Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
Ethanol is produced in a 10,000 L stirred bioreactor using an impeller of diameter
1 m. The density and viscosity of fermentation broth are 1000 kg m-3 and 1 cp,
respectively. The data relating the Power number and Impeller Reynolds number
is given below:
Reynolds number 1-5 5-500 > 105
Power number 70 10 5
Using the above data, the power required for the stirrer to operate at 300 rpm is
________ kW (Answer in integer).
Official Answer Key:
625 to 625
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2024 Q.56)**
**1. Governing Concept & Definition**:
- **Topic**: Bioreactor Power Consumption & Impeller Agitation
- In turbulent regimes (Reynolds number $Re > 10^4$), the power required for agitation is independent of $Re$ and governed by the Power Number ($N_p$):
$P = N_p \cdot
ho \cdot N^3 \cdot D_i^5$
**2. Detailed Step-by-Step Calculation**:
- **Given Parameters**:
- Impeller diameter $D_i = 1 ext{ m}$
- Agitation speed $N = 300 ext{ rpm} = rac{300}{60} = 5 ext{ s}^{-1}$
- Broth density $
ho = 1000 ext{ kg/m}^3$
- Impeller power number $N_p = 5.0$
- **Step 1: Power calculation in Watts**:
$P = 5.0 imes 1000 imes (5)^3 imes (1)^5$
$P = 5000 imes 125 imes 1 = 625,000 ext{ W} = 625 ext{ kW}$
**3. Final Answer**:
- **Calculated Value**: **625**
- **Official GATE Accepted Range**: **625 to 625**
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