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Control of Particle Size Distribution in an Emulsion Copolymerization Reactor Via Cascade Regulation of Growth and Nucleation

Mustafa T. Dokucu, Department of Chemical Engineering, University of California Santa Barbara, Department of Chemical Engineering, Santa Barbara, CA 93106-5080 and Francis J. Doyle III, Chemical Engineering/Biomolecular Science and Engineering Program, University of California Santa Barbara, UCSB, Santa Barbara, CA 93106-5080.

Emulsion polymerization has significant advantages over bulk and solution polymerization processes. These advantages result mostly from the multiphase and compartmentalized nature of the emulsion polymerization, delivering a high versatility to product qualities but adding to the complexity of the process. The control of the full particle-size distribution (PSD) in emulsion polymerization is vital for industrial applications where the target distributions are usually complex and/or multimodal. In these cases, end-use properties (mechanical, rheological, optical) of the polymer products depend strongly on the endpoint PSD. The evolution of the PSD is governed by the interplay of three major phenomena, which are nucleation, growth and coagulation of the polymer particles. The interaction among these phenomena and the complexity of their relation to process variables (flowrates of the monomers, surfactant, and initiator) creates a challenging control problem. Another difficulty is that PSD measurements have significant measurement delays compared to the inherent time scale of the system.

A population balance equation (PBE) system of a semibatch Vinyl Acetate/Butyl Acrylate copolymerization reactor is used as a benchmark for this study. The manipulated variables are the flowrates of the initiators, monomers, and the non-ionic surfactant, that can be actuated every sampling instant. The PSD is measured by CHDF every 12 minutes and the density measurements are available every minute. Further details about the experimental system that is simulated in this study can be found in [1]. In this work, a cascade control architecture is proposed for rejecting disturbances that may be experienced during the batch. This architecture relies on the fact that control of nucleation and growth kernels throughout the batch will result in effective regulation of the PSD. Although coagulation plays a major role in emulsion polymerization, it is not controlled due to the stochastic nature of this kernel and the need to minimize the computational cost of the closed-loop control. An advanced master controller determines the reference trajectories for nucleation and growth kernels. This master controller updates the trajectories of the kernels as PSD measurements become available every 12 minutes. Then, the slave controller manipulates the flowrates of the monomers, surfactant, and the initiators making the nucleation and growth kernels follow the updated kernel setpoints every minute.

A nonlinear model predictive controller is designed as the master controller, which utilizes the detailed population balance model developed earlier by Immanuel and Doyle III [2]. In this model, finite discretization is applied for solving the PBE using 250 states for representing the PSD. The controller is based on the methodology of Garcia [3] that uses the nonlinear plant model for predicting the future outputs given past inputs and the local linear models to formulate the optimization problem. This approach has the advantage of resulting with a quadratic problem at each time step rather than a computationally intense nonlinear optimization problem. The ill-conditioning and the high-dimensionality of the resulting dynamical system is removed by principal component analysis (PCA)-based model order reduction. The principal directions of variability in the high number of correlated variables are calculated by PCA, utilizing a database of 60 batches. The projection of the original states as well as the outputs and the current condition of the reactor onto the principal component space is established by an orthonormal transformation matrix. The performance of the proposed cascade control strategy is demonstrated against various unmeasured disturbances such as initial state and input concentration uncertainties and compared with the performances of a PID and a multi-rate model predictive controller.

[1] C.D. Immanuel and F.J. Doyle III. Evolution of multimodal particle size distribution in vinyl acetate/butyl acrylate emulsion copolymerizations. J. Polym. Sci., Polym. Chem., 14:2232-2249, 2003.

[2] C.D. Immanuel and F.J. Doyle III. Computationally efficient solution of population balance models incorporating nucleation, growth and coagulation: application to emulsion polymerization. Chem. Eng. Sci., 58:3681-3698, 2003.

[3] C.E. Garcia. Quadratic dynamic matrix control of nonlinear processes An application to a batch reaction process. Proc. AIChE Annu. Meet., San Francisco, CA, 1984.