The DuQMoGeM application to the numerical modeling of liquid-liquid columns

Abstract

• A multi-compartment population balance model was developed for an extraction column. • Test problems with known analytical solutions were solved by the DuQMoGeM. • Accurate regular moments and good distributions’ approximations were obtained. • A pilot plant Kühni column was modeled using the multi-compartment model. • DuQMoGeM results agree well with the experimental data for the Kühni column. This work extended the dual quadrature method of generalized moments (DuQMoGeM) to solve the population balance model for the hydrodynamics of liquid-liquid extraction columns using a multi-compartment model that represents batch and continuous well-mixed extraction vessels as particular cases. This model can either represent the actual sections of a column or its spatial discretization that can use moment preserving schemes for the advection and dispersion of the generalized moment set. The DuQMoGeM results were compared to analytical solutions for batch and continuous well-mixed vessels and extraction columns, showing that it is accurate for predicting the evolution of the low order moments and the drop number distribution along with the column height. We also modeled a Kühni column for which the simulation accurately predicted the steady-state experimental holdup, encouraging the DuQMoGeM usage to solve the population balance equation for heterogeneous systems and different columns.