Development of a computationally efficient model for the control of Ziegler-Natta catalysed industrial production of high density polyethylene

Doctoral Thesis


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University of Cape Town

High density polyethylene is commonly produced by the slurry phase co-polymerisation of ethylene and other alkenes, using heterogeneous titanium-based Ziegler-Natta catalysts. During grade transitions, when reactor conditions are manipulated to change polymer properties, significant quantities of off-specification product result. Implementing a model-predictive controller based on a dynamic reactor model may allow for minimising losses during unsteady-state operation. Such a model must be developed from a fundamental understanding of polymerisation reaction kinetics and the interaction of effects at various scales, including those of catalyst sites, catalyst/polymer particles and reactor hydrodynamics. The model must also be computationally efficient enough for application to real-time control. The recently-developed pseudo-sites model was used as a fundamental kinetic explanation of polymer property distributions and catalyst activity profiles, in contrast to empirical multi-site models. Laboratory polymerisation experiments were performed at industrially-relevant conditions. Kinetic parameters were fitted to the data, using a novel proposed regression procedure to extract meaningful kinetic parameters. A dynamic reactor model was developed, based on the Segregation Approach. Whereas the more common Population Balance Model must consider multivariate distributions of population members within a chosen volume and requires partial differential equation solution, the Segregation Approach can generate the moments of a distribution by evaluating the evolution of properties without requiring solution over the whole volume. The Segregation Approach and PBM were rigorously compared in the context of Particle Size Distributions, and the Segregation Approach shown to be an order of magnitude more computationally efficient. Steady-state industrial data was used to reconcile model predictions for laboratory and industrial polymerisation. This was the first application of the pseudo-sites model to laboratory data, and first extension to industrial scale. Unsteady-state data from three industrial grade transitions was used to validate the reactor model, which closely matched industrial reactor performance. The model simulated 30-40 hours of real time in 15-25 seconds of calculation time. The reactor model was used to propose improved grade transition strategies; transition duration and waste production were improved by 20-40%. The reactor model has been shown to accurately reproduce real-world results, and is computationally efficient enough to be applied to model-based control applications.