LLECMOD: A Bivariate Population Balance Simulation Tool for Liquid- Liquid Extraction Columns

Menwer M. Attarakiha, c, Hans-Jörg Bart*, a, Tilmann Steinmetza, Markus Dietzena, Naim M. Faqirb
a University of Kaiserslautern, Faculty of Mechanical & Process Engineering, Thermische Verfahrenstechnik, P.O.B. 3049, 67653 Kaiserslautern, Germany
b University of Jordan, Faculty of Engineering & Technology, Chemical Engineering. Department, 11942 Amman, Jordan
c Al-Balqa´ Applied University, Faculty of Engineering & Technology, Chemical Engineering Department, P.O.B. 15008, 1134-Amman, Jordan

© 2008 Attarakih et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the University of Kaiserslautern, Faculty of Mechanical & Process Engineering, Thermische Verfahrenstechnik , P.O.B. 3049, 67653 Kaiserslautern, Germany; E-mail:


The population balance equation finds many applications in modelling poly-dispersed systems arising in many engineering applications such as aerosols dynamics, crystallization, precipitation, granulation, liquid-liquid, gas-liquid, combustion processes and microbial systems. The population balance lays down a modern approach for modelling the complex discrete behaviour of such systems. Due to the industrial importance of liquid-liquid extraction columns for the separation of many chemicals that are not amenable for separation by distillation, a Windows based program called LLECMOD is developed. Due to the multivariate nature of the population of droplets in liquid –liquid extraction columns (with respect to size and solute concentration), a spatially distributed population balance equation is developed. The basis of LLECMOD depends on modern numerical algorithms that couples the computational fluid dynamics and population balances. To avoid the solution of the momentum balance equations (for the continuous and discrete phases), experimental correlations are used for the estimation of the turbulent energy dissipation and the slip velocities of the moving droplets along with interaction frequencies of breakage and coalescence. The design of LLECMOD is flexible in such a way that allows the user to define droplet terminal velocity, energy dissipation, axial dispersion, breakage and coalescence frequencies and the other internal geometrical details of the column. The user input dialog makes the LLECMOD a user-friendly program that enables the user to select the simulation parameters and functions easily. The program is reinforced by a parameter estimation package for the droplet coalescence models. The scale-up and simulation of agitated extraction columns based on the populations balanced model leads to the main application of the simulation tool.