Scaleup rules

Example 1.7 predicted that power per unit volume would have to increase by a factor of 100 in order to maintain the same mixing time for a 1000-fold scaleup in volume. This can properly be called absurd. A more reasonable scaleup rule is to maintain constant power per unit volume so that a 1000-fold increase in reactor volume requires a 1000-fold increase in power. Use the logic of Example 1.7 to determine the increase in mixing time for a 1000-fold scaleup at constant power per unit volume. 

In addition, the turbulent fluctuations set up a microscale type of shear rate. Microscale mixing tends to affect particles that are less than 100 /xm in size. The scaleup rules are quite different for macroscale controlled process in comparison to microscale. For example, in microscale processes, the major variables are the power per unit volume dissipated in various points in the vessel and the total average power per unit volume. In macroscale mixing, the energy level is important, as well as the geometry and design of the impeller blades and the way that they set up macroscale shear rates in the tank. 

If satisfactory suspension is obtained in a small tank, whether judged by visual observations, particle velocities, or mass transfer rates, the safe scaleup rule is to keep geometrical similarity and constant power per unit volume. The ratios DJDf — 5 and / >, = 5 are often recommended, though some prefer DJD, = 0.4 for solids suspension. The critical speed can be reduced by decreasing the clearance, but it may be hard to start the stirrer if it is in a layer of solids very near the bottom. 

SOME PRACTICAL DESIGN ASPECTS AND SCALEUP RULES... 

Although experts in agitator design are loath to admit to using such a simplistic rule, most scaleups of conventionally agitated vessels are done at or near constant power per unit volume. The consequences of scaling in this fashion are explored in Example 4.7... 

As a general rule, the operating speed of the mixer tends to go down, while the peripheral speed of the impeller tends to go up. The speed of the mixer is related to the average impeller zone macroscale shear and thus typically goes down in scaleup while the impeller peripheral speed is often related to the maximum impeller zone macroscale shear rate, see Fig. 5. Out in the rest of the tank (away from the impeller) there another spectrum of shear rates which typically is about a factor of 10 lower than the average impeller zone shear rate. These particular impeller zone shear rates tend to decrease on scaleup. 

One variable in particular is important. The linear superficial gas velocity should be run in a few cases at the levels expected in the full-scale plant. This means that foaming conditions are more typical of what is going to happen in the plant and the fermenter should always be provided with enough head space to make sure the foam levels can be adequately controlled in the pilot plant. As a general rule, foam level is related to the square root of the tank diameter on scaleup or scale-down. 

It should be noted that die smallest size packings in the Bolles-Fair correlation are nominally 12 mm (O.S in.) in diameter. If the general rule of 8 1 ctdunui packing diameter is to be maintained, then a minimum column size of 100 mm (4 in.) is indicated. This is a crucial point in the design of pilot facilities and the development of scaleup parameters. It is not yet possible to go to the tmy pacUngs for laboratory tests (using, say, column diameters of 25-50 mm) and s obtain reliable scaleup data. 

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