Question

Oxygen transfer rate (OTR) depends on

• A. Pressure only
• B. Temperature only
• C. Volume only
• D. Concentration gradient and \(k_{L}a\)

Hint:

Remember the most important formula in bioreactor engineering: \[ \boxed{\text{OTR}=k_{L}a(C^{*}-C_{L})} \] A higher value of \(k_{L}a\) means more efficient oxygen transfer to growing cells.

Answer 1

The Correct Option is D

Concept: In aerobic fermentation, microorganisms require a continuous supply of oxygen for growth and metabolism. Oxygen must be transferred efficiently from air bubbles into the culture medium and finally into the cells. The rate at which oxygen is transferred is called the Oxygen Transfer Rate (OTR). It is one of the most important parameters in bioreactor design and operation.

Step 1: Understand the OTR equation.
The oxygen transfer rate is expressed as: \[ \boxed{\text{OTR}=k_{L}a\left(C^{*}-C_{L}\right)} \] where,
• \(k_{L}a\) = Volumetric mass transfer coefficient
• \(C^{*}\) = Saturation concentration of oxygen
• \(C_{L}\) = Dissolved oxygen concentration in the medium

Step 2: Factors affecting OTR.
OTR increases when:
• The concentration gradient \((C^{*}-C_{L})\) increases.
• Agitation speed increases.
• Aeration rate increases.
• The value of \(k_{L}a\) increases. Thus, oxygen transfer depends mainly on both the concentration gradient and the volumetric mass transfer coefficient.

Step 3: Eliminate incorrect options.

• Pressure influences oxygen solubility but is not the only determining factor.
• Temperature alone cannot determine OTR.
• Reactor volume alone does not define oxygen transfer.
• The correct expression includes concentration gradient and \(k_{L}a\). Final Answer: \[ \boxed{Option (D) is correct \]