Hollow fiber membrane contactors (HFMCs) have been found as a novel technique for separation science for the last few decades. It is due to their dispersion free contact, higher mass transfer interfacial area and compactness of the unit that overcome the drawbacks of conventional extractors. HFMCs allow two phases to come into a direct contact without dispersion of one phase into another inside pores of membrane [1]. Numerical modeling and simulation of mass transport analysis of HFMCs has been remained a focus of interest for several researchers in recent years.

In the present study a 2-Dimensional axial-radial numerical model was developed to study the transport of copper (II) solute through a single hypothesised “flow-cell”, adapted from the previous study for the baffle less HFMC contactor module for liquid-liquid extraction [2]. The flow-cell consists of three sections i-e tube side, inside membrane and shell side. Aqueous feed that contains the solute flows in tube side while organic solvent flows in shell.

The aim of this work is to study the distribution of copper(II) in three sections of flow-cell through mathematical modelling and computational fluid dynamics (CFD) simulation. The solute transfer in shell side i-e “flow-cell” side and inside fiber occurs through diffusion and convection and is described by steady-state continuity equation. The transfer of solute through the hydrophobic membrane occurs through diffusion only. Similarly the velocity distribution inside fiber and shell is studied using Navier-Stokes equation [3].

The model equations with associated boundary equations are solved with CFD techniques. For this purpose COMSOL Multiphysics^TM software is used. COMSOL Multiphysics employs finite element method (FEM) for numerical solution of model equations. The finite element analysis is combined with adaptive meshing and error control using numerical solver of UMFPACK. A scale factor of 200 was applied in axial direction due to large difference between length and radius of module. Scaling the problem avoids excessive amounts of element and nodes and thus minimizes the cost of simulation.

It has been found from concentration profile simulations that as aqueous feed moves along membrane its concentration decreases while concentration of organic phase increases along its pathway because of continuous transfer of copper (II) solute from aqueous to organic phase. The effects of feed and organic flow rates were also investigated. It was found that decreasing feed flow rate increases solute removal efficiency while the organic flow rate has an opposite effect.

Keywords:  Mathematical modeling, Copper extraction, Hollow fiber membrane contactor, Computational fluid dynamics.

REFERENCES

[1]        A. Gabelman, S.T. Hwang, Hollow Fiber Membrane Contactors. J. Membr. Sci. 159 (1999) pp. 61-106

[2]   M. Younas, S.D. Bocquet, J. Sanchez, Kinetic and Dynamic Study of Liquid-Liquid Extraction of Copper in a HFMC: Experimentation, Modeling, and Simulation. AIChE J, 56 (2010), pp. 1469–1480.

[3] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, John Wiley & Sons, 1960.