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.
https://www.researchgate.net/publication/306520195_Dynamic_Modelling_of_Kuhni_Liquid_Extraction_Columns_using_the_Sectional_Quadrature_Method_Of_Moments_SQMOM