Correct Answer:

(a) Decrease in RPM of the impeller of the larger reactor

Explanation:

When scaling up a bioreactor (or any reactor) while keeping the power consumption per unit volume constant, the impeller RPM (rotations per minute) typically needs to decrease in the larger reactor. Here’s why:

Reactor Power and Scale-Up

In reactor scaling, the objective is often to maintain similar power consumption per unit volume, as power consumption can affect the shear forces, mixing, and aeration in the reactor. The power required for agitation (stirring) in a reactor is related to the impeller speed (RPM), the impeller design, and the scale of the reactor.

• As the reactor size increases, the volume and surface area change, requiring adjustments in impeller speed to maintain the same power consumption per unit volume. If you scale up the reactor, the power per unit volume should ideally remain constant to avoid excessive shear forces, which can damage sensitive cells or microorganisms in bioprocessing.

Power Consumption Equation

The power consumption in a stirred tank reactor is proportional to the impeller speed (RPM) raised to a certain exponent depending on the scale-up ratio, the impeller type, and other factors like viscosity. In general, the equation for power consumption looks like:

P∝RPM3×VolumeP \propto \text{RPM}^3 \times \text{Volume}P∝RPM3×Volume

When scaling up, if the volume increases, to keep the power per unit volume constant, the RPM must decrease. Specifically, for a geometrically scaled-up reactor, the RPM of the impeller needs to decrease by a factor of (V_{new}/V_{old})^{1/3}, where V is the volume of the reactor.

Why is the answer (a) correct?

• When scaling up, to maintain constant power consumption per unit volume, the RPM of the impeller needs to decrease. This helps to prevent excessive energy input that could disrupt the mixing and the process environment, especially when handling delicate biological systems.

Why are other options incorrect?

• (b) Holding the RPM of the impeller at the same value:
  If you hold the RPM constant during scaling, the power consumption per unit volume will increase as the volume of the reactor increases, which may result in excessive shear forces or poor mixing. Therefore, holding the RPM constant is not a suitable option.

• (c) Increase in RPM of the impeller of the larger reactor:
  Increasing the RPM when scaling up would increase the power consumption per unit volume, which goes against the goal of maintaining constant power consumption per unit volume. This would lead to excessive power input and potentially damaging effects.

• (d) Increasing or decreasing the RPM of the impeller depending on the type of impeller:
  While the type of impeller does affect the power requirement and scaling strategy, the general rule for scaling up is to decrease the RPM to maintain constant power consumption per unit volume, regardless of impeller type.

Conclusion

When scaling up a reactor and aiming to maintain constant power consumption per unit volume, the impeller RPM must decrease in the larger reactor. This adjustment ensures the energy input remains consistent and prevents issues like excessive shear forces. Therefore, the correct answer is (a) Decrease in RPM of the impeller of the larger reactor.