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:

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

where:
 * $$V$$ is the reactor volume
 * $$F_{Ao}$$ is the molar flow rate per unit time of the entering reactant A
 * $$X$$ 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:

$$V = F_{Ao} \int_0^X \frac{1} {-r_A}  dX $$

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 $$X$$.