x
dodecane conversion during a run yield of monochloride
= =
y
SUPERSCRIPTS h = reaction order for light intensity j
= reaction order for chlorine = reaction order for dodecane or dodecyl chloride
m
SUBSCRIPTS a = d, ds, dp,,m, p, or s b = bulkllquld c = chlorine d = dichloride d p = dichloride formed from primary monochloride ds = dichloride formed from secondary monochloride i = gas-liquid interface m = monochloride 0 = initial p = primary monochloride s = secondary monochloride SYMBOLS
( )
GREEK =
y
e
=
.F
yield ratio of secondary/primary monochlorides
YJYP.
= Higbie’s exposure time, = predicted?
(1961).
Calvert,’ J. G., Pitts, Jr., J. N., “Photochemistry,” Wiley, New York, N. Y., 1966. Danckwerts, P. V., “Gas-Liquid Reactions,” McGraw-Hill, New York, N. Y., 1970, Chapter 5. Danckwerts, P. V., Z@. Ens. Chem., 43, 1400 (1951). Davidson, J. F., Harrlson, D., “Fluidised Particles,” Cambridge University Press, London, 1963, p 53. Davies, 0. L., Ed., “The Design and Analysis of Industrial Experiments,” Hafner, New York, N. Y., 1967, p 533. Dewar, M. S., “Electronic Theory of Organic Chemistry,” Oxford University Press, London, 1949, p 268-269. Fredericks, P. S., Tedder, J. M., J. Chem. SOC.,144 (1960). Fredericks, P. S., Tedder, J. M., J. Chem. SOC.,3520 (1961). Gibson, G. E., Bayliss, N. S., Phys. Rev., 44,188 (1933). Harriott, P., Can. J. Chem. Eng., 48, 109 (19701. Hashimoto, K., Teramoto, M-., Nagayasu, T:, Nagata, S., J. Chem. Eng. Jap., 1, 132 (1968).
Hass, H. B., McBee, E. T., Hatch, L. F., Znd. Eng. Chem., 28, 1335 (1937).
Hatch, L. F.,’Ph.D. Thesis, Purdue University, Lafayette, Ind., 1937.
Higbie, R., Trans. Amer. Znst. Chem. Eng., 31,365 (1935). Inoue, H., Kobayashi, T., Chem. React. Eng., Proc. Eur. Symp., 4th, 1968, 147 (1968).
concentration
=
Calderbank, P. H., Moo-Young, M. B., Chem. Eng. Sci., 16, 39
T
Ramage, M. P., Ph.D. Thesis, Purdue University, Lafayette, Ind., 1971. Ramage, M. P., M.S. Thesis, Purdue University, Lafayette, Ind., 1969. Roberts, J. D., Caserio, M. C., “Basic Principles of Organic Chemistry,” W. A. Benjamin, New York, N. Y., 1965, pp 83-90.
literature Cited
Astarita, G., “Mass Transfer with Chemical Reactions,” Elsevier, New York, N. Y., 1967, Chapters 2 , 3 , and 5. Barilli, F., Calcagno, B., di Fiore, L., Ghirga, M., Znd. Eng. Chem.,
Russell, G. A., J.Amer. Chem. SOC.,79,2977 (1957). Russell, G. A., J. Amer. Chem. SOC.,80,4987 (1958). Silberstein, B., Bliss, H., Butt, J. B., Znd. Eng. Chem., Fundam., 8, 366 (1969).
62,62 (1970).
Stauff, J., Z . Elektrochem., 48, 550 (1942). Szekely, J., Bridgwater, J., Chem. Eng. Sci., 22, 711 (1967). Teramoto, M., Nagayasu, T., Matsui, T., Hashimoto, K., Nagata,
1969.
Teramoto, M., Fujita, S., Kataoka, M., Hashimoto, K., Nagata, K., J. Chem. Eng. Jap., 3, 79 (1970). van de Vusse, J. G., Chem. Eng. Sci., 21,631 (1966).
Bernstein, L. F., Fuqua, B. B., Albright, L. F., Symposium on Advances in Reaction Engineering: I11 International Congress of Chemical Engineering, Marianske Lazne, Czeckoslavkia, Blouri, B., Cerceau, C., Lanchec, G., Bull. SOC.Chem. Fr., 304
S . , J . Chem. Eng. Jap., 2,186 (1969).
RECEIVED for review April 3, 1972 ACCEPTED March 29, 1973
(1963).
Bratolyubov, A. S., Rues. Chem. Rw.,30 ( l l ) , 602 (1961).
Applications of the Time-on-Stream Theory of Catalyst Decay Roman A. Pachovsky, Donald A. Best, and Bohdan W. Wojciechowski* Department of Chemical Engineering, Queen’s University, Kingston, Ontario, Canada
A general theory describing catalyst aging as a function of time-on-stream only is presented. From general mechanisms proposed for catalytic cracking of cumene and of gas oil, four parameter models are developed to describe conversion in flxed bed catalytic reactors. The gas oil cracking model is further extended to describe conversion in moving and fluidized bed reactors. It is shown how the time-on-stream theory can be used to make quantitative comparisons of activity, refractivity, and the aging characteristics of various cracking catalysts and gas oils.
o n e of the most successful txocesses ever to be introduced in industry has been the catalytic cracking of petroleum. The enormous success of this process has had a large influence on the course of development of our modern industrial society. Catalytic cracking, however, did not develop to its present stature through an exploitation of a sound, basic knowledge of its kinetics. I n fact, it has only been recently that con254 Ind. Eng. Cham. Process Des. Develop., Vol. 12, No. 3, 1973
siderable effort has been devoted to the task of describingcatalytic cracking on the basis of nonempirical kinetics of general validity. The major reason for the slow development of suitable mathematical models has been the phenomenon of catalyst aging, a problem which plagues most catalytic processes to one degree or another. The practical problems it generates
have long been recognized and mastered in industry but the lack of general mathematical descriptions of the aging process has retarded progress in the kinetic modelling of cracking processes. I n the past this lack of general models for catalytic cracking has made comparisons of various gas oils, catalysts, and reactor systems largely a qualitative exercise. I n 1968 Wojciechowski proposed a general aging function which relates the catalyst activity solely to the length of time the catalyst is in use (time-on-stream). Wojciechowski's approach usually leads to a hyperbolic dependence of activity on time-on-stream but includes the exponential type of decay function first used by Weekman (1968). This aging model has two parameters (Le., a decay rate constant and an order for the decay reaction) both of which seem to us to be essential. In previous publications by Weekman (1968), Nace, et al. (1971), Crowe (1971), Crowe and Lee (1971), and Ogunye and Ray (1971a,b), these authors have all used simpler aging functions involving only one parameter, but in each case, their aging function can be derived by making certain simplifying assumptions, from our more general form. The fact that other authors have used 5arious simplified forms of our general decay equation appears to us t o strengthen the validity of the general model. Attempts have recently been made to apply Wojciechowski's decay function to the catalytic cracking of gas oil (Pachovsky (1971), Best (1971)) and cumene (Campbell (1971)). It is our intention here to summarize the various applications of the time-on-stream theory of catalyst decay and thus show how the theory offers promise as a general description of catalyst aging. We mill also show how the general nature of the theory allows quantitative comparison of various gas oils and catalysts. Theory
Catalyst Aging. The time-on-stream theory of catalyst decay (Wojciechowski (1968)) assumes that a catalyst ages simply as a result of being used. I n the case of cracking some catalyst sites may be lost during reaction as a result of impurities in the feed or due to the deposition of coke. Such a loss of active sites may be expressed as a function of catalyst time-on-stream. The rate of decay of a catalyst is therefore -d[S]/dt = kd[S]"[p] (1) The concentration of active sites can be expressed as a function of the initial site concentration
[SI=
[sole
Substituting eq 2 into 1 gives -dO/dt = kd["]'"-''[p]e" (3) If the concentration of poisons is assumed to be independent of t eq 3 can be simplified to -dO/dt = Kdem (4) Equation 4 can be integrated taking the initial conditions to be '6 = 1 a t t = 0. This leads to
e
= e-Kdt
= (1
0 = (1
+ Gt)-M
(7)
Substituting eq 7 into 2 gives [SI = [So](l
+ Gt)-M
(8)
Equation 8 describes the active site concentration as a function of time-on-stream. Generally an elementary kinetic rate expression for a catalyzed reaction can be written as d [ A ] / d ~= k[SIn[A]' Substituting eq 8 into 9a gives
(98)
+
d [ A ] / d ~= k ( [ S ~ ] ) ~ ( Gt)-N[A]" l
(9b)
where N = nM. In the above equation, the expression k ( [SO])"represents the total initial rate constant and the expression (1 Gt)-N represents the decay function. The first application of the time-on-stream theory of catalyst decay was to a hypothetical first-order catalytic reaction (eq 9b with a = 1) occurring in a plug flow, static bed reactor and requiring n active sites per deactivating event (Wojciechowski (1968)). The resulting model predicts the integral or average conversion as
+
x
=
1.0 -
+ G t ) - N ~ ] )dt
Iexp(-[k([S~])"(l tf
(loa)
where T is the space time. This application of the time-on-stream theory has led to the discovery of three distinct classes of aging behavior dictated by the numerical value of the aging exponent, N : class I (AT < l), class I1 ( N = I ) , class I11 ( N > 1). Cumene Cracking in a Static Bed Reactor. Campbell and Wojciechowski (1971) have postulated that cumene is cracked by zeolite catalysts according t o the following A mechanism
ZS S
Z where C is cumene, S is an active site, and Y and Z are products. By assuming that the Langmuir adsorption isotherm is valid for all adsorptions the above authors present a detailed development of a model for catalytic cumene cracking over aging catalysts. The time-on-stream decay function is employed to account for the aging of the catalyst. It is sufficient in this paper merely to present the final form of their rate expression.
wl, = 1
(54 m # 1 (5b) The exponential decay function used by Weekman (1968) results from the case of m = 1, while the more general case of m # 1 gives a hyperbolic decay function. For simplicity, the notation in eq 5b can be changed as follows 1 u = 1/(m - 1) (6) G = (m - 1)Kd
e
to yield
+ (m - 1)~dt)-"'"--')
+
P'Xe2 2Xe
8'
+
e X) In X____
x,- x
It was also shown that the cumulative conversion is calculated from
(11)
x in a run
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
255
I
400 TIME (8ECI
0
a00
Figure 1. Best fit of the 450' experimental data with the theoretical cumene cracking model
Correlating experimental data with the theoretical model given in eq 11 requires the estimation of four parameters: G, the aging constant; N , the aging exponent; p' and 8', combinations of the rate constant of the bond-breaking step and the adsorption equilibrium constants for components of the mechanism. Gas Oil Cracking in a Static Bed Reactor. Campbell and Wojciechowski (1969) have proposed the reaction mechanism
0
C
T
TIYE OW- 8TRLAY
I
I
w
40
I MIMI
(since moving beds operate a t steady state) and the fraction remaining obtained. In the j t h segment this is
The total amount converted after g segments is obtained by taking the products of eq 14 from j = 1 tog, S O E - - CAlCAZ
CAO
CAOCAI
CAW ...CAg-1
The fraction converted after g segments is 1
I A
B
as a simplified description of catalytic gas oil cracking. Here A is gas oil, B is desirable products, and C is undesirable products. Based on the assumption that gas oil cracking follows first-order kinetics (Blanding, (1953)), Pachovsky and Wojciechowski (1971) have developed a general model describing gas oil cracking in a static bed reactor. The model accounts for volume expansion, feed stock refractivity, and catalyst aging through the use of the time-on-stream decay function. The final form of the model is presented below
-
20
Figure 2. Comparison of model with experimental gas oil cracking data: catalyst 30-60 mesh REHX; stock, Mid Continent Gas Oil; temperature, 9OO0F
x
.;/ p,
10 CATALYST
1
- CA,/CAO
+ ~A(CAW/CAO)
The equation for the fluidized bed reactor can be written in more explicit terms. I n fact the final form of the equation is very similar to the static bed equation.
tf in this case is the mean residence time of the catalyst particles in the reactor. Procedure
I n a previous publication, Pachovsky and Wojciechowski (1971) have discussed the necessity for including in the rate expression a function accounting for chargestock refractivity. The parameter W is thus introduced into eq 13. As in the case of cumene cracking, the conversion in eq 13 is instantaneous and the cumulative conversion in a run is calculated from eq 12. Correlating experimental data with the model involves obtaining estimates of the four parameters N , G, K , and W. Gas Oil Cracking in Other Reactor Configurations. Pachovsky and Wojciechowski (1972) have extended their original gas oil cracking model to describe conversions in moving and fluidized bed reactors. I n extending the model, plug flow of both catalyst and feed was assumed for the moving bed reactor, and plug flow of feed and perfect mixing of solids was assumed for the fluidized bed reactor. The above authors chose to describe the moving bed as a series of fixed bed reactors charged with catalyst of constant age depending on the increment's position in the reactor. From eq 13 the instantaneous fraction converted can be obtained, hence the cumulative fraction converted is calculated 256 Ind.
Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
The model describing the catalytic conversion of cumene was fitted to several sets of experimental conversion data obtained in our own laboratories. The model for catalytic gas oil cracking however was applied to data not obtained in our laboratories. The most extensive sets of data were provided through the courtesy of a major oil company while the remainder were obtained from published material (Blanding (1953)). These data were obtained over natural clay, synthetic, and zeolite catalysts. The fitting of the cumene data presented somewhat less of a problem than the gas oil data. This was because the cumene data exhibited definite class I1 ( N = 1) aging behavior, thus leaving only three parameters to be determined. All computations were performed on the IBM 360 Model 50 computer using a minimum sum of squares of residuals as the criterion of fit. A residual was defined as the difference between cumulative conversion calculated from the model and that determined experimentally. The technique used was a numerical one due to Powell (1965). I n the case of gas oil data, the procedure was more complex. The fitting involved the determination of suitable values for
IO0
I
EXPERIMENTAL
MOOEL
CONST~TS
N = 0.763 G = 16.25 K = 5.237 Y
20
10
0
CATALYST
6.s
&.a
5i.w
TIME-ON-STRERM
sf.a
IMlNSl
x - I.Ul
-.
(MINI
Figure 3. Comparison of model with experimental gas oil cracking data: catalyst, 4-10 mesh REHX; stock, Mid Continent Gas Oil; temperature, 900°F
iiir
0.m
0 -0.71 U/!/U A - 0.97 + - 1.21
40
30
TIME-ON - S T R E A M
-
SPRtE VELOCITY
76.75
si.w
Figure 5. Comparison of model with Blanding’s gas oil cracking data: catalyst, natural; stock, 33.4 East Texas G.O. (602); temperature, 850°F
tI
1k.m
Figure 4. Comparison of model with Blanding’s gas oil cracking data: catalyst, natural; stock, 33.4 East Texas G. 0.(602); temperature, 800°F
the parameters G, N , K , and W . Unfortunately gas oil cracking displays class I11 aging behavior and thus no a priori value for N could be used. Because W remained as one of the parameters to be determined, an analytical solution to eq 13 was not available; consequently this equation also had to be solved by numerical methods. Again Powell’s method was used. All computations were performed as for cumene. The optimum values of G, K , N , and W determined by the above procedure were introduced into the models developed for moving and fluidized bed reactors (eq 16 and 17). Solutions to these models were obtained using the same IBM Model 50 computer. Discussion
I n the procedure, it was reported that a minimum sum of squares of residuals was used as the criterion for goodness of fit. This criterion itself is no guarantee that a particular model form is adequate. A more conclusive test involves the use of a statistical F test (Himmelblau (1970)). Coupled with this test, it is customary to plot the residuals against some suitable coordinate to determine if the residuals follow any trends. If a model satisfies the F tests and no trends can be seen in the residuals, then the model can safely be assumed to be adequate. These tests for model adequacy were performed whenever possible on the individual sets of data, and in all attempts, the model forms for both cumene and
Figure 6. Comparison of model with Blanding’s gas oil cracking data: catalyst, natural; stock, 33.4 East Texas G.O. (602); temperature, 900°F
gas oil cracking proved to be adequate representation of their respective data. I n the situations where insufficient data points were available to give meaningful results to these tests, it could only be inferred that the model forms represent these data sets equally well. Figures 1 to 6 inclusively show the experimentaI data points and the theoretical curves predicted by the model for several data sets treated. One of the unfortunate features of gathering data from literature is that the brevity of papers results in very sketchy descriptions of experimental techniques, apparati, and feed stocks. This problem was encountered with Blanding’s work (1953) and hence little is known about his catalysts, gas oils, and techniques. I n view of this, the discussion must be very general as it is not known which sets of data are strictly comparable. It is common knowledge that the reliability of parameter estimates increases with an increase in the number of data points used in their determination. For this reason the parameters for the cumene data and the parameters for the gas oil data sets obtained from the private source are believed to be good estimates of the true parameter values. I n these cases, all data sets contained greater than 20 data points. The same however cannot be said for the results reported by Blanding. In fact several sets contained as few as six points and the highest number in a particular set was twelve. Under these circumstances it can hardly be expected that the Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
257
CATlOlL
3 0
0 375
0 094 60 Y 0 Y U
5
-
40
0
30160 4/10
-
TIME ON STREAM, 1.
(SECS.1 0 5
0
Figure 7. Average conversion against catalyst time-onstream illustrating the three classes of aging catalysts
Table I. Parameter Values for Cumene Cracking Model Catalyst REY Parameters Temp, O C
400 450 500
N
G, sec-1
P 't sec
5
',
sec
m
1.00 0.020 1.01x 1 0 - 2 1.19 x 10-3 2.00 1.00 '0.013 1.09 X IOp2 1.04 X 2.00 1.00 0.013 5.67 X 3.38 X l o w 4 2.00
parameter values obtained from these data fittings are good estimates of the true values. We can, howe~er,be reasonably confident that their orders of magnitude are correct and that the general trends exhibited are meaningful. Figure 1 shows cumene conversion a t 450". Comparing the experimental data points with Figure 7, we see that cumene cracking over Y-sieve catalyst exhibits class I1 aging behavior (Campbell (1971)). For class I1 aging, the aging exponent must equal unity. This is not meant to imply that cumene cracking exhibits class I1 aging behavior over all types of catalysts, although recent work on cumene cracking over X-sieve catalyst a t our laboratories has also shown definite class I1 behavior. I n all of the cracking studies the time-on-stream theory of catalyst decay was incorporated to account for the aging of the catalyst during use. The low average deviations reported on Figures 1 to 6 indicate that the models were quite successful in correlating the experimental data. Additional credibility is given to the models and the decay theory by the fact that none of the parameters reported in Tables I and I1 are negative. This was gratifying since all the parameters were theoretically derived and negative values would not be physically interpretable. The significance of the trends in the parameter in Tables 1 and I1 can also be considered. It will be recalled that earlier it was shown that N is a convenient way of writing n / ( m - l), where n is the number of sites involved per reaction event and m is the number of sites involved per deactivating event. Cumene cracking studies have indicated that for this reaction, n is unity. I n gas oil cracking little information is available as to the value of n, however, based on the cumene studies and mechanistic considerations a value of unit seems reasonable. Knowing W , and assuming n = 1in all cases m is then easily calculated, and the results are reported in Tables I and 11. From these it is seen that most catalysts lose from one to three sites per deactivating event. Since it is impossible to lose a fraction of a site, the tabulated m values represent some kind of average 258 Ind.
Eng. Chem. Process Des. Develop., Vol. 12, No.
3, 1973
CATALYST
TIME
- ON - S T R E A M
10 (MINI
Figure 8. Comparison of moving bed performance with 30-60 and 4-1 0 REHX catalysts at 900°F
of the number of sites lost per deactivating event. These tabulated values of m appear to be reasonable in that they are all greater than unity. In cumene cracking m does not change with temperature, but in gas oil cracking m increases with temperature though the dependence is not strong. Unlike the case of cumene cracking where the existence of equilibria makes it difficultto isolate individual rate constants, in gas oil cracking the rate constant for the initial cracking rate is represented by the parameter K . As expected, Table I1 shows that K increases with increases in temperature. K also tends to be higher with synthetic catalysts than with natural clay catalysts for a given gas oil. This is not surprising since higher rate constants result in higher conversions a t a given time-on-stream. In fact the higher K values for synthetic catalysts attest to their higher activity. This of course is one of the major reasons for the popularity of synthetic as compared to natural catalysts. Another interesting feature is that the K values tend to be higher for heavy gas oils indicating that heavy gas oils tend to crack more readily. Finally the K values tend to be higher for zeolites than they are for either the synthetic or natural catalysts. This in part explains the popularity of modern zeolite catalysts. The parameter G has been used to represent the expression k(m - ~ ) [ S O ] ( ~ - ~Because ) [ P ] . of its complexity little can be said about G. At the present time, the physical significance of G is not fully understood and no discussion about the reasons for the behavior of the parameter will be attempted here. One noticeable feature of this parameter is that it decreases with increasing temperature. The last parameter to be discussed is W . This parameter appears in gas oil cracking and is intended to account for the fact that not all molecules in a chargestock have the same crackability. This problem is not encountered in pure reagent cracking (e.g., cumene cracking) because the chargestock in that case is homogeneous. From Table I1 it can be seen that W ranges from 0.0 to about 0.7 but many catalysts show the former value. Previously (Best (1971)) the authors have interpreted a W value of 0.0 as indicating diffusion limitations in an X-sieve catalyst. If this analysis is correct then the distinct possibility exists that some of the results reported by Blanding are for diffusion-limited catalysts. From the table it can also be seen that this parameter decreases with temperature. I n fact all but one of the W values of 0.0 occur a t temperatures of 850°F or lower. A possible explanation for this is that a t the low temperatures the catalyst becomes diffusion limited due to condensation within the catalyst pores. One final point of
Table II. Parameter Valuer for Gas Oil Cracking Catolyrt
Stock
30-60 REHX 4-10 REHX 10-80 natural clay Synthetic Natural clay Synthetic Synthetic Synthetic Natural clay Natural clay Natural clay Natural clay Synthetic Synthetic Synthetic Synthetic Synthetic Synthetic
MCGO MCGO ET00600 ETG0605 ETG0606 ETG0602 ETG0602 ETG0602 ETG0602 ETG0602 ETG0602 ETG0602 PG0483 PG0483 HVYPGO696 HVYPG0696 PG0486 PG0486
Temp,
K,
OF
hr-’
N
1423.8 133.9 0.798 7.128 7.085 9.585 6.686 17.443 4.990 5.237 7.442 4.095 8.292 9.687 37.770 62.032 3.847 9.468
3.60 3.68 0.81 0.48 0.61 0.63 0.44 0.72 0.94 0.76 0.77 0.59 1.13 0.92 0.77 0.64 0.69 1.00
900 900 850 850 850 800 850 900 800 850 900 950 850 920 850 920 850 920
interest is that the largest W value reported occurs with the 30-60 mesh X-sieve catalyst. This may be due to the sieving effect of zeolite catalysts. Such a sieving effect will tend to emphasiae molecular weight and shape distributions in a gas oil. When the gas oil cracking model was applied to idealized moving and fluidized bed reactors, i t was observed that the individual classes of catalyst aging behavior became indistinguishable. All catalysts behave as class I in these types of reactor configurations. The reason for this is that both these reactors operate a t steady state and consequently, the larger their catalyst holdup (tf), the higher the conversion they will produce a t a constant catalyst/oil feed ratio. Several other interesting features arose from the comparison of these two reactor configurations. The most important result is that conversion can always be made to reach 100% regardless of catalyst/oil ratio or catalyst size and type in both moving and fluidized beds. A more interesting result is that for a given catalyst and at a given temperature the moving bed reactor always produces a higher conversion than the fluidized bed reactor at an identical time-on-stream and catalyst/oil ratio. As catalyst/oil ratio increases, the fluidized bed tends to approach the results of the moving bed. These results are presented graphically in Figure 8. Moving bed reactors, however, require catalyst in the form of spherical pellets about 3 mm in diameter. Pellets of this size tend to be diffusion limited. Fluidized beds, on the other hand, use diffusion-free catalyst. Comparing conversion over a diffusionlimited catalyst in a moving bed with conversion over a diffusion-free catalyst in a fluidized bed shows that for industrial times-on-stream (10-15 min) conversion in a moving bed reactor is still superior. Because fluidized bed units often operate a t higher catalyst/oil ratios than moving beds, perhaps this advantage is not important industrially. At this time we are of course unable to “prove” our theory. What we have done is shown its general applicability and attempted to indicate some of the conclusions which are emerging from a survey of decay data. I n Table I11 we have attempted to show that most of the more recently reported decay functions are merely special cases of our more general model. The fact that other investigators have obtained reasonable fittings with their decay models only serves to support our model.
G,
18.2 9.32 3.2 84.6 143.56 45.74 29.41 9.74 17.31 16.25 6.27 1.81 21.48 22.69 22.02 16.39 25.51 12.65
Figure no.
W
m
0.72 0.00 0.05 0.13 0.22 0.00 0.00 0.50 0.00 0.10 0.55 0.26 0.00 0.00 0.12 0.31 0.00 0.23
1.28 1.28 2.24 3.00 2.57 2.55 3.30 2.38 2.06 2.31 2.31 2.69 1.88 2.09 2.30 2.56 2.45 2.00
hr-’
2 3
4 5 6
7
r
---
0.315 0,084
MOVINQ
e a
1
I
0 0
20
10 CATALYST
TIME - O N
- STREAM
30
4 0
(WIN)
Figure 9. Comparison of moving and static bed reactors with 30-60 REHX catalyst at 900°F
J
0’ O
6
10 CATALYST
2.0 TIME-ON-STREAM
3.0
I
4.0
(MINI
Figure 10. Comparison of fluidized and static bed reactors with 30-60 REHX catalyst at 900°F
What makes the model particularly pleasing, is that it has been derived from the widely accepted premise that the activity of a catalyst declines in mth order fashion (Szepe and Levenspiel (1968)). If no assumptions are made in solving the resultant differential equation, then a two parameter decay function must arise. Only by making certain assumptions can fewer parameters be obtained. Ind. Eng. Cham. Process Der. Develop., Vol. 12, No. 3, 1973
259
Table 111 Type of decay
Ref
Linear
Equation
Maxted (1951)
0 =
80
-
[AIL
Differential form
-dedt - [AI
Eley-Rideal (1941) Crowe (1970) Crowe-Lee (1971) Exponential
[AI lime = & a t t = 0
-de dt
- = [Ale
Weekman (1968) Ogunye-Ray (1970)
m = l
[AI Iime = & a t 1 = 0
kd =
-de - - - [AI02 dt
Germain-Maurel (1958) Ogunye-Ray (1971a,b) Miertschin-Jackson (1971)
Reciprocal
m=O kd =
Pease-Stewart (1925)
Hyperbolic
Equivalent constants of Wojciechowski model and limits
-d-B e3 dt - [AIS
Voorhies (1945)
m = 2 kd = [AI lime = e o a t t = 0
[A1/2
kd =
m = 2
lime Power function
Blanding (1953)
kd =
= m
att = 0
[BA]l/[Bl . .
lime
Nace, et al. (1971)
-dO _ _-
Wojciechowski (1968)
-de = kdem
dt
[Alem
=
[A](m
03
-
at t = 0
1)
>> 1
lime=latt=O
Woj ciechowski
dt
CAT I OIL
_ _ _ _ -------
3 0 0 37s 0 094
_ - - _ - - - - ---_
4/10
30/60
-
I
0
10 CATALYST
TIME-ON-STREAM
2 0
30
(MIN)
Figure 1 1 . Comparison of conversion at 9OOOF in a moving bed reactor with 4-1 0 mesh REHX catalyst and a fluidized bed reactor with 30-60 mesh REHX catalyst
Despite the fact that four parameters have been used in our gas oil cracking model as opposed to two in previous publications (Weekman (1968), Nace, et al. (1971)) none of the parameters appear to us to be extraneous. I n fact we use fewer parameters than may be necessary to describe the complex gas oil cracking system. If no assumptions are made, six parameters are needed: a rate constant for the cracking reaction, an order for the cracking reaction, a rate constant for the decay reaction, an order for the decay reaction, a t least one parameter to describe the stock refractivity, and a parameter t o account for volume expansion due to the 260 Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
G = kd(m - 1)
M = l / ( m - 1) lime= 1 a t t = O
cracking reaction. I n our model we have assumed, as had Blanding (1953) and others, that the cracking reaction is first order and have eliminated that parameter. Also by assuming that the volume expansion is a linear function of conversion we have eliminated the expansion parameter. This latter assumption is not strictly correct and may in future have to be reconsidered. We feel, however, that the parameter W is one which cannot be eliminated. It is difficult to believe that all feed stocks would process the same refractivity as suggested by Weekman (1968) and Nace, et al. (1971). The fact that our fitting of Weekman’s data results in a value for W of 0.7, which closely compares to the empirical value of 1 chosen by Weekman, further supports our argument since in many other cases it seems W departs from 1 to a significant degree. Conclusions
(1) The time-on-stream theory of catalyst decay was used to account for catalyst aging during use. In all cases studied thus far the data supported the proposed models and hence it can be concluded that the time-on-stream decay theory describes the observed aging behavior satisfactorily. (2) The time-on-stream decay theory predicts that there are three distinct classes of aging behavior observable in a static bed reactor. The individual classes depend on the value of the aging exponent AT, that is, whether N < 1 (class I), A: = 1 (class 11),or W > 1 (class 111). (3) The individual classes of aging behavior cannot be distinguished in moving and fluidized bed reactors. In these reactors the catalyst always behaves as class I.
(4) None of the parameters calculated from experimental data has been found to be negative. This was to be expected if the model is to have some validity since a negative parameter would not be physically meaningful in the theoretical derivation. ( 5 ) Catalysts lose one to three sites per deactivating event and the number of sites lost is not a strong function of temperature. (6) The rate constant K for gas oil cracking increases with temperatures and tends to increase in the order of natural clay, synthetic, and zeolite catalysts on any given gas oil. K values are also higher with heavy gas oils indicating that heavy gas oils crack more readily. (7) The aging parameter G decreases with increase in temperature. (8) The refractivity parameter W ranges from 0.0 to 0.7 with the highest value occurring on an X-sieve zeolite catalyst. This suggests that molecular sieving of the chargestock within the catalyst may cause the chargestock to look more inhomogenous to molecular sieve catalysts. Nomenclature
A B C
reactant in triangular mechanism, gas oil in this case desirable products in mechanism, gasoline in this case undesirable products in mechanism, coke and dry gas in this case G s aging parameter (hr-l) (function of temperature) K = (k01 koz) sum of the initial rate constants for the simplified catalytic cracking mechanism (hr-l) (function of temperature) K d = (kd[SO](m-i) [PI) deactivation constant containing nertinent Dronortionalitv factors (function of temDerature) M’ = agiAg exponent, i / ( m - 1); dimensionless N = aging exponent, n / ( m - l),dimensionless P = catalyst to reagent ratio or catalyst/oil ratio (volume of catalvst/volume of feed) ” , = concentration of poisons (function of temperature) = concentration of active sites a t time t (sites/mZ) = concentration of active sites initially (sites/m%) k-2 = composition parameter for the rate constant function (dimensionless) Y . 2 = aroducts in cumene cracking X’ = instantaneous fractional convGsion a t time t X A = instantaneous fraction of feed converted (dimensionless) X E = equilibrium fractional conversion (dimensionless) ZA = cumulative fraction of feed converted (dimensionless) a = order of reaction with respect to A b = proportionality constant for T a Ptt g = no. of static bed segments into which moving bed reactor is divided = = =
+
= rate constant per catalytic site (function of temperature) ko = initial rate constant in cracking mechanism (hr-1) (function of temperature) k d = deactivation rate constant (hr-l) (function of temperature) m = order of deactivation reaction n = order of cracking reaction with respect to the concentration of active sites p , p, s = model parameters p ’ , p’, s‘ = modified model parameters (sec) tr = catalyst time-on-stream or total run time of the experiment (hr) t = catalyst time-on-stream during an experimental run (hr) €A = volume expansion correction term based on initial conditions (= 1 for cumene cracking; = 2.4 for gas oil cracking) 7 = reagent contact time (hr) e = fraction of active sites available (dimensionless)
k
literature Cited
Best, D. A., Pachovsky, R. A., Wojciechowski, B. W., Can. J . Chem. Eng., 49, 809 (1971).
Blanding, F. H., Ind. Eng. Chem., 45, 1186 (1953). Campbell, D. R., Wojciechowski, B. W., J . Catal., 23, 307 (1971). Campbell, D. R., Wojciechowski,B. W., J . Catal., 20, 217 (1971). Crowe, C. M., Can. J . Chem. Eng., 48, 576 (1970). Crowe, C. M., Lee, S. I., Can. J . Chem. Eng., 49(3), 385 (1971). Himmelblau, D. M., “Process Analysis by Statistical Methods,” Wiley, New York, N. Y., 1970, pp 166 and 167. Eley, D. D., Rideal, E. K., Proc. Roy. SOC.,Ser. A, 178, 429 (1941).
Germain, J. E., Maurel, R., C . R. Acad. Sci., 247, 1854 (1958). Maxted, E. B., Advan. Catal., 3, 129 (1951). Miertschin, G. N., Jackson, R., Can. J . Chem. Eng., 49(4), 514
,-~.
11Q71 -,.).
Nace, D. M., Voltz, S. E., Weekman, V. W., Ind. Eng. Chem., Process Des. Develop., 10 (4), 530 (1971).
Ogunye, A. F., Ray, W. H., Ind. Eng. Chem., Process Des. Develop., 9(4), 619 (1970).
Ogunye, A. F., Ray, W. H., Ind. Eng. Chem., Process Des. Develop., 10(3), 416 (1971a).
Ogunye, A. F., Ray, W. H., Ind. Eng. Chem., Process Des. Develop., 10(3), 410 (1971b).
Pease, R . H., Stewart, L., J . Amer. Chem. SOC.,47, 1235 (1925). Pachovsky, R. A., Wojciechowski, B. W., Can. J . Chem. Eng., 49, 26.5 --- (1971). Pachovsky, R.A., Wojciechowski, B. W., Can. J . Chem. Eng., \--.
50(2), 306 (1972).
Powell, M. J., Computer J., 5, 147 (1962). Szepe, S., Levenspiel, O., Chem. React. Eng. Symp., Brussels f 1968). \--
~I
Voorhies, A., Ind. Eng. Chem., Process Des. Develop., 37, 318 (1945).
Weekman, V. W., Ind. Eng. Chem., Process Des. Develop., 7, 90 (1968).
Wojciechowski, B. W., Can. J . Chem. Eng., 46, 48 (1968). RECEIVED for review May 17, 1972 ACCEPTED February 7, 1973
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 3, 1973
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