Continuous Stirred-Tank Reactor That Loses Cooling

The exothermic reaction A → B takes place at steady state in a continuous stirred-tank reactor (CSTR) with a cooling jacket. The initial volumetric flow rate is 2 dm3/min when the cooling fails at 6 minutes. Once cooling is lost, the reactor temperature starts to increase. Use a slider to vary the volumetric flow rate to try to prevent thermal runaway. Use sliders to change the time at which the flow rate changes and the new volumetric flow rate. The dashed black line shows the behavior if the flow rate is not changed. The solid blue line represents the behavior if the flow rate is instantly changed to the new value. Select a button to plot either the temperature or concentration versus time.

Download the CDF file to view the simulation using the free Wolfram CDF player.





Details
For a CSTR operating at steady-state:
where CA,ss is the concentration of A at steady-state (mol/dm3), vo is the volumetric flow rate until cooling fails (dm3/mol), CA,0 is the inlet concentration of A (mol/dm3), V is reactor volume (dm3), rA,ss is the steady-state reaction rate (mol/[dm3 min]), kss and ko are the steady-state rate constant and pre-exponential factor (1/min), Ea is the activation energy (J/mol), R is the ideal gas constant (J/[mol K]), Tss is the steady-state temperature (K), cP,i is the molar heat capacity of component i = (A, B) (J/[mol K]), T0 and Ta are the inlet and coolant temperatures (K), UA is the heat transfer coefficient times heat transfer area (J/[K min]), and ΔH is the heat of reaction (J/mol).

Mass and energy balances are done to determine concentrations and temperature after cooling has failed:

where t is time (min), rA is the rate of reaction (mol/[dm3 min]), and k is the rate constant (1/min).

The volumetric flow rate v1 = vo until the valve is adjusted, and then v1 is set with a slider to avoid thermal runaway.