Modeling of Molecular Weight Distributions in Ziegler-Natta Catalyzed Ethylene Copolymerizations
Mathematical Modelling , Molecular Weight Distribution , Ziegler-Natta Catalyst , Estimability Analysis , Design of Experiments , Polyethylene , Parameter Estimation
The objective of this work is to develop mathematical models to predict molecular weight distributions (MWDs) of ethylene copolymers produced in an industrial gas-phase reactor using a Ziegler-Natta (Z-N) catalyst. Because of the multi-site nature of Z-N catalysts, models of Z-N catalyzed copolymerization tend to be very large and have many parameters that need to be estimated. It is important that the data that are available for parameter estimation be used effectively, and that a suitable balance is achieved between modeling rigour and simplification. In the thesis, deconvolution analysis is used to gain an understanding of how the polymer produced by various types of active sites on the Z-N catalyst responds to changes in the reactor operating conditions. This analysis reveals which reactions are important in determining the MWD and also shows that some types of active sites share similar behavior and can therefore share some kinetic parameters. With this knowledge, a simplified model is developed to predict MWDs of ethylene/hexene copolymers produced at 90 °C. Estimates of the parameters in this isothermal model provide good initial guesses for parameter estimation in a subsequent more complex model. The isothermal model is extended to account for the effects of butene and temperature. Estimability analysis and cross-validation are used to determine which parameters should be estimated from the available industrial data set. Twenty model parameters are estimated so that the model provides good predictions of MWD and comonomer incorporation. Finally, D-, A-,and V-optimal experimental designs for improving the quality of the model predictions are determined. Difficulties with local minima are addressed and a comparison of the optimality criteria is presented.