Abstract
A model is developed for prediction and interpretation of the observed steady-state axial dissolved oxygen concentration profiles in tall bubble columns. The observed concentration profiles are non-linear, unlike what would be expected if the hydrostatic pressure alone influenced the profiles. The non-linear profiles result from the axial mixing of liquid in the column. Several other factors influence the profiles, including the overall gas holdup, the volumetric overall gas–liquid mass transfer coefficient, and the static height of liquid in the column. The effect of mixing can be adequately accounted for using an axial dispersion coefficient. Because the axial dispersion coefficient is sensitive to the diameter of the column and to gas flow rate, the overall behavior of the profile is affected by the aspect ratio of the column and the superficial gas velocity in it. The mass transfer coefficient and the axial dispersion coefficient have mutually opposing effects on the shape of the profile. Because both those variables increase with increasing gas flow rate, the shape of the profile is affected less than would be the case if only mixing influenced the profile. The non-linearity of concentration profiles increases with increasing overall height of the column especially when the height exceeds about 2 m in a 0.24 m diameter column. The model-predicted axial concentration profiles agree closely – within ±3% – with the measured data. Using the measured profile, the model allows for calculation of the liquid-phase axial dispersion coefficients. This method does not require the use of tracers. Being a steady-state method, the operation of the bioreactor does not need to the interrupted in any way for the determination of the axial dispersion coefficient or the state of mixing. Consequently, the proposed method is particularly suited to characterizing the axial dispersion coefficient in an operating bioreactor without disturbing the operation. If the axial dispersion coefficient is known, the model allows for quantifying the spatial inhomogeneities in oxygen concentration in a bioreactor vessel.
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