Ind. Eng. Chem. Res. 1997, 36, 4243-4254
4243
PROCESS DESIGN AND CONTROL Nonlinear Control for Maximum Production Rate of Latexes of Well-Defined Polymer Composition Isabel Sa´ enz de Buruaga, Philip D. Armitage, Jose´ R. Leiza, and Jose´ M. Asua* Grupo de Ingenierı´a Quı´mica, Departamento de Quı´mica Aplicada, Facultad de Ciencias Quı´micas, Universidad del Paı´s Vasco, Apartado 1072, 20080 San Sebastia´ n, Spain
In this work, on-line strategies based on calorimetry were used to maximize the production of vinyl acetate/butyl acrylate latexes under safe conditions, maintaining simultaneously the copolymer composition of the polymer at predefined values. It was also shown that these strategies were able to avoid monomer accumulation in the reactor, and hence potentially dangerous thermal runaway situations, without any deleterious effect on the polymer composition, when a sudden inhibition was induced by deliberately adding a solution of hydroquinone. For this purpose, nonlinear model-based control strategies and conventional feedback controllers were used. Introduction Emulsion polymerization is currently an important polymerization technique used in industry to produce a great variety of polymers of multiple uses (e.g., paints, adhesives, coatings, binders). The importance of the emulsion polymerization process is that, because of its multiphase and compartmentalized nature, it offers the possibility of preparing polymers with unique properties that cannot be produced by other polymerization techniques. In addition, environmental regulations have led to the substitution of solvents-based polymers by waterborne latexes, further increasing the commercial importance of emulsion polymerization. From an industrial point of view, the main requirements to be fulfilled in any process leading to the production of a polymer latex are as follows: (i) Safety. The reactor temperature must be held within safe limits to avoid thermal runaways. In addition, violation of environmental regulations both in the plant environment and in the finished products must be avoided. (ii) Production rate. The current trends in industrial practice are concerned with the maximization of the product throughput, i.e., the optimization or reduction of batch (cycle) time in the reactor. (iii) Product properties. The required performance is determined by the end use properties such as viscosity, film-forming ability, tensile strength, flexibility, elasticity, toughness, and opacity among others. Finished products not meeting the required specifications must be discarded as waste or reprocessed at extra cost. In order to implement the process conditions that lead to the required specifications of safety, production rate, and product properties, it is necessary to develop suitable control strategies. To our knowledge, no control structure taking into account all the above-mentioned objectives has yet been formulated and implemented. However, during the last 3 decades, considerable efforts * To whom all correspondence should be addressed. Email:
[email protected]. Telephone: +34 43 216600 ext. 150. Fax: +34 43 212236. S0888-5885(97)00310-2 CCC: $14.00
have been devoted in developing and implementing control strategies to at least partially fulfill these objectives. Both open- and closed-loop (feedback) strategies have been developed. However, most of the control strategies were open-loop, based on mathematical models of the process or on extensive experimental work (Broadhead et al., 1985; Hamielec et al., 1987; Arzamendi and Asua, 1989, 1990, 1991; Arzamendi et al., 1993; Leiza et al., 1993; Van Doremaele et al., 1992; Schoonbrood et al., 1993; Canu et al., 1994; Gugliotta et al., 1995b). The reasons for using open-loop control strategies stem from the difficulties in developing robust and fast on-line sensors to measure either the end-use properties or related process variables of the latex (Chien and Penlidis, 1990; Hergeth, 1997); the lack of robust nonlinear feedback controllers to deal with the important nonlinearities arising in batch and semibatch emulsion polymerization processes (Bequette, 1991; Leiza and Asua, 1997); and the still limited knowledge of the mechanisms involved in emulsion polymerization (Gilbert, 1997; Van Herk, 1997; Tauer, 1997). Nevertheless, partial solutions of the generic problem have been attempted in closed-loop strategies by both computer simulations and real-time control strategies. Thus, feedback strategies for maximum production rate under safe conditions (Kozub and MacGregor, 1992; Sa´enz de Buruaga et al., 1997), polymer composition control (Guyot et al., 1981, 1984; Rios and Guillot, 1989; Oliveres et al., 1988; Leiza et al., 1992; Urretabizkaia et al., 1994; Kozub and MacGregor, 1992; Dimitratos, 1989; Dimitratos et al., 1989; Kravaris et al., 1989; Asua et al., 1995; Sa´enz de Buruaga et al., 1996), molecular weight distribution, and degree of branching (Kanetakis et al., 1985; Kozub and McGregor, 1992; Vega et al., 1995 a,b; Echevarrı´a, 1997) have been presented. All of these feedback control strategies were developed to control a specific polymer property but, in general, only that property was controlled without paying any attention to considerations such as safety and production rate. Only Kozub and McGregor (1992) treated (by computer simulation) the multivariable polymer quality control problem but without any additional consider© 1997 American Chemical Society
4244 Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997
Figure 1. Schematic of a jacketed stirred-tank calorimetric semibatch reactor.
ations of safety and maximum production. Their inferential nonlinear feedback control strategy was able to simulate successfully the simultaneous control of total conversion, instantaneous copolymer composition, and instantaneous weight-average molecular weight, in a styrene/butadiene semibatch emulsion polymerization. In this work, feedback control strategies are proposed to produce polymer latexes of vinyl acetate/butyl acrylate (VAc/BuA), taking into account considerations of both the safe maximum production rate and the polymer quality. The safe maximum production rate can be achieved if the heat generation rate is held at the safe maximum heat removal capacity of the reactor, and this basically means that the polymerization rate must be controlled. The property used to determine the quality of the polymer was the cumulative copolymer composition. The paper is organized as follows. First, in the Theory section, reaction calorimetry and its application to a commercial lab-scale calorimeter (RC1, MettlerToledo) are discussed; the estimation of the evolution of the film heat-transfer coefficient, hr, is explained, the use of calorimetric data to estimate conversion and copolymer composition is presented, the maximum production rate under safe conditions is discussed, the required conditions for preparing homogeneous copolymers are calculated, the control strategies developed are presented; and the constraints required to avoid thermal runaways are discussed. Second, experimental aspects are discussed. Finally, the validation of the proposed control strategy in real-time experiments aiming at maximizing the production of VAc/BuA latexes of different cumulative copolymer compositions under safe conditions is presented.
Fi, cpi, and Ti are the mass flow rate, specific heat capacity, and feed temperature, respectively, of the ith reactor feed; Qr is the heat generation rate due to chemical reaction; Qf is the heat flux across the reactor wall; Qs and Qc represent the heating due to stirring and the calibration heater, respectively; and Ql represents heat loss to the surroundings. The term on the left-hand side of eq 1 is known as the heat accumulated in the reactor. The heat of reaction, Qr, can be calculated from the other terms, if these can be determined with sufficient accuracy, this being the essence of heat flow reaction calorimetry. The largest of these terms is Qf, the heat flow from the reaction mixture to the reactor wall. Under steady-state conditions, Qf is given by the following equations in which all the temperatures can be measured:
Qf ) UA∆T
(2)
Qf ) Fcfcpcf(Tjout - Tjin)
(3)
where U is the overall heat-transfer coefficient, A is the transfer area, ∆T is the appropriate mean temperature difference, Fcf is the mass flow rate of the cooling fluid, cpcf is its specific heat capacity, Tjout is its outlet temperature, and Tjin is its inlet temperature. The term heat-flow calorimetry is used when Qf is calculated from eq 2, whereas in heat balance calorimetry, Qf is determined by means of eq 3. The RC1 equipment used in this work is a heat-flow calorimeter; namely, Qf is calculated from eq 2. The difficulty of using eq 2 (and also eq 3) is that, under non-steadystate conditions, it is not sufficiently accurate due to accumulation of heat in the reactor wall. This is particularly so when lab-scale calorimetric reactors are used, because of the significant amount of heat that can be accumulated in the reactor wall. In the RC1 calorimeter, the jacket fluid mass flow rate is so high that Tjout = Tjin and, under these conditions, eq 2 can be rewritten as
Qf ) hrA(Tr - Twx)0)
where hr is the film heat-transfer coefficient between the reaction mixture and the internal wall of the reactor jacket, whose temperature is Twx)0. In this work, Twx)0 is calculated by solving the following equation for onedimensional heat flow through the reactor wall
Theory Calorimetric Measurements. If a perfectly mixed semicontinuous reactor is considered and the heats due to dissolution and vaporization are neglected, the heat balance of the reaction medium is (according to Figure 1)
(cpins +
∑j
mjcpj)
dTr ) dt
∑i Ficp (Ti - Tr) + i
Fwcpw
∂Tw ∂2Tw ) kw ∂t ∂x2
(5)
with the initial boundary conditions
t)0
Tw(x) ) T0w(x)
x)0
-kw
Qr - Qf + Qs + Qc - Ql (1) in which cpins is the heat capacity of the reactor inserts (stirrer, calibration heater, measuring devices, etc.); mj and cpj are the mass and specific heat capacity, respectively, of the jth component in the reaction mixture; Tr is the temperature of the reaction mixture; t is time;
(4)
x ) dw
| | | | ∂Tw ∂x
-kw
x)0
∂Tw ∂x
(6)
) hr(Tr - Twx)0)
x)dw
) hj(Twx)dw - Tj)
(7)
(8)
where ρw, cpw, and kw are the density, specific heat capacity, and thermal conductivity, respectively, of the reactor wall, and hj is the film transfer coefficient
Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997 4245
between the heat-transfer medium and the outer reactor wall surface, whose temperature is Twx)dw. This approach differs from that of the commercial RC1 calorimeter, for which the following equation is used:
Qf ) UA(Tr - Ta)
(9)
Ta being an “apparent” jacket temperature, whose calculation method is not disclosed by the manufacturer of the equipment and that takes into account the nonequilibrium heat flow through the wall. The main drawback for the purposes of this work is that, in the RC1 control software, Ta is calculated accurately only at the end of the reaction, and hence eq 9 cannot be used for on-line calorimetric measurements. In order to determine on-line the heat released by polymerization, Qr, the remaining terms of eq 1 must be calculated. Ql is determined by filling the reactor with a nonreacting mixture and solving eq 1 in the steady state while maintaining the reactor under isothermal conditions. The term dTr/dt is calculated numerically on-line every 10 s. The heat due to stirring, Qs, was calculated using a nonreacting medium, and for the range of experimental conditions used during this work, it turned out to be negligible. Further details on the calculation of Qr can be found elsewhere (Sa´enz de Buruaga et al., 1997). Estimating the Evolution of the Film HeatTransfer Coefficient, hr. As shown in the earlier section, in this work Qr was calculated on-line by solving eq 1 at each sampling time. This requires that Qf be calculated and hence that hr be known at each sampling interval. The overall heat-transfer coefficient, U, and hence hr are determined by a number of factors, stirrer speed and viscosity being the most important for a given formulation. Since the stirrer speed is fixed during the polymerization, the effect of viscosity has to be measured in order to obtain an accurate value for hr, and consequently Qr. The viscosity of the reaction mixture for a nonseeded semibatch emulsion polymerization in which neat monomer is added varies from a few centipoise for the initial charge (initiator plus surfactant solution) to several poise for a completely converted latex at the end of the polymerization. The viscosity mainly depends on the solids content and, less strongly, on the particle size distribution (PSD) (Krieger, 1985). The commercial calorimeter used in this work, RC1 (Mettler-Toledo), does not allow a continuous estimation of hr or U to be obtained on-line (although Carloff et al. (1994) have reported a temperature-oscillating calorimeter where hr can be estimated on-line). Only the initial and final values of U (or hr) can be measured accurately by a calibration procedure. Therefore, to obtain the evolution of U, previously prepared latexes of different PSDs and solids contents were used to estimate the dependence of U on these variables. It was found that, for the range of PSDs studied, U (hr) only depends on the solids content. This means that, for a particular semicontinuous process, the curve U vs conversion is quite insensitive and may be used as a master curve. The dependence obtained by this procedure for U on the solids content was
U ) U0 + (Ue - U0)Φpφ
(10)
where U0 and Ue are the average values of the overall heat-transfer coefficients at the beginning and end of
Figure 2. Evolution of the overall heat-transfer constant with solids content.
the experiment, respectively, φ is an adjustable parameter, and Φp is the latex solids content. Figure 2 presents a typical evolution of the overall heat-transfer coefficient as a function of solids content for the VAc/BuA latex used throughout this work. Estimating Conversion and Copolymer Composition from Calorimetric Data. The global polymerization heat, Qr, is related to the rates of reaction of the individual monomers by eq 11, assuming that the heats of cross-propagation are equal to those of homopolymerization (Urretabizkaia et al., 1994). RpA and RpB
Qr ) RpA(-∆HA) + RpB(-∆HB)
(11)
are the rates of polymerization of the two monomers A and B; and -∆HA and -∆HB are the enthalpies of polymerization of monomers A and B, respectively. For a small time interval ∆t, eq 11 can be rewritten as
Qrt-1 + Qrt 2
)
At-1 + ∆A - At (-∆HA) + ∆t Bt-1 + ∆B - Bt (-∆HB) (12) ∆t
where Qrt is the overall rate of heat generation at time t, At and Bt are the amounts of A and B present in the reactor at time t, and ∆A and ∆B represent the moles of monomers A and B, respectively, added into the reactor during time ∆t. Applying the well-known Mayo-Lewis equation for the instantaneous copolymer composition to an emulsion copolymerization system, the following equation can be obtained:
YA )
RpA ) RpA + RpB
rA + [B]p
[B]p [A]p [B]p2
(13)
rA + 2 + rB [A]p [A]p2
where ri is the reactivity ratio of monomer i and [i]p is the concentration of monomer i in the polymer particles. Taking small time increments, such that the concentrations of the monomers in the particles do not vary significantly, eq 13 can be rearranged to the following expression:
4246 Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997
At-1 + ∆A - At ) At-1 + ∆A - At + Bt-1 + ∆B - Bt [B]p rA + [A]p
[ ] [ ] [ ]
rA + 2
[B]p
[A]p
a
+ rB
a
2
[B]p
[A]p
(14)
a
where the subscript a refers to the average concentrations between time samples t - 1 and t. Assuming that the concentrations of the monomers in the different phases are the equilibrium values, the partitioning of the monomers can be readily calculated using the equilibrium equations and the overall material balances by means of an iterative algorithm (Omi et al., 1985; Urretabizkaia and Asua, 1994). Here, the equilibrium equations were written in terms of constant partition coefficients as follows: i Kj,k ) [i]j/[i]k
(15)
i where Kj,k is the partition coefficient of monomer i between phases j and k; and [i]j and [i]k are the concentrations of monomer i in phases j and k, respectively. Equations 12 and 14 are a set of two algebraic equations with two unknowns, At and Bt. Their solution gives the time evolution of the amount of free monomers A and B during the course of polymerization, from which the conversion and the cumulative copolymer composition are readily calculated:
Xcal )
A0 +
∫0t FA dt + B0 + ∫0t FB dt - At - Bt AT + BT
the present trajectory is only applicable to formulations leading to stable latexes. Nevertheless, limited progressive reactor fouling, commonly encountered in industrial systems, might be accounted for by occassional estimates of U. Note that the control strategy required for maximum production rate requires that the Qlimx vs conversion curve be followed, which basically means that the polymerization rate must be controlled. Preparation of Emulsion Copolymers of Homogeneous Composition. The ratio of the individual polymerization rates in the polymer particles, Cinst, is given by the expression
n j NT NA RpA ) Cinst ) RpB n j NT (kpABpA + kpBBpB)[B]p NA (kpAApA + kpBApB)[A]p
(18)
where, kpij is the propagation rate constant of a radical having an ultimate unit of type i with monomer j, pj is the time averaged probability of finding a free radical with an ultimate unit of type j in the polymer particles, n j is the average number of radicals per particle, NT is the total number of polymer particles, and NA is Avogadro’s constant. Equation 18 can be rewritten in terms of the reactivity ratios, as follows:
Cinst )
[A]p rA +1 [B]p [B]p
(19)
rB +1 [A]p (16)
∫0t FA dt - At YA,cumul ) t t A0 + ∫0 FA dt - At + B0 + ∫0 FB dt - Bt
From eq 19 the ratio β of the monomer concentrations in the polymer particles can be obtained by
A0 +
(17) where A0 and B0 are the initial amounts of monomers A and B in the reactor; FA and FB are the flow rates of monomers A and B at time t, and AT and BT are the total amounts of monomers A and B in the formulation, respectively. Maximum Production Rate under Safe Condition. The maximum polymer production rate can be achieved if the heat generation rate is held at the safe maximum heat removal capacity of the reactor. The safe maximum heat removal capacity of an isothermal stirred-tank reactor can be expressed as Qlimx ) RUA(Tr - Tcmin), where R is a safety coefficient (90% activity) was used as the emulsifier. Sodium bicarbonate (99.5%, Fluka) was the buffer, and potassium persulfate (98%, Merck) was the initiator. In this work the experimental setup utilized by Sa´enz de Buruaga et al. (1997) was used. A commercial reaction calorimeter (RC1, Mettler-Toledo) was used to carry out semicontinuous unseeded emulsion polymerizations. It was equipped with a 1.5 L stainless steel jacketed reactor vessel (HP60, Mettler-Toledo) fitted with the manufacturer’s standard anchor stirrer, platinum resistance thermometer, electrical calibration heater, and sampling tube. In addition to the RC1 computer, an external computer was attached to the installation to solve on-line the material and energy balances of the reactor as explained in the Theory section and to monitor and control the reaction according to the strategies previously described. The flow rates calculated by the controller were adjusted by the external computer every 5 s with a PI control algorithm, by using pumps and balances also connected to the computer. In addition, the heat balance was determined at 20 s intervals. The RC1 was operated in isothermal mode at a set reactor temperature of 60 °C. A separate thermostatically controlled bath was used to circulate water at 65 °C through the reactor lid to help maintain a stable baseline. Additional details related to the operational procedure used to carry out the experiments can be found elsewhere (Sa´enz de Buruaga et al., 1997). Experiments aiming at maximizing the production of vinyl acetate/butyl acrylate homogeneous copolymer latexes of 50/50, 60/40, and 70/30 molar composition were carried out using the proposed control strategies. Strategy I. Following the control algorithm outlined in Figure 3, the polymerization rate was controlled by means of a PI controller plus dead-time compensation and the copolymer composition by the NLA controller. Using this control strategy, homogeneous 50/50 (runs 1 and 2) and 60/40 (run 3) VAc/BuA copolymer latexes were obtained at the safe maximum production allowed by the reactor. The recipes used in those polymerizations are shown in Table 1 and the parameters required by the control strategy in Table 2. Strategy II. The schematic of this strategy is depicted in Figure 4. As shown, both control variables, Qlimx and [B]p/[A]p, are controlled by nonlinear model-based controllers. For this control scheme, the maximum production of VAc/BuA copolymer latexes of homogeneous copolymer composition of 50/50 and 70/30 (runs 4 and
Table 1. Recipe Used To Obtain VAc/BuA Copolymers amount (kg) component
50/50 (runs 1, 2, 4, 6, and 7)
60/40 (run 3)
70/30 (run 5)
H2O SLS K2S2O8 VAc BuA stirrer speed (rpm)
0.8200 0.0040 0.0020 0.1740 0.2590 300
0.8200 0.0040 0.0020 0.2070 0.2048 300
0.8200 0.0040 0.0020 0.2652 0.1684 300
Table 2. Parameters Used in the Reactionsa parameter
value
KAw,d (Gugliotta et al., 1995c) KBw,d (Gugliotta et al., 1995c) KAw,p (Gugliotta et al., 1995c) KBw,p (Gugliotta et al., 1995c) kpA (L/(mol s)) (Delgado, 1986) kpB (L/(mol s)) (Delgado, 1986) rA (Urretabizkaia et al., 1993) rB (Urretabizkaia et al., 1993) (-∆HA) (J/mol) (Brandrup and Immergut, 1989) (-∆HB) (J/mol) (Brandrup and Immergut, 1989) δ (runs of strategy II) Fimin (kg/s) (all runs) Fimax (kg/s) (all runs) ∆Fimax (all runs) tdel(s) (all runs) Mmax (mol/m3) (run 7)
0.027 0.001 35 0.0323 0.0208 2.35 × 103 1.26 × 102 0.037 6.36 89.5 × 103 78.2 × 103 2.3 0 1.33 × 10-4 0.7Fik-1 70 6000
a A ) vinyl acetate. B ) butyl acrylate. k ) current sampling point.
5 respectively) monomer ratios were sought. The recipes used in those runs are shown in Table 1. Thermal Runaway Control. In order to check if the proposed control strategies were able to deal with a sudden inhibition and hence avoid thermal runaway situations, two experiments were carried out with the recipe of run 4. In both experiments strategy II was used for control, but in the first experiment, run 6, only the constraints on the manipulated variables were implemented (eqs 30 and 31) and at approximately 30% of conversion (measured calorimetrically) an aqueous solution of hydroquinone was deliberately added into the reactor. In the second experiment, run 7, the additional constraint on the maximum level of free monomer (eq 32) was incorporated in the control algorithm and a solution of hydroquinone was also added at the same level of conversion. Results and Discussion Strategy I. Figure 5 shows the evolution of the heat generation rate for three polymerizations, two aimed at producing a 50/50 (runs 1 and 2) and the third a 60/40 (run 3) molar VAc/BuA homogeneous copolymer at the safe maximum production rate. The two repeated experiments (runs 1 and 2) were carried out to check the reproducibility of the control strategy. In all three reactions, a time delay of 70 s was used to take into account the diffusional limitations of the monomer in reaching the polymerization loci (the polymer particles). It can be seen that the predetermined profile of the heat generation rate (Qlimx vs conversion), which represents the fall in the rate of heat-transfer capacity of the reactor as its polymer content increases, was reasonably well tracked in all cases. Besides, as can be seen in Figure 6, copolymers of the desired composition were
4250 Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997
Figure 5. Evolution of the heat rate generated during the reaction to produce 50/50 (runs 1 and 2) and 60/40 (run 3) molar VAc/BuA emulsion copolymers, using strategy I.
Figure 6. Evolution of the cumulative VAc copolymer composition for runs 1-3.
Figure 7. Evolution of the on-line calorimetric-based conversion and off-line gravimetric conversion for runs 1 and 2.
obtained. Figure 7 shows the evolution of both the online calorimetric-based conversion and the off-line gravimetric conversions for runs 1 and 2. The excellent agreement between the on-line and off-line conversions gives an idea of the accuracy of the calorimetric measurement. It is also worth noting that the control strategy devised provides a good reproducibility even though unseeded experiments were carried out and the monomers contained inhibitors. Note that the polymerization rate fell rapidly in the three runs, after all the vinyl acetate had been added, leading to extremely low BuA feed rates at conversions greater than 60%. This effect is due to the very different
Figure 8. Evolution of the heat rate generated during the reactions to produce 50/50 (run 4) and 70/30 (run 5) molar VAc/ BuA emulsion copolymers, using strategy II.
Figure 9. Evolution of cumulative VAc copolymer composition for runs 4 and 5.
reactivity ratios of the two monomers, such that the relative polymerization rate falls rapidly with the molar ratio of VAc to total monomer in the polymer particles (Gugliotta et al., 1995b). Strategy II. Figure 8 shows the heat generation rate of two reactions aimed at producing 50/50 (run 4) and 70/30 (run 5) molar homogeneous copolymer latexes at the safe maximum production rate allowed by the reactor (Qlimx vs conversion curve). As can be seen, the model-based control algorithm works reasonably well in maintaining the desired trajectory for the maximum heat removal capacity. In addition, Figure 9 shows that the copolymers produced in both experiments have the desired cumulative copolymer composition. Thermal Runaway Control. Throughout the earlier sections it has been demonstrated that either the combination of a conventional PI controller with a nonlinear model-based controllers (strategy I) or nonlinear model-based controllers (strategy II) allow the production rate to be maximized and the cumulative copolymer composition to be controlled simultaneously. However, in order to check if these strategies are safe enough to avoid dangerous situations such as thermal runaways, the procedure used by Sa´enz de Buruaga et al. (1997) to check this point was followed, as described in the Experimental Section. Figure 10 shows the evolution of the heat rate generation during run 6. At approximately 30% conversion, hydroquinone was added into the reactor and, as expected, the heat rate and hence the polymerization rate dropped. Once the inhibitor had been consumed
Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997 4251
Figure 10. Evolution of the heat rate generated during a 50/50 molar VAc/BuA emulsion copolymerization (run 6).
Figure 13. Evolution of the VAc flow rate in run 7.
Figure 11. Evolution of the VAc flow rate in run 6.
Figure 14. Evolution of the cumulative VAc copolymer composition for run 7.
Figure 12. Rate of heat generation with a limit to the amount of free monomer in the reactor (run 7).
and the polymerization recommenced, the heat rate generation increased sharply, exceeding the maximum heat removal rate. Figure 11 shows the flow rate of the less reactive monomer, FA, as a function of time. It can be seen that monomer addition was not stopped after the hydroquinone shot but, on the contrary, the controller increased the flow rate in order to compensate for the difference in the heat rate generation and the heat removal limit. This caused monomer accumulation and, once polymerization recommenced, the release of heat well in excess of the limit for safe operation, as shown in Figure 10. The constraint on the feed rate did not avoid the undesired situation. Figure 12 shows experiment run 7, where an additional constraint on the total amount of free monomer in the reactor was imposed in the control scheme. As before, hydroquinone was added to the reactor at approximately 30% conversion, causing a rapid fall in
the heat rate generation. Nevertheless, in this case, once the polymerization recommenced, the heat rate evolved smoothly to the level of maximum heat removal rate and then evolved as in the experiments where hydroquinone was not added. Figure 13 shows the flow rate of VAc and, as can be seen, the addition of VAc did not stop, but the amount of VAc added did not surpass the limit included in the constraint, and consequently when polymerization recommenced, there was no accumulation of monomer in the reactor, and polymerization proceeded smoothly. Figure 14 shows the cumulative copolymer composition obtained during the process. A homogeneous copolymer of the required composition was formed during the process, demonstrating once again the good performance of the proposed control strategy. It should be pointed out that the limit placed on the amount of free monomer (Table 2) was set arbitrarily at a reasonable value. However, this value can be more accurately determined to avoid a maximum temperature rise under adiabatic conditions (Gloor and Warner, 1996). Conclusions Reaction calorimetry was used to monitor and control on-line a semicontinuous emulsion polymerization. VAc/ BuA polymer latexes of well-defined compositions (50/ 50, 60/40, and 70/30 molar ratios) at the maximum production rate allowed by a reactor with limited heat removal capacity were prepared. This basically required that the polymerization rate and the ratio of the monomer concentrations in the polymer particles were controlled simultaneously. Two control strategies were developed and successfully implemented in real-time
4252 Ind. Eng. Chem. Res., Vol. 36, No. 10, 1997
emulsion polymerizations of VAc/BuA. In the first, a conventional PI controller was used to control the polymerization rate and a nonlinear model-based controller controlled the polymer composition. By means of this strategy, 50/50 and 60/40 molar composition copolymer latexes were produced at the maximum production rate. In the second strategy, both polymerization rate and monomer concentration ratio in the polymer particles were controlled by means of nonlinear model-based controllers. The strategy was also successfully implemented to maximize the production of 50/ 50 and 70/30 molar composition VAc/BuA latexes. Finally, constraints on the manipulated variables (flow rates of the monomers) and on the state variables (free monomer in the reactor) were implemented in the second control strategy to check the robustness of the controller when a sudden inhibition was deliberately induced by adding a radical scavenger during an exothermic phase of the polymerization. It was shown that the limitation of the range of monomer flow rates as well as the rate of change of these flow rates does not guarantee a safe reaction when a deliberate addition of hydroquinone is introduced into the reactor. Under such deleterious conditions, the process was safely carried out only when the total amount of free monomer was also limited. Acknowledgment The financial support from the Diputacio´n Foral de Gipuzkoa and the CICYT (Grant TAP 95-1020) is greatly appreciated. I.S.B. acknowledges the fellowship from the Basque Government. P.D.A. acknowledges the fellowship from the Human Capital and Mobility program (Grant ERB4001GT931751). Nomenclature A ) heat-transfer area of the reactor reactor, m2 cpcf ) specific heat capacity of the cooling fluid, J/kg/K cpi ) specific heat capacity of the ith reactor feed, J/kg/K cpj ) specific heat capacity of the jth component in the reactor mixture, J/kg/K cpins ) heat capacity of the internal reactor fittings, J/K cpw ) specific heat capacity of the reactor wall, J/kg/K Cinst ) ratio of the individual polymerization rates in the polymer particles Fcf ) mass flow rate of the cooling fluid, kg/s Fi ) mass flow rate of the ith reactor feed, mol/s Fimax ) maximum level of Fi, mol/s Fimin ) minimum level of Fi, mol/s hr, hj ) film heat-transfer coefficients at the internal and external reactor walls, respectively, W/m2 K i0 ) initial amounts of monomer i in the reactor, mol it ) amount of monomer i in the reactor at sample time t, mol iT ) total amount of monomer i in the recipe, mol [i]j ) concentration of monomer i in the phase j, mol/L [i]p ) concentration of monomer i in the polymer particles, mol/L kpij ) propagation rate constant for radicals having terminal monomer group i with monomer j, L/(mol s) kw ) thermal conductivity of the reactor wall, W/(m K) Ki ) integral gain (eq 24) Kij,k ) partition coefficient of monomer i between phases j and k Kp ) proportional gain (eq 24) mj ) mass of component j in the reactor, kg Mmax(t) ) maximum of free amount of monomer present in the reactor, mol
n j ) average number of radicals per polymer particle NA ) Avogadro’s constant, /mol NT ) total number of polymer particles pj ) time-averaged probability of finding a free radical with an ultimate unit of type j in the polymer particles Qc ) heat rate produced by the calibration heater, W Qet ) difference between the extrapolated heat rate of reaction and the heat removal capacity, Qlimx, W Qf ) heat flux from the reactor through the reactor wall, W Ql ) rate of heat loss to the environment, W Qlimx ) safe maximum heat removal capacity of an isothermal stirred-tank reactor, W Qr ) overall rate of heat generation by polymerization, W Qrdel ) estimated rate of heat generated by the reaction, (eq 23), W Qrt ) overall rate of heat generation at time t, W Qs ) rate of heat produced by stirring, W ri ) reactivity ratio of monomer i Rp ) overall polymerization rate, mol/s Rpi ) rate of polymerization of monomer i, mol/s t ) time, s tdel ) delay time (eq 23), s Ta ) “apparent” temperature of the reactor jacket, K Tcmin ) lowest achievable reactor coolant temperature, K Ti ) feed temperature of the ith reactor feed, K Tj ) temperature of the reactor jacket, K Tjin ) inlet temperature of the cooling fluid, K Tjout ) outlet temperature of the cooling fluid, K Tr ) reactor temperature, K Tw ) temperature of the reactor wall, K U ) overall heat-transfer coefficient, W/(m2 K) U0, Ue ) average value of the overall heat-transfer coefficient at the beginning and at the end of the experiment, W/(m2 K) Vi ) volume of the ith phase, L wi ) mole fraction of monomer i x ) position within the reactor wall, m Xcal ) calorimetrically-estimated conversion YA, YB ) instantaneous copolymer composition of each monomer, A or B, in the reactor at each sampling time YA,cumul ) cumulative copolymer composition Greek Symbols R ) safety coefficient (
