Geometric similarity fermentation

The power consumption by impeller P in geometrically similar fermenters is a function of the diameter Dl and speed N of impeller, density p and viscosity p. of liquid, and acceleration due to gravity g. Determine appropriate dimensionless parameters that can relate the power consumption by applying dimensional analysis using the Buckingham-Pi theorem. 

Based on the practical history of scale-up, most fermentation processes for alcohol and organic acid production have followed the concepts of geometric similarity and constant power per unit volume. From the above concept, and as a strong basis for translation of process criteria, only physical properties of the process were considered in the scale-up calculation. For power consumption in an agitated vessel, there is a fixed relation between impeller speed, N, and impeller diameter, l)t. The constant power per unit volume, for a mechanical agitated vessel is given by ... 

Unfortunately, relatively little information has been made available for industrial gas-liquid contactors. Further data from industry could permit significant tests of the reliability of the present correlations and their applicability to scale-up. Steel and Maxon (SI 1) reported on the power requirements during novobiacin fermentation in 20- and 250-liter pilot-plant vessels and in 12,000- and 24,000-gal vessels. The comparative data are difficult to evaluate because of changes that occurred in viscosity and gas retention during the course of the fermentation. In addition, geometric similarity did not prevail... 

The initial emulsification studies employed a 1 L reactor vessel with baffles originally designed for fermentation processes. Subsequent studies were successively scaled up from 1 L to 3, 10, and 100 L. Variations due to differences in reactor configuration were minimized by utilizing geometrically similar reactors with approximately the same D/Tratio (i.e., 0.36-0.40). Maa and Hsu contended that separate experiments on the effect of the baffle area... 

For anaerobic fermentation, the unaerated stirred tank discussed in Section 7.4 is used almost exclusively. One criterion for scaling-up this type of bioreactor is the power input per unit liquid volume of geometrically similar vessels, which should be proportional to for the turbulent range and to for the laminar range, where N is the rotational stirrer speed and L is the representative length of the vessel. 

Can you determine the power consumption and impeller speed of a 1,000-gallon fermenter based on the findings of the optimum condition from a geometrically similar one-gallon vessel If you cannot, can you scale up by using a different fluid system ... 

For the optimum design of a production-scale fermentation system (prototype), we must translate the data on a small scale (model) to the large scale. The fundamental requirement for scale-np is that the model and prototype should be similar. To ensure similarity, two conditions mnst be satished (1) geometric similarity of the physical boundaries and (2) dynamic similarity of the flow fields. The first requirement is obvions and easy to accomplish. The second is achieved when the values of the nondimensional parameters (such as Reynolds number and power nnmber) are the same. However, it is difficult, if not impossible, to satisfy the dynamic similarity when more than one dimensionless group is involved in a system, which creates the need for scale-np criteria. 

These reactors/fermenters will be geometrically similar if for example ... 

Where H is the height and D the diameter of the reactor/fermenter. As expressed by Johnstone and Thrings (1957), two bodies are geometrically similar when to every point in the one body there exists a corresponding point in the other."... 

The most immediate is geometric similarity, but on its own this is clearly not enough. In addition, keeping a constant kia throughout scales is one of the most widely used approaches when aerobic fermentations are involved. Alternatively, constant volumetric power consumption has also been commonly su ested. Other alternatives proposed as criteria for scale-up include constant tip speed, similar Reynolds number, or equal mixing times [1,21]. 

The available literature contains very few references to studies of the power consumption for agitation and the volumetric oxygen transfer coefficients of multi-stage impeller fermenters. Takeda and Hoshino (1968) showed experimentally that closely spaced impellers caused serious interference between the flow streams from adjacent impellers and an overall reduction in power consumption. On the other hand, Oldshue (1966) has indicated that within fairly large ranges of geometric variables, a similar oxygen transfer coefficient is obtained if the power per unit volume is maintained at similar values under a constant aeration rate. 

It has been possible here to deal only briefly with the correlations between the physical properties of fermentation fluids and the operating conditions in the fermenter found by many investigators. For example, if it were known what was required in the way of shearing action at each step of the fermentation process, then it would be possible to carry out a relatively rigorous calculation throughout the system. Thus, geometric non-similarity in scale-up of the fermenter could be applied to reduced or increased fluid shear stress. 

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