A few of us took the course offered by Scientific Update called Secrets of Batch Process Scale-up.  It is a 2 1/2 day whirlwind of slides and class exercises.  In my estimation it is a very worthwhile course for process chemists and I certainly got a lot out of it. It is taught by Francis X. McConville who is a gifted teacher as well as experienced process guy.  He is the author of “The Pilot Plant Real Book“. Th’ Gaussling is pleased to toot this horn because this class is a great example of how such things should be done.

Most chemists know that the changes that occur in scale-up come in large part from differences in heat transfer and mixing.  There are certainly other contributions, but these are the big issues. The parameter that is viewed as most useful in mixing is the mixing energy parameter, Ei, which has units of watts/kg soln. Many of the parameters are subject to large exponents, so one needs to be cautious about how well your intuition works in this non-linear space.  The point is, eyeballing the mixing speed in your benchtop apparatus is almost certainly inadequate in comparing conditions in scaleup.

Ei=(Np*N^3*d^5)/V, where Np = impeller power number (contains density and power units), N = rotational speed (1/sec), d = impeller diameter (m), and V = volume (cubic meters).  Because the mixing energy varies as the 5th power of the impeller diameter and the cube of the rotation speed, small changes in agitator speed or impeller diameter can result in large changes in power demands on the agitator motor.  Obviously,  one should be cautious in hand waving comparisons between your 1 liter kettle and that baffled 500 gallon pot in the plant.