Znd. Eng. Chem. Res. 1991,30, 1342-1350
1342
Herrero, A. A. End-product inhibition in anaerobic fermentation. Trends Biotechnol. 1983, I , 44-53. Hsu, S. T. Effects of pH on extractive fermentation for propionic acid production from whey lactose. M.S. Thesis, Department of Chemical Enpineering, The Ohio State Univemity, Columbue, OH, 1989. Jagirdar, G. C.; Sharma, M. M. Recovery and separation of mixtures of organic acids from dilute aqueous solutions. J. Sep. Proc. Technol. 1980, 1(2), 40-43. Kertes, A. S.; King, C. J. Extraction chemistry of fermentation product carboxylic acids. Biotechnol. Bioeng. 1986,28,269-282. Ricker, N. L.; Michaels, J. N.; King, C. J. Solvent properties of organic bases for extraction of acetic acid from water. J. Sep. h o c . Technol. 1979, I(l), 36-41. Ricker, N. L.; Pittman, E. F.; King, C. J. Solvent extraction with amines for recovery of acetic acid from dilute aqueous industrial streams. J. Sep. h o c . Tehcnol. 1980, 2(2), 23-30. Robinson, R. G.; Cha, D. Y. Controlled pH extraction in the separation of weak acids and bases. Biotechnol. Prog. 1986, I , 18-25. Tamada, J. A.; Kertes, A. S.; King, C. J. Extraction of carboxylic acids with amine extractants. 1. Equilibria and law of mass action modeling. Znd. Eng. Chem. Res. 1990, 29, 1319-1326. Tamada, J. A.; King, C. J. Extraction of carboxylic acids with amine extractants. 3. Effect of temperature, water coextraction, and proceas considerations. Znd. Eng. Chem. Res. 1990,29,1333-1338. Wardell, J. M.; King, C. J. Solvent equilibria for extraction of carboxylic acids from water. J. Chem. Eng. Data 1978, 23(2), 144-148. Wennersten, R. The extraction of citric acid from fermentation broth using a solution of a tertiary amine. J. Chem. Tech. Biotechnol. 1983,33B, 85-94. Yabannavar, V. M.; Wang, D. I. C. Integration of extraction with fermentation for organic acid production. Annual Meeting of AIChE, Miami, FL, Nov 1986.
extractant-diluent mixture needs to be further evaluated. If the amine extractant is to be used in an extractive fermentation process, the selection of the extractant will be dependent on the pH range for the fermentation. For anaerobic acetic acid fermentation, which usually requires a pH value higher than 6.0, b i n e 336 will not work well, and Aliquat 336 or other extractants that can work at high pH values must be used. Alamine 336, however, will be good for use in propionic acid, lactic acid, and butyric acid fermentations, which can tolerate a pH value as low as 4.0. A pH swing in the aqueous phase will be able to regenerate the amine extractant, making the extraction with Alamine 336 an attractive method for separating and recovering carboxylic acids from dilute, aqueous solutions. Registry No. Lactic acid, 50-21-5; acetic acid, 64-19-7; propionic acid, 79-09-4; butyric acid, 107-92-6; 2-octanol, 123-96-6.
Literature Cited Bar, R.; Gainer, J. L. Acid fermentation in water-organic solvent two-liquid phase systems. Biotechnol. B o g . 1987, 3, 109-114. Bueche, R.M.; Shimshick, E. J.; Yates, R. A. Recovery of acetic acid from dilute acetate solution. Biotechnol. Bioeng. Symp. 1982,22, 249-262. Daugulis, A. J. Integrated reaction and product recovery in bioreactor systems. Biotechnol, Prog. 1988,4,113-122. Dean, J. A., Ed. Lunge's Handbook of Chemistry, 13th ed.; McGraw-Hill: New York, 1985; pp 5-62-5-67. Helsel, R. W. Waste recovery: Removing carboxylic acids from acqueous wastes. Chem. Eng. Prog. 1977, 73(5),55-59. Henkel Corp. Alamine 336. Red Line Technical Bulletin; Henkel Technical Center: Minneapolis, MN, 1988. Henkel Corp. Aliquat 336. Red Line Technical Bulletin; Henkel Technical Center: Minneapolis, MN, 1988.
Received for review August 23, 1990 Accepted December 10, 1990
Copolymer Composition Control of Emulsion Copolymers in Reactors with Limited Capacity for Heat Removal Gurutze Arzamendi and Jos6 M. Asua* Crupo de Zngenier;? Quimica, Departamento de Qulmica Aplicada, Facultad de Ciencias Quimicas, Universidad del Pats Vasco, Apartado 1072, 20080 San Sebastibn, Spain
A method for the determination of the optimal monomer addition strategy to produce a homogeneous copolymer under conditions in which the reactor has a limited capacity for heat removal is presented. The method allows for the calculation of the monomer addition profiles for both constant and time-dependent heat removal rates. The approach was successfully applied to the emulsion copolymerization of vinyl acetate and methyl acrylate carried out in a laboratory reactor that had been transformed to reduce ita capacity for heat removal to the level of a large-scale reactor. Introduction The control of the composition of the copolymers prepared from monomers with widely different reactivity ratios is usually achieved by carrying out the polymerization under starved conditions (Snuparek and Krska, 1977; Basaet and Hoy, 1981; El-Aaeser et al., 1983). In this way, the polymerization becomes controlled by the addition rate and the reaction rate of both monomers is the same as the feed rate. This results in a copolymer of the same composition as the feed. However, under starved conditions, the concentration of the monomers in the polymer particles is low and this leads to long process times. For solution polymerization, Johnson et al. (1982) developed a control Strategy aiming at maintaining a constant
* To whom correspondence should be addressed. O888-5885f 91 f 2630-1342$02.50f 0
molar ratio of coreactants in the reactor by adjusting the addition rate of the more reactive monomer. Analytical solutions for this process have been obtained by Choi (1989). These solutions cannot be applied to emulsion polymerization because, in this multiphase system, the concentration of the monomers in the polymerization loci is different from the average concentration in the reactor. Guyot et al. (1981) controlled the composition of emulsion copolymers using a feedback strategy based on on-line gas chromatographic analysis of the monomer mixture. A more advanced feedback control strategy based on the use of a Kalman filter for state estimation has been presented by Dimitratos et al. (1989). An alternative method is the so-called optimal semistarved monomer addition strategy (Arzamendi and hua, 1989). In this feed-forward strategy, the reactor is initially charged with all of the less reactive monomer plus the amount of the more reactive monomer needed to initially 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991 1343 form a copolymer with the desired composition. Subsequent addition of the remaining more reactive monomer is made at a flow rate that ensures the formation of a copolymer of the desired composition. In order to calculate the optimal monomer addition policy, the partition of the monomer between the different phases should be taken into account. It was considered that the monomer concentrations are at thermodynamic equilibrium, namely, that the polymerization is not controlled by monomer mass transfer. In addition, the time evolutions of both the total number of polymer particles and the average number of radicals per particle, fi, are required. The variation of the number of polymer particles during polymerization can be minimized in semicontinuous seeded emulsion polymerization by adjusting the surfactant added into the reactor. The average number of radicals per particle is determined by the rates of entry and exit of radicals into and from the polymer particles and by the bimolecular termination in the polymer particles. These values cannot be accurately predicted and, although strategies for the determination of these parameters have been proposed (Asua et al., 1990, de la Cal et al., 1990), they are usually unknown. This difficulty has been overcome (Arzamendi and Asua, 1990, Arzamendi et al., 1991) by applying a semiempirical method for the calculation of the optimal monomer addition. This is an iterative approach that involves a series of semicontinuousemulsion polymerizations. Each reaction is used to correlate fi with the volume fraction of polymer in the latex particles and, hence, finding the time dependence of ii(t). This relationship is used to calculate a monomer feed rate profile for the next semicontinuous experiment. The approach converges rapidly giving the optimal feed rate profile after two to three semicontinuous emulsion copolymerizations. This method has been successfully applied to the methyl acrylate-vinyl acetate system (Arzamendi and Asua, 1990) and to the ethyl acrylate-methyl methacrylate system (Arzamendi et al., 1991). A variation of the method has been used by van Doremaele (1990)for the styrenemethyl acrylate system. These emulsion copolymerizationswere carried out in small reactors (1-2 L) with large heat removal rates. Therefore, the temperature of the reactor was readily controlled by using a constant-temperature bath. However, the heat removal rate per volume unit decreases during the scale-up from laboratory reactors to large-scale industrial reactors which have a limited capacity for heat removal. When a semicontinuous emulsion copolymerization is carried out following the optimal semistarved monomer addition strategy, a large amount of heat is generated at the beginning of the process because of the large monomer concentrations in the polymerization loci. If the rate of heat generated in the reactor exceeds the heat removal rate, the temperature of the reactor, and hence the polymerization rate, will increase. Consequently,the optimal monomer addition profile calculated at constant temperature will not lead to a homogeneous copolymer. In the present work,a method for the determination of the optimal monomer addition strategy under conditions in which the reactor has a limited capacity for heat removal is presented. This method is applied to the emulsion copolymerization of vinyl acetate (VAc or A) and methyl acrylate (MA or B) carried out in a laboratory reactor that has been transformed to reduce its capacity for heat removal. Optimal Feed Rate Profile When a reactor with limited capacity for heat removal is going to be used, the strategy envisaged by Arzamendi and Asua (1989) in which all of the less reactive monomer
plus some amount of the more reactive monomer are initially charged into the reactor cannot be readily used because of the large amount of heat generated at the beginning of the polymerization. Therefore, the reactor should initially be charged with a fraction of the less reactive monomer (VAc) plus some amount of the more reactive monomer (MA). Then, both monomers should be added at a time-dependent flow rate that ensures the formation of a copolymer of the desired composition. In order to calculate the amounts of monomers A and B that should be in the reactor to produce a homogeneous copolymer, the following constrainta should be taken into account:
(Kl - 1) + [(KI- U2+ ~ ~ A ~ E J G I ~ (1) &A 2rA (2) QR = R p ~ 6 m . J+ R P B ( - ~ B ) Equation 1 is the condition for constant copolymer composition, and (2) establishes that the rate of heat generation should be equal to a given heat removal rate, QR, which, for safety reasons, can be taken as a fraction of the maximum heat removal rate of the large-scale reactor. In (1)and (2) [Alp,and [BIp are the concentrations of monomers A and B, respectively, in the polymer particles; is the volume fraction of monomer i in the polymer particle; ui is the molar volume of monomer i; FA and rB are the reactivity ratios; RpA and RpB are the polymerization rates of monomers A and B, respectively; (-AHi) is the heat of reaction of monomer i; and Kl is given by [Alp [Blp
-=-=
+XUB
+:
(3) where YA is the desired molar fraction of vinyl acetate in the copolymer. Equations 1 and 2 should be solved together with the equilibrium equations and the overall material balances. The thermodynamic equilibrium equations are as follows: polymer particlesjaqueous phase (AG/RT)K = (AG/RT)%P
(4)
(AG/RT)g = (AG/R19bq aqueous phasejmonomer droplets
(5)
(AG/RT)p = (AG/RT)i
(6)
(AG/RT)bq = (AG/RF't
(7)
(AG/RT)iq = (AG/RT)i (8) where the partial molar free energies can be calculated using the equation proposed by Ugelstad et al. (1983). The overall material balances are
41 + +E + +f = 1 I#q
+
I##
+ +",s = 1
+i + +t + +i =1 @Vaq
+ #$VP + 4ivd = VA
(9) (10) (11) (12)
(13) #kqvaq + &Vd = VP
= V,l/4F
vw
(14) (15)
where Vaq, Vp, and v d are the volumes of the aqueous phase, monomer swollen polymer particles, and monomer
.~
1344 Ind. Eng. Chem. Res., Vol. 30, No. 6, 1991 Table I. Values of the Parameters Used in the Simulation (Temperature 60 "C) 2.09 x 10s 2.30 X l@ k*, kpBB, k,, k-t. cma mol-' 9.50 x 109 2.9 X 1O'O kU, kmB,b cm9 mol-' s-l 5.78 X10" 0.6 ki,' s-'; f XA~X , B ~ X, A B ~X B A ~ d XwAt XwB
(1 - m d , (1 - mB,), (1 - m d (1 - mBA) d (1 - mAp), (1 - mBp)i (1 - %A), (1 - m w d d
x y XBpBy XApB, XbpA' u,
dyn cm-'
(-MA)!
(-MB)'
dpd, nm; N d ,particles cmd of water UA,
UB? pPh
3.2 8.65 0.63 1.0 0.38 4.0
8.8 x 104 151.5 93.17
2.97 4.37 0.32 1.0 0.507
7.8 x 104 2.2 x 1014 90.15
23.00 X l@
2.32 X l@
-0,139
-0.126
-0.098 -1.703 0.706
0.0951 -0.471 0.398
1.205
Matheson et al., 1951; Mayo et al., 1948; Walling, 1957. *Walling, 1957; Eastmont, 1976; Brandrup and Immerfut, 1975. Hakoila, 1963. dugelstad et al., 1983. eIruin and Iriarte, 1987. 'Gardon, 1968. SJoshi, 1963, hBrandrup and Immerfut, 1975, Matheson et al., 1951.
droplets, respectively; VA, VB, and .Vware the volumes of A, B, and water, respectively; and 4; is the volume fraction of component j in phase i. Equations 1, 2, and 4-15 are a system of 14 nonlinear algebraic equations with 14 unknowns, namely, &, &, &, 4iq, 4iq,4tq, &, $$, 4& vaq, VP, v d , VA, and VB. The solution of this system gives the volume of monomers A and B that should be at any time in the reactor in order to obtain a copolymer of the desired composition at the maximum rate allowed, i.e., under conditions in which the reactor temperature can be controlled. Note that this solution is given in terms of the amount of copolymer ( Vpd) and water ( Vw). It should be pointed out that droplets are only present in the reactor for large values of QR,i.e., when most or all of the less reactive monomer can be initially charged into the reactor. Otherwise, no droplets are present in the reactor and their corresponding terms in (4)-(15) should be neglected. The volume of copolymer varies during polymerization as follows: (16) dVpl/dt = (RPAP~A + RPBPmB)/PP where P~ is the molecular weight of monomer i and pp the copolymer density. The polymerization rate of monomer i is
As an example of application of this method, let us consider the simulation of the monomer addition profiles for the production of a 50/50 homogeneous copolymers by means of a seeded emulsion copolymerization of vinyl acetate and methyl acrylate in a 14-m3jacketed reactor using neat monomer addition. The values of the parameters involved in the calculation are given in Table I. For this system, Arzamendi and Asua (1990) found that the average number of radicals per particle can be calculated by using the pseudobulk equation:
where f is the efficiency factor for initiator decomposition, kI is the rate constant for initiator decomposition, and k, is the average termination rate coefficient given by where k, = (k-PA2
2 k d ~ Pk t~d B 2 ) g
(25)
k, is the termination rate coefficient and the gel effect factor, g, was found to be as follows (Anamendi and Asua, 1990):
g = 4.52
X
- (5.24
X 10-2)4f
- (1.14
X
+
(2.20 x 10-2)4f? (26)
where NA is the Avogadro's number and Pi is the timeaverage probability of finding a free radical with ultimate unit of type i. These probabilities are given by (18)
where k, is the propagation rate constant. The total amounts of monomers A and B added into the reactor at any time are given by
41 > 0.3 Note that equal dependence of all of the termination rate constants on 4: was assumed. In addition, it should be pointed out that although the initiator decomposes in the aqueous phase, in (24) it was assumed that no termination in the aqueous phase occurred. Nevertheless, the errors associated with this assumption are compensated by the use of (26). The concentration of initiator is given by Z2 = Zz0 exp(-kIt) (27) The heat removal rate is as follows: QR = UA,AT
where the first term of the right-hand-side member of these equations accounts for the free monomer and the second accounts for the amount of monomer incorporated into the copolymer. From these total amounts, the time-dependent feed rates of monomers A and B can be calculated as follows: QA = d V ~ ~ / d t (22) QB = d V ~ ~ / d t (23)
(28)
where U is the overall heat transfer coefficient,A, is the heat-transfer surface area, and AT is the temperature driving force. The overall heat transfer coefficient was assumed to be equal to the convection coefficient from the jacket wall, h, that for six-bladed impellers in unbaffled reactors without cooling coils is given by (Nagata, 1975)
Ind. Eng. Chem. Res., Vol. 30, No. 6,1991 1345 Table 11. Geometric Characteristics of the Simulated Reactor D 236 cm b/D 0.15 H 315 cm d/D 0.33 n 200 rpm C/H 0.5
-
0.016
n L
I
0 0
(0
t
c 0
0.8
2
i
i
0.4
u) I
>
0.2
#?E u c (I)
2
i! 0.000L 0
I
1000
1500
Time (min) Figure 2. Time evolution of heat removal rate for the simulated large-scale reactor.
0.0
0.0 0.1
I
500
0.2
0.3
0.4 0.5
0.6
4
0.7
n
b
Solid content
02
Figure 1. Dependence of latex viscosity on emulsion solids content wed for simulation.
where D is the diameter of the reactor, d is the diameter of the impeller, k is the thermal conductivity of reaction mixture, n is the impeller revolutions per unit of time; p is the density of the reaction mixture, p is ita viscosity, is the viscosity at the wall, b is the impeller blade width; C is the impeller distance from the bottom of the reactor, and H is the liquid depth. The values of the geometric characteristics of the simulated reactor are given in Table 11. In addition, a temperature driving force of 4 "C was taken and it was assumed that the viscosity of the reaction mixture depended on the solid contents as in Figure 1. Since neat monomer addition was used, the solid content increased during polymerization and, hence, the rate of heat removal decreased. In order to calculate the monomer addition profile, (16) was integrated by using (l),(21, and (4)-(15) to calculate the concentrations of the monomers in the different phases and (24)-(27) to calculate il. In addition, Q R was determined by means of (28), (291, and Figure 1. The time evolution of the heat removal rate is given in Figure 2. The time evolutions of the total amounts of both monomers added into the reactor were calculated by using (20) and (21). From these data, the time-dependentfeed rates of monomers A and B presented in Figure 3 were calculated by using (22) and (23). The decreasing feed rate profiles are due to the decrease of the heat removal rate as the solids content increased. After some time (about 1150 min in the simulation), all of the less reactive monomer has been added into the reactor. Afterward, the approach proposed by Arzamendi and Asua (1989,1990) for the calculation of the feed rate profile of the more reactive monomer was applied.
* 0
* n
0 '
I;5
a; E n
Y
I
0
500
I
1000
1500
Time (min) Figure 3. Time-dependent feed rate profiles for vinyl acetate (m) and methyl acrylate ( 0 )for the simulated large-scale reactor.
materials were used as received. Distilled and deionized water (DDI) was used throughout the work. All polymerizations were carried out in the 2-L reactor equipped with a stainless steel stirrer, reflux condenser, sampling device, and inlet system for nitrogen. Figure 4 depicts the schematic diagram of the experimental system. In order to simulate the thermal characteristics of an industrial reactor, the jacket of the reactor was isolated and a small coil placed inside of the reactor was used for heat transfer. In order to determine the heat-transfer coefficient, the temperature of the constant-temperature bath was fixed at a given value (i.e., 60 "C). Then, the reactor was charged with a known amount of cold water and the temperatures of the coil as well as that at the entrance (TI)and exit (Tz) of the reactor (T)were monitored. The heat balance for this system is as follows:
Experimental Section
Monomers methyl acrylate and vinyl acetate were distilled under reduced pressure of dry nitrogen. The purified monomers were stored at -18 "C until use. The rest of
where U is the overall heat transfer coefficient, A, is the
1346 Ind. Eng. Chem. Res., Vol. 30,No. 6, 1991
r.T-d-l
Constant temp.
0
~~
Figure 4. Schematic diagram of the experimental system. Table 111. Recipe Used for the Seed Latex methyl acrylate vinyl acetate initiator: (NH4)2QZO8 buffer: NaHCOS surfactant: Aerosol MA-80 (C16HwO+Na) DDI water
300 g 300 B 1.19 g 1.79 g 13.50 g 1200 g
heabtransfer surface area, m is the mass of water charged into the reactor, C, is its specific heat, Q1is the rate of heat loss through surfaces other than that of the coil, and ATh is the logarithmic mean temperature driving force given by
UA, and Q1were determined from the slope and intercept, respectively, of the dT/dt vs ATh plot. The values of dT/dt were calculated by differentiation of the polynomial fit of the time evolution of the temperature of the reactor. Because the values of UA, depend on the volume of water charged into the reactor, different experiments were carried out using various amounts of water. It should be pointed out that although the overall heat transfer coefficient depends on the viscosity, the values of U calculated with water can safely used because in the range of solids content used in this work (
