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

Under certain conditions, an exothermic reaction in a continuous stirred-tank reactor (CSTR) with heat exchange can exhibit multiple steady-state solutions. Some solutions are stable, others are unstable, and some can exhibit sustained oscillations or limit cycles. The steady-state operating conditions for the reactor depend on how the reactor is started up (initial conditions). The first phase plane plot shows reactant concentration versus reactor temperature as a function of time as the reactor approaches a steady state (or a limit cycle) for five initial concentrations; you can change the initial temperature with a slider. The second phase plane plots conversion versus temperature for one set of initial conditions, and you can vary both the initial temperature and the initial concentration . Temperature and conversion are also shown as a function of time in separate plots for these initial conditions. The steady-state solutions change as you vary the residence time , and limit cycle behavior is observed for residence times greater than about 30 minutes. The last plot (energy versus temperature) shows heat generated and heat removed as a function of temperature, and the intersections of these two curves correspond to steady-state solutions to the mass and energy balances for the CSTR.


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The following variables and equations are relevant:
, specific heat capacity (),
, heat generated (),
, heat removed (),
is the rate constant (),
is the rate constant at mean temperature (),
is the mean temperature (K),
is the activation energy (),
is the temperature (K),
is the density of reactants (),
is the average heat capacity of reactants (),
is the residence time (min),
is the heat of reaction (),
is the concentration of feed (kmol ),
is the temperature of heat transfer fluid (K),
is the initial temperature (K),
is the heat transfer coefficient times heat transfer area (),
is the volume of reactor (),
is the concentration of reactant A (kmol ),
is the time (min).
[1] J. G. Ekerdt and J. B. Rawlings, Chemical Reactor Analysis and Design Fundamentals, Madison, WI: Nob Hill Publishing, 2002 pp. 296–316.
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