Key Parameters for Up-Pumping in Fermentation, Part 2

By Thomas Post, Lightnin

Note: Part 1 of this paper, which set the stage for discussing how to improve up-pumping in fermentation, covered the objectives, mechanical, and gas-related considerations. The introduction is repeated for your convenience.

Introduction
All axial flow impeller technology in fermentation (as well as in most other processes) is based on down pumping. The impellers circulate the fermentation broth in a downward motion to hold the gas down in the tank. In aerobic fermentation, therefore, the impeller pumps against the flow of the rising air. The shear sensitivity of most fermentations and the tendency of most fermentation broths to coalesce create an environment that does not respond optimally to down pumping. In fact, recent research suggests that high solidity hydrofoil impellers used in an up-pumping mode can increase mass transfer, improve blending and heat transfer, and decrease blend time. In the retrofit of actual systems, yield increases of 20 to 40% have been obtained. To better understand why up-pumping technology offers superior fermentation results, this paper discusses the key parameters to consider when designing a fermentation system and how these parameters are addressed by up-pumping technology.

The application dictates impeller design. Choose
the right impeller for lower horsepower,
to save energy...

...for low shear, or for anything
in between.

The K factor
The power imparted by the impellers decreases upon aeration and must be accounted for in the design of the fermenter. This power drop-off is defined as the ratio of gassed horsepower to ungassed horsepower and is known as the K factor. The lower the K factor, the more the fermenter design must compensate for the power loss. Simply speaking, this means if 100 hp is required to obtain the required mass transfer in the fermentation and the K factor is 1, then a 100-hp gearbox would be sufficient to meet the mixing objective. If, however, the K factor is 0.3 (which more closely reflects the K factors on Rushton and Smith Turbines), a 300 HP gearbox would be required to meet the same mixing objective.

Further complicating the design is the fact that if that same 300 HP gearbox were to run ungassed, the motor would be overloaded and burn out. Companies using traditional impeller technology must, therefore, design their fermentation systems around the limits imposed by the K factor, often using larger more expensive speed reducers to generate more power and variable speed motors to protect the mixer from running in ungassed conditions and burning out.

At equal diameter and speed, the Smith Turbine has a higher K factor than a Rushton Turbine. This means that in gassed conditions the Smith Turbine of the same diameter and speed imparts more power. Smith Turbines, with their curved blades, are more expensive than Rushton Turbines. Since the power of an impeller is a function of its speed and diameter, increasing the diameter or speed of the Rushton Turbine to compensate for the lower K factor is often a less expensive way to meet the same power requirement. The cost of the system must be weighed against the mixing objectives and the limitations placed by the K factor.

Because up-pumping A340 impellers do not pump against the flow of gas, there is little dropoff in horsepower upon aeration. In fact, A340 impellers have a K factor around 0.9. This means that more power is imparted in gassed conditions so mass transfer increases, and indeed the mass transfer rate of up-pumping A340s is generally 2-fold greater than that of traditional systems.

Mass Transfer Coefficient
All reactions start out as mass transfer-controlled. As the reaction progresses, however, it eventually becomes reaction rate-controlled. Oxygen (air) must first dissolve into the liquid phase, representing a gas-liquid mass transfer. At this point the dissolved oxygen can then either be diffused to a solid surface through liquid--solid mass transfer (in fermentation, this is when the oxygen passes through the cell wall) or the oxygen can become part of a chemical reaction. In general, chemical reactions are much faster than gas--liquid mass transfer. As long as the reaction is limited by mass transfer, improvements in the fermenter's mechanical configuration will improve the process result.

Temperature affects both the reaction rate and the mass transfer rate. Temperature increases increase both rates, while decreases in temperature will decrease both rates. Generally, an increase of 10° will double the reaction rate, but only increase mass transfer by 25%. Viscosity, on the other hand, has an extreme dampening effect on mass transfer.

Typically, the rate-limiting step in fermentation is mass transfer, especially in small-scale fermentations. But as stated earlier, in large-scale fermentation poor blending creates dead zones within the tank that in turn affect mass transfer. Both the transfer of oxygen from the gas to the liquid phase and blending are mass transfer limitations and are difficult to separate from each other.

The mass transfer coefficient is used to determine the mass transfer rate. Likewise, improvements in mass transfer are measured by looking at changes in the mass-transfer coefficient.

It is essential to note what test method was used to determine the mass transfer coefficient since each method yields different values. Therefore, the same test methodology must be employed when comparing the mass transfer coefficients between two systems. Conversely, comparing different fermentation systems based on mass transfer coefficients determined by different test methods is useless and misleading.

When studying the mass transfer coefficient of multiple up-pumping A340 impellers versus traditional multiple Rushton Turbines, the mass transfer coefficient was found to be up to two times greater regardless of the method employed to measure the mass transfer coefficient.

Shear Rates
Most common batch fermentations are bacterial, fungal, mycelial or yeast based broths. While all are affected by shear, mycelial fermentations are by far the most sensitive. Scaleup of mammalian cell culture and rDNA are also quite sensitive to shear. To understand how shear affects fermentations, average and maximum shear must be understood. In conventional fermentation systems, while average shear rates decrease on scale-up, maximum shear rates increase, with significant impact on the process results.

Time-independent fluid shear rate is defined by a velocity gradient, which is the change in average velocity over a given distance. When looking at time-independent shear, as described by average velocities, actual velocity fluctuations are obscured, but it is this variability in velocities that can affect shear-sensitive fermentations. To account for this, velocity fluctuations must also be taken into account by calculating the root mean square (RMS) value of the fluctuations (obtained by squaring the fluctuations, averaging them and then taking the square root). This is a useful representation of time-dependent shear.

Shear rates operate throughout the tank at different magnitudes and scales. The shear rate determined by the average velocities affects particles in the order of several hundred microns. The fluctuating velocity shear rates involve micro scale processes and affect particle sizes or cluster sizes of 200 microns or less. It is on the micro-scale level that both mass transfer and diffusion occur.

The highest shear rates are in the impeller zone, generated by the discharge velocity. This discharge velocity can be characterized by an average impeller shear rate and a maximum impeller shear rate. Regardless of impeller type, the average impeller shear rate is only a function of the impeller speed. Maximum shear rates, on the other hand, depend on the type of flow pattern generated. For radial flow impellers like the Rushton Turbine, the maximum shear rate is a function of impeller speed and diameter or tip speed. For axial flow impellers, like the A340 impeller, however, the maximum impeller shear rate is only a function of speed.

Impeller speeds are always less in production than in pilot scale equipment. Therefore, average shear is always less, whereas maximum shear rates always increase for radial impellers like Rushton Turbines but decrease for axial flow impellers like the A340 impeller at constant power per unit volume (P/V). Thus for full-scale shear-sensitive fermentations it is not unusual to see better yields when using A340 impellers.

Coalescence
Coalescence is the characteristic of substances coming together. In fermentation this describes the tendency for smaller bubbles to converge with other bubbles to form larger bubbles. Most pharmaceutical fermentation processes represent coalescing systems.

In studying aerobic fermentation processes, the gas-liquid behavior of these processes is traditionally evaluated using air-water models. While these models represent coalescing systems in theory, they do not predict their behavior in practice. Once the gas is dispersed in water it does not rapidly coalesce to create the "bubbling" and "surging" seen in real fermentations. Moreover, salts and electrolytes are often added to the fermentation broths as part of the testing process, further causing the medium to behave more like a non-coalescing system. This has implications for the traditional way fermentation processes have been analyzed and for the actual effect of shear on full-scale fermentation broths.

For dispersion processes where bubbles do not tend to coalesce, the effect of average shear rates and maximum shear rates on bubble size determine the ultimate dispersion. Therefore, if the process lasted long enough, and most fermentation processes last several days, the ultimate bubble size would be determined by the maximum shear rate around the impeller since all bubbles would eventually move through this zone.

This suggests that in a water-air model, which acts effectively as a non-coalescing system, the ultimate air bubble size would be determined by the maximum shear rate around the impeller. This is an inaccurate representation of most fermentations which have higher viscosities.

Because most fermentation processes are coalescing systems, they can not be adequately understood by air-water models which reflect non-coalescing systems. Fermentation broths are of significantly higher viscosity than water, and viscosity increases as the microorganisms multiply. Viscosity induces drag such that the reduction or lack of shear enables bubbles to increase in size (i.e. to coalesce). In aerobic fermentations, therefore, air bubbles will tend to coalesce and there is equilibrium between dispersion and coalescence. In this case the entire spectrum of shear rates within the tank becomes relevant.

Because of pressure differentials around an operating impeller, air bubbles tend to migrate toward and coalesce in areas of lower pressure. In aerobic fermentations large bubbles can get caught behind the impeller blades, a particular problem with Rushton turbines as well as with all down-pumping impellers. In contrast, the flow pattern generated by up-pumping A340 impellers follows the natural flow patterns of coalescing mediums. This eliminates the opportunity for bubbles to aggregate into larger bubbles and stall the impeller. Moreover, bubbles are mechanically sheared at each impeller zone as they flow upwards to the top of the tank. Laser Doppler Velocimetry (LDV) measurements show zero shear rates between impellers. This counters the tendency for these bubbles to coalesce, and thus maximizes the gas-liquid interface.

Conclusions
The mechanical design of a fermenter affects affect the multiple mixing goals of each fermentation process. Up-pumping A340 impeller technology offers significant process advantages in coalescing and shear sensitive fermentations because of improvements in blending, heat transfer, flooding, gas hold-up, the K factor and the mass transfer coefficient, all of which result in improved mass transfer.

Each fermentation process is unique, but the parameters to be considered during optimization are similar. As long as a process is mass transfer- rather than reaction rate- limited, improvements in the mechanical configuration of the mixer, as demonstrated by the introduction of up-pumping A340 impeller technology, will improve process results. Yield improvements at lower power consumption levels are therefore typical in laboratory and full-scale installations.

For more information: Thomas Post, vice president of technology, Lightnin, 135 Mount Read Blvd, Rochester, NY 14611. Tel: 716-436-5550.