Three-dimensional chain-length-branching-combination points distribution modeling of low density polyethylene in a continuous stirred tank reactor allowing for gelation

• Rigorous 3D model of chain length-branching-combination points distribution for ldPE.
• ‘Combinatorial Explosion’ as a result of termination by combination.
• Successful implementation of the combination termination reaction in the Galerkin–FEM.
• Correctly accounting for gel formation in comparison to the Monte Carlo simulations.

The focus of this paper is especially on the role of combination termination in the context of 3-dimensional population balance modeling of trivariate chain length/number of branch points/number of combination points distribution for low-density Polyethylene. Termination by combination is a well-known termination mechanism in radical polymerization and regarding low-density Polyethylene many authors have assumed this mechanism to be present. The ratio between disproportionation and combination termination in the previous studies varies, but usually the two mechanisms are thought of equal importance.Full 3-dimensional population balance equations are solved by a combination of the 2-dimensional Galerkin–finite element method and the pseudo distributions method to estimate chain length/branching/number of combination points distributions. Termination by combination is treated in a different scheme than the framework employed for other kinetic reactions. Good agreement with Monte Carlo results has been observed for low-density Polyethylene-like kinetics.

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