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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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: ,
Langmuir–Hinshelwood: ,
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 [2] explains how to use this Demonstration.
[1] H. S. Fogler, Essentials of Chemical Reaction Engineering, 1st ed., Upper Saddle River, NJ: Pearson Education, 2010 pp. 33–82, 445.
[2] Minimized Volume for Reactors in Series [Video]. (Sep 12, 2016) www.colorado.edu/learncheme/kinetics/MinVolumeForReactorsInSeries.html.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+