Znd. Eng. Chem. Res. 1987,26, 1965-1969
M = monomer molecule MI = adsorbed monomer molecule M1*, M2*, ..., M,* = active species, monomer, dimer,
Kd
...,
polymer of n monomer units, respectively [N] = total number of active sites by unit weight n = number of monomer molecules in the polymer P = polymer weight, g = average partial pressure of benzyl alcohol between the pAinlet and the outlet of the reactor, atm PAo,PA,= partial pressure of benzyl alcohol at the inlet and at the outlet of the reactor, respectively, atm P, = polymer of n monomer units R = polymerization rate, total number of monomer units in the polymer that are desorbed by unit catalyst weight and by unit time rpO,r p = polymer formation rates at t = ti and t > ti,respectively, g of polymer/ (g of catalystamin) S = solvent molecule S, = surface area, m2/g S1 = adsorbed solvent molecule T = temperature, K t , t d , ti = time and reaction time from the initiation period and initiation period, respectively, min Vp = pore volume, cm3/g Greek S y m b o l s a = parameter of eq 1
1965
= deactivation rate constant, mi& atm-l
pa, pr = particle density and solid density of
the catalyst, kg/m3
Registry No. A1,0,, 1344-28-1;SOz,7631-86-9;C6H,CHzOH,
100-51-6; C6H&H20H (homopolymer),27134-46-9. Literature Cited Bilbao, J.; Aguayo, A. T.; Arandes, J. M. Ind. Eng. Chem. Prod. Res. Dev. 1985, 24, 531. Clark, A. The Theory of Adsorption and Catalysis; Academic: New York, 1970; p 265. Clark, A.; Bailey, G. C. J . Catal. 1963a, 2, 230. Clark, A.; Bailey, G. C. J. Catal. 1963b, 2, 241. Guyot, A. J. Catal. 1964,3, 390. Guyot, A.; Daniel, J. C. J . Polym. Sci. 1963, A I , 2928. Hinshelwood, C. N. Kinetics of Chemical Change;Oxford University Press: New York, 1940; p 87. Langmuir, I. Trans. Faraday SOC.1921,17, 621. Maiti, M. M. J . Catal. 1975, 38, 522. Marquardt, D. W. J . SOC.Znd. Appl. Math. 1963, 11, 431. Olazar, M.; Bilbao, J.; Aguayo, A. T.; Romero, A. Ind. Eng. Chem. Res. 1987, preceding paper in this issue. Wukasch, J. E.; Rase, H. F. Ind. Eng. Chem. Prod. Res. Dev. 1982, 21, 558. Received f o r review December 3, 1985 Revised manuscript received February 19, 1987 Accepted June 24, 1987
Catalytic Oxidation of Decomposition Products from Spent Ion-Exchange Resins Faredoon N. Desai,* Howard L. Greene, and Prasad Subbanna Department of Chemical Engineering, University of Akron, Akron, Ohio 44325
As a method for lower temperature disposal of potentially hazardous waste, nuclear-grade ion-exchange resin was thermally decomposed at 450 "C, and the decomposition products were passed through catalyst-impregnated monolith reactors under oxidizing conditions. Among the four catalysts tested, alumina-supported 0.1% Pt-Pd and 10% V205were found to be the most active for oxidation of these products, probably because of their resistance to sulfur poisoning. A novel modeling technique was used t o obtain t h e effectiveness factors and the reaction rate constants for these catalysts. Incineration is often used for the volume reduction of low-level radioactive wastes. A typical incinerator consists of a waste decomposition chamber, an afterburner, and an off-gas treatment facility. The decomposition products are passed through an afterburner, where temperatures above 1200 "C are needed for complete homogeneous combustion. Supported transition metal oxide catalysts such as Cr203, CuO, and NiO and noble metal catalysts like Pt and Pd have been used in the afterburner to reduce this temperature (Powers, 1976). In the case of spent ion-exchange resin, incineration results in the formation of substantial SOz and SO3. Unfortunately, most transition metal oxide catalysts are poisoned by sulfur (Farrauto and Wedding, 1973; Yu Yao and Kummer, 1973; Yu Yao, 1973,1974,1975). The main objective of this work was to find and characterize an efficient, low-cost, sulfur-resistant, oxidation catalyst for effective use on these resins in the afterburner section. Considerable work has been done on the modeling of monolithic reactors. Lee and Aris (1976) have reviewed most of these papers. Many authors (Gill et al., 1975; Heck et al., 1976; Ablow and Wise, 1979; Harrison and Ernst, 1978; Bensalem and Ernst, 1982) have assumed that the catalytic agent is deposited as a very thin film on the inside surface of the monolith. De Bruijn et al. (1978) have integrated the mass balance equation in the solid phase to
determine the concentration gradient at the gas-solid interface. Finlayson and Young (1979) have generated an effectiveness factor curve by using a one-term collocation for small Thiele modulus and the asymptotic solution for large Thiele modulus. In the present research, the activities of four catalyst systems are determined and compared for their ability to oxidize the thermal decomposition products from a typical ion-exchange resin. The results are modeled by using the appropriate equations for conservation of mass along with the generalized plot of effectiveness factor vs. Thiele modulus. The effectiveness factor accounts for the concentration profile in the solid catalyst without explicitly determining it. The surface reaction rate constants and the effectiveness factors are subsequently determined for all the catalysts. Preparation of the Catalysts Hollow a-alumina tubes (total surface area = 38.64 m2, pore volume (Hg) = 0.229 cm3/g, and mean pore diameter = 1.45 pm) were obtained from Norton Co. and used as catalyst supports. A hollow alumina tube was used because it would model one cell in a honeycomb reactor. The tubes were 0.635 cm i.d. X 1.587 cm 0.d. X 22.9 cm long and were glazed on the outside to prevent the reactants and/or the products from diffusing out radially. Each tube was im-
0888-5885/ 87 2626- 1965$01.5010 0 1987 American Chemical Society
1966 Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 OPEN TO ATMOSPHERE FROM THE REACTOR OUTLET
1 r 1 WATER .ER NONCONDENSABLE GASES
AIR-SATURATED WATER OPlllii WBE
T
. THIDXCIYIPLi
Figure 1. Experimental setup.
pregnated by methods of incipient wetness using suitable salt(s) of the catalyst dissolved in water. The amount of catalyst salt used was much more than that needed to form a monomolecular layer of the catalyst on the support, resulting in probable catalyst coverage on all accessible pores. The porous catalyst support was saturated with the catalyst salt solution and then air dried. After heating at 110 "C for 8 h to drive off all the water, the catalyst tube was calcined with flowing air in a tube furnace for 6 h at 550 "C to obtain the catalyst in the oxide form. The procedure used to prepare the leached copper chromite catalyst has been described by Farrauto and Wedding (1973).
Experimental Procedure The ion-exchange resin used in this study is DOWEX MR-12, which is an intimate mixture of a strong acid cation-exchange resin in the H+ form (DOWEX HCRW2-H(C/N)) and a strong base anion-exchange resin in the OH- form (DOWEX SBR-P-OH(C/N)) in a 2:l (volume) ratio. The cation-exchange resin is a sulfonated copolymer of styrene (90% by weight) and divinylbenzene (10% by weight), whereas the anion-exchange resin is a copolymer of styrene (90% by weight) and divinylbenzene (10% by weight), which has been chloromethylated and reacted with trimethylamine. The ion-exchange resin did not contain any radioactive elements. The experimental apparatus (Figure 1)consists of three main parts: resin decomposition chamber, catalytic afterburner, and product collection system (Figure 2). To achieve thermal steady-state conditions, air from the compressed air cylinder was passed through the reactor for about 1h. The residence time of air inside the catalyst tube was about 0.3 s for a flow rate of 500 mL/min a t 1 atm and 21.1 "C. At time t = 0, a 1-g sample of the ionexchange resin was introduced into the resin decomposition chamber which was maintained at 450 "C. The products/air mixture was passed through the catalyst-impregnated tubular monolith placed inside the afterburner. Acetone/dry ice traps were used to remove all the condensables. It should be noted that, unlike the actual industrial incinerator, excess air was introduced below the resin decomposition chamber. This should not have affected the results since experiments showed that there was negligible homogeneous reaction even at higher temperatures. From 2 to 10 min during the experimental run, the noncondensable gases leaving the cold traps were collected in a carboy (Figure 2 ) initially filled completely with airsaturated water. The volume inflow of gas into the carboy was made equal to the outflow of water through the spigot
Figure 2. Product collection system.
at the lower end of the carboy, using a water manometer. This novel method of gas collection resulted in a negligible pressure drop a t the gas collection end. This technique was essential, since the alumina/quartz joints in the reactor were susceptible to leaks and even a few centimeters of water pressure drop in the product collection system would have been enough to make the material balance unacceptable. Temperatures were recorded periodically at various points in the reactor system. After 12 min, the ion-exchange resin residue was removed from the resin decomposition chamber and reweighed. Several 1-mL gas samples were taken from the carboy, and the molar ratios of oxygen to nitrogen at the outlet of the reactor (X,) were determined by using a Varian Model 9OP thermal conductivity gas chromatograph (GC). The GC had an 8 f t X 1/8 in. i.d. stainless steel column packed with 100/ 120-mesh Carbosieve S. Helium, with a flow rate of 40 mL/min, was used as the carrier gas. The column oven was held at room temperature for 4.5 min, after which it was ramped at the rate of 18 "C/min. The GC was equipped with a Leeds and Northrup Speedomax W strip chart recorder and a Columbia Scientific Model 38 digital integrator. Samples of air from the compressed air cylinder were also analyzed to find the molar ratios of oxygen to nitrogen a t the inlet of the reactor (Xi). Four different catalysts and a quartz blank were used in this study. All the runs with each catalyst were carried out using the same tube, allowing for cumulative exposure times of over several hours.
Results The oxidative strengths of the catalysts were compared by determining the amounts of oxygen consumed during reaction. The total amount of oxygen (STP) that enters the catalyst chamber during the run is [Xi/(l + Xi)]V,. The total amount (STP)of oxygen that leaves the catalyst chamber during the run is [X,/(l + X,)](V,- Voxy). Here ( V , - VOxJ represents the total volume (STP) of oxygen and nitrogen leaving the catalyst chamber. Therefore, the volume of oxygen (STP)that is consumed by reaction is given by voxy
-
(
xi )vt -
(")cv, + x, 1
This equation can be rearranged to give
- VOXY) (1)
Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 1967
xi xo (-)vt -
voxr =
It is worth emphasising that the basis used for comparing catalysts is the amount of oxygen consumed by reaction and not the amount of oxygen that is used up to form COz, H20, and SO2. The oxidation efficiency (e), which is defined as the percentage oxygen consumed by reaction vs. that needed for complete combustion (to C 0 2 ,H20, and SO2),is given by V O W
e = -100 vcc
xi - x, lOOV, 1 + xi vcc
=--
(3)
(4)
Table I lists the values of oxidation efficiency (e) for all the catalysts and the quartz blank a t 5 0 0 and 575 "C. Values are seen to vary from about 4% for the quartz blank up to about 40% for the 10% V205catalyst. I t is noted that the percent errors (standard deviations) in e are based on repeated analyses and not on repeated experiments. The reactor chosen for this study was low in pressure drop (as necessary commercially) and relatively easy to model mathematically. This choice of reactor mitigated against extremely high catalyst oxidation efficiencies primarily because of mass-transfer limitations in the present system. However, since the aim of this study was to carry out preliminary screening of sulfur-resistant oxidation catalysts, once the best catalysts are known, a honeycomb (multicell monolith) reactor can be used commercially to achieve higher catalyst oxidation efficiencies. Higher temperatures and residence times can also be used, if necessary, to achieve near-complete combustion.
Reactor Modeling A simplified mathematical model was developed for the laminar-flow, wall-catalyzed reactor. The following conditions or assumptions were applied. (1)All the carbon in the ion-exchange resin is in the form of styrene, which is vaporized a t a steady rate during decomposition. The mole fraction of styrene in air at the inlet of the catalyst tube is 0.016 (Le., 30% excess air). (2) In the presence of excess oxygen, the rate of oxidation of styrene is proportional to styrene concentration ( r = $z,C). This has been observed for high-temperature oxidation of many hydrocarbons (Satterfield, 1980). (3) The gas is in laminar flow (Reynolds number (Re) = 55). (4) The momentum entrance length is 1.7 cm. So, the velocity profile is fully developed. (5) Homogeneous reaction is negligible. This was confirmed experimentally. (6) The catalyst tube is mostly isothermal, since the maximum measured exotherms were about 7 "C. (7) There is no appreciable axial dispersion ( L / r i = 36). ( 8 ) Diffusivity of styrene in air is only a function of temperature. (9) The oxidation efficiency (e) includes contributions from heterogeneous and homogeneous reactions. The percentage conversion (t)of styrene is assumed to be equal to the oxidation efficiency for heterogeneous reaction only. Thus, t=e-e, (5) (10) For a particular catalyst, the effectiveness factor at a specific temperature is constant throughout its length.
Table I. Effect of Catalyst Type and Temperature on the Oxidation Efficiency (e) catalyst run catalyst type temp, OC e, % % error in e 1 0.1% Pt-Pd 575 34.3 3.8 2 0.1% Pt-Pd 575 34.0 2.9 3 0.1% Pt-Pd 500 25.2 3.1 4 575 10% CuCr204 4.1 39.7 575 10% CuCr204 5 32.3 2.6 575 10% CuCr204 6 28.9 3.2 500 7 10% CuCrzO, 21.2 5.6 500 8 21.4 10% CuCrz04 4.7 575 9 27.4 10% CuCr104 3.0 575 10 10% CuCr204 24.9 1.6 11 575 25.4 10% CuCr204 2.8 12 575 quartz 5.9 33.9 13 4.5 22.3 500 quartz 14 575 quartz 7.9 10.3 15 4.1 500 quartz 7.6 2.2 40.4 16 575 10% V205 575 10% V2O6 2.1 34.6 17 10% vzo5 2.2 34.5 575 18 10% Vz05 39.2 575 19 2.5 575 10% VzO6 2.3 34.7 20 21 10% Vz05 500 3.4 28.6 22 10% Vz05 500 27.4 2.3 575 7% CoMoO, 23 3.7 26.1 575 7% CoMoO, 24 3.8 21.6 575 2.2 7% CoMoO, 25 21.4 7% COMOO~ 575 26 2.4 22.9 7% CoMo04 500 27 15.4 3.3 7% CoMo04 2.4 500 28 15.8
I
GAS
I
VELOCITY PROFILE
POROUS SOLID
Figure 3. Sketch of the catalytic reactor.
A sketch of the monolithic tubular reactor is shown in Figure 3. The continuity equation and the boundary conditions in dimensionless form are 1 __ ac* (1 - r*2) - = a2C* + ax* &*2 r* dr*
(6)
and
r* = 0
(ii)
(iii)
dC*/dr* = 0 ac*
r*
= 1
dr* =
-(-)c* 17k&
2rDL
(8)
(9)
1968 Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 Table 11. First-Order Reaction Rate Constants and Effectiveness Factors for Different Catalysts catalyst 107k,, run catalyst type temp, OC 7 m?/(m,'d 0.1% Pt-Pd 575 26.7 0.33 4.0 1 3.9 0.34 575 26.4 2 0.1% Pt-Pd 0.42 2.4 500 21.1 0.1% Pt-Pd 3 0.27 6.5 575 32.1 10% CuCrzO, 4 3.3 0.36 575 24.7 10% CuCrzO, 5 2.5 21.3 0.42 575 10% CuCrz04 6 n 1.7 500 17.1 0.50 10% CuCrzO, 1.7 17.3 0.49 500 8 10% CuCrz04 2.2 19.8 0.44 575 9 10% CuCrzO, 1.7 0.49 575 17.3 10% CuCr,O, 10 1.8 17.8 0.48 575 11 10% CuCri04 0.26 7.0 575 32.8 16 10% v,05 0.33 4.1 575 27.0 10% VzO5 17 4.1 0.33 575 26.9 10% vzo5 18 6.2 575 31.6 0.27 10% v205 19 4.2 575 27.1 0.33 20 10% V205 3.3 0.37 500 24.5 21 10% Vz05 3.0 0.38 500 23.3 10% vzo5 22 1.9 18.5 0.47 575 23 7% CoMo04 1.3 575 14.0 0.56 24 7% CoMoO, 1.2 13.8 0.57 575 25 7% CoMoO, 1.4 0.53 575 15.3 7% COMOO~ 26 1.0 11.3 0.63 500 27 7% CoMoO, 500 11.7 0.62 1.0 28 7% COMOO,
1 0
It is assumed that the effectiveness factor, q , and the surface reaction rate constant, k,, remain constant for a particular catalyst at one temperature. If qk, is known, the continuity equation (eq 6) along with the boundary conditions (eq 7-9) can be solved to obtain the concentration profiles in the reador. The conversion at the outlet of the reactor can also be determined. Alternatively, if the conversion at the outlet of the reactor is known, q k , can be determined by using a trial-and-error procedure. The latter approach is used in this work. The Crank-Nicolson finite difference technique and the experimentally obtained values of conversion (E) are used to obtain qk, as follows. An initial guess for qks is made and the continuity equation solved numerically to determine the concentration profile at the outlet of the reactor. The outlet mixing cup concentration is compared with the experimental value. If the two are different, a new value of qks is guessed and the procedure continued until agreement is obtained. The Crank-Nicolson finite difference technique gives the value of the product 712,. In order to determine q and k , separately, it is necessary to have anotner equation relating q to k,. Since the Thiele modulus, 4, is a function of k,, the generalized plot of effectiveness factor ( q ) vs. Thiele modulus (4) (Froment and Bischoff, 1979) would yield the required relationship. The values of 7 and k, are listed in Table 11. The surface reaction rate constant, k,, varied from 1.0 X lo-' mp/(m,2,s) for the least active catalyst (CoMoO, at 500 "C, where q = 0.62) to 7.0 X mf3/(mp2.s)for the most active catalyst (V205a t 575 "C, where 9 = 0.26). The bulk concentration in the gas phase was about 5% greater than the concentration at the gassolid interface. So, external mass-transfer limitations were unimportant. However, since the effectiveness factor varied from 0.26 to 0.62, pore diffusion did significantly limit reaction rates. Discussion of Results One of the main objectives of this study was to utilize a sulfur-resistant oxidation catalyst to treat decomposition products from ion-exchange resins. Of all the base metal oxide catalysts tested, Vz05was the most active. Since it is a well-known fact that Vz05 is not poisoned by sulfur
. 0
0
T = 575Y
A C T I V E CATALYST D E A C T I V A T E D CATALYST
1
0 Pt-Pd
CoMoO,
a
20
40
60
BO
100
120
SURFACE-OXYGEN BOND ENERGY, qs
(Kcal/gm atom oxygen)
Figure 4. Effect of surface-oxygen bond energy, qs, on the activity of catalysts.
oxides under oxidizing conditions, it would have been futile to perform a long-term deactivation study on this catalyst. As discussed below, the next best base metal oxide catalyst (CuCr204)lost about half its activity during initial passage of sulfur oxides. At this stage, it was obvious that V205 was a better catalyst than CuCrz04and the deactivation study was terminated. Similarly, a detailed deactivation study was not performed on the CoMoO, because it turned out to be the least active of all the catalysts studied. The activities of catalysts were compared using k, values. The Pt-Pd and V205catalysts do not appear to have been poisoned by sulfur, at least in the short time (about 2 h) used in these experiments. In contrast, the activity of CuCrz04dropped by about 50% in the first hour, after which there was no perceptible change. Poisoning of the CuCr204catalyst could be due to sulfate formation (Farrauto and Wedding, 1973). The CoMoO, catalyst was deactivated rapidly, its activity decreasing by about 25% in 15 min. This could be due to the fact that CoMoO, is more active in the oxide form than in the sulfated form. One would expect the catalyst to become sulfated in the first few minutes of passage of SOz. The activities of the catalysts in oxidation of the ionexchange resin can be summarized as follows: 10% V205 I0.1% Pt-Pd > 10% CuCr,04 > 7% CoMoO,. Hence, the V z 0 5 catalyst can potentially be an inexpensive alternative to the use of noble metals. The above ranking uses the activities of poisoned CuCrzO, and CoMoO, catalysts for comparison. All oxidation reactions involve the formation or the breaking of oxygen-catalyst bonds. Hence the surfaceoxygen bond energy, qs, is a good measure of the activity and the selectivity of an oxidation catalyst. The effect of q, on the activity of test catalysts is correlated in Figure 4. For the complex metal oxides, CuCrz04and CoMoO,, the q, values for Crz03and MOO,, respectively, were used (Golodets, 1983). For the Pt-Pd bimetallic catalysts, the
Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 1969 mean qs value was used. As expected, Figure 4 shows that the initial activities of the base metal oxide catalysts decrease with increasing qs. This probably is because the oxygen mobility is low for catalysts that form strong surface-oxygen bonds (large qs). One would expect the plot of catalyst activity vs. surface-oxygen bond energy to go through a maximum, since the origin of the graph (0,O) also lies on this curve. The data suggest that this maximum would occur a t a qs value of less than 30 kcal/mol of oxygen; unfortunately, most base metal oxide catalysts with low qs values are poisoned by sulfur. Conclusions As expected, Pt-Pd and V205 catalysts were not significantly poisoned by sulfur compounds during resin oxidation experiments. Conversely, CuCrz04and CoMoO, catalysts did show a deactivation trend. The activities of the catalysts decreased in the following order: 10% V2O5 1 0.1% Pt-Pd > 10% CuCrz04 > 7% CoMoO,. For wastes containing sulfur, the V205 catalyst could be an inexpensive alternative to the more costly noble metals. The reactor model developed for this study can be used to determine the surface reaction rate constant, k,, and the effectiveness fador, for any first-order irreversible reaction occurring in an isothermal tubular monolith, provided that the conversion has previously been determined experimentally. In the present study, the surface reaction rate constants varied from 1.0 X mt/(m,2.s) for the least active catalyst (CoMo04a t 500 OC, where 7 = 0.62) to 7.0 X mt/(m,2,s) for the most active catalyst (V205 at 575 OC, where 7 = 0.26). Acknowledgment The assistance of Norton Co., Akron, OH, in preparing and characterizing the alumina support tubes is appreciated. Nomenclature a = total (internal mp2
+ external) surface area of the catalyst,
C = concentration, kmol/mf3 Ci = concentration at the inlet of the catalyst tube, kmol/mp C* = C/Ci = dimensionless concentration D = diffusivity, m?/s e = oxidation efficiency for the catalyst, % e, = oxidation efficiency for the blank, % k , = first-order surface reaction rate constant, m$/ (mp2.s) L = length of the catalyst tube, m m,32 = cubic meter of the fluid mp = square meter of the solid q, = surface-oxygen bond energy, kcal/mol of oxygen ri = inner radius of the catalyst tube, m r* = dimensionless radial distance (r/ri) Re = 2riu,p/p = Reynolds number t = time, s u, = mean gas velocity, m/s V,, = volume (STP) of oxygen needed for complete combustion of the decomposed resin sample to CO,, HzO, SOz, and NOz, m3
= volume (STP) of oxygen that is consumed by reaction, m3 V, = total volume (STP) of air flowing into the reactor during the run, m3 x* = dimensionless axial distance ( x / L ) X , = (O,/N,) at the inlet of the reactor, kmol/kmol X , = (Oz/N,) at the outlet of the reactor, kmol/kmol Greek Symbols 7 = effectiveness factor for the catalyst p = viscosity of the gas, kg/(m-s) p = density, kg/m3 4 = Thiele modulus 5 = conversion, % V,,
Registry NO, DOWEX MR-12,103458-13-5;V205,1314-62-1; Pt, 7440-06-4; Pd, 7440-05-3; CuCrzOr, 12018-10-9; CoMo04, 13762-14-6.
Literature Cited Ablow, C. M.; Wise, H. “Theoretical Analysis of Catalytic Combustion in a Monolith Reactor”, Combust. Sci. Technol. 1979, 21, 35-42. Bensalem, 0.; Ernst, W. R. “Mathematical Modeling of Homogeneous-Heterogeneous Reactions in Monolithic Catalysts”, Combust. Sci. Technol. 1982, 29, 1-13. De Bruijn, E. W.; De Jong, W. A.; Van Der Spiegel, C. J. Methanation in a Parallel Passage Reactor; Weekman, V. W., Jr., Luss, D., Eds.; ACS Symposium Series; Chemical Reaction Engineering: Houston, 1978; Vol. 65, pp 63-71. Farrauto, R. J.; Wedding, B. “Poisoning by SO, of Some Base Metal Oxide Auto Exhaust Catalysts”, J. Catal. 1973,33, 249-255. Finlayson, B. A,; Young, L. C. “Mathematical Models of the Monolith Catalytic Converter: Part 111. Hysteresis in ‘:arbon Monoxide Reactor”, AZChE J . 1979, 25(1), 192-196. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design; Wiley: New York, 1979; p 186. Gill, W. N.; Ruckenstein, E.; Hsiesh, H. P. ”Homogeneous Models for Porous Catalysts and Tubular Reactors with Heterogeneous Reactions”, Chem. Eng. Sci. 1975, 30, 685-694. Golodets, G. I. Heterogeneous Catalytic Reactions Involving Molecular Oxygen; Elsevier: Amsterdam, 1983; pp 91-95. Harrison, B. K.; Ernst, W. R. “Catalytic Combustion in Cylindrical Channels: A Homogeneous-Heterogeneous Model”, Combust. Sci. Technol. 1978,19, 31-38. Heck, R. H.; Wei, J.; Katzer, J. R. “Mathematical Modeling of Monolithic Catalysts”, AZChE J . 1976, 22(3), 477-484. Lee, S. T.; Aris, R. “Modeling the Monolith Some Methodological Considerations”, Chem. React. Eng., Proc. Znt. Symp., 4 t h ed., 1976, 232-239. Powers. P. W. How to DisDose of Toxic Substances and Industrial Wastes; N.D.C.: Newark, NJ, 1976; pp 77-85. Satterfield, C. N. Heterogeneous Catalysis in Practice; McGraw Hill: New York, 1980; pp 180-186. Yu Yao, Y. F.; Kummer, J. T. “The Oxidation of Hydrocarbons and CO Over Metal Oxides I. NiO Crystals”, J . Catal. 1973, 28, 124-138. Yu Yao, Y. F. “The Oxidation of Hydrocarbons and CO Over Metal Oxides 11. a-Crz03n:J. Catal. 1973, 28, 139-149. Yu Yao, Y. F. “The Oxidation of Hydrocarbons and CO Over Metal Oxides 111. Co304”,J. Catal. 1974, 33, 108-122. Yu Yao, Y. F. “The Oxidation of CO and CzH4Over Metal Oxides V. SOz Effects”, J. Catal. 1975, 39, 104-114. Received for review April 18, 1986 Revised manuscript received February 6, 1987 Accepted July 20, 1987
