Selectivity in a Semibatch Reactor

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The parallel reactions and
are carried out in an isothermal semibatch reactor. Both reactions are first-order in
. The desired reaction to form the product
is second-order in
, whereas the undesired reaction to form product
is first-order in
. Both reactions are irreversible and are not elementary. This Demonstration compares two scenarios: (1) pure
is fed to a reactor that initially contains only
, and (2) pure
is fed to a reactor that initially contains only
. The overall selectivity (the number of moles of
in the reactor divided by the number of moles of
in the reactor (
), is much higher when all the
is initially in the reactor and
is fed to the reactor. This scenario keeps the concentration of
high, which favors the desired reaction, which is second-order in
. For either scenario, the addition of the second reactant stops after 10 minutes, when the amount of the reactant added equals the amount of the other reactant initially in the reactor. Use sliders to vary the activation energy of each reaction and the isothermal reactor temperature to determine how selectivity and moles of products and reactants change with time. The amounts of both products increase with temperature because the reactions are irreversible.
Contributed by: Rachael L. Baumann (August 2013)
With additional contributions by: John L. Falconer and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The rate laws for the reactions are:
,
,
,
,
where the subscripts and
refer to the desired and undesired reactions,
and
are rates of reaction,
and
are rate constants,
and
are the concentrations of
and
,
and
are pre-exponential factors,
and
are activation energies,
is the ideal gas constant, and
is temperature.
The reactant and product concentrations and selectivity are:
=
,
=
,
=
,
=
,
=
,
where ,
,
, and
are moles of the component in the reactor,
and
are concentrations of
and
,
is volume which changes with time, and
is the selectivity of the desired product.
Material balances for system where is fed into pure
:
,
,
,
,
,
where is the inlet molar flow rate of
,
is the inlet volumetric flow rate, and
is time.
Mole balance for system where is fed into pure
:
Only and
differ from above balance:
,
,
where is the inlet molar flow rate of
.
The screencast video at [1] shows how to use this Demonstration.
Reference
[1] Selectivity in a Semibatch Reactor. www.colorado.edu/learncheme/kinetics/SelectivitySemibatchReactor.html.
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