Multiple Steady States in a Non-Isothermal CSTR: Summary
The answers to the ConcepTests are given below and will open in a separate window. 

Key points from this module:
  1. A plot of reactant or product concentration in the reactor versus reactor temperature with time as a parameter is known as a phase plane plot.
  2. A non-isothermal CSTR can have more than one steady-state operating point, and which one it operates at is determined by the starting conditions in the reactor.
  3. In a non-isothermal CSTR, a single reaction, with kinetics that are power order in reactants and/or products, can have either one or three steady-state solutions to the mass and energy balances.
  4. The steady-state solution that is obtained in a CSTR is determined by solving the transient mass and energy balances differential equations using as initial conditions the starting conditions in the reactor.
  5. Some operating points are not attained, and instead a CSTR exhibits a limit cycle in which the temperature and concentrations oscillate around the steady-state solution.
  6. Plotting reactor product concentration versus reactor temperature for the mass balance and the energy balance yields a plot that shows if multiple steady states exist.
  7. If the mass and energy balances for a non-isothermal CSTR has three steady-state solutions, the middle steady state is unstable, which means any perturbation will cause the reactor to drift away from that state to one of the steady-state solutions.
  8. A CSTR can operate at a steady-state condition that is not stable to perturbations. For example, if the feed temperature to a steady-state reactor were perturbed, the reactor could exhibit a dramatic increase or decrease in reaction temperature.

From studying this module, you should now be able to:
  1. Explain the reason for multiple steady states in non-isothermal CSTRs.
  2. Solve the unsteady-state material and energy balances for non-isothermal CSTRs to determine the steady-state operating point.
  3. Generate a phase plane plot for an non-isothermal CSTR.
  4. Determine if a steady-state solution for an non-isothermal CSTR is a stable or unstable operating point.
  5. Explain what a limit cycle is for a CSTR.
Prepared by John L. Falconer, Department of Chemical and Biological Engineering, University of Colorado Boulder