When undertaking process scale-up on stirred tank reactors from lab to plant it has been historically advised to scale up with constant geometric parameters, i.e. the same agitator, same $D$/$T$, same $H$/$T$, etc. This means that given properties of the vessel may change with scale.
It is often commented that the best scale-up method is to keep $P$/$V$ constant, the graph below shows the effect on the vessel properties if this is the case, e.g. if we scale up the vessel volume 1000 times at constant $P$/$V$ the mixing time of the vessel increases by just over 4.5 times. Therefore, we need to be very careful when scaling up, especially when several of the parameters are important or we are producing non-Newtonian products.
In the graph below look at the potential of scaling up based on other parameters, e.g. if we need a constant mixing time with scale, then if we scale the vessel volume a 1000 times we need 100 times the $P$/$V$ of the original scale for this. This shows how complex the scale-up can be.