Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
A microbial culture is being grown in a bioreactor with continuous aeration. The
dissolved oxygen probe provided with the system shows a reading of zero. In this
context, which of the following inferences is/are correct?
Options:
(A) The culture has died due to absence of oxygen
(B) The culture has run out of carbon source
(C) The culture growth becomes oxygen limited
(D) The culture growth is independent of dissolved oxygen
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2026 Q.44)**
**1. Governing Concept**:
- **Topic**: Bioprocess Engineering & Dissolved Oxygen Dynamics
- The dynamic dissolved oxygen (DO) mass balance in an aerated stirred bioreactor with active microbial respiration is:
$\frac{dC_L}{dt} = k_L a (C^* - C_L) - q_{O_2} X$
where $C^*$ is saturation dissolved oxygen concentration, $C_L$ is actual dissolved oxygen, $k_L a$ is volumetric mass transfer coefficient, and $q_{O_2} X$ is oxygen uptake rate (OUR).
- At steady state, $\frac{dC_L}{dt} = 0 \implies \text{OTR} = \text{OUR} \implies k_L a (C^* - C_L) = q_{O_2} X$.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Ignores the biological oxygen consumption rate.
- **Option (B) is INCORRECT**: Misplaces the sign of oxygen transfer driving force.
- **Option (C) is CORRECT**: Accurately equates oxygen transfer rate (OTR) to oxygen uptake rate (OUR) under quasi-steady state conditions where $k_L a(C^* - C_L) = q_{O_2} X$.
- **Option (D) is INCORRECT**: Violates the conservation of mass for dissolved gas.
**3. Final Answer**:
- **Correct Option**: **C**
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