COMSOL 6.4 - Polymerization in Multijet Tubular Reactor

Polymerization in Multijet Tubular Reactor

Production processes for polymers often involve turbulent flows and rapid reaction kinetics. The sophisticated interplay between fluid dynamics and fast chemical reactions can significantly impact the reactor performance, and thereby affect conversion and yield. Furthermore, the turbulent fluid mixing and its effects on the reaction can influence the average length of polymer chains, the molecular weight distribution, cross-linking, and chain-branching. All these properties are important for the integrity of the final material. This example demonstrates a polyester reactor, with multiple inlets, and includes heat transfer and temperature dependent kinetics. It employs the eddy dissipation model for the mean reaction rate in turbulent flows.

This application requires both the Chemical Reaction Engineering Module and the CFD Module.

Model Definition

Geometry

The geometry of the inlet section of a multijet tubular reactor is illustrated in Figure 1.

Figure 1: Inlet section of a multijet tubular reactor. Monomer A (diol) enters through the axial inlets while monomer B (diacid) enters through the radial ports.

Two reacting monomers enter through separate inlet ports. Monomer A enters through the axial inlets while monomer B enters through the radial ports.

Chemistry

Condensation reactions are fundamental to the production of many important polymers, such as polyamides, polyesters, polyurethanes, and silicones.

This model simulates a polyester reactor. Condensation polymerization of monomers A (a diol) and B (a diacid), forms the polyester linkage, L (Ref. 1, Ref. 2). The reactions take place in the presence of a solvent catalyst, S.

Table 1: Species used on the model.
Name	Description
A	Diol monomer
B	Diacid monomer
L	Polyester linkage (product)
S	Solvent catalyst (TiCl3)
C	Complexating water

The catalytic species, S, is temporarily trapped in an intermediary H2O complex, S · C, where C represents the complex-forming water in the irreversible reaction

(1)

The regeneration of solvent is governed by the reversible reaction

(2)

The reaction rates for each chemical reaction is determined by the law of mass action and the eddy dissipation concept (EDC) model. The law of mass action gives the rates (mol/(m3·s))

(3)

and

(4)

for reactions Equation 1and Equation 2, respectively, where the rate constants are given by the Arrhenius expression

(5)

In Equation 5, Aj is the frequency factor and Ej the activation energy (J/mol) for the jth reaction. The table below lists the values of the Arrhenius parameters for the reactions. The rates are adjusted for turbulent conditions according to the EDC model: If the time scale of the turbulent mixing is larger than the reaction kinetics derived by the law of mass action above, the turbulent mixing will be rate determining. For detailed information, see the section Eddy Dissipation Model in the CFD Module User’s Guide.

Transport

The 3D model geometry is illustrated in Figure 1.

Velocities and Pressure

The average velocities at the radial and axial inlets are set to 5 m/s. Furthermore, a constant pressure is set at the outlet and logarithmic wall functions are specified at the solid walls.

Mass Transport

Concentration boundary conditions apply at the inlets:

(6)

The catalytic solvent S is set as solvent in the mass transport model.

Energy Transport

The reactor is assumed to be insulated at the walls and all inlet streams are specified to 440 K temperature.

Summary of Input Data

For the rate expressions in Equation 3 and Equation 4 the following data is used (Ref. 1):

Table 2: kinetic data.
Quantity	Frequency factor	Activation energy	Turbulent parameters α and β
Forward Reaction 1	25.6	61.3[kJ/mol]	4, 0.5
Forward reaction 2	3.9e3	56.8[kJ/mol]	4, 0.5
Reverse reaction 2	4.7e3	102[kJ/mol]	4, 0.5

The material properties and boundary conditions used are (Ref. 1 and Ref. 2).

Table 3: Input data.
Property	Value
Diffusivity	1e-8[m^2/s]
Density of catalyst solvent	2640[kg/m^3]
Heat capacity of catalyst solvent	2550[J/kg/K]
Inlet velocity	5[m/s]
Inlet temperature	440[K]
Molar mass, monomer A	48[g/mol]
Molar mass, monomer B	104[g/mol]
Molar mass, complexating H2O	18[g/mol]
Molar mass, polymer L	164[g/mol]
Molar mass, catalyst S	154[g/mol]
Molar mass, catalytic species complex SC	172[g/mol]
Molar mass, species complex AC	66[g/mol]
Heat of reaction, Reaction 1	100[kJ/mol]
Heat of reaction, Reaction 2	40[kJ/mol]

Modeling in COMSOL

The polymerization reactions are first solved for using an ideal plug flow reactor model. This is performed using the Reaction Engineering interface, and produces the one dimensional development of the flow rates and temperature along the reactor.

To model the system in 3D, the Generate Space-Dependent Model feature, Reaction Engineering interface, is then used. A part from a 3D component, this also creates and a Reacting Flow multiphysics interface combining four physics interfaces. The Chemistry interface implements the reaction kinetics, using the same reactions as in the plug flow model. The Transport of Concentrated Species interface and the Heat Transfer in Fluids interface solves for the mass transport and heat transfer respectively, including the mass sources and heat of reactions as defined by the Chemistry interface. The Turbulent Flow k-ε interface solves for the velocity, pressure, and turbulent mixing, used in the equations for mass transfer and the heat transfer. The Reacting Flow multiphysics node controls the coupling between the individual physics interfaces.

Staged Solution

Since the chemical reactions are strongly dependent on the flow, the composition, and the temperature, the fully coupled system is often difficult to converge by starting from constant initial conditions. A faster and more robust solution procedure is to first solve for the velocity and pressure. And to use this as initial conditions, in a second step, to solve for the entire system.

Geometry

Due to symmetry, a sector of one 1/20 of the geometry shown in Figure 1 is modeled. The modeling results are rotated to the full geometry by sector datasets.

Mesh

The mesh is calibrated to resolve the shear layers that appear near the inlets of the reactor. Further downstream where the flow profile is expected to be more uniform, a simpler extruded mesh is used to save time and memory.

Results and Discussion

The results when solving for an ideal plug flow reactor of the same length as the 3D geometry are seen in Figure 2 below. As reactants are assumed fully mixed already when entering the reactor, the reactions go to completion over a small fraction of the reactor.

Figure 2: Flow rates and temperature in an ideal plug flow reactor.

In the 3D geometry the monomer reactants enter the reactor from different inlets and needs to be mixed before the reactions take place. Results from the 3D multijet tubular reactor model are shown below. Figure 3 shows the velocity field in a cut plane through the reactor. The figure indicates an intense mixing zone in the region were the axial and radial jets impinge. Plotting the streamlines of the velocity field Figure 4 provides more detailed information about the flow paths. Closer inspection at the entrance of the reactor reveals several recirculation zones.

Figure 3: Velocity field (m/s) in the multijet tubular reactor.

Figure 4: Streamlines of the velocity field shows the recirculation zones near the inlet orifices. The concentration of reactants decrease rapidly at after the inlet stretch.

The turbulent flow field transports and mixes the chemical species. Once monomer A comes into contact with the radial streams of monomer B, polymerization starts. Figure 5 shows the resulting concentration field of monomer A.

Figure 5: Concentration distribution of monomer A (mol/m3).

Figure 6 shows isosurfaces of the polymer linkage L concentration. Concentrated isolevels clearly mark the positions of where the inlet streams meet. But isolevels are also present throughout the recirculation zones.

Figure 6: Isosurfaces for the concentration of L (mol/m3) visualized using a clip plane.

As mentioned above, recirculation is evident in the entrance of the reactor. Recirculation will increase the effective residence time of the reactor. Figure 7 shows the concentration of polymer linkage, cL, with a surface slice plot. Clearly, the concentration of L is relatively low in the recirculation region. In polymerization processes, increasing linkage concentration can lead to dramatic changes in the properties of the reacting fluid, particularly viscosity. This in turn may cause fouling or even reactor failure.

Figure 7: Concentration distribution of polymer linkage, cL (mol/m3).

Figure 8 shows the axial development of the flow rates though the multijet tubular reactor. The flow rate of monomer B is initially zero since it is injected through radial inlets attached about 1.3 cm into the reactor. Following the injection, monomer B attains a maximum around 2 cm into the reactor. The other species evolve monotonically in the axial direction. It can be noted that the reaction zone in the 3D reactor is significantly longer compared to that in Figure 2 using the plug flow assumption.