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

Abstract

A generalized multiscale modeling framework is described for the digital simulation of a high-pressure low-density polyethylene (LDPE) tubular reactor. According to the proposed modeling approach, various models describing the complex physical and chemical phenomena at different length and time scales are linked together to assess the effects of reactor operating conditions on the molecular and rheological behavior of LDPE. The molecular properties of LDPE are determined by employing a comprehensive kinetic scheme. On the basis of the postulated kinetic mechanism, detailed population balance equations (PBEs) are derived describing the conservation of the various macromolecular polymer chains. A review of the potential methods for solving the governing PBEs is presented. In addition, a novel kinetic/topology Monte Carlo method to calculate the molecular and topological properties of the highly branched polymer chains and an advanced rheological model for the calculation of the viscoelastic properties of branched polymers in terms of their respective molecular and topological properties are described.

Polymerization Reactors

“…8 The total length of the tube ranges from 500 to 1500 m, while its internal diameter does not exceed 70-80 mm. With respect to the process heat requirements, the tubular reactor is divided into a number of zones (i.e., preheating, reaction, and coolant zones).…”

“…Thus, the monomer conversion can vary in the range of 20-35%, while the LDPE density ranges from 0.915 to 0.935 g cm À3 . 8 In Figure 5, a schematic representation of a high-pressure tubular LDPE plant is shown.…”

“…8 u denotes the velocity of the reaction mixture in the tube and z is the axial coordinate. Note that the total number of molar balance equations for the 'live' and 'dead' nonlinear polymer chains (see eqns [7] and [8]) will depend on the maximum number of long-chain branches, N b , and the maximum degree of polymerization, N n , that is, it will be equal to 3  N b  N n . Consequently, the computational effort required for the solution of the complete set of molar species differential balance equations is prohibitively high.…”

“…Consequently, the computational effort required for the solution of the complete set of molar species differential balance equations is prohibitively high. Thus, to calculate the joint (MWD-LCBD) distribution along the reactor tube, one needs to solve eqns [7] and [8] using a suitable numerical method (e.g., method of double moments, 'numerical fractionation,' global orthogonal collocation, orthogonal collocation on finite elements, fixed-pivot method, and stochastic Monte Carlo method). 8,12 Thermodynamic Considerations…”

Simulation of Polymer Reactors Using the Compartment Modeling Approach

“…Polymer reactor models are a widely used tool for reactor design. The challenge in this context is to represent the interaction of different phenomena occurring in polymerization reactors on very different time and length scales, as diffusion effects on micro scale and backmixing on macro scale 12–14…”