Advanced Polymer Production Models and Parameter Estimation Techniques

Abstract

The physical properties of commodity polymers such as polyethylene (PE) and polypropylene (PP) vary greatly depending on the chemical structures of the polymer molecules. The wide range of physical properties exhibited by these polymers makes them versatile for applications in many different end-use products. Microstructure characteristic that influence the polymer’s physical properties include average chain length, molecular weight distribution (MWD), copolymer composition distribution (CCD) and tacticity. Mathematical models are powerful tools that chemical engineers can use to control these microstructure characteristics, thereby producing polymer grades with targeted physical properties. First, three mathematical models for controlled degradation of polypropylene (CPP) are developed. These models predict tacticity changes in PP undergoing CPP via reactive extrusion. The first two models are deterministic models that are used to estimate tacticity-related kinetic parameters. The third model is a more versatile hybrid deterministic/Monte Carlo model that can account for more reactions simultaneously. The hybrid model provides improved predictions and improved parameter estimates. An advanced model for gas-phase production of linear low-density PE with a three-site metallocene catalyst is then developed. This model uses joint MWD and CCD data along with triad sequence data to estimate relevant model parameters. Although a large dataset is available for parameter estimation, the use of a multisite metallocene catalyst results in a model with many parameters (i.e., 36) that cannot all be reliably estimated from the available data. A subset-selection methodology is used to determine that 23 of the 36 parameters can be reliably estimated to avoid overfitting the data and the 23 parameter estimates are reported. Finally, an alternative Bayesian parameter estimation method is presented. This method is also useful for parameter estimation when the model contains many parameters and only limited data. A literature review is conducted on both Bayesian and subset-selection methodologies and their applications in chemical process models. Finally, a case study is used to explore the relative merits and shortcomings of each method.