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 in the Reaction Engineering interface to set up a membrane reactor model. You 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:
Here the reference concentration is 1 mol/m3. 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 an Arrhenius-type behavior:
The values of the frequency factors and activation energies are taken from literature (Ref. 1 and Ref. 2) and are presented in the table below.
Arrhenius parameters
 
FREQUENCY FACTOR
ACTIVATION ENERGY
Forward reaction 1
5.67e9 1/s
228.2 kJ/mol
Forward reaction 2
1e8 m3/(mol·s)
167.5 kJ/mol
Reverse reaction 2
1e8 m3/(mol·s)
149.8 kJ/mol
The chemical reactions given in Equation 1 and Equation 2 suggest that maintaining high concentration 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 in the reactor, V is the reactor volume, R is the species rate expression, 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 is a proportionality constant, pshell is the gas pressure on the shell side of the membrane, and preactor 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, and cshell is the concentration of hydrogen 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, and Q denotes the heat due to chemical reaction:
where Hj is the heat produced by reaction j, calculated from
(5)
In Equation 5, hi represents the species partial molar enthalpy 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 fH2 has to be specified and included in the material balance for hydrogen.
Solving the energy balance, Equation 4, requires the input of mixture molar heat capacity Cmix, and the partial molar enthalpies, hi, of the reacting species. In this example, these thermodynamic properties are calculated from the property package.
Results and Discussion
In a first simulation, the reactor is assumed to be a standard tubular reactor; that is, a reactor 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: Species concentrations (mol) 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. The biphenyl concentration is reduced versus that obtained from the first model. Clearly, the membrane reactor produces benzene with greater selectivity.
Figure 3: Species concentrations (mol) and Temperature (K) as function of reactor volume (m3) for a membrane reactor design with a continuous supply 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, “Kinetics of Thermal Hydrodealkylation of Mesitylene,m-Xylene, and Toluene,” Ind. Eng. Chem. Proc. Design Devel., vol. 5, no. 2, p. 146, 1966.
Modeling Instructions
The following step-by-step instructions guide you through the process of setting up a Thermodynamic system and a plug-flow reactor to simulate the thermal demethylation of toluene in the presence of hydrogen. The Thermodynamic system is created from the COMSOL thermodynamic database, which provides all necessary thermal properties for the reacting system. The first part of the model (tubular reactor) shows the nonisothermal process without a so-called additional source  (hydrogen). The second part of the model (membrane reactor) includes a hydrogen source supplied across the porous membrane.