187. Consider the scale up of a fermentation from a 10 L to 10,000 L while maintaining geometric similarity.
Agitation speed was maintained at 500 rpm in the 10 L fermenter. If scale up is done based on constant tip
speed, then the agitation speed in the larger reactor should be ………….rpm
1. 5000
2. 500
3. 50
4. 5

Introduction:

Scale-up in bioprocessing is crucial when increasing production volumes, especially in fermentation processes. The transition from a small-scale fermenter (e.g., 10 L) to a large-scale fermenter (e.g., 10,000 L) requires careful consideration of various parameters to ensure that the conditions are suitable for efficient microbial growth and product formation. One of the key parameters that need to be adjusted during scale-up is the agitation speed.

In this article, we explore the concept of geometric similarity and how it relates to scaling up fermentation processes. We specifically focus on the impact of constant tip speed on agitation speed during scale-up, helping you understand how to adjust the agitation speed for larger fermenters.

Key Concepts in Fermentation Scale-Up:

1. Geometric Similarity: Geometric similarity refers to the concept that the proportions of the different dimensions of the fermenter (e.g., height, diameter) remain consistent when scaling up. This ensures that fluid dynamics, mixing efficiency, and heat transfer remain similar between the small-scale and large-scale systems.

2. Tip Speed: The tip speed is the speed at which the tip of the impeller moves through the medium. In fermentation, maintaining constant tip speed during scale-up is important to ensure that the mixing and aeration conditions remain consistent. If the tip speed is kept constant, the agitation speed needs to be adjusted in proportion to the scale-up.

3. Agitation Speed and Its Relationship to Scale-Up: When scaling up a fermentation vessel, the agitation speed must be adjusted to account for the larger volume. The tip speed is related to the impeller diameter and the agitation speed (rpm), and maintaining constant tip speed ensures that mixing efficiency and shear forces are consistent across both scales.

Scale-Up Calculation:

To maintain constant tip speed when scaling up a fermentation process, the following relationship is used:

$$\text{Tip speed}=\pi \times D\times N$$

Where:

• D is the impeller diameter.

• N is the agitation speed (rpm).

• Tip speed should remain constant for both the 10 L and 10,000 L fermenters.

If geometric similarity is maintained, the ratio of the agitation speeds can be found using the ratio of the impeller diameters, as the volume scales up by a factor of 1000 (from 10 L to 10,000 L). Since volume scales with the cube of the scale-up factor, and impeller diameter scales with the cube root of the volume, the agitation speed must be reduced accordingly.

Calculation Steps:

• The scale-up factor is 1000 (10,000 L / 10 L).

• The impeller diameter in the large fermenter will be the cube root of 1000 times the diameter of the small fermenter, which leads to a proportional decrease in the agitation speed.

Thus, the agitation speed in the larger fermenter will be approximately:

Agitation speed in large reactor=Agitation speed in small reactorScale-up factor1/3\text{Agitation speed in large reactor} = \frac{\text{Agitation speed in small reactor}}{\text{Scale-up factor}^{1/3}}Agitation speed in large reactor=Scale-up factor1/3Agitation speed in small reactor​ Agitation speed in large reactor=500 rpm10001/3≈50 rpm\text{Agitation speed in large reactor} = \frac{500 \, \text{rpm}}{1000^{1/3}} \approx 50 \, \text{rpm}Agitation speed in large reactor=10001/3500rpm​≈50rpm

Answer:

The correct agitation speed in the larger reactor should be approximately 50 rpm.

Thus, the correct answer is:

3. 50