Scale-up correlation

S.3.2.3. Scale-up based on similarity principles scale-up correlations... 

Dimensionless numbers (Reynolds number = udip/jj., Nusselt number = hd/K, Schmidt number = c, oA, etc.) are the measures of similarity. Many correlations between them (known also as scale-up correlations) have been established. The correlations are used for calculations of effective (mass- and heat-) transport coefficients, interfacial areas, power consumption, etc. 

Known scale-up correlations thus may allow scale-up even when laboratory or pilot plant experience is minimal. The fundamental approach to process scaling involves mathematical modeling of the manufacturing process and experimental validation of the model at different scale-up ratios. In a paper on fluid dynamics in bubble column reactors, Lubbert and coworkers (54) noted ... 

Zlokarnik and Mann (paper at Mixing Conf., Rindge, New Hampshire, August 1975) have found the opposite of Kalin e, i.e., subsurface diffusers, subsurface sparged turbines, and surface aerators compare approximately as 4 2 1 respectively in terms of O2 transfer efficiency however, Zlokarnik [Adv. Biochem. Eng., 11, 157 (1979)] later indicates that the scale-up correlation used earlier might be somewhat inaccurate. When all available information is considered, it... 

A measurement technique for determining mean circulation times and their distribution, is available. A scale-up correlation for mean circulation time, ( ,., applicable to zero or low gas hold-up with the standard vessel con-flgu ration, is... 

On balance, a scale-up correlation somewhat like that for solid suspension seems suitable for solids distribution. However, the effect of the physical properties of the system is much more closely related to what is found with settling solids in other situations. Thus their effect is different from that found for solids suspension. In particular, particle size is much more significant. 

Figure 6.23 Scale-up correlations developed by Kapic and Heindel (2006). Note the original correlation by Kapic and Heindel inadvertently transposed the DJT fraction and has been corrected here.

Whitton, M.J., and Nienow, A.W. (1993), Scale-up correlations fr gas hold-up and mass transfer coefficients in stirred tank reactors in Proceedings of the 3rd International Conference on Bioreactor and Bioprocess Fluid Dynamics, 135-149. 

Figure 5.14 Example screen display of scale-up correlations obtained from a sequence of constant pressure filtration experiments using the Data Analysis module of FDS.

The approach used in this chapter is based on families of geometrically similar cyclones so that all design variables are omitted from the scale-up correlations (except the size of the underflow orifice which should be variable and is considered here to be an operating variable). 

Despite these qualifications, much can be gained from applying scale-up correlations to specific problems to establish guidelines and limits for performance. 

---