Batch Reactor Scale-Up With a Cooling Failure Scenario
A batch reactor with a 4 m3 vessel is charged with 1,800 kg of reaction mass having a specific heat of 3.0 kJ kg^-1 K^-1. The recipe adds 450 kJ of reaction heat per kilogram of charge over 90 minutes at 70 C, and the jacket can remove 120 kW at that temperature. Reaction calorimetry shows the maximum heat-release rate is 280 kW at 80 C, and the solvent boils at 110 C. The decomposition onset measured by DSC is 160 C. The vessel has a 150 mm relief line to a catch tank, no emergency cooling, and the current interlock trips feed at 85 C. The plant wants to increase batch size by 20% without changing the vessel or relief system, arguing that the 90-minute addition limits accumulation.
1. Calculate the adiabatic temperature rise and the maximum temperature of the synthesis reaction from 70 C. Assess the cooling-failure hazard.
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Total reaction heat is 1,800 kg x 450 kJ/kg = 810,000 kJ. The reaction-mass heat capacity is 1,800 kg x 3.0 kJ kg^-1 K^-1 = 5,400 kJ/K. The adiabatic temperature rise is 810,000/5,400 = 150 K. From a normal 70 C starting point, the maximum temperature of the synthesis reaction is 70 + 150 = 220 C. That exceeds the solvent boiling point of 110 C and the decomposition onset of 160 C, so a cooling failure can lead to boiling, two-phase relief and a secondary decomposition. At the maximum heat-release rate of 280 kW with 120 kW of jacket cooling, the net rate is 160 kW, or 160/5,400 = 0.0296 K/s = 1.78 K/min. The margin is too small for a 150 mm relief line with no emergency cooling.
2. Evaluate the proposed 20% batch increase. Include heat-release rate, accumulation and relief-system implications.
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A 20% increase raises the charge to 2,160 kg and the total heat to 972,000 kJ. If the heat per kilogram and specific heat remain the same, the adiabatic rise stays 150 K, so the MTSR from 70 C is still 220 C. The problem is the rate: maximum heat release becomes 1.2 x 280 = 336 kW, while the jacket area and 120 kW cooling capacity are essentially unchanged. Net heating becomes 216 kW, or 216/(2,160 x 3.0) = 0.0333 K/s = 2.0 K/min. If the same 90-minute addition is kept, the average feed rate and potential accumulation also rise by 20%. The existing 150 mm relief line was not sized for the larger two-phase load, and the 85 C feed trip is above the solvent boiling point. The increase should not be approved without calorimetry at the new scale, relief sizing and added heat-removal capacity.
3. Recommend engineering and procedural safeguards before any scale-up.
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Reduce the charge or extend the feed time to limit accumulation, and add emergency cooling or a dump tank. Lower the high-temperature feed trip to about 95 C, well below the 110 C boiling point, and add a redundant temperature sensor with independent shutdown. Re-run reaction calorimetry at the proposed scale and use the data to size the relief system for two-phase flow, not just vapor. Consider semi-batch operation with feed limiting so the maximum accumulated unreacted mass is bounded. Verify the catch tank can handle the relief discharge and that the relief line is not shared with incompatible service. The scale-up should be gated on a documented HAZOP and a demonstrated cooling-failure test.