Selectivity in a Semibatch Reactor

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
  • With additional contributions by: John L. Falconer and Nick Bongiardina
  • (University of Colorado Boulder, Department of Chemical and Biological Engineering)

SNAPSHOTS

  • [Snapshot]
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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
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