Two-Dimensional Model of Adiabatic Fixed-Bed Membrane Reactor
Membrane catalytic reactors can increase rates of conversion when a reaction is thermodynamically unfavorable. This Demonstration evaluates a dehydrogenation reaction in a two-dimensional tubular adiabatic fixed bed catalytic membrane reactor. The reversible endothermic reaction, , takes place in the tube side as hydrogen permeates through the membrane to the shell compartment, the membrane being permeable only to .
Steady-state mass and energy balances in this reactor are:
tube side ,
where and are the axial and radial coordinates; represents the reactant , and , the products; is the temperature; , and are maximum fluid velocity, fluid density and fluid heat capacity; , and are the diffusion coefficient, thermal conductivity and enthalpy of reaction; and is the rate of dehydrogenation, with
where and are pre-exponential factors; is the activation energy; and is the universal gas constant.
The boundary values are as follows:
, and , where and are the initial values of the concentration and temperature.
At , and :
and ; here, is the hydrogen permeation coefficient.
These equations are solved with the built-in Mathematica function NDSolve. You can vary the fluid thermodynamic properties, the fluid velocity and the distance along the reactor axis to determine their effect on the distribution of temperature and concentrations in different parts of the reactor.