Correction of the penetration theory based on mass-transfer data from bubble columns operated in the homogeneous regime under high pressure

A new correction term was developed which allows the classical penetration theory to be applied successfully to kLakLa data obtained from oblate ellipsoidal bubbles formed in bubble columns operated in the homogeneous regime at various pressures (0.1–4.0MPa). The correction factor is a function of both the Eötvös number Eo   and dimensionless gas density ratio. The new correlation was compared with literature kLakLa data in 18 pure organic liquids, 14 adjusted liquid mixtures and tap water. In some of the liquids (tetralin, xylene and ethanol) not only air but also other gases (nitrogen, helium and hydrogen) were used. In total, 263 experimental kLakLa points are fitted with an average relative error of 10.4%.In the theoretical approach for the kLakLa prediction, the gas–liquid contact time (used in the penetration theory) is defined as the ratio of bubble surface to the rate of surface formation. All further calculations are based on the geometrical characteristics (bubble length and height) of an oblate ellipsoidal bubble. It was found that the new correction factor fcfc gradually reduces with the increase of both superficial gas velocity uGuG and gas density ρGρG (operating pressure PP).