In transferring processes from one site to another or scaling up a process we often find that the process involves one or more stages that cannot be directly transferred due to either differences in equipment used or differences in scale. Mixing and lyophilisation are examples of such processing stages. Lyophilisation can be quite a challenge, and some users describe it as an artform rather than a science, so for now I’ll stick to using mixing as an example.
Ther are many mixer types but in this technical note I will concentrate on the mechanically stirred tanks as used in the batch production of pharmaceuticals and chemicals. This type of mixing is usually used for the blending, suspending and homogenization but is also used for gas absorption operations the control of chemical reactions.
The main problem is that the scale up of the mixing processes is not linear. If the batch size doubles, it’s not a simple matter of doubling the size of the mixer’s impellers or tank volume.
In fact, none of the key process parameters such as:
- Heat transfer area, (a volume increase of 1,000 only increases the heat transfer area by of 100 if the vessels geometry is maintained).
- Mixing time, as rule of thumb the mixing time is proportional to the cube of the impeller diameter.
- Impeller power input, again as a rule of thumb the power input is proportional to the power 5 of the impeller diameter(D5).
So direct scaling up of all mixing parameters is often impossible and usually the scale up process must determine which of the mixing parameters are crucial to the process. For instance, for biologics, not exceeding the maximum shear rate may be important, while for non-Newtonian liquids which change their viscosity – becoming thicker or thinner – the harder they are worked thus maintaining the power ratio may be the most important criteria, while for chemical reactions heat transfer area may be critical.
So, how do you approach mixer scale-ups?
Quite often with lower volumes – and here I’m thinking of <500L, mixing is often scaled up by practical means – running a short series of simulated mixing tests using substitute materials, taking samples demonstrating homogeneity – and to be honest this is quite acceptable, after all it is the end result which is important, the rest is only a means to the end.
However, if a scientifically based process is required, at least some nod to the theoretical mixing solution should be performed with practical experimentation used to validate the theory however much “rule of thumb” calculations are used.
Starting at the end point may be the best way. Determining the crucial mixing parameters should be the starting point – these are usually, but not always expressed as Critical Quality Attributes (CQA’s) or are derived from a process risk assessment. Don’t just try and dimensionally scale the impeller / tank dimensions.
Scale-up the vessel size and concentrate on ensuring that the CQA’s (perhaps impeller tip speed if shear rate is important) and then “work backwords” to determine the affect on the lesser important attributes, for instance by maintaining tip speed using a larger impeller may mean that impeller speed is reduced and thus mixing time may be increased.
For technology transfer purposes, the Critical Process Parameters (CPP) should be the principle concern. These could include:
- Mixing time
- Heat transfer (maintaining required temperature)
- Shear rate / impeller speed
- Mass transfer
- Chemical or physical kinetics
For blending and chemical reactions fast and complete blending is important, but for shear sensitive products shear rate may be the limiting factor. The transfer / scale-up is also affected by the viscosity of the liquid being mixed (Newtonian or non-Newtonian).
Finally, it’s important to know the relevant physical properties of the material in terms of rheology, and stability. If the system involves bubbles of gas, solid particles, or liquid droplets in suspension there will be interplay between the distributed phase properties and the bulk rheology and mixing behaviour.
The critical CPP will determine which of the tank parameter have to be controlled, and which vessel parameters can be scaled up without affecting the product quality. Starting with the end in mind is more straightforward when scaling down or scaling across because the initial system geometry is predefined.
For critical applications the theoretical calculations should be backed up by such as Flow Visualisation or Computational Fluid Dynamics studies – although the latter can be quite expensive for non-critical applications.
These notes are intended to introduce and help people to understand the technology transfer process, and as such I have purposely avoided the use of any mathematics, however if you wish to explore scaling up of mixing – or other technologies – please feel free to contact me.
On the other hand, if you are interested in the mathematics I can recommend Thomas Post “Understand the Real World of Mixing” – https://postmixing.com/publications/100315ceparticle.pdf
About The Author:
Trefor Jones is a technology transfer specialist with Bluehatch Consultancy Ltd. After spending over 30 years in the pharmaceutical / biopharmaceutical industry in engineering design, biopharmaceutical processes, and scale-up of new manufacturing processes, he now specializes in technology transfer especially of biotechnology and sterile products.
He can be reached at trefor ”at” bluehatchconsultancy.com.