1960
Ind. Eng. Chem. Res. 1987, 26, 1960-1965
Kuo, J.; Lenz, R. W. J . Polym. Sci., Polym. Chem. Educ. 1976, 14, 2749. Kuo, J.;Lenz, R. W. J . Polym. Sci., Polym. Chem. Ed. 1977,15, 119. Lefebre, G. Rev. Inst. Fr. Pet. Ann. Combust. Liq. 1963, 18, 1192. Lenz, R. W.; Luderwald, I.; Montaudo, G.; Przybylski, M.; Rinsdorf, H. Makromol. Chem. 1974, 175, 2441. Montaudo, G.; Bottino, F.; Caccamese, S.; Finocchiaro, P.; Bruno, G. J . Polym. Sei. 1970, 8, 2475. Nomiya, K.; Ueno, T.; Miwa, M. Bull. Chem. Soc. Jpn. 1980,53,827. Nomiya, K.; Makoto, M.; Yoshio, S. Polyhedron 1984, 3, 381. Pinkus, A. G.; W. H. J. Macromol. Sei. Chem. 1979, A13(1), 133. Romero, A.: Bilbao. J.: Gonzalez-Velasco, J. R. Afinidad 1979. 36. 472.
Romero, A.; Bilbao, J.; Gonzalez-Velasco,J. R. Afinidad 1980,37, 21. Romero, A.; Bilbao, J.; Gonzalez-Veslasco, J. R. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 570. Romero, A.; Bilbao, J.; Aguayo, A. T. An. Quim. 1982, 78, 365. Romero, A.; Bilbao, J.; Aguayo, A. T. An. Quim. 1983, 79, 393. Tsonis, C. P.; Hasan, M. U. Polymer 1983, 24, 707. Valentine, L.; Winter, R. W. J. Am. Chem. Soc. 1956, 78, 4767. Yermakov, Yu. I.; Mikhalchenko, V. G.; Beskov, V. S.; Grabovski, Yu. P.; Emirova, I. V. Plast. Massy 1970, 9, 7.
Received for review September 27, 1985 Revised manuscriDt received Februarv 19. 1987 Accepted June 24, 1987
Polymerization of Gaseous Benzyl Alcohol, 2. Kinetic Study of the Polymerization and of the Deactivation for a Si02/A1203Catalyst Javier Bilbao,* Martin Olazar, Jose M. Arandes, and Arturo Romero Departamento de Quimica Tgcnica, Uniuersidad del Pais Vasco, 48080 Bilbao, Spain
Langmuir-Hinshelwood's mechanism has been proposed for benzyl alcohol polymerization in the gas phase on an acidic catalyst of SiO2/AI2O3. Although the existence of these mechanisms in polymerization reactions on solid catalysts has already been defended, there was not a solid experimental base for their validity. T h e kinetic equation deduced for the proposed mechanism is eq 20. In order to calculate the kinetic constants of this equation, experiments were carried out in an isotherm fluidized bed, in the 250-310 " C range. The different length experiments are discontinuous for the catalyst and continuous for the gas, and the method of data analysis has been based on the calculation of the initiation period length and of the polymerization maximum rate, for different values of partial pressure of benzyl alcohol fed at the reactor. The deactivation kinetics has been studied. The equation obtained a t 270 " C is an expression of first order with respect to catalyst activity and to partial pressure of benzyl alcohol. In the first part of this work (Olazar et al., 1987), the high activity of amorphous Si02/A1,03 catalysts was determined in the process of obtaining polybenzyls from gaseous benzyl alcohol, via dehydration. In the same way, the mentioned work, the most suitable operating conditions were determined. After the effect of the temperature and monomer concentration on the polymerization rate is studied, the results obtained do not seem to correspond to a simple kinetic expression bid to a kinetic equation in which the numerator as well rls the denominator vary with temperature as it corresponds to a polymerization mechanism of the type proposed by Langmuir (1921) and Hinshelwood (1940) for contact catalysis. The Langmuir-Hinshelwood theory has allowed the development of mechanistic kinetic equations which are universally accepted as adequate for contact catalysis in reactions with hydrocarbons. In view of that, polymerization theories on solid catalysts (Clark and Bailey, 1963a,b;Guyot and Daniel, 1963; Guyot, 1964; Clark, 1970) based on the usual scheme of contact catalysis on active sites have been developed, that is to say, with three steps in the polymerization mechanism: adsorption, reaction, and desorption. However, there is poor experimental evidence about the validity of these mechanisms. In thiswork, Langmuir-Hinshelwood's mechanisms have been postulated for the polymerization, having obtained the corresponding kinetic equations whose validity will be proved by experimental data. With regard to the lack of methodology of data analysis when obtaining the kinetic equation in reactions as the one studied here, in this work the usual procedures for contact catalysis have been ap0888-5885/87/2626-1960$01.50/0
Table I. Catalyst Properties s, m2/g Vp, cm3/g pryg/cm3 Par g/cm3 Physical Properties 286 0.56 2.37 1.02 activity, mg of n-butylaminelg of catalyst %A1203 pK +6.8 pK +4.8 pK +3.3 pK +2.8 Chemical Properties 12.3 48 35 26 23
plied, even though difficulties appear due to the particular characteristics of the process, as the existence of an initiation period. Another difficulty of this process is the rapid deactivation of the catalyst. The deactivation kinetics has been studied, as this knowledge is necessary for the design of a reactor that provides the continuous production of polybenzyls on a large scale. Catalyst and Reaction Conditions The catalyst used, named 1-35, is a gel of Si02/A1203 prepared and characterized in our laboratory in accordance with the methods detailed in the first part of this work (Olazar et al., 1987). In Table I, physical properties and surface acidity of the catalyst are summarized. The experiments were carried out in reaction equipment with continuous monomer feed under atmosphericpressure (Olazar et al., 1987) in a glass reactor of 16-mm inside diameter in a fluidized bed regime. The working conditions are as follows: temperature, 250, 270, 290, 310 "C; space time, 0.4 g of catalyst.h/mol; partial pressures of benzyl alcohol at inlet (diluted with N,),0.02, 0.06, 0.12, 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 1961 Table 11. Computed Values of ti (min) and rpo(g of polymer/(g of catalyst *min)) PAO,atm a t 250 a t 270
O C
t:
O C
rpo ti rpo
a t 290 "C
ti
rpo
a t 310 "C
ti rpo
0.02
0.06
0.12
0.18
0.22
0.30
0.40
0.50
0.65
25.1 0.22 35.4 0.12 51.4 0.06 75.5 0.03
10.3 0.71 12.2 0.52 15.5 0.33 20.5 0.20
5.9 1.18 6.4 1.03 7.8 0.78 9.2 0.54
4.3 1.41 4.5 1.39 4.9 1.18 5.8 0.88
3.4 1.52 3.6 1.56 3.9 1.39 4.5 1.10
2.8 1.69 2.8 1.87 2.9 1.77 3.2 1.46
2.2 1.83 2.1 2.11 2.2 2.11 2.4 1.83
1.8 1.91 1.7 2.25 1.7 2.33 1.8 2.14
1.5 2.00 1.4 2.46 1.3 2.65 1.4 1.52
25C°C
P
t !mini
t
Im~nl
1
+I
-1
td
-
t
Figure 2. Polymerization steps.
The polymerization has an initiation period of ti length, which is the necessary time to form the active compounds and for the polymerization to reach steayd state. After this period (for t = ti),the polymerization rate reaches a maximum value, and then the polymerization rate decreases probably due to the catalyst deactivation. The data of Figure 1 have been fitted to the empiric equation
where t
t
(mini
Imin!
31O0C
t jmin,
Figure 1. Polymer vs. time.
0.18, 0.22, 0.30, 0.40, 0.50, and 0.65 atm; gas velocity at inlet, 40 cm/s; catalyst dilution (with SiOz gel), 10% (by weight); PA,,,reaction time; 0.02 atm, 8-70 min; 0.06 atm, 3-40 min; 0.12 atm, 1-12 min; 0.18 atm, 1-6 min; 0.22 atm, 0.5-4 min; 0.30 atm, 0.5-4 min; 0.40 atm, 0.5-3 min; 0.50 atm, 0.5-2 min; 0.65 atm, 0.5-1.5 min.
Kinetic Data After each experiment, catalyst plus polymer mass was drawn out of the reactor. Having cooled until it was at room temperature, the polymer had a pulverulent consistancy which allowed for mechanical separation from the catalyst. The results of polymer weight are plotted vs. time in Figure 1. The curves of Figure 1have a S-shape layout, and they have the steps outlined in Figure 2.
rpois the maximum rate of polymer deposition per catalyst mass unit (g of polymer/(g of catalyst-min)). The fitting was carried out by nonlinear regression in a TRS-80-11 microcomputer by a program based on Marquardt's method (1963). The results of this fitting are shown in Table 11, where values of initiation period, ti, and their corresponding polymer deposition rates, rpo, are summarized. The regression coefficient is 0.96 in the worst cases. The initiation period decreases with partial pressure of alcohol fed at the reactor, following the relation ti = 0.91PA00.93 (r2 = 0.98)
(3)
Polymerization Mechanism A polymerization mechanism of the Langmuir-Hinshelwood type and based on the theories of Clark and Bailey (1963a,b), Clark (1970), and Maiti (1975)) among others, has been proposed. 1. Adsorption and Activation Step (Initiation) M
+L
KM
MI
ki
MI*
(4)
1962 Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987
for a solvent
S + L 2 S 1
An assumption has been made in eq 10 that [M1I2is negligibly small compared to either 2[Ml] or 1. Expression 10 becomes
2. Reaction Step (Propagation) Mi
+ Mi*
MI
+ M2*
kP
-
M2*
P
MI + Mn-l*
M3*
R = [M]2(2kdkpk,K~2[L]2 + 2kskpk1K&M2[L]2[s]+
i
2k,k,klK~~[M][LI3) (11)
) (n - 1)Ml + MI*
kP
kP -+
Mn*
[Nl = 5 [ M n * l + [MI] + [S,]
Mn* ,
n=2
3. Desorption Step (Termination). 3.1. Spontaneous Desorption (Termination) Mn*
kd
P,
+L
+ [L]
(12)
The total concentration of active sites will be negligible, so the fiist summation of eq 12 can be rejected. With that consideration, eq 12 can be written as IN1 = KM[MlrL1 + KS[sl[Ll
3.2. Desorption by Monomer (Termination)
M,*
The total concentration of active sites, [N], is
+ [L1
(13)
from where
+ M1 --!%P, + L + M,
3.3. Desorption by Solvent (Termination) Mn* + S1
k,
P,
+ L + SI
Defining the reaction rate as the number of monomer units in the polymer per unit catalyst mass and unit time, it will be computed by the next expression as the summation of the contributions of terminations by spontaneous desorption and desorption by the action of the monomer and the solvent. m
R = (A n=2
m
n[P,])/At = k d ks
c n[M,*]
n=2
+
5n[Mn*l [SI] + 5n[Mn*l [MI1 (6) km
n=2
n=2
The terms of eq 6 are computed as m
Cn[Mn*] = 2kp[M,*][M,] + 3kp[M1*][M1]2+ ... +
When the feeding solvent is not adsorbed on the catalyst active sites, eq 15 becomes
R = [MI2 X
+
(2kdk,kl[N]2K~3 2k,k,k1[N]~K~~) [MI (1 + KM[MI)~
n=2
nkp[M1*][Mlln-l= 2kpkl[M1]2+ 3kpkl[M1]3+ ... + nkpki[Miln = kpki[Mi1(2[MiI + 3[MJ2 + ... + n[M1]"-') (7)
The parentheses of eq 7 represent a converging series for [M,] (=K,[M][L]) C 1. Integration of this series term by term results in an infinite geometric series: [M1I2 2+ + 3- [M1i3 3 2
... + -n [Mil" n
+
If the following parameters are introduced,
eq 16 becomes
The summation of this series is
When this equation is differentiated with respect to [M,], an expression for these terms taken from the parentheses of eq 7 is obtained:
Introducing this expression into eq 6 then yields
Kinetic Equation of the Polymerization Equation 19, which has been deduced theoretically from the mechanism supposed for the polymerization, can be expressed in a more practical way as a function of benzyl alcohol partial pressure on the gas stream:
Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 1963
I
/"
01
,.
L
'"E
i
183
1 7 5
e5
-ldI 90 1 / T 11T3 K-l]
Figure 3. Arrhenius plot of polymerization rate constants.
The experimental kinetic data related in Table I1 were fitted to eq 20. The method used was Marquardt's nonlinear regression. Pairs of values of reaction rate, rpo,and of benzyl alcohol partial pressure, PA, which is the average pressure between the inlet and the outlet of the reactor, were fitted. The computed values of the kinetic constants, km', kd', and K Mare shown in Figure 3 as Arrhenius plots. As a result of fitting the values to straight lines in Figure 3, the following relations are obtained:
(
lo3 exp -
k,' = 3.74
X
KM= 2.95
X
ex,(
7800:850)
9500 f 800
)
When these relations are substituted in eq 20, the kinetic equation in the temperature range between 250 and 310 "C is
[
rpo = PA2( 2.95 x 10-7 ex,(
104 e x p ( 5400 -T)
[
7)13[ 9500 7.50 x
+ 3.74 x 103 e x p ( - F )
]PA + . -
2.95
exp( 7)12[ 9500 7.50 X
X
104 exp(
-?)
I)/[
1
+
2.95 x 10-7 exp( T 9500 ) p A ] (21) In order to verify the validity of the computed kinetic constants, rpowas obtained by these constants by using eq 21. In Figure 4, the solid lines are the computed values and the points are the experimental data. The agreement between both demonstrates the validity of eq 21. The complexity of the rpovs. PA curves in Figure 4 is remarkable so that the curves corresponding to different temperatures cross each other. Due to that, as alcohol partial pressure increases, the maximum polymerization rate corresponds to a higher temperature in the range studied. From the values of the k,' and kd' kinetic constants, the effect of temperature on the termination step of the polymerization can be analyzed. The ratio of these parameters is
k,' - [N13kpk l km _ kd'
[Nl2k,Izlkd
- [Nlk,
-
kd
(22)
Figure 4. Polymerization rate at t = ti vs. average partial pressure of benzyl alcohol in the reactor: (-1 computed; (points) experimental data.
Assuming that the temperature has no effect on the active sites number, [ N ] ,the k,'/kJ ratio will indicate the ratio between termination rates by both routes. In this case, the k,'/ k J ratio increases with temperature, which indicates that the polymer proportion formed by termination of monomer will increase as well.
Catalyst Deactivation In order to use eq 21 to design the reactor, it will have to be considered that the catalyst deactivates considerably, so that the polymerization rate decreases with time. Consequently,a kinetic equation that describes accurately the catalyst deactivation will have to be known when designing the reactor. The general characteristics of the deactivation by coke deposition were studied before in alcohol dehydration reactions on Si02/A1203catalysts (Bilbao et al., 1985). The coke is not a well-defined compound but a material that is developing toward high condensation degrees, and it is interpreted that the intermediate compounds as well as the final carbonaceous product occupy acidic sites and contribute to catalyst deactivation (Wukasch and Rase, 1982). The kinetic study of the deactivation was carried out at 270 "C. The operating time values have been for various partial pressures (PA,)are as follows: 0.02 atm, 30,60,100, 150, 200, and 250 min; 0.06 atm, 8, 16, 50, 80, and 120 min; 0.12 atm, 6, 10, 15, 20, 30, 40, 50, and 60 min; 0.18 atm, 2, 4, 6, 8, 10, 15, 20, 25, 30, and 35 min; 0.22 atm, 2, 4, 6, 8, 12, 16, 20, 25, 30, and 35 min; 0.30 atm, 2, 4, 7, 10, 15, 20, 25, and 30 min; 0.40 atm, 2, 4, 6, 8, 12, 16, 20, and 24 min; 0.50 atm, 2, 3, 4, 6, 8, 10, 14, and 18 min; 0.65 atm, 1, 2, 3, 4, 6, 8, and 10 min. As the experiments were carried out in a fluidized bed and in a discontinuous regime for the catalyst, in order to obtain polymer deposition data corresponding to long reaction times (to which particle enlargement will stop the fluidization), it was necessary to work in several stages one after the other. At the end of each stage, the polymer was deposited outwardly, the catalyst particles were removed, and these particles were fed again into the reactor. This way, the additional polymer amount deposited for each stage was calculated. The total polymer amount deposited was calculated as the summation of that deposited for the successive stages. To separate the polymer from the catalyst without changes to its activity, that is to say, without decreasing it by sintering of acidic sites and without increasing it by catalyst partial regeneration (by burning of the polymer that is in the particles), a controlled combustion was chosen as the suitable method. Trying several temperatures and combustion times in the muffle oven, it was determined that after burning for 16 h and at 400 "C,the catalyst was free of the polymer that covered
1964 Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987
~-____---f
p -
tif 3 )
0
-!
--
4
G-L--
I '2
t
rr-
tjcrr
Figure 5. Polymer deposited vs. time for the different values of the partial pressure of benzyl alcohol in the feed a t 270 "C.
it outwardly and it had the same activity as before removing the polymer. Mechanic separation of the polymer was tried as well, obtaining the same results of deposited polymer amount as by controlled combustion of the polymer. In Figure 5 deposited polymer data against time are plotted. The data of Figure 5 have been fitted to eq 1 by a nonlinear regression subroutine based on Marquardt's method (1963). The values of rp0and ti calculated at 270 "C are identical with the ones shown in Table 11, which were calculated with eq 1 and the results of deposition in the initiation period. This shows the utility of eq 1 to represent the polymer deposition with time in the initiation period as well as in the deactivation period. Activity has been defined as
where td corresponds to the deactivation period time, after being over the initiation period. The calculated values of activity vs. time have been plotted in Figure 6. The data of Figure 6 have been fitted to the equation da
--
-- KdPAa
= 0.32PAa
dtd
PAcorresponds to the average value of benzyl alcohol partial pressure in the reactor for each value of reaction time: P A
=
-k
= pAn( 1-
2
%)
(25)
The conversion a t outlet referred to benzyl alcohol in the feed is 108 W XA = --rpoa FAO
-
3c
(26)
i
-
Figure 6. Calculated values of activity vs. time in the deactivation period for the different values of partial pressure of benzyl alcohol in the feed.
Substituting eq 26 into eq 25 for W/FAo= 0.4 g of catalyst.h/mol gives
PA= P A O ( 1 - 0.13rpoa)
(27)
Integration of eq 24 yields a=
exp[-0.32P,,(t - ti)] 1 - 0.13rPo(l- exp[-0.32PAo(t- ti)])
(28)
Conclusions A kinetic equation that fulfils the experimental results in the whole temperature range studied (250-310 "C) and in the whole feeding alcohol partial pressure range studied (0.02-0.65 atm) was obtained. This is an experimental support to the hypothesis that polymerization follows the proposed Langmuir-Hinshelwood mechanism, where the polymerization occurs by reaction of an adsorbed molecule of monomer with an adsorbed growing polymer chain. The decrease in the polymer formation rate with time can be attributed to the Si02/A1203catalyst deactivation by the irreversible deposition of carbonaceous material originating in the polymer degradation in the catalyst porous structure. This deposition causes at the same time a decrease in surface area, pore volume, and surface acidity of the catalyst. Data of activity vs. time for a polymerization temperature of 270 "C were fitted to a kinetic equation of first order with respect to activity and to partial pressure of benzyl alcohol. Nomenclature a = catalyst activity defined as ratio o f reaction rates KM,Ks = equilibrium constant of the adsorption of the monomer and the solvent, respectively, on an active site k d , k,, k s = rate constants of spontaneous desorption, desorption by monomer, and desorption by solvent, respectively kd/, k,' = parameters introduced by eq 17 and 18, respectively k , = propagation rate constant k , = rate constant of the monomer activation on the active site
L = free active site
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 Symbols 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 for 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
