Simulation of zinc extraction from aqueous solutions using polymeric hollow-fibers.
Zinc is a heavy metal that almost exists in the effluents discharged from wastewater of petrochemical and chemical industries. This metal has adverse impacts on clean environment. For this reason, separation and recovery of zinc from effluents is essential before discharging to the receiving waters [1, 2]. Nowadays, development of novel separation processes for successful removal and recovery of metallic elements has been of great interest. For this purposes, recently a membrane-based extraction system using a hollow-fiber membrane contactor has been investigated by several researchers. In this kind of contactor, both organic and aqueous phase solutions flow continuously, the First one through a tube of fibers and another one through the shell side of contactor. Both phases make contact through pores of the membrane wall [3-5],
In solvent extraction process, membrane contactors offer some superior characteristics compared to other traditional technologies. Among membrane contactors, hollow-fiber membrane contactors (HFMCs) offer excellent extraction efficiency for metal recovery, low risk of electrolyte contamination, and other numbers of benefits such as the fixed available surface area. The latter is due to independency of two phases in membrane contactors. Unlike conventional contactors used in extraction processes, in membrane contactors no density difference of phases is required between fluids. Furthermore, in HFMCs interfacial area is known and constant, which allows performance to be prognosticated more effortless than traditional dispersed phase equipment [6, 7].
In the context of membrane separation processes, the simulation methods may use different models based on various equations. Many research studies have dealt with models incorporate detailed resistance models such as pore-blocking resistance or cake resistance. Resistance-in-series models consider variety of mass transfer resistance for transport of metal from aqueous to organic phase. In this approach, mass transfer coefficients are determined experimentally by correlations which are not very accurate [8-11]. Recently, computational fluid dynamics (CFD) has been largely used as a powerful tool to model membrane separation processes. It provides a favorable approach to optimize the operational parameters [12-23]. Ghidossi et al.  overviewed novel CFD methods applied on simulation of membrane processes. They showed two approaches were particularly investigated: hydrodynamics and mass transfer. The authors considered the momentum and mass transfers only in the lumen side of membrane contactors. For practical purposes, all subdomains of HFMCs including lumen, fiber, and shell sides should be considered in the calculations.
The main goal of this study is to describe modeling and simulation of zinc removal in membrane extractors. Momentum and mass transfer is considered in the three compartments of a membrane extractor for laminar flow conditions. The main aim of the simulation is to calculate the concentration profiles of zinc in the extractor. The influence of various process parameters such as velocity of aqueous and organic phases on the mass transfer is evaluated. The numerical results are discussed in terms of extraction of zinc from lumen side of membrane extractor.
Chemistry of Process
Zinc is present in the aqueous solution mostly as divalent cations, i.e., [Zn.sup.2+] The extraction mechanism of Zinc with D2EHPA as extractant can be described in Eq. 1 :
[Zn.sup.2+] + 1.5[[bar.(HR)].sub.2] [??] [bar.Zn[R.sub.2](HR) + 2[H.sup.+]; [K.sub.ex,Zn] (1)
where the overbar refers to the solvent phase and [(HR).sub.2] represents the dimeric form of D2EHPA.
The equilibrium constant [K.sub.ex] of the reaction is expressed as :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
[K.sub.ex,Zn] = m[[[H.sup.+]].sup.2]/[[[[bar.(HR)].sub.2]].sup.1.5] (3)
where m is distribution coefficient and is expressed as [bar.[Zn[R.sub.2](HR)]/[[Zn.sup.2+]]
According to the kinetics of solvent extraction of [Zn.sup.2+] with carrier, it is accepted that formation and dissociation of the Zn-extractant complexes is remarkably fast compared to diffusion in the aqueous and solvent phases. Therefore, the contribution of resistance because of interfacial reaction is negligible.
Mass and Momentum Transfer Model
A comprehensive two-dimensional mathematical model was developed for zinc transport through an extractive membrane contactor in a wastewater aqueous solution. In the extractor, aqueous solution containing [Zn.sup.2+] cations passes in the tube side of hollow fiber extractor and after reaction of complex formation at the aqueous-organic interface on inner surface of membrane wall diffuse through membrane pores filled with organic phase. Furthermore, the complex is transferred through the boundary layer of organic phase in the shell side of membrane extractor and the separation is completed. This membrane configuration provides a high extraction rate, while separation and recovery of zinc from the wastewater is treated. Figure 1 shows the schematic view of the extraction process. An unsteady two dimensional mass and momentum balance was carried out for the model domain. The model is constructed based on the following assumptions:
1. The isothermal condition of extraction process.
2. The Newtonian fluid with constant transport coefficients and physical properties.
3. The laminar flow regime in the tube and shell sides of extractor.
4. No resistances of concentration polarization layer.
5. Reaction is limited at the aqueous-organic interface.
6. Aqueous and organic phases are completely immiscible.
Continuity equation is the basic equation that explains the solute transfer from feed solution to organic phase. This equation is derived from mass balance over [Zn.sup.2+]. The differential form of continuity equation for zinc can be expressed as follows :
[([nabla]. [C.sub.i]V) + ([nabla].[J.sub.i])] = 0 (4)
where [C.sub.i] the concentration of zinc (mol/[m.sup.3]), V the velocity vector (m/s), and [J.sub.i] the diffusive flux of any species (mol/[m.sup.2] s). The velocity vector can be determined analytically or with coupling a momentum balance to the equation for modeling and simulation system. The terms within the brackets describe convective flux and transport by diffusion, respectively :
[J.sub.i] = [-D.sub.i] [nabla] [C.sub.i] (5)
[N.sub.i] = [D.sub.i] [nabla] [C.sub.i] + [C.sub.i]V (6)
where [N.sub.i] is the mass flux vector mol/[m.sup.2] x s. The diffusion coefficient of zinc ions in the solvent is obtained by using interaction between the zinc and the carrier. It should be pointed out that the convection term in the mass transfer equations in radial direction is neglected because the velocity is in axial direction.
Equation 4 is the basic equation of mass transfer. To compute the continuity equation, velocity distribution is necessary. Velocity distribution is calculated by computing the momentum equation, i.e., Navier-Stokes equations. So, the momentum and continuity equation should be coupled and computed simultaneously to describe the concentration distribution of metal ions in the extractor. The Navier-Stokes equations are defined by Eq. 7. The momentum balances and continuity equation form a nonlinear system of equations with three and four coupled equations in 2D and JD, respectively :
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
where [eta] denotes the dynamic viscosity (kg/m s), V the velocity vector (m/s), [rho] the density of the fluid (kg/[m.sup.3]), p the pressure (Pa), and f is external force term (N). The latter is eliminated because there is no external force acting on the fluid. Boundary conditions are used in the equations are listed in Table 1. m is partition coefficient of Zinc between aqueous phase and organic phase.
Mass Balance Over Ammonia Tank
An equation is also necessary to predict the concentration of zinc in feed tank. This equation is obtained for the zinc tank using a mass balance. The mass balance equation over feed tank considering uniform mixing can be written as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
where Q is volumetric flow rate ([m.sup.3]/s) v is volume of feed ([m.sup.3]), t is time (s), and C is zinc concentration (mol/ [m.sup.3]). [C|.sub.Z=L] is concentration of zinc at the outlet of contactor which is inlet of the feed tank. It should be pointed out that the characteristic of inlet flow varies with time; therefore unsteady state equation of continuity for zinc in the contactor should be solved to obtain this parameter.
Numerical Solution of Model Equations
System specifications and physical conditions for [Zn.sup.2+] removal by the hollow-fiber membrane contactor were needed to solve the developing equations with the given boundary conditions. These specifications are listed in Table 2. The numerical solutions for the developed equations were acquired using the COMSOL Multiphysics software. The direct solver UMFPACK was employed because it is preferable for ID and 2D models. It employs the COLAMD and AMD approximate minimum degree preordering algorithms to permute the columns so that the fill-in is minimized. A system with the specifications of Intel[R] Core[TM] i5CPU M 460 @ 2.53 GHz and 4 GB Ram was used to solve the processes. Volume scale factor generated by COMSOL software are also indicated in Fig. 2. To avoid excessive amounts of elements and nodes, scaling factor of 100 was employed in z direction where COMSOL automatically scaled back the geometry after meshing. A variation of volume scale factor between 4.4e-10 and 6.5e-11 has been considered in the simulations.
RESULTS AND DISCUSSION
Validation of Model
Figure 3 shows the comparisons between simulated and experimental values. For this purpose, the unsteady state profile of concentration for [Zn.sup.2+] ions in the hollow-fiber membrane contactor is investigated. As it can be observed, simulation predictions are in great agreement with the experimental data during the extraction process . Figure 3 also reveals that at the beginning of the extraction process, the concentration changes are considerable due to higher concentration gradient at the beginning of the extraction process.
The concentration in the organic phase is plotted as a function of time and is demonstrated in Fig. 4. As it can be seen, the dynamic behavior of unsteady state concentration revealed an initial sharp increase followed by a very small change in the concentration of zinc.
Influence of Feed Flow Rate on Concentration Distribution in the Tube Side of Extractor
The [Zn.sup.2+] concentration distribution along the length of the module for different values of aqueous phase flow rates is demonstrated in Fig. 5. It refers to the effect of convection term on separation efficiency. As expected, the decrease in the aqueous phase flow rate increases the residence time of fluid in the module, which in turn increases the removal rate of metal ions. Furthermore, according to the figure the flow pattern in the contactor (extractor) is parallel and counter-current. The feed phase including the aqueous solution of [Zn.sup.2+] flows from one side of the contactor (z = 0) where the concentration of zinc is the highest value. Consequently, as the feed flows through the tube side, zinc moves towards the membrane due to the concentration difference.
Pressure Distribution in the Shell Side of Membrane Contactor
The pressure distribution of fluid in the shell side of hollow-fiber membrane contactor is illustrated in Fig. 6. Pressure drop in membrane contactors has to be monitored to maintain the appropriate phase pressure difference everywhere along the module and thus to prevent dispersion of both phases. As it can be seen from figure, the pressure drop in the shell side is not significant. Therefore, this is a one of key advantage of membrane extractors.
Influence of Feed Flow Rate on the Concentration at Outlet of Shell and Tube Side
Figure 7 shows the effect of aqueous phase flow rate on the concentration at outlet of shell and tube side of extractor. As it can be seen, increasing feed flow rates increases the concentration of zinc at the outlet of tube side of contactor. With increasing feed flow rate, residence time of feed in the contactor reduces and therefore mass transfer of the zinc from feed phase to organic phase decreases as well. In the other hands, in spite of decreasing extraction efficiency the concentration of zinc at the outlet of shell side also increases due to increasing solute flow rate at the inlet of tube side.
Influence of Organic Phase Flow Rate on the Concentration at Outlet of Shell and Tube Side
The effect of organic phase flow rate on the [Zn.sup.2+] concentration at the outlet of tube and shell side is presented in Fig. 8. It can be seen that it does not have a significant effect on the outlet concentration in the tube side of contactor and can be neglected. This is due to high partition coefficient of the zinc between feed and extractant phases which reduces mass transfer resistance in the organic phase. The concentration of zinc decreases at the shell side of extractor by enhancement of organic velocity.
A comprehensive mathematical model has been developed for estimating the influence of operating parameters on zinc ([Zn.sup.2+]) extraction in hollow-fiber membrane contactors. The predicted zinc concentration via time was validated with the experimental data from the literature. The simulation results agreed with the experimental data well. A parameter sensitivity analysis has been carried out and the results showed with increasing aqueous flow rate increases the concentration of solute at outlet of shell and tube side of hollow-fiber membrane extractor. The results also showed that the pressure drop in the shell side of membrane contactor is not significant. Consequently this is one of benefit of membrane extractors.
NOMENCLATURE C Concentration, mol/[m.sup.3] [C.sub.outlet] Outlet concentration of solute in the tube side, mol/[m.sup.3] [C.sub.intlet] Inlet concentration of solute in the tube side, mol/[m.sup.3] [C.sub.i-tube] Concentration of solute in the tube side, mol/[m.sup.3] [C.sub.i-shell] Concentration of solute in the shell side, mol/[m.sup.3] [C.sub.i-membrane] Concentration of solute in the membrane, mol/[m.sup.3] D Diffusion coefficient, [m.sup.2]/s [D.sub.i_shell] Diffusion coefficient of solute in the shell, [m.sup.2]/s [D.su.i-tube] Diffusion coefficient of solute in the tube, [m.sup.2]/s [D.sub.i-membrane] Diffusion coefficient of solute in the membrane, [m.sup.2]/s [J.sub.i] Diffusive flux of species i, mol/[m.sup.2]s L Length of the fiber, m m Distribution coefficient, dimensionless P Pressure, Pa Q Volumetric flow rate, [m.sup.3]/s r Radial coordinate, m [R.sub.1] Inner tube radius, m [R.sub.2] Outer tube radius, m [R.sub.3] Inner shell radius, m [R.sub.i] Overall reaction rate of any species, mol/ [m.sup.3].s T Temperature, K u Average velocity, m/s v Tank volume, [m.sup.3] V Velocity in the module, m/s [V.sub.z-shell] z-Velocity in the shell, m/s z Axial coordinate, m f Body force, N Zn Zinc Greek Symbols [epsilon] Membrane porosity [tau] Tortuosity factor Abbreviations CFD Computational fluid dynamics FEM Finite element method D2EHPA Di(2-ethylhexyl) phosphoric acid HFMCs Hollow-fiber membrane contactors
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Mehdi Ghadiri, Mehdi Parvini, Mahdiyar Ghasemi Darehnaei
School of Chemical, Gas and Petroleum Engineering, University of Semnan, Semnan 35196-45399, Iran
Correspondence to: M. Parvini; e-mail: firstname.lastname@example.org
Published online in Wiley Online Library (wileyonlinelibrary.com).
TABLE 1. Boundary conditions. Position Shell Membrane z = 0 (inlet) Mass: Convective flux Momentum: Mass: Insulated p = [p.sub.atm] z = L (outlet) Mass: [C.sub.I] = 0 Mass: Insulated Momentum: V = [V.sub.inlet] r = [R.sub.1] -- Mass: [C.sub.2] = [C.sub.1] x m r = [R.sub.2] Mass: [C.sub.3] = [C.sub.2] Mass: [C.sub.2] = [C.sub.3] Momentum: wall (no slip) r = [R.sub.3] Mass: [partial derivative]/ -- [partial derivative] = 0(symmetry) Position Lumen z = 0 (inlet) Mass: [C.sub.i] = [C.sub.0] z = L (outlet) Mass: Convective flux r = [R.sub.1] Mass: [C.sub.1] = [C.sub.2]/m r = [R.sub.2] -- r = [R.sub.3] -- TABLE 2. Characteristics of the hollow-fiber module used for the simulation (26). Hoechst Celanese Liqui-Cel extra-flow 2.5 x 8 membrane Description contactor model 5PCG-261 Shell characteristics Material Polypropylene Length (mm) 203 Inner diameter, 2[R.sub.3](mm) 63 Outer diameter, R (mm) 77 Fiber characteristics Material Celgard X-20 240 polypropylene hollow fiber Number of fibers, N 10,200 Effective length, L (mm) 198 Inner diameter, 2[R.sub.1] ([micro]m) 240 Outer diameter, 2[R.sub.2] ([micro]m) 300 Effective surface area, A ([m.sup.2]) 1.4 Effective area/volume ([cm.sup.2]/ [cm.sup.3]) 29.3 Avarage pore size, [r.sub.p] (nm) 15 Membrane porosity, [epsilon] 0.4 Membrane tortousity, [tau] 2.6
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|Author:||Ghadiri, Mehdi; Parvini, Mehdi; Darehnaei, Mahdiyar Ghasemi|
|Publication:||Polymer Engineering and Science|
|Date:||Oct 1, 2014|
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