Special Scale-Up Considerations

Once the process parameters and the rules for scale-up from the model dimensions have been determined by tests at various scales, the next step is to calculate the power rating for the industrial-scale system with the aid of the power characteristic. For Newtonian liquids this is no problem, in total contrast to non-Newtonian media, where the effective viscosity is always a function of agitator shaft speed [4]. 

A particular problem that frequently arises with suspension duties in very large stirred vessels with several side-entry agitators installed below the liquid surface is that on scale-up the volume increases in proportion to the cube of the linear scale-up factor whereas the surface area increases in proportion to its square. If the arrangement of the impellers found to give a certain rotary flow pattern for optimum suspension of the suspended solids at the model scale is retained at the industrial scale, a fundamentally different flow pattern would result that is totally unsuitable for suspension purposes. Particular account must be taken here of the fact that the secondary flow patterns in the large vessel are scale dependent on account of changed ratio of inertial to frictional forces. Other scale-up criteria derived from considerations of a theoretical free jet are required to achieve an optimum suspension of the particles. 

On suspension duties in abrasive media, the antidpated erosion problem places a limit on the impeller tip speed. In this case, the properties of the agitated medium and the materials of construction place limits on the general appUcabUity of the P/V = scale-up rules. 

A physical limit on the use of the PfV = rule where x 0 occurs on suspension duties when from a certain scale-up factor upward the agitator power input would in theory be less than the settling power of the solid particles. This cannot be the case when the energy balance is considered. An experienced agitator manufacturer has, however, sufficient practical data on agitated media, vessel size, and geometry to determine the lowest possible impeller tip speed. 

On suspension duties, attention must also be paid to the fact that during plant shutdown the sediment buildup in large vessels is considerably higher, more densely compacted, and, depending on the medium involved, can also set. This means that restarting the system is much more problematic than on a pilot scale. In addition, the settling times depend on the scale involved. 

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