Mechanistic models are often unable to provide accurate extrapolative predictions. One common cause of the poor prediction is that the models do not account for some phenomena occurring outside the nominal range of conditions for which the models were originally developed. To address this problem, one usually resorts to: (a) Continual improvement of mechanistic models by incorporating previously unobserved phenomena or reaction pathways; and/or (b) Development of strategies that take into account or compensate for the unforeseen mismatches that exist between the physical system and the process model

We have observed inaccurate extrapolative predictions by a mechanistic process model that Rantow et al. (2006) developed to capture/describe the dynamics of a high-temperature polymerization reactor. The kinetic parameters of the model were simultaneously estimated from off-line measurements of number-average and weight-average molecular weights, monomer conversion, and average-number of chain branches per chain. A state estimator was designed based on a reduced-order kinetic model, and its performance evaluated against simulated spectroscopic measurements (Rantow et al., 2004, 2005). The state estimator was designed using the multi-rate state estimation method (Zambare et al., 2003). In these studies, the following observations were made: (a) The model was able to predict accurately monomer conversion and number-average molecular weight data obtained from a lab-scale polymerization reactor; (b) The model over-predicted the polymer polydispersity index and under-predicted the average number of terminal double bonds per chain; and (c) An estimator designed based on a reduced-order kinetic model had a few tunable parameters. However, the reduced-order model provided no prediction for the polydispersity index. Discrepancies between model predictions and experimental data have been attributed to the unreliability of the model kinetic parameters and structure.

In this study, the multi-rate state estimation method of Zambare et al. (2003) is used to design a model-based state estimator for a lab-scale polymerization reactor. The performance of the estimator is evaluated in real-time against off-line measurements of polydispersity index and average number of terminal double bonds. Number of terminal double bonds is measured by proton nuclear magnetic resonance spectroscopy (1H-NMR). To estimate the polydispersity index, the estimator will be designed based on either (i) an extension to the reduced-order kinetic model or (ii) a method-of-moments based kinetic model. The choice of the model to be used in the state estimator design will be based on the complexity associated with number of tunable parameters in the state estimator. In the extended version of the reduced-order kinetic model, the polydispersity index is inferred from the number-average molecular weight, based on an empirical correlation developed from experimental trends that capture the relationship between number-average and weight-average molecular weight. The estimator will be implemented in real-time at DuPont Marshall Laboratory, and the estimation results will be presented at the AIChE Annual Meeting.

Rantow, F.S., Soroush, M., Grady, M.C., Kalfas, G.A., “Spontaneous Polymerization and Chain Microstructure Evolution in High Temperature Polymerization of n-Butyl Acrylate,” 47, 1431-1443, Polymer, 2006

Rantow, F.S., Soroush, M., Grady, M.C., “Model for Polymer Microstructure Monitoring and Control in Polymerization of Acrylates,” AIChE Annual Meeting, Cincinnati, OH, 2005

Rantow, F.S., Soroush, M., Grady, M.C., “High-Temperature Acrylate Polymerization: Decentralized Parameter Estimation and Multi-Rate State Estimation,” AICHE Annual Meeting, Austin, TX, 2004

Zambare, N., Soroush, M., Ogunnaike B.A., “A Method of Robust Multi-Rate State Estimation”, J. Process Control, 13, 337-355, 2003