Ind. Eng. Chem. Res. 1988,27, 1169-1174
1169
An Experimental Investigation of Optimal Active Catalyst Distribution in Nonisothermal Pellets Hua Wu, Quan Yuan,* and Baolin Zhu Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, Peopleb Republic
of China
This work for the first time experimentally studies the existence of the optimal active catalyst distribution and the dependence of the effectiveness factor vs Thiele modulus in nonisothermal pellets. For the hydrogenation of ethylene on Pd/A1203catalyst and the methanation of CO on Ni/A1203 catalyst, by use of the step distribution with the active layer of narrow width to approximately replace the distribution of the Dirac delta type, it is shown that there does exist an optimal location of the active layer within the pellet a t the given conditions and the optimal location moves toward the external surface as the Thiele modulus increases. The influence of the deviation of the active layer from the optimal location on the effectiveness factor is also investigated and compared. Values higher than unity for the effectiveness factor (maximum value is about 18) are measured. The measured dependence of the effectiveness factor vs Thiele modulus is in good agreement with the numerically calculated one. 1. Introduction The optimal activity distribution within a pellet to maximize the catalyst effectiveness has been investigated theoretically by a few scientists. Morbidelli et al. (1982) determined the optimmal activity distribution for an isothermal bimolecular Langmuil-Hinshelwood reaction. Wu and co-workers (1984) considered the optimal activity distribution for a more general nonisothermal reaction. Both investigations have shown that the optimal activity distribution is a Dirac delta function. This means that the active catalyst should be concentrated on a layer with negligible thickness at a specific location R within the pellet. In practice, the catalyst pellet with the above optimal activity distribution is unlikely to be prepared. From the experimental research in our laboratory, however, the behaviors of step distribution with an active layer of narrow width are rather similar to those of the optimal distribution. The purpose of this study is to experimentally investigate the existence of the optimal activity distribution within a pellet by determining the experimental effectiveness fadors of sets of catalyst pellets with suitable step distributions of narrow width and to obtain sufficient data to show the correlation between the experimental effectiveness factor and Thiele modulus. The results are also compared with numerically calculated data. The model reactions are hydrogenation of ethylene on Pd/ Alz03catalyst and methanation of CO on Ni/Al2O3, which are moderately or highly exothermic (AHh= -32.7 kcal/ = -42.8 kcal/mol). mol, AH,,,
2. Experimental Section The hydrogenation of ethylene was carried out in an internal recirculation, gradientless reactor. The apparatus and the main part of the reactor are shown schematically in Figure 1and Figure 2, respectively. The reaction rates on both pellets and particles (size W 1 0 0 mesh) which were obtained by crushing the catalyst with uniform activity profile were investigated a t the following conditions: pressure, temperature, feed composition, atmospheric; 280-340 K; 1-9.86 mol % Hz, 2-20.3 mol % C2H4. In the pellet test, the reactor was loaded with only one catalyst pellet. To enable a slab geometry to be assumed, the pellet was nested into a special Teflon mold with epoxide resin so that only one face was exposed to the bulk gas. *To whom all correspondence should be addressed.
Table I. Activity Profile Functions of the Pd/Al,OJ Catalvst Pellets Used in the Hydrogenation of Ethylene profile function no. ~
0
4 5
0 6 x 6 1 0.90 d x d 1 0 6 x < 0.90 0.94 < n d 1 0.83 S n Q 0.94 0 6 x < 0.83 0.92 < x 6 1 0.82 d x < 0.92 0 d x < 0.82 0.90 < x d 1 0.80 6 x 6 0.90 0 d x < 0.80 0.85 < x d 1 0.75 6 x 6 0.85 0 6 x < 0.75 0.47 < x d 1 0.37 d x 6 0.47 0 < x < 0.37
Table 11. Feed Compositions of CO Methanation twe no. CO,% H,.% Ar. % particles I 3.12 16.53 80.35 pellets I1 2.85 15.31 81.84 I11 3.65 8.42 87.9
The Pd/A120, catalyst pellets with step distribution were prepared by pressing together two alumina layers and one active layer which were all previously prepressed in a specific mold. The pellets are cylindrical (diameter X thickness = 19.2 X 6.7 mm) and have 187 m2/g of surface area (BET) in the unreduced state, 0.746 of porosity, and 1.18 g/cm3 of apparent density. Seven kinds of active step distribution pellets were prepared of which the distribution functions are tabulated in Table I. The mean palladium content in each pellet is 0.02% wt, and the dimensionless thickness of the active layer is 0.1. A 0.2-mm EA-2 thermocouple was fixed within each pellet to measure the internal temperature. The methanation of CO was performed also in an internal recirculation, gradientless reactor with a pressure of -1 MPa and range of temperatures of 483-633 K. Table I1 contains the feed compositions. The schematic diagram of the apparatus is shown in Figure 3. The preparation of the Ni/A1203catalyst pellets with Ni step distribution was similar to that of the Pd/A1203 ones. As the temperature of the methanation was 483-633 K and the sealing of the side and bottom faces of the pellet
0888-5885/88/2627~1169$01.50/0 0 1988 American Chemical Society
1170 Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988
8
I
Figure 4. Shape of the prepared Ni/AI2O3catalyst pellet.
Figure 1. Schematic diagram of apparatus for ethylene hydrogenation: 1, cylinder; 2, deoxygenator; 3, dryer; 4, regulator; 5, needle valve; 6, rotamater;7, reactor; 8, sampling.
Table 111. Activity Profile Functions of the Ni/A1,03 Catalyst Pellets Used in the CO Methanation profile function no. 0.78 d x d 1 0 6 x < 0.78 0.84 < x Q 1 0.62 d x d 0.84 0 d x < 0.62 0.77 < x Q 1 0.55 d x d 0.77 0 Q x < 0.55 0.69 < x Q 1 0.47 d x d 0.69 0 d x < 0.47
1
2 3
a c t 1v e
layer
4 5
- -p e l l e t
/
6 7
inlet
Figure 2. Single pellet reactor for ethylene hydrogenation. 8
9
16 lilJ
11
u
12
j
l
Figure 3. Schematic diagram of apparatus for CO methanation: 1-3, feedstock cylinders; 4,hydrogen cylinder; 5, deoxygenator;6,10, dryers; 7, regulator;8, reactor;9, water trap; 11, 12, rotameters; 13, 14, sampler; 15, chromatograph 16, microprocesser; 17, 18, needle valves.
was difficult, an alumina layer with suitable thickness was used at the side and bottom faces to reduce the mass transfer so that the pellet can be considered to be of one-dimensional geometry. The prepared pellet has the shape shown in Figure 4; it looks like a catalyst pellet which was nested in an alumina mold. The effective size of the pellets is taken 20 X 7.7 mm (diameter X thickness). The nickel content in the effective pellets is 5.5% wt. The activity distributions of the pellets used in our experiment are shown in Table 111. The methanation of CO is highly exothermic. The problem of the heat transfer was solved by reducing the content of carbon monoxide in the feedstocks such that the pellet was nearly isothermic. Both the hydrogenation of ethylene and the methanation of CO are the reactions with a volume decrease. In order to reduce the variation in total pressure within the
0
= (4.55
0.61 < x Q 1 0.39 Q x 6 0.61 0 Q x < 0.39 0.53 < x Q 1 0.31 d x 6 0.53 0 Q x < 0.31 0.45 < x d 1 0.23 Q x d 0.45 0 Q z < 0.23 0.30 < x d 1 0.08 Q x d 0.30 0 d x < 0.08 0.22 < x Q 1 0 d x Q 0.22
pellet and its effect on the reaction rate, we controlled the change in total moles to less than 1% in the hydrogenation of ethylene and 2% in the methanation of CO. Fresh Pd/A1203catalysts were reduced in a stream of pure hydrogen by heating to 353 K for 4 h and were kept at this temperature for 8 h. The reactor was then cooled to 340 K, and the stream of the feedstock was passed through it. The activities of the catalysts became steady after 20-24 h, and then the rates were measured for several temperature points and feed rates. The oxide form of the Ni/A1203catalysts was also activated by passing a stream of pure hydrogen through it. The temperature in the reactor rose very slowly at a speed of 30 "C/h until the end temperature, 653 K, arrived. This can prevent the big pellets from cracking. At the end temperature point, the reactor was cooled to 633 K and then the stream of the feedstock was introduced to start the methanation. Steady state was reached after about 12 h. 3. The Reaction Rate
The rate data were obtained from the runs of the fine catalyst particles in the internal recirculation, gradientless reactors. For the hydrogenation of ethylene, the data between 280 and 340 K can be correlated with the following equation: r = 7.71 X lo4 exp(-11.4 X 103/t)cH, (mol/(s-cm3)) (1)
i.e., under the given conditions, the kinetics is first order ~ zero order to cCzFH4. with respect to C H and For the methanation of carbon monoxide, the data between 483 and 633 K indicate that the kinetics has the
Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988 1171 form of bimolecular Langmuir-Hinshelwood reactions: 2.19 x 10" exp(-11.5 x 103/t)CCOCH>5
r=
[l
+ 2.06 X lo4 exp(1.96 X 1O3/t)c~oI2(mol/(s.g))
(2) Similar results were reported by Huang and Richardsen (1978) and Wedel and Luss (1984). 4. Mathematical Modeling The experimental results are simulated by using a one-dimensional model which does not consider any change in the physical properties. By combining the mass and heat balances within the pellet, the following dimensionless equation can be obtained:
d2C/dx2 = q!~~a(x)F(C)
(3)
subject to the boundary conditions dC/dx = O
at x = O
(44
C=1 at x = l For the hydrogenation of ethylene,
where w and I' are adjustable model parameters which are evaluated from unsteady-state diffusion measurements. The model parameters w and r have the values of 15.1 and 61 A for the Pd/A1203catalyst pellets and 4.81 and 116 A for the Ni/A1203 catalyst pellets. The effective diffusivities evaluated from TPM are in good agreement with those evaluated from the mean transport pore model (MTPM) proposed by Schneider and Gelbin (1985). The effective conductivities (A,) of the pellets were evaluated from the Prater number (p) which was obtained from the maximum experimental effectiveness factors. 5. Experimental Results The composition in the internal recirculation, gradientless reactor is constant at steady-state conditions, equal to that of the exit stream. So it is easy to evaluate the reaction rate of the pellet in the reactor. The observed reaction rates of pellets for the hydrogenation of ethylene were given by
(4b) where
For the CO methanation, the observed reaction rates of pellets were estimated by
where
4 = L [ k , C ~ , , ~ ' ~ / D e c+o (Ul) 2 ] 0 . 5 C T
c = Cco/Cco,,
= KCCO,s
P = (-m)DecOcCO,,/Aets Y = Ea/%& D = 3DeCOCC0,s/DeHzCHz,s
(6)
x = 1/L; a ( x ) is called the activity distribution function.
which is a normalized distribution function of active sites in the pellet and satisfies the following equation: J ' a ( x ) dx = 1
(7)
Also a(x) indicates the distribution of the concentration of the active component if the number of active sites is proportional to the amount of active component. The effectiveness factor of catalyst pellets is calculated by the expression qCal =
(dC/dx)x=i/42
(8)
where (dC/dx),=, is obtained by the numerical integration of the model equation (eq 3), and then qcal is compared with the experimental results, qexp. A two-parameter model (TPM) proposed by Wu et al. (1988)was used to determine the effective diffusivities (De) in the pellets. The resultant expression of TPM for De may be written:
In the above two cases, the change in the number of moles had been considered. The experimental effectiveness factors of pellets (qexp) were calculated by qexp
=
robs/rint
(15)
(a) Dependence of qexpvs 4. The reaction rates of the catalyst pellets were measured at several surface temperatures and concentrations. For the hydrogenation of ethylene, more than a 30 K temperature difference (At) was observed between the external surface and the inside of the pellet. The notable At must have remarkable influence on the observed reaction rate because the activation energy equals 94.8 kJ/mol, and when the reaction was run at 280-340 K, the reaction rate is much more sensitive to the change of the reaction temperature. Figure 5 describes the dependence of the experimental and simulant effectiveness factors of four kinds of catalyst pellets in Table I vs Thiele modulus at the same surface concentrations but at different surface temperatures. In the simulations of the experimental results, the influence of the surface temperature on y was considered, but the Prater number (P) was taken as constant because the effective diffusivity (De) in the numerator of the P expression increases slightly as the surface temperature t , increases, partially compensating the influence of t, in the denominator. The simulation indicates a good agreement with the experimental data for pellets 5 and 6. For pellets 0 and 1, qerpdecreases when the Thiele modulus is increased more rapidly than qcal does at larger Thiele modulus. When the pellets with an active layer at the external
1172 Ind. Eng. Chem. Res., Vol. 27, No. 7, 1988
, 20
4
8
I
2o
8
Ql
ai
I
I
I
1
0.2
Q
\ I
5
0 5 1
10
-$ Figure 5. Dependences of the measured and simulant effectiveness factors of four kinds of catalyst pellets in Table I vs Thiele modulus (ethylene hydrogenation): ( 0 )a&), (0) a , ( x ) , (0) a&), (m) a,&); p = 0.154,y = 11.4 X 103/t,.
01.
0.6
0.8
1.0
X*
Figure 7. Plot of experimental effectiveness factor vs the active layer location x* (=(xl x z ) / 2 ) , for ethylene hydrogenation: t, = 298 K, Y H ~= 5.89%, 6 = 0.1.
+
2.5
e
1.0
-
Q 0.l
-
P5
5
1
Figure 6. Dependences of the measured and simulant effectiveness factors of three kinds of catalyst pellets in Table I11 vs Thiele modulus (CO methanation): (0) al(x), ( 0 )a&), (0) a&); p = 0.031, y = 11.46 X lo3/&, u 3.15,C H ~ + / C C O , = ~ 7.85.
surface run at a higher surface temperature, the observed rate is greater, and the external transfer resistance may not be negligible. The influence of the external diffusion would therefore cause vexp to be smaller than vcd, and the higher the run temperature, the greater the influence. Similar results shown in Figure 6 were obtained by using the methanation of CO as a test reaction. It can be seen that, although the effect of the intrapellet temperature difference is small (8 = 0.031), both the observed and calculated maximum effectiveness factors are greater than unity (about 2). Since the methanation of CO is bimolecular Langmuir-Hinshelwood-typereaction and parameter a in eq 6 equals 3.15, the reaction in a certain range of reactant concentrations has negative-order characteristics; it is well-known that the effectiveness factor may increase with decreasing the reactant concentration. Again, for the pellet with the active layer a t the external surface, vexp decreases when the Thiele modulus is increased more rapidly than veal does when the Thiele modulus is larger. (b) Optimal Active Layer Location. It is clear that to demonstrate exgrimentally the existence of the optimal location within pellet we should have vexpof a set of pellets with different active layer locations but with the same reaction conditions. Figure 7 describes a dependence of verp on the active layer location (x* (=(xl + x 2 ) / 2 ) ) for the hydrogenation of ethylene at a given temperature and concentrations. It can be seen that under the given conditions there does exist an optimal active layer location (f* ~ 0 . 8 5where ) the effectivenessfactor can be maximized.
QL
0.6
0.8
1.0
x',
10
9
0.2
Figure 8. Measured and simulant (dot line) dependences of effectiveness factor on the active layer location x* for CO methanation: t , = 533 K,cco,s = 5.0 X lo4 mol/mL, C H ~ , J C C O , ~= 7.85.
The measured maximum effectiveness factor ( v , , ~ , ~ ~ is ) approximately equal to 16. Wu et al. (1984) derived a criterion (a- &), and then Wu (1986) extended it to more general situations. The parameter a has the following expressions
+ Dap al = m, - ciul/(l + ol + u2) az = m2 - ciaz/(l + ol + u2) a =
(16) (17)
(18)
for the reaction r = IZClmlCp/(l
+ K,c1 + KZC,)"
(19)
Since T increases with ml (or m,) and decreases with ci and u1 (or a2),the increase of m, (or mz)indicates the increase of the sensitivity of the reaction to the change of reactant concentration, and the increase of ci and ul (or az) gives rise to the decrease of the sensitivity, we call a the concentration sensitivity parameter of reaction. It is shown that when a - & 1 0, the optimal location of the active layer (3) for the optimal activity distribution, the Dirac delta function distribution is at the external surface of the pellet; when a - Pr
