#### 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:
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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:
• Explain the reason for multiple steady states in non-isothermal CSTRs.
• Solve the unsteady-state material and energy balances for non-isothermal CSTRs to determine the steady-state operating point.
• Generate a phase plane plot for an non-isothermal CSTR.
• Determine if a steady-state solution for an non-isothermal CSTR is a stable or unstable operating point.
• Explain what a limit cycle is for a CSTR.

Prepared by John L. Falconer, Department of Chemical and Biological Engineering, University of Colorado Boulder