Many chemical reactions require the drawdown and incorporation of gas from the head space of an agitated vessel into the liquid where the gas is available for reaction. Examples of these reactions include hydrogenations and nitrations.
There have been many studies relating the development of the vortex to the system vessel geometry and the impeller Froude number but this gives no information about the gas-liquid mass transfer rate which, ultimately, is needed for process design.
Giacomelli and Wyczalkowski (AIChE Annual Meeting, 2013) presented a definition of the minimum Froude number (FrMIN), when a stable vortex is drawn down to the level of the impeller, and a produced a correlation relating this Froude number to the ratios of the impeller submergence below the unagitated surface (S) and the impeller diameter (D) to the vessel diameter (T):
FrMIN = α (S/T)β (D/T)γ
The constants α, β and γ were determined experimentally.
Mass transfer coefficients (kLa) have been measured in agitated vessels operating with Fr ≥ FrMIN. On scale-up at equal Fr, kLa increases and the reason for this is that, at equal Fr, the power input by the agitator per mass of fluid increases with scale. This generates smaller bubbles and higher interfacial area for mass transfer.