Moutasem Jaradat

A CFD-Population Balance Model for the Simulation of Kühni Extraction Column

Abstract In this work, computational fluid dynamics (CFD) calculations coupled with DPBM are compared to LLECMOD (Liquid-Liquid Extraction Column MODule) simulations and to Laser Induced Fluorescence (LIF) measurement of the phase fraction using an iso-optical system of calcium chloride/water and butyl acetate. The results show a good agreement between the simulations and experimental data. The CFD requires a high computational load compared to LLECMOD, but gives local information about the droplet size and the phase fraction and is independent from geometrical constraints.

RDC extraction column simulation using the multi-primary one secondary particle method: Coupled hydrodynamics and mass transfer

Abstract Based on the multivariate population balance equation (PBE) and the primary secondary particle concept a mathematical model is developed for liquid extraction columns. It is extended to include the momentum balance for the dispersed phase. The resulting model is complicated by the integral source term of the PBE. To reduce this complexity, while maintaining most of the information from the continuous PBE, the concept of the primary secondary particle method is used. The effect of the number of primary particles (PP) on the final predicted solution is investigated. Numerical results show that the solution converge fast as the number of PP is increased. The terminal droplet velocity is found to be the most sensitive model parameter to the number of PP. The predicted steady state profiles (droplet diameter, holdup and the concentration profiles) along a pilot RDC extraction column are compared to the experimental data where good agreement is achieved.

Integral Formulation of the Population Balance Equation using the Cumulative QMOM

Abstract The integral formulation of the population balance equation using the CQMOM presents a novel and hierarchical method to couple the QMOM and the physically evolving particle size distribution. Here, not only is the cumulative number density function reconstructed, but also its low-order moments. The numerical analysis of the method shows two desirable properties: First, it can be considered as a free-mesh method, since the solution of each integral equation at the current grid point does not depend on the other ones. Second, the accuracy of the targeted low-order cumulative moments depend only on the nodes and weights of the cumulative Gauss-Christoffel quadrature, but not on sampling the continuous low-order cumulative moments. So, the CQMOM is a general integral formulation of the population balance equation and is an effective numerical scheme in which the QMOM is imbedded as a limiting case.

Detailed Mathematical Modelling of Liquid-Liquid Extraction Columns

Abstract A comprehensive bivariate population balance model for the dynamic and steady state simulation of extraction columns is developed. The model is programmed using visual digital FORTRAN and then integrated into the whole LLECMOD program [ 23 ]. As a case study, the simulation tool LLECMOD is used to simulate the steady state performance of pulsed packed and sieve plate columns. Two chemical test systems recommended by the EFCE are used in the simulation. Model predictions are successfully validated against steady state and dynamic experimental data, where good agreements are achieved.

Dynamic modelling and simulation of Kühni extraction columns

Abstract A robust rigorous mathematical model based on the population balance equation (PBE) is developed to predict the dynamic behaviour in Kuhni extraction columns; the developed model is extended to include the momentum balance equation to calculate the drop velocity. The effects of step changes in the important input variables (flow rates and rotational speed ( rpm )) on the transient holdup are investigated. The transient analysis reveals the fact that the response of the dispersed phase holdup is very fast due to the relative fast motion of the dispersed drops with respect to the continuous phase. The dynamic behaviour of the dispersed phase shows a lag time that increases away from the feed point. The predicted holdup dynamic profiles along the column height are compared to the experimental one where good agreement is achieved.