Recovery of molecular weight distributions from transformed domains. Part I. Application of pgf to mass balances describing reactions involving free radicals

https://bibliotecadigital.ipb.pt/bitstream/10198/336/4/CESCIENCE05.pdf

An improved general kinetic analysis of non-linear irreversible polymerisations

Modeling and optimization of a high-pressure ethylene polymerization reactor using gPROMS

Recovery of molecular weight distributions from transformed domains. Part II. Application of numerical inversion methods

Numerical Techniques for the Solution of the Molecular Weight Distribution in Polymerization Mechanisms, State of the Art

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.

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

We have incorporated mass balances of monomer, radical and polymer species to a previously developed mixing model for high pressure autoclave polymerization reactors. The customary quasi steady state approximation is not used, and the method of moments is used to simplify the mass balance calculations. The resulting moment model is able to calculate conversions, average molecular weights, long chain branching and melt flow indexes at any point in the reactor. It may also calculate concentration and temperature profiles along the reactor. Results for two base cases are presented in detail. Model predictions were compared with experimental data obtained at the industrial reactor; excellent agreement was obtained. The moment balance equations are presented in a modular way so that they may be easily adapted to be used with any other mixing model for this type of reactor.

Modeling of molecular weights in industrial autoclave reactors for high pressure polymerization of ethylene and ethylene-vinyl acetate

In this work we analyze the feasibility of using numerical inversion techniques for recovering MWD of actual polymers from a transformed domain, specifically the one defined by probability generating functions. We start from known experimental MWDs, transform them, and then apply two different numerical techniques to recover the MWD. We analyze the influence of noise in the calculated probability generating functions on the quality of the recovered molecular weight distributions. We also study how the range of molecular weight selected for the inversion procedure affects the results. We compare the recovered distributions obtained by both methods and suggest a criterion for establishing the reliability of a given solution. We find that this general strategy is appropriate for the recovery of MWDs whether they are monomodal, multimodal, wide or narrow. This provides a tool for the treatment of actual polymerization systems for which there is no analytical solution for the mass balance equations.

K. S. Whiteley

Papers

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

Modeling of molecular weights in industrial autoclave reactors for high pressure polymerization of ethylene and ethylene-vinyl acetate

Numerical inversion techniques in the recovery of molecular weight distribution expressed in different transformed domains. Experimental validation