A reaction that behaves in a one-litre flask can overheat in a ten-cubic-metre reactor with the same recipe. The chemistry is identical. The geometry has changed, and with it the rate at which the vessel can remove heat and mix its contents.
This series follows one example: an exothermic liquid reaction scaled from a 1 L lab reactor to a 100 L pilot reactor and then to a 10,000 L commercial reactor. This post covers what changes with size. Post 2 covers what the pilot plant must find out, and Post 3 turns the pilot data into a mass and energy balance.
Volume grows faster than surface area
Heat is generated throughout the volume of the liquid and leaves through the wall. When a vessel is made larger in every direction, its volume rises with the cube of the diameter and its wall area with the square. The area available per cubic metre therefore falls as the vessel grows.
Jacket area per unit volume = 4 ÷ diameter (for a vessel filled to a depth equal to its diameter)
From 1 L to 10,000 L the volume increases 10,000 times and the jacket area per cubic metre falls 21.5 times.
Worked example: can the jacket remove the heat?
Suppose the reaction releases 150 kJ for each kilogram of batch. A jacket removes heat at a rate set by three things: the heat transfer coefficient, the wall area and the temperature difference between the batch and the coolant.
Cooling capacity = U × A × ΔT = 300 W/m²·K × A × 30 K
Table 1. Cooling capacity at three scales, for U = 300 W/m²·K and ΔT = 30 K
| Scale | Volume | Diameter | Jacket area per volume | Cooling capacity | Shortest safe reaction time |
|---|---|---|---|---|---|
| Lab | 1 L | 0.11 m | 36.9 m²/m³ | 332.1 kW/m³ | 8 min |
| Pilot | 100 L | 0.50 m | 8.0 m²/m³ | 71.6 kW/m³ | 35 min |
| Commercial | 10,000 L | 2.34 m | 1.7 m²/m³ | 15.4 kW/m³ | 162 min |
The heat to remove is 150 kJ/kg × 1,000 kg/m³ = 150,000 kJ per cubic metre of batch, or 41.7 kWh. If the reaction is run in one hour, as in the lab, the heat is released at 41.7 kW per cubic metre.
The lab reactor can remove eight times the heat that is generated, and the pilot reactor 1.7 times. The commercial reactor can remove only 15.4 kW/m³ against 41.7 kW/m³ generated. With the lab recipe, its temperature would climb.
The usual answer is to add one reactant gradually, so the reaction can only proceed as fast as the feed arrives. The addition time must then be at least:
41.7 kWh/m³ ÷ 15.4 kW/m³ = 2.7 hours
A one-hour lab procedure becomes an addition of about three hours in the plant. That change affects the batch cycle time, the number of batches a year and the size of the reactor needed for a given output.
Try it: cooling capacity at your scale
Set the reactor volume and the reaction data. The calculator assumes a jacket on the wall only, a liquid depth equal to the diameter and a batch density of 1,000 kg/m³.
What else changes with size
Heat removal is usually the first limit, and several other quantities change at the same time. The table assumes the same vessel shape and the same agitator power per cubic metre at each scale.
Table 2. How key quantities change from 1 L to 10,000 L
| Quantity | Changes with | 1 L to 10,000 L | What it means in the plant |
|---|---|---|---|
| Jacket area per volume | 1 ÷ diameter | ÷ 21.5 | Less cooling and heating per kilogram of batch |
| Heat-up and cool-down time | Diameter | × 21.5 | Minutes in the lab become hours |
| Mixing time | Diameter to the power ⅔ | × 7.7 | Added reactant stays concentrated for longer, which can change selectivity |
| Agitator tip speed | Diameter to the power ⅓ | × 2.8 | More shear, which matters for crystals, emulsions and cells |
| Liquid depth | Diameter | × 21.5 | Higher pressure at the bottom changes boiling point and gas solubility |
No single rule keeps all of these constant. Scale-up means deciding which quantity matters most for the process and holding that one, then checking that the others stay acceptable. Finding out which one matters is the purpose of the pilot plant, covered in Post 2.
Three cautions
- The heat transfer coefficient is not constant. Thicker walls, glass lining and fouling all lower it at plant scale. Measure it on the pilot reactor and check the vendor's figure for the commercial vessel.
- Gradual addition only works if the reaction keeps up. If the reactant accumulates unreacted and then reacts all at once, the heat arrives faster than the feed rate suggests. Reaction calorimetry shows whether this can happen.
- Cooling failure must be assessed separately. This post covers normal operation. The temperature the batch could reach with no cooling at all is a process safety question and needs its own study.
To practise the calculations, try the free Engineering Scale Up Exam I and the Scale Up Calc Exam III.
Takeaway. Cooling capacity per cubic metre falls as the reactor grows. In the example it drops from 332 to 15.4 kW/m³, and a one-hour lab reaction needs at least 2.7 hours of controlled addition at 10,000 L.
The reaction, the vessels and the costs in this series are an illustrative example. The calculations are screening estimates and do not replace process safety testing or a design by a qualified engineer.
