Depth profile in tall aerated reactors: where are oxygen transfer rates typically the highest?

Difficulty: Easy

Correct Answer: Highest at the base of the reactor

Explanation:


Introduction / Context:
Oxygen transfer in tall aerated reactors varies with depth due to hydrostatic pressure and bubble dynamics. Understanding where OTR peaks helps in placing probes, sizing spargers, and interpreting gradients in large-scale fermentations.


Given Data / Assumptions:

  • Bottom sparging introduces bubbles near the base.
  • Hydrostatic pressure increases with depth.
  • Mixing is effective but not perfectly uniform over height.


Concept / Approach:
At greater depth, the saturation concentration C* is elevated, increasing the driving force for transfer. Bubbles at the base are smaller and more numerous due to compression and break-up near the sparger, raising interfacial area a and residence time. Consequently, kLa and OTR are generally largest near the bottom region and decline toward the surface where pressure (and thus C*) is lower and bubbles have enlarged by coalescence.


Step-by-Step Solution:
1) Identify key variables: C*, kLa, residence time—all favor higher OTR at depth.2) Recognize bubble evolution: small to larger as they rise; interfacial area decreases upward.3) Combine effects: OTR peaks at the base, then diminishes with height.


Verification / Alternative check:
Typical DO profiles show lower DO near the base (due to stronger uptake and transfer), consistent with high local OTR. Computational fluid dynamics of gas–liquid systems also predict higher mass-transfer coefficients at depth near the sparger zone.


Why Other Options Are Wrong:
Option A/C presume mid/surface dominance, which ignores pressure effects; Option D assumes perfect mixing; Option E refers to gas-phase headspace, not liquid-phase mass transfer.


Common Pitfalls:
Misplacing DO sensors only near the surface and inferring whole-tank behavior; depth matters in scale-up.


Final Answer:
Highest at the base of the reactor

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