COMSOL 6.4 - Hydrodealkylation in a Membrane Reactor

At high temperatures and pressures, and in the presence of hydrogen, toluene can be demethylated to produce benzene. Furthermore, benzene can react reversibly to produce biphenyl. The following example illustrates the simulation of the hydrodealkylation process, carried out in a membrane reactor. This reactor arrangement allows for continuous addition of hydrogen to the process, increasing the selectivity for the desired benzene product.

The example shows how you can easily modify the predefined Plug Flow reactor type in the Reaction Engineering interface to set up a membrane reactor model. We will also learn how to create a Thermodynamic System from Thermodynamics to get different thermodynamic and physical property functions for each compound and their mixture. After all species in Reaction Engineering have been coupled to a corresponding species in the Thermodynamic system, the required species and mixture properties will automatically be created and added to the package.

Model Definition

Two important reactions occur in the thermal hydrodealkylation (HDA) of toluene. The main reaction involves toluene reacting with hydrogen to produce benzene and methane:

(1)

The dealkylation reaction rate is first order in the toluene concentration and half order in the hydrogen concentration:

At the same time, biphenyl is reversibly formed from benzene:

(2)

The rate of the coupling reaction follows the mass action law:

In the above rate expressions, the rate constants follow Arrhenius type behavior:

The values of the frequency factors and activation energies (J/mol) are taken from the literature (Ref. 1 and Ref. 2) and are presented in Table 1.

Table 1: ARRHENIUS PARAMETERS.
	FREQUENCY FACTOR	ACTIVATION ENERGY
Forward reaction 1	5.67e9	228.2e3
Forward reaction 2	1e8	167.5e3
Reverse reaction 2	1e8	149.8e3

The chemical reactions given in Equation 1 and Equation 2 suggest that maintaining high concentrations of hydrogen would be beneficial to ensure a high benzene yield. Such process conditions can be achieved by using a membrane reactor. As illustrated schematically in Figure 1, hydrogen can be supplied continuously across the porous membrane.

Figure 1: Hydrogen is continuously supplied to the reactor through a porous membrane.

The species mass balance for hydrogen in the membrane reactor is given by:

where F is the molar flow rate (SI unit: mol/s) in the reactor, V is the reactor volume (SI unit: m3), R is the species rate expression (SI unit: mol/(m3·s)), and f is the molar flow rate per unit volume (SI unit: mol/(m3·s)) across the membrane. The velocity of the hydrogen gas across the porous membrane can be described by Darcy’s law:

where K (SI unit: m3/(N·s)) is a proportionality constant, pshell (SI unit: Pa) is the gas pressure on the shell side of the membrane, and preactor (SI unit: Pa) the pressure on the reactor side. The molar flow rate per unit volume across the membrane then becomes:

Above, a is the membrane surface area per unit volume (SI unit: m2/m3), and cshell is the concentration of hydrogen (SI unit: mol/m3) on the shell side.

Except for hydrogen, the other chemical species in the reactor do not pass through the membrane and their material balances thus follow the standard plug flow equations:

(3)

The adiabatic energy balance for the reactor is given by:

(4)

In Equation 4, Cmix represents the mixture (reacting system) molar heat capacity (SI unit: J/(mol·K)), and Q denotes the heat due to chemical reaction (SI unit: J/(m3·s)):

where Hj is the heat produced by reaction j, calculated from:

(5)

In Equation 5 hi represents the species partial molar enthalpy (SI unit: J/mol) and νij the stoichiometric coefficients.

The last term in the energy balance accounts for the energy transfer associated with the flow of hydrogen across the membrane:

The Reaction Engineering interface automatically sets up and solves Equation 3 and Equation 4 when you select the predefined Plug-flow reactor type. To adjust the default model to account for hydrogen entering the reactor through the membrane, the flow term fH has to be specified and included into the hydrogen material balance.

Solving the energy balance, Equation 4, requires the input of mixture molar heat capacities Cmix (SI unit: J/(mol·K)), and the partial molar enthalpies, hi (SI unit: J/mol), of the reacting species. In this example, these thermodynamic properties are calculated from the thermodynamic system.

Results and Discussion

In a first simulation, the reactor is assumed to be a standard tubular reactor, that is, without hydrogen entering through the reactor circumference. The reactor is fed with equal molar flows (10 mol/s) of hydrogen and toluene. At the inlet the reactant gas is held at 1200 K and 2 atmospheres. The result is shown in Figure 2.

Figure 2: Concentration (mol/m3) and temperature (K) as function of reactor volume (m3) for a tubular reactor design.

A second model simulates the membrane reactor, with a continuous supply of hydrogen through the membrane. Figure 3 shows the corresponding concentration distributions.

Figure 3: Concentration (mol/m3) and temperature (K) as function of reactor volume (m3) for a membrane reactor design with a continuous supply of hydrogen.

The biphenyl concentration is reduced versus that obtained from the first model. Clearly, the membrane reactor produces benzene with greater selectivity. However, note that this comparison is somewhat lacking in this particular model, the total amount of added hydrogen differs due to the flow across the membrane being an additional source. A more elaborate model, with irreversible reactions leading to unwanted byproducts, would however exhibit differences even after compensating for different amounts of hydrogen.

References

1. K.C. Hou and H.B. Palmer, “The Kinetics of Thermal Decomposition of Benzene in a Flow System,” J. Phys. Chem., vol. 69, no. 3, pp. 863–868, 1965.

2. S.E. Shull and A.N. Hixson, I&EC Process Design and Development, vol. 5, p. 147, 1966.

Chemical_Reaction_Engineering_Module/Thermodynamics/membrane_hda

This model is included in the booklet Introduction to Thermodynamic Properties.

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

Click

In the tree, select > .

Click

Reaction Engineering (re)

In this model, a will be created from . The includes all thermodynamic properties (such as enthalpy, entropy, etc) which are needed in the simulation of reacting system. The properties from are coupled to automatically.

In the toolbar, click

and choose .

First, select a phase state for the Thermodynamic System.

Select System

Go to the window.

Select phases .

From the list, choose .

Click the button in the window toolbar.

Select species hydrogen, methane, benzene, toluene and biphenyl.

Select Species

Go to the window.

In the list box, select .

Click

In the list box, select .

Click

In the list box, select .

Click

In the list box, select .

Click

In the list box, select .

Click

Click the button in the window toolbar.

Select Thermodynamic Model

Go to the window.

Click the button in the window toolbar.

Global Definitions

Vapor–Liquid System 1 (pp1)

Create a mixture function for enthalpy of formation to introduce a heat source used later in .

Right-click > > and choose .

Select Properties

Go to the window.

In the list box, select .

Click

Click the button in the window toolbar.

Select Phase

Go to the window.

Click the button in the window toolbar.

Select Species

Go to the window.

Click

Click the button in the window toolbar.

Mixture Property Overview

Go to the window.

Click the button in the window toolbar.

Global Definitions

Enthalpy of formation 1 (EnthalpyF_benzene_biphenyl_hydrogen_methane_toluene_Vapor11, EnthalpyF_benzene_biphenyl_hydrogen_methane_toluene_Vapor11_Dtemperature, EnthalpyF_benzene_biphenyl_hydrogen_methane_toluene_Vapor11_Dpressure)

Change the function name to hF_mixture.

In the window for , type hF_mixture in the text field.

Load model parameters by importing their definitions from a text file.

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file membrane_hda_parameters.txt.

Definitions

Add variable definitions from a text file.

Variables 1

In the window, under right-click and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file membrane_hda_variables.txt.

Note that some expressions use functions in and variables defined in the interface. These variables need to be specified with the scope of the node. For example, re.T specifies the temperature variable defined by the node with the identifier re.

Reaction Engineering (re)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the Q text field, type Q_mem.

This accounts for the heat transferred into the reactor due to the flow across the membrane.

Click to expand the section. In the p text field, type p_reactor.

Reaction 1

In the toolbar, click

In the window for , locate the section.

In the text field, type C6H5CH3+H2=>C6H6+CH4.

Locate the section. Select the checkbox.

In the Af text field, type 5.67e9[1/s].

In the Ef text field, type 228.2e3.

Locate the section. From the list, choose .

Locate the section. Find the subsection. In the text field, type 1.

Locate the section. In the rj text field, type re.kf_1*re.c_C6H5CH3*(re.c_H2/1[mol/m^3])^0.5.

Change the default kinetic expression by modifying the reaction order for hydrogen.

Reaction 2

In the toolbar, click

In the window for , locate the section.

In the text field, type 2C6H6<=>C12H10+H2.

Locate the section. Select the checkbox.

In the Af text field, type 1e8.

In the Ef text field, type 167.5e3.

In the Ar text field, type 1e8.

In the Er text field, type 149.8e3.

Additional Source 1

You will now add an feature to to the membrane reactor model.

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


Species	Additional rate expression (mol/(m^3*s))
H2	f_H2

The f_H2 term corresponds to the flow of hydrogen across the membrane.

Initial Values 1

The plug flow reactor requires you to input the inlet molar flow.

In the window, click .

In the window for , locate the section.

In the T0,in text field, type T_inlet.

Locate the section. In the table, enter the following settings:


Species	Molar flow rate (mol/s)
C6H5CH3	10
H2	10

Couple all species in to corresponding species in the created . For a coupled species, its thermodynamic properties will be set automatically to the coupled Thermodynamic System. When all species in are coupled (fully coupled), the properties of the reacting system (heat capacity, molar volume, etc) will be calculated from the Thermodynamic System.

In the window, click .

In the window for , locate the section.

Select the checkbox.

Locate the section. In the table, enter the following settings:


Species	From Thermodynamics
C12H10	C12H10
C6H5CH3	C7H8
C6H6	C6H6
CH4	CH4
H2	H2

In the present example the total reactor volume is 1 m3, so default solver settings can be used.

Tubular reactor

You have now set up a model for a nonisothermal tubular reactor. For the tubular reactor, the feature is disabled. First solve this model and review the results, then move on to study the related membrane reactor model with the feature.

In the window, right-click and choose .

In the dialog, type Tubular reactor in the text field.

Click .

Step 1: Stationary Plug Flow

In the window, under click .

In the window for , locate the section.

Select the checkbox.

In the tree, select > > .

Right-click and choose .

In the window, click .

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Results

1D Plot Group 1

In the toolbar, click

Global 1

Right-click and choose .

Global 2

In the window, right-click and choose .

Concentration and Temperature profile, tubular reactor

In the window for , type Concentration and Temperature profile, tubular reactor in the text field.

Locate the section.

Select the checkbox. In the associated text field, type Reactor volume (m<sup>3</sup>).

Select the checkbox. In the associated text field, type Concentration (mol/m<sup>3</sup>).

Select the checkbox.

In the table, select the checkbox for .

Select the checkbox. In the associated text field, type Temperature (K).

Concentration

In the window, under > click .

In the window for , type Concentration in the text field.

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
re.c_C6H5CH3	mol/m^3	Concentration
re.c_H2	mol/m^3	Concentration
re.c_C6H6	mol/m^3	Concentration
re.c_CH4	mol/m^3	Concentration
re.c_C12H10	mol/m^3	Concentration