title: Levenspiel plot
text: # 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 $X$.
  
  