GATE BT 2024 • Q61 NAT • 2 Marks

Section 4: Bioprocess Engineering and Process Biotechnology

Bioreactor types, scale-up

Subtopic: Fundamentals of Bioreactor types, scale-up

Question Statement:

Consider scale-up of fungal fermentation from a 20 L model-type to 20,000 L prototype stirred tank reactor. The model-type and prototype have the same aspect ratio during scale-up. The impeller speed in the model-type is 500 rpm and the scale-up criterion is constant shear. The impeller speed in the prototype reactor will be ________ rpm (Answer in integer).

Official Answer Key:

50 to 50

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2024 Q.61)** **1. Governing Concept & Definition**: - **Topic**: Bioreactor Scale-Up based on Constant Tip Speed - Criteria of constant impeller tip speed ($v_{tip} = \pi N D_i = ext{constant}$) during geometric scale-up ($V \propto D_i^3$). **2. Detailed Step-by-Step Calculation**: - **Scale-Up Ratio**: - Model volume $V_1 = 20 ext{ L}$, Prototype volume $V_2 = 20,000 ext{ L}$ - Volumetric scale factor: $ rac{V_2}{V_1} = rac{20000}{20} = 1000$ - Linear geometric scale factor: $ rac{D_{i,2}}{D_{i,1}} = (1000)^{1/3} = 10$ - **Constant Tip Speed Condition**: $N_1 D_{i,1} = N_2 D_{i,2} \implies N_2 = N_1 \left( rac{D_{i,1}}{D_{i,2}} ight) = rac{N_1}{10}$ - **Given Model Speed**: $N_1 = 500 ext{ rpm}$ $N_2 = rac{500}{10} = 50 ext{ rpm}$ **3. Final Answer**: - **Calculated Value**: **50** - **Official GATE Accepted Range**: **50 to 50**

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