Mixing Vessels Useful Clues for the Mixing Beginners Mixing Course

# Course 8 Basics of basics of scaling up

In this session, let us explain “scaling up”, which we believe many of you are interested in. To begin with, we will explain the basics of basics of scaling up so that you can have a clear image of what scaling up is. We will not use mathematical formulas at all, so take it easy and read the following explanation.

## Case study: In a new material R&D room of a chemical company

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.)

Max

I finally succeeded in developing dream high-function polymers! The sample is quite well-received by customers. This is the birth of a dream ultra-super engineering plastic adding an excellent processability to our unique heat and chemical resistance! Ha ha ha! Now, we can catch up with our competitor, Umiyama Chemical!

There Sales Mr.Ueda rushed into the room.

Mr.Ueda

Gosh! Our major customer, Sansan Automobile asked us for a new product sample in 1,000 times the amount before! Tell me the shortest delivery time right now!

What!? I cannot respond on such short notice. Only 1 L of the sample has ever been prepared. I cannot immediately determine how and by what equipment we could prepare 1,000 L of the sample.

No! No! Anyway, we have to manage to prepare 1,000 L of the sample.
It may determine the future of our company!

How absurd! Good grief...

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?

## What is the scaling up method that will never fail?

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...

### Figure 1. Scaling up without fail

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.

## Two ideas of scaling up

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.

### Figure 2. Scaling up of a tubular reactor

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.

### Figure 4. Scaling up a mixing vessel

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.

### Figure 5. Image of making a single huge product

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”.