Criteria of Scale-Up

Most often, power consumption per unit volume Pm0/v is employed as a criterion for scale-up. In this case, to satisfy the equality of power numbers of a model and a prototype, 

Note that Pmo/Df) represents the power per volume because the liquid volume is proportional to Df for the geometrically similar vessels. For the constant Pmo/Df, 

As a result, if we consider scale-up from a 20-gallon to a 2,500-gallon agitated vessel, the scale ratio is equal to 5, and the impeller speed of the prototype will be 

As a conclusion, there is no one scale-up rule that applies to many different kinds of mixing operations. Theoretically we can scale up based on geometrical and dynamic similarities, but it has been shown that it is possible for only a few limited cases. However, some principles for the scale-up are as follows (Oldshue, 1985)  

It is important to identify which properties are important for the optimum operation of a mixing system. This can be mass transfer, pumping capacity, shear rate, or others. Once the important properties are identified, the system can be scaled up so that those properties can be maintained, which may result in the variation of the less important variables including the geometrical similarity. 

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