Population balance modeling of full two-dimensional molecular weight and branching distributions for ldPE with topological scission in continuous stirred tank reactor

A full extensive 2-dimensional (2D) model of low-density Polyethylene chain length/branching distribution is provided in this paper. 2D Population Balance Equations are solved by the Galerkin-finite element method to obtain the distributions, accounting for 2D 'topological scission'; a manner to approximate random scission by an estimated fragment length distribution. Explicit assumptions have been made concerning the redistribution of branch points on scission fragments.The calculations without scission show that in the 2D case a finer grid of chain length is required in comparison to the 1-dimensional case because of the narrow shape of the branching distribution at the given chain length. With a fine grid, results are in exact agreement to Monte Carlo simulations, which demonstrates the success of the implementation. In the present implementation it was necessary to assume a fragment length independent redistribution of branch points, as was done in an earlier 2D model by Krallis et al. (2007) and Krallis and Kiparissides (2007). We demonstrated that the shape of the branching density distribution is sensitive to this assumption.