A simplified steady‐state model to predict MWDs of ethylene/butene and ethylene/hexene copolymers produced industrially using heterogeneous Z‐N catalysts is developed. Estimability analysis is used to guide model simplification and to determine which parameters can be estimated using the available data. Scaling of response variables and parameters using information about their uncertainties ensures that appropriate results are obtained from the estimability analysis. Parameter estimates are obtained to provide good predictions of the measured MWDs. Although the parameter values obtained are specific to the Z‐N catalyst of our industrial sponsor, the method should be useful for parameter estimation and model simplification in other catalytic polymerization systems.magnified image

A simplified steady‐state model has been developed to predict molecular weight distributions and average compositions of ethylene‐hexene copolymers produced using heterogeneous Ziegler‐Natta catalysts in gas‐phase reactors. The model uses a simplified reaction scheme to limit the number of parameters that must be estimated. The number of parameters is further reduced by assuming that different types of active sites share common rate constants for some reactions. Estimates of kinetic parameters are obtained using deconvolution analysis of industrial copolymer samples produced using a variety of isothermal steady‐state operating conditions. The parameter estimates should prove useful as initial guesses for future parameter estimation in a non‐isothermal model.magnified image

Reliable model predictions require an appropriate model structure and also good parameter estimates. For good parameter estimates to be obtained, it is important that the data used in parameter estimation are informative. Alphabet-optimal experimental designs can be used to ensure that new experiments are as informative as possible. This work presents the development of D-and A-optimal sequential experimental designs for improving parameter precision in a molecular-weight-distribution model for Ziegler-Natta-catalyzed polyethylene. Novel V-optimal designs techniques are developed to improve the precision of model predictions, and anticipated benefits are quantified. Problems with local minima are discussed and comparisons between the optimality criteria are made.

Industrial ethylene‐hexene copolymer samples produced using a supported Ti‐based Ziegler‐Natta catalyst were deconvoluted into five Flory molecular weight distributions (MWDs). Relationships between reactor operating conditions and deconvolution parameters confirmed that temperature and hydrogen and hexene concentrations influenced the MWD. The two sites that produced low‐molecular‐weight polymer responded similarly to changes in reactor operating conditions, as did the three sites that produce high‐molecular‐weight polymer. Increasing hexene concentration resulted in relatively more polymer being produced at the two low‐molecular‐weight sites and less at the high‐molecular‐weight sites. The information obtained will be useful for making simplifying assumptions during kinetic model development.