Scale-up of mixing systems

Various methods of scale-up have been proposed all based on geometric similarity between the laboratory equipment and the full-scale plant. It is not always possible to have the large and small vessels geometrically similar, although it is perhaps the simplest to attain. If geometric similarity is achievable, dynamic and kinematic similarity cannot often be predicted at the same time. For these reasons, experience and judgment are relied on with aspects to scale-up. 

A scale ratio R is used for scale-up from the standard configuration as shown in Table 7-2. The procedure is  

Determine die scale-up ratio R, assuming dial die original vessel 

586 Modeling of Chemioal Kinetios and Reaotor Design The ratio of the volumes is then 

Using the value of R, ealeulate the new dimensions for all geometrie sizes. That is, 

Determine the scale-up ratio R, assuming that the original vessel is a standard cylinder with DX1 = HThe volume V, is 

The selected scale-up rule is applied to determine the agitator speed N2 from the equation  

---

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. 

The scale-up of mixing data has been treated with a variety of approaches, some to rather disastrous results. The principles are now W ell established, and it is a matter of truly understanding the par ticular systems that poses... 

Much of the literature on scale-up of reaction systems has focused on continuous systems. However, scale-up methods for batch and semibatch operations have been included in several books, including Oldshue (1983), Whitaker and Cas-sano (1986) Carberry and Varma (1987) Froment and Bischoff (1990), Tatterson (1991), Hamby et al. (1992), and Baldyga and Bourne (1999). Correlations for heat transfer, mass transfer, Uquid-liquid dispersions, solids suspensions, and dissolntion are available and are discussed iu these references and in several chapters of this book. Mixing requirements for scale-up of homogeneous reactions are discussed in Chapter 13, including explanation of the limitations of the nsnal mixing scale-up parameter of equal power per unit volume. The reader is referred to the texts listed in the references, in which these correlations are well developed. These correlations are not reproduced in this chapter. 

Hydrothermal Synthesis Systems. Of the unit operations depicted in Figure 1, the pressurized sections from reactor inlet to pressure letdown ate key to hydrothermal process design. In consideration of scale-up of a hydrothermal process for high performance materials, several criteria must be considered. First, the mode of operation, which can be either continuous, semicontinuous, or batch, must be determined. Factors to consider ate the operating conditions, the manufacturing demand, the composition of the product mix (single or multiple products), the amount of waste that can be tolerated, and the materials of constmction requirements. Criteria for the selection of hydrothermal reactor design maybe summarized as... 

This is another common processing operation, usually for chemical reactions and neutralizations or other mass transfer functions. Pilot plant or research data are.needed to accomplish a proper design or scale-up. Therefore, generalizations can only assist in alerting the designer as to what type of mixing system to expect. 

Holland, F.A. Scale-Up of Liquid Mixing Systems, Chemical Engineering, Sept. 17, 1962, p. 179. Chen, S.J., MacDonald, A.R. Motionless Mixers for Viscous Polymers, Chemical Engineering, Mar. 19, 1973, p. 105. 

When deciding on the type of the reactor required for a particular chemical or physical transformation, the first question that needs to be addresses is whether the cavitation enhancement is the result of an improved mechanical process (due to enhanced mixing). If this is the case, then cavitation pretreatment of a slurry may be all that is required before the system is subjected to conventional type transformation scheme and the scale up of the pretreatment vessel would be a relatively simpler task. 

The scale-up of liquid mixing systems can be divided into two categories the scale-up of process result and the scale-up of power data. 

HTU is subjected to the effects of both radial and axial mixing, and these are not readily quantified, so scale-up of columns of this kind is often not based on fundamentals, but rather on correlations determined from detailed studies of several systems in the particular design of column chosen. 

When a process is dominated by a mixing operation, another gambit for the effective scale-up of geometrically similar systems involves the interrelationships that have been established for impeller-based systems. Tatterson (58) describes a number of elementary scale-up procedures for agitated tank systems that depend upon operational similarity. Thus, when scaling up from levels 1 to 2,... 

---