EFFECT OF INTRAPARTICLE DIFFUSION
ON CATALYST FOULING Y U l C H l M U R A K A M I , T A K E S H I K O B A Y A S H I , T A D A S H I H A T T O R I , A N D M O R I Y O S H I M A S U D A '
Department of Synthetic Chemistry, Nagoya University, A7agoya, Japan
The problerri of catalyst fouling influenced b y intraparticle diffusion in a single pellet was studied theoretically and experimentally. Some theories were confirmed b y experiment. Two reaction schemes were studied: parallel reaction and series reaction. When the intraparticle diffusion resistance is small, coke deposition occurs from the inner part o f the pellet in the latter, while in the former it occurs from the outer part. With a large diffusion effect, deposition occurs from the outer part in both reaction schemes. A higher catalyst activity or greater diffusion resistance is accompanied b y a more rapid degradation of the over-all reaction rate in both reaction schemes, but in the series reaction scheme with a large diffusion resistance, the rate of the production of the intermediate product does not decrease as much.
catalytic reactions are usually accompanied by a lowering of the catalytic activity, fouling, and poisoning. Poisons involved in the reactants as impurities adsorb on the catalyst surface, causing poisoning, while fouling is caused by the deposit of carbonaceous materials, so-called "coke," produced by a side reaction. The effect of intraparticle diffusion is one of the most important problems in heterogeneous catalytic reactions; it causes many interesting phenomena. \Vheeler (1 951) studied the effect of intraparticle diffusion on catalyst poisoning and showed that, with a great diffusion resistance even if the active sites near the external !surface corresponding to only 10% of the whole pellet are poisoned, the over-all activity decreases to only 10% of the initial value. The regeneration of fouled catalysts by the combustion of coke with oxygen was studied by IVeisz and Goodwin (1 963), .who showed the rate-determining step of the regeneration process to be the intraparticle diffusion of oxygen. Catalyst fouling is more complicated than these two problems, and most published works on fouling have not considered the effect of intraparticle diffusion. Recently, Masamune and Smith (1966) dealt mathematically with the problem of much slower fouling than the main reaction, considering intraparticle diffusion by the pseudo-steady-state method. I n the present paper, the problem of relatively fast fouling in view of the intrapartic1.e diffusion was solved exactly, and some important results were confirmed experimentally. Two reaction schemes were studied. The fouling reaction proceeds simultaneously with the main one in a parallel reaction scheme, and consecutively to the main one in a series reaction scheme. Each reaction was assumed to be irreversible and of first-order kinetics under isothermal conditions. I n the parallel reaction scheme, the A reactant diffuses into the porous spherical catalyst, reacts on the active sites, and turns into the desirable product, B, or coke, C. I n the series reaction scheme, coke C is converted from the desirable product, B, remains on the active site, and makes the site inactive. Thus one coke destroys one active site (strictly speaking, one group of active sites) and causeis fouling. Therefore, the reaction rate constant, k , is expressesd by the product of the initial reaction rate constant, k,, and the fraction of activity left, p, defined as the ratio of the number of unfouled sites to that of the total sites, or k = k,p. ETEROGENEOUS
Present address, Mitsui Petrochemical Industry Go., Ltd., Tokyo, Japan.
Some of the results of this theoretical study were unexpected and had never before been observed experimentally. T o confirm them, two reactions were studied : disproportionation of toluene as a sample parallel reaction scheme, and dehydrogenation of primary alchols as a sample series reaction scheme. I n the former reaction, toluene reacts a t a first-order reaction rate (Ai et al., 1965) and should produce benzene equimolar to xylene, but the yield of benzene is always larger than that of xylene. This excess yield of benzene is caused by the demethylation of toluene proceeding simultaneously with the disproportionation of toluene; another product of demethylationLe., coke-lowers the catalytic activity (Izumi et al., 1963). This reaction is expressed by the following parallel reaction scheme : Toluene ( A )
+ xylene
Toluene (A)
-+
+ benzene + benzene
(B)
coke (C)
I n the dehydrogenation of primary alcohols, the intermediate product, aldehyde, is dehydrogenated and condensed on the active sites, and then converted to coke; this final product, coke, does not desorb from the active sites and lowers the catalyst activity. Thus, the series reaction scheme is followed here: Alcohol (A)
-+
aldehyde (B)
+
coke (C)
Theoretical Work
Parallel Reaction. p B Desirable reaction A
\C
Fouling reaction
Reactant A reacts on an active site in a catalyst pellet and becomes the desirable product, B, or coke, C. B leaves the active site and diffuses from the pellet, but C deposits on the active site, making it inactive. T h e mass balances of A and B in a spherical pellet are
As the coke, C, remains on the active site, the effective diffusivity is equal to zero, and the mass balance of C is:
- -a"
kospCa
at
VOL. 7
NO. 4
NOVEMBER 1 9 6 8
(3) 599
Assuming that the concentration of the initial active sites is A, the concentration of C is expressed by X(l - (a). Therefore, Equation 3 becomes:
Here,
(4) The initial conditions are :
C A = CB = 0 ,
(a
= 1 ; t = OforR
2
r
20
(5)
At the center of the catalyst, the concentration gradients of A, B, and (a are all equal to zero :
bCA - bCB b(a - - - = - = 0; r br br ar
=
0 for t
>
The quantity of coke which has deposited on the catalyst is defined by the following dimensionless equation :
lR
0
4 ar2(1
By equating the surface flux to the rate of bulk mass transport, the boundary conditions for A and B at the exterior surface of a pellet are found to be :
(CD) =
- (a)),
dr =
4
4
3 TR'CA'
1
_3
x2(1 -
(a)
dx
(20)
0
When (a is equal to zero, it is easily integrated:
(CD), = l / q ko
(CBb
- CB')
; r = R for t
= DB -
1
br
>0
(8)
r-R
Furthermore, the authors assumed that the concentration of A in the bulk, CAb,is always constant, C ,, and that the concentration of B in the bulk, CBh, is negligible in comparison with CAh-that is, CBhis nearly equal to zero. Here, k G is the mass transfer coeEicient in the gas film on the catalyst surface, and C A Sand CBs are the surface concentrations of A and B, respectively.
(CD), means all the coke that can be deposited on the entire catalyst pellet. The ratio of (CD) to ( C D ) , is the fraction of fouled sites on the entire pellet. Equations 9 through 20 have been solved numerically by the use of a digital computer. In numerical calculations, the 0.2, method of forward-difference form is used for p = 0 while after p = 0.2 the method of Crank and Nicholson (1947) is used.
-
Series Reaction.
Expressing Equations 1 to 8 in dimensionless form : (9)
I.C.
a = b =
B.C.
-
bx Arm
- (1 2
-bb ax
- a,)
h'B i
--b
2
b(a - = -qsm2(aa dP 0, q = 1 ; p = Ofor 1 2 -
bx
ba bX
= -;
db bX
-p-; s -
-
0; x =
2
o for p > o
x = 1 for p
0
A
+ .
B Desirable reaction
B
+ .
C
Fouling reaction
A reacts on active sites in the catalyst pellet and converts B like a parallel reaction. Some B diffuses out of the particle, and some B further reacts on the active sites to produce C, which remains in the pellet and causes fouling. The mass balances of A, B, and C in dimensionless form are :
(11) x
2 ba ba -+--=-+m2(aa ax2 x bx bp
@a
(12) (13)
>0
x=lforp>O
The over-all reaction rates are expressed by using the effectiveness factors ( E F ):
The initial and boundary conditions are the same as in Equations 12 to 15. The ( E F ) values for the series reaction are defined as:
Since these ( E F ) cannot be measured easily in experiments, (e) is defined as the ratio of the present ( E F ) to the initial (EF)rHere,
600
l&EC FUNDAMENTALS
(21)
3NBt
( E F ) r A=
m coth m
-
1
% m coth m - N B 1 / 2+ 1
(28)
1.0 (A
--
i -
500
IC D)
(EF), 0.1
100 50
0.01
0
0.02
0.04
0.06
0.08
1.03
'3 P Figure 1. Effect of q on ( E F ) , for parallel reactions = p = 1 ,m = 10, Nni = 20
10
1
+m
coth m
m coth m
+
AVBP -
2P
m coth rn
1 -
4;
-
0.2
0 0.2 X
0.6
1.0
Figure 2. Coke profiles in a pellet for various dimensionless tirne p
---
Concentration of A. (Parallel reaction) s = p = 1 , N e ; = 20, q = 1 / 5 0 0 . Left,.m = 2. Right, m = 20
1.0
0.8 0.6
8.
-I 0.4 0.2 0.0 1.0
0.6
0.2 0 0.2 X
0.6
1.0
Figure 3. Coke profiiles in a pellet for various dimensionless time p
----
Concentration of B. q = 1/500.
N g i = 20,
(Seuies reaction) s = p = 1, left, m = 2. Right, m = 20
for s = p
(29a)
for s # p
(29b)
1
+-1 2P 1 1 Bt
+ ?Ei -1 2P
m coth (m$)
0.6
1000
Figure 4. Effect of m on EA, (EF),, and (CD)for parallel reaction s = p = 1 , NE^ = 20,q = 1 /500
-
1.0
100
P
lo
(CD)and ( C D ) , are the same as before. These equations have also been solved numerically by the use of a digital computer. Results of Theoretical Work
The number of active sites was deduced from the data of the chemisorption of hydrogen on nickel (about 101jatoms per cc.; Ashmore, 1963) or the data of the number of acidic sites on a silica-alumina catalyst (about lo2' per gram; Murakami et al., 1963). As C.4bis usually about mole per liter, the ratio of the bulk concentration of '4 to the concentration of active q has a great sites, q, \vi11 have a value of from 10' to effect on the rate of fouling. I n the case of a small q value, the rate of fouling is slow and q p becomes only a time-scaling parameter, as shown in Figure l . O n the other hand in the case of a large q, q p cannot be regarded as a time-scaling parameter in the initial period of fouling. Figures 2 and 3 show, respectively, the radial profiles of the fraction of the destroyed sites and of the coke deposited in the pellet. Figures 4 and 5 show, respectively, the effect of the Thiele modulus (m) on the effectiveness factor ( E F ) , (e), and the amount of coke in a pellet ( C D ) . Fouling proceeds faster at a larger m . A comparison between Figures 4 and 5 indicates that fouling proceeds faster in the parallel reaction scheme than in the series reaction scheme under the same conditions, because of the difference in the concentration of the component which converts to coke. The concentration of A in the parallel reaction scheme is higher than that of B in the series scheme. VOL. 7
NO. 4
NOVEMBER 1 9 6 8
601
I .o 500
E.
(CD)
0.1
100
50
(FFI.
0.01
10
100
1
Figure 7. Effect of Biot number on < A , (EF)B, and (CD) for parallel reaction s = p = 1, m = 10, q = 1 /500
I"
1
10
P
100
1wo
Figure 6. Effect of s on €4, (€FIB,and (COl for series reaction p = 1,m = 10,Nsi = 20,q = 1/500
Figure 8. Cross section of catalyst pellet after 10 minutes' reaction of disproportionation of toluene Left, 440'
Figure 6 shows the effect of the selectivity, I ( = ko2/kol). A larger I value causes faster fouling, which is to be expected because k,, is the reaction-rate constant of cake formation. The same result was obtained in the parallel reaction scheme. Figure 7 shows the effect of Biat number (= 2kc R / D ) in a parallel reaction scheme. A larger NBi value causes faster fouling, while the effect of N,, on the fouling rate in a series reaction scheme is not as large. Of course, the effect of Nst on ( E F ) is great in both cases. The effect of p (= D B / D d ) is small in both reaction schemes.
Materials a n d Procedure. An alumina-horia catalyst with 10 weight yo boria was used in the disproportionation of toluene, and an alkaline-alumina catalyst with 10 weight sodium in the dehydrogenation of primary alcohols. Both catalysts were prepared by the impregnation technique; spherical alumina pellets 5 mm. in diameter were impregnated with boric acid or sodium carbonate, and dried up. The alumina pellets used (Neobead D-5, Mizusawa Chemical Industry Co.) had a continuous and nearly homogeneous pore structure. The activation of the catalysts was carried out in a nitrogen flow a t the reaction temperature for 90 minutes just before each run. In the disproportionation of toluene, the toluene was fed as a saturated vapor a t 30° C. in nitrogen flowing a t a constant velocity (125 ml. per minute) and flowed over scores of catalysts (1.5 to 4.5 grams) in a borosilicate glass reactor with 15.7-mm. i.d. I n the dehydrogenation of alcohols, ethyl alcohol was fed in by the aid of a microfeeder, at the rate of 0.0976 X lo-' mole per second, and n-butyl mole per second; in alcohol, at the rate of 0.0623 X
iafc
Right,
530' C. Black
part represents coke deposited
neither case was a diluent gas used. Several pellets of an alkaline-alumina catalyst (0.1 to 1.0 gram) were used in the reactor described above. A constant exit flow was sent intermittently to the analytical system by the use of a six-way cock a t the end of the reactor, and was analyzed by gas chromatography using a silicone D.C. 550 column 0.5 meter long a t 80' C. for the disproportionation of toluene, and a triacetine column 0.6 meter long at 60' C. for the dehydrogenation of thr alcohol. Results
Experimental
602
C.
FUNDAMENTALS
Disproportionation of Toluene. Most of the hydrocarbon in the exit flow of the reactor was toluene; benzene and xylene accounted for less than 270, so this reactor can be regarded as the differential reactor. The benzene yield was about twice as much as the xylene yield, which suggests a large quantity of coke deposition and a rapid degradation of catalyst activity. Figure 8, D and b , shows crass sections of the catalyst pellet after 10 minutes' reaction; in both photographs the black part represents the coke deposited. The effect on the heat in the pellet can be ignored, using the criterion proposed by Anderson (1963). Figure 9 shows the degradation of the total reaction rate oftoluene with the operation time. Dehydrogenation of Primary Alcohols. T h e exit flaw of the reactor contained 98 to 99% of alcohol, 1 to 2% of aldehyde, and very little olefin, dehydration product, or polymers of aldehyde, but the differences between the blank test (when inert material was packed in the reactor instead of the catalyst)
u 10
20
30
reaction t i m e (min) Figure 9. Plot of reaction rate against time for disproportionation of toluene
0 '
10
20
30
Figure 1 1 . Plot of reaction rote agoinst time for dehydrogenation
