Performance of a Plug Flow Reactor with Recycle

Consider a second-order reaction (2A → B) with a reaction rate, , that takes place in a plug flow reactor with recycle. The recycle ratio is
.
The volume of the reactor needed to achieve a final conversion is given by
,
where is the volumetric flow rate, V is the reactor's volume, and is the reactor's conversion of species A.
There are two limiting cases:
gives a plug flow reactor without recycle case ( has the lowest value).
gives mixed flow reactor behavior ( has the highest value).

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O. Levenspiel, Chemical Reaction Engineering, New York: John Wiley & Sons, 1999.
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