Accumulation-Limited Exotherm: MTSR, TMRad and a Scale-Up Sign-Off
A 1.20 mol batch of an aromatic substitution runs in a 6 L jacketed reactor at 40 C. Reaction calorimetry gives a reaction enthalpy of -240 kJ per mol of limiting substrate; the charged mass is 3.6 kg with a mean heat capacity of 2.5 J g-1 K-1. Electrophile dosing takes 30 min, and at the end of the dose the RC1 shows 85% of the substrate still unreacted because the intrinsic reaction rate at 40 C is slow. The isolated product shows a decomposition onset of 95 C by DSC at 5 K/min with a decomposition enthalpy of 1,100 J/g. Accelerating rate calorimetry on the in-process mixture gives TMRad of 24 h at 62 C and 9 h at 67 C. Cooling water is available at 10 C, and the measured heat-transfer capacity of the 6 L reactor at working volume is 55 W/K. The EHS reviewer must sign off a threefold scale-up in a vessel whose heat-transfer capacity per unit volume is 2.2 times lower.
1. Calculate the adiabatic temperature rise and the maximum temperature of a synthesis reaction (MTSR) at the end of dosing. Does the process meet the usual safety criteria?
Read the worked answer
Adiabatic temperature rise. Heat released Q = 1.20 mol x 240 kJ/mol = 288 kJ. Heat capacity of the charge C = 3.6 kg x 2.5 J g-1 K-1 = 9.0 kJ/K. Therefore delta-Tad = 288 / 9.0 = 32 K.
MTSR. MTSR = process temperature + (fraction accumulated x delta-Tad) = 40 + (0.85 x 32) = 40 + 27.2 = 67.2 C.
Decomposition severity. delta-Td = 1,100 J/g / 2.5 J g-1 K-1 = 440 K of adiabatic rise if the decomposition is triggered. That is a catastrophic inventory; the only defence is to keep the mixture far below the onset of 95 C.
Criteria check. The standard criterion is that the MTSR lies below the temperature at which TMRad is 24 h (the TD24, here about 62 C), so that a cooling failure still leaves at least a day to intervene. The MTSR of 67.2 C is above 62 C, and TMRad at the MTSR is only 9 h. The process therefore does not meet the criterion under the current dosing regime: the hazard is not the normal heat load but the 85% accumulation waiting to react if cooling or agitation is lost.
2. Propose a modified operating regime that would satisfy the criterion, and describe how you would verify it experimentally.
Read the worked answer
Two levers, and the arithmetic for each. To keep the MTSR below 62 C you need either a lower accumulation or a lower reaction temperature. At 40 C, accumulation must fall below (62 - 40)/32 = 69%, which still leaves TMRad far shorter than 24 h, so that is not enough on its own. Target under 20% accumulation: MTSR = 40 + 6.4 = 46.4 C, where TMRad is many hours. But the reaction is intrinsically slow at 40 C, so slow dosing alone extends the cycle time badly.
Recommended regime. Run at 55 C and dose slowly enough to hold accumulation below (62 - 55)/32 = 22%, targeting 15-20%. The higher temperature raises the intrinsic rate so the dose can still be completed in a workable time, and the MTSR of 55 + 6.4 = 61.4 C stays below TD24. Treat the maximum dose rate, and the minimum dose time, as critical process parameters.
Verification. Repeat the RC1 experiment at 55 C with three dose rates and derive the accumulated fraction from the heat-flow curve, not from offline conversion alone. Obtain TMRad by ARC on the actual in-process mixture at 15-20% accumulation, not on the isolated solid, because the mixture is what would decompose. Finally, run the scenario where dosing stops but the jacket fails, and the scenario where cooling fails at the end of the dose, and record the time available for operator action.
3. The threefold scale-up halves the heat-transfer capacity per unit volume. Does that change your conclusion, and what else must be verified before sign-off?
Read the worked answer
Normal heat removal is not the limiting case. The reaction heat rate at lab scale is 288 kJ over 1,800 s = 160 W, which at 55 W/K needs only a 2.9 K jacket-to-bulk difference. At threefold scale the heat rate is 480 W and the capacity is 55 x 3 / 2.2 = 75 W/K, so the required difference is 6.4 K. Cooling is still comfortable, so the scale-up factor does not by itself change the safety verdict on the reaction phase.
What does change. The adiabatic temperature rise is scale-independent, but everything about detection and response is not: mixing time, the measured U in the plant vessel, the response time of the temperature trip, and the ability to crash-cool or quench. A larger vessel also has a longer dose time for the same dose rate, which lowers accumulation, but production pressure to shorten the dose to protect throughput would raise it again.
Before sign-off, verify: U measured in the plant vessel at working volume; the MTSR recomputed at the plant dose time rather than the lab dose time; the alarm and trip setpoints with their response times; the availability of a quench or dump line; and the maximum dose rate written into the batch record as a critical parameter. A flow process, with inventory below a few hundred millilitres, would remove the accumulation hazard altogether and should be evaluated rather than assumed unnecessary.