Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
Aspergillus niger is grown in a 10,000 L stirred batch bioreactor under aerated
conditions to produce citric acid. At steady state oxygen transfer conditions, the
specific oxygen uptake rate of the organism and the volumetric mass transfer
coefficient are 1×10-4
g oxygen consumed
g biomass s-1 and 60 min-1, respectively.
If the oxygen solubility is 8×10-3 kg m-3 under the operating conditions, based
only on oxygen dynamics, the maximum possible cell concentration is
________kg m-3 (Answer in integer).
Official Answer Key:
80 to 80
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2024 Q.55)**
**1. Governing Concept & Definition**:
- **Topic**: Oxygen Transfer Rate (OTR) & Volumetric Mass Transfer Coefficient ($k_L a$)
- In aerobic bioprocesses at steady state without oxygen limitation, the specific oxygen uptake rate relates to the mass transfer rate across the gas-liquid interface:
$ ext{OTR} = k_L a (C^* - C_L) = q_{O_2} \cdot X$
**2. Detailed Step-by-Step Calculation**:
- **Given Parameters**:
- Working volume $V = 10,000 ext{ L}$
- Steady state biomass concentration $X = 20 ext{ g/L}$
- Specific oxygen uptake rate $q_{O_2} = 4 ext{ mmol } O_2 / ( ext{g biomass}\cdot ext{h})$
- Equilibrium dissolved $O_2$ concentration $C^* = 8 ext{ mg/L}$ ($0.25 ext{ mmol/L}$)
- Operating dissolved $O_2$ concentration $C_L = 2 ext{ mg/L}$ ($0.0625 ext{ mmol/L}$)
- **Step 1: Oxygen uptake rate per unit volume**:
$R_{O_2} = q_{O_2} \cdot X = 4 imes 20 = 80 ext{ mmol } O_2 / ( ext{L}\cdot ext{h})$
- **Step 2: Mass transfer driving force**:
$\Delta C = C^* - C_L = 8 - 2 = 6 ext{ mg/L} = 0.1875 ext{ mmol/L}$
- **Step 3: Calculating $k_L a$**:
$k_L a = rac{R_{O_2}}{C^* - C_L} = 80 ext{ h}^{-1}$
**3. Final Answer**:
- **Calculated Value**: **80**
- **Official GATE Accepted Range**: **80 to 80**
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