Levenspiel plot explained

A Levenspiel plot is a plot used in chemical reaction engineering to determine the required volume of a chemical reactor given experimental data on the chemical reaction taking place in it. It is named after the late chemical engineering professor Octave Levenspiel.

Derivation

For a continuous stirred-tank reactor (CSTR), the following relationship applies:^{[1] [2]}

V = F _{Ao} \left ( (1)/(- r _{A}) \right ) X

where:

V is the reactor volumeF _{Ao} is the molar flow rate per unit time of the entering reactant AX is the conversion of reactant A- r _{A} is the rate of disappearance of reactant A per unit volume per unit time

For a plug flow reactor (PFR), the following relationship applies:

V = F _{Ao} \int ^{X} _{0} (1)/(- r _{A}) dX

If

F _{Ao} \over - r _{A} is plotted as a function of X , the required volume to achieve a specific conversion can be determined given an entering molar flow rate.

The volume of a CSTR necessary to achieve a certain conversion at a given flow rate is equal to the area of the rectangle with height equal to

F _{Ao} \over - r _{A} and width equal to X .

The volume of a PFR necessary to achieve a certain conversion at a given flow rate is equal to the area under the curve of

F _{Ao} \over - r _{A} plotted against X .

References

1. Book: Fogler, H. Scott. 2006 . Elements of Chemical Reaction Engineering . Prentice Hall . 4th . 45–65 . 0130473944 .
2. Book: Skogestad, Sigurd . 2008 . Chemical and Energy Process Engineering . CRC Press . 265 . 9781420087567.