Drybench Bioreactor.

Scale-up calculator: constant P/V, tip speed or kLa

Agitation at a larger scale by three rules side by side: constant power per volume, constant tip speed and constant kLa, with their assumptions stated.

Agitation at a larger, geometrically similar vessel by three rules side by side, at the same gas flow per volume: constant ungassed power per volume, constant impeller tip speed and constant kLa by Van 't Riet's correlation. They disagree because a larger vessel at the same vvm has a higher superficial gas velocity.

Small vessel diameter (m)

Small impeller diameter (m)

Small volume (L)

Small agitation (rpm)

Gas flow (actual vvm at reactor conditions)

Scale factor (large volume ÷ small)

Large vessel: diameter 1.02 m, impeller 0.408 m, 700 L.

Rule	Agitation (rpm)	Tip speed (m/s)	kLa (per hour)	Pg/V (W/m³)
The small vessel	600	2.76	106	1,890
Constant P/V	216	4.61	215	1,620
Constant tip speed	129	2.76	120 extrapolated	376
Constant kLa	116	2.48	106 extrapolated	277

The small vessel
Agitation (rpm)
600
Tip speed (m/s)
2.76
kLa (per hour)
106
Pg/V (W/m³)
1,890
Constant P/V
Agitation (rpm)
216
Tip speed (m/s)
4.61
kLa (per hour)
215
Pg/V (W/m³)
1,620
Constant tip speed
Agitation (rpm)
129
Tip speed (m/s)
2.76
kLa (per hour)
120 extrapolated
Pg/V (W/m³)
376
Constant kLa
Agitation (rpm)
116
Tip speed (m/s)
2.48
kLa (per hour)
106 extrapolated
Pg/V (W/m³)
277

Unverified: Van 't Riet's range not yet checked against Van 't Riet 1979.

Ignores cooling, mixing time and shear. Every kLa is the correlation's, flagged outside its fitted range, with no prediction interval.

Agitation in the large vessel, by each rule:

Constant P/V 216 rpm

Constant tip speed 129 rpm; kLa extrapolated

Constant kLa 116 rpm; kLa extrapolated

Tank and impeller diameters and the ungassed liquid height are drawn to one scale; the headspace and the impeller's position are not to scale. Each rule gives its own agitation; the numbers are in the table, and none of the three is recommended here.

Each rule's agitation and tip speed from its scaling rule, and kLa and Pg/V from the correlations, at the small and the large vessel; nothing here is measured.

Unverified: Van 't Riet's range not yet checked against Van 't Riet 1979.

Agitation in the large vessel, by each rule:

Constant P/V 10,000 rpm; kLa extrapolated

Constant tip speed 10,000 rpm; kLa extrapolated

Constant kLa: No agitation from 1 to 10,000 rpm gives the small vessel's kLa here: even at 10,000 rpm the correlation gives the large vessel less.

Each rule's agitation and tip speed from its scaling rule, and kLa and Pg/V from the correlations, at the small and the large vessel; nothing here is measured.

Unverified: Van 't Riet's range not yet checked against Van 't Riet 1979.

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Limits

Teaching and estimation model, not a validated process model.
The rescue cascade stays within the agitation, gas-flow and oxygen-enrichment limits you enter, and ignores cooling capacity, vessel pressure and gas-safety limits. Oxygen enrichment near flammable solvents or vapours is a fire and explosion hazard. Do not run a vessel from these outputs without your own engineering review.

A simulation, not a forecast. Every output follows from the model equations and the parameters you entered. It is a teaching and estimation model, not a validated process model, and not a prediction for any real strain, vessel or process.

Equations