Minimized Volume for Reactors in Series
A plot of (feed molar flow rate)/(rate of reaction) versus fractional conversion is used to demonstrate how to minimize total reactor volume for two isothermal reactors in series. Select the order of the plug flow reactor (PFR) and continuous stirred-tank reactor (CSTR) with buttons. Use buttons to select the reaction kinetics for ; the reaction can be first order, second order or a Langmuir–Hinshelwood mechanism . The colored areas are proportional to the reactor volumes. The PFR volume is proportional to the area under the curve (from inlet to outlet conversion), and the CSTR volume is the difference between inlet and outlet conversion multiplied by the axis ratio at the reactor outlet. Use sliders to select the fractional conversion exiting each reactor.
Contributed by: Nicholas R. Larson (May 2014)
With additional contributions by: Rachael L. Baumann, John L. Falconer and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA
The reactor volumes for a continuous stirred-tank reactor (CSTR) and plug flow reactor (PFR) are:
where is the inlet molar flow rate of reactant , is the rate of disappearance of reactant and and are the inlet and outlet reactor conversions.
Assuming constant reactor inlet flow rate , the molar flow rate of is . The concentration of can be written in terms of conversion .
The reaction rates for the different reaction types are:
first order: ,
second order: ,
assuming , the Langmuir–Hinshelwood rate law can be written in terms of conversion :
where is the rate constant, and and are the adsorption equilibrium constants for and .
The screencast video at  explains how to use this Demonstration.
 H. S. Fogler, Essentials of Chemical Reaction Engineering, 1st ed., Upper Saddle River, NJ: Pearson Education, 2010 pp. 33–82, 445.
 Minimized Volume for Reactors in Series [Video]. (Sep 12, 2016) www.colorado.edu/learncheme/kinetics/MinVolumeForReactorsInSeries.html.