Effect of liquid height on oxygen transfer: if higher liquid height increases gas hold-up, where in the reactor will the oxygen transfer rate be higher?

Introduction / Context:
Oxygen transfer rate (OTR) in aerated bioreactors depends on both the mass-transfer coefficient (kLa) and the driving force (C* − C), where C* is the saturation concentration. Hydrostatic pressure increases with depth, raising C* for oxygen. Therefore, depth-dependent effects can produce spatial variation in OTR.

Given Data / Assumptions:

• Liquid height is increased, raising overall gas hold-up.
• Aeration and mixing maintain bubbles through the column.
• Temperature and gas composition are unchanged.

Concept / Approach:
Henry’s law implies that C* increases with partial pressure; at the base, hydrostatic pressure is higher, so the effective oxygen solubility is higher. Additionally, bubbles entering at the bottom are smaller (due to compression) and have more residence time, often raising local interfacial area a and kLa. Combined, these effects make OTR generally higher near the base than near the surface.

Step-by-Step Solution:
1) Recognize depth → higher hydrostatic head → higher C* at the base.2) Bubble compression at depth → smaller effective size → larger a.3) OTR = kLa*(C* − C) → both kLa and driving force tend to be larger at the base.4) Conclude OTR is higher at the base under typical conditions.

Verification / Alternative check:
Measured dissolved oxygen profiles in tall, sparged reactors often show higher transfer (and lower DO) near the sparger region, consistent with stronger mass-transfer activity at the bottom.

Why Other Options Are Wrong:
Uniform or “higher throughout” ignores hydrostatic effects; “lower at base” contradicts increased C* and residence time; “lower throughout” misinterprets the role of gas hold-up.

Common Pitfalls:
Assuming perfect axial mixing eliminates gradients; in practice, gradients remain, especially in tall vessels.

Final Answer:
Higher at the base of the reactor