A modified collocation modeling framework for dynamic evolution of molecular weight distributions in general polymer kinetic systems

Abstract

General modeling and optimization with molecular weight distributions (MWDs) are essential to determine optimal designs and operations for polymerization processes. Orthogonal collocation methods in two dimensions can capture the dynamic feature of MWD in time and the distributive feature in chain length. However, there are still computational challenges for complex reactions using this method. This study proposes a general framework based on the collocation methods. For different mathematical operations caused by different types of polymeric reactions, we propose corresponding model reformulation methods with specific coefficient matrices, including moment operations caused by chain propagation and disproportionate termination, moment operation without closure caused by scission, and convolution operation caused by coupling termination. The chain-length dependent rate can also be handled well through this general framework. Case studies show the effectiveness, accuracy, and generality of our approach.