Prediction of molecular weight distributions by probability generating functions. Application to industrial autoclave reactors for high pressure polymerization of ethylene and ethylene‐vinyl acetate

Abstract

We develop a mathematical model able to describe the complete molecular weight distributions of polyethylene and elhylene‐vinyl acetate copolymers obtained in high pressure autoclave reactors. We apply probability generating function definitions to the mass balances of radical and polymer species in the reacting medium. We use three different definitions of probability generating functions, each one directly applicable either to the number, weight or chromatographic distributions. These probability generating functions are numerically inverted to obtain the corresponding calculated molecular weight distribution. The capabilities of two different inversion methods are compared. Predictions are compared with experimental data obtained in an industrial reactor; good agreement is obtained. The approach presented here is applicable to other types of polymerization reactors and post‐polymerization processes.

Mathematical Modeling of Molecular Weight Distributions in Vinyl Chloride Suspension Polymerizations Performed with a Bifunctional Initiator through Probability Generating Functions

“…The probability generating function (pgf) technique is used here to calculate the MWD of the polymer resin and of the individual populations of polymer chains resulting from the VCM free radical suspension polymerization performed with the bifunctional initiator. The pgf method has been successfully employed for modeling the MWD of different free radical polymerization systems, including non‐isothermal operation, complex kinetic mechanisms and branched polymers . Some of these systems include the peroxide modification of polyethylenes and polypropylenes, styrene polymerizations performed with bifunctional initiators and high‐pressure ethylene polymerizations performed in tubular reactors …”

“…The pgf method has been successfully employed for modeling the MWD of different free radical polymerization systems, including non-isothermal operation, complex kinetic mechanisms and branched polymers. [8,27,37,38] Some of these systems include the peroxide modification of polyethylenes [56] and polypropylenes, [57] styrene polymerizations performed with bifunctional initiators [8] and high-pressure ethylene polymerizations performed in tubular reactors. [58] The pgf is a transform on a probability distribution p l (n) defined as…”

“…Several mathematical models and numerical approaches have been proposed to deal with the calculation of MWD's in polymerization processes, [8,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] including Monte Carlo procedures, [30] orthogonal collocation on finite elements, [31] discrete weighted Galerkin techniques, [32] sectional grid methods, [33] Laplace transforms, [27] and probability generating functions (pgf), [8] among others. Interestingly, few works have reported the calculation of MWDs for PVC.…”

Optimal process operation for the production of linear polyethylene resins with tailored molecular weight distribution

“…1 and 2), one of the established methods has to be employed to approximate the complete MWD. Among others, these methods include the generating function, 41 the finite molecular weight moments, 13 the differentiation of the cumulative MWD 40 and the orthogonal collocation method. [16][17] In this work, orthogonal collocation 42 in the setting of a discrete weightedresidual method is used to compute an approximation of the MWD.…”

An improved general kinetic analysis of non-linear irreversible polymerisations

“…After Miller et al (1996) have shown the potential of this method, Sarmoria and collaborators have been using it in process modelling of polyolefines viscosity breaking by peroxides (Asteasuain et al, 2002a) and both linear (Asteasuain et al, 2004) and branched (Brandolin et al, 2002) simple free radical polymerisations.…”