Abstract: Weijie Lin and Lorenz T. Biegler

Chemical Engineering Department
Carnegie Mellon University, Pittsburgh

Model Building and Dynamic Optimization: A Case Study in Tool and Process Development for Advanced Polymer Products

Interpenetrating polymer networks (IPN) refer to an advanced polymerization technology, which interlaces two or more polymers in different network forms. The synthesized polymer composite can have versatile physical properties, usually exceeding any of its components. It is used in a wide range of industries, including medical diagnosis and products, automotive, coatings, aerospace etc. However, IPN products are often limited by the ability to process them cost effectively. In particular, the relationship between process operation and product properties is still not well understood, and experimental studies are usually difficult and time-consuming. While recent advances in polymer modeling technology have led to significant successes in prediction and control of polymer properties, the lack of a comprehensive model still hinders the development of IPN technologies. In this talk, we present a systematic modeling and optimization framework to deal with this important application.

Driven by the complexity of this dynamic polymerization process, advanced strategies for model development, parameter estimation and process optimization were developed and investigated. In particular, we apply and extend simultaneous dynamic optimization strategies for multi-stage process modeling and optimization. Using large-scale nonlinear programming tools, we have developed parameter ranking, selection and estimation strategies for this large-scale model, in order to demonstrate diffusion limited features of polymer reactions, and to develop molecular weight distributions (MWD) of the complex polymer network. Moreover, using the NLP sensitivity approach, the parameter covariance matrix from a maximum likelihood formulation can be extracted easily from a pre-factored KKT matrix. This approach enables statistical inference and systematic parameter selection to be conducted within this model building study.

The development and application of these optimization-based tools has led to detailed models of a multi-stage polymerization process that include detailed kinetic mechanisms including polymerization, crosslinking, grafting, degradation and multiple representations of population balance models (including a novel fixed pivot technique). These provide comprehensive information on the MWD of the IPN to predict product properties. Moreover, these models were developed in tandem with an industrial experimental program that complemented the modeling study and ensured process validation. The predictive model also enabled dynamic optimization of the process in order to control the product quality and reduce production time. The optimal results were also validated on the process and indicated that significant performance gains (around 20%) can be obtained with novel operating strategies for this polymer process.

Finally, the results of this case study demonstrate the potential of advanced nonlinear programming formulations and tools for model building and process optimization. Coupled with challenging issues related to obtaining informative process data, industrial practices also highlight the need for uncertainty quantification and the incorporation of uncertainty within the optimization formulation. Novel strategies and initial results in this direction are described as future work for this task.


Aachen Institute for Advanced Study in Computational Engineering Science (AICES)
at RWTH Aachen University, Germany. Email: acces11@aices.rwth-aachen.de
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