Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
An enzyme immobilised in a porous spherical pellet, catalyses a strongly
mass-transfer limited first-order reaction. The effectiveness factor for the
immobilised enzyme reaction increases with the
Options:
(A) decrease in the size of the pellet
(B) increase in the pore diffusivity within the pellet
(C) decrease in the enzyme turnover number
(D) increase in the enzyme concentration within the pellet
Official Answer Key:
A;B;C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2025 Q.54)**
**1. Governing Concept**:
- **Topic**: Enzyme Engineering & Internal Mass Transfer Limitations (Thiele Modulus)
- For an immobilized enzyme in a porous spherical bead operating in a **strongly internal diffusion-limited (mass-transfer limited) regime**:
- Thiele modulus $\Phi \gg 1$.
- Internal effectiveness factor $\eta \approx \frac{3}{\Phi} \propto \frac{1}{R} \sqrt{\frac{D_{\text{eff}}}{k_v}}$.
- The apparent reaction rate is controlled by the rate of intraparticle diffusion through the pores rather than the intrinsic biochemical turnover rate.
- **Remedies to relieve internal diffusion limitation**:
1. **Decrease bead radius ($R$)**: Shortens diffusion distance, increasing effectiveness factor $\eta$.
2. **Increase effective diffusivity ($D_{\text{eff}}$)**: Using pellets with larger pore diameter or higher porosity.
3. **Decrease enzyme loading / activity per volume ($k_v$)**: Brings the reaction rate closer to the diffusion rate, reducing Thiele modulus.
**2. Option Analysis**:
- **Option (A) [Decreasing the size of the pellet] is CORRECT**: Smaller particle radius decreases the diffusion path length, elevating internal effectiveness factor $\eta$.
- **Option (B) [Decreasing enzyme loading inside the pellet] is CORRECT**: Lowers the Thiele modulus, reducing internal diffusion resistance.
- **Option (C) [Increasing the pore size of the pellet] is CORRECT**: Increases intraparticle effective diffusion coefficient $D_{\text{eff}}$, facilitating faster transport.
- **Option (D) [Increasing the size of the pellet] is INCORRECT**: Exacerbates internal diffusion limitation by lengthening diffusion path.
**3. Final Answer**:
- **Correct Options**: **A, B, C**
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