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Choose Shaft Speed; Size Impeller System to Draw Required Gassed Power

      It is possible to invest the same power at different shaft speeds by using different impeller sizes. In essence, high shaft speeds use smaller impellers and low shaft speeds use larger impellers. There are process, mechanical, and cost implications to this decision, as described in Chapters 6 and 17 and Ref. [2]. So, when we choose an initial speed, we may have to go back and choose another, as in the decision diamonds in Figure 2.1.

Though not all gear drives match the American Gear Manufacturer’s Association (AGMA) standard speeds, they are a good place to start, prior to engaging in detailed mechanical design. The speeds relevant for agitator design, in rpm, are 30, 45, 56, 68, 84, 100, 125, 155, 190, 230, 280, and 350 rpm. Laboratory units may have considerably higher speeds than this range.

Decision Point: D/T and Gassing Factors OK?

      As described in Chapter 6, D/T has effects on power, performance, and gassing factors (gassing factor is the ratio of power draw in the gassed condition to that in the ungassed condition). For example, we have found that designs requiring a D/T of more than 1.0 are unlikely to be successful. In general, smaller D/T ratios have less impact of gas flow changes on power draw than large ones, but create a less uniform bubble size and may be difficult to design mechanically. Also, the need for internal heat transfer surfaces may limit the maximum D/T.

      If the chosen shaft speed causes problems with gassing factors or mechanical interference, go back and choose a different shaft speed. If it is OK, go to the next step.

Mechanical Design

      This actually involves several things. It includes how the agitator is to be mounted (Chapter 16), gear drive selection and shaft/impeller design (Chapter 17). Some designs may not be feasible due to shaft critical speed or a complex shaft design, such as one requiring multiple steady bearings. The mechanical design at the chosen shaft speed should be deemed feasible or not.

Decision Point: Is the Mechanical Design Feasible?

      If the answer is no, go back and try a different shaft speed and repeat until one or more feasible designs are found.

Repeat to Find Lowest Cost

There may be several mechanically feasible designs at different shaft speeds. These different designs may have different costs. Higher speed means less torque and a less expensive gear box. However, the shaft design may be more expensive. There is no straightforward rule of thumb for this; each design must be fleshed out and a cost estimate made. In general, we would choose the least capital cost design unless there are other constraints. Once a semi‐final design is selected (for the entire optimization process we go through here, not just shaft speed), equipment vendors are generally helpful in optimizing capital cost.

Repeat for Different Aspect Ratios

      All of the previous steps were within the confines of the starting aspect ratio. So, up to this point, hopefully we have an optimum design for that ratio. However, that ratio may not be optimum overall. So, ideally the entire process should be repeated over the range of aspect ratios that are not constrained by other factors, such as site restrictions and shop‐fabricated vs field‐fabricated issues. Only by doing this will we find the economically optimum design. The capex and opex of the agitator, vessel, and compressor should ideally be included.

Repeat for Different Process Conditions

      All of the above was for the process conditions chosen at the start. But for some processes, these conditions can also be varied within limits. For example, the back pressure on the vessel can be varied, though there may be an upper limit, such as that required to allow exit of CO₂. But, for example, raising the pressure from 0 to 0.5 bar‐g may reduce agitator power requirements by 15–20%. Operating at a lower temperature increases oxygen solubility, reducing power but also reducing the metabolic processes within the organism. Lowering the peak cell population density can lower OUR but because the production rate will also be lowered, more total volumetric capacity will be required, albeit with a lower total power input. This is a classic case of capex vs opex. So, there are many potential options here.

Finish

      When all of the steps are completed as many times as it takes to get the final optimum, the capex and opex per unit of capacity will be optimized. As you may have surmised, that is a lot of work. However, the savings could be quite significant. Moreover, a very experienced agitator designer can quickly go through the optimization for a given set of conditions and aspect ratio by instinctively avoiding designs that his experience indicates are poor or infeasible.

The balance of the book provides background information and details needed to complete these steps to the degree possible. Outside resources will be needed for cost data. The individual chapters are not organized as extensions of the step‐by‐step procedure, but, rather, as sources of information and calculation methods, as well as providing enough fundamental understanding to use the procedures described herein.

Summary of Chapter

      This chapter has presented a series of steps to arrive at optimum fermenter design and operation. All of these steps will be covered in this book, in varying degrees of detail. The book will not follow this logic chapter by chapter, as a lot of background information and principles must be established before optimization can begin. The next several chapters will do that. The optimization steps begin in Chapter 8. There will also be several chapters after those covering optimization that will deal with special issues such as heat transfer, aspect ratio, and viscous fermentation. Sorry if this summary seems a bit repetitively redundant after the section “Finish.”

      List of Symbols

      CPHeat capacity at constant pressureDImpeller diameterkThermal conductivityTTank diameterZLiquid height

References

      1 1 Hicks, R.W., Morton, J.R., and Fenic, J.G. (1976). How to design agitators for desired process response. Chemical Engineering Magazine: 22–30.

      2 2 Fasano, J.B., Bakker, A., and Penney, W.R. (1994). Advanced impeller geometry boosts liquid agitation. Chemical Engineering 7 pages.

3 Agitator Fundamentals

      Before delving into details of agitation specific to bioreactors, we must establish a common framework of terminology and principles common to all agitation systems. This chapter will cover basic terminology, how experimental data are usually correlated, and some basic viscosity models used in fermentation broths.

Agitated Tank Terminology

A very simplified view of an agitated tank may be found in Figure 3.1. Though simplified, all

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