Two-Dimensional Model of Adiabatic Fixed-Bed Membrane Reactor

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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
.
Contributed by: Clay Gruesbeck (August 2022)
Open content licensed under CC BY-NC-SA
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Steady-state mass and energy balances in this reactor are:
tube side ,
and
,
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
and
,
where and
are pre-exponential factors;
is the activation energy; and
is the universal gas constant.
The boundary values are as follows:
At :
,
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.
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