Modeling and Transport Analysis of Silver Extraction in Porous Membrane Extractors by Computational Methods

Abstract

A comprehensive two-dimensional mathematical model was developed for the transport of \( {\text{Ag(CN)}}_{ 2}^{ - } \) ions through porous membrane extractors. Extraction of \( {\text{Ag(CN)}}_{ 2}^{ - } \) with n-heptane solution of N,N-bis(2-ethyl hexyl) guanidine as extractant (LIX79) was investigated theoretically. Simulations were done using computational fluid dynamics of momentum and mass transfer in all subdomains of a hollow-fiber membrane extractor by COMSOL Multiphysics software. The latter uses finite element method for numerical simulations. Parabolic velocity profile was used for the aqueous feed in the tube side and the solvent flow in the shell side that was characterized by Happel’s equation. The distribution of concentration was obtained for the solute in the membrane module. Simulation results indicated that increasing feed flow rate reduces the extraction efficiency of silver from aqueous phase to organic phase. Dimensionless concentration distribution (C/C0) of silver ions in the tube side of membrane extractor in axial and radial direction shows that it moves to the membrane due to the concentration difference, and then it is swept by the moving extractants in the shell.