Agitator Design for Gas-Liquid Fermenters and Bioreactors. Gregory T. Benz

Figure 2.1 Agitator design flow chart.

The other exception is fermentation of highly viscous liquids, such as Xanthan gum or Gellan gum. At peak concentrations in the broth, such materials may have viscosities at a shear rate of 1 per second of 30 000 cP or even higher and apparent viscosities at the impeller of 2 000–10 000 cP. They are also quite non‐Newtonian. We will describe some viscosity models and effects in Chapter 3 and specific issues with viscous fermenter design in Chapter 12.

      With the foregoing in mind, the first step in our flow chart, defining process results, will focus on the required mass transfer rate, MTR. Since most fermenters consume oxygen, and the feed gas is air, most of this book will use aerobic fermentation with air feed for examples and calculations. So, we will usually refer to the mass transfer rate as the OTR, or oxygen transfer rate. Units are normally either mass per volume–time or moles per volume–time. The most common units of this type are mg/l‐h or mmol/l‐h. Relatively speaking, an “easy” fermentation would have an OTR of less than 100 mmol/l‐h, an “average” one would have around 150–200, and a difficult one would be 300 and up. There are huge implications on equipment size and power costs at these different levels.

      Because mass transfer correlations are generally no more accurate than about ±30% when developed for the actual broth and can be much greater in error if generic, published correlations are used, the design OTR should be increased over the required OTR by a suitable factor.

      Chapter 11 will deal with cases where the feed gas is not air. For such cases, it may not be possible to optimize power the way we present it in this flow chart, as the cost of the feed gas is not just the power required to deliver it to the tank, and there may be other process constraints.

      Note that evolving gas from solution is a separate issue from dispersing gas. Evolving gas is already dispersed, though it affects power draw, performance, and mechanical behavior in a similar way to dispersing gas.

Define Process Conditions

      All conditions impacting the agitator design, the mass transfer rate, and ancillary functions such as heat transfer must be delineated. A partial list follows:

       Fluid density (e.g. specific gravity or density such as kg/m3)

       Fluid viscosity (e.g. cP or Pa‐s). If the fluid is non‐Newtonian, the model and parameters describing it must be included

       Operating temperature

       Mean barometric pressure

       Back pressure in vapor space

       Heat capacity of the process fluid at constant pressure, CP. Sample units J/g‐C or BTU/lb‐F

       Thermal conductivity of the process fluid, k. Sample units J/h‐m‐C or BTU/h‐ft‐F.

       For the ancillary heat transfer calculations, need the above thermal properties for the heat transfer medium as well

       For the heat transfer calculations, need the available flow and temperature of the heat transfer medium

       Concentration of oxygen (or other species to be transferred) in the feed gas (usually, we will assume air at 21% oxygen)

       Henry’s law constant, or alternatively, saturation concentration at feed gas concentration at process temperature at a reference pressure (typically 1 atm)

       Minimum required dissolved oxygen concentration for organisms to thrive

       Maximum allowable CO2 concentration in the exit gas, either as mole fraction or as actual partial pressure

       Any other process constraints affecting design

Choose Tank Geometry

      In principle, many tank shapes can be used. That can include cylindrical, rectangular, and spherical tanks. However, odd‐shaped tanks may be hard to baffle and agitate properly. Rectangular tanks may be harder to clean and sterilize if they have sharp corners. Most tanks used in this industry are cylindrical. Most are mounted with their axis vertical. However, the author knows of at least one installation where a multitude of horizontal cylindrical tanks were used. This is decidedly not recommended, for a host of reasons. Just a few worth mentioning: Multiple gear drives per tank are required, increasing agitator cost. Very random hydraulic forces occur, causing more frequent mechanical failure. Low absolute liquid height fails to take advantage of higher oxygen solubility at the bottom of the tank due to liquid head. Harmonic flows in the sparge system can occur.

      For the purposes of this book, we will stick to vertical cylindrical tanks. With that restriction, the geometry to be decided is the ratio of liquid height to tank diameter (Z/T), often referred to as aspect ratio. Fermenters have been built with a wide variety of aspect ratios, for various reasons. The most common or popular designs normally have aspect ratios between 2 and 3, but that may be more related to tradition than because it is optimum for a particular set of circumstances.

      Chapter 19 discusses aspect ratio in detail, in terms of its effect on capital and power costs, which provides an opportunity for optimization. However, we have to begin somewhere to go through the rest of this flow chart. In the absence of any restrictions on geometry, an aspect ratio between 2 and 3 seems reasonable to start with.

      There can be restrictions on aspect ratio due to building constraints. If the vessel must fit within a given floor space, that may place restrictions on the diameter, forcing a certain minimum aspect ratio. Sometimes, local building codes carry height restrictions. So, the allowable aspect ratio range may be bound by such constraints, among others.

Calculate Equivalent Power/Airflow Combinations for Equal Mass Transfer Rate

      It is possible to achieve the same mass transfer rate using a small amount of air and a lot of agitator power, or a lot of air with low agitator power, and an infinite number of steps between.

      There are upper and lower airflow limits, however. The minimum airflow is where the OTR is stoichiometrically balanced; that is, the molar flow of oxygen in the incoming air stream exactly matches the molar rate of consumption. In other words, this would require 100% mass transfer. That would require an infinite amount of agitator power!

      The upper bound would be when either the vessel or the agitator is flooded. We will define these conditions in Chapters 4 and 8. Suffice it to say for now that there is such a thing as too much airflow.

      To keep calculation effort reasonable, the calculations should be performed incrementally: say, starting with 25% more than the minimum and stepping in about 5‐10% increments on that, up to the maximum.

      Chapter 8 describes this procedure in detail.

Choose Minimum Combined Power

      From the above combinations of agitator power and airflow, calculate the agitator brake power, which is the shaft power divided by the mechanical efficiency of the agitator, which includes gear drive losses as well as seal losses. Calculate the compressor brake power, including pressure losses through lines, filters, and sparger as well as compressor efficiency. Add the agitator and compressor brake power together and choose the combination with the lowest total, unless other constraints govern, such as CO₂ in the exhaust gas.