Gas–liquid mixing power:\nCompared at the same rotational speed, how does the power drawn by an agitator change when the system is gas-sparged versus gas-free?

Introduction / Context:
When gas is sparged into a mechanically agitated vessel, bubbles alter local density, slip velocities, and blade loading. Engineers must know whether gassing increases or decreases the impeller power draw at fixed speed, because this influences motor sizing and scale-up correlations.

Given Data / Assumptions:

• Agitator speed is the same in both cases.
• Geometry and liquid properties are unchanged.
• Gas holdup is in the typical industrial range (no flooding or complete gas disengagement anomalies).

Concept / Approach:
In most practical regimes, introducing gas lowers the measured power draw at constant speed compared to ungassed operation. The gas phase displaces liquid near the blades, reduces effective density, and modifies circulation patterns, resulting in a “gas-induced power reduction.” This is captured in correlations using a power reduction factor P_g/P_u < 1, where P_u is ungassed power and P_g is gassed power at identical N.

Step-by-Step Solution:

Verification / Alternative check:
Power curves from literature plot P_g/P_u as a function of superficial gas velocity and impeller type; values generally fall below 1 until flooding transitions complicate behavior.

Why Other Options Are Wrong:

• More than/same as: contradict the typical reduction effect.
• “None”: a clear trend exists.
• “Greater only at very low Re”: not a general rule.

Common Pitfalls:
Confusing power draw with oxygen transfer; KLa can increase with gas even as power falls.

Final Answer:
Lesser than in a gas-free system