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

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 *h*‑*p*-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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