Prediction of bubble size and axial position distribution through hybridization of population balance modelling and dynamic gas disengagement

Abstract

Bubble Column Reactors (BCRs) are suitable for multiphase fluid systems due to their low energy consumption, ease of fabrication and relatively high degree of mixing. When predicting the properties of the bubble population, it was shown in our previous study that the global Bubble Number Density Distribution (BNDD) could be determined through the coupling of Electrical Resistance Tomography (ERT) to the Dynamic Gas Disengagement (DGD) process. However, due to the low spatial resolution associated with the ERT, the local BNDD, bubble coalescence and breakage rates of the fluid dispersion, and the BCR hydrodynamic parameters could not be predicted.In the present paper, these limitations are addressed by hybridizing the steady-state Population Balance Model (PBM) with the DGD results. In the first stage of the hybridization, the PBM having the source terms of bubble coalescence and breakup rates was solved to simulate the bubble evolution process in a BCR of height 1.56m and diameter 0.29m designed with a porous tubular gas distributor. The PBM solution was utilized as an initial condition for a modelling of the unsteady state DGD process as an advection transport of mean bubble sizes under the influence of bubble expansion rates. The unsteady state PBM that models the DGD process was solved by the method of characteristics to obtain an analytical solution of the local transient disengaging gas volume. Accordingly, the inlet mean and standard deviation of bubble sizes parameters, the coalescence and breakage rates, and the local flux gradient parameter during DGD were adjusted to ensure the modelled local static and dynamic gas holdups during DGD process agree with the corresponding experimental measurements.Validation was achieved through comparison of the macro-properties that can be determined from the resolved BNDD. Such properties include the axial distributions of Sauter Mean Bubble Diameter (SMBD), gas holdups, and the volumetric gas-liquid mass transfer rates of the steady-state bubble population swarming. The comparison of predicted hydrodynamic parameters with two literature results yielded R-squares of 0.88 and 0.82, Chi-squares of 0.86 and 1.08 and f-statistics of 35.96 and 27.24 indicating good agreement. It is therefore proposed that hybridization of the PBM and DGD process yielded a high spatial prediction of the Size and Axial Distribution (SAD) of bubble dispersion and the bubble coalescence and breakage rates even though ERT offers a relatively low spatial resolution.