Shortening the Computation Time of the Polymer Flow Model for Olefin Copolymerization Using Quasi Steady-State Approximations

Abstract

We developed two distinct quasi steady-state approximation (QSSA) solutions to speed up the computation time of the polymer flow model for ethylene/1-olefin copolymerization. One solution assumed that the radial monomer fraction profiles were constant and the other that they were variable. The two QSSA solutions were compared with dynamic solutions that assumed either uniform (approximate dynamic solution) or nonuniform radial distributions (rigorous dynamic solution) of active site concentration in the polymer particle. The adequacy of the QSSA solutions was evaluated at different ethylene and 1-olefin Thiele moduli using particle growth factors, ethylene and 1-olefin mass transfer efficiencies, polymer molecular weight distributions and averages, and short chain branch distributions. After a short period of time, both QSSA solutions matched the approximate dynamic solution well, but they agreed with the rigorous dynamic solution only when the Thiele modulus for ethylene was not too high. The Thiele modulus for 1-olefin had a lesser effect on the model predictions. As the Thiele modulus increased, both QSSA solutions deviated more from the rigorous dynamic solution, but this does not limit the use of these solutions under relevant industrial conditions because severe mass transfer resistances are undesirable in commercial reactors. Finally, the QSSA solutions were integrated with a Monte Carlo model to simulate distributions of polymer particles with different sizes and reactor residence times. These simulations confirmed that the proposed QSSA solutions are more adequate to simulate large polymer particle populations than traditional methods used to solve single-particle models.