Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
The maximum cell concentration (g l
-1) expected in a bioreactor with initial cell concentration of
1.75 g l-1 and an initial glucose concentration of 125 g l-1 is (Yx/s = 0.6 g cell/g substrate) ________
Official Answer Key:
76.7 to 76.9
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2013 Q.46)**
**1. Governing Concept & Definition**:
- **Topic**: Bioprocess Stoichiometry & Maximum Cell Density
- In a substrate-limited batch reactor:
$X_{\max} = X_0 + Y_{X/S} \cdot S_0$
**2. Detailed Step-by-Step Calculation**:
- Substituting given initial cell concentration $X_0$, yield coefficient $Y_{X/S}$, and initial substrate $S_0$ yields:
$X_{\max} = 76.8\text{ g/L}$
**3. Final Answer**:
- **Calculated Value**: **76.8 g/L**
- **Official GATE Accepted Range**: **76.7 to 76.9**
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