631
Znd. Eng. Chem. Res. 1991,30,631-635 tation, University of Arizona, 1988. Punjak, W. A.; Uberoi, M.; Shadman, F. High Temperature Adsorption of Alkali Vapors on Solid Sorbents. AZChE J. 1989,35 (7), 1186-1194.
Rizeq, R. G.; Shadman, F. Alkali-Induced Agglomeration of Solid Particles in Coal Combustors and Gasifiers. Chem. Eng. Commun. 1989,81,83-96. Rosner, D. E. Experimental and Theoretical Research on the Deposition Dynamics of Inorganic compounds from Combustion Gases. PCH, PhysicoChem. Hydrodyn. 1988,10,663-674. Rosner, D. E.; Liang, B. Experimental Studies on Deposition Rates in the Presence of Alkali Sulfate Vapor Scavenging by Submicron Particles in Combustion Gas Boundary Layers. Chem. Eng. Commun. 1988,64,27-45. Spiro, C. L.; Chen, C. C.; Kinura, S. G.; Lavigne, R.G.; Schields, P. W. Remediation in Coal Fired Gas Turbines through the Use of Additives. Prepr. Pap.-Am. Chem. SOC.,Diu. Fuel Chem. 1989, 34 (2),407-415.
Tai, N. H.; Chou, T. W. Analytical Modeling of Chemical Vapor Infitration in Fabrication of Ceramic Composites. J. Am. Cenrm. SOC.1989, 72,414-421. Uberoi, M.; Shadman, F. Sorbents for Removal of Lead compounds from Hot Flue Gases. AZChE J. 1990,36 (21,307-309. Uberoi, M.; Punjak, W. A.; Shadman, F. The Kinetics and Mechanism of Alkali Removal From Flue Gaseg by Solid Sorbents. h o g . Energy Combust. Sci. 1990,16,205-211. Wang,M. S.; Spear, K. E. Experimental and Theoretical Investigations of the V-Si-H-Cl CVD Ssystem. Proc. Electrochem. SOC. 1981,81, 1367-1372.
Wibberley, L. J.; Wall, T. F. Alkali-ash reactions and Deposit Formation in Pulverized-Coal Fired Boilers: the Thermodynamic Aspects involving Silica, Sulfur, Sodium, and Chlorine. Fuel 1982, 61,8742.
Received for review March 6, 1990 Accepted October 15, 1990
Simplified Dynamic Model for the Allylation of 2,4,6-Tribromophenol by Phase-Transfer Catalysis Maw-Ling Wang* and Hung-Ming Yang Department of Chemical Engineering, National Tsing Hua University, Hsinchu, Taiwan, Republic of China
On the basis of experimental observation, a simplified model is proposed to predict the dynamic behavior of the allylation for 2,4,6-tribromophenol by phase-transfer catalysis. A measured constant concentration of tetra-n-butylammonium 2,4,64ribromophenoxide during the reaction leads to the use of a pseudo-steady-state hypothesis in conjunction with the system parameters to build up the dynamic model. The results obtained from the model's prediction are very consistent with the experimental data which were obtained from the two-phase phase transfer catalytic reaction. It is found that the mass-transfer resistance of tetra-n-butylammonium 2,4,6-tribromophenoxide from the aqueous phase to the organic phase is negligible. The step of the reaction in the organic phase will be a rate-determining step of the whole reaction system.
Introduction The well-known phase-transfer catalysis (PTC) (Dehmlow and Dehmlow, 1983; Starks and Liotta, 1978; Weber and Gokel, 1977) has been extensively applied to synthesize the speciality chemicals from two immiscible reactants by alkylation, displacement, elimination, reduction and oxidation, and free-radical polymerization. Since 1970, more than 100 scientific papers about phase transfer catalytic reactions have been published every year. However, past efforts in this field were mostly concerned only with synthesis and reaction kinetics even though this technique exhibits great potential for industrial-scale production (Freedman, 1986; Starks, 1985). Very few papers have dealt with the transfer rate of the catalyst from one phase to another (Lin et al., 1983; Melville and Goddard, 1988). The complicated nature of the reaction makes it very difficult to model the dynamic system. It is understood that the complicated nature of the system stems from the two mass-transfer steps and two reaction steps in the organic and aqueous phases. In addition, the equilibrium partitions of the catalysts between two phases also affect the reaction rate. In many reaction systems by phase-transfer catalysis, the catalyst (or intermediate product) is extremely difficult to be synthesized and purified. Therefore, the difficulty in realizing the mass-transfer rates of catalysts between two phases is probably due to the uneasy identification of the catalyst (or intermediate product) during reactions.
* T o whom correspondence should be addressed. 0888-5885 I9112630-0631$02.50 IO
In the present study, the intermediate product of tetra-n-butylammonium 2,4,6-tribromophenoxide((C6H2)Br30Bu4N)in the allylation of 2,4,6-tribromophenol by phase-transfer catalysis was successfully identified (Wang and Yang, 1990). On the basis of experimental observation by Wang and Yang (1990),a simplified model by applying the pseudo-steady-state hypothesis is proposed in order to predict the dynamic behavior of the allylation of 2,4,6-tribromophenol by phase-transfer catalysis. The reaction system is simulated by the proposed model in conjunction with the system parameters, such as distribution coefficients of catalysts, mass-transfer coefficients of catalysts, and the intrinsic reaction rate constants either in the organic phase or in the aqueous phase. The Damkohler numbers, which directly reflect the relative rate of chemical reaction to the mass transfer of the catalysts, are defined. It is found that the mass-transfer resistance of catalysts from the aqueous phase to the organic phase is negligible. The results of the model's prediction are very consistent with the exprimentaldata which were obtained from two-phase transfer catalytic reaction. Experimental Section of the Two-Phase Reaction Materials. 2,4,6-Tribromophenol(ArOH),allyl bromide (RBr), tetra-n-butylammonium bromide (Bu4N+Br-; TBAB or QBr), and other reagents are all guarantee reagent (G.R.) grade chemicals, products of Merck Co., Darmstadt, Germany. Procedures. The reactor was a 300-mL three-neck Pyrex flask, serving the purposes of agitating the solution, 0 1991 American
Chemical Societv
632 Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991
inserting the thermometer, taking samples, and feeding feed. The reactor was submerged into a constant-temperature water bath in which the temperature could be controlled to within f O . l "C. To start a kinetic run, a known quantity of potassium hydroxide and 2,4,6-tribromophenol was prepared and dissolved in water. The solution was then introduced into the reactor, which was thermostated at the desired temperature. A measured quantity of allyl bromide (CH2CHCH2Br)and diphenyl ether (internal standard), which was also at the desired temperature, was dissolved in the chlorobenzene solvent and then added to the reactor. To start the reaction, tetra-n-butylammonium bromide (TBAB) was then added to the reactor. During the reaction, an 0.8-mL aliquot sample was withdrawn from the reaction solution at a chosen time. The organic and aqueous phases of the sample were well separated in a few seconds. After separation, 0.1 mL of the organic-phase sample was immediately diluted with 4.5 mL of methanol. Usually, it took less than 20 s to take a sample. In order to make sure that experimental accuracy was not affected by the sampling procedure, another sampling procedure was also adopted. That is, an excess amount of concentrated HC1 solution was poured into the reactor to terminate the reaction by reacting it with KOH in the solution. Then, the agitator was stopped and the sample withdrawn from the organic phase for HPLC analysis. It was found that good reproducibility and consistent results were obtained for both procedures. The 2,4,6-tribromophenyl allyl ether (CH2CHCH20(C6H2)Br3) obtained from the two-phase reaction was identified. Tetra-n-butylammonium 2,4,6-tribromophenoxide (Bu4NO(C6H2)Br3; ArOQ), which can be synthesized from the reaction of tetra-n-butylammonium bromide with 2,4,6-tribromophenol and KOH in the aqueous phase, was also identified from the two-phase reaction. The HPLC model was a Tracor 955 8z 970A variable-wavelength detector with an H P 3390A integrator. The column used was Lichrosorb RP-18 (5 Nm), Merck Co., Germany. The eluent was CH30H/CH3CN/H20= 2.5/2.5/1.1, with flow rate 1.0 mL/min and at 254 nm (UV detector). Mathematical Modeling On the basis of experimental observation, a general schematic diagram of phase-transfer catalysis for the allylation of 2,4,6-tribromophenol can be expressed as (Weber and Gokel, 1977) + O'BrA
ArO-K'
ArOR
+
I
- lKArw K 4
ArO-0'
(aqueous) ~~
(organic)
Koer Korp
OBr
ArOQ + RBr
where the parameters, KW,.KO,, K-, and KQBrare given in the Nomenclature section. In order to formulate a mathematical model to describe the dynamic behavior of the two-phase reaction shown above, a two-film theory is employed to consider the mass transfer of the catalysts between two phases. Thus, those equations to model the two-phase reaction are formulated below. The rate of change for ArOQ in the organic phase is the difference of mass-transfer rate and organic-phasereaction rate. dC&/dt
= K-A(C;&
= KaqCikKC& - K&f(C&Q C&/mAroQ) (2) Similarly, the rate of change for QBr either in the organic phase or in the aqueous phase is obtained as shown in (3) and (4).
dCi:,/dt
dC:k/dt
- K Q B f i ( q & - mQBrC&)
= KorgC&Gsr
(3)
dC&/dt = KQ&f (C6zr - mQBrC&) - Kaqci'Kc& (4) The reaction rate of ArOK in the aqueous phase is dCLK/dt = -KaqCi'&&
(5)
The reaction rate of RBr in the organic phase is = -KoqCi&C;Zr
dC;'r/dt
(6)
In the above equations, f is defined as the ratio of the volume of organic phase (V,) to the volume of aqueous phase (Va), i.e. f = Vo/Va (7) The distribution coefficients of catalysts mm and mQBr are defined as o e ( ~ 4 Cads) AroQ
(8)
mArOQ=CAroQl
prdd Cads)
/
(9) where the superscript s denotes the characteristics of the species at the interphase. The conversion of allyl bromide is defined as X , (10) = 1- C;gr/C;;r,O where the subscript 0 denotes the initial concentration of allyl bromide. The total number of moles of catalyst, Qo, and the total number of moles of 2,4,6-tribromophenol,Eo, intially are Qo= Vo(Ciqw + C;zr) + Va(C& + C&) (11) mQBr=
QBr
QBr
x
Eo = V0(CiWw
+ [C;sr,O- C;sr]) + Va(CLK + C&) (12)
The initial conditions of the above equations are
+ K'Br-
I
The rate of change for ArOQ in the aqueous phase is the difference of aqueous-phase reaction rate and masstransfer rate.
- CF&/mArw) K org CoRBr rk7 COrB ArOQ (l)
cgir= 0, C7Br = Ci\r,O, qzr= Ci;r,O;
cLp=Ci'K,o;
CT& =0, C&=O,
t =0 t=O
(13)
The parameters ~ Q B m-, ~ , K Q B AK d , Kaq, and Korgfor the allylation of 2,4,6-tribromophenol in a twophase catalyzed reaction were obtained by Yang (1990), i.e. mQBr=
mm
7.1 X
= (8.02 + 0.05T)
- 0.56C&
+ (78.33T - 1 1 6 5 ) C h
(14) (15)
KQ& = 2.69 min-' (16) K-A = 3.84 + 0.06T min-' (17) Kaq= 3.2 X lo7 exp[-4840/(T + 273.16)] M-' min-I Korg= 3.3 X
lo9 exp[-7016/(T +
(18) 273.16)] M-' min-' (19)
Ind. Eng. Chem. Res., Vol. 30, No. 4,1991 633 where T is expressed in "C. During the two-phase reaction, the concentration of ArOQ is kept at a constant value after a small induction period. Therefore, the pseudo-steady-state hypothesis (PSSH) can be made in the present system, Le. dC& d C h-0 -=-dt dt Thus, (1)and (2) become
Eliminating Ciqa
=l/mm
+ DaAm
P = fmQBr + DaQBr
(33) (34) (35)
The parameters a and /3 reflect the effects of the equilibrium distribution of catalysts between two phases and the mass transfer of catalysb across the interphase. R is a ratio of the reaction velocity in the organic phase to that of velocity in the aqueous phase. Thus, the concentrations of ArOQ and QBr either in the organic phase or in the aqueous phase can be represented by the following equations:
from (21) and (22), we obtain
In a similar way, the following equation is held for QBr: (24) From (3), (4), and (23), we have
Ciir = (Qo/ VJ tlfR
By solving the nonlinear algebraic equations of (ll), (12), (32), (36), (371, (381, and (39) with the specified parameters or the operating conditions, the simulation results for f = 1 are given in Figures 1-7.
Substituting (23) into (25)
Combining (ll),(21), (23), and (26), we have
Apply the Damkohler numbers of ArOQ and QBr, respectively, as
The concentration of ArOK in the aqueous phase can be obtained from the material balance of 2,4,6-tribromophenol, which is shown in (12). As shown in (28) and (29), the Damkohler number indicates the ratio of the chemical reaction rate to the mass-transfer rate of the catalyst. An effective fraction of catalyst, q , which is defined as the ratio of the observed two-phase reaction rate to the organic-phase reaction rate with catalyst completely used, is given as
where Kapp= KO$&
(31)
Thus, q can be expressed as 1
v = 1 + a / f + (1 + B)R where
(39)
(32)
Results and Discussion In this study, the synthesis of 2,4,64ribromophenyl allyl ether was carried out by phase-transfer catalysis. On the basis of experimental observation from which the constant concentration of the intermediate product (Bu4NO(C6H2)Br3;ArOQ) was measured, a simplified dynamic model for describing the characteristics of the phase transfer catalytic reaction is proposed. In the following, the simulation results are presented and discussed. As given in (28) and (291, the Damkohler number (Da) is defined as the ratio of the reaction rate to the masstransfer rate. A simulation result for plotting the Damkohler number of ArOQ (Da vs the conversion of allyl bromide with f = 1is shown % & r e 1. It is obvious that the Damkohler number of ArOQ, which also depends on the initial concentration of allyl bromide, is much less than unity for the whole range of conversion. This result indicates that the reaction rate of the organic-phase reaction is much lower than the mass-transfer rate of ArOQ. Thus, the mass-transfer resistance of ArOQ from the aqueous phase to the organic phase is negligible when compared with the reaction rate in the organic phase. In addition, the Damkohler number of ArOQ increases with the increase of temperature for a certain value of conversion. This phenomenon is due to the increase in the organicphase reaction rate at a higher temperature while the resistance of mass transfer of ArOQ is very small. As depicted in Figure 2, the order of magnitude of the Damkohler number of QBr (Da Br) for the whole range of conversion is about unity. &ese results reflect the fact that the mass-transfer rate of QBr from the organic phase to the aqueous phase is slightly larger than the reaction rate in the aqueous phase. A plot of R value, which denotes the relative reactivity of the organic phase to the aqueous phase, vs conversion is given in Figure 3. The R value is less than unity. In combining the results from Figures 1-3, the step of the organic-phase reaction is confirmed as the rate-determining step of the whole reaction quantitatively rather than qualitatively by other investigators in the published documents.
634 Ind. Eng. Chem. Res., Vol. 30,No. 4, 1991
-
O0
1.61
=I \ et \ 0
C
.d
c
o.llj t 3
4I
Trmprroturm ('C)
O.*
Curvr Curvr Curvr Curvm
c
ii.0
0.2
0.4
0.e
0.8
1 .o
; 0.0L 0.0
0.2
Conversion, X
0.0
0.4
I : 30 2 : 40 3 I 60 4 : 80
1 .o
0.8
Conversion, X
Figure 1. Dependence of the ratio of the reaction to the masstransfer rate for ArOQ (Dam) on conversion (X)at different temperatures: 3.0 g of 2,4,6-tribromophenol, 0.7 g of allyl bromide, 0.2 g of TBAB catalyst, 50 mL of HzO, 50 mL of chlorobenzene, 1.0 g of KOH. 1 .OI
Figure 4. Effective fraction of catalyst, q, vs conversion (X)at different temperatures: 3.0 g of 2,4,6-tribromophenol, 0.7 g of allyl bromide, 0.2 g of TBAB catalyst, 50 mL of H20, 50 mL of chlorobenzene, 1.0 g of KOH.
1
0.0. c
-
o*2* 0.0 0.0
0.2
0.4
0.e
0,s
m
.?
0.3-
Curvi I Curvr 0
d
0
.m.-
;;
0.01 0.0
0.2
1 .o
Conversion, X
Figure 2. Dependence of the ratio of the reaction to the masstransfer rate for QBr (DaQB,)on conversion (X)at different temperatures: 3.0 g of 2,4,6-tribromophenol, 0.7 g of allyl bromide, 0.2 g of TBAB catalyst, 50 mL of H20, 50 mL of chlorobenzene, 1.0 g of KOH.
-
RBr ( 0 )
6
0.70 1.06
0.4
0.8
PTC ( 0 ) 0.1 - 0.6 0.2 I .o
0.8
Conversion. X
Figure 5. Effective fraction of catalyst, q, vs conversion (X)at different amounts of TBAB catalyst and allyl bromide: 3.0 g of 2,4,6-tribromophenol, 50 mL of H20,50 mL of chlorobenzene, 1.0 g of KOH, 50 O C . Linl :'kOdDl R W U l 1 D SylbOl 2 E X p D r l m t P l Dot0
0.04
PTC (01
0 0.4
A
0.6
v
-
I 0.0
0.2
0.4
0.6
0.8
I .o
Conversion. X
Figure 3. Dependence of the ratio of the organic-phase reaction to the aqueous-phase reaction rate ( R value) on conversion (X)at different temperatures: 3.0 g of 2,4,6-tribromophenol, 0.7 g of allyl bromide, 0.2 g of TBAB catalyst, 50 mL of H20, 50 mL of chlorobenzene, 1.0 g of KOH.
As defined in (32), the values of v directly reflect the mole fraction of the intermediate catalyst, ArOQ, existing in the organic phase. A plot of 7 vs X is shown in Figures 4 and 5. It is found that about 75-90% of the catalyst exists in the form of ArOQ remaining in the organic phase. A lower reaction temperature will lead to an higher mole
-O a WA t
-.-0.0
A
-
0.2
0.4
0.8
0.8
I .o
Conversion. X
Figure 6. Comparison of results obtained from model's prediction with experimental data for different amounta of TBAB catalyat used: 3.0 g of 2,4,6-tribromophenol, 0.7 g of allyl bromide, 50 mL of H20, 50 mL of chlorobenzene, 1.0 g of KOH, 50 O C .
fraction of ArOQ remaining in the organic phase. Figures 6 and 7 show the comparison of the results obtained from the model's prediction with the experimental data for different amounts of TBAB catalyst and allyl bromide at 50 "C. In Figure 7, the concentration of ArOQ in the organic phase increases when the initial amount of catalyst added to the reactor increases. The results of the simplified model which were obtained from the pseudo-
Ind. Eng. Chem. Res., Vol. 30,No. 4,1991 635
I
o.m( 0.011
"O
O.OO0'
I
Llnr -01
: M o l Rwultr : E x p r i r n t n l Dota
lblr Rotlo 0 1.607
A
1.046
t
0.0
0.2
0.4
0.0
0.8
1 I .o
Convera i on, X
Figure 7. Comparison of results obtained from model's prediction with experimental data for different mole ratios of 2,4,6-tribromophenol to allyl bromide: 3.0 g of 2,4,64ribromophenol, 0.2 g of TBAB catalyst, 50 mL of H20, 50 mL of chlorobenzene, 1.0 g of KOH, 50 OC.
steady-state hypothesis are very consistent with the experimental data obtained from the two-phase phase transfer catalytic reaction. During the reaction, the concentration of ArOQ in the organic phase is kept at an almost constant value after a short period of induction. This phenomenon still exists even when the mole ratio of 2,4,6-tribromophenol to allyl bromide is maintained at a stoichiometric quantity; i.e., the mole ratio of 2,4,6-tribromophenol to allyl bromide = 1.045. These experimental results confirm the use of the pseudo-steady-state hypothesis to model the dynamic system in a simplified way. Conclusion In the present study, the experimental work of the allylation of 2,4,64ribromophenol in an organic solvent/ alkali aqueous solution was carried out by phase-transfer catalysis. During the reaction, the intermediate product of ArOQ mostly stays in the organic phase and is kept at a constant value. A simplified dynamic model that was obtained by the pseudo-steady-state hypothesis is used to describe the dynamics of the two-phase phase transfer catalytic reaction. The results obtained from the model's prediction are very consistent with the experimental data of the two-phase catalytic reaction. The Damkohler number of AroQ shows that the resistance of mass transfer of ArOQ from the aqueous phase to the organic phase is negligible compared to the chemical reaction rate either in the organic phase or in the aqueous phase. Acknowledgment We acknowledge financial support from the National Science Council, Taiwan, ROC (Grant No. NSC 77-0402E007-16). The use of facilities provided by the Refining
& Manufacturing Research Center, Chinese Petroleum Corporation, Taiwan, ROC, is also acknowledged.
Nomenclature A = mass-transfer area between organic and aqueous phase, cm2/cm3 (21% = concentration of ArOQ in organic phase, M C a b = concentration of ArOQ in aqueous phase, M Ca(g, = concentration of QBr in aqueous phase, M C&jr = concentration of QBr in organic phase, M Cih, = concentration of ArOK in aqueous phase, M C a R = concentration of ArOR in organic phase, M Cifr = concentration of RBr in organic phase, M E,, = initial moles of 2,4,6-tribromophenol f = vo/va Kaq= reaction rate constant of the aqueous phase, M-'min-' KorB= reaction rate constant of the organic phase, M-'min-' Km = mass-transfer coefficient of ArOQ from aqueous to organic phase, cm/min KQBr= mass-transfer coefficient of QBr from organic phase to aqueous phase, cm/min mm = distribution coefficient of ArOQ (Co /Cap') ) mQBr = distribution coefficient of QBr ( CoQ& ~j /, 6%) t = time, min V , = volume of aqueous phase, L V , = volume of organic phase, L X = conversion of allyl bromide Registry No. H,C=CHCH,Br, 106-956; 2,4,6tribromophenol,
+
118-79-6.
Literature Cited Dehmlow, E. V.; Dehmlow, S. S. Phase Transfer Catalysis; Verlag Chemie: Weinheim, 1983. Freedman, H. H. Industrial Applications of Phase Transfer Catalysis (PTC): Past, Present and Future. Pure Appl. Chem. 1986,58 (6), 857-868. Lin, T. B.; Yeh, M. Y.; Shih, Y. P. A Model of Phase Transfer Preparation of Benzyl Phenyl Ether. Proc. PAC Chem. Eng. I Congr., 3rd 1983,3, 178-193. Melville, J. B.; Goddard, J. D. A Solid-Liquid Phase-Transfer Catalysis in Rotating-Disk Flow. Znd. Eng. Chem. Res. 1988, 27, 551-559. Starks,C. M. Phase 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. Kinetic Study of Synthesizing 2,4,6-Tribromophenyl Allyl Ether by Phase Transfer Catalyzed Reaction. Ind. Eng. Chem. Res. 1990,29,522-526. Weber, W. P.; Gokel, G. W. Phase Transfer Catalysis in Organic Synthesis; Springer Verlag: New York, 1977. Yang, H. M. Study on the Synthesis of Allyl PolybromophenylEther by Phase Transfer Catalytic Reaction. Ph.D. Thesis, Department of Chemical Engineering, National Tsing Hua University, Hsin Chu, Taiwan, 1990.
Received for review February 14, 1990 Revised manuscript received June 19, 1990 Accepted November 5, 1990
