course 9 Basics of scaling up

This is a meeting room of a chemical company. A serious meeting is being held by Director Ueda from the Sales Department, Dr.Nano from the Manufacturing Department, and Max from the Research Department.

At the end of the previous session, we said that scaling up of a mixing vessel is 60% of theory, 20% of courage, and 20% of luck. Here, the courage and luck does not mean recklessness, but means hypotheses built up (decisions made) by engineers and the certainty of them.
In other words, as long as you understand some key points, you can make appropriate decisions about scaling up with a higher probability. Let us explain the key points of scaling up of a mixing vessel while paying attention to the key words hidden in the conversation of the three.

Key point 1:
The laboratory stage is an important stage to obtain scaled down data of the expected mass production equipment.

Asking “Have you already determined the operating conditions of the mass production equipment?” means asking “Have you collected data enough to examine the performance of the production equipment, at the laboratory stage?”
At the laboratory stage, they give priority to getting high evaluation by the customer for the sample, and therefore the manufacturing method tends to be neglected also because they can manage to produce the product by hand at this stage. Giving priority to somehow making the product by using the laboratory equipment they are accustomed, they are slow in performing verification by varying the factors, such as the type of impeller, baffle plates, rotation speed, and mixing power.
This is probably because researchers tend to think that mass production equipment ought to be designed by the production engineering department or construction department and researchers should give priority to realizing high-function samples.

What is important is to know how the reaction rate and product quality are affected when the conditions, such as the impeller, rotation speed, and baffle plates, are varied, at the laboratory stage.
Especially, the change in the rotation speed affects the power by the square or cube, and therefore the rotation speed is highly influential on the selection of the motor capacity for the mass production equipment. Only with the data indicating that even if decreasing the rotation speed of the laboratory machine by 20%, it has only a small influence on the productivity, you may be able to decrease the motor capacity by 30 to 50%.
Thus, the first key point is that the wide range of conditions at the laboratory stage plays an important role in determining the equipment specification at the production stage.

Key point 2:
It is unreasonable to run the mass production equipment with the same rotation speed as the laboratory testing machine, in the turbulent flow region.

Regarding scaling up in the normal turbulent flow region (unit power constant etc.), it is common that the rotation speed of the mass production equipment is significantly lower than that of the laboratory machine. An idea of mixing fluids by rotating the same impeller at the same rotation speed to maintain the geometric similarity seems to be a safe way at first glance, but in the case of scaling up in the turbulent flow region (rotation speed constant), it may result in an unrealistic mixing equipment with an excessive motor capacity for the liquid capacity.
The changes of the unit power and rotation speed before and after scaling up are compared between the two case, “rotation speed constant” and “unit power constant”, in Figure 1.

We believe you understand that scaling up with a constant rotation speed results in an excessive required power. In the meeting above, Max from the Research Department should have immediately answer, “The rotation speed was 300 rpm in the laboratory, but I think it is possible to run at around 65 rpm as long as the unit power is constant.” Plant operators knows the key point through their long experience that larger mixing vessel can be operated in lower rotation speed. Researchers who are not experienced in operation using mass production equipment are inevitably tend to reassure themselves by maintaining the rotation speed. It may be an safer decision to avoid risks for researchers, but not acceptable as engineers.

Key point 3:
Imagine what function you want to maintain after scaling up.

As we explained in the previous session taking okonomiyaki as an example, you cannot scale up a mixing vessel while maintaining all the mixing characteristics (such as mixing, heat transfer, dispersion, micronization, solution, and gas absorption). The most important key point here is whether you can say clearly, “The most important purpose of mixing using this vessel is ◯◯!” As long as you can say that, you can move on to the next step of examining how to scale up giving priority to the relevant factors. For example, if you judge that since the product has a low viscosity and a high reactivity, reaction heat removal has a great influence on the production speed, in other words, what is possible to become a bottleneck is heat transfer (that is, heat transfer limited), you should maintain the factors of “heat transfer area / liquid volume” after scaling up even by changing the arrangement of the heat transfer coil inside the mixing vessel. In general, in the case of geometrically similar scaling up, when the inside diameter of vessel increases to 10 times, the liquid capacity increases to 1,000 times, which is the cube of 10 times, but the heat transfer area only increases to 100 times, that is, the square of 10 times.
It means that the “heat transfer area / liquid volume” will decrease to one tenth after scaling up. Since the heat generated during reaction is proportional to the liquid volume, the larger the vessel is, the less advantageous it is in reaction heat removal. If the viscosity is low, and therefore the mixing property is not expected to deteriorate, it is effective to take measures against the increase of the heat transfer area after scaling up by changing the heat transfer coil from single to double.

Additionally, when removing the reaction heat by latent heat of evaporation in boiling polymerization, there is a concern about entrainment of reaction solution due to an increase in evaporation gas due to scaling up. In such a case, it is also necessary to change the slenderness ratio (liquid height / inside diameter of vessel) of the vessel after scaling up as shown in Figure 3 to bring the boiling gas velocity in the liquid close to that in the laboratory machine.

We believe you understand that “Understanding the purpose of mixing”, which is one of the important points to understand mixing and which we said in the first session, is closely connected to this “Key point 3”.
To close this session, we hope Max can explain what function should be maintained in the mixing vessel he intends to scale up to the parties concerned with confidence.
In the next session, we will explain “What's the heat transfer performance of a mixing vessel?”, which is an important factor also in scaling up.