Economic Trade-Offs in the Operation of a Single Reactor

Consider an irreversible first-order reaction (A → products) taking place in a single isothermal CSTR (Continuous Stirred-Tank Reactor). We suppose that the unconverted reactant cannot be recycled. There is thus a trade-off between investment cost and raw material cost. Indeed, there is a low investment cost and high raw material consumption at low conversions for a specified production rate. On the other hand, high conversions require large reactor volumes but low raw material costs. The total annual cost, TAC, is given by the blue curve. This curve is convex, which guarantees that we can find a global minimum for the TAC. This optimum point is represented by a blue dot. The red curve represents the behavior of raw material cost with conversion for a fixed production rate. The behavior of the reactor investment cost as a function of conversion is shown in green. For high conversions, one needs large reactor volumes, which will be expensive. TAC is given by the following expression; the first term and second terms take into account raw material cost and the investment cost:
where is the conversion, is the production rate, is density, is a rate constant for the first-order reaction, and and are cost coefficients for the reactor and raw material.
This Demonstration plots the TAC function and the various contributions to this function versus conversion, for user-specified values of the cost coefficients.


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


J. M. Douglas, Conceptual Design of Chemical Processes, International ed., New York: McGraw–Hill, 1988.
    • 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+