Power input/volume

Gas holdup and volumetric gas-liquid mass-transfer coefficients are correlated with the gassed power input/volume and with the aeration rate (actual gas superficial velocity), e.g., the correlation of van t Riet [Ind. Eng. Chem. Proc. Des. Dev. 18 357 (1979)] for the volumetric mass-transfer coefficient of coalescing and noncoalescing systems ... 

The aeration rate will drastically alter the effective density of the liquid in the vessel. Due to this density effect, a fully gassed bioreactor has half the theoretical power input compared to an ungassed vessel. Using the power input/volume determined from process development scale and the bioreactor geometry at large scale, the equivalent large-scale impeller speed can be calculated. 

From equation 23, it can be seen that the higher the power input per unit volume, the lower the oxygen transfer efficiency. Therefore, devices should be compared at equal transfer rates. AH devices become less energy efficient as rates of transfer increase (3). 

Having estabhshed the residence time and power input, the scale-up can Be now done using the principle of geometric similarity together with equal power per unit volume discussed earlier. 

If the process can be operated adiabaticaUy, the production capacity is scaled up as the cube of diameter since geometry shear rate, residence time, and power input per unit volume all can be held constant. 

Mass-transfer coefficients seem to vary as the 0.7 exponent on the power input per unit volume, with the dimensions of the vessel and impeller and the superficial gas velocity as additional factors. A survey of such correlations is made by van t Riet (Ind Eng. Chem Proc Des Dev., IS, 3.57 [1979]). Table 23-12 shows some of the results. 

The scale-up criterion that is probably most widely used for mixing-limited unit operations is based on constant power input per unit volume according to (Harnby etal., 1992). 

Figure 12-95. Axial compressor Type AV100-16, during erection. Note stationary and rotating blades. Two identical steam turbine-driven machines supply air to blast furnace at steel works. Suction volume = 560,000 NmVh discharge pressure = 6.2 bar power input = 52,000 kW each. (Used by permission Bui. 26.13.10.40-Bhj. Sulzer Turbo Ltd.)...

Selection should be made for minimum power input, which is also likely to be the quietest fan for the duty. Performance is usually quoted for a standard condition of 1.2 m /kg. Calculations of system resistance are best carried out at the same condition. The user may find only the static pressure quoted. If total or velocity pressure are also quoted or the outlet velocity can be calculated the designer can calculate how much pressure can be recovered after the exit. Any mismatch due to difficulty in calculating system resistance will cause the volume to rise or fall, to settle on the fan characteristic curve. 

Agitation of fermentation broth creates a uniform distribution of ah in the media. Once you mix a solution, you exert an energy into the system. Increasing power input reduces the bubble size and this in turn increases the interfacial area. Therefore the mass transfer coefficient would be a function of power input per unit volume of fermentation broth, which is also affected by the gas superficial velocity.2,3 The general correlation is expected to be as follows ... 

The mass transfer, KL-a for a continuous stirred tank bioreactor can be correlated by power input per unit volume, bubble size, which reflects the interfacial area and superficial gas velocity.3 6 The general form of the correlations for evaluating KL-a is defined as a polynomial equation given by (3.6.1). 

P Power input to impeller per volume of gas-free liquid... 

Assuming the depth of liquid is equal to the tank diameter, then the volume of ihe pilot scale unit is [(7774)0.62 x 0.6] = 0,170 in3 and the power input per unit volume is (0.157/0.170) - 0.884 kW/m3 The volume of the full-scale unil is given by ... 

For purposes of scale-up, it is generally most satisfactory in the laminar region to maintain a constant speed for the tip of the impeller, and mixing time will generally increase with scale. The most satisfactory basis for scale-up in the turbulent region is to maintain a constant power input per unit volume. 

The power input to the fluid by the pump, Q AP, increases dramatically upon scaleup, as The power per unit volume of fluid increases by a factor of... 

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