Mathematical Modeling and Advanced Parameter Estimation for Polymerization Processes

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When developing a mathematical model, modelers make interconnected decisions about the complexity and detail required, simplifying assumptions that will be made, and techniques that will be used to estimate model parameters. Appropriate decisions depend not only on the physics and chemistry of the system being modeled, but also on experimental information that is already known, costs of performing further experiments, and the  intended use of the model (e.g., process control, monitoring, scale-up or optimization). The long-term goals of my research program are: i) to build novel fundamental models for specific polymerization systems, and ii) to develop model-building tools that address key problems faced by researchers when developing and applying mechanistic models. Three projects are described in the proposal. In the first, a model will be developed to describe carbocationic homopolymerization of 4-(2-chloroisopropyl) styrene in semi-batch reactors. More importantly, copolymerization of isobutylene with this inimer (to produce tailored rubber molecules for biomedical applications) will be modeled.  The models will predict evolution of branching and molecular weight distribution in response to temperature, initial concentrations and feed rates. Data from the lab of J.E. Puskas (U. of Akron) will be used for parameter estimation and model testing. The proposed models will be a significant advance over current models because they will account for consumption of Lewis acid and for the exchange reaction that generates inimer. In the second project, maximum-likelihood methods for parameter estimation in stochastic differential equation models will be extended and tested. These methods and models are attractive for industrial reactors because they account for unknown initial conditions, data collected at irregular time intervals, and disturbances that influence future process operation. New objective functions will be developed to account for prior knowledge about model parameters. Diagnostic methods will be developed to determine which stochastic differential equations should include nonstationary random error terms so that the best possible model predictions can be obtained.  Estimability analysis methods are used to decide which parameters should be estimated in complex models using limited experimental data and which should be left at nominal values, so numerical problems can be avoided and reliable predictions obtained. The third project will extend popular estimability analysis techniques to account for operating conditions where good predictions are required, especially in the difficult case where the Fisher Information Matrix is non-invertible.  New methods for sequential design of experiments when some parameters cannot be estimated will also be explored. Students will be trained in all three projects and will develop skills desired in Canadian industry.