1868
Ind. Eng. Chem. Res. 1992,31, 1868-1875
Dynamic Model of the Triphase Catalytic Reaction Maw-Ling Wang* and Hung-Ming Yang Department of Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan, R.O.C.
In this study, a mathematical model, which includes the mass transfer of readants in the bulk phases, the diffusion of reactants through pores of the catalyst particle, and the intrinsic reactions of the reactants, was used to describe the dynamics of a triphase catalysis. A solution of the dynamic behavior was obtained by the finite difference method. In order to understand the effect of the mass-transfer resistance on the observed reaction rate, an internal effectiveness factor, vi, was considered. The calculated internal effectiveness factor was compared with that of the conventional one for heterogeneous catalysis. The calculated apparent reaction rate constant, which depends on the diffusivities of the reactants and the intrinsic reaction rate constants, is very consistent with that of the experimental results. Introduction The reaction problem of two immiscible reactants was not solved until Jarrouse (1951) found that the two-phase reaction is enhanced by adding a small catalytic quantity of a quaternary salt. The use of quaternary salt as a phase-transfer catalyst in the two-phase reaction to synthesize speciality chemicals was, thus, extensively studied (Dehmlow and Dehmlow, 1983; Starks and Liotta, 1978; Starks,1985). Today, phase-transfer catalysis (PTC) is considered to possess a great poential in industrial-scale application, because the reaction is promoted greatly even at a moderate temperature (Freedman,1986; Sttuks, 1985). Although there are several advantages in using PTC to synthesize organic chemicals, the separation of the catalyst from the product in the purification processes is difficult. The reason is that the chemical equilibrium separation processes which are used in the purification of the product usually consume a lot of energy to get a product of a high purity. In order to overcome this difficulty, Regen and his co-workers (Regen, 1975, 1977; Regen and Besse, 1979; Regen et al., 1979a,b) proposed a so-called "triphase catalysis", in which the catalyst is immobilized on a solid support. From the industrial application point of view, the catalyst can be easily separated from the finalproducts simply by mechanical separation, such as centrifugation or filtration. In addition, either the plug flow reactor (PFR) or the continuous stirred tank reactor (CSTR) can be used to carry out the reaction. Several reactions for hydrolysis and displacement (Ohtani et al., 1981; Regen, 1975; 1977; Regen and Besse, 1979; Regen et al., 1979a,b) were investigated. The reaction of the triphase catalysis is, thus, carried out in a three-phase liquid (organic)-solid (catalyst)-liquid (aqueous) condition. The characteristics of a three-phase slurry reactor have been examined in detail (Chaudhari and Ramachandran, 1980; Marconi and Ford, 1983). However, the dynamic behavior of the triphase catalytic reactions has seldom been investigated by scientists, even though the reaction mechanism has already been identified. In the present study, the dynamics of a triphase catalysis in a liquid-solid-liquid three-phase batch reaction system were studied. A mathematical model, which considers the m a s transfer of reactants in the bulk phases, the diffusion of reactants within the catalyst pellet through pores, and the intrinsic reaction of reactants, was built up. The initial process of the triphase reaction system is that the solid catalyst pellet is initially presented. The aqueous-phase
* To whom correspondence should be addressed.
and organic-phase reactants are then added to the reactor simultaneously to start the diffusion and reaction. The solutions of the equations, which describe the behavior of a triphase catalytic reaction in a batch reactor, were obtained by the finite difference method. The effectiveness factor of the triphase catalytic reaction, which reflecta the relative importance of the mass-transfer resistance to the reaction resistance, was found and compared with that of conventional analysis of the heterogeneous catalysis. Formulation of the Mathematical Model In general, the reaction between two immiscible reactants by triphase catalysis may involve (i) mass transfer of reactants from the bulk solution to the surface of the catalyst pellet, (ii) diffusion of reactants to the interior of the catalyst pellet through pores, (iii) surface or intrinsic reaction of reactantswith the active sites of catalyst pellet, (iv) diffusion of products outward to the exterior of the catalyst pellet through pores, and (v) mass transfer of product to the bulk solution from the surface of the catalytic pellet. In a three-phase transfer catalytic reaction, the molar flux of product is equal to that of the reactant either in the pore or in the bulk solution. Therefore, it is reasonable to assume that the transfer of product by steps (iv) and (v) need not be considered in formulating the dynamic model. For example, the allylation of 2,4,6-tribromophenol in an alkaline solution by a trphase catalysis can be written as
where K+Y-(,! and RX,,) represent potassium 2,4,6-tribromophenoxlde in the aqueous phase and allyl bromide in the organic phase, respectively. QXc,,and QY(,) are the solid pellet catalysts. RY,, ) is the product, i.e., allyl and k,, are the intrinsic 2,4,64ribromophenyl ether. reaction rate constant in the aqueous phase and in the organic phase, respectively. Thus, the concentration of the catalytic active sites within the catalyat, qW, can be written as (Yang, 1990)
gaq
For reactants, the mass-transfer limitations which include the film resistance of the bulk solution and pore diffusion resistance are considered in the following. The concentrations of the two immiscible reactants, RX and Y-, within the particulate phase of the spherical
0888-5885/92/2631-1868$03.00/00 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 8,1992 1869 particle can be expressed as
w = 1:
(20)
forg -at aCRX
bulk phases dfRX,b
-uor;
where r denotes the radial direction of the spherical coordinates. The initial process of the triphase system is that the catalyst pellet is initially presented in the form of QX. The aqueous, organic, and solid phases are added to the reactor simultaneously to start the diffusion and reaction. The corresponding initial and boundary Conditions for C, CY, and 4gx are t = 0: C R X = C Y = 0, q Q X = qQX.0 (6) r = 0
d r = 3Bim(fRX,b
- fRX.8)
(22)
initial conditions 7 = 0: f R X , b = fY,b = 1 (24) where the dimensionless variables and parameters are
CRX,s
(7)
fRXa
=9
CY.8
fY,s
CRX,O
= -!
CRX,b
fRX,b
CY,O
CYb
fY,b
= -9
bRX
C Y ,o
=
CRX,O ,
=
CRX,O CY,O
by=-
PsqQX,O
PsqQX,O
In a batch reactor, the mass balance equations for RX and Y- in the bulk phases are
a = -k a q , r =
where K, and Ky are the mass-transfer coefficient of RX and Y-in the organic phase and in the aqueous phase, respectively. The initial conditions of CRX,b and C y , b are t=O CRX,b = CRX.0; C Y b = cY,O (12) For convenience, eqs 3-12 can be expressed in a dimensionless form by defining the following Thiele modulus, 4, and mass Biot number, Bi,, as
4 = R(pskorgqQX,0/DRX)”2
(13)
Bi, = K R x R / D R X
(14)
Thus, the dimensionless forms of eqs 3-12 are within the particulate phase QQX
afQX 7 = -42[6YafYfQX
- bRXfRX(1 - fQX)l
(15)
0
w=o:
fRX
= f Y = 0,
fQX
=1
w = -r R
Effectiveness Factor of the Triphase Catalysis In a heterogeneous catalytic reaction, the intraparticle effectiveness factor, vi, for a first-order reaction within a spherical catalyst at steady state is (Aris, 1975) = (3/42)(4coth 4 - 1)
(25) where 4 is the Thiele modulus. In order to understand the effect of the mass-transfer resistance on the observed reaction rate, the internal effectiveness factor is usually employed to account for this effect. In a triphase catalysis, the reaction rate for Y,, ) with QX,,) is always faster than that for RX,,,,) with Q$(s). Therefore, the limiting step of the reaction is the intrinsic reaction of RX!-) with QY(s). Thus, the intraparticle effectiveness factor is suitably expressed as a function of the organic-phase reaction and defined as vi
=
7’=
+ faq)R2’
Equations 15-24 were solved numerically by the finite difference method. The computation results are given in Figures 1-16.
JvkorgCRX(qQX.O
initial and boundary conditions
DRXt (forg
korg
l$orgCRX,s(qQX,O
- q Q X ) dV - qQX,s) dV
for t > 0
(26)
Many experimental works with three-phase catalytic reactions have indicated that the reaction of the organic reactant is the rate-determining step. Thus, the reaction rate by triphase catalysis is sometimes expressed as pseudo first order with respect to the organic reactant (Wang and
1870 Ind. Eng. Chem. Res., Vol. 31, No. 8, 1992
Yang, 1991a). For this,the conventional expression is used to correlate the experimental results in order to obtain the diffusion coefficient of the organic reactant within the pores. In this work, the derived intraparticle effectiveness factor is compared with that of the conventional analysis of the heterogeneous catalysis. For using a spherical particle, the mass balance equation of RX,,,,, in the bulk organic phase can be written as
0.8
0.8
I i
0.4
0.2 n n V."
Combining eqs 10 and 27, we obtain cRX,s
=
0.0
CRX,b 1 + qi(Pskorg/KRXa)(qQX,O- qQX,s)
02
0.4
0.e
0.8
I .o
W
(28)
As shown in eq 28, CRX,sis dependent upon the fraction of the active sites on the surface of the catalysts. Substituting eq 28 into eq 10, we obtain
Figure 1. Concentration profiie of the organic reactant (RX) within the catalyst pellet: 6 = 20, Bin = 100, [ = 1,X = 1, ps = 1.0 g/cm3, V , = Vow,m = 2, n = 0.06, CRX,O= 0.1 M,qQX,O = 1.0 mmol/g, and kaq/ko, = 8.282. I .o
1-'-
0.8 0.e
If the observed reaction rate of the organic reactant can be correlated as pseudo-first-order kinetics, the apparent reaction rate constant, kepp,can be expressed as r
*
e
0.4
0.2
1-1
0.0
0.4
0.0
where n is VWt/VOq: As shown in eq 30, it is obvious that the apparent reaction rate constant is a function of the fraction of the catalytic active sites on the surface of catalyst pellet, fQX,S,and the intraparticle effectiveness factor, qi. That is, the apparent reaction rate constant is a function of both the internal and external mass-transfer resistances. If the overall effectiveness factor, to,is introduced, the rate of change of RX in the bulk solution is expressed as
0.8
0.8
I .o
W
Figure 2. Concentration profile of the aqueous reactant (Y)within the catalyst pellet: 6 = 20, Bin = 100,t = 1, X = 1,ps = 1.0 g/cm3, V,, = VOm,m = 2, n = 0.06, CRX,O= 0.1M, qQX.0= 1.0 mmol/g, and ka,/ko, = 8.282.
Combining eqs 10 and 31, we obtained the overall effectiveness factor, to, qo=
[- + ,li
korgPsqQX,O(1 - fQX,s)
KRXa
Writing eq 32 in a dimensionless form (#'2(1 - fQX.s) 3Bi,
]
(32)
0.0
0.2
0.8
0.4
0.8
1
I .o
W
]
-1
(33)
In a heterogeneous catalytic reaction, the overall effectiveness factor for a first-order reaction in a spherical catalyst at steady state is (Aris, 1975)
]
4 coth 4 - 1 = 3 [ 1 + (l/Bi,)(# coth 4 - 1)
2
0.0'
(34)
Results and Discussion The simulation results, shown in Figures 1-3, indicate the concentration profiles of the readants, f R x and f y , and the catalytic active sites, fQx,for $, = 1,Bi, = 100, and 4 = 20 at various 7. A higher value of Bi, (say Bi, = 100) indicates a mass-transfer resistance within the porous
Figure 3. Concentration profile of the active catalyst (QX)within the catalyst pellet: 6 = 20, Bi, = 100,t = 1, X = 1, ps = 1.0 g/cm3, V , = Vow,m = 2, n = 0.06, CRX,O= 0.1 M,qQX,o = 1.0 mmol/g, and kaqJkow= 8.282.
medium is dominant rather than in the bulk solution. In general, the apparent reaction rate was influenced by the diffusion rates of aqueous-phase and organic-phase reactants in a triphase system. The Thiele modulus was used to investigate this effect of diffusion in this study. For a strong diffusion limitation with 4 equal to 20, as shown in Figure 1, the reactant of RX almost stays at the catalyst surface initidly and only trace amounts of RX diffuse into the catalyst center. For 7 > 0.09, the concentration of RX in the region of 0 < w < 0.5 almost keeps at a constant value. Comparing the results shown in Figure 2 with Figure 3, the reaction of Y with QX occurred at w larger than 0.5, whereby Y was almost consumed and no more of Y diffused into the catalyst center. It depicts that the
Ind. Eng. Chem. Res., Vol. 31, No. 8,1992 1871
0.8
0.e 20
K x
0.4'
0. I 0.0
0.2
0.e
0.4
0.8
I .o
o.00.0 0
i 1
30
0.2
0.4
Dimensioniess Time
.
o.e
0.8
I 2.(I
W
Figure 4. Concentration profile of organic reactant (RX), aqueous reactant (Y), and product (RY) in the bulk phase: Q = 20, Bi, = 100, f = 1, X = 1, pI = 1.0 g/cm3, Vaq = V,, m = 2, n = 0.06,CRX,O = 0.1 M, qRX.0 = 1.0 mmol/g, and k,,/k,, = 8.282.
Figure 7. Concentration profile of the organic reactant (RX) within sthe catalyst pellet: Q = 1, Bi, = 100,f = 1, X = 1, p, = 1.0 g/cm3, V , = V,,, m = 2, n = 0.06, C R X ,=~ 0.1 M, qQX,O = 1.0 mmol/g, and k,,lk,, = 8.282.
0.8
0.e x K 'c
0.4 0.2
I.1
0.0
0.2
0.4
0.6
0.8
I .o
W
I
? 0.20
0.8
0.e. K x
e
0.4:
0.2
L-
0.0 0.0
A
0.2
0
/
3
0.4
0.10
Im
Dlneneionleee Time.
Figure 5. Concentrationprofile of the organic reactant (RX) within the catalyst pellet: 6 = 10, Bi, = loo,[ = 1, X = 1, pa = 1.0 g/cm3, vaq= vow,m 2, n = 0.06, CRX,O= 0.1 M, qQx,o 1.0 mmol/g, and kaq/k,, = 8.282. n, . .-
0.01
0.6
0.8
I .o
W
Figure 6. Concentrationprofile of the organic reactant (RX) within the catalyst pellet: Q = 5, Bi, = 100, f = 1, X = 1, pI = 1.0 g/cm3, V,, = Vow,m = 2, n = 0.06, Cm,o= 0.1 M, Q Q X , ~= 1.0 mmol/g, and kaq/kow= 8.282.
diffusion of reactant is dominant as the controlling step of the reaction. The catalytic active sites are almost consumed on the exterior of the catalytic pellet; i.e., the phase-transfer reaction is conducted near the surface of the catalyst pellet. Hence, a large diffusion resistance within the porous medium affecta the reaction. Therefore, the apparent reaction rate of RX in the bulk solution behaves as a pseudo-firstorder kinetics as shown in Figure 4 regardless of the diffusion as the limiting step. From the results shown in Figures 1,5,and 6, the concentration of RX at the center of catalyst increases with the increase of the Thiele modulus, 4. However, the reactant, Y, still does not exist in the region of 0 < w < 0.5 even when the Thiele modulus equals 5. Hence, the
1o.m
7
Figure 8. Intraparticle effectiveness factor vs dimensionless time for different Thiele moduli: Bi, = 10, f = 1, X = 1, pI = 1.0 g/cm3, V , = Vow,m = 2, n = 0.06, CRx,o= 0.1 M, qQX,o = 1.0 mmol/g, and k,,/k, = 8.282.
phase-transfer reaction, which occurs within the catalyst, is strongly limited not by the intrinsic reaction but by the diffusion of reactants. For the case of Thiele modulus equal to 1.0, as shown in Figure 7, the apparent reaction rate is obviously not limited by the diffusion effect but controlled by the intrinsic reaction of RX with active center QX. The distribution profile of RX within the catalyst is almost flat after the induction period. Nevertheless, the apparent reaction of RX in the bulk solution still behaves as a pseudo-first-order kinetics for Thiele modulus equal to 1,5,and 10 after a short induction period. Often the experiments for triphase catalyzed systems in the published papers were observed as pseudo-first-order kinetics. From the dynamic modeling of a triphase reaction system in this paper, the kinetics of RX in the bulk organic solution is indeed first order, either for diffusionlimited systems or for reaction-controlled systems. Thus, the pseudo-first-order behavior of the triphase-transfer system in the past published papers can be adequately demonstrated using this dynamic model. A plot of the intraparticle effectiveness factor, vi, vs dimensionless reaction time, 7 , with Bi, or I#I as a parameter is given in Figures 8 and 9. Figure 8 shows the effect of the Thiele modulus on the intraparticle effectiveness factor, vi. It is obvious that a larger diffusion resistance within the particle (i.e., large 4 value) will lead to a slower intraparticle effectiveness factor. The longer induction period for the present study shows that less efficiency of the catalyst is exhibited. Also, the dimensionless induction period is decreased as the Thiele modulus increases. from Figure 9, the intraparticle effectiveness factor approaches
1872 Ind. Eng. Chem. Res., Vol. 31, No. 8,1992 1.m
-Thla 0 c
c
Convmtlonol analyolo
0. I O
0.4
0.2
0.0
0.e
0.8
work (7-1)
Thle work (Z-IO)
0.04 . . . . * 0.6 I .o
I .o
10.0
a ,O
0
Z
Figure 9. Intraparticle effectiveness factor vs dimensionless time: 4 = lo,$ = 1, = l,ps = 1.0g/cm3, V , = V, m = 2, n = 0.06, Cm,o = 0.1 M,qQX,o = 1.0 mmol/g, and k,/k,, = 8.282.
Figure 11. Overall effectiveness factor vs Thiele modulus: f = 1, A = l,ps = 1.0g/cm3, V, = Vow,m = 2, n = 0.06, Cm,o = 0.1 M, qpxo = 1.0 mmol/g, and k,,/k,, = 8.282.
I .o
0.03
n-0.08
m 0
c
- Thla
v
work
P
"--I //c/
Convontlonal anolyele
xB 0.01
0.6
.
'
. .' I .o
10.0
1
n m
20.0
,
I\// I,,
0.1'
a constant value at a longer reaction time. Within the induction period (for T < 0.3), the mass-transfer rate strongly affects the performance of qi. In general, the effect of mass-transfer resistance on the reaction rate can be neglected for Bi, > 500. A similar result is also obtained by plotting vi vs r$ with Bi, as a parameter and is shown in Figure 10. Figure 10 depicts a comparison of the intraparticle effectiveness factors obtained from the conventional analysis at steady state at T = 1.0. Since the conventional analysis was obtained at steady state, it cannot be used to predict the intraparticle effectiveness factor at the induction period as r$ < 5 very well, but it is predictable with little deviation as T reaches 10. When r$ is larger than 10, the prediction by conventional analysis has about 18% deviation. In general, the conventional results at steady state can be used to correlate the experimental data at a longer dimensionless time and to calculate the diffusion coefficient and intrinsic reaction rate constant. A comparison of the overall effectiveness factor, v0, obtained from the conventional analysis and the present study is given in Figure 11. Similar results are obtained for the overall effectiveness factor by using conventional analysis at steady state. A t T = 1.0, the prediction of the triphase catalysis by using conventional analysis is not promising. The prediction is good for the whole range of q5 from 0.5 to 20 at T = 10. For q5 > 3, both results obtained from different reaction systems are almost the same. This implies that the model of the conventional analysis can be employed to predict the reaction of the triphase catalysis when the effect of diffusion within the porous medium on the reaction is significant. The corresponding apparent reaction rate constant, kapp,is given in Figure 12. From
.-
I
,
p-,
CD Figure 10. Intraparticle effectivenessfactor vs. Thiele modulus: T = 1, = 1, = 1,pa = 1.0 g/cm3, V , = VomLm= 2, n = 0.06, Cm,o = 0.1 M, qQX.0 = 1.0 mmol/g, and k,/k,, - 8.282.
2.0
I
0.2
Dimensionless Time.
T
Figure 12. Calculated k,,, vs dimensionless time for different molar ratios of reactants and amount of catalyst: 4 = 10, Bi, = 100, f = 1, X = 1, ps = 1.0 g/cm3, V,, = Vorg,Cm,O = 0.1 M,qQX.0 = 1.0 mmol/g, and k,,/k,, = 8.282.
0.4'
0.0
I
\
0.2
0.4
0.8
0.6
Dimensionless Time.
I.o
I
Figure 13. Bulk concentration of reactant, RX, vs dimensionless time for different molar ratios of reactants and amounts of catalyst: = 10, Bi, = 100, f = 1, X = I, pa = 1.0 g/cm3, V,, = V,, Cm,o= 0.1 M,qQx,o = 1.0 mmol/g, and k.,/k, = 8.282.
+
the plot of Figure 12,one can conclude that the logarithm of f R X , b vs T is a straight line after a certain period of > 1. This phenomenon can be induction when Cy,o/CRx,o observed in Figure 13. It is obvious that the apparent reaction rate constant does not approach a constant value when CY,O/CRX,O < 1. In general, the obtained lz,, is in agreement with the result obtained from experiments (Weber and Gokel, 1977). The effect of the diffusivity ratio or the mass-transfercoefficient ratio of Y to RX on the effectiveness factor is shown in Figure 14. As a reference state for 5 and X to be unity, the ratio of the intraparticle effectiveness factor is slightly greater than 1 for f > 1and sharply decreases
h 2.,0
l.;iO
:.
3,.0
4.0 ~
,1
6.0 ,.e
0.8 .
Sumbol: Exprrinrntal dato Line : Model rarulta
x 1.1
.LI
1.0
OaD
Ind. Eng. Chem. Res., Vol. 31, No.8,1992 1873
. d
t
1
0 c
Figure 14. Effects of diffusivity ratio and mass-transfer coefficient ratio of rsactants on the intraparticle effectiveneae factor: I$ = 5, Si, = 10, E = 1, A = 1, p . = 1.0 g/cm3, V,, = Vow,qQX,$ = 1.0 mmol/g, m = 2, n = 0.06. Table I. Parameters Needed in Solving the Dynamic Equations (eom = e.q = 0.065, E = 1.43, p, = 0.92, qex.0 = 0.717 mmol/g, R = 0.030 cm) T ("C) 106Day. (cm2/min) A Si, B 30 1.62 0.53 1788 3.23 40 2.34 0.58 1348 3.89 50 3.30 0.61 1101 4.63 60 4.56 0.64 917 5.46
0
P
Y)
Bo
en
iP
IW
Time (min)
Figure 15. Conversion of reactant (RX) va time for various amounts of catalyst ueed: 3.0 g of 2,4,6-tribromophenol;0.7 g of allyl bromide; 1.0 g of K O H 50 mL of chlorobenzene;50 mL of water; 50 "C; and amounts of catalyst used (40-80 mesh), (0)0.488 g (A)0.866 g, (0) 1.299 g, (0)2.165 g.
I
I .01
-
0.8
I
Symbol: Experlnental dato Line : Model resul t s
0.6.
"From Wang and Yang (1991a).
for < 1. This phenomenon shows that the reaction of QX with Y- to form QY exhibits ita importance as the diffusivity of Y is smaller than RX within the catalyst. Therefore, if the diffusivity ratio of Y is smaller than RX within the catalyst, the transformation of QX to QY will be the controlling step; i.e., the mass-transfer coefficient of Y between the bulk solution and the catalyst pellet is always larger or equal to that of RX because the organic solution generally is in the dispersion phase. As shown in Figure 14, the effect of the mass-transfer-coefficientratio of Y to RX on the overall effectiveness factor is insignificant. In order to compare the experimental results with the estimated values, the conversion of organic reactant, X, is defined: = - CRX,b/CRX.O (35) Then, eq 29 can be expressed as In (1 - X) = -kappt (36)
As shown in eq 30, the apparent reaction rate constant, kapp,depends on the mass-transfer coefficient of organic reactant (RX)in the bulk organic phase, KRx,the intrinsic organic reaction rate constant, koW,the fraction of the catalytic active sites on the surface of the catalyst pellet, f xal and the intraparticle effectiveness factor, vi. In simdatmg the reaction, the parameter Km can be estimated from the experienced formula given by Levins and Glasstonbury, noted by Oldshue (1983). The intrinsic reaction rate constants in the aqueous phase (k,) and in the organic phase (koW)were obtained from the work of Wang and Yang (1991b). The diffusivity of RX and Y in the bulk solution are determined from the WilkeChang empirical correlation (Reid et al., 1977). The interfacial area of liquid-solid interphase is obtained from experimenta. The additional parameters which are needed to solve the dynamic equations are listed in Table I.
o
P
Y)
Bo
BO
i
m
m
i
o
Time (min)
Figure 16. Conversion v8 time for different reaction temperatures: 3.0 g of 2,4,6-tribromophenol;0.7 g of allyl bromide; 50 mL of chlorobenzene;50 mL of water; 1.0 g of KOH; 0.866 g of catalyst (40-80 40 "C,(A)50 "C, (0)60 "C. mesh); and temperatures, (0)30 "C,(0)
On the basis of the above theoretical analysis, experiments were carried out by reacting 2,4,6-tribromophenol with allyl bromide in an alkaline solution/chlorobenzene solvent using the immobilized quaternary ammonium salts as the phase-transfer catalyst (Wang and Yang, 1991a; Yang, 1990). A comparison of the experimental results and the simulation results is given in Figures 15 and 16. The experiments were carried out by reacting 2,4,6-tribromophenol with allyl bromide in an alkaline/chlorobenzene solution using the immobilized quaternary ammonium salts as a phase-transfer catalyst in a batch reactor (Wang and Yang, 1991%Yang, 1990). It is seen that the calculated apparent reaction rate constant is very consistent with that of the experimental results.
Conclusion In the present study, an attempt was made to build up a dynamic model of triphase catalysis. The mass transfer of reactants both in the bulk solutions and within the porous medium as well as the kinetics of the reaction were used to successfully describe the dynamics of triphase catalysis in a batch reactor. A solution of the dynamic behavior was obtained by the finite difference method. The mass Biot number, E,,and the Thiele modulus, 4, are the two important parameters in reflecting the relative importance of the mass-transfer resistance to the resistance of the reaction kinetics. The intraparticle and overall effectivenessfactors, which are functions of both the mass Biot number and the Thiele modulus, were obtained. It is found that the conventional intraparticle effectiveness
1874 Ind. Eng. Chem. Res.,Vol. 31, No. 8, 1992
factor for a heterogeneous reaction system can be used to describe the present reaction system without much error. Using the published data of the reaction parameters and the transport parameters, the numerical results are very consistent with the experimental results which were obtained from the allylation of 2,4,6-tribromophenol in an alkaline solution using a triphase catalyst in a batch reactor.
Nomenclature a=
interfacial area of liquid-solid interphase
Bi, = mass Biot number
= concentration of organic reactant (RX) within particulate phase CRY = concentration of organic product (RY) within particulate phase Cy = concentration of aqueous reactant Cy-) within particulate phase C R X b = concentration of organic reactant (RX) in bulk phase CRXr = concentration of organic reactant (RX) on surface of catalyst particle CY,b = concentration of aqueous reactant (Y-) in bulk phase Cy,, = concentration of aqueous reactant (Y-) on surface of catalyst particle D R X = diffusivity of organic reactant (RX) within particulate phase Dy = diffusivity of aqueous reactant (Y-) within particulate phase fQx= dimensionless concentration of the catalytic active sites, QX ~ Q K= ? total dimensionleasconcentration of the catalytic active sites, QX f m = dimensionless concentration of organic reactant (RX) within particulate phase f y = dimensionless concentration of aqueous reactant (Y-) within particulate phase f v , b = dimensionless concentration of organic reactant (RX) in bulk phase fy,! = dimensionless concentration of aqueous reactant (Y-) in bulk phase fRxg = dimensionless concentration of organic reactant (RX) on surface of catalyst particle fy,, = dimensionless concentration of aqueous reactant (Y-) on surface of catalyst particle kapp= apparent reaction rate constant k , = intrinsic aqueous reaction rate constant korg = intrinsic organic reaction rate constant Km = mass-transfer coefficient of organic reactant (RX) in bulk organic phase Ky = mass-transfer coefficientof aqueous reactant (Y-) in bulk aqueous phase = CY,O/CRX,O n = VcatIVorg q Q X = concentration of active site of catalyst (QX) qQy = concentration of active site of catalyst (QY) q x o = total concentration of active site of catalyst = catalyst (QX) on surface of catalyst particle QY,,, = catalyst (QY) on surface of catalyst particle r = spatial coordinate in radial direction R = radius of catalyst particle RX,,,, = organic reactant in organic phase RY,,) = organic product (RY) within the pores of the catalyst particle t = time V = volume V,, = volume of aqueous phase V,, = volume of catalyst Vorg= volume of organic phase W,= mass of catalyst w = dimensionless spatial coordinate in the radial direction X(,) = aqueous reactant (X-) on surface of catalyst particle CR?
Qk.)
Y(%)= aqueous reactant (Y-) within the pores of the catalyst particle Y(,) = aqueous reactant (Y-) on surface of catalyst particle
Greek Symbols = ratio of k, /korg 8RX = ratio of &X,O Over (PnqQX,o) 6y = ratio of Cy,o over (psqQx,o) T = dimensionless reaction time 5 = ratio of Dy over D R X X = ratio of K Y I K R X vi = intraparticle effectiveness factor, defined by eq 26 vo = overall effectiveness factor, defined by eq 31 4 = Thiele modulus, defined in eq 13 p , = density of solid particle e,, = volume fraction of aqueous phase within the pore eorg = volume fraction of organic phase within the pore uaq= ratio of t , over (eorg + ea,) UQX = reciprocal of (eorg + e,,) uOrg= ratio of torgover (eorg + e,,) ua(,= ratio of V,, over Vcat(torg + e,), uorg = ratio of Vorgover Vcat(eorg + caq) CY
Subscripts aq = aqueous phase b = bulk phase org = organic phase s = within the catalyst particle
Literature Cited Aris, R. The Single Reaction in an Isothermal Pellet. The Mathemutical Theory of Diffusion and Reaction in Permeable Catalysis; Oxford University Press: London, 1975;Vol. I, Chapter 3,pp 119-126. Chaudhari, R. V.; Ramachandran, P. A. Three Phase Slurry Reactor~.AZChE J. 1980,26,177-201. Dehmlow, E. V.; Dehmlow, S. S. Phase Transfer Catalysis. Verlag Chemie: Weinheim, 1983;pp 1-45. Freedman,H. H. Industrial Applications of Phase Transfer Catalysis (PTC): Past, Present and Future. Pure Appl. Chem. 1986,58, 857-am. Jarrouse, J. The Influence of Quaternary Ammonium Chloride on the Reaction Labile Hydrogen Compounds and ChlorineSubstituted Chlorine Derivatives. C. R. Hebd. Seances Acad. Sci., Ser. C 1951,232,1424-1434. Marconi, D. F.;Ford, W. T. Catalytic Effectiveness Due to Mass Transfer Limitationa in %phase Catalysts by Polymer-Supported Quaternary Onium Salts. J. Catal. 1983,163-167. Ohtani, N.;Wilkie, C. k;Nigam, A.; Regen, S. L. Triphase Catalysis. Influence of Percent Ring Substitution on Active Site Mobility, Macroenvironment, Microenvironment, and Efficiency. Macromolecules 1981,14,516-520. Oldshue, J. Y. Liquid-Solid Mass Transfer. Fluid Miring Technology; McGraw-Hik New York, 1983;Chapter 11, pp 237-239. Regen, S. L. Triphase Catalysis. J. Am. Chem. SOC.1975, 97, 5966-5958. Regen, S.L. Triphase Catalysis, Applications to Organic Synthesis. J. Org. Chem. 1977,42,875-879. Regen, S. L.; Besse, J. J. Liquid-Solid-Liquid Triphase Catalysis, Consideration of the Rate-limiting Step, Role of Stirring, and Catalysts Efficiency for Simple Nucleophilic Displacement. J. Am. Chem. SOC.1979,101,4059-4063. Regen, S.L.; Heh, J. C. K.; McLick, J. Triphase Catalysis. Consideration of Catalyst and Experimental Conditions for Simple Nucleophilic Displacement Reactions. J. Org. Chem. 1979a, 44, 1961-1964. Regen, S.L.; Besse, J. J.; McLick, J. Solid-phase Cosolvents. Triphase Catalytic Hydrolysis of 1-Bromoacamantane. J.Am. Chem. SOC. 1979b,101,116-120. Reid, R. C.; Prausnitz, J. M.; S h e r w d , T. K. Diffusion Coefficients. The Roperties of Gases and Liquids; McGraw-Hill: New York, 1977;Chapter 11, pp 567-571. Starks,C. M. P h u e Transfer Catalysis: An Overview. ACS Symp. Ser. 1985,326,1-7. Starks,C. M.; Liotta, C. Phase Transfer Catalysis, Principles and Techniques; Academic Press: New York, 1978. Wang, M. L.;Yang, H. M. A Pseudo Steady State Approach for
Ind. Eng. Chem. Res. 1992,31,187&1880 Triphaee Catalysis in a Batch Reactor. Znd. Eng. Chem. Res. 1991a, 30,2384-2390. Wang, M. L.; Yang, H. M. Dynamica of Phase Transfer Catalyzed Reaction for the Allylation of 2,4,6-TribromophenoL Chem. Eng. Sci. 1991b, 46,619-627. Weber, W. P.; Gokel, G. W. Phase Transfer Catalysis in Organic Synthesis; Springer Verlag: New York, 1977.
1875
Yang,H. M. Study on the Synthesis of Allyl Polybromophenyl Ether by Phase Transfer Catalytic Reaction. Ph.D. Thesis,Department of Chemical Engineering, National Taing Hue University, Hsinchu, Taiwan, 1990.
Received for review November 20,1991 Accepted May 8,1992
Magnesium and Silicon as ZSM-5Modifier Agents for Selective Toluene Disproportionation Maria A. Uguina,* Jose L. Sotelo, David P. Serrano, and Rafael Van Grieken Chemical Engineering Department, School of Chemistry, Compluteme University of Madrid, 28040 Madrid, Spain
Magnesium and silicon have been studied and compared as ZSM-5 modifier agents for selective toluene disproportionation. For both agents, para-selectivity corresponding to the primary product was loo%, p-xylene being the unique isomer able to leave the modified pore structure due to the coupled effects of the steric constraints, enhanced by the modifier agents, and the fast internal isomerization. The further decline of para-selectivity with conversion is caused by the primary product isomerization on the external acid sites. The best para-selectivity/activity relationship obtained with the silicon modification has been assigned to the deposition of this agent on the external zeolite surface, an assumption that showed to be in good agreement with kinetic and adsorption-diffusion measurements. The lower conversion exhibited by the magnesium-modified samples has been related to higher diffusional limitations and a decrease in the number of acid sites due to ion exchange with magnesium species.
Introduction Toluene disproportionation in the vapor phase over a variety of acid zeolites is a commercial way to yield the different xylene isomers and benzene (Schriesheim, 1961; Oliver and Ione, 1970;Bhavikatti and Patwardhan, 1981; Beltrame et al., 1985;Meshram et al., 1986;Chang et al., 1987). When the reaction is carried out over ZSM-5 zeolite, the product distribution can be directed to the selective formation of p-xylene, the moet valuable isomer, modifying the shape-selectivityof the zeolite. It is known that ZSM-5 modification by treatment with different agents and by means of several procedures leads to an enhancement of the selectivity to p-xylene (Kaeding and Butter, 1975; Kaeding and Young, 1977;Kaeding et al., 198la,b;Young et al., 1982), obtaining a proportion of p-xylene rather higher than the thermodynamic equilibrium value (24mol % p-xylene). Olson and Haag (1984)have proposed a reaction scheme for selective toluene disproportionation over modified ZSM-5 zeolites. According with them, toluene disproportionation inside the zeolite structure yields benzene and a xylene mixture known as initial product. Then, this product diffuses out of the channel system but simultaneously it undergoes isomerization reactions which take place within the zeolite crystal,giving the primary product, the first observable outside the zeolite pore and capable of being determined at conversions approaching zero. A p-xylene proportion in the primary product higher than the value initially obtained is expected since ita least minimum diameter allows a faster diffusion than the other two isomers. Finally, the primary product undergoes a second isomerization by reentry into the channel network or over the acid sites located on the external zeolite surface, yielding the secondary product observed in the effluent of each experiment. *To whom correspondence should be addressed.
In agreement with this mechanism, the para-selectivity enhancement and the decrease on toluene conversion observed in the modified ZSM-5 zeolites can be related with the following roles of the modifier agent: (a) Pore blockage in the ZSM-5 zeolite by deposition of the modifier agent. Tortuousity of the channel system is increased, which delays the diffusion of the different molecules involved in the reaction. This effect favors the relative p-xylene diffusion, para-selectivity in the primary product being enhanced. Likewise, these steric constrainta prevent the isomerization of the primary product by reentry but may cause a decline on catalytic activity if toluene diffusion is delayed. (b) Deposition or linkage of the modifier agent to the unselective acid sites located on the external surface of the zeolite crystals, an effect which avoids the external isomerization of the primary product. Although the percentage of external acid sites is suppose to be very low, their catalytic effect has to be taken into account since the intrinsic rate constant for isomerization is much higher than the one for disproportionation ( k I / k D31 7000 according to Olson and Haag (1984)). Among the high number of elements and compounds which have been used as ZSM-5 modifier agents (Kaeding et al., 1981a,b;Young et al., 1982;Olson and Haag, 1984) in order to enhance ita para-selectivity in different reactions (xylene isomerization, toluene disproportionation, and toluene alkylation with methanol, ethanol, etc.), in the present work, magnesium and silicon have been selected with the aim of studying and comparing their effects on catalytic and diffusional properties of ZSM-5 zeolite. Whereas magnesium is well-known as a conventional modifier agent of ZSM-5 zeolite (Chen et al., 1979;Kaeding et al., 1981a,b;Olson and Haag, 1984;Derewinski et al., 1984;Meahram, 1987),there is not much information about the use of silicon polymers in order to enhance the zeolite shape-selectivity (Rodewald, 1983). Recently, Wang et al. (1989)(toluene alkylation with ethylene) and Handreck
088&5885/92/2631-1875$03.00/0 0 1992 American Chemical Society
