Experimental Determination of Catalyst Fouling Parameters Diffusivities James T. Richardson1
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Esso Research and Engineering Co., Synthetic Fuels Research Laboratory, P.O. Box 4265, Baytown, Tex. 77520
The chromatographic method is used to measure the diffusivity of Ar/He mixtures in fouled Nalco 471 catalysts containing an increasing amount of carbon. Results show that the major part of diffusion occurs in the large pores of the fresh catalyst and is bulk diffusion. The fouled catalyst, however, exhibits Knudsen diffusion in micropores. The measured diffusivity decreases linearly with carbon content. The surface area shows a similar linear decrease so that the Thiele modulus is approximately constant up to 16 wt % carbon. The implications of these results to current models of catalyst fouling are discussed.
Theoretical models describing catalyst bed fouling and deactivation require calibration through the experimental determination of crucial parameters. A previous paper in this series (Richardson, 1972) shows how carbon concentration profiles in fouled catalyst pellets may be used in the model of RIasamune and Smith (1966). These authors derived expressions for the deactivation of the bed with time. Results are dependent on the Thiele modulus of the catalyst for the reactant and/or poisoning component. This parameter must either be treated as a system variable and determined through a curve-fitting procedure or estimated from independent information on the catalyst and feed properties. The key to this step is a knowledge of the effective diffusivity, Deff,of the characteristic molecular species. Unfortunately, experimental techniques for measurements on the most common components of complex reactant streams are lacking, especially under process conditions. It is necessary to use approximations developed for gaseous and liquid diffusivities, D , outlined by Satterfield and Sherwood (1963). The effect of the catalyst porosity is then estimated from
where u and 7 are the constriction and tortuosity factors, respectively, usually only given as ( . / T ) , and e is the porosity. Effective diffusivities are measured with inert gas mixtures of known D (or DI, for Knudsen diffusion). The ideal value of ( u / T ) is then applied to the unknown system, although larger and more complex molecules may not necessarily exhibit the same ( u / T ) . It is important to establish the effect of the carbon deposit on the diffusivities in fouled pellets, especially since Masamune and Smith (1966) assumed a constant Thiele modulus. If experiment shows this assumption does not hold under the applicable conditions, then the model must be modified. 1 Present address, Department of Chemical Engineering, Vniversity of IIouston, 3801 Cullen Boiilevard, Houston, Tex. 77004.
12 Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 1 , 1972
The most direct method of measuring diffusivities 15 the steady-state counterdiffusion techniaue described by Henry et al. (1961). The result is independent of any assumed porosity factors. However, this technique is not easily applicable to practical catalysts such as extrudates taken from a reactor. I n addition, the method does not adapt easily to high temperature measurements. Eberly (1969) has described a chromatographic method which does not have these disadvantages. This paper demonstrates the application of this procedure to a series of coked catalyst, The objective was to measure the ( u / T ) factor and to determine its response to the level of coke deposit. Experimental
Catalysts and Deactivation. T h e catalyst was Nalco 471, cobalt molybdena catalyst, preparecl as l/s-in. extrudates. The catalyst was deactivated in an experimental pilot unit with a coal-derived, full boiling liquid under hydrotreating conditions. The flow of feed was stopped at a certain process time and the reactor cooled. Samples of catalysts were taken at increasing depths in the bed. Carbon analysis showed t h a t a coke concentration profile existed in the bed, so that selected segments represented the catalyst a t different stages of the fouling. The catalysts were washed in methylethylketone to remove occluded oil and then pyridine-extracted with a Soxhlet extractor. Finally, the catalysts were heated in a stream of nitrogen a t 600°C for several hours. This removed all but the residue coke-Le., that boiling above 600OC. Diffusivity Measurement. T h e apparatus was similar to that described by Eberly (1969). The reactor was a stainless steel tube 90 em in length and 1.6 cm i d . , containing approximately 30 grams of catalyst. Helium carrier gas passed into one side of a Gow-Mac conductivity cell through the reactor and the second side of the cell. Flom velocities varied from 2-50 cm/sec (interstitial). A Perkin-Elmer gas sampling ~ of argon into the helium valve introduced a 0 . 2 5 . ~pulse stream just ahead of the input to the conductivity cell. Figure 1 shows the resulting broadening of the pulse as it passed through the bed.
I
t
I1
Im
I
I J U rL-
Dell = effective dif(usivity of A r I H e in the pores.
I
I
1
O.O't -
1
0
10 C A R B O N , WT. %
0
20
Figure 3. Effect of carbon content on diffusion parameters
Column
---.__
___7
\
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d = diometer of pellet, F!, = bed porosity, 8 = pellet porosity
MEASUREMENT
He + 2 5 cc A i
\
OF EFFECTIVE DIFFUSIVITY
Figure 1 . Chromatographic method for measuring diffusivities I
01
0
-
0
10
Co :0.0451 se-
20
I
200
T E M P E R A T U R E . "C
I
300
40
30
VELOCITY i c m l s e c )
Figure 2. Typical results of
H
vs.
U
At each velocity, Lr, the value of the height of equivalent theoretical plates, 11, was calculated from
by use of the experimental parameters shown in Figure 1. The variation of H with C is shown in Figure 2 for a typical set of results. The experimental points were fitted to the Van Deeinter equation B H = d +-+CU ( 3)
Figure 4. Temperature dependence of diffusivity
All connecting lines were kept to a niinimum, b u t i t was necessary to apply a small experimental correction to t, and t , at each I'. I n addition, instrumental peak broadening in the reactor was determined by measuring the slope in Equation 3 for a bed of cylindrical '/*-in. nonporous, ceramic pellets. This correction was subtracted from the slope C before using Equation 4. Other Catalyst Parameters. Pellet densities, p p , were measured with a methanol pycnometer after first saturatiiig the catalyst in methanol and superficially drying. Helium densities, d,, were determined with a -Micromeritics Model 1302 helium-air pyconometer. Surface areas, S, were obtained from a Rlicromeritics Model 2100 Surface Area analyzer and pore volumes, V,, from a BET deterniination. Carbon contents were found by burning the carbon in a stream of Oz/He and measuring the C 0 2evolved. Results and Discussion
The results for room temperature measurements are given in Table I. I n each case the porosities were calculated from
(5)
u
with a regression analysis. The constant C is given by
where F = void space e = pellet porosity d, = pellet diameter, cm D,rf = effective diffusivity, cm2/sec
I
400
0.0905sec
+fC:
/
100
so that the diffusivities reflect the total pore structure. The surface areas, porosity, and diffusivity all decrease, but the pellet density increases as the carbon content increases. There was no change in the dimensions of the pellet; therefore, the carbon does fill the pores of the pellet. Figure 3 shows that the decrease in diffusivity is linear with carbon content. However, the Thiele modulus is proportional to (S
$)
-112
.
When the relative value of the Thiele
modulus is plotted as a function of carbon content, t,here is Ind. Eng. Chern. Process Des. Develop., Vol. 11, No. 1, 1972
13
Table 1. Effective Diffusivities at 25°C for Fouled Catalysts Argon-Helium Mixtures Catalyst:
Fresh Pyridine-extracted Heated at 6OOOC 7.96% C 9.01% c 15,3% C 19.9% c
extrudate, Nalco 471 cobalt molybdate-A1203
PPI
d,
gm/cm3
g/cm3
1.284
3.356
1.395 1.410 1.498 1.564
3.069 3.078 2.976 2.619 “Radius A >loo0
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300-1000 100-300 35-100 15-35
a constant value u p to about 15% carbon. Thus, the assumption in the Masaniuiie arid Smith model that the Thiele modulus is independent of the extent of fouling is a good one for this system under moderate coking conditioiis. However, with the decrease in surface area, a corresponding decrease in the specific activity (per unit gram) will also occur. This is included in the inherent treatnient of llasamune and Smith. These conclusions apply to the averaged effect over the pellet. The author has shown the existence of carbon coiiceiitration profiles. I n view of the constancy of the Thiele modulus, i t does not seem necessary to further refine the model with a diffusivity profile. I n cases of extreme fouling, however, this should be considered. An insight into the diffusion mechanism is seen from the temperature dependence for the fresh and heavily fouled catalyst (Figure 4). The diff usivity-temperature relationship for the fresh catalyst is close to a T3iZdependence. A precise pore size distribution was not available for this catalyst. However, BET adsorption results yield a micropore radius of 42 with the incremental pore volumes oshown in Table I. Over 80% of the pores are less than 100 A. The possibility of a macropore distribution must be considered. By assumiiig that this is the case and that diffusion in macropores is by bulk diffusion only, the random walk model of Wakao and Smith (1962) gives a didusivity of 0.0289 cm2/sec. This differs from the measured value by a factor of two, which is not unreasonable for this model. Furthermore, after normalization at 25’C, the model predicts the temperature dependence
14 Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 1 , 1972
S, W g
vg,
Deffr
cma/g
el
cmZ/sec
270
0.47
0.6170
0.0546
219 180 160 49.2
0.22 0.23 0.21 0.08
0.545 0.542 0.297 0.403
0.0485 0.0357 0.0350 0.0281
Pore vo1, cmZ/g 0.027 0.041 0.051 0.265 0.085
showii by the dashed line in Figure 4. These results are consistent, with most of t’hediffusion occurring in the larger pores. From the D e f fof the fresh catalyst and the assumption of bulk diffusion, the value of ( u / T ) is 0.0747. This low number is not unusual in extruded pellets. The fouled catalyst shows a T1’zdepeiidence. This agree: with Knudseii diffuyioii but indicates a pore radius of 106 A (assuming a / r = 1). This type of behavior would be expected if carbon fills the larger pores with a resulting decrease in pore diameters. Conclusions
Diffusivity and other measurements on fouled catalysts have s h o w that the Thiele modulus is coiistant for carbon contents up to 16% ; therefore, the assumptions of blasamune a i d Smith (1966) are correct. An upper limit to the factor ( u / T ) was obtained and may be used in the estimate of approximate effective diffusivities for other feeds and conditions. literature Cited Eberly, P. E., Znd. Eng. Chcni. Fundnni., 8 , 25 (1969). Henry, J. P., Chennakesvan, B., Smith, J. RL., AIChE J., 7, 10 (1961). Rlasamune, S., Smith, J. hl., AZChE J., 12, 384 (1966). Richardson, J. T., 11, 8 (1972). Satterfield, C. N., Sherwood, T. K., “The Role of Iliffusion in Catalvsis,” hlcGraw-Hill, New York, N.Y., 1963, pp 5-12. Wakao, N:, Smith, J. RI., Chem. Eng. Sci., 17, 825 (1962).
IZECEIVCD for review July 13, 1970 ACCEPTED July 16, 1971
