The Scale-up of Real Batch Reactors

The principles and methods of scale-up can be applied to chemical reactors. In the absence of significant thermal effects, i.e., when the ratio 2r/ Vr may be considered negligible, ideal batch reactors do not show any problem of scale-up, because the volume Vr does not appear in the mathematical model (2.17), so that their performance is only determined by chemical kinetics (see Sect. 2.3). On the contrary, a very complex behavior is expected for real reactors in fact, this behavior cannot be analyzed in terms of mathematical models, and the design procedures must be largely based on semi-empirical rules of scale-up. 

For the sake of completeness, two different scale-up rules are briefly considered here, and their different results are shown. First, let us define the stirring power P as 

If the power per unit volume P/Vt is assumed to determine the effectiveness of the mixing, it is possible to introduce the scale-up criterion P/Vr = constant, which gives the scale-up prescriptions 

An alternative criterion is derived by considering that the velocity of the stirrer tips, v = jrdsco, determines the shear stress on the fluid and, consequently, its micro mixing. The scale-up criterion ds(o = constant gives 

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