Question

In an aerobic fermentation with air sparging, which of the following options can be used to increase the volumetric mass transfer coefficient for oxygen transfer?

• A. Using pure oxygen in place of air
• B. Increasing the volumetric flow rate of air
• C. Reducing the bubble diameter
• D. Decreasing the agitation rate

Hint:

\(k_L a\) is set by bubbling hydrodynamics (area and turbulence), not by gas composition, so separate it from the oxygen driving force.

Answer 1

The Correct Option is B, C

Step 1: Recall what the volumetric mass transfer coefficient represents.
The volumetric mass transfer coefficient, written \(k_L a\), is the product of the liquid-side mass transfer coefficient \(k_L\) and the specific interfacial area \(a\) (gas-liquid contact area per unit volume of broth).
It is a hydrodynamic quantity: it depends on bubble size, gas holdup, turbulence and mixing, and it sets how fast oxygen crosses from the gas bubbles into the liquid.
The oxygen transfer rate itself is \(OTR = k_L a (C^{*} - C_L)\), where \(C^{*}\) is the saturation dissolved oxygen concentration and \(C_L\) is the actual dissolved oxygen concentration.

Step 2: Check option (A), using pure oxygen instead of air.
Switching from air to pure oxygen raises the partial pressure of oxygen in the gas phase, which raises the saturation concentration \(C^{*}\) by Henry's law.
This increases the driving force \((C^{*} - C_L)\) and so increases OTR, but it does not change the hydrodynamics of bubbling, so \(k_L a\) itself stays the same. So (A) is not correct for this question.

Step 3: Check option (B), increasing the volumetric flow rate of air.
A higher air flow rate increases the gas holdup (the fraction of the vessel occupied by bubbles) and the total number of bubbles present at any instant, which raises the total interfacial area \(a\).
Since \(k_L a\) rises directly with \(a\), this increases \(k_L a\). So (B) is correct.

Step 4: Check option (C), reducing the bubble diameter.
For a fixed gas holdup, smaller bubbles give a much larger surface area to volume ratio (interfacial area per unit gas volume scales as \(1/d_b\), where \(d_b\) is bubble diameter).
Smaller bubbles mean more interfacial area \(a\), so \(k_L a\) increases. Higher agitation, finer sparger orifices and anti-coalescing additives are practical ways to shrink bubble size. So (C) is correct.

Step 5: Check option (D), decreasing the agitation rate.
Lower agitation means less shear to break bubbles apart, so bubbles coalesce into larger ones, gas holdup drops, and interfacial area \(a\) falls.
This decreases \(k_L a\), the opposite of what the question asks for, so (D) is wrong.

Final Answer:
Only increasing the air flow rate and reducing bubble diameter genuinely raise the volumetric mass transfer coefficient \(k_L a\); pure oxygen raises OTR through the driving force, not \(k_L a\), and lower agitation lowers \(k_L a\).
\[ \boxed{\text{(B) Increasing the air flow rate and (C) Reducing the bubble diameter}} \]