Dynamic modelling of Kühni liquid extraction columns using the sectional quadrature method of moments (SQMOM)

In this work, the Sectional Quadrature Method Of Moments (SQMOM) is extended to a one-dimensional physical spatial domain and resolved using the finite volume method. To close the mathematical model, the required quadrature nodes and weights are calculated using the analytical solution based on the Two Unequal Weights Quadrature (TUEWQ) formula derived by Attarakih et al. (Attarakih, M., Drumm, C., & Bart, H.-J., (2009), Solution of the population balance equation using the Sectional Quadrature Method of Moments (SQMOM). Chemical Engineering Science, 64, 742-752). By applying the finite volume method to the spatial domain, we end up with a semi-discreet ordinary differential equation system which is solved using the MATLAB standard ODE solvers (ode45). As a case study, the SQMOM is used to investigate the dynamic behavior of a Kühni DN150 liquid-liquid extraction column. As an independent validation step, the SQMOM prediction is compared with the PPBLab software which utilizes the extended fixed pivot technique as a built-in population balance model solver. Furthermore, the SQMOM is validated using the available dynamic experimental data from a Kühni liquid extraction column using water-acetone-toluene chemical test system. The dynamic analyses of the Kühni column show very interesting features concerning the coupled column hydrodynamics and mass transfer and the droplet breakage and coalescence as well.