Figure 41. Schematic of typical data from fermentation showing the change in oxygen content of gas, C02 content in liquid and fermentation yield.
If the pilot plant is to duplicate certain properties of fluid mixing, then it may be necessary to use non-geometric impellers and tank geometries to duplicate mixing performance and not geometric similarity. As a general rule, geometric similarity does not control any mixing scaleup property whatsoever.
It may also not be possible to duplicate all of the desired variables in each run, so a series of runs may be required changing various relationships systematically and then a synthesis made of the overall results.
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.
In duplicating maximum impeller zone shear rates on a small scale, there may be a very severe design problem in the mechanics of the mixer, or the shaft speed, mechanical seals and other things. This means that careful consideration must be given to the type of runs to be made and whether the pilot plant or the semi-work-scale equipment must be available at all times to duplicate the maximum impeller zone shear rates in the plant or whether this sort of data will be obtained on a different type of unit dedicated to that particular variable.
Figure 37 shows what often happens in the pilot plant in terms of correlating mass transfer coefficient, Kq a, with power and gas rate in the pilot plant. This curve is then translated to a suitable relationship for full scale. It is possible to consider that with the higher superficial gas velocity, the power level may be reduced in the full scale to keep the same mass transfer coefficient. The box on the right in Fig. 37 shifts to the box on the left. This should be considered, but it should be borne in mind that this changes the ratio of the mixer power to gas power level in the system; changes the blend time; changes the flow pattern in the system; the foaming characteristics and also can markedly affect the liquid-solid mass transfer rate if that is important in the process.
In all cases, a suitable mass transfer driving force must be used. Figure 42 illustrates a typical case for fermentation processes and illustrates that there is a marked difference between the average driving force, the log-mean driving force, and the exit gas driving force. In a large fermenter, it is this author's experience that gas concentrations are essentially step-wise stage functions and a log-mean average driving force has been the most fruitful.
Figure 43 illustrates a small laboratory fermenter with a Z/T ratio of 1, and in this case, depending on the power level, an estimate must be made of the gas mixing characteristics and an evaluation made of the suitability of the exit gas concentration for the driving force compared to the log-mean driving force. This is one area which needs to be explored in the pilot program and the calculation procedures.
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