378117 Spatial Modeling of a Tubular Reactor for the High Pressure Synthesis of Ldpe

Monday, November 17, 2014
Galleria Exhibit Hall (Hilton Atlanta)
Sebastian Fries, TU Darmstadt, Darmstadt, Germany and Markus Busch, Ernst-Berl-Institute, TU Darmstadt, Darmstadt, Germany

Low-density polyethylene is produced at high temperatures (140 330 C) and high pressures (1000 3500 bar) under free radical conditions. The heat of polymerization (3.5 kJ/g) must be continuously removed to maintain a steady reaction. Therefore in technical tubular reactors water is used as coolant, which flows around the inner tube in an annular gap. In continuous operation often a reduction in heat exchange can be observed. The cause of this process which is known as fouling is still not completely revealed. In literature it is discussed as an insulating polymer film on the reactor wall or as a viscous polymer rich hydrodynamic boundary layer.[1,2] A deepened understanding could lead to an improved process control here, as fouling can affect the quality of the product as well as the productivity and operation safety of a tubular reactor. Therefore in this work the effects of poor mixing within a fouling layer on spatial temperature profiles and polymer properties are analyzed.

A model for characterization of the conditions at the reactor wall with a possible fouling layer has to capture the reaction environment and the micro-structure of the polymer. In steady-state conditions this requires the solution of a system of partial differential equations in two dimensions: radial and axial position along the reactor axis. The complexity and thereby the computational demand can be reduced by treating heat transmission and heat balance of the cooling water separately in a one dimensional model. Additionally, further detail in microstructural information can be gained by compartmentalization of the two dimensional model. Therefore by using the software PREDICI a model is developed which comprises three modules:

1.    One dimensional module:
In the one dimensional module the mass and heat balances based on ordinary differential equations are solved assuming radial homogeneity. The mass balances capture a complex reaction network consisting of primary and secondary radicals.[3] Through the condition of constant radial heat flux density this module supplies reactor wall temperatures along the axial reactor axis which can be used as boundary condition in the radial module. Another important dimension for the radial module is the thickness of the assumed fouling layer. Here this thickness is estimated by the wall roughness of the implemented pressure drop calculation as in technical reactors a correlation between reduced heat exchange and pressure drop has been found.[4]
Detailed information about microstructure is obtained by using the discrete Galerkin hp-method for calculating the rigorous molecular weight distribution.[5] Moreover, by implementing massless counter species radial averaged values for the short-chain and long-chain branching density can be calculated.

2.    Radial module:
The radial module yields spatial mass and temperature profiles for every axial position. The resulting partial differential equations are solved numerically efficient on a self-adaptive grid using the h-p-Galerkin approach. Average values of the molecular weight distribution are achieved by the method of moments.

3.    Compartment module:
The compartment module consists of at least two ideally mixed compartments representing the center and wall flow layer. Mass exchange between those compartments is allowed and the temperatures for each compartment are derived from the radial module. Due to the reduction of the mass balances to ordinary differential equations the computation of the rigorous molecular weight distribution for each compartment becomes possible and a detailed look at the polymer properties in the vicinity of the reactor wall can be achieved.

[1] A. Buchelli et al., Ind. Eng. Chem. Res. 2005, 44, 1474 1479.

[2] M. Krasnyk et al., Proceedings of the 22nd ESCAPE 2012.

[3] M. Busch, Macromol. Theory Simul. 2001, 10, 408 429.

[4] T. Herrmann, PhD Thesis, 2011.

[5] M. Wulkow, Macromol. React. Eng. 2008, 2, 461 494.

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