Figure 38. Typical curves of KqO versus power and various gas rates for radial flow turbines, (a) R100; (b) A-315.
However, before retrofitting a large fermentation tank it should be realized unless there is some process data arising from understanding the relationship between the mass transfer and the biological oxidation requirement, retrofitting existing radial flow turbine installations with A315 impeller types does not always give an improvement in process result. The average is normally about two or three times as frequent for a plus result as for neutral or negative results.
It is very difficult to study the effect of fluidfoil impellers in the pilot plant since the pilot plant in general has much shorter blend time and a much more uniform blending composition than appears in the full scale tank. Thus, putting fluidfoil impellers in the pilot plant improves the blending under a situation where the blending is already much improved over full scale performance.
There are four ways in which mixers are often specified when considering installation of more productive units in a fermentation plant. This can involve either a larger tank with a suitable mixer or improvement of the productivity of a given tank by a different combination of mixer horsepower and gas rate. These are listed below:
a. Change in productivity requirements based on production data with a particular size fermenter in the plant.
b. New production capacity based on pilot plant studies.
c. Specification of agitator based on the sulfite absorption rate in aqueous sodium sulfite solution.
d. Specification of the oxidation uptake rate in the actual broth for the new system.
6.1 Some General Relationships in Large Scale Mixers Compared to Small Scale Mixers
In general, a large scale mixing tank will have a lower pumping capacity per unit volume than a small tank. This means that its blend time and circulation time will be much larger than in a pilot tank.
There is also a tendency for the maximum impeller shear rate to go up while the average impeller zone shear rate will go down on scaleup. In addition, the average tank zone shear rate will go down as will the minimum tank zone shear rate.
This means that there is a much greater variety of shear rates in the larger tank, and in dealing with pseudoplastic slurry it will have a quite different viscosity relationship around the tank in the big system compared to the smaller system.
Microscale shear rates operate in the range of300 microns or less, and are governed largely by the power input.
The power input from the gas per unit volume will increase on scaleup. This is because there is a greater head pressure on the system, and there is also an increasing gas velocity.
It may be that the power level for the mixer may be reduced since the energy from the gas going through the tank is higher in order to maintain a particular mass transfer coefficient, KqO; however, this changes the relative power level compared to the gas and other mass transfer rates, such as the liquid-solid mass transfer rate. The capacity for the blending type flow pattern is not affected in the same way with changes in the mixer power level as is the gas-liquid mass transfer coefficient.
6.2 Scale-Up Based on Data from Existing Production Plant
If data are available on a fermentation in a production-size tank, scaleup may be made by increasing, in a relative proportion, the various mass transfer, blending and shear rate requirements for the full-scale system. For example, it may be determined that the new production system is to have a new mass transfer rate of x% of the existing mass transfer rates, and there may be specifications put on maximum or average shear rates, and there may be a desire to look at changes in blend time and circulation time. In addition, there may be a desire to look at the relative change in C02 stripping efficiency in the revised system.
At this point, there is no reason notto consider any size or shape of tank. Past tradition for tall, thin tanks, or short, squat tanks, or elongated horizontal, cylindrical tanks does not mean that those traditions must be followed in the future. To illustrate the principle involved in the gas-liquid mass transfer, look at Fig. 36 which gives the three different mass transfer steps commonly present in fermentation. The mass transfer rate must be divided by a suitable driving force, which gives us the mass transfer coefficient required. The mass transfer coefficient is then scaled to the larger tank size and is normally related to superficial gas velocity to an exponent, power per unit volume to an exponent, and to other geometric variables such as the D/T ratio of the impeller.
A thorough analysis takes a look at every proposed tank shape, looks at the gas rate range required, calculates the gas phase mass transfer driving force, and then calculates the required KqO to meet that. Reference is made to data on the mixer under the condition specified and to various D/T ratios to obtain the right mixer horsepower level for each gas rate.
At this point, the role of viscosity must be considered. Figure 39 shows the effect of viscosity on mass transfer coefficient. It is necessary to measure viscosity with a viscosimeter which mixes while it measures viscosity. Figure 40 illustrates the Stormer viscosimeter which is one device that can be used to establish viscosity under mixing conditions with shear rates that can be established.
In looking at the new size tank, estimates should be made of the shear rate profile around the system, and then using the relationship that viscosity is a function of shear rate, and the fact that it is shear stress
Shear stress = fx (shear rate)
that actually carries out the process, one can then estimate the viscosity throughout the tank, and the product of viscosity and shear rate to give the shear stress. Estimates can then be made of how different the proposed new tank may be compared to the existing known performance of the production tank.
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