Levenspiel plot

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]

${\displaystyle V=F_{Ao}\left({\frac {1}{-r_{A}}}\right)X}$

where:

• ${\displaystyle V}$ is the reactor volume
• ${\displaystyle F_{Ao}}$ is the molar flow rate per unit time of the entering reactant A
• ${\displaystyle X}$ is the conversion of reactant A
• ${\displaystyle -r_{A}}$ is the rate of disappearance of reactant A per unit volume per unit time

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

${\displaystyle V=F_{Ao}\int _{0}^{X}{\frac {1}{-r_{A}}}dX}$

If ${\displaystyle F_{Ao} \over -r_{A}}$ is plotted as a function of ${\displaystyle X}$, 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 ${\displaystyle F_{Ao} \over -r_{A}}$ and width equal to ${\displaystyle X}$.

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 ${\displaystyle F_{Ao} \over -r_{A}}$ plotted against ${\displaystyle X}$.

References

1. Fogler, H. Scott (2006). Elements of Chemical Reaction Engineering (4th ed.). Prentice Hall. pp. 45–65. ISBN 0130473944.
2. Skogestad, Sigurd (2008). Chemical and Energy Process Engineering. CRC Press. p. 265. ISBN 9781420087567.