New Approach for Gas Holdup Prediction in Bubble Columns Operated Under Imperfect Homogeneous Conditions

In bubble column (BC) reactors, the reliable predictions of mean bubble diameter and gas holdup are very important for the estimation of the mass transfer efficiency. Most of the correlations for prediction of the gas holdup are empirical without any theoretical considerations. In the present work, the semi-theoretical gas holdup model of Nedeltchev and Schumpe (2008) has been applied to experimental gas holdups measured by monitoring the aerated bed height under imperfect homogeneous conditions in two different BCs (0.14 and 0.46 m in ID) operated with an air-distilled water system at different clear liquid heights (0.4 m, 0.65 m, 1.33 m, 1.41 m, 1.82 m, etc.). The smaller column has been equipped with a perforated plate (PP) gas distributor (121 holes x Ø 1.32 mm) corresponding to an open area (OA) of 1.08 %. The bigger column has also been equipped with a PP gas sparger having much more holes (241) and bigger hole diameter (Ø 3.0 mm). In such a way, practically the same OA (1.04 %) has been achieved.

The model of Nedeltchev and Schumpe (2008) takes into account the geometrical characteristics of the oblate ellipsoidal bubbles and the available two definitions of the gas-liquid interfacial area in the homogeneous regime. Based on the estimation of the Sauter-mean bubble diameter (Wilkinson et al., 1994) and the subsequent calculation of the Tadaki number, it has been determined that the formed bubbles in the imperfect homogeneous regime have oblate ellipsoidal shape. Since one of the definitions of the gas-liquid interfacial area is strictly valid for rigid spherical bubbles, a correction factor is needed. It has been found that the one proposed by Nedeltchev and Schumpe (2008) is valid only for classical homogeneous conditions. Since the above-mentioned gas distributors generate gas maldistribution (Nedeltchev, 2020) at low superficial gas velocities U_g and then follows the imperfect homogeneous regime, a new correction factor f_c is needed. The new f_c definition is a simple function of the Eötvös number Eo under ambient conditions: f_c=0.348Eo^0.83. As U_g increases, the f_c values decrease. The correction factors vary between 0.836 and 0.868.

Fig. 1 shows that the experimental gas holdups in the bigger column (0.46 m in ID) can be predicted reasonably well. The average relative error (ARE) is 4.67 %. Such successful predictions in large BCs are important for the industrial applications. The model and the new correction factor are applicable up to superficial gas velocity U_g of 0.05 m/s. This critical velocity corresponds to the upper boundary of the homogeneous regime (i.e. the onset of the transition flow regime), which has been identified by a new parameter called degree of randomness (Nedeltchev et al., 2020).

References

Nedeltchev S., Schumpe, A., “A New Approach for the Prediction of Gas Holdup in Bubble Columns Operated Under Various Pressures in the Homogeneous Regime”, J. Chem. Eng. Japan 41, 744-755 (2008)

Nedeltchev, S., "Precise identification of the end of the gas maldistribution in bubble columns equipped with perforated plate gas distributors", Chem. Eng. J., 121535, in press (2020). https://doi.org/10.1016/j.cej.2019.04.115

Nedeltchev, S., Top, Y., Hlawitschka, M., Schubert, M., Bart, H.-J., "Identification of the regime boundaries in bubble columns based on the degree of randomness in the signals", The Can. J. Chem. Eng., in press (2020). DOI: 10.1002/cjce.23719

Wilkinson, P. M., Haringa, H., Van Dierendonck, L. L., “Mass Transfer and Bubble Size in a Bubble Column under Pressure”, Chem. Eng. Sci. 49, 1417-1427 (1994)