Batch Reactor Cooling Failure and Emergency Quench Decision
A 5 m3 jacketed batch reactor is charged with 4.0 m3 of solution containing 1.5 kmol/m3 of a limiting reactant in an organic solvent (density 850 kg/m3, cp 2.2 kJ/kg K). The reaction has delta H = -180,000 kJ/kmol. At 80°C the jacket cooling water fails, and the reactor temperature begins to rise at 6 K/min. The solvent is stable to 140°C; above that, a secondary decomposition with much larger heat release begins. The reactor has a 100 mm emergency dump line to a 15 m3 quench tank that currently holds 8 m3 of water at 25°C. The dump valve can be opened manually in about 2 minutes. The relief valve is sized for external fire exposure, not for a runaway reaction. No spare cooling water and no fire water are available for 20 minutes.
1. Calculate the adiabatic temperature rise and estimate the time available before the 140°C onset. Is the observed 6 K/min conservative?
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Adiabatic temperature rise = (-delta H) C_A0/(rho cp) = (180,000 kJ/kmol x 1.5 kmol/m3)/(850 kg/m3 x 2.2 kJ/kg K) = 270,000/1,870 = 144 K. Starting from 80°C, a fully adiabatic runaway would reach about 224°C, far above the 140°C decomposition onset. The required rise to 140°C is 60 K. At the observed initial 6 K/min, that is 60/6 = 10 minutes. This is an upper bound, not a conservative estimate: the reaction rate increases with temperature, so the ramp will accelerate and the real time is shorter, perhaps 5-7 minutes. The operator has only a few minutes to act after the temperature trend is recognized. Waiting for the relief valve or hoping cooling returns is not defensible.
2. Evaluate whether the quench tank can absorb the full heat release. Calculate the final mixed temperature and state any necessary conditions.
Read the worked answer
Total heat release = 1.5 kmol/m3 x 4.0 m3 x 180,000 kJ/kmol = 1.08 x 10^6 kJ. The quench tank holds 8,000 kg of water with cp = 4.18 kJ/kg K; dumped reaction mass is 4.0 x 850 = 3,400 kg with cp = 2.2 kJ/kg K. Mixed heat capacity = 8,000 x 4.18 + 3,400 x 2.2 = 33,440 + 7,480 = 40,920 kJ/K. Adiabatic mixing rise = 1.08 x 10^6/40,920 = 26.4 K, so the final temperature is about 25 + 26 = 51°C before considering any unreacted material continuing to react. Even with continued reaction, the tank is large enough to keep the mixture well below 140°C, provided the tank is vented, agitated, and the dump line is clear. The 15 m3 tank would contain about 12 m3 after dumping, leaving 3 m3 freeboard. The quench is viable and should be used immediately.
3. Recommend an action sequence and explain why restarting jacket cooling or relying on the relief valve is inferior.
Read the worked answer
Sound sequence: alarm and clear the area, stop feed and heating, keep the agitator running to avoid stratification, open the dump valve immediately, and confirm flow to the quench tank. Add quench water and vent the tank. Restarting cooling is unreliable because the cooling-water failure may persist and the jacket cannot remove heat fast enough once the reaction is accelerating. The relief valve was sized for fire, not for a runaway, and a gassy or two-phase relief may be undersized. The dump removes the reacting mass from the confined reactor and dilutes it in a large heat sink; it is the only action that reliably prevents reaching the decomposition onset. The 2-minute valve-opening time should be reduced by a remote or automatic dump system in the future.