Geometric similarity of fermenter geometry is a pre-requisite for applying established scale-up relationship. It´s expressed as follows: DT2/DT1 = (VT2/VT1)1/3, where DTi is fermenter diameter and VTi total fermenter volume. Geometric similarity also assumes reasonably constant impeller geometry such as impeller diameter (DI) and number of impellers (N).
However, the industry doesn’t really use the word “Scaleup” or “Scale down” in this sense. All they mean is production at higher scale. This is the most practical meaning in the industry. The industry usually develops the inventory of reactors of different sizes over the period of years. The reactors are procured for a particular purpose but with time, the purpose keeps changing. Thus, the reactors are designed by different designers and/or procured from different vendors. The reactors are of different volumes with different design concepts.
The essence of scale-up of a fermentation process is to demonstrate fermentation production at large scale resulting in the same productivity and quality as that developed at small scale. One of the outcomes of a process scale-up is to finalize a detailed large-scale process description with settings of all operational parameters and their ranges at scale.
The task for technology transfer teams/Scaleup/commercialization teams is to produce the product in any available reactor of the required capacity. There is no geometric similarity in design at different scales. Still, the concepts of equal tip speed, equal shear, equal P/V are followed to calculate impeller speed. The result, of course is not great.