Physical explanation of the empirical coefficients of gas–liquid mass transfer equations

Equipment design and scale up is one of the biggest problems that chemical engineers face. A lot of research has been done at laboratory and pilot plant scale. However, experimental data are, many times, useless in equipment scale up because they overlook the processes involving bubbles. Therefore, a new approach considering the hydrodynamics of the bubbles is proposed to explain and understand the mass transfer rates. Semi-theoretical equations have been developed for bubble columns and stirred tanks based on hydrodynamic considerations of the flow, the bubbles and dispersions in the tank. These equations are able to explain the physical meaning, identify the effect of the scale on mass transfer rates and even predict the coefficients of the empirical correlations for kLa based on the hydrodynamic processes that bubbles experience. It can be concluded that the proportional constant of the correlations for kLa depends on the bubble size, on the physical and transport properties and on the size of the tank because it affects the mixing. Meanwhile, the exponents related to the power input and the superficial gas velocity depend on bubble break up and coalescence, and the dispersions generated. In the case of stirred tanks, the physical effect of the impeller on the bubbles also plays an important role on the exponents.