Scale-Up for Mixing

If it is assumed that the two most important parameters in mixing are shear rate and residence time, then scale-up rules can be derived that will keep these parameters constant. The shear rate is approximately  

If L/D is constant, then Eq. 8.187 requires that the screw speed be constant. From Eq. 8.186, it can be seen that with constant N the ratio of diameter to channel depth also must be constant. Thus, the scale-up factors for mixing become  

The effect of these geometric scale-up factors on extruder performance is shown in Table 8.5. The main problem with this scale-up approach is that the output increases much faster than the melting capacity. This approach, therefore, will not work 

A comparison of the effect on output of the different scale-up strategies is shown in Table 8.6. If the diameter of the small extruder is 50 mm (2 in) and the output 100 kg/hr (220 Ibs/hr), the output for a 150-mm (6 in) extruder will be as shown in Table 8.6. 

Common scale-up factors Scale-up for heat transfer Scale-up for mixing (geometric) 

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Baldyga, J., J. R. Bourne, B. Dubuis, A. W. Etchells, R. V. Gholap, and B. Zimmerman (1995). Jet reactor scale-up for mixing-controlled reactions. Transactions of the Institution of Chemical Engineers 73,497-502. 

Baldyga )., Bourne J.R., Dubois B., Etchells A.W., Gholap R.V., Zimmermann B.,fet reactor scale-up for mixing-controUed reactions, Trans IChemE 73 (1995) A, July, p. 497-502... 

The scale-up proposed by Carley and McKelvey [92] is the same as the scale-up for mixing also called geometrical scale-up, discussed in Section 8.8.3. The scale-up proposed by Maddock [93] is the same as the common scale-up discussed in Section 8.8.1. The scale-up proposed by Pearson is the most comprehensive and consistent. There is good balance between solids conveying, melting, and melt conveying further, the specific energy consumption is constant. A drawback of the Pearson scale-up is that the output increase is rather low this makes the scale-up unattractive in practice. More scale-up methods are listed in Table 8.8. 

As stated above under TNMe, in Ger during WWII, the prepn of TeNMe by this process was scaled up for use as an intermediate and as a substitute for nitric acid in the V-2 rocket (Ref 26). A pilot plant was built at Newark, NJ for prodn using this procedure. It was destroyed by an expln in 1953 and not rebuilt (Refs 33 44). Other prepns of lesser importance are by the action of Ag nitrite on iodotrinitro-methane (Ref 3) by the action of 90% nitric acid and 25% oleum on malononitrile, yield 45% (Ref 40) by the action of mixed acid on a number of aromatic nitrocompounds, of which nitrobenzene, dinitrobenzene, and nitronaphtha-lene gave the best yields (Ref 13a) and by the action of nitryl chloride on salts of TNMe. 

Thus, the ratios of the various forces occurring in mixing vessels can be expressed as the above dimensionless groups which, in turn, serve as similarity parameters for scale-up of mixing equipment. It can be shown that the existence of geometric and dynamic similarities also ensures kinematic similarity. 

A dimensionless dispersion number, based on the probable number of passes through the shear zone for an ingredient to be dispersed, was developed for scale-up of mixing of short fiber... 

Prepare transfection mix A that contains 1 fig of Renilla luciferase target plasmid (e.g., p-R-luc-4 sites) and 100 /(I of optiMEM (Invitrogen, CA). This is enough transfection mixture for 1 well, and can be scaled up for multiple transfections. For cultures that are to receive miR duplex, add 2 nM (calculated for a final volume of 500 fiL for each well). 

There are several methods to achieve appropriate scale-up of mixing. The first method involves geometric similarity. This technique employs proportional scale-up of geometric parameters of the vessel. The scaled-up parameters may include such geometric ratios as T)/r ratio, where D is diameter of the impeller and T is diameter of the tank, and Z/T ratio, where Z is the height of the liquid in the vessel. Similar ratios are compared for both the small-scale equipment DiTi) and the larger size equipment (D2T2). For example,... 

The second method for achieving appropriate scale-up of mixing uses dimensionless numbers to predict scale-up parameters. The use of dimensionless numbers simplifies design calculations by reducing the number of variables to consider. The dimensionless-number approach has been used with good success in heat transfer calculations and to some extent in gas dispersion (mass transfer) for mixer scale-up. Usually, the primary independent variable in a dimensionless-number correlation is the Reynolds number ... 

In dealing with chemical process engineering, conducting chemical reactions in a tubular reactor and in a packed bed reactor (solid-catalyzed reactions) is discussed. In consecutive-competitive reactions between two liquid partners, a maximum possible selectivity is only achievable in a tubular reactor under the condition that back-mixing of educts and products is completely prevented. The scale-up for such a process is presented. Finally, the dimensional-analytical framework is presented for the reaction rate of a fast chemical reaction in the gas/liquid system, which is to a certain degree limited by mass transfer. 

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 direct synthesis is in principle a one-step process, which is simpler and easier to scale-up for large capacity plants than the AO route. However, it also suffers from major drawbacks, for example continuing low yields and the hazards of mixing flammable gases. Various technical solutions are envisaged in the patent literature to minimize the risks of explosion and fire, such as the dilution of hydrogen and oxygen with an inert fluid. 

Simple Guidelines for Scale-Up of Mixing-Sensitive Homogenous Reactions... 

This problem is due to the fact that stirring experiments are generally carried out in small laboratory devices (D < 1 m), in which the micro-scale turbulence is predominant. They therefore often do not supply reliable information on scale-up for that mixing operation in which macro-scale turbulence is essential. The latter is... 

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