Predicting molecular weight and degree of branching distribution of polyethylene for mixed systems with a constrained geometry metallocene catalyst in semibatch and continuous reactors

The problem of finding the bivariate chain length (n)/number of branch points (N) distribution for polyethylene produced by a mixed metallocene catalyst system in continuous (CSTR) and semibatch reactors is addressed in two ways. The first uses distinct classes of chains with a certain number of branches, the second the "pseudodistribution" approach, both generating population balances solved with the Galerkin finite element approach of PREDICI. A nine-classes model yields the exact bivariate distribution up to chains of n = 10 000. Until this limit, classes and pseudodistribution models yield identical results, both being based on identical assumptions. Results also coincide with an analytical solution for a CSTR single catalyst system. In view of their importance for deriving architectures and architectural properties, chain statistics were examined by calculating average segment lengths. In the single catalyst CSTR, these turn out to be independent from the number of branches on a chain, which holds untrue for mixed system CSTRs and all semibatch reactors. Concerning the distribution shape of N at fixed n, growing chains at the branching catalyst are always more narrowly distributed than a binomial distribution. A new method, the variable power binomial distribution (VPBD), enables a correct description of the branching distribution shape. The model allows performing sensitivity calculations for both reactor systems under varying conditions, including dynamic behavior in a semibatch reactor. The effect of catalyst ratio and hydrogen was explored. The remarkable bimodality in the molecular weight distribution at catalyst ratios around 0.5 already observed before for a semibatch reactor persists in the CSTR.