Control of the Copolymer Composition in Suspension

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Ind. Eng. Chem. Res. 2004, 43, 7312-7323

Control of the Copolymer Composition in Suspension Copolymerization Reactions Fabricio Machado Silva, Enrique Luis Lima, and Jose´ Carlos Pinto* Programa de Engenharia Quı´mica/COPPE, Universidade Federal do Rio de Janeiro, Cidade Universita´ ria, CP 68502, Rio de Janeiro, 21945-970 Rio de Janeiro, Brazil

A new strategy for control of the copolymer composition is proposed for suspension copolymerizations. The control strategy assumes that one of the monomers is soluble in the continuous (aqueous) phase, as in the case of vinyl acetate (VAc)/acrylic acid (AA) copolymerizations. First, a hypothetical suspension copolymerization reaction is studied through simulation in order to illustrate the main features of the proposed control scheme. Then, the control strategy is implemented experimentally for actual control of the copolymer composition during VAc/AA suspension copolymerizations. The strategy is based on a detailed model developed to describe the process behavior and the AA partitioning between the organic phase and the aqueous phase, which is a fundamental point for the successful description of both conversion and copolymer composition. The proposed model was used to design monomer feed rate profiles in order to keep the copolymer composition constant throughout the batch. It is shown that the proposed control procedure is indeed able to keep the copolymer composition constant throughout the batch, despite the huge differences of reactivity between the monomer species. 1. Introduction One of the main challenges in the polymerization field is the production of copolymer materials with homogeneous chemical composition. Several polymer resins of industrial interest are obtained from monomers that present very different reactivities, which leads to the preferential polymerization of the most reactive monomer. For this reason, if a control procedure is not developed and implemented, produced copolymer chains are richer in the most reactive monomer in the beginning of the reaction and richer in the least reactive species at the end. The distinct monomer reactivities are the main factors that limit the production of polymer materials with uniform composition, if control strategies and monitoring techniques are not implemented in polymerization processes. Copolymerizations of vinyl acetate (VAc) and acrylic acid (AA) are typical examples of processes that present monomers with very different reactivities. For this reason, it is impossible to produce VAc/AA copolymers with uniform composition in batch reactors. However, semibatch emulsion processes have been developed for the production of VAc/AA copolymers with uniform composition.1 The development and implementation of a model that is able to predict the course of suspension copolymerizations properly may be of great importance for the correct determination of the best process operation conditions and attainment of the final product specifications. This may be particularly true when it is necessary to maintain the copolymer composition constant, as in the case of VAc/AA copolymers intended for biotechnological applications and production of medical pills. The control of the copolymer composition and of the composition distribution in copolymers is important for the proper understanding of the structure/property * To whom correspondence should be addressed. Fax: +5521-2562-8300. E-mail: [email protected].

relationship. Although the final average composition of the copolymer can be well-controlled in some cases, the control of the copolymer composition distribution (CCD) along the batch may be very difficult. Depending on the reactivity ratios of the monomers, different CCDs can be obtained. Besides, CCDs can vary very significantly along the polymerization because of changes of the monomer compositions in the reaction medium and because of the gel effect. Therefore, the development of techniques that allow for control of the copolymer composition is desirable.2 Despite the importance of suspension polymerization processes, very little has been made regarding control of the copolymer composition in these processes, and few practical mechanisms have been developed for effective control of the copolymer composition in suspension reactors. Semibatch operation policies have been developed and applied successfully for control of the copolymer composition in solution and emulsion polymerization processes. Normally, the main objective in these cases is to obtain copolymers with uniform composition throughout the batch through manipulation of the reaction rates of the monomers, through addition of Lewis acids,3 through manipulation of the reaction temperature,4 but most frequently through addition of fresh monomer feed during semibatch reactions.5-21 Thus, control of the copolymer composition almost always leads to the semibatch operation and development of monomer feed policies. In suspension reactors, monomers are normally insoluble in the suspending aqueous phase. Therefore, it is much more difficult to attain homogeneous compositions inside the suspension reactor during the continuous feed operation because the newly formed monomer droplets do not dissolve into the continuous phase. Besides, there is no guarantee that the fresh monomer feed will be distributed uniformly among the suspended droplets because mass-transfer limitations are much more severe in suspension polymerizations than in

10.1021/ie034267t CCC: $27.50 © 2004 American Chemical Society Published on Web 09/16/2004

Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7313

emulsion polymerizations, given the much larger sizes of polymer particles (and much smaller mass-transfer areas) in suspension reactors. Because the reaction rates are also much smaller in suspension reactors than in emulsion reactors, starved polymerization conditions are of no practical use in suspension polymerization processes. Additionally, it is not possible to avoid the formation of new polymer particles during fresh monomer feeding, especially when an initiator is dissolved in the fresh monomer stream to avoid the continuous drift of initiator concentrations along the batch. Because mass transfer occurs primarily through particle coalescence and breakage, the particle-size distribution and the reactor stability depend strongly on the monomer feed rates. Then, it is not unusual to observe uncontrolled coagulation of polymer particles during semibatch experiments. For all of the reasons discussed above, suspension copolymerizations are normally performed in batch at azeotropic conditions.22 In the present work, an alternative method is proposed for the open-loop control of the copolymer composition during suspension copolymerizations. The method is based on the manipulation of the phase equilibrium of the reaction system and depends on the availability of a process model that is able to describe monomer partitioning between the continuous and suspended phases. It is usually assumed that monomers are insoluble in the aqueous phase. However, in certain cases, at least one of the monomers is totally or partially soluble in water. In this case, at least one of the monomer species can be dissolved in the aqueous phase and partitioned between the organic and aqueous phases. Therefore, the aqueous phase can serve as a monomer reservoir, supplying monomer for the organic phase in controlled form during the reaction course. As an additional advantage, the proposed method would allow for adequate homogenization of the suspended droplets during the semibatch operation, given that the soluble monomer does not form new organic droplets in the medium. The proposed method is validated with actual experimental data obtained for VAc/AA suspension copolymerizations. It is shown that the proposed method allows for production of copolymers with uniform composition in suspension processes. 2. Theoretical Analysis The main objective in this section is to perform simulations in order to analyze the dynamic behavior of the reaction system for different values of the monomer partition coefficient, at distinct operation conditions. Besides, it is analyzed whether monomer feed policies can be developed in order to keep the copolymer composition constant along the course of the polymerization reaction. (Unless stated otherwise, all compositions are given in molar basis and copolymer compositions are defined as the molar fraction of monomer 1.) The study is divided into two main stages: in the first stage, it is assumed that the least reactive monomer is soluble in the aqueous phase, while in the second stage, it is assumed that the most reactive monomer is soluble in the aqueous phase. Simulations are accomplished for a hypothetical copolymerization system, where partition coefficients are allowed to vary. Kinetic parameters were selected for a typical VAc/ methyl methacrylate copolymerization, as described by Pinto and Ray23 and presented in Table 1. Assuming that the physical properties are essentially constant and that the terminal model can be used to

Table 1. Kinetic Parameters Used for Simulations of VAc/Methyl Methacrylate Copolymerizations Parameters kD ) 1.58 × 1015 exp(-30800/RT) s-1 f ) 0.8 R ) 1.987 cal/(mol K) ζ ) 120 I ) 0.04 mol/L VAc kP11 ) 3.2 × 107 exp(-6300/RT) L/(mol s) 9 kT11 ) 3.7 × 10 exp(-3200/RT) L/(mol s) r1 ) 0.015 Methyl Methacrylate kP22 ) 7.0 × 106 exp(-6300/RT) L/(mol s) kT22 ) 1.76 × 109 exp(-2800/RT) L/(mol s) r2 ) 20

describe the kinetic mechanism, the following process model can be written for the batch reaction performed at constant temperature:

Mass balance for monomer 1

(

)

(

)

kP22 dM1 ) -(kP11P + kP21Q)MI1 ) - kP11P + Q MI1 (1) dt r2 Mass balance for monomer 2

kP11 dM2 P + kP22Q MI2 (2) ) -(kP12P + kP22Q)MI2 ) dt r1 where kPij are the propagation constants, Mi is the total amount of monomer i in the reactor, and Mji is the amount of monomer i in phase j. Thus, it is possible to write

M1 ) MI1 + MII 1

(3)

M2 ) MI2

(4)

as monomer 1 is partitioned between the organic and aqueous phases as

MI1 ) KMII 1

(5)

where K is the partition coefficient. Following the usual quasi-steady-state assumption,

kS )

kP21 MI1 kP12 MI

2

Q)

(

)

K kP21 M1 K + 1 kP12 M2

(6)

)

2fkDI

1/2

(7)

kS2kT11 + 2ζkSxkT11kT22 + kT22 P ) kSQ

(8)

When eqs 1-8 are combined, it is possible to write

[

]

dM1 K K )k P+ k Q M1 ) dt K + 1 P11 K + 1 P21 kP22° kP11°P + Q M1 (9) r2°

(

)

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Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004

(

)

kP11° dM2 ) -(kP12P + kP22Q)M2 ) P + kP22°Q M2 dt r1° (10) kS )

kP21° M1 kP12° M2

(11)

where

kP11° )

K k K + 1 P11

kP12° ) kP12 kP21° )

K k K + 1 P21

kP22° ) kP22

(12) (13) (14) (15)

r1° )

K r K+1 1

(16)

r2° )

K+1 r K 2

(17)

Equations 9-17 clearly indicate that the suspension polymerization performed when one of the monomers is soluble in water is equivalent to the traditional suspension polymerization of a hypothetical reaction system, where the kinetic constants have been redefined. Similar equations were derived by Schuller24 for emulsion copolymerizations, when the monomers are partially soluble in the aqueous phase. Particularly, more homogeneous copolymers can be produced through manipulation of the partition coefficient and of the pseudo reactivity ratios. For instance, if r1 is large and r2 is small, differences can be reduced by using a small value for K. In other words, if monomer 1 is more reactive than monomer 2, composition drifts can be reduced by dissolving monomer 1 in the aqueous phase. In terms of the real thermodynamic partition coefficient (R) I

V K ) R II V

(18)

where Vi is the volume of phase i. The thermodynamic partition coefficient is given as the ratio between the concentrations of monomer M1 in the organic and aqueous phases:

R ) [M1]I/[M1]II

(19)

Therefore, K can be made equal to any desired positive value through manipulation of the volumes of the individual phases. However, a constant K value can only be obtained if R is approximately constant; otherwise, feed policies would have to be developed and implemented to keep K constant. For the sake of simplicity, K is assumed to be constant in this section, although this assumption will be relaxed in the following section. 2.1. Least Reactive Monomer Soluble in the Aqueous Phase. Simulations are performed first for the case where the least reactive monomer is soluble in the aqueous phase. The partition coefficient is allowed

Figure 1. Accumulated copolymer composition for different values of K and different initial copolymer compositions when the least reactive monomer is soluble in the aqueous phase (temperature ) 350 K): (A) M1 ) 10.0 mol, M2 ) 0.2 mol; (B) M1 ) 0.2 mol, M2 ) 10.0 mol; (C) M1 ) 5.6 mol, M2 ) 5.6 mol.

to vary in order to define the operation range (maximum and minimum values) where K influences the copolymerization process. Figure 1 shows that there is a range of K values where significant alterations can be detected for the composition of the produced copolymer (0.01 < K < 100). Similar behavior can be obtained for all analyzed feed conditions, indicating that outside these limits any decrease or increase of the partition coefficient does not alter the composition of the formed copolymer. This also indicates that appreciable modifications of the copolymer properties should only be expected if the partition coefficients can be manipulated between these well-established limits that guarantee the presence of significant amounts of monomer in the two phases. Figure 2 shows the dynamic composition profiles of the produced copolymer during the course of reaction. It was assumed that the initial copolymer composition was the same for all simulations performed with dif-


Figure 2. Accumulated copolymer composition for different values of K and equal initial copolymer compositions when the least reactive monomer is soluble in the aqueous phase (temperature ) 350 K): (A) initial copolymer composition ) 0.43; (B) initial copolymer composition ) 0.024. Table 2. Initial Conditions Used To Perform Simulations Presented in Figure 2Aa K M1 a

Initial Copolymer Composition Equal to 0.024 0.0001 0.001 0.01 0.1 1 100 28050 2810 283 30.84 5.6 2.84

1000 2.81

M2 ) 5.6.

Table 3. Initial Conditions Used To Perform Simulations Presented in Figure 2Ba K M1 a

Initial Copolymer Composition Equal to 0.43 0.0001 0.001 0.01 0.1 1 100 50050 5010 506 55.05 10 5.06

1000 5.01

M2 ) 0.2.

ferent values of the partition coefficient K. This way it is possible to analyze whether pronounced variations of the polymer composition occur as the partition coefficient changes. It can be clearly observed that the partition coefficient does not exert any relevant effect on the polymer composition. The slopes of the composition profiles practically do not change for the different values of K. Therefore, any attempt to control the copolymer composition would not be successful when the least reactive monomer is soluble in the aqueous phase. In a certain way, that could already be expected because the polymer is initially richer in the most reactive monomer. If the least active monomer is partially removed by the aqueous phase, this effect is expected to be magnified. Tables 2 and 3 show the initial amounts of monomer used to perform the simulations presented in Figure 2.

Figure 3. Accumulated copolymer composition for different values of K and different initial copolymer compositions when the most reactive monomer is soluble in the aqueous phase (temperature ) 350 K): (A) M1 ) 10.0 mol, M2 ) 0.2 mol; (B) M1 ) 0.2 mol, M2 ) 10.0 mol; (C) M1 ) 5.6 mol, M2 ) 5.6 mol.

It is observed that smaller values of the partition coefficient demand larger amounts of the least reactive monomer in the beginning of the reaction, to meet the initial specification of the copolymer composition. Low K values are not desirable when the least reactive monomer is soluble in the aqueous phase, because very large volumes of the reaction medium would be required, leading to infeasible polymerization conditions. 2.2. Most Reactive Monomer Soluble in the Aqueous Phase. As in the previous section, simulations are performed to analyze the influence of the partition coefficient on the system behavior when the most reactive monomer is soluble in the aqueous phase. Figure 3 shows the evolution of the accumulated copolymer composition for different values of K and different initial conditions. It can be observed once more that copolymer composition profiles change very significantly when K values are allowed to vary within the range 0.01 < K < 100. Outside this interval, modifica-

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As observed previously, when the partition coefficient is small, large amounts of the soluble monomer are required in the aqueous phase. Thus, high values of K are desirable, because the polymerization reaction can be driven with smaller amounts of the most reactive monomer in the aqueous phase. 2.3. Control of the Copolymer Composition. On the basis of the previous results, it is assumed that the most reactive monomer species is soluble in the aqueous phase and that the copolymer composition can be controlled through the addition of the soluble monomer into the reaction medium. Therefore, a monomer feed policy is sought to keep the copolymer composition constant throughout the batch. It is assumed that the additional amount of monomer can shift the position of the thermodynamic equilibrium while maintaining the copolymer composition in the specified range. The balance equations that describe the polymerization process can be written as

Mass balance for monomer 1

[

]

dM1 K kP22 K Q M1 + F1 )kP11P + dt K+1 K + 1 r2 Mass balance for monomer 2

(

)

kP11 dM2 )P + kP22Q M2 dt r1 Figure 4. Accumulated copolymer composition for different values of K and equal initial copolymer compositions when the most reactive monomer is soluble in the aqueous phase (temperature ) 350 K): (A) initial composition ) 0.32; (B) initial composition ) 0.91. Table 4. Initial Conditions Used To Perform Simulations Presented in Figure 4Aa K M1 a

Initial Copolymer Composition Equal to 0.32 0.0001 0.001 0.01 0.1 1 100 995.8 99.7 10.06 1.006 0.2 0.101

1000 0.1

M2 ) 10.

K M1 a

[

]

dp1 K kP22 K Q M1 ) kP11P + dt K+1 K + 1 r2

(22)

Mass balance for incorporated monomer 2

(

)

kP11 dp2 P + kP22Q M2 ) dt r1

(23)

where F1 is the feed rate of monomer 1. The remaining variables are as defined before. uP, the instantaneous copolymer composition, can be defined as

[

]

K kP22 K Q M1 kP11P + dp1 K+1 K + 1 r2 ) (24) uP ) dp2 kP11 P + kP22Q M2 r1

1000 2.8

M2 ) 5.6.

tion of K does not have an appreciable influence on the polymer composition. Figure 4 shows dynamic profiles for the accumulated copolymer composition, when the initial copolymer composition is the same, for different values of K. It can be observed that significant variations of the copolymer composition occur along the reaction course in all cases, in the range of interest of K. Therefore, it seems that the partition coefficient can be manipulated in order to modify the copolymer composition and to generate a composition control strategy, when the most reactive monomer is partitioned between the aqueous and organic phases. Tables 4 and 5 show the initial amounts of monomer used to perform the simulations presented in Figure 4.

(21)

Mass balance for incorporated monomer 1

Table 5. Initial Conditions Used To Perform Simulations Presented in Figure 4Ba Initial Copolymer Composition Equal to 0.91 0.0001 0.001 0.01 0.1 1 100 27970 2800 282.5 30.77 5.6 2.83

(20)

(

)

which leads to

[

] (

K K kP22 kP11P + Q M1 K+1 K + 1 r2 kP11 P + kP22Q M2 ) 0 (25) uP r1

)

When eqs 6-8 are inserted into eq 25, it is possible to write the following equation:

(K K+ 1) k 2

2

P11kP21M1

+

(K K+ 1)k

P12kP21(1

- uP)M1M2 -

uPkP12kP22M22 ) 0 (26)


Figure 5. Monomer feed rate profiles required to maintain the copolymer composition constant and equal to 0.33 (temperature ) 350 K).

If one defines

Ξ) Λ)

(K K+ 1) k 2

P11kP21

)

(K K+ 1) k

kP22

2

P11

r2

(27)

K k k (1 - uP) ) K + 1 P12 P21 K kP11 kP22 (1 - uP) (28) K + 1 r1 r2 σ ) uPkP12kP22 ) uP

kP11 k r1 P22

(29)

then eq 26 can be written as

ΞM12 + ΛM1M2 - σM22 ) 0

(30)

To keep uP constant along the batch, eq 30 must be regarded as an algebraic constraint. When eq 30 is derived with respect to time, the following equation can be written:

(

)

2σM2 - ΛM1 dM2 dM1 ) ) dt 2ΞM1 + ΛM2 dt

(

-

)(

)

2σM2 - ΛM1 kP11 P + kP22Q M2 (31) 2ΞM1 + ΛM2 r1

When eqs 20 and 31 are combined, it is possible to write the following control law:

F1 )

[

]

K K kP22 kP11P + Q M1 K+1 K + 1 r2 2σM2 - ΛM1 kP11 P + kP22Q M2 (32) 2ΞM1 + ΛM2 r1

(

)(

)

Equation 32 indicates how the monomer feed rate must vary along the reaction time in order to keep the copolymer composition constant, as a function of the kinetic and thermodynamic properties of the system and of the desired copolymer composition. Therefore, at least in theory, it is possible to control the copolymer composition during suspension copolymerizations if the most reactive monomer is soluble in the aqueous phase.

Figure 6. Accumulated copolymer composition for feed rate profiles of Figure 5. (Simulations performed with the different K values led to the same copolymer composition profiles.)

Figure 5 shows how the monomer feed rate must vary in order to maintain the copolymer composition constant and equal to 0.33 for different values of the partition coefficient. A slow decrease of the feed flow rates can be observed along the reaction course. This is due to the consumption of the least reactive monomer species in the organic phase. As observed in eq 24, when M2 diminishes, M1 has to diminish as well in order to keep uP constant. Figure 5 also shows pronounced variations of the feed flow rates with the value of K. This is because the amount of M1 in the organic phase, where reaction takes place, depends strongly on the partition coefficients. Obviously, to guarantee that the feed policy is feasible, it is necessary that F1 be positive along the whole batch. For the studied conditions, this can be accomplished for K values above 0.05, which means that the operation would not be feasible when K is too low. As shown in Figure 6, the copolymer composition can be, in fact, maintained at the desired setpoint value with the proposed control strategy in a wide range of K values. (This is why the simulations performed with the different K values led to the same copolymer composition profiles.) 3. Experimental Study There is a growing interest in the production of VAc/ AA copolymers for use in biotechnological and medical applications. For practical reasons, these applications require that VAc/AA copolymers present uniform composition and large average molecular weights. Production of VAc/AA copolymers in solution leads to resins with relatively low molecular weights. Production of VAc/AA copolymers in emulsion leads to significant AA polymerization in the aqueous phase and difficult control of the copolymer composition. Therefore, it seems that VAc/AA copolymers should be produced in suspension reactors. The interesting feature in this case is that the most reactive monomer (AA) is completely soluble in the aqueous phase, while the least reactive monomer (VAc) is essentially insoluble in the aqueous phase when the aqueous phase contains small amounts of AA.25,26 (As shown experimentally,25,26 the addition of AA to the aqueous phase causes the very significant reduction of the aqueous VAc solubility within the temperature range where polymerizations are normally performed.) On the basis of the results presented previously, it may be possible to derive and implement a monomer feed policy to keep the copolymer composition constant throughout the batch and simultaneously produce poly-

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Figure 7. VAc/AA suspension copolymerization: (9) experimental conversion; (b) experimental copolymer composition; (s) Silva et al.;25 conversion and composition; (- - -) this work; conversion and composition. Initial AA molar composition: (A) 2.5%; (B) 5%; (C) 10%; (D) 20%.

mer resins of large molecular weights. This is indeed possible, as shown in the following paragraphs. In this section, new experimental and theoretical results are presented for the VAc/AA copolymerization in suspension. The experimental procedure and analysis are the same as those presented by Silva et al.25 and are omitted here to avoid repetition. The control of copolymer composition in suspension is performed as described in the previous section, through feeding of monomer into the reaction medium during the polymerization. The equations that describe the suspension copolymerization process can be written as

Mass balance of incorporated monomer 2 (AA)

[

(33)

Mass balance of monomer 1 (VAc)

(

)

dM1 MI2 ) -(kP11PI) MI1 + dt r1 Mass balance of monomer 2 (AA)

[

MI2

dM2 ) -(kP11PI) + dt r1

]

r2 (MI2)2 r1 MI 1

(34)

kP11PI )

(

)

(37)

( )

I r2 MI2 1 1 1 r2 M2 + 2ζ + ψ1 (ψ1ψ2)1/2 r1 MI1 ψ2 r1 MI1

ψi )

kPii2 kTii

kPii02 ) g(T,xM) kTii0

i ) 1, 2

2

(38)

(39)

In the VAc/AA copolymerization system, it is fundamental to consider the solubility of AA in water because the amount of monomer available for polymerization inside the organic droplets is different from the total amount of monomer added into the reactor. The amounts of AA in the organic and aqueous phases can be given by

(35)

M2 1+K

(40)

MII 2 )

K M 1+K 2

(41)

where

Mass balance of incorporated monomer 1 (VAc) MI2 dp1 ) (kP11PI) MI1 + dt r1

x

2fkDII

MI2 ) + F2

1

where

Mass balance of initiator dI ) -kDII dt

]

dp2 MI2 r2 (MI2)2 + ) (kP11PI) dt r1 r1 MI

(36)

VII K)R I V

(42)


The partition coefficient of AA in the system AA/VAc/ water was studied by Silva et al.26 The partition coefficient was shown to be a very complex function of the aqueous phase AA composition and of temperature. An empirical model was built to describe available experimental data in the form of

[

R(T,[M2]II) ) A + B[M2]II +

C ([M2]II)2

]

-1

(43)

where the coefficients A-C are temperature-dependent adjustable parameters, described as

A ) -16.67 + 0.455(T - 273.15) 2.92 × 10-3(T - 273.15)2 (44) B ) 23.02 - 0.594(T - 273.15) + 3.96 × 10-3(T - 273.15)2 (45) C ) 0.317 - 9.02 × 10-3(T - 273.15) + 6.04 × 10-5(T - 273.15)2 (46) Equations 43-46 do not account for the presence of polymer. It is known that the AA partition coefficients tend to decrease when the polymer content in the organic phase increases,26 indicating that AA tends to remain in the aqueous phase when the organic phase contains polymer material. However, it is not clear how partition coefficients depend on the polymer content and on the copolymer composition. Because polymer effects are expected to become important only at the end of the batch,25 this effect has been neglected in this work. As performed in the previous section, the instantaneous copolymer composition (uP) can be defined as

uP )

dp1 ) dp2

(

(kP11PI) MI1 +

[

)

MI2 r1

]

MI2 r2 (MI2)2 (kP11P ) + r1 r1 MI I

1

Figure 8. AA feed rate profiles to maintain the copolymer composition constant: (A) pure AA; (B) 0.025 M solution of AA.

(47)

Equation 47 can be manipulated in order to derive the control law that keeps uP constant throughout the reaction course. However, different from that performed in the previous section, K cannot be assumed to be constant here. First, as shown in eqs 43-46, R is a strong function of the instantaneous aqueous phase composition and changes continuously during the batch. For this reason, it is convenient to write the control law as

F2 ) (kP11PI)

[

{ ()

Figure 9. AA feed rate profiles to maintain the copolymer composition constant and equal to 20% of AA in molar basis. The feed stream is a 0.025 M solution of AA.

MI2 r2 (MI2)2 + + r1 r1 MI

r2 MI2 1 + uP r1 MI 1

1

2

] }

r2 MI2 1 (1 - uP) - 2uP r1 r1 MI 1

(

MI1

)

MI2 + r1

dMII 2 (48) + dt

which is similar to eq 32, without assuming that K is constant.

A second important point regards the composition of the feed stream. The monomer feed profile described by eq 48 assumes that pure AA is fed into the reaction medium. However, solutions containing different concentrations of AA can be added into the reaction medium. This complementary amount of water may exert a strong influence on the stabilization of the reaction system and can be used to control the suspension viscosity. In this case, the addition of water avoids the increase of the polymer concentration, keeping the polymer holdup at safe levels and avoiding particle agglomeration.

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{[

]

Then, the control law must be written as

S)

1 (k PI) ℵ2 P11

() (

r2 MI2 1 + uP r1 MI 1

r2 MI2 1 (1 - uP) - 2uP r1 r1 MI

}

MI2 r2 (MI2)2 dMII 2 + + r1 r1 MI dt

(kP11PI)

1

Figure 10. Evolution of AA copolymer compositions during the batch and semibatch reactions.

2

1

)

MI2 + r1

MI1 +

0 < ℵ2 e 1 (51)

According to Silva et al.,25 some kinetic parameters of the VAc/AA copolymerization system, such as the cross-termination constant and the gel effect correlation, depend on the reaction conditions. From the point of view of composition control, the existence of a distinct group of kinetic parameters for distinct experimental conditions can disturb very significantly the implementation of the monomer feed rate profiles required to keep the copolymer composition constant. To derive a single set of kinetic parameters for the whole range of experimental conditions analyzed previously, it was assumed that both the cross-termination constant and the gel effect correlation depend on the system composition as

g(T,xM) ) exp{-146.8(vf - vf0) - 1076.3(vf - vf0)2} + Figure 11. Evolution of global monomer conversion during the semibatch reaction.

92.9(vf - vf0) (52)

[

]

M2 ζ ) 107.84 exp -63.64 M1(1 + φ) + M2

(53)

where vf is the free volume as defined by Silva et al.25 Figure 7 compares the results obtained with the parameters presented in eqs 52 and 53 and the ones obtained by Silva et al.25 It can be observed that the largest deviations are obtained when the AA concentrations in the initial reactor charge are large. In the other cases, deviations are not significant, and the model performance can be regarded as very good. In Figure 7 (and also in the remaining figures), the global conversion describes the overall polymer content as the ratio between the amounts of produced polymer and the total organic load (in weight) as Figure 12. MWD of the final batch (with 20% AA in the initial charge) and semibatch (constant polymer composition of 20% AA) polymer materials.

When the addition of water is considered, eq 35 can be written as

[

]

MI2 r2 (MI2)2 dM2 + + ℵ2S ) -(kP11PI) dt r1 r1 MI 1

(49)

where ℵ2 is the molar fraction of AA in the monomer feed stream. The amount of water can be computed as

dW ) (1 - ℵ2)S dt

(50)

xM )

MW1p1 + MW2p2 MW1(M1 + p1) + MW2(M2 + p2)

(54)

As a matter of fact, the inadequacy of eqs 52 and 53 for large AA concentrations does not represent a serious problem. This is because copolymer resins with high AA contents (above 35% in molar basis) present very low glass transition temperatures and are not of commercial interest.27 Besides, because AA is much more reactive than VAc, AA compositions are expected to be kept at low levels throughout the course of the copolymerization. Figure 8 shows monomer feed rate profiles that should be used to maintain the copolymer composition constant at different operation conditions. Feed rate profiles are smooth functions of time and are easy to implement in line.


Figure 13. Feed rate profiles as a function of the initiator composition (polymer composition of 20% AA): (A) evolution with time; (B) evolution with global conversion.

Figure 9 shows the feed rate profiles when an AA solution of concentration 0.025 M is used to maintain the copolymer composition constant and equal to 20% in molar basis. The feed rate profile was implemented in line. Figure 10 shows the results obtained for both the semibatch and batch reactions. In this last case, the initial AA content was equal to 20% in molar basis. It can be observed that it is indeed possible to obtain copolymer resins with uniform chemical composition throughout the reaction course if the proposed control scheme is implemented, despite the very different monomer reactivities. Very similar results can be obtained for different AA copolymer compositions. Figure 11 shows experimental and simulated global monomer conversions for the semibatch experiment, intended to keep the copolymer composition constant and equal to 20% of AA in molar basis. It can be observed that the proposed model tends to underestimate the global monomer conversion. This is probably due to the complex dependence of the kinetic constants with respect to modifications of the system composition, as explained before. Despite that, the copolymer composition is kept at the desired value, as shown in Figure 10. It is also important to say that the relatively low monomer conversions at the end of the batch are characteristic of VAc/AA suspension copolymerizations, are caused by strong diffusion limitations, as shown by Silva et al.,25 and are not related to the semibatch operation. Silva et al.25 showed that the molecular weight distributions (MWDs) of VAc/AA copolymers produced

Figure 14. Feed rate profiles as a function of the initiator efficiency (polymer composition of 20% AA): (A) evolution with time; (B) evolution with global conversion.

in batch reactions are normally very broad and tend to present bimodal behavior. This is because the reaction conditions change very significantly along the batch. Figure 12 shows that copolymer resins with uniform chemical composition obtained through semibatch operation present much narrower MWDs than copolymer resins obtained in batch reactions. Particularly, Figure 12 shows the disappearance of the bimodal behavior when the polymer is obtained through semibatch operation. The semibatch operation guarantees that the reaction is performed at much more stable reaction conditions, which also contributes to the improvement of the MWD of the final polymer material. Similar results are obtained in other conditions. Several simulations were then performed to verify how sensitive the semibatch operation can be to modifications of important process variables, such as the initiator concentration and the initiator efficiency, and to the cross-termination constant. Figures 13 and 14 show that the computed feed rate profiles are not very sensitive to fluctuations of the initiator feed concentration and of the initiator efficiency. This becomes clear when the feed rate profiles are presented as functions of the overall monomer conversion. Figures 13 and 14 show that the computed feed rate profiles can be easily tuned in line to remove perturbations of the initiator activity if the overall monomer conversion is monitored in line. In terms of monomer conversion, fluctuation of (10% in the activity level of the initiation system would require corrections of (2-3% of the feed flow rates. Figure 15 shows how

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sion during the reaction course. It can be observed that monomer conversions are quite sensitive to variations of this coefficient. As shown in Figure 16, it seems that ζ is somewhat smaller than assumed. This probably indicates that more fundamental kinetic studies are needed for the VAc/AA copolymerizations. 4. Conclusions Assuming that the most reactive monomer is soluble in the aqueous phase during suspension copolymerization reactions, it was shown both theoretically and experimentally (for the VAc/AA copolymerizations) that effective monomer feed rate policies can be designed and implemented in order to keep the copolymer composition constant and equal to specified levels throughout the reaction course. Because reaction conditions are kept more constant during semibatch reactions, the MWD of the final semibatch copolymer resins is also more uniform than that obtained during batch operation. The proposed control strategy was shown to depend weakly on the reaction activity, allowing for production of copolymer material with uniform composition in the presence of significant experimental and model inaccuracies. Acknowledgment

Figure 15. Semibatch responses to perturbations of the feed flow rates (polymer composition of 20% AA): (A) conversion behavior; (B) composition behavior.

Figure 16. Overall monomer conversion as a function of the crosstermination constant.

the copolymerization variables respond to variations of the rates computed with the model. It can be seen that, unless variations are unexpectedly large, the copolymer composition can be kept essentially constant throughout the semibatch reaction and equal to the desired value. This indicates that the proposed control scheme is very robust and can filter model and experimental inaccuracies efficiently. This probably explains why results presented in Figure 10 are so good even when the overall conversion trajectory is not modeled properly, as shown in Figure 11. Finally, Figure 16 illustrates how the cross-termination constant can influence the global monomer conver-

The authors thank Coordenaç aõ de Aperfeiç oamento de Pessoal de Nı´vel Superior (CAPES) and Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico (CNPq) for providing scholarships. The authors also thank Rhodia Brasil Ltda for supplying VAc and AA and Instituto de Macromolećulas (IMA) for the NMR analyses. Nomenclature f ) initiator efficiency Fi ) feed flow rate of species i g ) combined gel and glass effect correlation I ) mass of the initiator K ) partition coefficient kD ) kinetic constant for initiator decomposition kPij ) kinetic constant for propagation of radical i with radical j kPij° ) pseudo kinetic constant for propagation of radical i with monomer j kTij ) kinetic constant for termination of radical i with monomer j Mi ) mass of monomer i Mji ) mass of monomer i in phase j MWi ) molecular weight of monomer i P ) total concentration of living radicals of species 1 Q ) total concentration of living radicals of species 2 ri ) reactivity ratio of monomer i ri° ) pseudo reactivity ratio of monomer i t ) reaction time T ) reaction temperature Vi ) volume of phase i vf ) free volume of the reaction system vf0 ) free volume of the reaction system at zero conversion xM ) monomer conversion W ) concentration of water Greek Symbols R ) thermodynamic partition coefficient ζ ) cross-termination constant ℵ2 ) molar fraction of acrylic acid in the feed stream uP ) instantaneous copolymer composition

Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7323 Superscripts I ) organic phase II ) aqueous phase Subscripts 1 ) vinyl acetate 2 ) acrylic acid

Literature Cited (1) Tang, L. G.; Weng, Z. X.; Pan Z. R. Kinetic studies on emulsion copolymerization of vinyl acetate and acrylics in the batch process. Eur. Polym. J. 1996, 32 (9), 1139-1143. (2) Ramakrishnan, S. Well-Defined Ethylene Vinyl Alcohol Copolymers via HydroborationsControl of Composition and Distribution of the Hydroxyl Groups on the Polymer Backbone. Macromolecules 1991, 24, 3753-3759. (3) Xu, G. J.; Meng, Y. Z.; Song, H.; Lin, Q. S. Free-Radical Copolymerization in the Presence of Lewis-Acids. 1. Alternating Copolymerization of Vinyl-Acetate with Acrylic-Acid in the Presence of GeCl4 and BCl3. J. Polym. Sci., Part A: Polym. Chem. 1989, 27, 1817-1829. (4) Tirrell, M.; Gromley, K. Composition Control of Batch Copolymerization Reactor. Chem. Eng. Sci. 1981, 36, 367-375. (5) Gugliotta, L. M.; Arotç arena, M.; Leiza, J. R.; Asua, J. M. Estimation of Conversion an Copolymer Composition Semicontinuous Emulsion Polymerization Using Calorimetric Data. Polymer 1995, 36, 2019-2033. (6) Gugliotta, L. M.; Leiza, J. R.; Arotç arena, M.; Armitage, P. D.; Asua, J. M. Copolymer Composition Control in Unseeded Emulsion Polymerization Using Calorimetric Data. Ind. Eng. Chem. Res. 1995, 34, 3899-3906. (7) Buruaga, I. S.; Arotç arena, M.; Armitage, P. D.; Gugliotta, L. M.; Leiza, J. R.; Asua, J. M. On-line Calorimetric Control of Emulsion Polymerization Reactors. Chem. Eng. Sci. 1996, 51, 2781-2786. (8) Vieira, R. A. M.; Sayer, C.; Lima, E. L.; Pinto J. C. Detection of Monomer Droplets in a Polymer Latex by Near-Infrared Spectroscopy. Polymer 2001, 42 (21), 8901-8906. (9) Vieira, R. A. M.; Sayer, C.; Lima, E. L.; Pinto J. C. In-Line and In Situ Monitoring of Semi-batch Emulsion Copolymerizations Using Near-Infrared Spectroscopy. J. Appl. Polym. Sci. 2002, 84 (14), 2670-2682. (10) Vieira, R. A. M.; Sayer, C.; Lima, E. L.; Pinto, J. C. ClosedLoop Composition and Molecular Weight Control of a Copolymer Latex Using Near-Infrared Spectroscopy. Ind. Eng. Chem. Res. 2002, 41 (12), 2915-2930. (11) Choi, K. Y. Copolymer Composition Control Policies for Semibatch Free Radical Copolymerization Processes. J. Appl. Polym. Sci. 1989, 37, 1429-1433. (12) Arzamendi, G.; Asua, J. M. Copolymer Composition Control During the Seeded Emulsion Copolymerization of Vinyl Acetate and Methyl Acrylate. Makromol. Chem., Macromol. Symp. 1990, 35/36, 249-268. (13) Arzamendi, G.; Asua, J. M. Copolymer Composition Control of Emulsion Copolymers in Reactors With Limited Capacity for heat Removal. Ind. Eng. Chem. Res. 1991, 30, 1342-1350.

(14) Arzamendi, G.; Leiza, J. R.; Asua, J. M. Semicontinuous Emulsion Copolymerization of Methyl Methacrylate and Ethyl Acrylate. J. Polym. Sci., Part A: Polym. Chem. 1991, 29, 15491559. (15) Van Doremaele, G. H. J.; Schoonbrood, H. A. S.; Kurja, J.; German, A. L. Copolymer Composition Control by Means of Semicontinuous Emulsion Copolymerization. J. Appl. Polym. Sci. 1992, 45, 957-966. (16) Canu, P.; Canegallo, S.; Morbidelli, M.; Storti, G. Composition Control in Emulsion Copolymerization. I. Optimal Monomer Feed Policies. J. Appl. Polym. Sci. 1994, 54, 1899-1917. (17) Sayer, C.; Lima, E. L.; Pinto, J. C.; Arzamendi, G.; Asua, J. M. Kinetics of the Seeded Semicontinuous Emulsion Copolymerization of Methyl Methacrylate and Butyl Acrylate. J. Polym. Sci., Part A: Polym. Chem. 2000, 38 (2), 367-375. (18) Sayer, C.; Lima, E. L.; Pinto, J. C.; Arzamendi, G.; Asua, J. M. MWD in Composition Controlled Emulsion Copolymerization. J. Polym. Sci., Part A: Polym. Chem. 2000, 38 (7), 11001109. (19) Sayer, C.; Arzamendi, G.; Asua, J. M.; Lima, E. L.; Pinto, J. C. Dynamic Optimization of Semicontinuous Emulsion Copolymerization Reactions: Composition and Molecular Weight Distribution. Comput.-Aided Chem. Eng. 2000, 8, 457-462. (20) Sayer, C.; Arzamendi, G.; Asua, J. M.; Lima, E. L.; Pinto, J. C. Dynamic Optimization of Semicontinuous Emulsion Copolymerization Reactions: Composition and Molecular Weight Distribution. Comput. Chem. Eng. 2001, 25 (4-6), 839-849. (21) Sayer, C.; Arau´jo, P. H. H.; Arzamendi, G.; Asua, J. M.; Lima, E. L.; Pinto, J. C. Modeling MWD in Emulsion Polymerization Reactions with Transfer to Polymer. J. Polym. Sci., Part A: Polym. Chem. 2001, 39 (20), 3513-3529. (22) Cavalcanti, M. J. R.; Pinto, J. C. Modeling and Optimization of Suspension SAN Polymerization Reactors. J. Appl. Polym. Sci. 1997, 65, 1683-1701. (23) Pinto, J. C.; Ray, W. H. The Dynamic Behavior of Continuous Solution Polymerization ReactorssVII. Experimental Study of a Copolymerization Reactor. Chem. Eng. Sci. 1995, 36, 367375. (24) Schuller, H. Copolymerization in Emulsion. In Polymer Reaction Engineering; Reichert, K., Geiseler, W., Eds.; Verlag: Heidelberg, 1986; pp 137-145. (25) Silva, F. M.; Lima, E. L.; Pinto, J. C. Acrylic Acid/Vinyl Acetate Suspension Copolymerizations. 2. Modeling and Experimental Results. Ind. Eng. Chem. Res. 2004, 43, 7324-7342. (26) Silva, F. M.; Lima, E. L.; Pinto, J. C. Acrylic Acid/Vinyl Acetate Suspension Copolymerizations. I. Partition Coefficients for Acrylic Acid. J. Appl. Polym. Sci. 2004, 93, 1077-1088. (27) Pinto, J. C. Technical Report PEQ/COPPE/UFRJ, Rio de Janeiro, Brazil, 2001.

Received for review November 24, 2003 Revised manuscript received August 9, 2004 Accepted August 9, 2004 IE034267T

Control of the Copolymer Composition in Suspension

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