Course 8 Basics of basics of scaling up

Max wearing a white lab coat is talking to himself while shaking a flask in his hand.
(Max is really a chemical engineer, but this time, acts as a laboratory researcher.)

Oh my goodness! Max was asked to prepare 1,000 L of what had been ever prepared only in a 1 L glass beaker, all of a sudden. All the employees turn their eyes to him with expectation and anxiety. How would you do if you were in his place? Can you develop a scaling up method that will never fail as well as equipment that can surely prepare the required amount of the sample by the deadline?

More than 30 years ago, a university professor, who is an authority on mixing, taught us the secret of “the scaling up method that will never fail” at a university lecture. He said “Once you have succeeded in producing a product using a 1 L-size laboratory testing machine, purchase additional 999 units of the same machine secretly, make shelves with a imitation of a mixing vessel, arrange the 1,000 testing machines on the shelves, and produce the product by operating the testing machines at a time. You can produce the same product without fail. However, to save your face as an engineer, never forget to make the imitation vessel closely to actual 1,000 L mixing vessel in apperance!” Apart from the professor with a proud face, the classroom got quiet, and no one laughed...

In the actual business, however, we usually hope to produce the product we have produced in a 1 L beaker in a 100 times, 1,000 times, or more larger vessel at once. Though it may sound a little strange, let us explain scaling up taking okonomiyaki.

Generally speaking, there seem to be two ideas of scaling up (increasing the production).

Idea 1:
Once succeeded in making a small product, make 1,000 pieces of the same product.

This idea is applicable to continuously running tubular reactors or the like. Once the conditions for the reaction in a single “tube with a length L” are determined, you only have to bundle 1,000 pieces of the same “tube with a length L”. Then, you can scale it up with an extremely low risk as long as you take care about uniform distribution of multiple materials at the inlet of each tube and the uniformity of temperature and pressure inside each tube.

This is like cooking 1,000 dishes of small okonomiyaki*1 at a time. It is similar to the idea of a certain university professor mentioned above, isn’t it? By this method, it kind of seems that we can cook okonomiyaki of the same taste whether 1 dish or 1,000 dishes. Also here you have to be careful about the uniformity of temperature of each okonomiyaki (overall strength of fire) as with the case of a tubular reactor.

*1 Okonomiyaki is a Japanese-style pizza made from egg, flour and water with lots of toppings.

Idea 2:
Once succeeded in making a small product, make one huge product using a 1,000 times larger vessel.

This idea of scaling up is applicable to mixing vessels and the like. Mixing engineers are never allowed to purchase 1,000 of 1 L beakers. We are destined to use a 1,000 L vessel to increase the production to 1,000 times. Additionally, there is an implicit rule that this scaling up process shall be achieved under the condition of geometric similarity! It means that the shape of the huge vessel must maintain the proportion of a 1 L beaker. That is, the dimensions (such as the impeller diameter, impeller width, liquid level, and baffle width) of the huge vessel must be determined keeping their proportion to one another the same as that in the 1 L beaker, in other words, maintaining geometric similarity.
Then, why geometric similarity is given importance? We believe you are smart enough to be already aware that it is because as long as geometric similarity is maintained, we can use dimensionless numbers, such as the Reynolds number Re and power number Np we explained before.

This is just like cooking a 1,000 times larger okonomiyaki in the same way as cooking a small one. What kind of hot plate should be used? Is okonomiyaki grilled well with such a big size? Are cabbage and meat scattered uniformly? In the first place, is the geometric similarity of cabbage and meat maintained? Is it possible to reproduce the taste and flavor of the small okonomiyaki by cutting the huge one into 1,000 pieces? To tell the truth, there are many concerns.

How was it? Can you somehow imagine scaling up of a mixing vessel? We think there are the pros and cons of taking okonomiyaki as an example, but we want to tell you that in scaling up of a mixing vessel, the field for reaction greatly changes, for example, from 1 L to 1,000 L. We also want you to imagine that even if geometric similarity is maintained, physical similarities such as “liquid volume and heat transfer area” and “liquid volume and gas/liquid interface area” are collapsed.
In other words, we want you to know that even if geometric similarity is maintained and the unit power is constant, it is not enough, but there are essential contradiction and difficulty.

After reading up to this point, you may feel that scaling up of a mixing vessel is very difficult. Don’t worry. Scaling up of a mixing vessel is 60% of theory, 20% of courage, and 20% of luck. The courage and luck, which occupy 40% in total, are determined by the experience and intuition of engineers who are making the best efforts in the field to deliver as good products as possible to customers. Let us talk about that in the next session, “Basics of scaling up”.