Multiple Steady States in a Continuously Stirred Tank Reactor

A continuously stirred tank reactor (CSTR) with heat transfer is used to carry out the reversible, exothermic reaction: A ↔ B .
This Demonstration shows how the steady-state solutions change as you vary the feed temperature, the heat transfer coefficient, and the pre-exponential factor for the reverse reaction. Plots of concentration of product B versus reactor temperature are shown for the mass balance and the energy balance; the intersections of these two balances correspond to the steady-state solutions for the reactor. Either one or three solutions are possible, and when three solutions are obtained, the middle solution (at the intersection of the two plots) is unstable.


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The mass balance is nonlinear
= concentration of product B
= pre-exponential factor for forward reaction
= pre-exponential factor for reverse reaction
= spacetime
= activation energy for forward reaction
= activation energy for reverse reaction
= reactant feed concentration
= ideal gas constant
= temperature of CSTR
The energy balance is linear and has two terms that correspond to: (1) the energy needed to change the feed temperature to the reactor temperature; and (2) the energy removed or added by heat transfer to a cooling/heating fluid, which is at a constant temperature of 310 K.
= volumetric flow rate
= density of bulk fluid
= mass heat capacity of feed
= feed temperature
= coolant temperature
= heat transfer coefficient
= heat transfer area
= heat of reaction
As the feed temperature increases from a low value, the reactor temperature increases until the reactor reaches a temperature above which three steady-state solutions are possible. The upper and lower solutions are stable, and the middle solution is unstable. The operating conditions of the reactor depend on how the reactor is started up. As the feed temperature increases further, a temperature is reached above which only one solution is possible, and this has a high conversion.
When you vary the heat transfer coefficient, the slope and intercept of the energy balance line both change, and this can change the number of steady-state solutions.
When you increase the pre-exponential factor for the reverse reaction, the mass balance curve changes, and the maximum conversion decreases because the equilibrium conversion is less than 1.
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