200
Ind.
Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
h a , c., White, E. T.. "Kinetics of Crystallization of Aluminum Trihydroxide from Seeded Caustic Aluminate Solutions", AlChE Sixty-second Annual Meeting, Washington, D.C., Nov 16-20, 1969. Nuttal, H. E., Randobh. A. D.. Simpson, K. 0.. "User Manual for MARK 1-A, C and D for CDS Simulation", University of Arizona, Tucson, Ariz., 1975. Randolph, A. D.. Larson, M. A., "Theory of Particulate Processes", Academic Press, New York. N.Y., 1971. Randolph, A. D., White, E. T., R o c . Queens/. SOC.Sugar Cane Techno/., 43 (1976).
Randolph, A. D., White, E. T., Chem. Eng. Sci., 32, 1067 (1977). White, E. T., Wright, P. G., Chem. Eng. Prog., Symp. Ser., 67, No. 110, 81 (1971).
Receiued for reuzew April 14, 1977 Accepted September 27, 1977
Presented at the AIChE Meeting, Atlanta, Ga., March 1978.
Deactivation Disguised Kinetics S. Krishnaswamy and J. R. Kittrell' Depariment of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 0 1003
For rapidly deactivating systems, the apparent kinetics of the primary reaction can be disguised by the presence of deactivation effects. It has been shown that the assumed kinetic model for the primary reaction will lead to potentially inaccurate deactivation models which nevertheless adequately fit experimental data. Conversely, the order of the primary reaction can be disguised by the kinetics of the deactivation reaction. For catalytic cracking of gas oil in a transfer line reactor and hydrogen peroxide decomposition in a fixed bed reactor, second-order conversion, concentration-independentdeactivation and first-order conversion, concentration-dependentdeactivation model forms are indistinguishable for conversion of feed. For the case of a moving bed reactor, the model forms are similar and lead to generally equivalent degrees of fit of experimental data.
For the design and optimization of industrial reactors employing a solid catalyst, knowledge of the kinetics of the primary reaction as well as the deactivation reactions is required. A summary of many laboratory investigations of deactivation kinetics has been presented by Butt (1972). Levenspiel and co-workers (1971,1972)have observed that nth order decay models describe many cases of catalyst fouling and have suggested experimental strategies to evaluate deactivation kinetics. A variety of more complex deactivation models have been investigated theoretically, as typified by those of Froment and Bischoff (1961) and by Smith and co-workers (1966, 1967). However, application of concentration-dependent deactivation models to experimental data has been limited. For many reacting systems, such as the catalytic cracking of gas oil, deactivation occurs a t a sufficiently rapid rate that examination of the kinetics of the primary reaction must be interpreted simultaneously with the deactivation kinetics. For example, Weekman and Nace (1970) presented the gas oil cracking rate constant as a function of the catalyst residence time, as shown in Figure 1. Extrapolation of these data to provide information of the kinetics of the primary reaction without the encumbrance of deactivation effects is frequently fruitless. In fact, Weekman and Nace (1970) simultaneously analyzed the kinetics of the primary reaction and of the deactivation reaction. By contrast, Blanding (1953) attempted an analysis of the primary reaction kinetics ignoring deactivation. Furthermore, the use of a transfer line reactor by Paraskos et al. (1976) can result in the reaction time coordinate being equivalent to the deactivation time coordinate, thereby obviously requiring a simultaneous interpretation Of the kinetics of the primary reaction and the deactivation reaction. The purpose of the present paper is to illustrate that the simultaneous presence of deactivation effects can disguise the apparent kinetics of the primary reaction. Specifically, equivalent degrees of fit of experimental data and, in cases, 0019-7882/78/1117-0200$01.00/0
identical equation forms can be achieved by a variety of assumptions regarding the kinetics of the primary and deactivation reactions. In catalytic cracking of gas oils, for example, Voge (1958) and Nace (1969) have reported first-order kinetics for pure compound studies. The somewhat analogous hydrocracking process, which has sufficiently slow deactivation that the primary reaction kinetics can be studied independently of deactivation, exhibits first-order kinetics for both pure compounds and complex gas oil mixtures (Stangeland and Kittrell, 1972). However, the rapidly deactivating system of catalytic cracking of complex gas oil feeds is generally interpreted with second-order kinetics (Weekman and Nace, 1970; Paraskos et al., 1976). This behavior has been attributed to a wide spectrum of cracking rate constants in the gas oil constituents. However, for many cases, the present paper illustrates that this phenomenon could also be explained by deactivation disguised kinetics in rapidly deactivating systems.
Catalytic Cracking: Transfer Line Reactor Based on the model of Weekman and Nace (1970), Paraskos et al. (1976) present a general reaction path for gas oil cracking, consisting of a second-order conversion of gas oil to gasoline and a subsequent first-order reaction of gasoline to lighter hydrocarbons and coke, as shown in eq 1 and 2. gas oil
-
-
gasoline
+ (light hydrocarbons and coke)
(1)
gasoline (light hydrocarbons and coke) (2) . If the gas oil conversion is represented by a second-order reaction, and the deactivation rate is represented by a firstorder, concentration-independent model, the balances become (3) (4)
0 1978 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
Model
IO
0
tc ,
CATALYST
RESIDENCE
30
20
prediction
60
5
T I M E , MIN
Figure 1. Extrapolation of initial catalyst activity (Weekman and Nace, 1970).
50
40
201
Figure 2. Correlation of gas oil kinetics (Paraskos et al., 1976).
1
da _ -- -ma da where y1 and y2 are the instantaneous weight fractions of gas oil and gasoline, respectively, a is the activity of the catalyst, and 7 is the flowing space time. The solution to these equations provides a dependence of the fraction of unconverted gas oil upon the flowing space time as shown in eq 6 and a relationship of the weight fraction of gasoline in the fluid to reaction parameters and the unconverted gas oil weight fraction as given by eq 7. Paraskos has also discussed the excellent fit of this model to catalytic cracking data in the transfer line reactor.
predictions
M O ~ D I
order
F,.SI
rode,
I -C 1 = 0 7 9 , C 2 : 0
=-
Second
0
14
C I = O ~ ~ , C Z = O Z ~
0 2
Order made1 1 P o r c S k o f et 0 1 , 1 9 7 6 ,
I
I
1
04
06
08
IO
i l - Y l I
where
An alternative description of this cracking process is shown in eq 8 through 10, assuming first-order conversion of the gas oil molecules in accordance with the pure compound data, a first-order conversion of gasoline into coke and light gases, and a concentration-dependent deactivation (eq lo), wherein the rate of deactivation is dependent upon both the fraction of active sites on the catalyst and the concentration of gas oil in the fluid.
Figure 3. Correlation of gasoline yield kinetics.
Figure 2, the f i t of both of these models is identical and adequate to describe the gas oil cracking data of Paraskos. The solution giving the weight fraction of gasoline in the fluid as a function of the reaction parameters and the weight fraction of gas oil in the fluid is shown in eq 12, for the firstorder cracking, concentration-dependent deactivation model. The form of this equation is notably simpler than the aualogous equation for the second-order conversion process (eq 7 ) . However, as shown in Figure 3, the adequacy of fit of this simpler form of the equation to the gas oil cracking data of Paraskos is equivalent to that of the more complex model form. j’p
=
(-)1 - C’ C1
[s””L
- y1]
where The solution of these equations results in an alternative relationship of unconverted gas oil to flowing space time, as shown in eq 11.
Note that the form of eq 11 is identical with that of eq 6, leading to the conclusion that the degree of fit of the firstorder cracking, concentration-dependent deactivation model must be identical with that of the second-order cracking, concentration-independent deactivation model. As shown in
It may be concluded, therefore, that the gas oil cracking data from a transfer line reactor may be satisfactorily fit either by the second-order conversion model with concentration-independent deactivation kinetics or with the first-order conversion model with concentration-dependent deactivation kinetics. With the data base available, it cannot be determined which of these model forms best represents the experimental system, thereby leading to a case of deactivation disguised kinetics.
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 2, 1978
202
I O
Second order
0
I , 1 0
0 08
0 24
/’
model (Weekman and Noce,,9701 model
1
I
016
Firs1 order
032
0 40
cz
Figure 4. Contour plot of gasoline model parameters. Heavy contour defines 95% confidence region. 0
Comparing eq 6 and 11 we find that
02
k l = R1
(13)
P = ( m + R1)
(14)
06
04
PREDICTED
WT
FRACTION
08
IO
CONVERSION
Figure 5. Observed and predicted gas oil weight fractions, moving
bed data.
and Even though eq 6 and 11 have identical forms under isothermal conditions, the relationship between the parameters required for the two models, as shown in eq 13 and 14, would indicate that the parameters in both models cannot both have the simple exponential temperature dependence desired in describing the kinetics of the cracking reaction. Specifically, if (Y and R1 have an exponential temperature dependence, p cannot have an exponential temperature dependence, unless the deactivation reaction and the primary reaction have equal activation energies. Therefore, data taken over a wide range of temperatures should be satisfactory in defining the relative applicability of these two model forms. For the simpler model form of eq 12, estimation of the reaction parameters is relatively straightforward. Differentiation of eq 12 with respect t o y l leads to eq 15 and 16, giving the reaction parameters in terms of the gas oil conversion associated with the maximum in Figure 3 and the initial slope of Figure 3. Although the initial slope of Figure 3 is relatively well defined, data have not been taken which allow a precise definition of the location of the maximum in the curve. I t is not surprising, therefore, that the magnitude of the parameters associated with these data are imprecisely estimated, as shown in Figure 4.
It is apparent from Figure 4 that a wide range of values of the parameter Cz can be used to describe the data, expected because the maximum in the curve of Figure 3 is not well defined. Therefore, as shown in Figure 3, the data can be well represented by parameters of sufficiently wide range that extrapolation to the higher conversion portion of the curve, of interest in current commercial operations, cannot be well predicted. Extension of the data base into these high conversion areas may be sufficient to discriminate between the models represented by eq 7 and 12.
Catalytic Cracking: Moving Bed Reactor Weekman and Nace (1970) have used an analogous set of mass balances to those of eq 3 through 5 for catalytic cracking of gas oil in a moving bed reactor and derived a relationship of the fraction of gas oil in the fluid as a function of liquid
space time and catalyst residence time shown in eq 17. (17) The relationship of the gasoline fraction to the gas oil fraction is identical with that of eq 7. If the gas oil conversion is assumed to be first order and the deactivation rate to be dependent upon both the gas oil concentration and the activity of the catalyst, analogous to eq 8 through 10, the gas oil model of eq 18 can be derived. The gasoline model thus derived is identical with eq 12.
Note, for this case, that the equations describing the fraction of gas oil in the fluid at any time (eq 17 and 18) are not identical, as they were in the case of the transfer line reactor discussed above. They will become identical, however, for a small relative reaction severity parameter (hlT/PtJ
