Efficient modeling of distributions of polymer properties using probability generating functions and parallel computing

Abstract

High-fidelity models of polymer processes should include the prediction of distributions of polymer properties, including multivariate distributions. Deterministic models with this capability usually involve a large system of equations, which compromises the model performance in terms of CPU time. The probability generating function (pgf) technique is a powerful method for modeling distributions of polymer properties, including multivariate distributions. It can be applied to systems described by complex kinetic mechanism and requires no a priori assumptions about the distribution shape. The structure of this modeling method makes it particularly suitable for parallel computing. This work describes the application of the pgf technique for modeling uni- and bivariate distributions of polymer properties with parallelization of the model code. It is shown that accurate results can be achieved in very short running times, which makes the technique suitable for models to be employed in optimization and online control tasks.