4734
Ind. Eng. Chem. Res. 1997, 36, 4734-4739
A Dynamic Study on Axial Dispersion and Adsorption in Catalytic Monoliths Go1 ksel O 2 zkan and Gu 1 ls¸ en Dogˇ u* Department of Chemical Engineering, Gazi University, Maltepe, Ankara 06570, Turkey
A dynamic procedure was used for the measurement of the axial dispersion coefficient, as well as the adsorption equilibrium and rate constants of CO, O2, CH4, and C3H6 tracers on a monolithic catalyst washcoated by Pt-Al2O3. Using a transient axial dispersion model, moment expressions were derived for the inert and adsorbing tracers. From the second central moment of inert tracer response peaks, an average value of the axial dispersion coefficient was determined as 2.65 × 10-4 m2/s for a ceramic monolith containing cells with square cross section. The results indicated that axial dispersion in such a monolith is higher than the corresponding value in a circular tube. The adsorption equilibrium constants of the adsorbing tracers (CO, O2, CH4, C3H6) and the heat of adsorptions were determined from the time delay of the response curves measured in the temperature range of 76-300 °C, while the adsorption rate parameters were evaluated from the second central moments. A detailed analysis of the results indicated that pore diffusion resistance in the Pt-Al2O3 layer is negligible and also that film mass-transfer resistance is much smaller than the adsorption resistance. Introduction Control of pollutants from mobile sources is a major application of catalytic monoliths. Due to the lowpressure drop of such catalysts, they also found a number of applications in nonautomotive catalytic reaction systems (Irandoust and Andersson, 1988). Heatand mass-transfer resistances, as well as hydrodynamic properties, have a direct effect on automobile emission levels. Leclerc and Schweich (1992) reviewed the significance of elementary processes governing the performance of such a converter. They also proposed a model for the steady and transient behavior of such catalytic monoliths. In a number of modeling studies, plug-flow assumption was made in the channels of the monolith. Heck et al. (1976) assumed a uniform radial velocity profile. Two- or three-dimensional models were proposed in later studies (Zygourakis, 1989). The possible effects of axial mixing were not taken into consideration in many of the published literature. In a single channel, the flow behavior is expected to be laminar in most applications. For many of the monolithic converters, the cross section of the channels is in a square shape. Understanding of the significance of axial mixing is very important from the point of view of performance of such monolithic converters. In the work of Votruba et al. (1975), correlations were proposed for Sherwood and Nusselt numbers in monolithic converters. Heat conduction and heat loss are some very important factors affecting the performance of monoliths. Mu¨rtezaogˇlu et al. (1995) proposed a dynamic procedure for the measurement of the effective thermal conductivity of monoliths. Using the moment technique, they reported experimental values for axial and radial effective thermal conductivities of ceramic monoliths and they also proposed a predictive model for these parameters. Dynamic methods have been frequently used for measuring transport and adsorption rates in beds packed with catalyst pellets (Schneider and Smith, 1968; Hsu and Haynes, 1981) and also in single porous pellets (Dogˇu and Smith, 1976; Baiker et al., 1982; Dogˇu et al., 1989a,b, 1993; Cabbar et al., 1994). In the * To whom all correspondence should be addressed. S0888-5885(97)00102-4 CCC: $14.00
chromatographic techniques applied to packed beds, the moments of the response peaks to concentration pulses of inert, adsorptive, or reactive tracers were analyzed for the evaluation of the interpellet and intrapellet rates and equilibrium parameters. In the present study, a dynamic procedure was proposed for the evaluation of axial dispersion coefficients and adsorption rate and equilibrium constants for a catalytic monolith. The moment expressions were derived for inert and adsorptive tracers, and the experimental results were obtained for the axial dispersion coefficient and adsorption parameters of CO, O2, CH4, and C3H6 on a ceramic monolith coated with Pt-Al2O3. Experimental Work Materials Used. The ceramic monolith used in this work was obtained from Corning. A schematic crosssectional view of the monolith used is given in Figure 1. Its dimensions and physical properties are summarized in Table 1. Cylindrical ceramic monoliths of 2.5 cm in diameter and of different lengths (7.37 and 3.99 cm) were first washcoated with Pt-Al2O3. Following the literature (Aarons, 1971; Podschus et al., 1972), the ceramic monolith was treated with 1% HF solution in an ultrasonic bath for 5 min before the washcoating procedure, to improve the coating characteristics of the support surface with colloidal alumina. During this HF treatment, 6.1% weight loss of the ceramic monolith was observed. Then, the monolith was coated with alumina (Lennard et al., 1987) by successive treatment with a colloidal slurry (flowing through the channels of the monolith) and drying at 110 °C after each treatment. With this procedure, 7.95% weight increase of the monolith was achieved. The alumina-coated monolith samples were then treated with chloroplatinic acid solution by flowing this solution through the channels of the monolith. The samples were then dried at 120 °C, calcined at 500 °C in flowing air for 40 min, and reduced in hydrogen atmosphere at 450 °C for 2 h. The surface area and pore structure of the samples were measured using the nitrogen adsorption technique and Quantachrome 60000 psi mercury intrusion porosimeter. The thickness of the Pt-Al2O3 layer over the ceramic support was determined by an electron microscope. The distribution of the washcoat material was © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4735
Figure 3. Typical residence time distribution curve obtained with CH4 tracer at 258 °C at a carrier gas flow rate of 60 mL/min.
Figure 1. Schematic cross-sectional view of the monolith. Table 1. Physical Properties and the Dimensions of the Monoliths Used no. of cells per cm2 open frontal area fraction (void fraction; b) cell size (2a), cm wall thickness (2b), cm thickness of active layer (δ), cm nitrogen adsorption surf area, m2/g lengths of monolithic catalyst samples, cm diameter of monolithic catal sample (dt), cm platinum amt, mg/g of solid
60 0.73 0.1092 0.018 4.55 × 10-4 24.5 7.37, 3.99 2.5 1.53
(helium) and adsorbing (CO, O2, CH4, C3H6) tracers (0.5 mL) were injected into the nitrogen carrier gas flowing through the reactor. Concentration response peaks of these tracers were measured by a TCD detector at the reactor outlet. Experiments were repeated at different carrier gas flow rates as well as at different temperatures. A typical residence time distribution curve obtained with an adsorbing tracer (CH4) is given in Figure 3. Before the start of each run, the catalyst was conditioned in flowing nitrogen atmosphere for about 3 h. No coke formation and no change of adsorption characteristics of the catalyst were observed during the experiments. The experimental value of the nth moment of a response peak was determined from
mn )
∫0∞C(t,L)tn dt
(1)
The time delay of the response peak (first absolute moment)
µ1 )
m1 m0
(2)
and the variance (second central moment)
µ2 )
Figure 2. Schematic diagram of the single-pellet reactor.
not perfectly uniform over the surface. More accumulation was observed at the corners of the square channels. The average thickness of this layer was determined to be 4.55 µm. Method and Procedure. The cylindrical monolithic catalyst was placed into a specially designed singlepellet reactor (Figure 2). The single-pellet monolithic reactor was placed into a temperature-controlled oven. In the dynamic technique used in this work, inert
m2 - µ12 m0
(3)
were then evaluated and compared with the corresponding moment expressions. The moments of the response curves are expected to be functions of the axial dispersion coefficient, the adsorption equilibrium and rate constants, the effective diffusivity in the alumina layer, and the film mass-transfer coefficient. The experimental moments also contain contributions from the dead volumes between the injector and the monolith inlet and also between the monolith outlet and the detector. Possible flow nonuniformities at the inlet chamber of the reactor may also have some contribution to the dispersion of the tracer. Before the analysis of the moment data for the evaluation of system parameters, such dead volume contributions have to be corrected. For this purpose, inert tracer experiments were conducted with pellets of different lengths and differences of moments were used in the analysis of the data. With this procedure, dead volume corrections were eliminated. Corrections to the moments were also estimated from the pulse response experiments conducted in the same system without the monolithic catalyst (O ¨ zkan, 1997).
4736 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
Theory For an adsorbing tracer, the mass conservation equations in the gas phase of the monolithic catalyst and in the porous active alumina layer covering the surface of the channels of the monolith are
Dz
|
∂2C ∂C 2bDe ∂Ci - U0 2 ∂z a ∂y ∂z 2
De
∂ Ci ∂y
- Fp
2
y)δ
∂C ∂t
) b
∂Cads ∂Ci ) p ∂t ∂t
|
∂Ci ∂y
y)δ
(6)
|
(8)
)0
Following a similar procedure as described by Schneider and Smith (1968) for a packed-bed system, eqs 4-8 are solved in the Laplace domain, and the following moment expressions were derived for an adsorbing tracer injected into the inlet of the monolithic catalyst (O ¨ zkan, 1997):
µ1,corr )
µ′2,corr )
(
[
)]
Lb 2δp FpKA 1+ 1+ U0 a p
[
(9)
]
2 2L Dzb γ + γ2 + γ3 + γ4 U0 U 2 1 0
(10)
Equations 9 and 10 do not contain the correction terms due to the injection time and the dead volumes before and after the monolithic catalyst. In these expressions, b, γ1, γ2, γ3, and γ4 are defined as
b )
a2 (a + b + δ)2
{
2δp FpKA 1+ a p
γ1 ) 1 +
γ2 )
(
2bδ(FpKA)2 a(Fpkads)
(11)
)}
(15)
(5)
(7)
y)0
2δ2bp2 FpKA 1+ kfa p
2
γ4 )
(14)
Axial Dispersion in Monoliths. The axial dispersion coefficient appears in the second central moment expression. For a nonadsorbing tracer, the difference of the second moments obtained with two monoliths of different lengths can be expressed as
) kf(C - Ci|y)δ)
∂Ci ∂y
2
Results and Discussions
This assumption is generally justified for dilute systems (Dogˇu and Smith, 1976; Schneider and Smith, 1968). In the boundary conditions of eq 5, a possible contribution of the film mass-transfer coefficient was also considered.
De
) )
2δ3bp2 FpKA 1+ 3aDe p
(4)
Considering that the thickness of the active alumina layer (δ) is very small, slab geometry was assumed in writing eq 5. A linear reversible adsorption process was assumed between the gas phase (Ci) and adsorbed (Cads) concentrations within this porous layer.
∂Cads ) kads(Ci - Cads/KA) ∂t
( (
γ3 )
2
(12)
(13)
U0 1 ) (Dzb2γ*1) 2 + γ*3 + γ*4 (16) ∆µ′2 2(L1 - L2) U0 where
{
2δp a
γ*3 )
2δ3bp2 3aDe
(18)
γ*4 )
2δ2bp2 kfa
(19)
γ*1 ) 1 +
}
2
=1
(17)
The value of γ*1 is close to unity. In principle, the axial dispersion coefficient can be obtained from the slope of the ∆µ′2(U0/2(L1 - L2)) vs 1/U02 relation. The intercept will then give γ*3 + γ*4. The effective diffusivity in the active layer was estimated (using pore size distribution data) to be of the order of magnitude of 10-6 m2/s for helium tracer in nitrogen (O ¨ zkan, 1997). Similarly, the film mass-transfer coefficient, kf, was estimated from the correlation suggested by Votruba et al. (1975), to be about 1.5 × 10-3 m/s. Then, the order of magnitudes of γ*3 and γ*4 were estimated to be 10-3 s and 10-6 s, respectively, indicating the insignificance of the pore diffusion and film mass-transfer terms on the variance of the response curves for an inert tracer. Second central moment data obtained at 185 °C with helium tracer for two monolithic pellets of different lengths (7.37 and 3.99 cm) and the differences of second moments are shown in Figure 4. Analysis of the data showed that (O ¨ zkan, 1997) the intercept of the ∆µ′2(U0/ 2(L1 - L2)) vs 1/U02 curve is very close to zero, also indicating the insignificance of pore diffusion and masstransfer resistances. This result is consistent with the order of magnitudes of γ*3 and γ*4 estimated above. Consequently, the second moment data were used only for the prediction of axial dispersion coefficients in the monolithic catalysts. For this purpose, the slope of the relation between the differences of second moments of the two pellets (∆µ′2) and 1/U03 was used (Figure 5) to determine an average value of Dz in this flow rate range (Dz ) 2.65 × 10-4 m2/s). The value of the axial dispersion coefficient obtained for the monolithic catalyst is about 1.8 times greater than the molecular diffusion coefficient. Considering the small deviations from the linear relation in Figure 5, Dz values were also evaluated at each data point, and the results are shown in Figure 6. In this figure, the effect of the Reynolds number on axial dispersion is illustrated. With an increase of axial dispersion, the conversion level is expected to decrease. The ratio of
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4737
Figure 4. Second central moment data for inert tracer (T ) 185 °C).
Figure 7. Corrected first absolute moment data for CO.
Figure 8. Corrected first absolute moment data for O2. Figure 5. Linearized relation for the second central moment data for inert tracer.
Figure 9. Temperature dependence of the adsorption equilibrium constants of CO and O2. Figure 6. Experimental results on axial dispersion in the monolith (Sc ) 0.22 at 185 °C).
exit concentrations of a real reactor and a plug-flow reactor depends upon the rate law, conversion level, and the value of Dz/U0L (Levenspiel, 1972). At an exhaust gas velocity of 1 m/s (which corresponds to a Dz/U0L value smaller than 3 × 10-3), the effect of dispersion on the exit concentration ratio is less than 2% at a 95% conversion level. On the other hand, for a Dz/U0L value of 3 × 10-2, the effect of dispersion on the exit concentration ratio would be as high as 20%. Adsorption Equilibrium Constants. The adsorption equilibrium constants of the tracers CO, O2, CH4, and C3H6 were determined from the time delay of the response curves. Pulse-response experiments were conducted in the temperature range of 76- 300 °C. First absolute moment data (corrected values for the dead volumes) obtained with CO and O2 tracers are given in Figures 7 and 8, respectively. The slopes of the linear relations given in these figures were then used for the
evaluation of adsorption equilibrium constants.
slope ) b +
(
)
2δbp FpKA 1+ a p
(20)
The temperature dependences of the adsorption equilibrium constants of CO and O2 are illustrated in Figure 9. Some typical values of adsorption equilibrium constants are given in Table 2. These values correspond to the adsorption on the Pt-Al2O3 covering the monolithic support but not necessarily to the adsorption on the platinum sites. The heats of adsorption of both CO and O2 tracers were found to be very low (-4024 J/mol for CO and -1750 J/mol for O2). The heat of adsorption of CO over Pt, reported by Oh and Cavendish (1982) in a modeling study for CO oxidation, is about twice the value obtained in our study. On the other hand, Kunst et al. (1995) estimated the value of the heat of adsorption of CO as -4790 J/mol from the Hegedus (1975) data. This value is quite close to the value obtained in
4738 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
Figure 10. First absolute moment data for CH4 and C3H6 tracers (T ) 258 °C).
Figure 11. Second central moment data for CO.
Table 2. Typical Values of the Adsorption Equilibrium and Rate Constants with Different Tracers tracer temp, °C adspn equilib const, FpKA adspn rate const, Fpkads, s-1
CO
O2
CH4
C3H6
250 54.3 11.9
250 45.5 14.8
258 54.0 21.6
258 185.7 47.9
our work. Carbon monoxide is expected to be adsorbed strongly on the metal surface at low temperatures. In fact, metal surface areas may be estimated from CO adsorption (Chen et al., 1991). On the other hand, with an increase of temperature, spillover to the support surface and desorption from the support also gain importance. In the temperature ranges of the experiments conducted in the present study, the adsorption equilibrium constant reflects the combined effects of chemisorption and physisorption phenomena on both alumina and platinum. The heat of adsorption of oxygen is very low, indicating physical adsorption. As it is discussed by Ma et al. (1996), Pt has a relatively high ionization potential and the oxide is of lower stability than Pd and Rh. The adsorption equilibrium parameters of O2 found in the present work probably correspond to the physical adsorption on the support with a possible contribution of the metal. First moment data obtained with CH4 and C3H6 tracers at 258 °C are illustrated in Figure 10. The values of the adsorption equilibrium constants are given in Table 2. Second Central Moment Analysis. As indicated by eq 10, the intercept of a (µ′2,corr)(U0/2L) vs 1/U02 curve gives the summation of the three parameters, namely, γ2, γ3, and γ4. These parameters are proportional to the adsorption, pore diffusion, and film mass-transfer resistances, respectively. Experimental second central moment data obtained for CO and O2 tracers are illustrated in Figures 11 and 12, respectively. Second central moment data obtained at 258 °C for CH4 and C3H6 tracers are shown in Figure 13. The effective diffusion coefficients of these tracers were estimated using the pore-size distribution data and predicting the tortuosity factor from the Wakao and Smith model. Also, the external film mass-transfer coefficient was estimated from the correlation proposed by Votruba et al. (1975). For a typical run with a CO tracer, the estimated values of De, kf, γ3, and γ4 are given in Table 3. In the same table, the experimental values of the intercepts of the relation between (µ′2,corr)(U0/2L) and 1/U02 are also given. Noting that this intercept corresponds to γ2 + γ3 + γ4, the corresponding values of adsorption rate constants are determined. The
Figure 12. Second central moment data for O2.
Figure 13. Second central moment data for CH4 and C3H6 tracers (T ) 258 °C). Table 3. Second Central Moment Data Analysis (Tracer: CO) temp, intercept 106De*, 103kf*, °C (Figure 11) m2 s-1 104γ3 m s-1 76 101 185 250 a
10.97 6.87 4.29 3.09
1.01 1.06 1.24 1.36
6.5 4.6 2.5 1.8
1.16 1.24 1.52 1.73
γ4
Fpkads, s-1
γ2
0.37 0.26 0.13 0.10
8.91 10.55 10.52 11.92
10.60 6.61 4.15 2.99
The * signifies estimated values.
results given in Table 3 show that γ3 is 4 orders of magnitude smaller than the value of the intercept, indicating that pore diffusion resistance is negligible. The contribution of film mass-transfer resistance (γ4) to the value of intercept is less than 5%. These results show that the major resistance is due to the adsorption rate on the solid surface. Similar conclusions were reached with other tracers. The adsorption rate constants determined for CO with this procedure are also given in Table 3. Typical values of the adsorption rate
Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4739
constants of other tracers are listed in Table 2. The results indicated that the adsorption rate and equilibrium constants of CO, O2, and CH4 tracers are close to each other. This is another indication of the contribution of the support to the adsorption, since the sticking probability of CH4 on Pt is generally reported to be much smaller than the sticking probability of CO. The adsorption rate and equilibrium constants of C3H6 are found to be higher than the other tracers. The temperature dependence of the adsorption rate constant of CO (Table 3) was also found to be very weak, indicating almost nonactivated adsorption. Conclusion It was shown that axial dispersion and adsorption rate and equilibrium parameters can be determined by the moment technique developed in this study for the monolithic catalysts. The technique can also be easily extended to reaction systems and irreversible adsorption. From the inert tracer experiments, it was concluded that the value of the axial dispersion coefficient in a square channel monolith is higher than the axial dispersion coefficient in a corresponding circular tube at the same Reynolds number. The moment technique developed here allowed the independent evaluation of both adsorption equilibrium and rate constants. The results obtained with CO, O2, CH4, and C3H6 tracers indicated that pore diffusion in the Pt-Al2O3 layer is negligible and the major resistance in adsorption is due to the adsorption rate. Acknowledgment The Turkish Scientific and Research Council (TU ¨ BI˙ TAK) (MI˙ SAG-57) and Gazi University (MMF 06/93-14) research grants and the contributions of Prof. Dr. Timur Dogˇu of Middle East Technical University are gratefully acknowledged. Nomenclature a ) cell dimension (Figure 1) b ) wall thickness of the monolith (Figure 1) C ) concentration in the channels of the monolith Cads ) adsorbed concentration Ci ) concentration in the pores of the Pt-Al2O3 layer De ) effective diffusion coefficient Dz ) axial dispersion coefficient dt ) reactor diameter kads ) adsorption rate constant kf ) film mass-transfer coefficient KA ) adsorption equilibrium constant L ) length of the monolith U0 ) superficial velocity Greek Letters δ ) thickness of the Pt-Al2O3 layer b ) void fraction of the monolith p ) porosity of the Pt-Al2O3 layer Fp ) apparent density of the Pt-Al2O3 layer
Literature Cited Aarons, R. High Surface Area Alumina Coatings on Catalyst Supports. U.S. Patent 3,554,939, E. I. du Pont de Nemours and Company, Wilmington, DE, June 8, 1971. Baiker, A.; New, M.; Richarz, W. Determination of Intraparticle Diffusion Coefficients in Catalyst Pellet. A Comparative Study of Measuring Methods. Chem. Eng. Sci. 1982, 37, 643. Cabbar, C.; Dogˇu, G.; Dogˇu, T.; McCoy, B. J.; Smith, J. M. Analysis of Diffusion and Sorption of Chlorinated Hydrocarbons in Soil
by Single-Pellet Moment Technique. Environ. Sci. Technol. 1994, 28, 1312. Chen, S. L.; Zhang, J. H.; Contescu, C.; Schwarz, J. A. Effect of Alumina Supports on the Properties of Supported Nickel Catalysts. Appl. Catal. 1991, 73, 289. Dogˇu, G.; Smith, J. M. Rate Parameters From Dynamic Experiments with Single Catalyst Pellets. Chem. Eng. Sci. 1976, 32, 123. Dogˇu, G.; Mu¨rtezaogˇlu, K.; Dogˇu, T. A Dynamic Method for the Effective Thermal Conductivity of Porous Solids. AIChE J. 1989a, 35, 683. Dogˇu, G.; Pekediz, A.; Dogˇu, T. Dynamic Analysis of Viscous Flow and Diffusion in Porous Solids. AIChE J. 1989b, 35, 1370. Dogˇu, G.; Cabbar, C.; Dogˇu, T. Single-Pellet Technique for Irreversible and Reversible Adsorption in Soil. AIChE J. 1993, 39, 1895. Heck, R. H.; Wei, J.; Katzer, J. R. Mathematical Modeling of Monolithic Catalysts. AIChE J. 1976, 22 (3), 477. Hegedus, L. L. Temperature Excursion in Catalytic Monoliths. AIChE J. 1975, 21, 849. Hsu, L. K. P.; Haynes, H. W., Jr. Effective Diffusivity by the Gas Chromatography Technique: Analysis and Application to Measurement of Diffusion of Various Hydrocarbons in Zeolite NaY. AIChE J. 1981, 27, 81. Irandoust, S.; Andersson, B. Monolithic Catalysts for Nonautomobile Applications. Catal. Rev. Sci. Eng. 1988, 30, 341. Kunst, J. A. F.; Cybulski, A.; Xiaoding, X.; Moulijn, J. A. Estimation of Kinetic Parameters From Non-Isothermally Operated Monolthic Reactors: Oxidation of Carbon Monoxide. Chem. Eng. Sci. 1995, 50, 2845. Leclerc, J. P.; Schweich, D. Modelling Catalytic Monoliths for Automobile Emission Control. In Chemical Reactor Technology for Environmentally Safe Reactors and Products; deLasa, H. I., Dogˇu, G., Ravella, A., Eds.; NATO ASI Series 225; Kluwer Academic: Dortrecht, 1992; p 547. Lennard, B. L.; Lo¨wendahl, L. O.; Otterstedt, J. E. In The Effect of the Chemical Nature of the Wash-Coat on the Catalytic Performance of CO Oxidation Catalysts of Monolith Type, Catalysis and Automotive Pollution Control, Crucq, A., Frennet, A., Eds.; Elsevier Science: Amsterdam, 1987; p 333. Levenspiel, O. Chemical Reaction Engineering; John Wiley and Sons: NewYork, 1972. Ma, L.; Trimm, D. L.; Jiang, C. The Design and Testing of an Autothermal Reactor for the Conversion of Light Hydrocarbons to Hydrogen. Appl. Catal. A 1996, 138, 275. Mu¨rtezaogˇlu, K.; Oray, E.; Dogˇu, T.; Dogˇu, G.; Sarac¸ ogˇlu, N.; Cabbar, C. Effective Thermal Conductivity of Monolithic and Porous Catalyst Supports By Moment Technique, J. Chem. Eng. Data 1995, 40, 720. Oh, S. H.; Cavendish, J. C. Transients of Monolithic Catalytic Converters: Response to Step Changes in Feedstream Temperatures as Related to Controlling Automobile Emissions, Ind. Eng. Chem. Prod. Des. Dev. 1982, 21, 29. O ¨ zkan, G. Axial Dispersion, Adsorption and Reaction Study in Catalytic Monoliths for Automobile Emission Control. Ph.D. Thesis, Gazi University, Ankara, Turkey, 1997. Podschus, E.; Dorn, L.; Heinze, G. Process for the Production of Highly Porous Bead-Form Silica Catalyst Supports. U.S. Patent 3,676,366, Farbenfabriken Bayer Aktiengesellschaft, Leverkusen, Germany, July 11, 1972. Schneider, P.; Smith, J. M. Adsorption Rate Constants From Chromotography. AIChE J. 1968, 14, 762. Votruba, J.; Mikus, O.; Nguen, K.; Hlavacek, V.; Skrivanek, J. Heat and Mass Transfer In Honeycomb CatalystsII. Chem. Eng. Sci. 1975, 30, 201. Zygourakis, K. Transient Operation of Monolith Catalytic Converters: A two Dimensional Reactor Model and the Effect of Radially Nonuniform Flow Distributions. Chem. Eng. Sci. 1989, 44, 2075.
Received for review February 3, 1997 Revised manuscript received June 27, 1997 Accepted July 11, 1997X IE9701027
X Abstract published in Advance ACS Abstracts, October 1, 1997.
