-500. Barthomeuf, D., 1979, A general hypothesis on zeolites physicochemical properties. Applications to adsorption, acidity, catalysis and electrochemistry. J. phys. Chem. 83, 249-256. Blue, R. W. and Engle, C. J., 1951, Hydrogen transfer over silica-alumina catalysts. Ind. Engng Chem. 43,494-501. Butt, J. B., Watchter, C. K. and Billimoria, R. M., 1978, On the separability of catalytic deactivation kinetics. Chem. Engng Sci. 33, 1321-1329. Corella, I., Bilbao, R., Molina, J. A. and Artigas, A., 1985, Variation with time of the mechanism, observable order and activation energy of the catalyst deactivation by coke in the FCC process. Ind. Engng Chem. Process Des. Deu. 24.625-636. Corella, J. and Menendez, M., 1986, The modelling of the kinetics of deactivation of monofunctional catalysts with
for FCC modelling
1049
an acid strength distribution in their non-homogenous
surface. Application to the deactivation catalysts in the FCC process. Chem. 1817-1826.
of commercial Engng Sci. 41,
Fukase, S. and Wojciechowski, B. W.. 1988. The kinetics of
cumene cracking on HZSM-5. J. Coral. 109, 180-186. Kemp, R. R. D.-and Wojciechowski, B. W., 1974, The kinetics of mixed feed reactions. Ind. Engng Chem. Fundam. 13, 332-341. Lanner. B. E., 1981. Coke formation and deactivation of the catalyst in .reactibn of propylene on calcined NaNH,-Y. Ind. Engng Chem. Process Des. Dew. 20, 326-331. Levenspiel, O., 1972, Chemical Reaction Engineering, p. 25. Wiley, New York. Mikhail, R. S. and Robens, E., 1983, Microstructure and Thermal Analysis of Solid Surface, p. 216. Wiley, New York. Moscou, L. and Mone, R.. 1973, Structure and catalytic properties of thermally and hydrothermally treated xeolites-acid strength distribution of REX and REY. J. Catal. 30, 417-422. Onal. I. and Butt, J. B., 1980, Kinetic separability of catalyst poisoning, in Proceedings of the 7th International Congress Catalyst, p. 1940, Tokyo. Pachovskv, R. A.. Best. D. A. and Woiciechowski. B. W.. 1971, APplications of the time-on-s&n theory ‘of catal lyst decay. Ind. Engng Chem. Process Des. Dev. 12. 254-261. Pachovsky, R. A. and Wojciechowski, B. W., 1972, Theoretical interpretation of gas oil conversion data on an X-sieve catalyst. Can. J. them. Engng 49, 365-369. Pratt, K. C., 1982, A mathematical model for characterization of a catalyst having a skewed unimodal acid strength distribution. J. Catal. 76, 294-299. Rice, N. M. and Wojciechowski, B. W., 1991, Coke and deactivation. Catalyst decay in the presence of chain processes in catalytic cracking Con. J. them. Engng 69, 1 loo-1 105. Rollman, L. D. and Walsh, D. E., 1979, Shape selectivity and carbon formation in xeolites. J. Catal. 56. 139-140. Weekman, V. W., Jr., 1979, Lumps, Models’and Kinetics in Practice. A.1.Ch.E. Monograph 75. Wojciechowski, B. W. and C&ma, A., 1986, Catalytic Cracking-catalysts, Chemistry and Kinetics, p. 221. Marcel Dekker, New York.
A ONE-PARAMETER MODEL OF CATALYST DEACTIVATION FOR FCC MODELLING A. K. DAS Indian Oil Corporation, R&D Center,Faridabad,India and B. W. WOJCIECHOWSKI’ Departmentof Chemical Engineering, Queen’s University, Kingston, Ontario, Canada K7L 3N6
(First receiued20 November 1991; accepted for publicationin revised form 19 May 1992) Abstract-A one-parametermodel of catalyst deactivation, based on the distribution of acid site strengths, is proposed.The model describes the deactivation rate as a function of time-on-stream (TOS) and accounts for the very fast initial rate of decay observed in commercial FCC. All of the model parameters are temperature-invariant and are shown to apply to feeds and catalysts not too different from the base case. The proposed model can be used to generate the catalyst deactivation profile at very short times-on-stream (TOS < 6 s) from experimental data obtained at relatively large TOS (> 30 s). Tbe same data is fitted using two forms of the TOS decay function. An examination of the resultant parameters indicates that decay in the first few seconds of TOS, is of a high kinetic order. Subsequently, the catalyst decays by processes which remove active sites by reactions of a lower order, one which is probably related to the chemical mechanism of catalyst poisoning. It is this change in kinetics which will not allow a valid extrapolation to short on stream times when the conventional TOS function, 0 = (1 + Gc)-~, is applied to data at t > 30 s.
INTRODUCHON
Deactivation of cracking catalysts is of primary concern in the laboratory, the pilot plant and, most importantly, in commercial cracking reactors. Though there are various causes of cracking catalyst deactivation, the present work deals with that deactivation due to fouling by coke. A review of published deactivation data shows large variations (Corella et al., 1985) in the observed rate of deactivation with time-on-stream (TOS). Moreover, a high kinetic order for the deactivation reaction is reported at very short TOS (Corella et al., 1985). This very rapid initial rate of decay at low TOS is an important phenomenon of major commercial interest. The problem is made more serious as the rate of decay observed at the long times,on-stream normally studied in the laboratory, cannot be safely used to simulate commercial FCC operation where much shorter times-on-stream are encountered. Furthermore, Wojciechowski and Corma (1986) have shown that both the activity and selectivity obtained in laboratory fixed-bed reactors is distorted by the time-averaging of catalyst decay. A decay expression based on a satisfactory model of catalyst decay which accurately describes the first few seconds of TOS on the basis of the more readily obtainable laboratory decay data at longer TOS, would be very useful since it would allow the use of easily obtained laboratory data to predict the behaviour of commercial units. It is clear from titration and TPD studies that surface heterogeneity is a common phenomenon in cracking catalysts [see for example Mikhail and ‘Author to whom correspondence should be addressed
Robens (1983)]. Use of an overall decay function in such situations has been occasionally reported to fail to simulate experimental data (Onal and Butt, 1980; Bakshi and Gavalas, 1975).To overcome this, Butt et al. (1978) and Corella and Menendez (1986) have proposed the use of the acid strength distribution to describe surface heterogeneity and proceeded to derive decay functions from this. The work of Butt et al. (1978) mostly concerns the separability of the decay function based on an empirical activity distribution. Corella and Menendez (1986), in turn, showed how surface. heterogeneity can account for the change of the decay rate with TOS. Their model contains four unknowns: the acid strength distribution, 5, sensitivity of the activation energy to acid strength, as expressed by yt and ya, and the decay constant I&,. In that work, the parameters are found to be dependent on temperature and, thus, cannot be readily used to simulate the behaviour of the near-adiabatic conditions encountered in commercial riser reactors. More important is the fact that there are many unknowns in the model which must be evaluated for each new feed, temperature and catalyst system. The evaluation of each set of model constants demands that accurate deactivation data be obtained for both short and long times-on-stream. This is not an easy matter in practice. In a more recent development, Rice and Wojciechowski (1991) proposed a very different model of decay based on the inhibition caused by the accumulation of less and less reactive surface species. They have shown that in the cases where such inhibition is offset to some extent by the occasional restoration of the site activity to its pristine condition, as by a
1041
A. K.
1042
DAS
and B. W. WOJCIECHOWSKI
hydrogen transfer followed by desorption, two distinct episodes of decay can be distinguished. The first rapid decay, characterized by a high decay order if the TOS function is applied, is due to the rapid establishment of quasi steady-state coverage of the pristine active sites by hydrocarbon species of lower activity than the original pristine sites. These lower activity sites, based on adsorbed carbenium ions, proceed to decay more slowly as their average activity level continues to decrease with TOS. It is this second stage of decay which is commonly observed in the laboratory. In this paper we develop an equation which attempts to model both stages of decay from observations made only on the second stage of decay. The model we describe below is based on premises similar to those of Corella and Menendez (1986) but contains only one unknown parameter: Four other parameters which appear in our model are insensitive to a reasonably wide range of changes in feed and catalyst properties. More importantly, none of our parameters varies with temperature, thereby making the modelling of commercial semi-adiabatic conditions much easier. THE KINETIC
where nr is the concentration of active sites in the range q to q + dq. (9) The rate of feed conversion is taken to obey the rate expression Y‘J,=o = k&G.
(3)
It is important to note that in a homologous series of cracking reactions, the order m will vary with feed composition, temperature and catalyst. Pachovsky and Wojciechowski (1971) have shown how to use such an approach to take account of the effects of refractoriness. The method of accounting for system heterogeneity is based on the theoretical work of Kemp and Wojciechowski (1974). With these assumptions, eq. (1) can be rewritten as Yq = (k,p%,
(4)
where a, is the activity of sites with energy q. Assuming the activation energy for a cracking reaction to vary linearly with the heat of chemisorption of the active site, we can write
MODEL
Catalytic cracking is a very complex process. The introduction of surface heterogeneity makes it even more difficult to treat the problem systematically. Some of the assumptions which help in making the problem trackable were made by Corella and Menendez (1986) and will be used here to develop our expressions for catalyst decay. We assume that:
(1) The catalyst is monofunctional and diffusion free.
(2) Heterogeneity exists in the activity of the catalytic sites. (3) Catalyst deactivation is somehow connected with coke. (4) We will consider only the main reaction: Feed + Product + Coke so that coke is a primary product of the reaction. (5) Decay is assumed to be non-selective. (6) Each active site is characterized by its acid strength 4. (7) Separable decay for each individual site is applicable so that the rate on each site can be written as Yr = (r,lt=o)(o,)
(1)
where y4 is the rate and a4 is the activity on sites of strength q. (8) The overall reaction rate is the summation of rates on all sites
k, = k0 exp (-
E, - B&/R T
(5)
where k, is a temperature- and acid-strength-independent frequency factor. This assumption presupposes that the strength of chemisorption on a site does not affect the configuration and, hence, the entropy of the transition state. The only effect of site strength is to change the energy required to cause reaction. Individual active sites may decay by first- or higherorder processes. Studies of pure components have generally shown orders around two, while mixed feeds show decay orders ranging from one up to more than two (Wojciechowski and Corma, 1986).The equations we develop here are based on first-order decay as a function of site concentration. Thus, as = exp (-
kdp t).
(6)
We believe that the change of k,, with temperature and acid strength is not as simple as that assumed by Corella et al. in their model (1985). As found by Pachovsky and Wojciechowski, k,, does not follow an Arrhenius relationship. Corella et al. (1985) have also shown that the activation energy for deactivation (&) changes with acid strength. At the same time, it was shown by many authors [e.g. Moscou and Mone (1973)] that strong sites are responsible for more coke than weak sites (Barthomeuf, 1979). In short, temperature and acid strength both have complex influences on the deactivation constant. For this reason, we assume that both the pre-exponential factor and the activation energy of deactivation increase with increasing site strength. To explain our assumption, we first look at the proposed mechanism of coke formation in gas oil cracking.
1043
One-parametermodel of catalystdeactivationfor FCC modelling MECHANISM
OF COKE FORMATION
amount and nature of the total coke formed during catalytic cracking is dependent on the type of feed, the nature and strength of active sites and on the reaction conditions. There is little general agreement in various reports on coke formation but a few points are clear.
rate constant for such a system is represented by
The
(1) Olefins and poly-aromatics are the primary contributors to coke formation.
(2) Cracking, condensation, cyclization, hydrogen
transfer and &hydrogenation are all steps leading to coke formation. (3) The higher the acid strength of the site, the lower the activation energy for conversion and the lower the coking activation energy. In other words, at higher temperatures strong sites tend to produce less coke (Blue and Engle, 1951; Walsh and Rollman, 1977). (4) As shown by Langner (1981), coke formation occurs by two distinctly different paths. (0 By tde formation of non-diffus& high molecular weight hydrocarbons. This phenomenon dominates at low temperatures or on weak sites where the probability of /3 scission is low. The coke formed by this path contains more saturates and its deactivation efficacy appears to be rather low perhaps because these species can take part in chain processes. (ii) At high temperature or on sites with strong acidity, most coke precursors desorb from the site very rapidly. Some of these precursors, nonetheless, dehydrogenate or fuse together to produce “aromatic coke”. If this occurs, the coke precursors lose their ability to promote reaction via the chain mechanism and gradually lead to a loss of activity by a process of increasing inhibition. The “inhibition” picture of decay suggests that some or most sites initially acquire carbenium ions whose activity to conversion is lower than that of the pristine sites. This is responsible for the initial phase of rapid decay. Subsequently, these carbenium ions change into less and less active forms thereby causing the second, slower phase of catalyst decay normally observed in laboratory studies. The dual coking mechanism illustrates the fact that the absolute amount of coke cannot be correlated with catalyst deactivation in any general way. Both the amount and nature of coke must be considered. (5) In a homologous series of reactions like those associated with coke formation, the free-energy change, AG, often remains almost constant for different reactants. This compensation effect occurs when both the frequency factor and the activation energy change so that an increase in one is echoed by an increase in the other. The
k = k,exp(ASjR
- AH/RT)
(7)
where AS and AH are the changes in entropy and enthalpy of the system. In the case of compensation, both AS and AH change in the same direction as reactants in a homologous series are changed. We will assume that both follow a linear relation with 4. Therefore, we write the deactivation constant kdq as k, = k,,exp(B,q/R)exp(-
&q/RT)
(8)
where B1 and & are two constants of proportionality and k,, is a site-independent pre-exponential term. Equation (8) can be rewritten as k, = k,,exp(-
Bzq/RCl/T-
IlGl)
(9)
where & = T,B,. The activity of the catalyst at any time t is defined as rate of reaction at time t - ~ rate of reaction at t = 0 and, hence,
a=
a = Y/YO
(10)
4ln n,~. dq I ;:
(11)
s ga
n,y,o dq
Equation (11) is our defining equation for catalyst activity. THE SITE DISTRlBUTlON
Butt et al. (1978) have examined expressions for various acid strength distributions. Corella and Menendez (1986) have applied these distributions and found that a Gaussian distribution fits the measured FCC catalyst strength distribution very well with u = 4000 kcal/mol in eq. (12). This was confirmed by the work of Pratt (1982). A Gaussian-type distribution will, therefore, be used here: n,=n,exp[-
l/2(4-F’2)1].
Equation (11) can now be rewritten as
a=
*In “.Y~o ar dq I ‘O ‘I”. n.y.0 dq Im
(12)
A. K. DAS and B. W.
1044
WOJC~ECHOWSKI
and substituting from the above we have
cqm%e*p(+
Bd,qlRT)exp(- kdot)exp{(- B2qIWC11T- l/Gl)dq
%
exp(&alRT)da
where fi,, = n&t,-, In the normalized form,
J0
n,=exp[-
iiRexp(y,l/RT)dA
1/2rq)s]
(14)
(13 Yk =
A4m
- da/dt = k,a”.
Yd= ,&a Equation (13) is not as simple as one might like and would be of little use if it were not for the fact that we find we can correlate a range of systems using only one parameter, kdO_ It is worthwhile to compare eq. (13) with the model 3 equation of Corella and Menendez (1986) where the activity is given as 1 c
ii,‘W’(&/R~)exP
chain cracking. If we assume that the concentration of carbenium ions is constant on the reacting surface with TOS and conversion, then we can write the decay equation as
[(-
kd,~)exP(~dA/RT)l
a
(13’) using a notation similar to that of eq. (13). We note that all the terms of eqs (13) and (13’) are the same except for the term for the activation energy of decay. Physically, this difference is critical and is best understood by considering the temperature sensitivity of eq. (13). In decay governed by eq. (13’), the deactivation rate will decrease with an increase in site strength whereas the reverse is predicted by eq. (13). In fact, experimental data presented by Corella et al. (1985) confirm that the deactivation rate increases rapidly with an increase in site strength. This happens in our model for T> To. To see the mechanistic behaviour which lies behind the semi-empirical form of eq. (13), we turn to the TOS formulation. The standard “sudden death” TOS description of decay is based on the assumption that activity is directly proportional to the total number of all active sites. The loss of activity is then directly proportional to the loss of sites by some agent formed in the cracking reaction. This agent is a portion of “coke” and is made from precursor species which are indistinguishable from carbenium ions involved in
(19)
The value of n is 1 for cases where one site is lost per deactivating event, 2 if a two-site mechanism is involved or > 2 if pore blockage is the agent of deactivation. We can also write eq. (19) as - da/dt = k,a + k,a2 + kdam.
(20)
If n is a free parameter in eq. (20), we might as well return to eq. (19X integrate and obtain u = (1 + Gt)-N
(21)
where G = k,(n -
1)
(22)
N = l/(n-
1).
(23)
Equation (20) can also be derived by considering a decay mechanism, a gradual inhibition of active sites with possible reactivation, as put forward by Rice and Wojciechowski (1991). As shown there, occasional reactivation of active sites will lead to a change in the slope of the activity-time curve to produce two regions of catalyst decay. Both regions can be represented by functions of the type given by eq. (21), each with its own parameters, or by the detailed formulas presented by Rice and Wojciechowski or, it turns out, by eq. (13). We see the relationship between eq. (13) and the inhibition-dependent decay model to be as follows. Both models visualize rapid initial loss of activity; eq. (13) attributes this to the rapid loss of a small population of strong active sites. Thereafter, the decay proceeds more slowly in an exponential or hyperbolic fashion according to the form of the acid strength distribution of the remaining active sites. The inhibition model does not assume a preexisting distribution of activities and the inclusion of such a distribution will not change the predictions of the model. Instead, it assumes that the total activity of a catalyst consists of that due to pristine sites plus that due to
One-parameter model of catalyst deactivation various adsorbed carbenium ions which propagate “chain cracking”. The pristine sites are more active than the carbenium ions and it is the covering of these pristine sites by carbenium ions which is responsible for the initial rapid loss of activity. The subsequent, slower loss of activity is due to the chemical changes in the population of adsorbed carbenium ions. With time, this population becomes less reactive in the chain cracking process and in the limit completely poisons the pristine sites. The result is loss of activity due to a gradual inhibition of sites rather than “sudden death”. The generalized TOS decay function (Pachovsky et al., 1973) assumes that all processes in eq. (20) are active and the experimental value of n will reveal which is most important. In fact, most pure hydrocarbons on Si /Al, LaY and HY show values of n = 2 (Abbot and Wojciechowski, 1987). Cracking on HZSM-5, however, shows n % 2 suggesting that pore blockage is the decay mechanism for this catalyst (Fukase and Wojciechowski, 1988). In the following, we will investigate the fit of eqs (18)-(20) with n = 3, for catalyst decay data obtained from Corella and Menendez (1986). NUMERICAL
COMPUTATION
Equation (13) must be solved in order to obtain the activity vs time relationship. It contains five unknowns: 5, yL, yd, T, and k,,. If we have a suitable measure of the acid strength distribution of the catalyst, 5 may be calculated independently. The other four unknowns, or all five if t is unknown, are obtained from a least-squares fit of experimental data. The most important step in this is the computation of the integral which contains ill-behaved functions. The Gauss-Chebychev method used by Corella and Menendez (1986), seems to be the best method of integration in this case, with other methods giving poor results. A non-linear Marquardt method was used to find the best fit to experimental data. The experimental data themselves have been taken from Corella and Menendez (1986) and Corella et al. (1985). The sum of squares of residuals was minimized in computing the optimum parameters. The models based on eqs (19) and (20) are much simpler to use and require no special precautions. EXPERIMENTAL
DATA
activity function given by eq. (13) was fitted for four unknowns yk, yd, To and k,, using < and the initial values from Corella et al. (1985). To was taken to lie somewhere in the range of temperatures used for cracking since decay has been found to increase or to decrease with temperature depending on the system (Wojciechowski and Corma, 1986) suggesting that the change from positive to negative dependence lies in the range of experimental temperatures. Therefore, only yd, y, and k,,, were varied to fit the a vs I curve in Fig. 1. Because the data was hard to read from the published figures (Corella et al., 1985), the ‘experiThe
for FCC modelling
1045
t. min --) Fig. 1. Activity vs TOS for catalyst MZ-7P and gas oil GOII at 520°C. Solid line shows fit obtained using eq. (13) to data Points from the work of Corella et al. (1985). The parameters used are reported in Table 1.
mental” data was calculated using eqs (47) and (48) of the above-mentioned paper to produce the a vs t curves at various temperatures. We note that a significant difference exists in the final (I vs t curves depending on whether model 3 or model 5 is used [eqs (21)-(23) or eqs (47) and (48)] in the reference. To obtain all other data, experimental points were read from original data in Fig 8 of Corella et al. (1985). The values tabulated for various model constants in the source (Table 1, Corella and Menendez, 1986) did not seem to fit these data. We realize that these are not entirely satisfactory procedures as in obtaining the parameters of our model, in some cases we are attempting to fit the function of model 3 proposed by Corella et al. (1985) while, in evaluating other experimental data, we are dependent on digitization of graphical data. Any statistical evaluation of our fit is of little, if any, use in this case. RESULTS
Experimental data obtained on the MZ-7P catalyst using GO-II at 520°C were fitted by eq. (13) to obtain ya, yr, To and kdo. Figure 1 shows that our model fits the data very well. That is to say, our model behaves exactly the same as Coreila’s model 3. Once the parameters were obtained for this catalyst, feed and temperature, we find that eq. (13) can be used to fit the a vs t behaviour for other reported reaction temperatures for this feed. Figure 2 shows the fit of calculated and experimental activity at various times on stream for the same system at 480, 500 and 540°C. The parameters used are those shown in Table 1. Only the temperature was changed. Models based on eqs (19) and (20) had to be fitted separately to each data set as the parameters are temperature-dependent. Parametric sensitioity
Since the mechanism of coke formation is almost the same in all cracking reactions irrespective of feed,
1046
A. K. DAS and B. W. WOICIECHOWSKI
CAT. OIL: x A . -
M27P GOII 4E%o*c 500°C 540°C
t
t
a
a
0
I.,
0
I
I
I
I
I
I
I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 0.1 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9
1 I
t,min-
t. min --) Fig. 2. Effect of temperature on 509°C and (0) 540°C. The gas oil is MZ-7P. Only the temperature has The parameters remain as for Fig.
activity.
(x) 480-C,
(4)
GO-II and the catalyst is
been changed in eq. (13). 1. Points represent data
from Corella et al. (1985).
Fig. 3. Effect of the decay constant kdoon the morphology of activity curves. Curves l-4 correspond to kro = 0.00462 0.011, 0.023 and 0.090 min-‘, respectively. All other parameters are the same as shown in Table 1 for GO-II on MZ-
7P.
we may suppose that yd and T, should not change with the system. There is a suggestion of this in the work of Corella and Menendez (1986), where ya remained constant for various feeds and catalysts. A priori knowledge of catalyst strength distribution can, in principle, be used to estimate the value of {, which is independent of the temperature. Therefore, only k,, and yr may be expected to change. The effect of kdo on the a vs t curve is shown in Fig. 3, keeping all other parameters constant. Figure 4 shows the effect of yk on a vs t. We see that the sensitivity of the activity to site strength, as measured by y,,, is small. Comparing Figs 3 and 4, it is clear that the behaviour of the a vs t is similar for variations in yk and k,,, at least in the neighbourhood of values examined here. This means
1.0 0.9 0.8 0.7 0.6 t a
0.5 0.4 0.3 0.2 0.1
0 0 0.1 0.2 0.3
that kd,, can serve as the one and only parameter which needs to be adjusted to fit data for various feed,
temperature and catalyst combinations.
Table
Eq. (13) model
‘All parameters
0.5
0.6
0.7
0.8
0.9
Fig. 4. Effect of the reactivity parameter yI = /3kqmon the morphology of activity curves. Curves 1-3 correspond to yt
E&t offeed and catalyst Having established the values of <, yh, Y,,and T,, we can fit a variety of experimental a vs t curves obtained with different catalysts and feeds using k,, as a parameter. This is illustrated in Fig. 5, where the a vs t curves for two different feeds and catalysts have been fitted by changing k,, only. The experimental data for these systems was also obtained from the work of Corella et al. (1986).
Conditions
0.4
t. mine
= 2.5, 7.5 and 12.5 kcal/mol. respectively.All other parameters are as in Table 1 for GO-II on MZ-7P.
Site selective decay In eq. (13), the fast decay at time = 0 and the reduction of the decay rate with TOS can be understood to be the result of different rates of decay for active sites of different acid strengths. Figure 6 represents the contribution to the instantaneous activity
1. Values of model parameters’
Feed Catalyst
GO-II MZ-6s
GO-II MZ-7P
ys(kcaI/mol) y (kcal/mol) 5 To (K) kdo(min-‘)
25.0 7.5 0.165 481.0 O-0332
25.0 7.5 0.165 481.0 0.0462
are temperature-invariant.
GO-AV MDZ-7P
2% 01165 481.0 0.023
One-parameter model of catalyst deactivation for FCC modelling
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0.9 1.0 t.
min --+
Fig. 5. Fitting of systems consisting of various feeds and
catalysts. Curve 1 is for GO-AV on MDZ-7P at 520°C using k,, ; 0.0332 min-I. Curve 2 is for GO-II on MZ-6S ai 520°C using kdo = 0.023 min- ‘. All other parameters are the same as for GO-II on MZ-7P at 520°C in Fig. 1 and Table 1.
1047
of various active sites with changing TOS. Initially, almost 60% of the activity is contributed by the strong sites, but within 2 s, about 50% of the strong sites are decayed. After 30 s, most of the activity comes from medium and weak sites. Interestingly, a similar conclusion is reached by starting with an entirely different decay mechanism; the gradual inhibition of sites by a less and less efficient chain process, as proposed by Rice and Wojciechowski (1991). They have shown that a catalyst with a homogeneous initial surface will also show such a behaviour, as pristine sites on the framework are at first rapidly reduced in activity by the attachment of carbenium ions. This phase is followed by a slower reduction of activity of the adsorbed cations due to reactions such as dehydrogenation and cyclization. Although the two models differ from one another in detail, they lead to similar conclusions and the model proposed here seems to offer a more readily applicable formula. DEXXJSSION
I
1.01
0.9 0.8
0.6
t
0.5
a
0.4 0.3 0.2 0.1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fig. 6. The contribution of sites of various strengths to the total activitv as TOS increases.At t = 0 much of the activitv is due to strbng sitesas shown by curve 1. As TOS inere.a& to
t = 0.03, 0.10 and 0.30 min the distribution
of surviving active sites shifts to lower strengths and narrows.
Table 2. Multiple Cotiditions
Fed
site decay model constants
GO-II MZ-7P 520
GO-II MZ-7P 540
GO-AV MZ-7P 540
42.3 0.8 1 34.39 2.23
57.23 0.78 44.7 2.28
67.1 0.78 52.4 2.28
29.15
0.75 12.5 25.0
0.70 12.0 47.0
0.70 12.5 62.0
0.75
GO-II
MZ-7P Catalyst Temperature (“C) 500 Hyperbolic decay constants [eq. (21)]
Multiple
decay
(W
N kd (min-‘) m k, (min-‘) k, @in-‘)
constants rw.
G @in-‘)
n =
31
k, (min-‘)
In the heterogeneous model of catalyst decay, the sole adjustable parameter kdOhas been made to account for all the effects caused by changing feed and catalyst. In that sense, it is a “lumped” parameter and despite the obvious advantages of this approach to decay rate modelling, we can extract little mechanistic interpretation from the variation of k,,. The TOS model is more cumbersome in that all its parameters are temperature-dependent. Nevertheless, they can also be more informative as to the nature of the processes occurring on the surface. For example, Table 2 shows that the TOS exponent N and, hence, n, the order of the decay, is fairly constant over the range of systems studied. The “lumped” orders of the decay in the various systems are grouped near 2.30, indicating that similar mechanisms are responsible for catalyst decay in all the systems and that some higherorder (> 2) decay process is present; presumably pore blocking. When we attempt to break down the TOS expression into its constituent terms, as per eq. (20), we must assume the value of n, the number of sites lost per average pore blocking event. No quantitative information exists on this matter and we have chosen
0.77 22.7 2.29
8.5 15.0
GO-II MZ-6s 520 47.3 0.73 34.77 2.36 0.75 11.5 24.0
1048
A. K. DAS and B. W. WOJCIECHOWSKI
n = 3. With this assumption, a satisfactory fit is obtained with the rate constants for first- (= k, ), second(= k,) and third-order (= k,) terms as shown in Table 2. We now consider the relative magnitudes of k,, k2 and k,. Clearly, the higher the order of a reaction, the more rapidly its rate decreases with the extent of reaction. In a mechanism where three parallel reactions of order 1, 2 and 3 are present, the high-order reaction will be significant early on in the process only if it has a large initial rate constant. We see, therefore, that, in all three systems, third-order decay will dominate the loss of activity in the initial stages of the reaction. We interpret this as indicative of pore plugging being the dominant form of decay in the first few moments on stream. This is followed by secondorder decay, as is found for most pure components. This second-order decay dominates throughout most of the test period and weighs heavily on the observed average order. Finally, at long times-on-stream, firstorder decay takes over as site density is depleted to the point where few site pairs are available. The temperature effect on rate constants k, and k, is small or zero. This we take to indicate that decay which proceeds by a chemical process on the catalytically active sites requires essentially no activation energy. It simply seems to be a stochastic process governed by chance “malignant” reactions of coke precursors. The k, value, the one that accounts for pore blocking, has a strong temperature dependence. This suggests that pore blocking involves a free radical, uncatalyzed surface reaction dependent on normal free-radical activation processes. Differences between the catalysts are also reflected in the values of the ks. MZdS has larger pores than MZ-7P, and we see that, whereas k, and k, are similar for the two, k3 is smaller by a factor of two on the large pore catalyst. We conclude that small pores are easier to block. Work on HZSM-5 confirms this very clearly (Fukase and Wojciechowski, 1988). Finally, the gas oil GO-AV is much lighter than GO-II, and we see that pore blocking by this feed is much reduced while k, and k, are not affected as strongly. In summary, all three models describe decay adequately. The heterogeneous model is clearly the one which requires the least number of parameters but requires complex calculation procedures and the establishment of four semi-fixed parameters. The standard TOS model is simple to fit and requires two parameters. It may fail at very short times-on-stream if the initial decay is very rapid and data is gathered from very short to very long timeson-stream. For that reason, it cannot be used for riser cracker simulation if the decay parameters were obtained at long times-on-stream. The detailed TOS model requires three parameters, gives an adequate fit and reveals a wealth of mechanistic information. It is to he preferred for research purposes in gas oil cracking but requires data from short times-onstream to obtain parameters valid for short on-stream times.
We propose that the model described by eq. (13) is the most convenient for predicting that behaviout at commercially important short TOS while only requiring data obtained from conventional MAT or fixed-bed type experiments. This useful capability comes from the fact that the “constant” parameters 5, y,,, yk and To are largely responsible for the shape of the curve at short TOS while kdo, which determines the rate of decay on some absolute scale can be obtained from data at longer TOS. CONCLUSIONS
The heterogeneous model developed here is based on the assumption of a distribution of activities on a cracking catalyst. Its advantage over similar models in the literature (Corella et al., 1985; Butt et al., 1978) is that it allows activities of a range of catalyst-feedstock systems to be modelled using only one variable parameter kdo. Temperature effects are accounted for by simply using the appropriate absolute temperature in the equations. This is an attractive property for the simulation of commercial cracking operations which do not take place at isothermal conditions. Computational difficulties are readily overcome by the use of computers, whereas considerable experimental difficulty is avoided by being able to model the near-adiabatic operation of a riser cracker, without the need to establish model parameters at a variety of temperatures, at short times-onstream. Although the number of parameters in this model is larger than in model 3 of Corella et al. (1985), we found that for purposes of commercial interest yr, y,, and To remain almost constant. < is obtained from experimental data on acid strength distribution. Thus, only k,, remains as an unknown to be determined by experiment. Therefore, in a situation where the feedstock, catalyst and process conditions are not much different from some initial base case (whose parameters are known) it is possible to determine k,, even from long TOS data and to use eq.113) to predict short TOS decay kinetics. The detailed TOS model is less useful for reactor simulation as it requires three temperature-dependent constants. It is, on the other hand, more informative regarding the nature of the decay process. Both approaches seem to fit experimental data adequately. Acknowledgements-Thiswork was supported by the financial aid from UNIDO and iointlv oraanized bv Indian Oil Corporation, Faridabad, India “and- Queen’sv University, Kingston, Ontario, Canada. We thank Dr. S. Ghosh of Indian Oil for his valuable suggestions at the beginningof this work. NOTATION a
E G k&
KY
activity of sites activation energy for the conversion decay parameter in the TOS decay function rate constant for decay of sites of strength q rate constant for conversion on sites of strength q
One-parameter m
model of catalyst deactivation
exponent in the rate expression for conversion
N
decay
n
exponent in the rate expression for decay number of sites of strength between q and q
a,
+
PA 4 Greek A
Y
e
exponent
in the TOS
decay
function
4
partial pressure of reactant A acid strength of site letters
proportionality constant describing the dependence of activation energy on site strength rate of conversion fraction of sites remaining active at a given TOS REFERENCES
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