Control of polymerisation processes is an extremely challenging task, as these processes often present highly exothermic reactions and significant viscosity variations along the reaction path, leading to complex heat transfer and fluid dynamics. Besides, the dynamic behaviour of polymerisation reactors is highly non-linear (Ray and Villa, 1999). Product quality is a much more complex issue in polymerisation than in more conventional short chain reactions. The molecular structure of the polymer is so sensitive to operating conditions that any disturbance in feed conditions, mixing, reactor temperature and initiator concentration can affect the critical molecular properties such us molecular weight distribution, copolymer distribution, etc.

Online process performance monitoring and product quality prediction in real time ensure safe and profitable operation of batch processes because they provide the opportunity to take corrective actions before the effects of excursions from normal operation ruin the batch. When Statistical process control is applied, process operation is considered successful if all the variables remain within acceptable limits during the batch course and the product has a desirable quality. As changes in the operating conditions during critical periods affect product quality, the implementation of on-line monitoring and fault diagnosis techniques for polymerization processes allows to detect faults and take correction actions prior the completion of the run.

Multivariate statistical techniques have been proposed for online monitoring and fault detection of batch processes. Multiway Principal Component Analysis (MPCA) and Multiway Partial Least Squares (MPLS) were developed by Nomikos and MacGregor (1994, 1995). Using a model of the normal process behavior in a reduced space of latent variables, these techniques monitor process performance by comparing the time progression of the data with those of the normal batch.

In earlier works, a batch-wise unfolding of the three-way data matrix was used to obtain the PCA model. Regarding, hypothesis testing this procedure presents the advantage of considering the batch history because a row of the data matrix represents the whole batch run. Nevertheless, during the on line monitoring the complete batch trajectory is unknown, then estimations for the future measurements are needed to obtain a conformable observation vector. To overcome this problem a time-wise unfolding of the data matrix has been proposed by Wold et al. (1998), which presents the disadvantage that no historical information of the batch course is taken into account because each time slice is used independently from the previous ones.

The control of final product quality in industrial batch of semi-batch reactors presents additional difficulties. One of the most important is the fact that reliable on-line sensors are rarely available. Rather, product properties are usually measured on the final product once the batch has ended. In consequence, the process state is generally determined without information about the values of the product properties. Thus, even if the process is under control, properties depending on the historical profile of all variables, such as product quality variables, could be unacceptable.

In this work a multivariate exponential weighted moving average (MEWMA) method is applied to take into account the batch history when the time-wise unfolding is applied. MEWMA method may be applied before or after obtaining the PCA model, resulting MEWMA-PCA and PCA-MEWMA respectively. By choosing an appropriate value of the weighting parameter of the MEWMA method, the batch history can be properly included. The system under study is the batch polymerisation of styrene using dibenzoyl peroxide as initiator. Based on a non-linear model of the process, an optimal temperature profile (set point) is designed that minimizes the batch time and ensures satisfaction of a number of constraints on the reactor and jacket temperature, monomer conversion, the product's molecular weight and the coolant flow rate. The process is controlled by measuring the reactor temperature, and by manipulating the coolant flow rate. Results obtained by the proposed method are compared with the ones provided by the classical MPCA.

References

Nomikos, P. and J. F. MacGregor, “Monitoring Batch Processes Using Multiway Principal Component Analysis,” AIChE J., 40, 1361-1375 (1994). Nomikos, P. and J. F. MacGregor, “Multiway Partial Least Squares in Monitoring Batch Processes,” Chemometr. Intell. Lab., 30, 97-108 (1995). Ray, W. H., and C. M. Villa, “Nonlinear Dynamics Found in Polymerization Processes – a Review,“ Chem. Eng. Sci., 55, 275 (1999). Wold, S., N. Kettaneh, H. Fridén and A. Holmberg, “Modelling and diagnostics of batch processes and analogous kinetic experiments,” Chemom. Intell. Lab., 44, 331-340 (1998).

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