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Every exothermic reactor is designed to remove its heat of reaction. The safety question is what happens when that stops: a pump trips, a cooling water valve sticks, or the power fails. The answer depends on how much heat is still to come and how hot it can make the batch.
This series uses examples from earlier posts. This part takes the 10,000 L reactor from the scale-up series. Post 2 runs a HAZOP on the feed heater from How to Read a PFD and a P&ID, and Post 3 shows how a small change can undo both.
Four temperatures decide the outcome
A cooling failure assessment compares four temperatures. The method is widely used in the fine chemical and pharmaceutical industries and was set out by Francis Stoessel.
Table 1. The four temperatures in a cooling failure assessment
| Temperature | Meaning | Example |
|---|---|---|
| Process temperature | The normal operating temperature of the batch | 60 °C |
| MTSR | Maximum temperature of the synthesis reaction: how hot the batch gets if cooling stops and the remaining reactant reacts | Calculated below |
| MTT | Maximum temperature for technical reasons. For a reactor open to a condenser, this is the boiling point of the batch | 110 °C |
| TD24 | The temperature at which a decomposition, with no cooling, would take 24 hours to reach its maximum rate. Measured by thermal stability tests | 150 °C |
The first is set by the process. MTT comes from the equipment and the solvent. TD24 comes from laboratory tests on the reaction mixture. MTSR is calculated.
Step 1: the adiabatic temperature rise
If no heat leaves the reactor, all the heat of reaction goes into warming the batch. The rise in temperature is:
ΔTad = heat of reaction ÷ heat capacity = 150 kJ/kg ÷ 2.0 kJ/kg·K = 75 K
The reaction and heat capacity are the ones used in the scale-up series. If the whole reaction could still happen after the cooling fails, the batch would climb 75 K above its starting temperature.
Step 2: how much reaction is still to come
In the plant the reactant is added over three hours, so at any moment only part of it is in the reactor unreacted. That unreacted part is called the accumulation. Only the accumulated reactant can still release heat if the feed stops when the cooling fails.
MTSR = process temperature + accumulation × ΔTad
Reaction calorimetry measures the accumulation during the addition. In the example the highest value is 20%:
MTSR = 60 °C + 0.20 × 75 K = 75 °C
Had all the reactant been charged at once, as in a simple lab procedure, the accumulation would be 100% and the MTSR 135 °C. The batch would reach its boiling point.
Step 3: place the result in a criticality class
The order of the four temperatures gives a criticality class from 1 to 5.
Table 2. Criticality classes for a cooling failure
| Class | Order of temperatures | What it means |
|---|---|---|
| Class 1 | MTSR < MTT < TD24 | Neither boiling nor decomposition is reached. Avoid holding the batch hot for long. |
| Class 2 | MTSR < TD24 < MTT | Boiling is not reached, but decomposition starts below the boiling point. Avoid long holds. |
| Class 3 | MTT < MTSR < TD24 | The batch boils before it can decompose. Condenser and vent must handle boiling at full rate. |
| Class 4 | MTT < TD24 < MTSR | Boiling comes first, but decomposition can follow. Evaporative cooling must be proven. |
| Class 5 | TD24 < MTT, TD24 < MTSR | Decomposition starts before boiling. Boiling gives no protection. Change the process. |
With the three-hour addition, the example is Class 1: 75 °C is well below both the boiling point and TD24. Charged all at once it would be Class 3. The batch would boil, and the condenser and vent would have to cope with the remaining third of the reaction heat, about 0.5 GJ, boiling off around 1,250 kg of solvent.
Accumulation is the number to protect
The semi-batch result holds only while the reaction keeps up with the feed. If the reaction slows and the feed carries on, unreacted material builds up and the MTSR rises with it.
Table 3. MTSR for different accumulations in the example
| Accumulation | MTSR | Class | When it could happen |
|---|---|---|---|
| 0% | 60 °C | Class 1 | Reactant consumed as fast as it is added |
| 20% | 75 °C | Class 1 | Normal operation, measured in calorimetry |
| 40% | 90 °C | Class 1 | Feed slightly too cold |
| 60% | 105 °C | Class 1 | Reaction slowed, for example by low temperature or weak catalyst |
| 80% | 120 °C | Class 3 | Reaction barely running while feed continues |
| 100% | 135 °C | Class 3 | Reaction never started; all reactant added |
The common causes of high accumulation are a feed that is too cold, a reaction that has not started, a missing or weak catalyst, and poor mixing. That gives three practical rules for the plant:
- Stop the feed when cooling is lost. An interlock on cooling water flow or reactor temperature that stops the feed pump caps the accumulation at its current value.
- Confirm the reaction has started before adding at full rate. A small first portion, followed by a check that heat is being released, shows the reaction is running.
- Do not add reactant below the minimum temperature. A cold batch reacts slowly while the feed continues. The HAZOP in Post 2 finds exactly this case on the feed heater.
Try it: cooling failure at your conditions
Set the reaction data and the three limiting temperatures. The calculator gives the MTSR and the criticality class.
What this assessment does not cover
- Gas generation. A reaction or decomposition that releases gas can pressurise the reactor well below the temperatures above. Gas release must be measured separately.
- Relief sizing. A Class 3 or 4 result means the vent must be sized for boiling or two-phase flow. That is a specialist calculation.
- The data. Heat of reaction, accumulation and TD24 come from calorimetry and thermal stability tests on the actual mixture. Literature values are a starting point only.
To practise the underlying calculations, try the free Reactor Design Exam.
Takeaway. Calculate how hot the batch could get if cooling fails, and compare it with the boiling point and the decomposition temperature. In the example, a three-hour addition with 20% accumulation keeps the MTSR at 75 °C. Charging everything at once would give 135 °C.
The reaction, temperatures and equipment in this series are an illustrative example. The calculations are screening estimates. They do not replace calorimetry testing, a formal hazard study or a design by a qualified engineer.
