Monitoring and Control of Free-Radical Polymerizations Using Near

of the final product quality, process productivity, and security. The process is ... Online monitoring is essential in polymerization processes becaus...
0 downloads 0 Views 334KB Size
Download PDF
Ind. Eng. Chem. Res. 2004, 43, 7383-7391

7383

Monitoring and Control of Free-Radical Polymerizations Using Near-Infrared Spectroscopy Nida Sheibat-Othman,*,† Dominique Peycelon,‡ and Gilles Fe´ votte† LAGEP-Universite´ Lyon I, Baˆ t 308, 43 Blvd du 11 Nov 1918, 69622 Villeurbanne Cedex, France, and Coatex ZI Lyon Nord, 69727 Genay, France

A nonlinear geometric control is used to control the concentration of the monomer in solution polymerization processes. The concentration of the monomer is an important parameter in terms of the final product quality, process productivity, and security. The process is monitored using a near-infrared spectrometer that was calibrated using the partial least-squares optimization technique to estimate the concentration of the monomer in the reactor. The control strategy makes use of a high gain observer to estimate the reaction rate necessary in the control loop. The controller was implemented on an industrial pilot reactor during the solution polymerization of acrylic acid. 1. Introduction Online monitoring is essential in polymerization processes because the reaction is exothermic, rapid, and sensitive to small impurities. The nonreproducibility of the reaction makes it difficult to simulate it with an open-loop model. Some online information about the process is necessary to control the process, to obtain the desired polymer properties, and to optimize the process productivity. The monomer concentration in the reactor is one of the important process parameters to be controlled in order to ensure product quality and process security. On the one hand, the monomer concentration influences the reaction rate that determines the heat produced by the reaction. Therefore, the amount of monomer in the reactor must be optimized in a way that allows us to minimize the process time and at the same time to ensure the capability of the reactor cooling system to evacuate the heat produced by the reaction. On the other hand, the monomer conversion influences the polymer molecular weight and the polymer composition in polymerization processes involving more than one monomer. For these reasons, a control system of the monomer concentration is important. In offline monitoring of solution polymerizations, gravimetry is usually the most used technique to measure the monomer conversion. For online monitoring and control of polymerization reactions, several techniques have been developed. Kammona et al.1 presented a review of conversion, copolymer composition, and particle size monitoring. The existing online monitoring sensors can be divided into two groups. The first group consists of using a sampling system with sensors originally developed for offline use. For example, Ponnuswamy et al.2 presented a comparative study of some common techniques employed for online measurements of the polymer quality (densimeter, viscometer, size-exclusion chromatograph, and torque meter) in a batch reactor equipped with a sampling system. Budde * To whom correspondence should be addressed. Fax: 3304-72431699. E-mail: [email protected]. † LAGEP-Universite´ Lyon I. ‡ Coatex ZI Lyon Nord.

and Reichert3 used a densimeter and a viscometer to monitor the monomer conversion, the polymer solution viscosity, and the molecular weight in free-radical polymerizations. In this case, the polymer solution was pumped as a bypass through the sensors. Chien and Penlidis4 used an online densimeter to monitor the monomer conversion in continuous solution methyl methacrylate polymerization reactors. Cowley and Choi5 used online densimetry to monitor batch solution polymerizations and to control the polymer molecular weight by manipulating the reactor temperature. Barudio et al.6 used density data to monitor the monomer conversion in solution copolymerization processes. Karago¨z et al.7 used an online viscometer to monitor the polymer viscosity and molecular weight and to calculate the process optimal temperature profile. The refractive index also gives information about the reaction rate. Bahr and Pinto8 used the refractive index of solution polymerization reactions to evaluate the extent of reaction. Zaldivar et al.9 used refractive indexes to inline monitor the monomer conversion and the copolymer composition. Ultrasound propagation velocity measurements were also used to monitor the monomer conversion in a bulk polymerization reactor (see, for example, Cavin et al.10). There are, however, several limitations of the techniques involving an external circulating loop. The circulating pump may form bubbles in the loop, which disturbs the measurements. It is also necessary to maintain the loop at the reaction temperature in order to ensure good results. For these reasons, a very important effort is now applied to use inline probes. For instance, UV and fluorescence spectroscopy were used by Kim et al.11 to monitor solution and bulk polymerizations inline. Pekcan and Yilmaz12 used an online fluorescence probe to monitor the polymerization rate of methyl methacrylate and to detect the autoacceleration due to the gel effect. The most widely used online sensor over the past 30 years remains calorimetry in both safety studies and process optimization. Several references deal with maximizing productivity, estimating polymer properties, and controlling free-radical polymerizations using calorimetry (Tirrell and Gromley,13 Arzamendi and Asua,14 Gugliotta et al.,15 Buruaga et al.,16 Gloor and Warner,17

10.1021/ie049968k CCC: $27.50 © 2004 American Chemical Society Published on Web 10/07/2004

7384

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

and Sheibat-Othman et al.18). In most of these studies, an offline measurement of the monomer conversion, usually by gravimetry, is required in order to update the unknown process parameters such as the heattransfer coefficient between the reactor and the jacket. Samples are therefore withdrawn at discrete intervals in order to obtain these offline measurements. However, industrially, taking samples during the reaction is not preferable. Moreover, during the time interval where no samples are withdrawn, some error of estimation may be done, which may be important especially under a high reaction rate as at the beginning of the reaction. For this reason, a great effort is now made to implement spectral probes in industrial reactors. Infrared and Raman spectroscopy can now be used for inline monitoring of polymerization processes. Olinga et al.19 used online light-fiber coupled attenuated total reflectance (ATR)-transform near-infrared (NIR) transmission spectroscopy and ATR-Fourier transform midinfrared (FT-MIR) spectroscopy to monitor the solution polymerization of methyl methacrylate. Lousberg et al.20 used NIR spectroscopy to determine the monomer conversion in styrene bulk polymerization by performing multivariate calibration. The authors found that the estimations were not influenced by variations in the reaction temperature (75-85 °C) and in the polymer molecular weight distribution. Sasic et al.21 used both online FT-NIR transmission and FT-MIR spectroscopy to monitor the methyl methacrylate solution polymerization. The authors compared different chemometric approaches to estimate the concentration of the monomer and polymer. The multivariate curve resolution and the partial least-squares (PLS) methods gave good results with MIR spectral data. For NIR data, the best results were obtained with multivariate calibration. Cherfi and Fe´votte22 used NIR spectroscopy to monitor the methyl methacrylate concentration in solution polymerizations. Fontoura et al.23 used NIR spectroscopy to monitor and control simultaneously the monomer conversion and polymer molecular weight in solution polymerization of styrene. Raman spectroscopy was used by Van Den Brink et al.24 to monitor solution copolymerizations. Both univariate and multivariate approaches were tested and gave good estimations of monomer concentrations. The aim of this work is to monitor and control the concentration of acrylic acid (AA) in solution polymerization. The polymerization of AA is known to be very rapid and exothermic. Controlling the concentration of the monomer is therefore essential to ensure process security. Moreover, the concentration of the monomer in the reactor influences the product quality, mainly the polymer molecular weight. NIR spectroscopy is used for process monitoring. Nonlinear estimation and control techniques are implemented because of the nonlinearity of the process model. After a presentation of the system setup, a calibration model based on the NIR spectrum is developed to estimate the concentration of the monomer in the reactor. In the second part, a high-gain nonlinear estimator of the reaction rate is constructed for implementation in the control strategy. Finally, a nonlinear geometric control is developed to control the concentration of the monomer at every moment during the reaction.

Figure 1. Description of the NIR apparatus.

2. Experimental Setup The process studied in this work consists of a solution free-radical polymerization of AA. The reaction takes place in a metallic jacketed, well-mixed reactor of 30 L equipped with an internal reflux condenser. A stirrer equipped with a Rushton turbine is employed at a stirring rate of 150 rpm. Addition of initiators, monomer, and solvent to the reactor is done using four volumetric pumps that can be manipulated online. Four flowmeters give the flow rates of the pumps. The reactor temperature is measured using Pt100-Ω probes. Measurements of temperatures and flow rates are acquired and stored on a computer. The NIR transmission probe is immersed in the reactor and is connected through fiber optics to a FOSS NIRSystems industrial spectrometer. The spectrometer is composed of three main parts: a source lamp of incoherent light, a concave halographic grating, and a detector, as shown in Figure 1. The spectral data are acquired and processed by a second computer. The state observer and the control law described below are computed and applied using the same computer. Both computers are connected in order to exchange data. The reactor is initially charged with water, a small amount of initiator, and solvent (isopropyl alcohol), which plays the role of a chain-transfer agent during the polymerization. The ratio of water to solvent in this charge is 1.09%. This charge is then heated to 80 °C by circulating water vapor in the jacket. Monomer is then introduced using a pump at the flow rate calculated by the controller. The total amount of monomer is calculated in order to have a final solids content of 45%. The polymerization is initiated by a redox-type reaction. The initiators are therefore introduced using two different pumps at constant flow rates. Because the reaction is very exothermic, the reactor does not need to be heated but needs to be cooled during the reaction. Cooling the reactor is automatically done in an open-loop manner through the condenser, which allows the reactor temperature to be maintained around 80 °C by condensing the evaporated solvent (boiling point 83 °C). During model development, samples are withdrawn from the reaction medium and analyzed for the residual amount of AA by high-pressure liquid chromatography (HPLC). 3. Calibration of the NIR NIR spectroscopy has found wide-spread use in monitoring of polymerization processes because it has several advantages. First of all, the fiber optic inserted in an existing reactor is directly in contact with the reaction medium, which ensures rapid measurements

Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7385

Figure 2. NIR spectrum obtained at the beginning and at the end of a semicontinuous polymerization of AA (reaction time ) 2 h).

because there is no need for sample preparation. Fiber optics allow the spectrometer to be placed far away from the reactor while ensuring rapid and precise data transmission. Furthermore, a set of characteristics of the sample can be obtained from the same spectrum by developing different calibration models that can be transferred easily to other instruments. The quality of the results of the NIR analysis depends on a number of arguments. First of all, a change in the required properties must have an impact in the NIR region. The method used for offline measurements needed for calibration also plays an important role in the model development. Finally, the performance of the instrument has an impact on the quality of the estimation, and the mathematical treatment of the spectrum has to be adapted to the process. The NIR spectrum is the result of the energy absorbed or scattered by the molecules. The part of the energy absorbed by the molecules depends on the chemical and physical nature of the constituents, on their concentrations, and on the volume of transmission. Concerning the part of the energy scattered with partial penetration in the sample, the intensity of the reflection depends on the wavelength and on the surface of the particles in heterogeneous processes. For instance, the energy scattered is more important with little particles and with large wavelengths. This is why the intensity of the spectrum increases with large wavelengths. The NIR spectrum is therefore very rich in information about the analyzed product. However, wavelength overlapping renders the spectrum analysis difficult. Therefore, multivariable calibration methods, such as PLS and multiple linear regression, are necessary to obtain the required information. A software (Vision) was used for the spectrum treatment and model development. The spectrum was first corrected for reflection and normalized. Then its second derivative was used for model development. For model

derivation, the Savitsky-Golay algorithm was used. This algorithm is based on performing a least-squares linear regression fit of a polynomial of degree k over at least k + 1 data points around each point in the spectrum to smooth the data. The derivative of the spectrum is then the derivative of the fitted polynomial at each point. Spectral discrimination was done regarding the spectral distance from the center using the Mahalanobis distance that is measured in terms of standard deviations from the mean of the training samples. The Mahalonobis distance is known to be more sensitive to intervariable changes in the training data than the Euclidean distance because the Euclidean distance only measures a relative distance from the mean point in the group while the Mahalonobis distance takes into account the distribution of the points in the group. The calibration model was developed using the PLS technique with cross-validation to correlate the spectrum with the offline measurements of the concentrations of AA, obtained by HPLC. This technique was generally found to have a superior predictive ability than the principal component regression technique, especially for complex mixtures. In this method, the full spectrum is used to estimate the concentration; it comprises a single-step decomposition and regression, and the eigenvectors are directly related to constituents of interest rather than to the largest common spectral variations. The calibration used 290 data points and resulted in six factors. The calibration and validation errors were 2500 and 2700 ppm, respectively, and the determination coefficient was R2 ) 0.97. Figure 2 shows the difference between the spectrum obtained at the beginning of a classical semicontinuous polymerization of AA and that obtained 2 h later, at the end of the reaction. The main change in the spectrum during the polymerization is noticed between 1600 and 1900 nm. Figure 3 shows the coefficients of the model developed to estimate the concentration of the monomer. Validation of this model is shown in Figure 4 during a semibatch reaction where monomer and initiators are added in a semicontinuous way while solvent and water are completely introduced in the initial charge. It can be seen that the increase in the reaction temperature during the reaction, shown in Figure 5, does not affect the NIR measurements. Actually, the temperature profile is proportional to the reaction rate that might not be reproducible for processes with similar operating conditions because of experimental variations, such as inhibition. However,

Figure 3. Calibration of the concentration of AA. Model coefficients and calibration results.

7386

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

Figure 4. Evolution of the reaction temperature during a classical reaction (experiment 125).

rate (mol/s), kp is the propagation rate constant (cm3/ mol/s), and [R*] is the concentration of radicals (mol/ cm3). To apply a model-based controller to the process, an estimate of the reaction rate would be necessary. Using the measurement of the concentration of the monomer obtained by NIR analysis, the reaction rate becomes observable from eq 1. The concentration of radicals in the reactor [R*] can be estimated if kp is known. To estimate RP, it must be written as a state variable in an augmented system. The first state in this system must be a function of the process output NAA, measured by the NIR spectrometer. Because the dynamic of RP is unknown, it is represented by the unknown variable  as follows:

It is important to notice that NAA in system 2 is equivalent to that obtained by the material balance in eq 1. We notice also that the matrix A is negative. However, to construct a high-gain observer of RP, it should be positive. Therefore, a change of coordinates is required to put the system under a canonical form of observability. We propose the following change of coordinates:

rP ) -RP Figure 5. Validation of the model estimating the concentration of the monomer during a semicontinuous experiment (experiment 125).

variations in the reaction temperature do not exceed 4-5 °C during the reaction, which does not influence the NIR measurements, and therefore we did not need to control the reaction temperature at a constant setpoint. It is important to mention, however, that controlling the reaction temperature would be important for controlling the product quality, such as its molecular weight. This will require a more important range of temperature variation during the reaction and a study of the process kinetics in this entire range. In our case, this would, therefore, require performing the reaction in a closed reactor under pressure because the solvent boiling point is 83 °C. In this work, our attention was concentrated on controlling the process by manipulating uniquely the flow rate of the monomer, which can be adjusted in a way that controls the polymer molecular weight, but no attempt was made to control the reaction temperature. 4. Reaction Rate Estimation The material balance of AA in a semicontinuous reactor takes the following form:

where NAA is the number of moles of AA, Qin AA is the inlet molar flow rate of AA (mol/s), RP is the reaction

(3)

System 2 becomes

This system is observable with respect to NAA and RP because the matrix A is now positive. A high-gain observer can be constructed to estimate these states (Gauthier et al.25) as follows:

[ ] [ ] [ ][ ] [ ]

N ˆ˙ AA 2˙ θ Q˙ in 1 1 N˙ AA AA ) + - 2 (N ˆ AA - NAA) 0 0 r˘ P rˆ˘ P θ˙ 0˙ (5)

This is an exponential observer of the states NAA and rP. RP can now be calculated from rP using eq 3. θ is a positive parameter. A high value of θ gives a rapid convergence of the observer but a higher sensitivity to measurement noise. A low value of θ allows filtering of the measurement noise but a decrease in the rapidity of convergence. The value of θ is therefore a compromise between rapidity of convergence and sensitivity to measurement noise. The observer was first validated by simulation. Figure 6 shows the estimated reaction rate and the number of moles of AA. The observer was initialized with 5% error and 5% of noise was added to the process output NAA. It can be seen that the observer converges rapidly to the real values. We notice that the estimated value of NAA is less noisy than the real one, which is due to the value of θ. The observer of NAA acts therefore as a filter of the output. Also RP converges rapidly to the real value with less noise. It can be noticed that RP converges to

Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7387

Figure 6. Demonstration of the estimator of RP and NAA by simulation of a semicontinuous reaction.

Figure 7. Estimation of RP during a semicontinuous reaction based on the NIR measurement of NAA (experiment 120).

the flow rate of the monomer because of the rapidity of the reaction. The observer was then applied during a real experiment. In this experiment, an inhibition retarded the initiation of the reaction. Figure 7 shows that the amount of residual monomer is higher than that obtained in a classical reaction (Figure 4). This influences the reaction rate, which takes more time to join the monomer flow rate. The increase in the reaction rate increases the heat produced by the reaction, and therefore the reactor temperature. Because the reactor is automatically cooled by the condenser in a classical reaction, in a case of accumulation of the monomer, the condenser is overcharged and might overflow. Moreover, the increase in the amount of residual monomer influences the polymer molecular weight. Therefore, the concentration of the monomer influences the polymer quality and the process security. This is why, in the next part, a controller is developed to maintain the concentration of the monomer at a predefined value. 5. Control of the Concentration of the Monomer The amount of monomer in the reactor is obtained online by NIR analysis and can be controlled by manipulating the flow rate of the monomer as shown in the following scheme:

To construct the controller, the following system is used:

N˙ AA ) Qin AA - RP y ) NAA

(6)

In general, this process model is nonlinear. Actually, the concentration of radicals in the reactor is a result of radical decomposition and termination and depends on the initiator flow rates. Moreover, the reaction parameters, such as kp, and the decomposition coefficients depend on the reaction temperature. This means that several states are involved in eq 1 and are interacting in a nonlinear manner. Under constant reaction temperature and a constant flow rate of initiators, the concentration of radicals attains quickly a stationary state and the process model becomes linear. However, if one is interested in constructing a controller for the general case of eq 1, the controller must be adapted to a nonlinear model, such as the differential geometric control, in order to ensure good results. The differential geometry was adapted for the analysis and design of nonlinear control systems by Herman and Krener,26 Hunt et al.,27 and Isidori.28 The results generalize concepts and tools from linear control theory for a class of nonlinear systems, such as the state feedback. The idea of globally linearizing a nonlinear system in an input/output (I/O) sense was first introduced by Gilbert and Ha.29 The GLC framework is the calculation of a static-state feedback, under which the closed-loop I/O system is exactly linear. The state of the model does not need to be transformed into a linear one. Once the inner loop is closed, the controller design reduces to the design of an external linear controller.

7388

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

The nonlinear geometric control has been applied to control some free-radical polymerization processes in simulation (i.e., Alvarez et al.30). Soroush and Kravaris31 applied the GLC method to a batch polymerization reactor to control the reaction temperature. Then the authors32,33 applied this technique to continuous polymerization reactors to control the monomer conversion and the reaction temperature by manipulating the monomer flow rate and the rate of heat addition to the jacket circulating system. The monomer conversion was inferred by density and temperature measurements. In these works, the authors used a proportional-integral (PI) controller in the external loop. Sampath et al.34 used an I/O linearizing control with a robust control as an external loop to control the monomer conversion and the polymer molecular weight in batch solution methyl methacrylate polymerization by manipulating the reaction temperature. In this work, we aim to develop a controller of a semicontinuous process for the general process model given by eq 1, that is, nonlinear. An I/O linearizing control is proposed and applied to an industrial process. Let us consider the elements necessary to develop the nonlinear I/O linearizing control. Consider the following nonlinear system:

[f, g] )

∂g ∂f fg ∂x ∂x

To control NAA, eq 8 is used with r ) 1: 1

υ)

βkLkf h + (-1)0β1〈dh,ad0f (g)〉u ∑ k)0

) β0h + β1

∂h ∂h f + β1 g ∂x ∂x

) β0N1 + β1(-RP1) + β1u

(8a)

The input u ) QAA (mol/s) is now calculated from this transformation as follows:

u) )

υ - β0N1 + β1RP1 β1 υ - β0N1 + RP1 β1

(9)

The external input υ can be used to add a linear proportional loop as follows:

x˘ (t) ) f[x(t),u(t)] y(t) ) h[x(t)]

(7)

where x(t) ∈ M, in which M ∈ Rn is the state space, y ∈ Rp is the measured output, and u ∈ U, in which U ∈ Rm is the bounded input space, given f, g, and C∞ vector fields on Rn and h, a C∞ scalar field on Rn. The relative order, or the linearizability index r, is the smallest order of the derivative that depends explicitly on the input. For nonlinear systems, it can be calculated, as for linear systems, by calculating the derivative of the output. For system 6, the relative order is equal to 1, which means that the first derivative of the output (NAA) shows explicitly the input (QAA). A geometric nonlinear I/O linearizing control can therefore be constructed to control NAA. The following state feedback transformation was defined by Kravaris et al.35 for the system:

which means that if β0 ) κP, then υ can be replaced by the setpoint. Hence, the complete control variable becomes

u ) Q1 )

1 (κ ) + RP1 β1 P

(11)

The parameters β0 and β1 must be chosen in a way that ensures the stability of the states of the model. In eq 11, β1 can be taken to be equal to 1 without any loss of generality. If υ is taken to be a proportional linear controller, the stability of the system is governed by κP. The proportional parameter must therefore be chosen in a way that guarantees stable and rapid convergence to the desired values.

r

υ)

βkLkf h + (-1)r-1βr〈dh,adr-1 ∑ f (g)〉u k)0

(8)

where the Lie derivative (Lfh) is the directional derivative of the function h(x) in the direction of the vector f(x). One may also differentiate h(x) first in the direction of f(x) and then in the direction of g(x): n

Lfh(x) ) 〈dh,f〉 )

fi(x) ∑ i)1

∂h(x) ∂xi

where 〈.,.〉 denotes the dual product. The successive Lie brackets are defined by

ad0f (g) ) g ad1f (g) ) [f, g] l adkf (g) with

) [f, adk-1 (g)] f

Equation 12 shows that the nonlinear controller of NAA requires the estimation of RP that is obtained from the high-gain observer. By this term, the controller accounts for the model nonlinearity. This means that the controller has two actions. First, it compensates the amount of monomer consumed by the reaction, which depends on the reaction temperature, the concentration of radicals, and the concentration of the monomer. Second, it adjusts the residual amount of monomer as a function of the difference between the desired and real values. Actually, even if the value of NAA is equal to the desired point (therefore,  ) 0), the monomer flow rate will not be equal to zero, as in a simple proportional controller, but will be equal to the value of the reaction rate of the monomer. In the nonlinear controller, the proportional action (P) is indispensable in order to account for the setpoint. Also, an integrator (I) can be added in order to eliminate possible steady-state offsets, due to modeling uncertainties. However, if a PI controller is applied, the flow rate will not be zero at the setpoint because

Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7389

Figure 8. Simulation of the nonlinear I/O linearizing controller (κP ) 0.008) with a slightly decreasing concentration of radicals.

Figure 9. Results obtained by simulation of the PI controller (κP ) 0.05 and τI ) 0.0001) with a slightly decreasing concentration of radicals.

Figure 10. Simulation of the PI controller with a high variation in the concentration of radicals (κP ) 0.1 and τI ) 0.001).

the integral part would take into account some of the modeling error that would be sufficient if the process model is not highly nonlinear. The controller was first validated by simulation and compared to a PI controller. The setpoint profile consists of several steps with 5% of noise in order to test the controller robustness. For the first simulations, a slightly decreasing concentration of radicals was imposed. Figure 8 shows the simulation results of the nonlinear controller with κP ) 0.008. It can be noticed that NAA attains rapidly the setpoint and that the controlled flow rate is not oscillating. This controller was compared to a PI controller as given by the following equation:

The results of the PI controller are presented in Figure 9 with the parameters κP ) 0.05 and τI ) 0.0001. It can be seen that the PI controller gives acceptable results when the concentration of radicals is varying smoothly. In this case, the process model is close to a linear one and the PI controller can be used. Using the nonlinear controller becomes interesting when the process model is highly nonlinear. In the following simulation, a highly varying flow rate of the initiator was applied. The nonlinear controller gives results similar to those shown in Figure 8. The results obtained by the PI controller are shown in Figure 10. The figure shows that the controller is destabilized by the nonlinearity of the model when the concentration of radicals is varying a lot, while it acts very well when the concentration of radicals in the reactor is almost constant (Figure 9).

7390

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

Figure 11. Control of NAA using the nonlinear controller with a step-varying setpoint (experiment 170).

Figure 12. Control of NAA using the nonlinear controller with a smooth variation of the setpoint (experiment 173).

These simulations show that the PI controller acts well under specific conditions but, in general, the nonlinear controller is best adapted to the process model. With the nonlinear controller, planned or unexpected variations in the flow rate of the initiator or in the reaction temperature do not influence the controller performance. For this reason, the nonlinear controller was implemented experimentally. In the following experiments, a constant flow rate of the initiator was applied with a reaction temperature close to that shown in Figure 5. Therefore, under these specific conditions, the PI controller could be applied. Figure 11 shows the results obtained during experiment 173, with the setpoint used in simulation and a proportional constant κP ) 0.004. The figure shows that the number of moles of AA converges slowly to the setpoint at the beginning of the reaction. This convergence time is due, on the one hand, to the fact that there is no monomer in the initial charge. Introducing an amount of monomer in the initial charge can ameliorate the delay in the convergence. However, this can be critical during the heating phase and should be avoided in an industrial reactor. On the other hand, the delay in the convergence is amplified by the inhibition phenomena during the first few minutes of the reaction and by the sudden change in the reaction rate at the beginning of the reaction. Finally, the imprecision of the NIR measurements of NAA as a result of the small monomer concentration present at the beginning of the reaction causes oscillations in the measurement and, therefore, in the controller. These conditions remain acceptable because the concentration of the monomer

converges more quickly to the setpoint if the setpoint is changed during the reaction. With a smoother setpoint profile, such as that applied in experiment 170 (Figure 12), a rapid convergence of NAA to the setpoint is observed (κP ) 0.005). During the reaction, NAA does not deviate from the setpoint. This is due to the fact that, once the reaction is started, the reaction rate varies smoothly and the NIR measurements are more precise. The figure shows that the controlled flow rate is oscillating a little. These oscillations are due to experimental variations such as a second local controller between the pump and the flowmeter and can probably be ameliorated. What is important to notice is that the controller avoids having any accumulation of monomer at the beginning of the reaction until the reaction starts. This is interesting in the control of the process productivity and the product quality. 6. Conclusion The control strategy developed in this work has been implemented on an industrial pilot reactor. It allows one to maintain the concentration of the monomer in the reactor at a predefined value that can be calculated in a way such that the heat produced by the reaction does not influence the reaction temperature and that the production of the desired polymer molecular weight is ensured. The controller gives good results even under highly varying setpoints and high model nonlinearity. The control strategy is applicable to systems equipped with online measurements of the concentration of the

Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7391

monomer in the reactor. It can be applied to high-scale reactors where maximizing the productivity is an important issue. Acknowledgment Funded by Coatex. Literature Cited (1) Kammona, O.; Chatzi, E. G.; Kiparissides, C. Recent developments in hardware sensors for the online monitoring of polymerization reactions. J. Macromol. Sci., Rev. Macromol. Chem. Phys. 1999, C39 (1), 57-134. (2) Ponnuswamy, S.; Shah, S. L.; Kiparissides, C. Online monitoring of polymer quality in a batch polymerization reactor. J. Appl. Polym. Sci. 1986, 32 (1), 3239-3253. (3) Budde, U.; Reichert, K. H. Automatic polymerization reactor with on-line data measurement and reactor control. Makromol. Chem. 1988, 161, 195-204. (4) Chien, D. C. H.; Penlidis, A. Effect of impurities on continuous solution methyl methacrylate polymerization reactors. I. Openloop process identification results. Polym. React. Eng. 1994, 2 (12), 163-213. (5) Cowley, T. J.; Choi, K. Y. Experimental studies on optimal molecular weight distribution control in a batch-free radical polymerization process. Chem. Eng. Sci. 1998, 53 (15), 2769-2790. (6) Barudio, I.; Fe´votte, G.; McKenna, T. F. Density data for copolymer systems: butyl acrylate/vinyl acetate homo- and copolymerization in ethyl acetate. Eur. Polym. J. 1999, 35, 775780. (7) Karago¨z, A. R.; Hapoglu, H.; Alpbaz, M. Generalized minimum variance control of optimal temperature profiles in a polystyrene polymerization reactor. Chem. Eng. Process. 2000, 39, 253-262. (8) Bahr, D.; Pinto, J. C. Refractive index of solutions containing poly(vinyl acetate) and poly(methyl methacrylate). J. Appl. Polym. Sci. 1991, 42 (10), 2795-2809. (9) Zaldivar, C.; Iglesias, G.; del Sol, O.; Pinto, J. C. On the preparation of acrylic acid/vinyl acetate copolymers with constant compositions2. Refractive indexes for in-line evaluation of monomer conversion and copolymer composition. Polymer 1997, 39 (1), 247-251. (10) Cavin, L.; Renken, A.; Meyer, Th. Online conversion monitoring through ultrasound velocity measurements in bulk styrene polymerization in a recycle reactorspart II: mathematical model. Polym. React. Eng. 2000, 8 (3), 225-240. (11) Kim, Y. S.; Sook, C.; Sung, P. UV and fluorescence characterization of styrene and methyl methacrylate polymerization. J. Appl. Polym. Sci. 1995, 57 (3), 363-70. (12) Pekcan, O.; Yilmaz, Y. Real time monitoring of polymerization rate of methyl methacrylate using fluorescence probe. Polymer 1997, 38 (7), 1693-1698. (13) Tirrell, M.; Gromley, K. Composition control of batch copolymerization reactors. Chem. Eng. Sci. 1981, 36, 367. (14) Arzamendi, G.; Asua, J. Copolymer composition control of emulsion copolymers in reactors with limited capacity for heat removal. Ind. Eng. Chem. 1991, 30, 1342-1350. (15) Gugliotta, L. M.; Vega, J. R.; Entonione, C. E.; Meira, G. R. Emulsion copolymerization of acrylonitrile and butadiene in an industrial batch reactor, Estimation of conversion and polymer quality from on-line energy measurements. Polym. React. Eng. 1999, 7 (4), 531-552. (16) Buruaga, I. S.; Armitage, P. D.; Leiza, J. R.; Asua, J. M. On-line Control for maximum production rat of emulsion polymers of well-defined polymer composition. ECCE1 1997, 4 (7), 117120. (17) Gloor, P. E.; Warner, R. J. Developing feed policies to maximize productivity in polymerization process. Thermochim. Acta 1996, 289 (2), 243-265.

(18) Sheibat-Othman, N.; Fe´votte, G.; McKenna, T. F. Biobjective control of emulsion polymerizations: control of the polymer composition and the concentration of monomer in the polymer particles. Chem. Eng. J. 2003, in press. (19) Olinga, A.; Winzen, R.; Rehage, H.; Siesler, H. W. Methyl methacrylate online polymerization monitoring by light-fiber Fourier transform near infrared transmission spectroscopy and Fourier transform mid infrared/attenuated total reflection spectroscopy. J. Near Infrared Spectrosc. 2001, 9 (1), 19-24. (20) Lousberg, H. H. A.; Boelens, H. F.; Le Comte, E. P. Online determination of the conversion in a styrene bulk polymerization batch reactor using near-infrared spectroscopy. J. Appl. Polym. Sci. 2002, 84 (1), 90-98. (21) Sasic, S.; Ozaki, Y.; Olinga, A.; Siesler, H. W. Comparison of various chemometric evalutation approaches for online RT-NIR transmission and FT-MIR/ATR spectroscopic data of methyl methacrylate solution polymerization. Anal. Chim. Acta 2002, 452, 265-276. (22) Cherfi, A.; Fe´votte, G. Online conversion monitoring of the solution polymerization of methyl methacrylate using nearinfrared spectroscopy. Macromol. Chem. Phys. 2002, 203 (9), 1188-1193. (23) Fontoura, J. M. R.; Santos, A. F.; Silva, F. M.; Lenzi, M. K.; Lima, E. L.; Pinto, J. C. Monitoring and control of styrene solution polymerization using NIR spectroscopy. J. Appl. Polym. Sci. 2003, 90 (5), 1273-1289. (24) Van Den Brink, M.; Hansen, J. F.; De Peinder, P.; Van Herk, A. M.; German, A. L. Measurement of partial conversions during the solution copolymerization of styrene and butyl acrylate using online Raman spectroscopy. J. Appl. Polym. Sci. 2000, 79 (3), 426-436. (25) Gauthier, J. P.; Hammouri. H.; Othman, S. A simple observer for nonlinear systems. Application to bioreactors. IEEE Trans. Autom. Control 1992, 37, 875-880. (26) Herman, R.; Krener, A. Nonlinear controllability and observability. IEEE Trans. Autom. Control 1977, AC-22, 5. (27) Hunt, R.; Su, G. M. Global transformations of nonliner sustems. IEEE Trans. Autom. Control 1983, AC-28, 24-31. (28) Isidori, A. Nonlinear control systems. An introduction, 2nd ed.; Springer-Verlag: Berlin, 1989. (29) Gilbert, E.; Ha, I. J. An approach to nonlinear feedback control with applications to robotics. IEEE Trans. Syst. Manage. Cybern. 1984, SMC-14, 879. (30) Alvarez, J.; Suarez, R.; Sanchez, A. Semiglobal nonlinear control based on complete input-output linearization and its application to the start-up of a continuous polymerisation reactor. Chem. Eng. Sci. 1994, 49 (21), 3617-3630. (31) Soroush, M.; Kravaris, C. Nonlinear control of a batch polymerization reactor: an experimental study. AIChE J. 1992, 38 (9), 1429-1448. (32) Soroush, M.; Kravaris, C. Multivariable nonlinear control of a continuous polymerisation reactor: an experimental study. AIChE J. 1993, 39 (12), 1920-1937. (33) Soroush, M.; Kravaris, C. Nonlinear control of a polymerization CSTR with singular characteristic matrix. AIChE J. 1994, 40 (6), 980-990. (34) Sampath, V.; Palanki, S.; Cockburn, J. C. Robust nonlinear control of polymethylmethacrylate production in a batch reactor. Comput. Chem. Eng. 1998, 22, S451-S457. (35) Kravaris C.; Chung, C. B. Nonlinear state feedback synthesis by global input/output linearization. AIChE J. 1987, 33, 4.

Received for review January 8, 2004 Revised manuscript received September 9, 2004 Accepted September 10, 2004 IE049968K