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

Abstract

Abstract: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.

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

“…A good review of which is presented by Gourdon et al, [21]. Recently, much work has been done using the population balance modeling in extraction columns [4][5][6][21][22][23][24][25].…”

“…This source term is described in detail by Attarakih et al, [6] and is summarized below for the purpose of clear presentation of the population balance model in LLECMOD. The inflow of disperse phase is considered as a point source term at the level d z using the Dirac delta function !…”

“…Whereas the source term for brekage S B and for coalescence S F are given in details by Attarakih et al, [6].…”

“…To solve the PBE in the simulation program LLECMOD [5,6], the fixed-pivot technique [34] is extended to take into account solute transfer and external coordinate (column height) [5,6]. In this way, the bivariate PBE with respect to droplet size and concentration is decoupled into two population balances: One takes into account the droplet hydrodynamics and the other one takes into account solute transfer.…”

“…The main objective of this work is to develop a model that is capable to describe the dynamic and steady state behavior of pulsed packed and sieve tray extraction columns. The models of both columns are integrated into the existing program: LLECMOD [5,6], which can also simulate agitated extraction columns (RDC and Kühni). LLECMOD simulates steady state and dynamic behavior and takes into account the effect of dispersed phase inlet (light or heavy phase is dispersed) and the direction of mass transfer (from continuous to dispersed phase and vice versa) [7].…”