9827

Dynamics of a Coupled Reactor-Separator System with Time Delay

This Demonstration analyzes the effect of time delay on the behavior of a coupled non-isothermal continuous-flow stirred tank reactor (CSTR) with a separator.
The effluent of the reactor is fed to an isothermal separator and the liquid stream of the separator is recycled to the reactor. A first-order exothermic irreversible reaction takes place in the reactor and there is a time delay in the transport from the reactor to the separator. The dimensionless delay-differential equations that describe the system (equations 8 and 9 in [1]) are
,
,
,
.
In these equations, represents the mole fraction of species in the reactor, is the reactor dimensionless temperature, and is the dimensionless time. , , and are the Damköhler number, the dimensionless heat transfer coefficient, and the dimensionless adiabatic temperature rise; these dimensionless numbers are defined in terms of system variables in the reference.
The mole fractions of species in the reactor fresh feed, the distillate stream, and the recycle stream are , , . The equations are solved with and . In the absence of delay, the coupled system exhibits damped oscillations leading to a steady state for low and high values of the Damköhler number and oscillations without a steady state for intermediate values of the Damköhler number. Delay induces new regions of dynamic instability: increasing the delay beyond a lower threshold value can either destabilize the system or lead to isolated states of stability.

SNAPSHOTS

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

DETAILS

References
[1] P. Balasubramanian, S. Pushpavanam, and A. Kienle, "Delay Effect in a Coupled Reactor-Separator System Sustaining Non Isothermal Reaction," Proceedings of the National Conference on Nonlinear Systems & Dynamics, Indian Institute of Technology, Kharagpur, India, Dec. 28–30, 2003 pp. 189–192. ncnsd.org/proceedings/proceeding03/html/pdf/189-192.pdf.
[2] Wikipedia. "Damköhler Numbers." (Feb 26, 2013) en.wikipedia.org/wiki/Damk% C3 % B6hler_numbers.
    • 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.









 
RELATED RESOURCES
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 © 2014 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+