Bioreactor Scale-Up Criterion Comparator (2D)

Highlighted Rule

Vessel & Agitation

Production volume 2,000 L

Bench impeller speed N₁ 300 rpm

Highlighted Rule Readouts

N₂ (production rpm)

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P/V dev. from bench

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k_La dev. from bench

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Mix time dev. from bench

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Impeller tip speed — bench → production

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How it works

Geometric similarity is assumed: production tank diameter T and impeller diameter D grow with the cube root of the volume ratio, T/D held at 3. Four classic scale-up rules pick which quantity stays constant as N (impeller speed) is re-derived for the new diameter — and because they don't agree, they demand four genuinely different production speeds:

Power/volume:  P/V ∝ N³D²         → const. P/V:      N₂ = N₁(D₁/D₂)^(2/3)
Tip speed:     v_tip = πND        → const. tip speed: N₂ = N₁(D₁/D₂)
Gas transfer:  k_La ∝ (P/V)^0.4·v_s^0.5, v_s ∝ D (fixed vvm) → const. k_La: N₂ = N₁(D₁/D₂)^1.083
Mixing time:   θ_m ∝ T^(2/3)/(P/V)^(1/3) → const. θ_m:  N₂ = N₁  (impeller speed unchanged)

The bar chart on the right computes N₂ under all four rules at once from the same bench point and target volume — the spread between the bars is the scale-up dilemma. Choosing "constant tip speed" (to protect shear-sensitive cells) under-mixes and starves oxygen transfer at large scale; choosing "constant k_La" (to protect oxygen supply) can push tip speed and local shear far above the bench value. There is no rule that keeps every quality attribute constant at once — this is exactly why a cGMP tech-transfer package needs a comparability protocol and a defined "quality range" for each critical quality attribute, not a single formula.

Rule buttons — highlight which quantity the readouts on the left describe; the bar chart always shows all four rules simultaneously.
Production volume — sets the target scale (100 L–20,000 L); the production tank's diameter follows T₂ = T₁·(V₂/V₁)^(1/3).
Bench speed N₁ — the starting agitation rate at 10 L bench scale that everything else is scaled from.
Impellers — the two small schematic vessels spin at N₁ (bench) and at the highlighted rule's N₂ (production), so you can see the speed mismatch, not just read it.

Bench-scale vessel (N₁) Production-scale vessel (N₂, highlighted rule)