Same chemistry.
Different scale.
The 10× scale-up calculation and the feedback loop behind thermal runaway.
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Ten times the volume. Less than half the cooling per litre.
For geometrically similar vessels, volume grows with length cubed, while surface area grows with length squared. Increase working volume from 1 litre to 10 litres at the same fill fraction:
| Quantity | Calculation | New / old |
|---|---|---|
| Volume | 10 | 10.00× |
| Linear dimension | 101/3 | 2.15× |
| Heat-transfer area | 102/3 | 4.64× |
| Area per litre | 4.64 / 10 | 0.464× |
Heat removed per volume = U × (A / V) × ΔT
With the same overall heat-transfer coefficient U and temperature driving force ΔT, the heat-removal rate per litre falls to 46.4% of its original value. That is a 53.6% drop. “About half” is the useful shorthand.
This is a geometry calculation, not a plant design rule. A flask and an industrial tank are not geometrically identical. Jackets, internal coils, mixing, viscosity, boiling and utilities all change the result. The comparison holds those effects constant to isolate the scale penalty.
What actually feeds back?
- Hotter mixture. If reaction heat is not removed fast enough, the reacting material warms.
- Faster reaction. For a typical exothermic reaction with temperature-sensitive kinetics, warming increases the reaction rate.
- More heat per second. Faster conversion releases heat faster, which can make the mixture hotter again.
The third step feeds back into the first. Cooling and other heat losses compete with that loop. Runaway becomes possible when heat generation outpaces removal and the temperature rise accelerates the chemistry further.
Heat removal can therefore constrain feasible reactor size and throughput, alongside mixing, residence time, pressure and other design limits. A successful small batch does not prove that a scaled-up batch is safe.
Further reading: the University of Illinois scale-up reaction safety guide describes this temperature feedback and the need for a scale-specific risk assessment. These notes are educational, not a safe operating procedure or a substitute for calorimetry and qualified process-safety review.
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