Mathematical Modeling of Bivariate Distributions of Polymer Properties Using 2D Probability Generating Functions. Part II: Transformation of Population Mass Balances of Polymer Processes

Abstract

This is the second of two works presenting a new mathematical method for modeling bivariate distributions of polymer properties. It is based on the transformation of population balances using 2D probability generating functions (pgf) and a posteriori recovery of the distribution from the transform domain by numerical inversion. Part I of this work was devoted to the numerical inversion step. Here the transformation of the population balances to the pgf domain is analyzed. A 2D pgf transform table is developed, which allows a simple transformation of any typical polymer balance equation. Three copolymerization examples are used to show the application of the complete procedure of this modeling technique.