(376y) Prediction of Rheological Properties of Ldpe Produced in High-Pressure Tubular Reactors

Low density polyethylene (LDPE) has been commercially produced in high-pressure tubular reactors for decades. The high global demand of this polymer is principally due to its large number of applications, including packaging, films and coatings, among others. LDPE is very versatile due to the wide variety of molecular properties that it may present. The increasing demand of LDPE for very specific applications requires polymer manufacturers to meet stricter quality requirements in terms of molecular characteristics of the product that lead to end-use properties. Polymerization reactor modeling can be very useful to manufacturers, helping to establish high-fidelity relationships between the required polymer molecular characteristics and the means for obtaining them: reactor configuration and operation conditions.

The end-use properties of polymers (thermal, mechanical, and rheological) are directly affected by the average and distributed molecular properties of the polymer chains, such as average molecular weights, molecular weight distribution, and long or short chain branching distributions. In the particular case of LDPE, the rheological properties of the polymer are affected by long-chain branching. Specifically, this type of branching affects the extensional and shear viscosity of the molten polymer. This has motivated recent efforts to develop rheological models capable of using information on the topology of the branched molecules to predict rheological properties.

Two of the most popular rheological measurements in molten polymers are the steady-shear viscosity as a function of the shear rate (or flow curve) and the melt index (MI). The latter allows a straightforward quality control for polymer producers. The MI resumes the polymer rheological information into a parameter that can be easily measured. For this reason, periodic measurement of MI is a way of controlling that the production is within specification. In the particular case of LDPE production, the different grades are usually identified by their MI values. However, since the residence time in the polymerization process is shorter than the MI measurement time, there is room for off-spec LDPE production. For that reason, a mathematical model able to predict the MI in real time could be economically convenient.

Mathematical models, with different levels of detail, have been developed to predict molecular architecture of the highly branched LDPE produced in high-pressure tubular reactors.^1-3 Few of them subsequently include rheological predictions.^{4, 5} The mathematical modeling of the polymer viscoelastic behavior in terms of the chain properties is still a topic of continuous study. Models for linear polymer chains are based on the reptation theories of de Gennes⁶ and of Doi and Edwards.⁷ They use the molecular weight distribution of the polymer chains as input. The theory of double reptation has also been applied to describe the relationship between viscoelastic properties and the molecular weight distribution.⁸ For branched polymers, rheological predictions are more complex because there is an extra distributed property to be taken into account, the long chain branching. The joint distribution of molecular weights and long chain branching should be considered in the calculations. There are two main approaches proposed in the literature for this purpose. The first one, called “hierarchical model”,⁹ is based on the idea that branched polymers relax hierarchically starting from the outer branches of the molecule, finishing with the backbone relaxation. The second approach, or “branch-on-branch model,” is based on the tube theory and its extensions for branched polymer melts.

The viscoelastic results obtained from the above models generally include the stress relaxation, storage and loss modulus and the complex viscosity as functions of frequency. This information allows the estimation of the MI. This may be achieved by finite element models or empirical approximations. The first approach is computationally time consuming and requires viscoelastic information such as the extensional viscosity. On the other hand, empirical approximation models only use the flow curve as input and employ a phenomenological description of the flow of the polymer in the melt flow indexer rheometer. These models describe the flow of the molten polymer through a rheometer barrel terminated in a short capillary. Up to now, Rohlfing and Janzen¹⁰ developed the only available approximation model for MI prediction. Basically, they considered that the sum of the pressure drops in the barrel, the entrance region and the capillary of the melt indexer is equal to the applied pressure.

This work presents a high-fidelity deterministic model for the production of LDPE in a high-pressure tubular reactor that predicts several rheological properties such as the flow curve and the MI. The model is an extension of a previous one developed by the authors.^{11, 12} The previous model predicted average properties such as number and weight average molecular weights and number of long and short chain branches every 1000 C atoms, as well as molecular weight distributions and bivariate molecular weight-long (or short) chain branching distributions. The present extension incorporates the prediction of the rheological properties through an adaptation of the hierarchical model, which uses as input the obtained molecular distributions. The model is successfully used to evaluate operating points for the production of different LDPE grades distinguished by their MI values.

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(2) Meimaroglou, D.; Pladis, P.; Baltsas, A.; Kiparissides, C. Prediction of the Molecular and Polymer Solution Properties of LDPE in a High-Pressure Tubular Reactor Using a Novel Monte Carlo Approach. Chem. Eng. Sci. 2011, 66, 1685-1696.

(3) Kim, D. M.; Iedema, P. D. Modeling of Branching Density and Branching Distribution in Low-Density Polyethylene Polymerization. Chem. Eng. Sci. 2008, 63, 2035-2046.

(4) Pladis, P.; Meimaroglou, D.; Kiparissides, C. Prediction of the Viscoelastic Behavior of Low-Density Polyethylene Produced in High-Pressure Tubular Reactors. Macromol. React. Eng. 2015, 9, 271-284.

(5) Kiparissides, C.; Krallis, A.; Meimaroglou, D.; Pladis, P.; Baltsas, A. From Molecular to Plant-Scale Modeling of Polymerization Processes: A Digital High-Pressure Low-Density Polyethylene Production Paradigm. Chem. Eng. Technol. 2010, 33, 1754-1766.

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(12) Dietrich, M. L.; Sarmoria, C.; Brandolin, A.; Asteasuain, M. LDPE Production in Tubular Reactors: Comprehensive Model for the Prediction of the Joint Molecular Weight-Short (Long) Chain Branching Distributions. 2019, 58, 4412-4424.