# Multiple Steady States in a Continuous Stirred-Tank Reactor with Heat Exchange

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A continuous stirred-tank reactor (CSTR) with heat exchange is used for an exothermic reaction. Multiple steady-state solutions are observed; they can be stable, unstable, or exhibit sustained oscillations (limit cycles). The steady-state operating conditions depend on initial conditions (CSTR start up) and on the residence time, and limit-cycle behavior is observed for residence times greater than about 30 minutes. Select "phase plane 1" to plot reactant concentration versus reactor temperature for five initial concentrations; change the initial reactor temperature with a slider. Select "phase plane 2" to plot conversion versus temperature for one initial condition; set the initial reactor temperature and initial reactant concentration with sliders. The reactant feed concentration is 2 and the feed temperature is 298 K. In both plots, the arrows indicate the direction of time. Set the initial conditions with sliders for *"*phase plane 2", "temperature vs. time" and "conversion vs. time" plots; these show how a steady state (or a limit cycle) is approached. Select "energy vs. temperature" to plot heat generated and heat removed versus temperature; the intersections of the straight blue line and green curve correspond to steady-state solutions to the mass and energy balances for the CSTR. The heat transfer fluid is at a constant temperature of 300 K.

Contributed by: Rachael L. Baumann (January 2014)

With additional contributions by: John L. Falconer and Nick Bongiardina

(University of Colorado Boulder, Department of Chemical and Biological Engineering)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Mole balance:

,

,

where is the concentration of reactant (), is the feed concentration of (), is time (min), is residence time (min), is the rate constant (1/min), is the rate constant at mean temperature (1/min), is reactor temperature (K), and is activation energy (kJ/kmol).

Energy balance:

,

where and are the heat transfer fluid and feed temperatures (K), is the overall heat transfer coefficient times heat transfer area (kJ/[min K]), is reactor volume (), is specific heat capacity (), is density of reactants (), is average heat capacity of reactants (kJ/[kg K]), and is heat of reaction (kJ/kmol).

The heats generated and removed are:

,

,

where and are in units of ().

Conversion of reactant is:

.

The screencast video at [2] explains how to use this Demonstration.

References

[1] J. G. Ekerdt and J. B. Rawlings, *Chemical Reactor Analysis and Design Fundamentals*, Madison, WI: Nob Hill Publishing, 2002 pp. 296–316.

[2] *Multiple Steady States in a Continuous Stirred-Tank Reactor with Heat Exchange*. www.colorado.edu/learncheme/kinetics/MultipleSteadyStatesCSTR.html.

## Permanent Citation