Mathematical Model and Parameter Estimation for Gas‐Phase Ethylene/Hexene Copolymerization With Metallocene Catalyst

Abstract

Summary: Models were developed to simulate gas‐phase ethylene/hexene copolymerization using a silica‐supported (BuCp)2ZrCl2 catalyst in a semi‐batch laboratory reactor. The models are able to predict ethylene consumption rate, gas composition drift during the experimental runs, as well as number‐and weight‐average molecular weight, and short‐chain branching levels, and triad sequence distributions of copolymer removed from the reactor at the end of each run. A single‐site model was first developed, but it failed to accurately predict the molecular weight data and its distribution. Sequentially, a two‐site model was built to improve model predictions. Parameter estimability analysis was performed to guide model simplification and to ensure that the parameter estimation problem would be well conditioned. After model simplification, which reduced the number of unknown parameters from 55 to 37, the parameters were estimated and good fitting of most experimental data was obtained. The simplified two‐site model was validated using the data from four extra experimental runs, which were not employed in the parameter estimation process. Most of the model predictions fall within the 95% confidence intervals of the experimental data.Model validation of hexene concentration. (The lines are model predictions and the solid diamonds with error bars are experimental data.)magnified imageModel validation of hexene concentration. (The lines are model predictions and the solid diamonds with error bars are experimental data.)

Model for a solid–liquid stirred tank two-phase partitioning bioscrubber for the treatment of BTEX

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“…ter estimation in a variety of chemical [11][12][13][14][15][16][17] and biochemical [18][19][20] models. It selects parameters for estimation based on information about uncertainties in each of the initial parameter values, sensitivity of model predictions to the various parameters, and the quantity and quality of the dynamic experimental data.…”

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