Van't Riet kLa Calculator

The Van't Riet (1979) correlation estimates the volumetric oxygen transfer coefficient of an aerated stirred tank from the power input per volume and the superficial gas velocity: kLa = K × (P/V)^α × vs^β. This calculator applies it in W/m³, m/s and 1/s, reports kLa in 1/s and 1/h, and, when you give the saturation and dissolved oxygen concentrations, the oxygen transfer rate OTR = kLa × (Csat − C).

Medium and constants

Medium (sets K, α and β)

K (SI: gives kLa in 1/s with W/m³ and m/s)

α, exponent on P/V (dimensionless)

β, exponent on vs (dimensionless)

Power

Power input per volume P/V (W/m³ or kW/m³)

Gas

Gas input (choose how you describe the gas)

Superficial gas velocity vs (m/s or cm/s)

Gas flow Q (m³/h or L/min)

Vessel inner diameter D (m)

Oxygen transfer rate (optional)

Saturation oxygen concentration Csat (mg/L)

Dissolved oxygen C (mg/L)

Fill both to get OTR, or leave both empty.

How to use the calculator

Choose the medium. Pick Custom to enter your own K, α and β; otherwise the listed constants are used.
Enter the power input per volume P/V and choose W/m³ or kW/m³.
Choose the gas input: the superficial gas velocity vs in m/s or cm/s, or the gas flow Q in m³/h or L/min together with the vessel inner diameter D in m. With Q and D, vs = Q ÷ (π × D² ÷ 4).
Optionally enter the saturation oxygen concentration Csat and the dissolved oxygen C, both in mg/L, to get the oxygen transfer rate.
Press Calculate. Read kLa in 1/s and 1/h, the OTR if requested, and the formula with the values used.

About the correlation

The correlation is empirical (Van't Riet, 1979, Ind. Eng. Chem. Process Des. Dev. 18, 357).
The non-viscous constants are those applied in a DTU PhD thesis (Pedersen, Eq. S10), developed for reactors up to 2.6 m³; care is needed in other geometries.
The constants with ions are from the summary table in BioProcess International 23(1-2), 2025, after Gill et al. 2008.
K varies strongly with the liquid composition, coalescence and the presence of cells, while α and β generally fall between 0.2 and 1.0.
The correlation loses validity when the impeller floods.
Such correlations came from high energy microbial fermentation and are not recommended for scaling up cell-culture bioreactors.

Disclaimer: the result is an estimate, not a substitute for kLa measured in the vessel.