(107f) Investigation of Mass Transfer in Poly-Disperse Gas-Liquid Systems by Using a Multi-Variate Population Balance and CFD

The simulation of momentum and mass transfer together with chemical reactions is complicated by the fact that the gas phase is poly-dispersed, namely it is constituted by bubbles characterized by a distribution of velocity, size and composition values. Phase coupling can be successfully described only if the modeling approach acknowledges the existence of this distribution, whose evolution in space and time is governed by a multi-variate population balance equation. A very efficient is represented by quadrature-based moment methods, where the evolution of the relevant properties is decoupled by tracking pure moments only and where the so-called closure problem is overcome by employing a quadrature approximation. When for example a quadrature approximation with two nodes is used the bubbles are represented by two distinct bubble classes, each characterized by its own velocity, size and composition. This procedure allows to accommodate four moments of the distribution with respect to bubble size (mean, variance and skewness) and two moments with respect to bubble velocity and composition (mean and variance). Another interesting advantage is that the final equations can be easily implemented in commercial Computational Fluid Dynamics codes. The method is here applied to the simulation of a system investigated by other authors for which experimental data are available in the literature for model validation. In these works mass-transfer was studied in conjunction with bubble coalescence and breakup. As it possible to see in the figure, reporting the contour plot of characteristic size of bubble classes 1 and 2 and mean Sauter diameter (m), bubbles enter the reactor with a mean size of about 3 mm completely determined by the gas sparger and then due to coalescence and breakage the bubble size distribution completely changes, deeply affecting phase coupling. Simple mass transfer experiments are here used for model validation: the reactor is fluxed with nitrogen and then after switching to oxygen the time evolution of species concentration in the liquid and gas phase is tracked. Model predictions and comparison with experimental data show that in order to properly describe the global mass transfer rate it is essential to represent the poly-dispersity of the gas phase, proving the validity of the approach.