Scale-Up of Heterogeneous Systems

In broad terms scale-up is an engineering technique for translating performance in a small system to performance in a large system. A useful review of the formal material available on theories of models, similitude, dimensional analysis, etc., written from the chemical engineering point of view, is available in a recent book (J4). The practical applications of these theories involve the use of dimensionless groups, such as Reynolds number, in correlations which describe the performance of a system in terms equally applicable to large or small systems. This method of scale-up is familiar to all engineers. 

Some particular aspects of mixing systems should be considered in relation to the general principles of model theory. First, if a general correlation is to be used for scale-up, it must be certain that the variables used in the correlation are the only ones acting in the given situation. Because of the complexity of mixing systems, we often lack 

Another complication in the use of generalized dimensionless correlations for scale-up of mixing systems lies in the difficulty of establishing an adequate performance parameter. In some cases there may be several different parameters, like conversion and purity, for example, or particle size and catalytic activity the correlations between the different parameters and the agitation system properties may not be the same, and this may make the scale-up more difficult and more arbitrary. 

It is difficult to predict from fundamental considerations that constant power per unit volume should be a generally significant scale-up criterion. In fact, as Rushton (R8) shows, use of equal power per volume for scaling can result in serious error in many cases. Thus, the successful application of this concept to certain operations must be regarded as a somewhat fortuitous result of the specific interactions present in those particular cases. 

Another more general scale-up criterion is that of impeller Reynolds number, DzNp/fi. This approach, strongly recommended by Rushton (R8), is based on the observation that in many mixing operations the performance of the system can be successfully described by relations like Eq. (44) or (45), involving the familiar Nusselt or Sherwood numbers and the impeller Reynolds number. For geometrically-similar systems and constant material properties, these relations reduce to the forms 

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