In order to carry out a biotech process optimized in a small reactor just as well as in a much larger reactor, this larger reactor must offer the organisms the same optimal conditions as the small reactor does.

The critical process parameters should therefore remain as constant as possible. This is usually simple for parameters such as temperature, pH value and nutrient concentration: the values of the small reactor are adopted.

Particularly with regard to the mixing and flow conditions and thus the design of the agitator, the question arises as to which criteria should be used to increase the latter so that the tried and tested process can also be run equally productively in the large reactor. As the size of the vessel increases, it becomes increasingly difficult to achieve good mixing with low concentration gradients of the nutrients and low local mechanical stress on the organisms due to the shear forces of the stirring system.

Tip speed, i.e. the tangential speed at the tips of the stirring blade, is usually a suitable scale-up criterion for the rapid determination of suitable values for speed, stirrer diameter and drive power.

This value should be the same for the large reactor as for the small reactor, with the ratio of the reactor inside diameter to the stirrer outside diameter being as equal as possible.

So v_T = constant = D. π . n [m/s]

The Tip speed v_T is therefore equal to the product of stirrer diameter D, shaft speed n and π.

In this way, a suitable speed and the corresponding power requirement of the agitator for the large reactor are quickly obtained.

Other simple scale-up criteria to create the same conditions in the large reactor are

• Same volume-specific power input P/V = const.
• Same oxygen transfer rate: k_La = const.
• Same mixing time t_m = const.

Usually the same volume-specific power input and the same oxygen transfer rate lead to similar results with regard to stirrer design as the tip speed. If the mixing time is kept constant, however, this can result in an unrealistically powerful agitator that can hardly be realized technically.

In practice, tip speed has proven to be a suitable scale-up criterion.

If overly sophisticated methods are used to increase the scale of the reactor, this often results in complex, failure-prone and above all expensive technical solutions that give little pleasure to the user and hardly enable better productivity.