Mathematical Modeling of Free-Radical Ethylene Copolymerization in High-Pressure Tubular Reactors

Abstract

A comprehensive mathematical model is developed for the free-radical copolymerization of ethylene with various comonomers (e.g., vinyl acetate, methyl or ethyl acrylate, and acrylic or methacrylic acid) in high-pressure tubular reactors. Polar copolymers usually exhibit lower crystallinity and yield strength than low-density polyethylene grades and are used for applications requiring flexibility, toughness, stress-cracking resistance, and adhesion to coatings. In the present study, a detailed kinetic mechanism is proposed to describe the molecular and compositional developments in the free-radical copolymerization of ethylene with a comonomer. On the basis of the postulated kinetic mechanism, a system of differential mass balance equations are derived for the various molecular species, total mass, energy, and momentum in the polymerization system. The model equations are coupled with a set of algebraic equations for estimating the thermodynamic and transport properties of the reaction mixture. The number and weight molecular weight and copolymer composition averages, short-and long-chain branching frequencies, etc., are calculated in terms of the leading moments of the bivariate number chain-length distributions of "live" and "dead" copolymer chains. The predictive capabilities of the mathematical model are demonstrated by a direct comparison of the model predictions with industrial experimental data on the reactor temperature profile and pressure, the overall monomer conversion, and the final molecular and compositional properties of copolymers. Simulation and experimental results are presented for different copolymer grades including ethylene-ethyl acrylate, ethylene-methyl acrylate, and ethylene-vinyl acetate copolymers.

From Molecular to Plant‐Scale Modeling of Polymerization Processes: A Digital High‐Pressure Low‐Density Polyethylene Production Paradigm

“…The method of moments [23][24][25][26] is based on the statistical representation of the average molecular properties (i.e., number and weight average molecular weights) of the polymer chains in terms of the leading moments of the number chain length distribution (NCLD). The method of double moments [10,27,28] can provide additional information on the number and weight average copolymer composition as well as on the number and weight average degree of long-chain branching.…”

“…In response to this slowly changing disturbance, the reactor operation undergoes periods of accumulation and purging of impurities. The industrial importance of high-pressure tubular reactor technology has led to a great number of modeling studies in the past 30 years [10][11][12][13].…”

“…A detailed description of the tubular reactor model can be found in the previous publication of Kiparissides et al [10]. In Figs.…”

Prediction of the molecular and polymer solution properties of LDPE in a high-pressure tubular reactor using a novel Monte Carlo approach

“…LDPE and its copolymers have been commercially produced in high-pressure reactors for more than five decades (Kiparissides et al, 2005). The present strong market demand for LDPE underlines its commercial importance since a large number of applications in packaging, adhesives, coatings, films, etc.…”

Detailed Molecular Structure Modeling – A Path Forward to Designing Application Properties of ldPE

“…However, the base is a standard tank in series model with back flow. A more recent work of Kiparissides et al [9] proposed an ethylene copolymerization model for tubular reactors based on the method of moment. However, the reactor is considered as ideal and not every part of the kinetic model providing M n , M w and average branching indices is explained.…”