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