2946
Ind. Eng. Chem. Res. 1996, 35, 2946-2954
Interaction of Reaction and Mass Transfer in Ion-Exchange Resin Catalysts† Son-Ki Ihm,*,‡ Jou-Hyeon Ahn,§ and Young-Do Jo| Department of Chemical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Kusung-dong, Yusung-Ku, Taejeon 305-701, Korea, Department of Chemical Engineering and RIIT, Gyeongsang National University, 900, Kajwa-dong, Chinju 660-701, Korea, and Korea Gas Safety Corporation, 332-1, Daeya-dong, Shihung-shi, Kyonggi-do 429-010, Korea
A two-phase model has been proposed for a macroreticular resin catalyst to analyze the reaction activities in terms of the micro- and macroeffectiveness factors and the fraction of active sites on the surface layer. The accessibility of sulfonic acid groups was investigated through the sucrose inversion and benzene alkylation. Internal functional groups were found to be more active than external ones in the synthesis of methyl tert-butyl ether and the hydration of isobutylene. It was also shown that the distribution and local concentration level of sulfonic acid groups within a gellular microparticle of the macroreticular resin had a significant influence on the catalytic activity of 1-butene isomerization and the deactivating patterns of ethanol dehydration. I. Introduction Ion exchangers, by common definition, are insoluble solid materials which carry exchangeable cations or anions. The most important class of ion exchangers is the organic ion-exchange resins. The high-performance ion-exchange resins of practical importance have been synthesized since two chemists (Adams and Holmes, 1935) discovered that the condensation products of phenol and formaldehyde exhibit ion-exchange properties. To date, ion-exchange resins have found practical applications in a number of areas and are particularly used as catalysts for hydration (Ihm et al., 1988; Velo et al., 1990), hydrolysis (Fuchigami, 1990), alkylation (Kim and Ihm, 1982; Park and Ihm, 1985; Patwardhan and Sharma, 1990a), esterification (Petrini et al., 1988; Patwardhan and Sharma, 1990b), dehydration (Chee and Ihm, 1986), etherification (Lee and Ihm, 1987; Hejtmankova et al., 1990; Rehfinger and Hoffmann, 1990; Lee et al., 1991; Parra et al., 1994), and isomerization (Ahn et al., 1988; Li, 1989). Early reviews on ion-exchange resin catalysts were published by Astle (1957), Polyanskii (1962, 1970), Pittman and Evans (1973), and Polyanskii and Sapozhnikov (1977). Widdecke (1988) and Neier (1991) have published a useful review on the ion-exchange resin catalysts. The most recent work by Chakrabarti and Sharma (1993) is valuable in terms of highlighting all the processes in which ion-exchange resin catalysts have been exploited. This includes a unique review of separations achieved by employing selective reactions to transform only one component of a mixture. The text by Gates (1992) contains an excellent chapter on ionexchange resin catalysts. In spite of these reviews, there are scarcely any review papers on the models for the interaction of reaction and mass transfer in ion-exchange resin catalysts. Mingle and Smith (1961), Carberry (1962), and O ¨ rs and Dogu * To whom correspondence should be addressed. Telephone: +82-42-869-3915. Fax: +82-42-869-5955. † Dedicated to Professor Eli Ruckenstein on the occasion of his 70th birthday. ‡ Korea Advanced Institute of Science and Technology. § Gyeongsang National University. | Korea Gas Safety Corp.
S0888-5885(95)00724-X CCC: $12.00
(1979) have derived expressions for the micro- and macroeffectiveness factors. In their calculations the resulting overall effectiveness factor was essentially the product of the micro- and macroeffectiveness factors, and the contribution from macropore walls to reaction is assumed to be negligible. Tartarelli et al. (1970) analyzed a second-order reaction by introducing a generalized Thiele modulus and calculated the effectiveness factor for an isothermal condition by a numerical method. For resin catalysis, Frisch (1962) proposed a model with radially oriented cylindrical macropores in the gel structure and considered diffusion-limited first-order reversible reactions catalyzed by macroreticular ionexchange resins in which both macropore and matrix diffusion in the polymer were taken into account. Ruckenstein et al. (1971) developed a similar macromicropore model for transient sorption in solids having bidisperse pore structure which showed the influence of the competing effects of macropore and micropore diffusions. From the viewpoint of the scanning electron micrograph, the cylindrical geometry of the macropore may not be adequate for describing the macroreticular ion-exchange resin catalyst. In this paper, therefore, the author’s two-phase model with internal and external functional groups has been described, and the interactions between reaction and diffusion in a macroreticular resin have been explained in each reaction. Two types of morphology in cross-linked polymer resins have been studied: one is a gellular resin and the other is macroporous. The gellular resin does not have permanent pores, and the polymer chains are somewhat mobile when contacted with good solventestablishing pores. The pore dimensions are influenced by the properties of the solvent employed. The macroporous resin has permanent pores and is relatively rigid. The pore dimensions of macroporous resins do not appreciably change with solvent properties. Acid ion-exchange resin catalysts are used commercially in a bead form. Macroreticular resins consist of agglomerates of a spherical microparticle with free space between them, which accounts for the porosity of the resin. Two different kinds of functional groups exist in the microparticle of a macroreticular resin. A fraction of the total functional groups is located on the surface © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 2947
of the microparticle and provides easy access to the reactants. However, the remaining functional groups are located within the polymer matrix of the microparticle. Reactants must penetrate through the polymer matrix in order to gain access to the internal functional groups. The reaction and mass transfer in the macroreticular resins were investigated (Frisch, 1962; Ruckenstein et al., 1971), and a two-phase model was also proposed by the authors (Ihm et al., 1982). For a sulfonic acid resin catalyst, catalytic function is due to the association of several -SO3H groups in a nonaqueous medium and the catalytic activity increases nonlinearly with increasing the concentration of sulfonic acid groups. Dooley et al. (1982) suggested that the sulfonic acid groups on the surface of gel microparticles are less active than those within the microparticle. Klein et al. (1984) demonstrated that the distribution of the sulfonic acid groups with the resin catalysts could be controlled so that different concentration profiles were obtained, and the properties and reaction behavior of the resin catalysts were varied to a large extent by the local concentration and distribution of the sulfonic acid groups. In the present paper, the two-phase model has been described and applied to investigate the accessibility of functional groups, the activity difference between internal and external functional groups, and the effect of the local concentration and distribution of functional groups in various reactions, which have been important topics in understanding catalytic reaction using macroreticular resins and designing an optimum resin catalyst.
space
(
)
( )
Da d dCa 3(1 - ) dCi γe ra2 ) kCan + Di 2 dr dra Va Ri dri ra a and for the microparticle
( )
Di d 2 dCi (1 - γ)e n ri ) kCi 2 dr dr n′Vi ra i i
(2)
The appropriate boundary conditions are given as
Ca ) Co at ra ) Ra
and
dCa ) 0 at ra ) 0 dra
Ci ) Ca at ri ) Ri
and
dCi ) 0 at ri ) 0 dri
By defining the dimensionless variables as
ya )
Ca Ci ra ri x ) , yi ) , xa ) Co Co Ra, i Ri
(3)
and the parameters as
x
ekCon-1 VaDa
(4)
(1 - γ)ekCon-1 n′ViDi
(5)
ma ) Ra
x
mi ) Ri II. Two-Phase Model The macroreticular resin can be envisaged as two phases, i.e., microspheres of uniform size and pore formed by the space between the microspheres. It is assumed that the size of the microparticles is uniform and much smaller than that of the resin particle. Two different kinds of active sites exist in the microsphere of a macroreticular resin. The fraction γ of total active sites is located on the surface of the microparticle. The reaction can proceed on these external active groups without being preceded by permeation into the microparticle. However, the remaining functional groups of fraction 1 - γ are located within the polymer matrix of the microparticle. The molecules from the external phase must penetrate through the polymer matrix in order to gain access to the inner active functional groups. The larger the surface area of porous polymer, the more the fraction of external surface groups increases. The external active groups and a large surface area due to high cross-linking are the characteristics of macroreticular resins, which can catalyze reactions even in a nonpolar medium while gellular resins cannot. The active acidic sites are uniformly distributed over the pore wall (surface of the microparticle) and also in the inner gellular phase of the microsphere. Reaction occurs on the pore walls as well as inside the gellular microparticle. A schematic diagram of a macroreticular resin catalyst is shown in Figure 1. For the pore space, diffusional flux is balanced by disappearance due to reaction on the walls and diffusion into microparticles, and for the microparticle, diffusional flux is balanced only by reaction. The governing equations at steady state can be written for an nth order irreversible reaction for the pore
(1)
ri)Ri
the equations can be rewritten as follows:
( )
ma2 dyi 2 dya 2 n + ) γma ya + 3(1 - γ) 2 dxa2 xa dxa mi dxi
d2ya
d2yi 2
+
dxi
(6)
xi)1
2 dyi ) mi2yin xi dxi
(7)
dya ) 0 at xa ) 0 dxa
(8a)
ya ) 1 at xa ) 1
(8b)
dyi ) 0 at xi ) 0 dxi
(8c)
yi ) ya(xa) at xi ) 1
(8d)
where mi represents the Thiele modulus for a microparticle and ma the Thiele modulus for the pore space. The microeffectiveness factor of a microparticle is defined as
ηi )
( ) 3 mi2yan
(9)
xi)1
Introducing eq 9 into eq 6 gives a more general form
d2ya dxa
2
+
2 dya ) ma2[γ + (1 - γ)ηi]yan xa dxa
(10)
2948 Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 Table 1. Properties of Macroreticular Resins properties
Amberlyst 15
Amberlyst XN-1010
wt capacity of dry resin (mequiv/g) % of surface -SO3H groups (γ × 100) internal surface area (m2/g) porosity vol (%) av pore diameter (Å) cross-linkage (%)
4.50 4.39 55 36 265 20-25
3.30 52.78 540 50 51 a
a No data on cross-linkage of Amberlyst XN-1010 are available, but it may be much higher than that of Amberlyst 15, comparing the other properties.
As an illustration of the two-phase model, some experimental results obtained by the authors are explained in the following. III. Temperature Effect Figure 1. Schematic diagram of a resin particle.
Before solving eqs 7 and 10, it can be shown that the overall effectiveness factor ηov is expressed in terms of the average microeffectiveness factor ηj i, the macroeffectiveness factor ηa, and the fraction γ of active sites located on the pore wall as follows:
ηov )
( )
3 dya ma2 dxa
(11)
xa)1
The liquid-phase esterfication of phenol and acetic acid was performed in a batch reactor using macroreticular ion-exchange resin catalysts in Table 1, and experimental data on the initial reaction rate were analyzed by the present model (Suh and Ihm, 1980). Because the size of the resin particle does not affect the overall rate, ηa ) 1 under the experimental conditions. Therefore, the overall initial reaction rate rov could be expressed as
rov ) rxηov ) rx[γ + (1 - γ)ηi]
or
j i]ηa ηov ) [γ + (1 - γ)η
(12)
∫01xa2yanηi dxa η ji ) ∫01xa2yan dxa
(13)
3 dya M2 dxa
(14)
ηa )
( )
xa)1
where M is the modified Thiele modulus defined as
M ) maxγ + (1 - γ)η ji
(15)
η j i is the averaged value of the local effectiveness factor ηj i for a microparticle which, except for a first-order reaction, depends upon the radial position of the resin particle as the concentration in the pore space varies along the radial position. For the two-phase model described above, we can postulate the limiting cases of γ ) 0 and γ ) 1. If γ ) 0, the present model is the same as the bidisperse porous catalyst models, and the effectiveness factor becomes simply the product of the micro- and macroeffectiveness factors
j iηa ηov ) η
(16)
The same relation can be obtained from the model proposed by O ¨ rs and Dogu (1979) and also by Carberry (1962). If γ ) 1, the governing equation reduces to that for a single pore or uniformly porous catalyst, for which numerous studies can be referenced (Aris, 1975). It is the merit of the two-phase model that three possibilities in typical heterogeneous catalysts, i.e., a single pore, a biporous catalyst, and an ion-exchange resin catalyst, can be explained by a single expression.
(17)
where rx is the intrinsic reaction rate. In the range of low reaction temperature most reaction occurs on the surface layer of the microparticle (the pore walls) because the reactant cannot easily penetrate into the highly cross-linked gel phase of the microparticle. Therefore, microeffectiveness factor ηj i becomes very small. As the reaction temperature increases, the gel phase can participate in the reaction due to increased swellability and this results in a higher microeffectiveness factor. In the extreme case of high reaction temperature where the mobility of the gel phase increases, the reactant molecules move easily into the microparticle and the microparticle effectiveness factor becomes unity. These phenomena can be written in the following expression for ηa ) 1
j i ) 0); low-temperature range ηov ) γ (η j i < 1); intermediate range γ + (1 - γ)η j i (0 < η 1 (η j i ) 1); high-temperature range and are illustrated as an Arrhenius plot in Figure 2. Sucrose inversion was performed in a batch reactor, varying the particle sizes and the reaction temperature by using also Amberlyst 15 and Amberlyst XN-1010 (Ihm and Oh, 1984) (Figures 3 and 4). In this case the overall initial reaction rate, rov, is written as
rov ) kCoηov ) kCo[γ + (1 - γ)ηj i]ηa ) kovCoηa
(18)
where kov is the observed reaction rate constant, or
kov ) k[γ + (1 - γ)ηj i]
(19)
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 2949
Figure 2. Arrhenius plot of reaction rate for macroreticular resin catalyst with large γ.
Figure 3. Correlation of experimental results for sucrose inversion on Amberlyst 15.
Figures 3 and 4 show the relation between the initial observed reaction rate and particle size for Amberlyst 15 and for Amberlyst XN-1010, respectively. The effect of particle size on Amberlyst 15 is slightly stronger than that on Amberlyst XN-1010 as the temperature increases due to the increased diffusion limitations. Figures 5 and 6 show good agreement between the theoretical effectiveness factors and the experimental ones. The macroeffectiveness factors decrease as the particle size and temperature increase for both resins. Figure 5 also shows that with Amberlyst 15 the microeffectiveness factor increases as the temperature increases. This is because the swellabilty of the gellular microparticle is increased with temperature. In Figure 6 for the case with Amberlyst XN-1010, it is shown that the behavior of the overall effectiveness factor is the same as that of the macroeffectiveness factor since the microparticle is inert (i.e., ηi ) 0).
Figure 4. Correlation of experimental results for sucrose inversion on Amberlyst XN-1010.
Figure 5. Effectiveness factor in the sucrose inversion on Amberlyst 15.
IV. Reaction Arena As described above, two different kinds of sulfonic acid groups exist in the microparticle of macroreticular sulfonic acid resin. The larger the surface of porous polymer, the more the fraction of external surface groups increases. In general, large surface area results from high cross-linking. If the reaction is microparticlediffusion-controlled, the reaction rate increases with increasing surface area. In sucrose inversion (Ihm and Oh, 1984) and alkylation of benzene with 1-dodecene (Park and Ihm, 1985), Amberlyst 15 was observed to be slightly less effective than Amberlyst XN-1010 (Figures 7 and 8). Although the capacity of Amberlyst 15 is larger than that of Amberlyst XN-1010, reaction which occurred near the pore walls of Amberlyst 15 must be much less than that of Amberlyst XN-1010 due to the much smaller value of γ. All of the active sites in Amberlyst 15 are less
2950 Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996
Figure 6. Effectiveness factor in the sucrose inversion on Amberlyst XN-1010.
Figure 8. Arrhenius plot of observed rate constants in the alkylation of benzene with 1-dodecene.
took place only on the pore surface of a gellular XN microparticle, i.e., η15 ) 0, i ) ηi 15 kXN ov /kov = 13.3
(22)
It is expected that the rate constant kXN ov of Amberlyst XN-1010 is about 10 times larger than k15 ov . However, the fact that the reaction rate is about 5 times larger at most indicates that the surface sulfonic acid groups may participate mainly in the reactions with Amberlyst XN-1010, while some of internal sulfonic groups are utilized for reactions with Amberlyst 15. The main reaction arena seems to be the pore space for ionexchange resin catalysts with high cross-linkage. V. Activity Difference between the Internal and External Sulfonic Acid Groups
Figure 7. Arrhenius plot of observed rate constants in the sucrose inversion.
effectively used than in Amberlyst XN-1010; hence, the initial reaction rates of Amberlyst 15 become less than those of Amberlyst XN-1010. Since the pore diffusion limitation can be neglected for the above reactions, eq 19 becomes
kov ) k[γ + (1 - γ)ηi]
(20)
For two ion-exchange resin catalysts, the ratio of reaction rate constants is as follows
kXN ov k15 ov
kXN[γXN + (1 - γXN)ηXN i ] )
=
k15[γ15 + (1 - γ15)η15 i ] XN 0.53 + 0.47ηi
(21)
0.04 + 0.96η15 i
where superscripts “XN” and “15” denote Amberlyst XN1010 and Amberlyst 15, respectively. If the reaction
The active sites of a cationic exchange resin are sulfonic acid groups. Gates et al. (1972) observed that the activity became higher with an increase of the active site concentration in the dehydration of tert-butyl alcohol, and they proposed the mechanism of a hydrogen bridge between the reactant and the network of sulfonic acid groups. Dooley et al. (1982) suggested the active sites on the surface of gel microparticles are less active than those within the microparticles in the reesterification reaction. Chee and Ihm (1986) also suggested the possibility of a higher activity of the internal sulfonic acid groups than the external ones in their study on the deactivation behavior of macroreticular resins for ethanol dehydration. According to the two-phase model, the observed rate constant can be expressed on the assumption that the activity between internal and external active sites is different:
kov ) ηa[γka + (1 - γ)η j iki]
(23)
where ka and ki denote intrinsic rate constants in the pore space and gellular microparticle phase, respectively. Without pore diffusional limitation (ηa ) 1), the ratio of the overall reaction rates of Amberlyst XN-1010 and Amberlyst 15 can be written as
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 2951
kXN ov k15 ov
j XN ηXNka + (1 - γXN)η i ki )
γ15ka + (1 - γ15)η j 15 i ki
(24)
It is assumed that ki and ka for both resins are the same, respectively, because the active sites are all the same. The association among the sulfonic groups which decides the intrinsic rate constant is different, mainly dependent upon their location (i.e., external or internal). Equation 24 will show the maximum value when η j XN ) 1 and η j 15 i i ) 0 and the minimum value when XN 15 η j i ) 0 and η j i ) 1. Therefore, the ratio will have the following range: XN
XN
γ kov γXN e 15 e 15 15 γ + (1 - γ )(ki/ka) kov
+ (1 - γXN)(ki/ka) γ15 (25)
From the values of γ, the ratio of kov should fall between γXN and 1/γ15 (0.528 and 22.8), if the activity ratio of the internal and external active sites is unity (i.e., ki ) ka). If the activity ratio is less than unity, the maximum value of the ratio of kov is larger than 22.8. If it is larger than unity, the minimum is smaller than 0.528. In the hydration of isobutylene (Ihm et al., 1988) and MTBE synthesis (Lee and Ihm, 1987), the ratio of kov was smaller than 0.528 as shown in Table 2, which implies that the internal sulfonic groups have higher activities than the external ones. In Amberlyst XN-1010, the degree of cross-linking is about 70-75%, which means that the gel microparticles are too rigid to be swollen and the diffusion of reactants into the microparticles would be highly suppressed. Moreover, the fraction of the external sulfonic groups is about 0.528, and it is expected that the reactants are catalyzed mostly on the surface of the gel microparticles. Therefore, it can be assumed on the basis of eq 23 that the value of η j XN approaches zero for Amberlyst XNi 1010. With these assumptions, ka can be estimated as XN ka ) kXN ov /γ
(26)
On the other hand, ηj iki can be expressed for Amberlyst 15 as
ηj iki )
15 k15 ov - γ ka
1 - γ15
(27)
where η j i is a function of Di and ki. Gupta and Douglas (1967) investigated the diffusivity of isobutylene in the gel-type sulfonic acid exchange resin and obtained the value of 0.07-0.2 cm2/h as a function of temperature in the range 75-85 °C. With Di known, the values of ηj i and ki can be determined. VI. Effect of Sulfonic Acid Group Distribution For a given polymer resin, the functional group distribution can be controlled by the functionalization reaction (Klein et al., 1984; Chee and Ihm, 1986; Ahn et al., 1988). A model has also been proposed to predict the reaction rate of the functionalization and the distribution of functional groups in gellular (Jo and Ihm, 1992) and macroreticular (Ihm et al., 1989) beads. The functional group distribution varies with reaction conditions in the functionalization. In the case of gellular
Figure 9. Experimental results of ethanol conversion with the time (b, catalyst A; 2, catalyst B). Table 2. Ratios of kov in Amberlyst XN-1010 and Amberlyst 15 reaction
temp (°C)
15 kXN ov /kov
hydration of isobutylene
50 60 70 80 83 92 105
0.457 0.352 0.337 0.246 0.261 0.259 0.277
MTBE synthesis
resin beads which are accessible only by swelling, the distribution of functional groups can be easily observed by X-ray energy dispersive analysis (EDAX). On the other hand, the rate of functionalization for a macroreticular resin bead is affected not only by the diffusion in the pore space but also by the gellular permeation through the microparticles. Two types of macroreticular resin catalysts with different distribution were prepared in the author’s laboratory. The overall distribution is uniform over the porous resin, while the sulfonic group distribution in the microparticle is uniform (catalyst A) or peripheral (catalyst B). However, the overall ion-exchange capacities of the two catalysts are the same (1.0 mequiv of H+/g of cat). Ethanol conversion obtained with catalysts A and B prepared in a membrane form was shown in Figure 9. The activity of the catalysts decreased as the reaction proceeded. Deactivation patterns of the two catalysts were quite different, implying that the difference in the sulfonic group distribution influenced the deactivation patterns. After catalyst A showed a maximum in conversion, the conversion decreased slowly. On the other hand, the initial deactivation rate of catalyst B was higher than that of catalyst A, which implies that the local concentration of the acid groups in catalyst B is higher than that in catalyst A. It was known from this work that the deactivation rate of the catalyst with a nonuniform and high local capacity was higher. VII. Effect of the Local Concentration of Sulfonic Acid Groups For a sulfonic acid resin catalyst, catalytic function is due to the ensembles of several -SO3H in nonaqueous
2952 Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996
Figure 10. Schematic diagrams for two types of functional group distribution.
medium and catalytic activity increases nonlinearly with increasing the concentration of sulfonic acid groups. The properties and reaction behavior of the resin catalysts are varied to a large extent by the local concentration and distribution of the sulfonic groups. However, the experimental results obtained can be complicated by interactions with solvents and in addition by polymer swelling. If highly cross-linked resins are used in nonpolar medium, these effects can be suppressed. Polymeric acid catalysts used in such a system involve the isomerization of olefins or the alkylation of benzene with olefins. The two-phase model can be extended to analyze the effect of the local concentration and distribution of the functional groups on the catalytic activity. This includes a breakdown of the effect of the gel-phase permeation on the reaction rate. There are still many uncertainties about the effect of the local capacity level of the functional groups on the catalytic activity for sulfonated porous resins. According to Gates et al. (1972), it has been proposed that the reaction rate constant per unit mass of sulfonated polymer catalyst has a power dependence on the local capacity level in units of milliequivalents per unit mass of sulfonated polymer matrix, i.e. m k′ ) k′o(C′L/C°′ L )
(28)
where k°o is the reaction rate constant per unit mass of a fully sulfonated polymer matrix. Jerabek et al. (1973) demonstrated that m was the number of the active sites participating in the rate-determining step of tert-butyl alcohol dehydration. According to the two-phase model, the overall effectiveness factor can be expressed in terms of the fraction of functional groups on the external surface, the macro- and microeffectiveness factors.
j i]ηa ηov ) [γ + (1 - γ)η
(12)
Its analytic solution can be obtained for a first-order irreversible reaction as
ηj i )
(
3 1 1 mi tanh mi mi
)
(29)
where mi ) Rixk′/Di. Without pore diffusional limitation (ηa ) 1), the observed rate constant per unit capacity is written as
kov ) k[γ + (1 - γ)ηj i]
(19)
where k ) k′/e′. For the present study, it will be more straightforward to start with rather simple distributions. Therefore, two types of functional group distribution can be postulated, as shown in Figure 10.
Type A distribution can be obtained from uniform local capacity level C°L through ion exchange with Na+ ion, which results in uniform deactivation (Klein et al., 1984). For type B distribution all the functional groups are located only on the surface of the microparticle, and hence γ ) 1. The capacity of acid resin catalyst is usually measured by the titration method. The capacity measured in such a way is the value averaged over the entire bead volume, and it does not explain the functional group distribution in full. The measured capacity, e, for a gellular microparticle is related to the local capacity level CL as
∫0R 4πri2CL(ri) dri i
e)
4 πR 3 3 i
(30)
where the units of both e and CL are taken as milliequivalents per unit mass of an unsulfonated polymer matrix. In order to know the external capacity, eγ, it will be necessary to know the characteristic depth of the external layer of a sulfonated polymer matrix. If the depth is defined as l, eγ can be expressed by
∫RR-l4πri2CL(ri) dri i
eγ )
i
4 πR 3 3 i
[ (
) CL 1 - 1 -
)]
l Ri
(31)
3
Since it is very difficult in reality to know the value of l, setting a standard experimental technique measuring eγ is preferred. eγ can be measured experimentally from the adsorption and desorption of ammonia carried out by Prokop and Setinek (1974a,b). CL, milliequivalents per unit mass of an unsulfonated polymer matrix, and C′L, milliequivalents per unit mass of a sulfonated resin, are related to each other as
C′L )
1 1/CL + 0.08
(32)
Based on the above concept, the intrinsic rate constant k can be expressed as
( )
k′o e′ m ; ηj i(mi) e′ e′m
Type A:
k)
Type B:
k′o C′L m k) ; γ)1 e′ e′m
( )
(33)
In the author’s laboratory, acid catalysts with different sulfonic group distributions, types A and B, have been prepared using macroporous poly(styrene-co-divinylbenzene) resin beads of high cross-linking and used in the isomerization of 1-butene. The reaction data were analyzed through the above model. In the case of type B distribution (γ ) 1), the following equation can be obtained from eqs 19 and 33:
k′ov ) k′ ) k′o(C′L/e′m)m
(34)
Taking the logarithm of eq 34 gives m ln k′ov ) m ln C′L + ln(k′o/e′ m)
(35)
Ind. Eng. Chem. Res., Vol. 35, No. 9, 1996 2953
portant properties for understanding the catalytic function of macroreticular resin catalysts and will also give useful information for designing an optimum resin catalyst. Nomenclature
Figure 11. Change of the catalytic activity with the local capacity level of the type B distribution in the isomerization of 1-butene.
The logarithmic plot of k′ov versus C′L will provide m from the slope and k′o from the intercept at C′L ) 1. The values of m and k′o were obtained from Figure 11 and the intrinsic rate constants k′ could be related to the local capacity level C′L as
k′ ) (2.9 × 10-3)(C′L/3.42)2.4(mol/g‚min) for 40% DVB k′ ) (2.9 × 10-3)(C′L/3.26)2.4(mol/g‚min) for 50% DVB (36) For the type A catalyst, k′ov can be derived as
k′ov ) k′[γ + (1 - γ)ηj i]; η j i[mi(k′,Di)]
(37)
Since the value of k′ was already known from eq 36, η ji could be obtained and, in turn, mi and Di could be obtained. VIII. Conclusion Macroreticular ion-exchange resin catalyst has been envisaged as two phases: the microparticles and the pore space formed between them. The overall effectiveness factor ηov can be expressed in terms of the average microeffectiveness factor ηj i, the macroeffectiveness factor ηa, and the fraction γ of active sites located on the pore walls, or
j i] ηov ) ηa[γ + (1 - γ)η In addition to the case of a macroreticular resin catalyst with some fraction of the active sites on the pore walls, two other possible cases of heterogeneous catalyst can be explained by the present model in terms of different ranges of γ, i.e., a bidisperse porous catalyst for γ ) 0 and a catalyst with uniform pore size for γ ) 1. The two-phase model can be also applied to interpret the accessibility of sulfonic acid groups, the activity difference between internal and external functional groups, and the effect of the local concentration and distribution of functional groups. These are very im-
Ca ) concentration in the pore, mol/cm3 Ci ) concentration in the microparticle, mol/cm3 Co ) concentration in the bulk, mol/cm3 CL ) local concentration of functional groups based on unsulfonated polymer matrix; C°L, when saturated, mequiv/g C′L ) local concentration of functional groups based on sulfonated polymer matrix; C°′ L, when saturated, mequiv/g Da ) effective diffusivity in the pore, cm2/s Di ) effective diffusivity in the gellular microparticle, cm2/s e ) measured capacity based on unsulfonated polymer matrix; eγ, the capacity of external functional groups, mequiv/g e′ ) measured capacity based on sulfonated polymer matrix; e′m, when saturated, mequiv/g k ) intrinsic reaction rate constant based on milliequivalents of functional groups; ka, in the pore space; ki, within the gellular microparticles; kov, observed, mol/(mequiv‚ min) k′ ) intrinsic reaction rate constant based on unit mass of sulfonated polymer matrix; k°ov, observed, mol/(g‚min) l ) depth of the external layer, cm m ) power for eq 28 ma ) Thiele modulus for the pore space, dimensionless mi ) Thiele modulus for a microparticle, dimensionless M ) modified Thiele modulus defined in eq 15, dimensionless n ) reaction order n′) number of microparticles in a resin particle ri ) radial position from the center of a gellular microparticle, cm ra ) radial position from the center of a resin particle, cm rov ) observed initial reaction rate rx ) intrinsic reaction rate Ra ) radius of a resin particle, cm Ri ) radius of a gellular microparticle, cm Va ) volume of a resin particle, cm3 Vi ) volume of a microparticle, cm3 Greek Symbols γ ) fraction of functional groups distributed over the pore walls, dimensionless ) porosity η ) effectiveness factor; η j i, for a microparticle; ηa, for the pore space; ηov, for a resin bead, dimensionless Subscripts a ) resin particle or surface of the microparticles i ) within the microparticle ov ) overall or observed Superscripts XN ) Amberlyst XN-1010 15 ) Amberlyst 15
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Received for review December 4, 1995 Revised manuscript received May 6, 1996 Accepted May 23, 1996X IE950724X X Abstract published in Advance ACS Abstracts, August 15, 1996.
