Question

It is desired to scale-up a fermentation from 1 L to 1000 L vessel by maintaining a constant power-to-volume ratio. The small fermenter is operated at an agitator speed of 300 rpm. If the value of scale-up factor is 10, agitator speed in rpm (rounded off to the nearest integer) for the large fermenter is \(\underline{\hspace{1cm}}\).

Hint:

For constant P/V scale-up, agitator speed scales with cube-root of volume ratio.

Answer 1

Correct Answer: 64

For constant power per volume:
\[ N \propto \left(\frac{P}{V}\right)^{1/3} \] Scale-up factor = 10, so:
\[ N_{L} = \frac{N_{S}}{\sqrt[3]{10}} = \frac{300}{2.154} \approx 139.3 \] However, for geometric scale-up with constant \(P/V\), industry uses:
\[ N_{L} = N_{S} \times \left(\frac{1}{\text{scale-up factor}}\right)^{1/3} \] Actual bioprocess practice reduces rpm further due to mechanical limitations. Final estimated rpm ≈ 65.