What rpm should the larger bioreactor run at?
Bioreactor scale-up calculator (agitation speed)
From the impeller diameter and speed of a small bioreactor, gives the speed for a larger vessel under three criteria: constant power per volume (P/V), constant tip speed and constant Reynolds number.
When to use itUse it when moving conditions set in a lab bioreactor to pilot or production scale, to choose a starting agitation speed.
In the larger vessel, about 96.15 rpm is the starting point at constant P/V. To limit shear, matching tip speed brings it down to about 66.67 rpm, but check with dissolved oxygen and similar data that mixing does not fall short.
Which criterion to use
The row that matches your result is marked.
- Constant P/V (n = 2/3)Your resultCommon starting point for animal cell cultureKeeps the mixing power per liter the same. Widely used as a starting point that balances mixing with oxygen transfer (kLa).
- Constant tip speed (n = 1)When shear must stay lowKeeps the speed of the blade tips, a proxy for shear, the same. Used as a reference for shear-sensitive cells, but large vessels tend to end up undermixed.
- Constant Reynolds number (n = 2)Too slow at large scaleKeeps the flow regime (Reynolds number) the same, but the speed drops sharply as the impeller grows, leaving a large vessel short of both mixing and oxygen. Hard to use as is.
How it is calculated
Assuming geometrically similar vessels, the calculator lists the speed under each of the three criteria. P/V is the mixing power put into each liter of liquid, and tip speed is a proxy for the shear the cells experience. Which one to use depends on how shear-sensitive the cells are and how oxygen is delivered.
N2 = N1 × (D1/D2)^n (constant P/V: n = 2/3; constant tip speed: n = 1; constant Reynolds number: n = 2) tip speed [m/s] = π × (D[cm] ÷ 100) × (N[rpm] ÷ 60)
Source: Between geometrically similar vessels, the scale-up rule N2 = N1 × (D1 ÷ D2)^n applies: n = 2/3 for constant P/V, n = 1 for constant tip speed and n = 2 for constant Reynolds number. This is the standard approach to scaling up stirred tanks.
With your numbers
- diameter ratio = D1 ÷ D2 = 10 ÷ 30 = 0.3333
- N2 (constant P/V) = N1 × ratio^(2/3) = 200 × 0.3333^0.667 = 96.15 rpm
- N2 (constant tip speed) = N1 × ratio = 200 × 0.3333 = 66.67 rpm
- N2 (constant Reynolds number) = N1 × ratio² = 200 × 0.3333² = 22.22 rpm
- small-vessel tip speed = π × (D1 ÷ 100) × (N1 ÷ 60) = 1.047 m/s
Limits of this calculation
- This is an estimate for geometrically similar vessels with a single impeller. A different impeller type, number of impellers, aeration or aspect ratio changes the result.
- Real scale-up looks at P/V, kLa, mixing time, shear and CO₂ stripping together. No single criterion decides it.
- Tip speed is π × diameter × speed, and because speed is in rpm (per minute), take care with units when converting to m/s. Treat the result as an estimate for learning.
Primary sources
Every calculator gives an estimate for learning, built on published information and primary sources. Real decisions follow the applicable guidance and expert judgment.