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]

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

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 $X$ .

References

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

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[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.