As mentioned in the article that Mr. Hernandez sent you, you must take into account the KLa but also the Power (P) that you must implement.
On the other hand, never forget that the diameter (d) of your stirrer (impeller) changes when you increase the size of your fermenter (bioreactor) and therefore you must respect this formula v = Pi *N*d where v: peripheral speed must remain constant for the scaling up, Therefore "d" which increases, N (RPM) decreases and this has an impact on the power of your engine (see Enfors articles)
Scaling is an interesting process. The scale-up criterions such as keeping kLa, P/V, or vvm constant are common, but depend on the bioprocess to be optimal for your goal. If you want to go in more depth look at our lecture notes.
As Rob told you, the choice of one or the other similarity parameter for scaling-up will depend on the objective and the nature of your fermentation. For example, if your process is heavily dependent on oxygen availability, constant kla, or better yet, constant OTR (see this paper Article Scale-up strategy for bioreactors with Newtonian and non-New...
) is suggested. Of course, all equations available in the literature assume geometric similarity.
Scaling up of a bioprocess is extremely interesting and would depend upon several interconnected factors. First of all one has to look at the organism used and production kinetics. For other factors to be considered one may follow the attached slide. There are several theories of bioprocess scale up and my experience says that none of them should be followed in toto. Rather, a rationale should be developed depending on the specific bioprocess and a combined approach would be better. I have mostly used gassed power per unit volume concept in conjunction with constant Kla and constant tip speed based theories. However in case of the later, one has to be sure about shear tolerance of the organism used in the specific process. Whereas, in case of constant Kla, one should be aware about rheological changes in fermentation broth during the process. In fact, sometimes, it may be required to alter the design of impeller to achieve the desired yield and productivity. In my opinion, the most basic points one should consider during scale up are effect of scale up on mass and heat transfer during fermentation. Hope this helps.
Stirred tank bioreactors up to 1000 L can be considered to behave as perfectly mixed vessels so, you can state a mass balance under this consideration and develop a system of ordinary differential equations to calculate the time evolution of viable and not viable cells substrates including Oxygen and products produced during the fermentation.
The KLa mass transfer coefficient also determines the dissolved oxygen concentration (DO) of the aerobic fermenter. The air to fermenter's media mass-transfer rate of oxygen (Na) should be dependent on the local oxygen deficit: Na = KLa·(Cs-C). Here, Cs is the DO that would apply for saturation of the fermenter's broth and C is the measured DO. A mean concentration difference can be defined (ΔCm) after accepting some convenient mixing model, so that: KLa = OTR / ΔCm, where OTR stands for oxygen transfer rate. Agitation should contribute for KLa. Such a modelling-based approach implicitly takes into account other variables that may influence KLa; including temperature (T) or pH. Further details on this kind of approach, were given at the following reference (MSc Thesis):
Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...