COKE FORMATION KINETICS ON SILICAALUMINA CATALYST Anabsis Y U l C H l OZAWA1 AND K E N N E T H B. BISCHOFF2 T h e University of Texas, Austin, T e x .
A theoretical kinetic study of coke formation was performed. The relation between the weight of coke on catalyst and process time followed from the effect of coke on the activity of the catalyst. The deactivation function of the catalyst, expressed linearly in terms of the weight of coke on the catalyst, agreed reasonably well with experimental data. The rate constants for the cracking and the coke formation reactions were then determined. The activation energies for the main reaction and the coke formation reaction were estimated to be 13.1 and 12.5 kcal. per mole, respectively. The proposed kinetics was also applied to other experimental data for the cracking of n-hexadecane over a silica-alumina catalyst. of catalyst activity is observed in many gas-solid catalytic reactions, due to the deposition of carbonaceous material on the catalyst, which decreases the active sites for the chemical reaction. This poisoning may be due to a side reaction involving the same reactant with the main reaction, to a further reaction of the primary product of the main reaction, or to an impurity in the reactant. As the coke is accumulated on the catalyst, the activity of the catalyst for both main and side reactions usually decreases gradually. T h e coke may also affect the rate of diffusion of the reactant gas through the catalyst pores, if enough is deposited. I n previous work on obtaining fundamental kinetic expressions for these situations, Pozzi and Rase (1958) developed an expression for the fouling reaction during isobutylene hydrogenation over a nickel catalyst based on a variation of the extended Langmuir-Hinshelwood treatment. Masamune and Smith (1966) derived equations to describe the bulk rate of a gaseous reaction on a porous catalyst whose activity changes because of a fouling reaction, and a pellet effectiveness factor was evaluated by a numerical solution of the mass balances. A similar study by Takeuchi et al. (1966a) expressed the effect of coke in terms of the effectiveness factor. T h e nonisothermal case was also considered for a packed-bed reactor. Takeuchi et al. (1966b) expressed the activity factor of the catalyst as a function of the coke formed for the hydrogenation of isobutylene over a supported nickel catalyst. Froment and Bischoff (1961) suggested that the change of conversion of the main reaction due to the coke formation reaction should be directly related to the amount of coke formed instead of to process time as is often done. Expressions derived by Froment and Bischoff were used by Massamune and Smith (1966) and were applied by Van Zoonen (1965) to fixed-bed hydroisomerization of olefins over a silica alumina-nickel sulfide catalyst. T h e latter study assumed that both main and fouling reaction rates were inversely proportional to the amount of coke.
A
DECREASE
or formation reaction. T h e cracking reaction is simply described in terms of an initial reaction gas and products
A (9)
+
(1)
€3 (g)
T h e fouling reaction (the coke formation reaction) proceeds either in series or parallel with the main reaction, Parallel. A(g) Series.
B(g)
-+
-+
C(s)
C(s)
(2)
(3)
where A, B, and C acnote reactant, product, and coke, respectively. Equations for Concentrations within the Pellet
T h e material balance equations for reactant A and product B within the spherical catalyst pellet can be written as follows: PARALLEL MECHANISM
where Q represents the effect of coke on the rate of the main and coke formation reactions (assumed to be the same for both). T h e rate equation for the coke formation reaction is: (5) SERIESMECHANISM.Similarly,
T h e material balance for product B is:
For the coke formation reaction, Theoretical Considerations
T h e reaction kinetics may be represented by two independent reactions, the main or cracking reaction, and the fouling Present address, Mobil Oil Co., Paulsboro, N.J. Present address, Department of Chemical Engineering, University of Maryland, College Park, Md. 20742 72
I&EC PROCESS DESIGN A N D DEVELOPMENT
where CAt and CBt are the concentrations of A and B; DA and DB are effective diffusivities of A and B within the catalyst pellet; kA, k A , and k B , are rate constants for the main reaction and for the parallel or series fouling reactions, respectively;
q is the concentration of coke on catalyst; RA, RA,,, RBI, denote concentration-dependent parts of the main reaction rate expressions on CAi and fouling reaction on cAtand cBt; p s is the density of catalyst pellet; and e p is the internal void fraction of catalyst pellet. Initial and boundary conditions for the differential equations are : INITIAL CONDITION
Equation 18 becomes BOUNDARY CONDITIONS
I
bcAi
- (kAoEA f kA,r"EA,,) Jvfisc~s = o
47rrO2D A -
~
br 1
l=lo
(21) Finally, substituting the boundary condition Equation 12, kc,A
where CASand CBBare the concentrations of A and B a t the exterior surface of the catalyst pellet, and k c , A and k c , B are the gas film mass transfer coefficients of A and B.
*
S,Z(CA- CA') = (kA"E.4
+ ~ A , I " E A wnsc~s ,/) (22)
T h e gas film mass transfer can be shown to be much faster than the reaction rate, and CASin Equation 22 can be replaced by CA. Thus, combining Equations 14 and 22,
FCAo
=
FCA
+ (kAoEA f ~ A , , " E A , ,WQCA )
(23)
Equations for Concentration outside the Pellet
T h e reactor to be considered (Ozawa and Bischoff, 1968) is considered to be a differential reactor, so that the concentration of gas throughout the reactor is uniform and the inlet and outlet flow rates are essentially equal. Thus, the material balance equations for reactant A and product B outside the catalyst pellet are
Estimation of Effectiveness Factor
The effectiveness factor for a spherical catalyst pellet and for a first-order irreversible reaction is expressed as (Satterfield and Sherwood, 1963)
E =
3[h coth (h) h2
- 11
(25)
.-
Simplification of Equations
T h e effective diffusivities, D A and D,, can be considered constant with time (Ozawa and Bischoff, 1968). The accumulation terms in Equations 4, 6, and 7 can be neglected, since the transient coke deposition is slow and the O-function does not change significantly in the time necessary to reach steady state (see also Masamune and Smith, 1966). Previous investigators have indicated that the catalytic cracking reaction was reasonably well represented by a first-order irreversible reaction kinetic scheme (Greensfelder et al., 1945 ; Panchenkov and Lolesnikov, 1959). The coke formation reaction is also assumed irreversible and of first order with respect to reactant. After some preliminary calculations, the parallel mechanism was chosen because of its better agreement with experiment. Equations 4 and 5 are thus simplified as follows:
where h is a Thiele modulus. T h e effective diffusivity of the catalyst pellet for hydrogen a t room temperature was obtained by Weisz's method, and transformed into the value for ethylene at the reaction temperature by using the expression for Knudsen diffusion :
in which R is the gas constant and M is molecular weight. T h e following values were substituted into Equation 26. r,, = 0.2 cm. k = 0.8 cc./min. g.-cat. (approximate maximum value on basis of Table I ) p s = 1.28 g./cc. D e = 0.5 sq. cm./min.
Hence,
h = 0.29 Multiplying Equation 1 6 by 4m2, integrating with respect to r , and using the boundary conditions, give
(1 8) Introducing the following expressions, defining effectiveness factors, gives
and so E can be taken as unity. This value of the effectiveness factor is somewhat greater than those sometimes obtained for the cracking of large molecules (Satterfield and Sherwood, 1963). According to the expression for Knudsen diffusivity, the effective diffusivity becomes smaller for larger molecules, causing a larger Thiele modulus and a smaller effectiveness factor. Moreover, the estimation of the effective diffusivity for larger molecules based on the value obtained experimenVOL. 7
NO. 1
JANUARY 1968
73
presented four forms of the Q-functions for poisoning of the aS,)-l, catalyst: R = 1 - US,, R = exp(--a&), R = (1 and R = (1 US,)^/^, where S, is the relative poison concentration and a is a constant. Maxted (1951) proposed the linear aC, to represent the poisoning effect on a platiform, Q = 1 num catalyst, where C is the concentration of poison. T h e hyperbolic form of R with respect to the weight of coke, R = 1/(1 aq), was also applied to the hydrogenation of isobutylene over a supported nickel catalyst. In the present investigation, the form of Q was determined as a function of q graphically, by plotting Q against q . Introducing the dimensionless variables, + A = ( C A / C A " ) , Z= [ ( k A o k A , / " ) W / F ] , and e = ( k A , I " C A " . t ) , Equations 23 and 24 become
tally by using hydrogen and Equation 27a may be erroneous, since a portion of the pores may be too small for penetration by larger molecules and the diffusion process of large molecules through micropores may not always be treated as Knudsen diffusion. Therefore, calculated values of the effective diffusivity for large molecules could be greater than the actual values, causing a smaller effectiveness factor. However, the calculated value of the diffusivity for the present case is considered to be correct because of the relatively small size of the ethylene molecule. As a result of these calculations, one can conclude that pore diffusion resistance through the catalyst pellet was negligible for the present case and take E A = E A , , = 1.0. Estimation of
R
+
-
-
+
+
as a Function of 4
1=
T h e quantity R represents the effect of the coke on the activity of the catalyst and should be directly related to the weight of coke on catalyst. Several forms of the R-functions have been proposed. Froment and Bischoff (1961) assumed a n exponential form Q = exp(-aq), and a hyperbolic form R = 1/(1 pq) where a and /3 are constants. Masamune and Smith (1966) suggested the linear form R = 1 - q / q o where qo is the concentration of the coke on the catalyst when deactivation is complete. Anderson and Whitehouse (1 961)
d'A
+
(28)
ZRd'A
Modifying Equation 28,
+
0.03
The quantity 01
I
can be obtained from the conversion data
@A
I
I
I
I
I
Figure 1 . Determination of fouling function at
500"
C.
I--------------t077
0.01
I
0
I
I
10
20
I
I
30
40
I
50
I
I
60
70
WEIGHT OF COKE ON CAT. I q x l &
0.0:
Figure 2. Determination of fouling function at
450" C.
z
0.0 4C.C
082
0.c
-
097
I
74
I L E C PROCESS DESIGN A N D DEVELOPMENT
-
I
I
I
I
I
I
0
098
0
080
Figure 3.
A
099
of fouling function at 400' and 350" C.
Determination
400 'C 8 350 *C
0
0
I
I
I
10
20
30
WEIGHT OF COKE ON C A T . (q x104)
T h e values of (1 - @ A ) / # A thus obtained are plotted against q as shown in Figures 1 , 2 , and 3, where the run numbers correspond to the reaction conditions discussed in the previous article. T h e a-function can be represented by a straight line over much of the range of variables, but not in the initial portion where the catalyst activity is very rapidly declining. However, because of serious problems in reproducibility in this region in practice, it was felt that the best approach was merely to extrapolate the longer-time straight lines and use the simple linear form for the entire range in subsequent calculations. I t was also felt that this would be the most useful practical scheme for design applications. W i t h the consideration of Boundary Condition 10, the %function can therefore be written as follows:
Q = l - a q
and k a , f o are listed in Table I with the values of a for different temperatures. The values of kA' and k A , f o were then plotted against 1 / T in the usual fashion in order to find the activation energies of the cracking and the coke formation reactions in the Arrhenius-type equation, where T is the reaction temperature in OK. (see Figure 4 ) . T h e activation energies for the main kA"
Table 1.
Temp., O
c.
500
450 400 350
Rate Constants for Different Temperatures kAo,
kA,IO,
Cc./G. Min.
Cc./G. Min. 0.508 0.279 0.153 0.063
a
0.244 0.125
24.0
0.075 0,033
226.6
77.1 457.4
(31)
where a is a constant. Hence,
ZQ = Z
- Zaq
(32)
T h e intercept of a straight line obtained by the plot of Z Q q gives the value of Z and the slope of this line gives the value of a. Combining Equations 28 and 29, as.
Substituting Relation 31 into 33 and integrating with respect to q and 8 give 1 Zq - - ln(1 - aq) = 8 = Kt (34) a
Substituting the values of Z and a graphically obtained, the left-hand side of Equation 34 is calculated and plotted against process time, t (minutes). T h e slope of the straight line thus obtained yields the value of K ( = k A , f " . C,"), since 0 = k A , , O CAot. All experimental data were then processed by a nonlinear regression program, using these graphical values as initial guesses. T h e values of a, K , and Z were thus improved to give the best fit to Expression 34. Because of the ignored initial data points, these k o values are not the "true" ones for fresh catalyst but represent "slightly aged" figures that should be more reproducible. T h e rate constants for the main reaction, k A o , and for the coke formation reaction, k~,,",were calculated from the values of Z and K thus obtained. T h e arithmetic mean values of
I l lx
lo'
Figure 4. Arrhenius plot of rate constants and fouling parameter VOL. 7
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JANUARY 1 9 6 8
75
catalyst is greater a t the initial stages and a linear form of Qfunction would not be satisfactory here.
reaction and the coke formation reaction were 13.1 and 12.5 kcal. per mole, respectively. kAo and kA,lo can thus be written as a function of temperature: kAo = 2.69 X.A,yo
=
x
1OaeXp. (-1.31
8.05 X 10'exp. (-1.25
x
1O4/RT)
(35)
Interpretation of Empirical Constant a
X lO4/RT)
(36)
The empirical constant, a, can be partially interpreted according to Langmuir-Hougen-Watson adsorption-type mechanisms (Pozzi and Rase, 1958). Let No be the molar concentration of active sites on the unfouled catalyst and N t be that a t any time t. Then,
T o check the validity of the kinetic expressions, the theoretical values o f t required to produce the given amount of coke q were calculated, based on Equation 37, Zq
t =
1
- -In U
(1
- aq)
No
(37)
= aiq
(38)
where a1 is some proportionality constant. By dividing Equation 38 by No and rearranging
K
and the values in Figure 4. T h e results thus obtained are shown in Figures 5, 6, and 7 along with the experimental data. Solid lines represent the calculated values and points represent experimental data. Accordance between calculated and experimental points is reasonably good. The deviation observed for smaller values of t is expected, since Equation 34 is derived based on Equation 31 which is valid only after a certain length of time. The effect of coke on the activity of
Figure 5.
- N,
NJNO = 1 Since N t / N o is equal to
- a,q/No
(39)
kA/kAo
=
kA/kA'
- a1q/N0
1
Hence,
L Y I I N=~ a
Comparison
of calculated and experimental results
PROCESS TIME(Min.1
1
Figure 6. Comparison of calculated and ex-
I
I
I
1
-
50
perimental results
I
I
t
40 30 0 X 0
I
/
099
A
0
10
20
30
I
I
I
I
40
50
60
70
PROCESS TIME (Mi" )
76
l&EC PROCESS DESIGN A N D DEVELOPMENT
Figure 7. Comparison of calculated and experimental results
PROCESS TIME(Min.1
If In a is plotted against 1 / T , a can be also approximately expressed in the Arrhenius form as follows (Figure 4) :
a = 1.30 X lO-4exp(1.90 X lO4/RT)
(45)
(42)
Similarly for the coke formation reaction,
Hence,
No
= al
X (1.30)-l X lO4exp(-1.90
X lO4/RT)
(43)
p
where
T h e activation energy in Equation 43 is close to that of Equation 35, which would be expected if ko is proportional to No.
= SRl/F
.
(47)
Initial and boundary conditions are:
Application of Proposed Kinetics to Other Reactants
(48)
T h e proposed linear expression of Q with respect to q was applied to the experimental data of Eberly et al. (1966) for the cracking of n-hexadecane obtained in a long packed bed or integral reactor. T h e material balance equation for reactant A in a packed bed can be written as
(49) Introducing a new variable
bq-311
in which SR is the total cross section of reactor, z is longitudinal distance from the bottom of the packed bed, and p B is the bulk density of the catalyst. Introducing the dimensionless variables + A = CA/CAQ,t = t i l , 8 = F t l S ~ t l and , a = pe(k~' kA,,O)/F, where 1 is the depth of the packed bed, gives
- c
I
I
1
I
I
I
I
I
0.12
0
e
8
g 0.06-
W
0.04-
0 02
-
+A
~ ( 1 aq)
(51)
I
0
LHSV=I.O
0
LHSV~2.O
-
Figure 8. Relation of ( 1 conversion) and weight of coke for cracking of n-hexadecane Data of Eberly ef al. ( 1 9661
\\ \\-
b
0-t
' 4
z
2%
=
Differential Equations 50 and 51 with initial and boundary conditions 48 and 49 may be solved with a procedure used by DuDomaine et al. (1943) (see also Froment and Bischoff, 1961). T h e solutions are:
+
5
r)
I
I
I
I
I
I
I
I
I
l O Q ( l / q h , t = I)
VOL. 7
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77
Nomenclature
a
(53)
CA, C B C, DA,
d T h e average weight of coke on catalyst q throughout the bed is
p
=l l q d ( = 1
a
- - In aa
[I
+
e-@q(eU
1 a
- I)]
+ -aa1 In
h
=
[@A,&ll
(54)
The quantity @ a , ~ can - l be calculated from the conversion a t the outlet of the reactor. According to Equation 54, a plot of p us. log [ @ A , & l ] should yield a straight line, if the proposed form of Q is reasonable. The experimental data for the cracking of n-hexadecane over silica-alumina catalyst at 500' C. obtained by Eberly et al. (1966) were used for this purpose. Straight lines can roughly approximate the data in the range of LHSV greater than 1.0 (process time from 10 to 60 minutes), although the consistent deviations indicate that more study is required (Figure 8). The weight per cent of coke under these conditions falls in the practical range of less than 5%. The intercepts of these straight lines gave values of a which fell in the range of 10; this value is of the same order of magnitude as the one obtained in our study a t the same temperature, indicating that a may be dependent mainly on the type of catalyst. This might be expected, based on the adsorption mechanism interpretation. Other simple forms of the %function such as 1/(1 a q ) , or exp(-aq) were examined in order to obtain better agreement with the data of Eberly et al. (1966). However, none seemed to do a much better job, and the linear form served as well, especially in the practical range of less than 5% coke. This indicates that simple kinetic schemes may not represent the coke formation and fouling problem adequately.
+
Conclusions
The general mass balance equations representing the simultaneous main and coke fouling reactions along with any possible diffusion effects were discussed. For the experimental data to be used in the analysis, the diffusional resistances were negligible, which led to fairly simple equations for analyzing the kinetics. An approximate linear function for the decline of catalyst activity with coke level was found to represent the observed effects adequately, except for the initial period of very rapid activity decline. T h e rate constants calculated followed the usual Arrhenius formula over the 150' C. temperature range. A simple interpretation based on Langmuir-Hinshelwood-Hougen-Watson concepts was also presented for the fouling parameter. The same treatment only approximately reproduced some other literature data and so a truly general method is not yet available. Acknowledgment
T h e support of the National Science Foundation through Grant NSF GP-865 for part of the work is gratefully acknowledged.
78
E F
l h E C PROCESS DESIGN A N D DEVELOPMENT
DB
= empirical constant = concentration of A or B, g./cc. = weight per cent of coke on catalyst
effective diffmivity of A or B, sq. cm./min. diameter of catalyst pellet, cm. = catalyst effectiveness factor = flow rate, cc./min. = Thiele modulus
= =
K = kA,/OCA' kA, kA,/ = rate constant for main and coke formation reaction; k~', kA.1' = k A , k A , / a t t = 0 , CC./g. Cat. min. k c , A , kc,B = gas film mass transfer coefficient of A or B, cm./ min. = concentration of coke on catalyst, g./g. cat. Q RA, RA,, = concentration-dependent part of rate expression for main reaction and fouling reaction = radial distance from center of pellet; y o = radius Y of pellet, cm. = exterior surface area of catalyst, sq. cm. sez = cross section of reactor, sq. cm. SR = reaction temperature, O C. T t = process time, min. W = weight of catalyst, g. Z = W(kA' kA,/o)/F
+
GREEKLETTERS = constants e, 7 = dimensionless variables = density of catalyst, g./cc. P6 = density of catalyst bed, g./cc. PB a, p 6, E, s2 EP
= =
k/k"
internal void fraction of catalyst
SUBSCRIPTS A = reaction gas B = reaction product = fouling reaction f = inside the catalyst SUPERSCRIPT S = a t catalyst surface literature Cited
Anderson, R. B., Whitehouse, A. M., Ind. Eng. Chern. 53, 1011 (1961). DuDomaine, J., Swain, R. L., Hougen, 0. A., Ind. Eng. Chern. 35, 546 (1943). Eberly, P. E., Jr., Kimberlin, C. N., Miller, W. H., Drushel, H. V., IND. ENG. CHEM.PROCESS DESIGNDEVELOP. 5, 193 (1966). Froment, G. F., Bischoff, K. B., Chern. Eng. Sci. 16, 189 (1961). Greensfelder, B. S., Voge, H. H., Good, G. M., Ind. Eng. Chern. 37, 984 (1945). Masamune, S., Smith, J. M., A.I.Ch.E. J . 12, 384 (1966). Maxted, E. B., Aduan. Catalysis 3, 186 (1951). Ozawa, Y., Bischoff, K. B., IND. END. CHEM.PROCESS DESIGN DEVLLOP. 7, 67 (1068). Panchenkov, G. M., Lolesnikov, I. M., Izu. Vysshikh Uchebn. Zauedenii. 9 , 79 (1959). Pozzi, A. L., Rase, H. F., Ind. Eng. Che;. 50,1075 (1958). Satterfield, C. N., Sherwood, T. K., Role of Diffusion in Catalysis," Addison Wesley, Reading, Mass., 1963. Takeuchi, M., Kubota, H., Shindo, M., Kugaku Kogaku 30, 523 (1966a). Takeuchi, M., et al., Kuguku Kogaku 30, 531 (1966b). Van Zoonen, D., Proceedings of Third International Congress on Catalysis, p. 1319, Interscience, New York, 1965. RECEIVED for review January 16, 1967 ACCEPTED August 8, 1967
