Q.23 A batch bioreactor is to be scaled up from 10 to 10,000 liters.
The diameter of the large bioreactor is 10 times that of the small
bioreactor. The agitator speed in the small bioreactor is 450 rpm.
Determine the agitator speed (rpm) of the large bioreactor with same
impeller tip speed as that of the small bioreactor.
__________
Bioreactor Scale-Up: Calculate Impeller Tip Speed & Agitator RPM
Correct Answer & Calculation
The agitator speed in the large bioreactor is 45 rpm.
Impeller tip speed vt follows vt = πDN/60, where D is impeller diameter and N is speed in rpm.
For constant tip speed:
πDsNs/60 = πDlNl/60
DsNs = DlNl
Given Dl = 10Ds and Ns = 450 rpm:
Nl = (Ds × 450)/(10Ds) = 45 rpm
Volume scales from 10 to 10,000 L (1,000×), but diameter ratio directly governs impeller scaling here.
Why Constant Tip Speed?
Constant tip speed preserves maximum shear stress and circulation velocity across scales, ideal for shear-sensitive cells like mammalian cultures.
- Matches oxygen transfer and blending time in lab-to-production transitions.
- Common criterion when geometry (impeller/tank ratio) scales geometrically.
Options Analysis (GATE Q.23)
This GATE-style question implies multiple-choice: 45, 60, 75, 90 rpm.
| Option | RPM Value | Why Incorrect/Correct |
|---|---|---|
| A | 45 | Correct: Direct inverse proportionality to 10× diameter keeps vt constant |
| B | 60 | Incorrect: Might assume partial geometric scaling or volume1/3 (10× vol ~2.15× linear, but problem states 10× diameter). |
| C | 75 | Incorrect: No standard criterion yields this; ignores exact 10× ratio. |
| D | 90 | Incorrect: Underestimates diameter impact; perhaps confuses with constant power/volume (N ~ scale-2/3) |
Scale-Up Criteria Comparison
| Criterion | Speed Scaling Rule | Large RPM Example | Use Case |
|---|---|---|---|
| Constant Tip Speed | Nl = Ns(Ds/Dl) | 45 rpm | Shear-limited processes |
| Constant Re | Nl = Ns(Ds/Dl)2 | 4.5 rpm | Laminar mixing |
| Constant P/V | Nl = Ns(Ds/Dl)2/3 | ~126 rpm | Turbulent power |
For biotech fermentation, tip speed balances oxygen demand and cell viability.
