Design of Optimal Sequential Experiments to Improve Model Predictions from a Polyethylene Molecular Weight Distribution Model Duncan E. Thompson, Kim B. McAuley,* P. James McLellan Introduction Owing to the multi-site nature of Ziegler-Natta catalysts, kinetic models of ethylene copolymerizations that use these catalysts tend to be very large with many parameters that need to be estimated. [1–7] Experimental runs on industrial reactors are expensive, especially when the required setpoints lie outside of the normal pattern of process operating conditions. Because of the expense of obtaining custom experimental data and difficulties that can be associated with parameter estimation, it is important to design experiments and to use data as effectively as possible when building mathematical models. It is also important to extract all of the available information from prior experiments that may have been performed for other purposes. Many end-use and processing properties of polyethylene are influenced by molecular weight distribution (MWD) and comonomer incorporation. [8] Industrial polyethylene producers desire mathematical models that can predict the MWD of ethylene/hexene and ethylene/butene copoly- mers produced in gas-phase reactors using Ziegler-Natta catalysts. If models that predict MWDs from reactor operating conditions are combined with models that predict end-use properties from MWDs, [9] then end-use properties that are important to customers can be predicted directly from reactor conditions. To this end, our research group has used industrial data to develop simplified models to predict the MWD and comonomer incorporation in mren.200900033 Full Paper 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 D. E. Thompson, K. B. McAuley, P. J. McLellan Department of Chemical Engineering, Queen’s University, Kingston, ON, K7L 3N6, Canada Fax: þ1 613 533 6637; E-mail: kim.mcauley@chee.queensu.ca 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 anticip- ated benefits are quantified. Problems with local minima are discussed and comparisons between the optimality criteria are made. Macromol. React. Eng. 2009, 3, 000–000 ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim DOI: 10.1002/mren.200900033 1 Early View Publication; these are NOT the final page numbers, use DOI for citation !! R