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]
[math]\displaystyle{ V = F_{Ao} \left ( \frac{1} {-r_A} \right ) X }[/math]
where:
- [math]\displaystyle{ V }[/math] is the reactor volume
- [math]\displaystyle{ F_{Ao} }[/math] is the molar flow rate per unit time of the entering reactant A
- [math]\displaystyle{ X }[/math] is the conversion of reactant A
- [math]\displaystyle{ -r_A }[/math] is the rate of disappearance of reactant A per unit volume per unit time
For a plug flow reactor (PFR), the following relationship applies:
[math]\displaystyle{ V = F_{Ao} \int_0^X \frac{1} {-r_A} dX }[/math]
If [math]\displaystyle{ F_{Ao} \over -r_A }[/math] is plotted as a function of [math]\displaystyle{ X }[/math], 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 [math]\displaystyle{ F_{Ao} \over -r_A }[/math] and width equal to [math]\displaystyle{ X }[/math].
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 [math]\displaystyle{ F_{Ao} \over -r_A }[/math] plotted against [math]\displaystyle{ X }[/math].
References
- ↑ Fogler, H. Scott (2006). Elements of Chemical Reaction Engineering (4th ed.). Prentice Hall. pp. 45–65. ISBN 0130473944. https://books.google.com/books?isbn=0130473944.
- ↑ Skogestad, Sigurd (2008). Chemical and Energy Process Engineering. CRC Press. p. 265. ISBN 9781420087567. https://books.google.com/books?isbn=1420087568.
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