Parallel Nonisothermal Reactions in Batch and Semibatch Reactors

The use of semibatch reactors can be advantageous when a reaction has unwanted side reactions or a high heat of reaction. This Demonstration compares the behavior of a batch and a semibatch reactor in which a complex nonadiabatic reaction takes place.
Consider the parallel reactions and , where products {D} and {U} are desirable and undesirable, respectively. Both reactions are irreversible, exothermic and first order in ; the first reaction that forms the desired product is second order in , while the undesired reaction is first order in . The batch reactor initially has 100 moles of each reactant, whereas the semibatch reactor initially has 100 moles of one reactant, and 100 moles of the other reactant is added at a constant rate. Both reactors have a heat exchanger inside with a constant exchanger temperature; the initial temperatures of the reactors and the feed to the semibatch reactor are the same.
Significant differences in the behavior of the two reactors for the process considered here are:
1. The yield (number of moles of formed) and the overall selectivity (the ratio of to ) are higher in the semibatch reactor than in the batch reactor when reactant is initially in the reactor and is fed to the reactor. Because the concentration of is high, this favors the desired reaction, which is second order in .
2. For the same reason, the overall selectivity in the semibatch reactor increases with decreasing flow rate when is fed to .
3. Temperature control is more efficient in the semibatch reactor because the reaction rate is slower.


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The rate laws for the reactions are:
, and
where and are rates of reaction,
and are rate constants,
and are the concentrations of and ,
and is temperature.
The reactant and product concentrations and selectivity in the batch reactor are:
where , , and are the numbers of moles in the reactor,
and are the concentrations of the products,
is the time-dependent volume,
and is the selectivity of the desired product.
Material balances for the semibatch reactor when is fed into :
, and
where is the inlet volumetric flow rate,
is the concentration of in the feed,
is time,
and is the initial volume of the semibatch reactor.
The material balances when is fed into are the same except:
, and
where is the concentration of in the feed.
Material balances for the batch reactor are:
, and
Here the concentrations are:
= ,
= ,
= , and
= .
Energy balance for the semibatch reactor is:
and for the batch reactor is:
where is the heat exchanger overall heat transfer coefficient,
and are the heat of reaction,
and are the constant temperatures of the heat exchanger and the feed to the semibatch reactor, respectively,
and , , etc. stand for heat capacities of the reactants.
[1] University of Colorado Boulder. "Selectivity in a Semibatch Reactor." (Nov 8, 2017) www.colorado.edu/learncheme/kinetics/SelectivitySemibatchReactor.html.
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