Please cite this article as: Brandolin, Adriana., Balbueno, Ayslane Assini., & Asteasuain, Mariano., Improved numerical inversion methods for the recovery of bivariate distributions of polymer properties from 2D probability generating function domains.Computers and Chemical Engineering http://dx.
GRAPHICAL ABSTRACTIn this work two 2D pgf inversion methods are developed, for which the pgf is regarded as a complex variable. These methods provide an outstanding accuracy in the inversion, thus allowing extending the 2D pgf technique for modeling bivariate distributions without restrictions in the range of values of its independent domains HIGHLIGHTS Advanced modeling of polymer processes. Prediction of bivariate (2D) distributions of polymer molecular properties. Improvement of the pgf modeling method. Development of new pgf inversion methods that use complex and/or real pgf. Accurate modeling of 2D distributions with domains of different orders of magnitude.
AbstractThe 2D probability-generating function technique is a powerful method for modeling bivariate distributions of polymer properties. It is based on the transformation of bivariate population balance equations using 2D probability generating functions (pgf) followed by a recovery of the distributions from the transform domain by numerical inversion. A key step of this method is the inversion of the pgf transforms. Available numerical inversion methods yield excellent results for pgf transforms of distributions with independent dimensions with similar orders of magnitude, for example bivariate molecular weight distributions in copolymerization systems.However, numerical problems are found for 2D distributions in which the independent dimensions have very different ranges of values, such as the molecular weight distributionbranching distribution in branched polymers. In this work, two new 2D pgf inversion methods are developed, which regard the pgf as a complex variable. The superior accuracy of these innovative methods makes them suitable for recovering any type of bivariate distribution. This enhances the capabilities of the 2D pgf modeling technique for simulation and optimization of polymer processes. An application example of the technique in a polymeric system of industrial interest is presented.