Gas holdup in fermenters — The volumetric gas fraction (gas hold-up) depends mainly on which operating parameter(s)?

Introduction:
Gas hold-up, the fraction of reactor volume occupied by gas, is a key hydrodynamic variable affecting mass transfer and mixing. In aerated stirred tanks and airlift reactors, hold-up responds strongly to how much gas is introduced and how vigorously the liquid is agitated.

Given Data / Assumptions:

• Continuous aeration with steady gas flow.
• Mechanical agitation or internal circulation contributing energy dissipation.
• Newtonian approximation for qualitative discussion.

Concept / Approach:
Higher superficial gas velocity increases bubble population and volumetric gas fraction. Greater specific power input (P/V) promotes bubble breakup and longer residence through better dispersion, often raising hold-up up to a point. Thus, both gas rate and agitation intensity are the primary levers controlling gas hold-up, while headspace composition alone is insufficient to determine holdup in a well-mixed system.

Step-by-Step Solution:
Relate holdup to gas flow: increase in superficial velocity increases gas fraction.Relate holdup to agitation: higher P/V reduces bubble size and increases dispersion, enhancing holdup.Select the combined option capturing both dominant dependencies.

Verification / Alternative check:
Empirical correlations for gas hold-up include both superficial gas velocity and power input terms, validating the combined dependence.

Why Other Options Are Wrong:

• (a) Incomplete: ignores strong effect of agitation.
• (b) Incomplete: ignores strong effect of gas rate.
• (d) Headspace composition alone does not set holdup; it is a hydrodynamic outcome.
• (e) Impeller design influences hold-up via dispersion, so the statement is incorrect.

Common Pitfalls:
Over-aerating beyond flooding limits, which can reduce effective holdup and k_La; assuming holdup is fixed for a given reactor independent of operating conditions.

Final Answer:
Both (a) and (b)