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CFD simulation of an industrial copper electrowinning cell
CFD simulation of an industrial copper electrowinning cell Mahjabin Najminoori, Ali Mohebbi, Babak Ghadami Arabi, Shahram Daneshpajouh PII: DOI: Reference:
S0304-386X(15)00031-6 doi: 10.1016/j.hydromet.2015.02.005 HYDROM 4037
To appear in:
Hydrometallurgy
Received date: Revised date: Accepted date:
10 February 2014 8 February 2015 23 February 2015
Please cite this article as: Najminoori, Mahjabin, Mohebbi, Ali, Arabi, Babak Ghadami, Daneshpajouh, Shahram, CFD simulation of an industrial copper electrowinning cell, Hydrometallurgy (2015), doi: 10.1016/j.hydromet.2015.02.005
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ACCEPTED MANUSCRIPT CFD simulation of an industrial copper electrowinning cell Mahjabin Najminoori a, Ali Mohebbia, , Babak Ghadami Arabib, Shahram Daneshpajouhb Department of Chemical Engineering, Faculty of Engineering, Shahid Bahonar University of
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a
Kerman, Kerman, Iran
Sarcheshmeh Copper Complex, Iran
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b
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Abstract
Copper electrowinning is the process of winning a high purity copper from an
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aqueous pregnant liquor acid electrolyte in the presence of impurities. In this study, a three-dimensional, steady and two-phase (liquid-gas) computational fluid
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dynamics (CFD) simulation was applied, together with experimental field
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measurements, to investigate the performance of an industrial electrowinning cell in the Sarcheshmeh copper complex, Iran. This simulation was based on Eulerian-
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Eulerian method. The continuity and momentum equations with inclusion of buoyancy, drag, turbulent dispersion and concentration-related buoyancy forces were solved by the finite volume method. In order to calculate the velocity distribution in the cell, the k-ω turbulence flow model has been used. To find the concentration distribution of copper, the transport equation of copper ions was solved. There was a good agreement between the simulation results and the experimental measured data of the electrowinning cell. After validation of the model, the effects of electrical current density, volumetric flow rate of feed and the distance between the electrodes were studied on the performance of the cell and copper concentration distribution. The simulation results show that there are two upward flows in the cell, one is near the anode because of oxygen generation and the other is near the cathode due to depletion of copper ions from the electrolyte
Corresponding author: Tel & Fax: +983432118298 E-mail addresses: [email protected] , [email protected] (A. Mohebbi).
ACCEPTED MANUSCRIPT and buoyancy force. In the middle of the cell, the electrolyte recirculation zone causes a downward flow. Increasing electrical current density decreases copper concentration near the cathode and increases gas volume fraction near the anode,
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which is in accordance with Faraday′s Law. With decreasing volumetric flow rate
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and distance between the electrodes, copper mass concentration on the cathode
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decreases.
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Keywords: Copper electrowinning cell; CFD; Simulation; Electrolyte
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1. Introduction
The Sarcheshmeh copper complex is one of the world ′s largest industrial
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complexes. It is the largest producer of copper in Iran. Its geological storage is
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over one billion and two hundred million tonnes of ore with an average grade of 0.7% copper. It is located in Kerman province in the southeast of Iran and is on the
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central Zagros mountain range. It currently processes up to 41,000 t/d. Copper is extracted from its ore by two principal methods; pyrometallurgical and hydrometallurgical. The pyrometallurgical method is used for sulfide ore and the hydrometallurgical method is used for extracting copper from oxide ores. Hydrometallurgical operations extract metals from aqueous solutions containing metal ions. Because of the advantages of this method compared to pyrometallurgy (such as reduced pollution and energy consumption), it has progressed quickly, and now accounts for a significant share of metal production in the world. Although some CFD works for electrorefining cell (Hemmati et al. (2013); Leahy and Schwarz (2010); Leahy and Schwarz (2011)) and hydrometallurgy process (Sadeghi et al. (2011a); Sadeghi et al. (2011b)) have been done, only a limited number of CFD modeling studies of EW have been reported. Ziegler and Evans (1986) collected limited data of the velocity profile in a large system and compared the velocity profiles with a simple fluid dynamics model with some
ACCEPTED MANUSCRIPT success. Filzwieser et al. (1999) primarily investigated the hydrodynamics of fluid flow and obtained experimental data of the velocity profiles in a copper
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electrowinning cell; he analyzed the benefit of the fluid flow onto the mass transport, but did not compare the results of their CFD model with the
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experimental data. Filzwieser et al. (2002) discussed about diffusion boundary
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layer (δN), limiting electrical current density (ilimit) and copper concentration distribution near the cathode as a function of distance from the bottom of the
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cathode. Leahy and Schwarz (2010) used a two-dimensional, steady and two-phase CFD model to study the hydrodynamics of flow in a single plate pair of a copper Leahy and Schwarz (2014) developed a CFD model to
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EW cell. Recently,
simulate bubble-driven hydrodynamics, copper distribution and instabilities along
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electrodes in an electrowinning cell consisting of a single anode–cathode pair.
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Their CFD model predicted a recirculation zone in all cases, due to the oxygen bubbles rising along the anode and dragging electrolyte upwards. They also
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concluded strong eddies arise along the cathode where copper depletion becomes large enough to drive buoyancy instabilities. In this study, a three-dimensional simulation has been applied using CFD to predict performance of a copper electrowinning cell in a real industrial case. This simulation uses CFD modeling to describe the hydrodynamics occurring between the electrodes of a copper EW cell. This work represents for the first time, a threedimensional, steady, two-phase (gas-liquid), CFD model with inclusion of a large number of electrodes instead of one pair of electrodes. Moreover, the CFD results were validated with the experimental data measured in an industrial plant (i.e. Sarcheshmeh copper complex) and the effects of electrical current density, volumetric flow rate of feed and distance between the electrodes on the cell performance were studied.
ACCEPTED MANUSCRIPT 2. Theory
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In the Sarcheshmeh copper winning cells, the cathodes are made of stainless steel 316L and anodes are made of Pb-Sn-Ca alloy. Electrolyte contains a high
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concentration of copper (>30g/L) and sulfuric acid (160-200g/L), along with other
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metals and chemical additives. In the process of winning copper from an electrolyte, copper ions in electrolyte are deposited on the cathode by passing an
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electric current through the electrolyte (Leahy and Schwarz, 2010). Copper electrowinning entails:
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a) At the anode, water molecules are hydrolysed and oxygen bubbles are formed at the anode surface.
E=-1.23V
(1)
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1 H 2 O H OH O2 2H 2e 2
b) The electrons produced by reaction (1) are conducted towards the cathode
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through the external circuit and power supply. c) Movement of copper cations from electrolyte to the cathode by convection and diffusion and electromigration in the boundary layer. d) A reduction reaction takes place at the cathode according to the following equation:
Cu 2 2e Cu
E=0.34V
(2)
That is, for every two electrons, one copper atom is plated on the cathode. The overall electrowinning reaction is the sum of reactions (1) and (2), sulfate ions is added into two side of reaction (Davenport et al., 2002): 1 Cu 2 SO42 H 2O Cu O2 2 H SO42 2
ζ=-0.89V
(3)
Natural convection arises in electrolyte cells due to density gradients in the electrolyte. At the cathode, because of electrodeposition of copper on the surface of it, copper-ion concentration decreases in the vicinity of the cathode, and natural
ACCEPTED MANUSCRIPT convection upwards occurs. Near the anode the buoyancy and drag forces acting on oxygen bubbles move them upward. The buoyancy acting on a gas bubble
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accelerates bubbles upward, and drag on the liquid then moves the solution upward (Filzwieser et al., 1999). Electrolyte recirculates in the space between the plates,
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causing downward flow.
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It is well known that anodically generated oxygen enhances mass transfer at the top of the cathode, but the effect is not pronounced at the bottom (Nieminen et al.,
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2010). The local mass-transfer coefficient increases with the distance from the lower edge of the cathode. That is due to accumulation of rising bubbles, which
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causes more intense fluid flow resulting in an acceleration of the mass transport (Filzwieser et al., 1999). The oxygen bubbles cause a large recirculation zone to
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develop in the space between the electrodes and this recirculation has a strong
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effect on the mass transfer to the cathode because of the mixing nature of the
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recirculation (Leahy and Schwarz, 2010). 3. Experimental
The mass concentration of copper ions for the current electrowinning cell in the Sarcheshmeh copper complex was measured between an anode and a cathode. These data were used for validating our CFD modeling. Solution samples at different distances between an anode and a cathode, in the middle of the cell and at a height of 30 cm from the top of the cell, were obtained by micropipette. Then, the mass concentrations of copper in the samples were measured by using titration. In titration we added potassium iodide to the samples, and then titrated with sodiumthiosulphate. In this titration, copper ions were reduced and deposited: 2Cu 2 4I 2CuI (s) I 2
(4)
Produced iodine was measured with Sodium-Thiosulphate, then the copper ions measured by stoichiometry.
ACCEPTED MANUSCRIPT 2 Na2 S2O3 I 2 Na2 S4O6 2 NaI
(5)
Starch glue was used to detect the end point of titration. To ensure
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reproducibility, each experiment was performed at least twice under the same conditions. Concentration changes along the widths of the anode and cathode
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plates were neglected because the widths of the plates were much larger than the
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distance between them.
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4. Model description 4.1. Governing equations
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The EW model used in this work is a two-phase (liquid-gas) model, which
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solves the time-averaged Navier-Stokes equations with inclusion of buoyancy, drag, turbulent dispersion forces and concentration-related buoyancy forces. A
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transport equation is solved for the copper concentration, with inclusion of a sink at the cathode boundary based on Faraday′s Law. The flow is assumed steady, turbulent, incompressible and isothermal. The Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy driven flow (also known as free convection or natural convection). For a uniform wall mass flux, the modified Rayleigh number is defined as: Ra
g. .m .H 4 2 .D
(6)
, H, ν and D are acceleration due to gravity, copper ion expansion where g , β, m
coefficient, flux of desired metal, characteristic length (in this case, the height of electrode), kinematic viscosity and diffusion coefficient respectively. If the Rayleigh number is more than 1010 the free convection is turbulent. In our work the calculated Rayleigh (Ra) number between the electrodes was about 71015 .
ACCEPTED MANUSCRIPT 4.1.1. Continuity equation The continuity equation in steady state is given by (ANSYS CFX-Solver
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Theory Guide, 2009):
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( i i U i ) S i
(7)
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where for phase i (i=1 is liquid and i=2 is gas), i is the phase density, i is the
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phase volume fraction, U i is the time-averaged mean velocity vector and S i is the
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mass source/sink term (e.g., at the anode and the cathode).
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4.1.2. Momentum equation
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In steady-state, the time-averaged Navier-Stokes equation in vector form is
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expressed as follows (ANSYS CFX-Solver Theory Guide, 2009):
(i i Ui U i ) iP i2 (i U i ) M i
where for phase i, i and
P are
(8)
the dynamic viscosity and the (modified) pressure
respectively. i is considered as summation of laminar viscosity ( L,i ) and turbulent viscosity (T ,i ) , which is given as follows: i L,i T ,i
(9)
The turbulent viscosity in Eqs. (9) and (19) is calculated by using the well-known k-ω turbulent model (Leahy and Schwarz, 2010; Menter, 1993): T
k
(10)
where k and ω are turbulent kinetic energy and eddy frequency respectively.
ACCEPTED MANUSCRIPT The k-ω turbulent model was solved for the continuous liquid phase and then the same turbulence quantities (i.e. k and ω) was used for the dispersed gas phase.
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Typically, the gas turbulent viscosity ( T , 2 ) is multiplied by the ratio of the phases’ density and then by dividing by the turbulent Prandtl number (taken as 1 since
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the bubble relaxation time is short compared to the turbulence dissipation time
2 T ,1 1
(11)
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T , 2
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scales. (Leahy and Schwarz, 2010; 2014):
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M i in Eq. 8 is the sum of the body forces that is given as follows:
(12)
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M i B i F i T i Ai
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where B i , F i , T i and A i are the phase-related buoyancy force, bubble drag force,
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turbulent dispersion force and concentration-related buoyancy force, respectively. The forces are given in below:
B i i ( i ref ) g
F 2 F1
(13)
3 CD 1 2 U 2 U 1 U 2 U 1 4 d
(14)
T 2 T 1 Ctd i k 2 Ai i i g (C C ref )
(15)
, A2 0
(16)
where g is the gravity vector, ref is the reference density taken as that of the
electrolyte (i=1), CD is the drag coefficient, U 2 U 1 is the slip velocity , U 2 U 1 is the size (modulus) of the slip velocity, Ctd is the turbulent dispersion coefficient
ACCEPTED MANUSCRIPT (taken as 1), k is the turbulence kinetic energy, is the concentration-related coefficient of expansion for the copper sulphate solution, C is the concentration of
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copper and Cref is the reference concentration of copper (i.e. initial and inlet
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concentration).
The drag coefficient is dependent on the bubble size and, for small bubbles, this is
24 0.687 1 0.15 Re b Re b
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CD
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well described by the Schiller-Naumann equation:
(17)
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d b 1 U 2 U 1
1
(18)
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Re b
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where Reb (−) is the bubble Reynolds number given by the following:
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where db (m) is the characteristic length scale (bubble diameter). The transport equation for the copper species Cu 2 in steady state is given by (ANSYS CFX-Solver, 2009; Leahy and Schwarz, 2010): T ,1 C S Cu 1C U 1 1 1 D ScT 1
(19)
where D, ScT and S Cu are the diffusion coefficient of copper ions, the turbulent Schmidt number and source term, which describes the flux of copper at the cathode respectively.
ACCEPTED MANUSCRIPT 4.2. Boundary conditions
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The quantity of material undergoing oxidation/reduction during electrolysis is
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related to the quantity of electrical charge passing through the cell by Faraday′s Law (Gamburg and Zangari, 2011). Based on this law, the total volume of oxygen
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generated at the anode is linearly related to the electrical current density (Al
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Shakarji et al., 2011). According to Faraday′s Law the superficial gas production rate is given by (Leahy and Schwarz, 2010): 1 iRT 4 Patm F
(20)
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gas
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where R J K 1mol 1 is the gas constant, T is temperature (K), Patm (Pa) is
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current density.
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atmospheric pressure, F (A s mol-1) is Faraday′s constant, and i (A m-2) is electrical
.
Therefore, the oxygen mass flow rate m oxygen can be calculated based on the superficial velocity from Eq. 20 as follows:
m oxygen gas Aan gas
(21)
where Aan (m2) is the area of the anode. From Faraday′s Law, the flux of copper deposited at the cathode is given by:
mCu
i M Cu ZF 1000
(22)
where m Cu is the flux of copper (kg m2 s-1), MCu is the molecular weight of copper (g mol-1), Z(-) is the valency of the ions involved in the reaction (Leahy and Schwarz, 2010). For all of other walls, no-slip boundary conditions are considered, whereas at the top free surface, a free slip (i.e. no friction) and a degassing
ACCEPTED MANUSCRIPT boundary conditions are used. The input volumetric flow rate of solution to the cell was 8 m3/hr. Volumetric flow rate and atmospheric pressure were considered for
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input and output boundary conditions respectively.
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5. Cell geometry and measured data
Sarcheshmeh copper complex electrowinning unit contains 50 cells that are
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positioned in two sections. Each section includes 25 cells that are connected in series with each other. Cells are 6100 mm long. They are wide and deep (1206 mm
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1216 mm) and each contains 61 anodes and 60 cathodes. Electrolyte containing
CuSO4–H2SO4–H2O continuously enters the bottom of the cell by a loop
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distributor. The loop contains orifices with 8 mm diameter, through which
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electrolyte enters the cell. The dimensions of the cell plates and other measured
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parameters are given in Table 1.
The distance between neighbouring anodes and cathodes was 42.8 mm. This value was very small compared to the length of the electrowinning cell (i.e. 6100mm). It is not possible to run a CFD model of a system containing 121 electrodes using present computer resources. Therefore, the geometry of the selected system for the present study contained only 19 electrodes and the length of the cell was one sixth of the original cell, but no changes were made to other dimensions. Since the length of the cell does not affect the Reynolds number, the Reynolds numbers in both cases were the same. Therefore, shortening the length of the cell is a secondary effect, and can be considered in future study as a sensitivity on the cell performance. The geometry of the cell was symmetrical with respect to the YZ-plane, so the governing equations were solved for half of the solution domain (see Fig. 1a). In Fig. 1a, the Z-axis is in the flow direction, the Y-axis is perpendicular to the flow in a vertical plane and the X-axis is the horizontal axis.
ACCEPTED MANUSCRIPT This figure also shows the electrolyte inlets, which are placed at the bottom of the
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cell. The electrolyte exits from the top of the cell by two channels.
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6. Method of Solution
Copper mass concentration profile was obtained by solving Eqs. (7), (8), (19)
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and k–ω equation simultaneously. These equations were solved by using
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commercial ANSYS CFX-12 software package (ANSYS CFX-Solver, 2009). ANSYS CFX-12 package uses the finite volume method to treat a generalized
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unstructured mesh in Cartesian coordinates.
An inflated grid was used because the gradients of concentration and velocity
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were different over the domain of solution. The grid was compacted around the
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electrodes in which the gradients were high (see Fig. 1b). The grid for the whole
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cell was generated by dividing the cell to four zones and each zone was discretized separately. Then these zones were joined together again in the software. The thickness of the first cell layer of the calculated grid in the front of the electrodes was 2 mm. Around an anode and a cathode, total numbers of nodes and elements were 43,000 and 130,000 respectively. To test the grid independency three different three-dimensional meshes, which contained 750,000, 900,000 and 1,200,000 cells were used. Comparison of measured copper concentration and those of calculated values showed that error percents for these cells were 8%, 6% and 3%, respectively; therefore, 1,200,000 cells were selected for producing the grid independent solution.
ACCEPTED MANUSCRIPT 7. Results and discussion
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7.1. CFD validation
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To validate the CFD model, the results were compared with experimental data
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measured in the electrowinning cell of the Sarcheshmeh copper complex. Fig. 2 shows the comparison of CFD results with experimental data for copper mass
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concentration at different distances from cathode 5. This figure shows a fairly good agreement between the simulation results and the experimental data. The average
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absolute deviation (AAD) error between the simulation results and the experimental data was 0.85 %. The AAD is calculated from the following
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1 n Csim Cexp 100 n i 1 Cin Cout
(23)
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AAD
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equation:
where Cin and Cout are inflow and outflow concentrations. Fig. 3 illustrates the concentration distribution of copper between the anode and the cathode at different heights from the bottom of the cathode 5. As one can see from this figure, there is a reasonable agreement between simulation results and experimental data, so this figure is another confirmation for CFD results. According to this figure, copper concentration decreases with an increase in the distance from the bottom of the cathode. The AAD error between simulation results and experimental data for this figure is 8.56 %.
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7.2. CFD model base case results
Fig. 4 illustrates the flow pattern between an anode and a cathode in the middle
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of the cell. This figure shows an up-flow near the anode caused by the generated
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oxygen bubbles that rise quickly and drag liquid upward, as well as an up-flow near the cathode as a result of copper depletion near the cathode, copper
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concentration gradients and by the associated natural convection buoyancy. However, there is a down-flow in the middle of the gap between plates resulting
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from the electrolyte recirculation zone.
Fig. 5 shows electrolyte vertical velocity as a function of distance from the
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cathode 5 at different heights from the bottom of the electrodes. Moreover, this
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figure indicates a slow downward flow in the middle of the cell, a fast up-ward
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flow near the anode and a low level of upward flow near the cathode. As mentioned previously, during electrowinning by applying electrical current, cations are transported from bulk to the cathode surface. In general, mass transfer close to the cathode surface occurs by diffusion. This transportation occurs in a hydrodynamic boundary layer that forms close to the cathode where convection is low and diffusion limits copper mass transfer and copper depleted in the boundary layer. A concentration gradient in this layer is created by depletion of copper ions on the cathode and causes an upward flow in this thin layer. This zone is shown in enlargement in the inset graph on the upper left hand side of Fig. 5. In this study, after the validation of the results the effect of different operating parameters on the production efficiency of the electrowinning cell in the Sarcheshmeh copper complex has been investigated with the aid of CFD simulation as discussed in following sections. The effect of width of the electrodes
ACCEPTED MANUSCRIPT in X direction was neglected on the performance of the cell, because the width was
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very long in comparison with the distance between the electrodes (i.e. 42.8 mm).
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7.3. Effect of electrical current density
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To investigate the effect of electrical current density on the performance of the cell, three electrical current densities, namely 191, 250 and 300 A/m2 were used.
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Fig. 6 shows the effect of electrical current density on the copper mass concentration between cathode 5 and anode 6 at the middle of the cell. As one can
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see, with increasing electrical current density, copper mass concentration decreases by about 0.3% on the whole region between the electrodes. This finding is in
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accordance with Faraday′s Law and means by increasing the electrical current
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density the copper deposited on the cathode increases.
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As shown in Fig. 7, increasing electrical current density results in a decreasing of the copper mass concentration at different height positions from the bottom of the cathode. Fig. 8 indicates by increasing electrical current density, vertical velocity of electrolyte near the anode increases by about 17%. This is due to increasing oxygen generated on the anode. Near the cathode because of increasing amount of electrolyte depletion and deposition of copper ions on the cathode, the density of the electrolyte decreases: the electrolyte accelerates in this narrow zone due to resultant buoyancy. By increasing electrical current density, the vertical velocity of the electrolyte near the cathode increases by about 11%. Moreover, in the middle of the cell, the downward flow moves faster. This change in the velocity profile indicates that with increasing electrical current density, natural convection increases. Consequently, mass transportation and the production efficiency of the cell increases. However, as the applied current density increases, the surface concentration of copper cations as discussed by Leahy and Schwarz,
ACCEPTED MANUSCRIPT 2014 approaches to zero. The value of current density at which the surface concentration is zero is known as the limiting current, iL. The limiting current D
C
(24)
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i L nF
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density of any reducible species such as Cu2+ is given by (Joy et al.,2010):
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where iL , D, , C are limiting current density of Cu2+, effective diffusivity of Cu2+, thickness of Nernst diffusion boundary layer, and bulk electrolyte of Cu 2+
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respectively. Increasing the current density above iL results in a nodular deposit, which can trap impurities. Therefore, it is necessary to determine the limiting
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current density for the cell. The copper mass transfer rate predicted by the CFD model can be used for this purpose (Leahy and Schwarz, 2014). Decreasing the
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boundary layer thickness, , increases the limiting current. This can be achieved by
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increasing the velocity past the cathode, or by introducing flow instabilities. To determine the limiting current density for this study, further investigation by
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applying a zero concentration boundary condition at the cathode needs to be done. Fig. 9 shows the effect of the electrical current density on gas vertical velocity distribution between the electrodes in the middle of the cell. This profile is similar to the vertical velocity of the electrolyte in Fig. 8. In this study, the size of bubbles was 50 µm (Filzwieser et al., 1999; Leahy and Schwarz, 2010). For bubbles with 50 µm diameter, the bubble Reynolds number is 0.5 (see Eq. 18). This causes drag coefficient (i.e. CD) to be large, which means that the Stokes drag regime is prevalent, where the drag is so high the two phases have almost the same velocity. This finding is in accordance with Leahy and Schwarz (2010). Fig. 10 illustrates the effect of electrical current density on the gas volume fraction between an anode and a cathode. As one can see from this figure, with increasing electrical current density, oxygen volume fraction between electrodes
ACCEPTED MANUSCRIPT increases because the generated oxygen on the anode increases. This is in
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accordance with Faraday′s Law.
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7.4. Effect of volumetric flow rate
The effects of volumetric flow rate on the vertical velocity of the electrolyte and
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gas, the distribution of copper concentration and the oxygen volume fraction were
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studied. Three flow rates, namely 8, 9.5 and 11 m3/hr were used. The results are shown in Fig. 11. This figure shows that by increasing the flow rate, the maximum vertical velocity near the cathode and the anode increased by about 5.8 and 4%
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respectively, and the electrolyte moves downward with a lower velocity in the
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middle of the cell. This is due to increasing the forced convection and the velocity
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of the electrolyte at the entrance; consequently, the velocity of fluid that moves between the electrodes increases. Fig. 12 shows the effect of increasing volumetric flow rate on gas velocity distribution. By increasing the volumetric flow rate, the gas velocity increases slightly at distance closest to the cathode. Figs. 13 and 14 illustrate how the volumetric flow rate of the entering electrolyte to the electrowinning cell affects the concentration distribution of copper between the electrodes and the variation of copper concentration at different heights from the bottom of the cathode 5 respectively. These figures show that by increasing the volumetric flow rate, the copper mass concentration increases by about 0.2%. By increasing the flow rate the entering copper ions to the cell increase whereas in our calculation the electrical current density is equal for different flow rates; therefore, according to Faraday's Law, deposited copper on the cathode is the same. As a result for higher flow rate the remaining copper ions
ACCEPTED MANUSCRIPT in electrolyte that cannot precipitate on the cathode increase and the copper mass concentration between the electrodes increases. It would be expected that increased
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flow velocity would improve mass transfer, so improve plating quality, because with increasing flow rate, the boundary layer thickness near the cathode plate
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decreases. In the present study, the amount of copper deposited on the cathode (see
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Eq. 22) is calculated by Faraday's Law. However, this law does not consider the effect of forced convection on deposition rate. Therefore, to define Faraday's Law
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as a suitable boundary condition with considering the effect of forced convection on the boundary layer thickness and copper deposition rate, more studies need to
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be done.
Fig. 15 shows increasing the volumetric flow rate does not affect the oxygen
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D
volume fraction between the electrodes. 7.5. Effect of change of the distance between the electrodes of the
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electrowinning cell
The distance (D) between electrodes was another important parameter investigated in this simulation. The real distance between electrodes was 42.8 mm and we modelled the flow with another two distances, namely 38 and 34 mm, for electrical current density of 191 A/m2 and volumetric flow rate of 8 m3/hr. Because of these reductions in the distance between electrodes, the length of the electrowinning cell was 86 and 158 mm shorter than that of the real cell, respectively. Fig. 16 shows electrolyte vertical velocity for three distances between electrodes. As one can see from this figure, by decreasing the distance between the electrodes the maximum velocity near the cathode and the anode increases by about 19 and 16% respectively, and in the middle of the cell the electrolyte moves downward with faster velocity.
ACCEPTED MANUSCRIPT Fig. 17 shows the effect of decreasing the distance between electrodes on the gas velocity distribution. This figure indicates that by decreasing the distance the
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maximum velocity near the anode increases and in the middle of the cell gas moves faster downward.
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Figs. 18 and 19 show how changing the distance between electrodes affects the
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concentration distribution between electrodes and the variation of copper concentration at different heights from the bottom of the cathode 5 respectively. By
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decreasing the distance between the electrodes from 42.8 to 34 mm, the copper
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mass concentration decreases by about 0.15%. These little changes in concentration show reducing the distance between the electrodes does not affect the amount of copper deposited on the cathode. The amount of copper entering the
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area between the electrodes is the product of velocity and area. With reducing the
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distance between the electrodes, the cross-sectional area between the electrodes
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reduces. As a result the velocity of electrolyte increases, but the volumetric flow rate of electrolyte entering the area between the electrodes is probably constant. Therefore, at constant overall flow rate and constant boundary condition for deposition of copper on the cathode, the overall concentration changes is not considerable.
Fig. 20 illustrates how the distance between the electrodes affects the oxygen volume fraction. Since the electrical current density is the same for all the different distances, the generated oxygen for different distances are the same. However, with decreasing distance between the electrodes, oxygen disperses in a smaller volume; therefore, the volume fraction of oxygen increases.
ACCEPTED MANUSCRIPT 8. Conclusions and recommendations In this study, a three-dimensional CFD simulation was applied together with
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experimental field measurements to study the performance of an industrial electrowinning cell in the Sarcheshmeh copper complex, Iran. To validate the
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model, the CFD results were compared by the experimental data. After the
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validation of the model, the effects of different parameters on the performance of the cell were investigated. On increasing electrical current density, from 191 to 300
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A/m2, more copper deposited on the cathode and the electrolyte copper ion
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concentration between the electrodes decreased by about 0.3% (i.e. from 33.49 to 33.4 g/L). Thus, increasing the electrical current density leads to an increase in cell
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production efficiency, which corresponded with Faraday's Law.
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Increasing the volumetric flow rate from 8 to 11 m3/hr at constant electrical current density, increases the electrolyte vertical velocity at all points between the
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electrodes. On increasing the flow rate, the entering copper ions to the cell increases, so the mass concentration between the electrodes increases. To improve mass transfer to the cathode with increasing flow rate, electrical current density must be also increased. Because as flow rate increases the Nernst boundary layer thickness decreases, this causes the limiting current density to increase. On reducing the distance between the electrodes from 42.8 to 34 mm, the copper mass concentration on the cathode decreases by about 0.15 %. This is due to a decrease in the amount of copper entering to the volume between the electrodes. Decreasing the distance from 42.8 to 38 mm, the copper mass concentration between the electrodes does not change considerably. In this CFD simulation, the effect of forced convection on limiting current density was not investigated. Moreover, in an industrial electrowinning cell, the presence of other ions such as iron affects the copper deposition on the cathode;
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performance of an electrowinning cell.
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Acknowledgments
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The authors would like to express their appreciation to the Sarcheshmeh copper complex in allowing them to access the experimental data. Also, reviewers are
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acknowledged for their valuable comments.
ACCEPTED MANUSCRIPT References Al Shakarji, R., He, Y., Gregory, S., 2011. The sizing of oxygen bubbles in copper
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electrowinning, Hydrometallurgy 109, 168-174.
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ANSYS CFX-Solver Theory Guide, Release 12, 2009 ANSYS, Inc.
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ANSYS CFX 12 User's Guide, copyright 1996–2009, ANSYS, Ltd.
Davenport, W.G., King, M., Schlesinger, M., 2002. Extractive metallurgy of copper, fourth ed.
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Elsevier Science Ltd. 327-338.
Filzwieser, A., Hein, K., Hanko, G., 1999. Application of a two phase hydrodynamic modeling
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to an electrowinning cell, Copper 99- Cobre 99, Proc. Of the 4th Intl. Conference Vol. III, Phoenix, Arizona, USA, pp. 695-709. Harlow, F, and P. Nakayama: Transport of Turbulence
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Energy Decay Rate. Report LA-3845, Los Alamos Science Lab, University of California.
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Filzwieser, A., Hein, K., Mori, G., 2002. Current density limitation and diffusion boundary layer
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calculation using computational fluid dynamics, JOM, 54, 28-31. Gamburg, Y.D., Zangari, G., 2011. Theory and Practice of Metal Electrodeposition. Springer Science, New York 1–4.
Hemmati, H., Mohebbi, A., Soltani, A., 2013. CFD modeling of the electrolyte flow in the copper electrorefining cell of Sarcheshmeh copper complex. Hydrometallurgy 139, 54-63. Joy, S., Staley, A., Moats, M., Perkins, C., Uhrie, J., Robinson, T., 2010. Understanding and improvement of electrowinning current efficiency at FMI Bagdad, Proceedings of Copper 2010, 4, 1379-1392. Leahy, M.J., Schwarz, M.P., 2010. Experimental validation of a computational fluid dynamics model of copper electrowinning, Metall and Mater Trans B, 41, 1247-1260. Leahy, M.J., Schwarz, M.P., 2011. Modelling natural convection in copper electrorefining: describing turbulence behavior for industrial sized systems. Metall. Mater. Trans. B, 42, 875– 890. Leahy, M.J., Schwarz, M.P., 2014. Flow and mass transfer modelling for copper electrowinning: development of instabilities along electrodes. Hydrometallurgy 147–148, 41–53.
ACCEPTED MANUSCRIPT Menter, F.R., 1993. Zonal two equation k–ω turbulence models for aerodynamic flows. AIAA 93–2906.
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Nieminen, V., Virtanen, H., Ekman, E., 2010. Copper electrowinning with high current density, Proceedings of Copper, 4, 1545-1557.
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Sadeghi, R., Mohebbi, A., Baniasadi, M., 2011a. CFD modeling of the launder of settler of an
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industrial copper solvent extraction plant: A case study on Sarcheshmeh copper complex, Iran. IJMP 98, 55-65.
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Sadeghi, R., Mohebbi, A., Sarrafi, A., Soltani, A., Salmanzadeh, M., Daneshpojooh, Sh., 2011b. CFD simulation and optimization of the settler of an industrial copper solvent extraction plant: A
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case study, Hydrometallurgy 106, 148-158.
Ziegler, D., Evans, J., 1986. Mathematical modeling of electrolyte circulation in cells with planar
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vertical electrodes, J. Electrochem. Soc, 133, 567–576.
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Parameter
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Current density (A/m2) Flow rate in inlet (m3/hr) Electrolyte density (kg /m3) Electrolyte kinematic viscosity (m2/s) Dimensions of cathode (height thickness depth) (mm) Dimensions of anode (height thickness depth) (mm)
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Table 1 Measured parameters and dimensions of an anode and a cathode in Sarcheshmeh copper complex electrowinning cell.
191 8 1220 1.34e-6 1015 3.2 1052 943 6 920
ACCEPTED MANUSCRIPT Highlights
A three-dimensional CFD simulation for an industrial copper electrowinning cell was
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done. The CFD model results were compared with measured data.
A large number of electrodes instead of one pair of electrodes for simulation were used.
The effects of operating parameters such as current density on the performance of the cell
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The k-ω turbulence flow model was used to calculate liquid velocity profile.
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were studied.
S0304-386X(15)00031-6 doi: 10.1016/j.hydromet.2015.02.005 HYDROM 4037
To appear in:
Hydrometallurgy
Received date: Revised date: Accepted date:
10 February 2014 8 February 2015 23 February 2015
Please cite this article as: Najminoori, Mahjabin, Mohebbi, Ali, Arabi, Babak Ghadami, Daneshpajouh, Shahram, CFD simulation of an industrial copper electrowinning cell, Hydrometallurgy (2015), doi: 10.1016/j.hydromet.2015.02.005
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ACCEPTED MANUSCRIPT CFD simulation of an industrial copper electrowinning cell Mahjabin Najminoori a, Ali Mohebbia, , Babak Ghadami Arabib, Shahram Daneshpajouhb Department of Chemical Engineering, Faculty of Engineering, Shahid Bahonar University of
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a
Kerman, Kerman, Iran
Sarcheshmeh Copper Complex, Iran
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b
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Abstract
Copper electrowinning is the process of winning a high purity copper from an
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aqueous pregnant liquor acid electrolyte in the presence of impurities. In this study, a three-dimensional, steady and two-phase (liquid-gas) computational fluid
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dynamics (CFD) simulation was applied, together with experimental field
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measurements, to investigate the performance of an industrial electrowinning cell in the Sarcheshmeh copper complex, Iran. This simulation was based on Eulerian-
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Eulerian method. The continuity and momentum equations with inclusion of buoyancy, drag, turbulent dispersion and concentration-related buoyancy forces were solved by the finite volume method. In order to calculate the velocity distribution in the cell, the k-ω turbulence flow model has been used. To find the concentration distribution of copper, the transport equation of copper ions was solved. There was a good agreement between the simulation results and the experimental measured data of the electrowinning cell. After validation of the model, the effects of electrical current density, volumetric flow rate of feed and the distance between the electrodes were studied on the performance of the cell and copper concentration distribution. The simulation results show that there are two upward flows in the cell, one is near the anode because of oxygen generation and the other is near the cathode due to depletion of copper ions from the electrolyte
Corresponding author: Tel & Fax: +983432118298 E-mail addresses: [email protected] , [email protected] (A. Mohebbi).
ACCEPTED MANUSCRIPT and buoyancy force. In the middle of the cell, the electrolyte recirculation zone causes a downward flow. Increasing electrical current density decreases copper concentration near the cathode and increases gas volume fraction near the anode,
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which is in accordance with Faraday′s Law. With decreasing volumetric flow rate
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and distance between the electrodes, copper mass concentration on the cathode
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decreases.
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Keywords: Copper electrowinning cell; CFD; Simulation; Electrolyte
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1. Introduction
The Sarcheshmeh copper complex is one of the world ′s largest industrial
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complexes. It is the largest producer of copper in Iran. Its geological storage is
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over one billion and two hundred million tonnes of ore with an average grade of 0.7% copper. It is located in Kerman province in the southeast of Iran and is on the
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central Zagros mountain range. It currently processes up to 41,000 t/d. Copper is extracted from its ore by two principal methods; pyrometallurgical and hydrometallurgical. The pyrometallurgical method is used for sulfide ore and the hydrometallurgical method is used for extracting copper from oxide ores. Hydrometallurgical operations extract metals from aqueous solutions containing metal ions. Because of the advantages of this method compared to pyrometallurgy (such as reduced pollution and energy consumption), it has progressed quickly, and now accounts for a significant share of metal production in the world. Although some CFD works for electrorefining cell (Hemmati et al. (2013); Leahy and Schwarz (2010); Leahy and Schwarz (2011)) and hydrometallurgy process (Sadeghi et al. (2011a); Sadeghi et al. (2011b)) have been done, only a limited number of CFD modeling studies of EW have been reported. Ziegler and Evans (1986) collected limited data of the velocity profile in a large system and compared the velocity profiles with a simple fluid dynamics model with some
ACCEPTED MANUSCRIPT success. Filzwieser et al. (1999) primarily investigated the hydrodynamics of fluid flow and obtained experimental data of the velocity profiles in a copper
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electrowinning cell; he analyzed the benefit of the fluid flow onto the mass transport, but did not compare the results of their CFD model with the
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experimental data. Filzwieser et al. (2002) discussed about diffusion boundary
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layer (δN), limiting electrical current density (ilimit) and copper concentration distribution near the cathode as a function of distance from the bottom of the
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cathode. Leahy and Schwarz (2010) used a two-dimensional, steady and two-phase CFD model to study the hydrodynamics of flow in a single plate pair of a copper Leahy and Schwarz (2014) developed a CFD model to
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EW cell. Recently,
simulate bubble-driven hydrodynamics, copper distribution and instabilities along
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electrodes in an electrowinning cell consisting of a single anode–cathode pair.
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Their CFD model predicted a recirculation zone in all cases, due to the oxygen bubbles rising along the anode and dragging electrolyte upwards. They also
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concluded strong eddies arise along the cathode where copper depletion becomes large enough to drive buoyancy instabilities. In this study, a three-dimensional simulation has been applied using CFD to predict performance of a copper electrowinning cell in a real industrial case. This simulation uses CFD modeling to describe the hydrodynamics occurring between the electrodes of a copper EW cell. This work represents for the first time, a threedimensional, steady, two-phase (gas-liquid), CFD model with inclusion of a large number of electrodes instead of one pair of electrodes. Moreover, the CFD results were validated with the experimental data measured in an industrial plant (i.e. Sarcheshmeh copper complex) and the effects of electrical current density, volumetric flow rate of feed and distance between the electrodes on the cell performance were studied.
ACCEPTED MANUSCRIPT 2. Theory
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In the Sarcheshmeh copper winning cells, the cathodes are made of stainless steel 316L and anodes are made of Pb-Sn-Ca alloy. Electrolyte contains a high
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concentration of copper (>30g/L) and sulfuric acid (160-200g/L), along with other
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metals and chemical additives. In the process of winning copper from an electrolyte, copper ions in electrolyte are deposited on the cathode by passing an
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electric current through the electrolyte (Leahy and Schwarz, 2010). Copper electrowinning entails:
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a) At the anode, water molecules are hydrolysed and oxygen bubbles are formed at the anode surface.
E=-1.23V
(1)
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1 H 2 O H OH O2 2H 2e 2
b) The electrons produced by reaction (1) are conducted towards the cathode
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through the external circuit and power supply. c) Movement of copper cations from electrolyte to the cathode by convection and diffusion and electromigration in the boundary layer. d) A reduction reaction takes place at the cathode according to the following equation:
Cu 2 2e Cu
E=0.34V
(2)
That is, for every two electrons, one copper atom is plated on the cathode. The overall electrowinning reaction is the sum of reactions (1) and (2), sulfate ions is added into two side of reaction (Davenport et al., 2002): 1 Cu 2 SO42 H 2O Cu O2 2 H SO42 2
ζ=-0.89V
(3)
Natural convection arises in electrolyte cells due to density gradients in the electrolyte. At the cathode, because of electrodeposition of copper on the surface of it, copper-ion concentration decreases in the vicinity of the cathode, and natural
ACCEPTED MANUSCRIPT convection upwards occurs. Near the anode the buoyancy and drag forces acting on oxygen bubbles move them upward. The buoyancy acting on a gas bubble
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accelerates bubbles upward, and drag on the liquid then moves the solution upward (Filzwieser et al., 1999). Electrolyte recirculates in the space between the plates,
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causing downward flow.
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It is well known that anodically generated oxygen enhances mass transfer at the top of the cathode, but the effect is not pronounced at the bottom (Nieminen et al.,
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2010). The local mass-transfer coefficient increases with the distance from the lower edge of the cathode. That is due to accumulation of rising bubbles, which
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causes more intense fluid flow resulting in an acceleration of the mass transport (Filzwieser et al., 1999). The oxygen bubbles cause a large recirculation zone to
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develop in the space between the electrodes and this recirculation has a strong
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effect on the mass transfer to the cathode because of the mixing nature of the
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recirculation (Leahy and Schwarz, 2010). 3. Experimental
The mass concentration of copper ions for the current electrowinning cell in the Sarcheshmeh copper complex was measured between an anode and a cathode. These data were used for validating our CFD modeling. Solution samples at different distances between an anode and a cathode, in the middle of the cell and at a height of 30 cm from the top of the cell, were obtained by micropipette. Then, the mass concentrations of copper in the samples were measured by using titration. In titration we added potassium iodide to the samples, and then titrated with sodiumthiosulphate. In this titration, copper ions were reduced and deposited: 2Cu 2 4I 2CuI (s) I 2
(4)
Produced iodine was measured with Sodium-Thiosulphate, then the copper ions measured by stoichiometry.
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Starch glue was used to detect the end point of titration. To ensure
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reproducibility, each experiment was performed at least twice under the same conditions. Concentration changes along the widths of the anode and cathode
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4. Model description 4.1. Governing equations
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transport equation is solved for the copper concentration, with inclusion of a sink at the cathode boundary based on Faraday′s Law. The flow is assumed steady, turbulent, incompressible and isothermal. The Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy driven flow (also known as free convection or natural convection). For a uniform wall mass flux, the modified Rayleigh number is defined as: Ra
g. .m .H 4 2 .D
(6)
, H, ν and D are acceleration due to gravity, copper ion expansion where g , β, m
coefficient, flux of desired metal, characteristic length (in this case, the height of electrode), kinematic viscosity and diffusion coefficient respectively. If the Rayleigh number is more than 1010 the free convection is turbulent. In our work the calculated Rayleigh (Ra) number between the electrodes was about 71015 .
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The turbulent viscosity in Eqs. (9) and (19) is calculated by using the well-known k-ω turbulent model (Leahy and Schwarz, 2010; Menter, 1993): T
k
(10)
where k and ω are turbulent kinetic energy and eddy frequency respectively.
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Typically, the gas turbulent viscosity ( T , 2 ) is multiplied by the ratio of the phases’ density and then by dividing by the turbulent Prandtl number (taken as 1 since
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the bubble relaxation time is short compared to the turbulence dissipation time
2 T ,1 1
(11)
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T , 2
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scales. (Leahy and Schwarz, 2010; 2014):
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M i in Eq. 8 is the sum of the body forces that is given as follows:
(12)
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M i B i F i T i Ai
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where B i , F i , T i and A i are the phase-related buoyancy force, bubble drag force,
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turbulent dispersion force and concentration-related buoyancy force, respectively. The forces are given in below:
B i i ( i ref ) g
F 2 F1
(13)
3 CD 1 2 U 2 U 1 U 2 U 1 4 d
(14)
T 2 T 1 Ctd i k 2 Ai i i g (C C ref )
(15)
, A2 0
(16)
where g is the gravity vector, ref is the reference density taken as that of the
electrolyte (i=1), CD is the drag coefficient, U 2 U 1 is the slip velocity , U 2 U 1 is the size (modulus) of the slip velocity, Ctd is the turbulent dispersion coefficient
ACCEPTED MANUSCRIPT (taken as 1), k is the turbulence kinetic energy, is the concentration-related coefficient of expansion for the copper sulphate solution, C is the concentration of
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copper and Cref is the reference concentration of copper (i.e. initial and inlet
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concentration).
The drag coefficient is dependent on the bubble size and, for small bubbles, this is
24 0.687 1 0.15 Re b Re b
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CD
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well described by the Schiller-Naumann equation:
(17)
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d b 1 U 2 U 1
1
(18)
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Re b
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where Reb (−) is the bubble Reynolds number given by the following:
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where db (m) is the characteristic length scale (bubble diameter). The transport equation for the copper species Cu 2 in steady state is given by (ANSYS CFX-Solver, 2009; Leahy and Schwarz, 2010): T ,1 C S Cu 1C U 1 1 1 D ScT 1
(19)
where D, ScT and S Cu are the diffusion coefficient of copper ions, the turbulent Schmidt number and source term, which describes the flux of copper at the cathode respectively.
ACCEPTED MANUSCRIPT 4.2. Boundary conditions
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The quantity of material undergoing oxidation/reduction during electrolysis is
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related to the quantity of electrical charge passing through the cell by Faraday′s Law (Gamburg and Zangari, 2011). Based on this law, the total volume of oxygen
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generated at the anode is linearly related to the electrical current density (Al
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Shakarji et al., 2011). According to Faraday′s Law the superficial gas production rate is given by (Leahy and Schwarz, 2010): 1 iRT 4 Patm F
(20)
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gas
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where R J K 1mol 1 is the gas constant, T is temperature (K), Patm (Pa) is
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current density.
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atmospheric pressure, F (A s mol-1) is Faraday′s constant, and i (A m-2) is electrical
.
Therefore, the oxygen mass flow rate m oxygen can be calculated based on the superficial velocity from Eq. 20 as follows:
m oxygen gas Aan gas
(21)
where Aan (m2) is the area of the anode. From Faraday′s Law, the flux of copper deposited at the cathode is given by:
mCu
i M Cu ZF 1000
(22)
where m Cu is the flux of copper (kg m2 s-1), MCu is the molecular weight of copper (g mol-1), Z(-) is the valency of the ions involved in the reaction (Leahy and Schwarz, 2010). For all of other walls, no-slip boundary conditions are considered, whereas at the top free surface, a free slip (i.e. no friction) and a degassing
ACCEPTED MANUSCRIPT boundary conditions are used. The input volumetric flow rate of solution to the cell was 8 m3/hr. Volumetric flow rate and atmospheric pressure were considered for
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input and output boundary conditions respectively.
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5. Cell geometry and measured data
Sarcheshmeh copper complex electrowinning unit contains 50 cells that are
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positioned in two sections. Each section includes 25 cells that are connected in series with each other. Cells are 6100 mm long. They are wide and deep (1206 mm
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1216 mm) and each contains 61 anodes and 60 cathodes. Electrolyte containing
CuSO4–H2SO4–H2O continuously enters the bottom of the cell by a loop
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distributor. The loop contains orifices with 8 mm diameter, through which
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electrolyte enters the cell. The dimensions of the cell plates and other measured
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parameters are given in Table 1.
The distance between neighbouring anodes and cathodes was 42.8 mm. This value was very small compared to the length of the electrowinning cell (i.e. 6100mm). It is not possible to run a CFD model of a system containing 121 electrodes using present computer resources. Therefore, the geometry of the selected system for the present study contained only 19 electrodes and the length of the cell was one sixth of the original cell, but no changes were made to other dimensions. Since the length of the cell does not affect the Reynolds number, the Reynolds numbers in both cases were the same. Therefore, shortening the length of the cell is a secondary effect, and can be considered in future study as a sensitivity on the cell performance. The geometry of the cell was symmetrical with respect to the YZ-plane, so the governing equations were solved for half of the solution domain (see Fig. 1a). In Fig. 1a, the Z-axis is in the flow direction, the Y-axis is perpendicular to the flow in a vertical plane and the X-axis is the horizontal axis.
ACCEPTED MANUSCRIPT This figure also shows the electrolyte inlets, which are placed at the bottom of the
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cell. The electrolyte exits from the top of the cell by two channels.
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6. Method of Solution
Copper mass concentration profile was obtained by solving Eqs. (7), (8), (19)
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and k–ω equation simultaneously. These equations were solved by using
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commercial ANSYS CFX-12 software package (ANSYS CFX-Solver, 2009). ANSYS CFX-12 package uses the finite volume method to treat a generalized
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unstructured mesh in Cartesian coordinates.
An inflated grid was used because the gradients of concentration and velocity
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were different over the domain of solution. The grid was compacted around the
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electrodes in which the gradients were high (see Fig. 1b). The grid for the whole
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cell was generated by dividing the cell to four zones and each zone was discretized separately. Then these zones were joined together again in the software. The thickness of the first cell layer of the calculated grid in the front of the electrodes was 2 mm. Around an anode and a cathode, total numbers of nodes and elements were 43,000 and 130,000 respectively. To test the grid independency three different three-dimensional meshes, which contained 750,000, 900,000 and 1,200,000 cells were used. Comparison of measured copper concentration and those of calculated values showed that error percents for these cells were 8%, 6% and 3%, respectively; therefore, 1,200,000 cells were selected for producing the grid independent solution.
ACCEPTED MANUSCRIPT 7. Results and discussion
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7.1. CFD validation
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To validate the CFD model, the results were compared with experimental data
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measured in the electrowinning cell of the Sarcheshmeh copper complex. Fig. 2 shows the comparison of CFD results with experimental data for copper mass
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concentration at different distances from cathode 5. This figure shows a fairly good agreement between the simulation results and the experimental data. The average
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absolute deviation (AAD) error between the simulation results and the experimental data was 0.85 %. The AAD is calculated from the following
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1 n Csim Cexp 100 n i 1 Cin Cout
(23)
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AAD
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equation:
where Cin and Cout are inflow and outflow concentrations. Fig. 3 illustrates the concentration distribution of copper between the anode and the cathode at different heights from the bottom of the cathode 5. As one can see from this figure, there is a reasonable agreement between simulation results and experimental data, so this figure is another confirmation for CFD results. According to this figure, copper concentration decreases with an increase in the distance from the bottom of the cathode. The AAD error between simulation results and experimental data for this figure is 8.56 %.
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7.2. CFD model base case results
Fig. 4 illustrates the flow pattern between an anode and a cathode in the middle
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of the cell. This figure shows an up-flow near the anode caused by the generated
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oxygen bubbles that rise quickly and drag liquid upward, as well as an up-flow near the cathode as a result of copper depletion near the cathode, copper
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concentration gradients and by the associated natural convection buoyancy. However, there is a down-flow in the middle of the gap between plates resulting
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from the electrolyte recirculation zone.
Fig. 5 shows electrolyte vertical velocity as a function of distance from the
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cathode 5 at different heights from the bottom of the electrodes. Moreover, this
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figure indicates a slow downward flow in the middle of the cell, a fast up-ward
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flow near the anode and a low level of upward flow near the cathode. As mentioned previously, during electrowinning by applying electrical current, cations are transported from bulk to the cathode surface. In general, mass transfer close to the cathode surface occurs by diffusion. This transportation occurs in a hydrodynamic boundary layer that forms close to the cathode where convection is low and diffusion limits copper mass transfer and copper depleted in the boundary layer. A concentration gradient in this layer is created by depletion of copper ions on the cathode and causes an upward flow in this thin layer. This zone is shown in enlargement in the inset graph on the upper left hand side of Fig. 5. In this study, after the validation of the results the effect of different operating parameters on the production efficiency of the electrowinning cell in the Sarcheshmeh copper complex has been investigated with the aid of CFD simulation as discussed in following sections. The effect of width of the electrodes
ACCEPTED MANUSCRIPT in X direction was neglected on the performance of the cell, because the width was
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very long in comparison with the distance between the electrodes (i.e. 42.8 mm).
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7.3. Effect of electrical current density
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To investigate the effect of electrical current density on the performance of the cell, three electrical current densities, namely 191, 250 and 300 A/m2 were used.
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Fig. 6 shows the effect of electrical current density on the copper mass concentration between cathode 5 and anode 6 at the middle of the cell. As one can
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see, with increasing electrical current density, copper mass concentration decreases by about 0.3% on the whole region between the electrodes. This finding is in
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accordance with Faraday′s Law and means by increasing the electrical current
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density the copper deposited on the cathode increases.
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As shown in Fig. 7, increasing electrical current density results in a decreasing of the copper mass concentration at different height positions from the bottom of the cathode. Fig. 8 indicates by increasing electrical current density, vertical velocity of electrolyte near the anode increases by about 17%. This is due to increasing oxygen generated on the anode. Near the cathode because of increasing amount of electrolyte depletion and deposition of copper ions on the cathode, the density of the electrolyte decreases: the electrolyte accelerates in this narrow zone due to resultant buoyancy. By increasing electrical current density, the vertical velocity of the electrolyte near the cathode increases by about 11%. Moreover, in the middle of the cell, the downward flow moves faster. This change in the velocity profile indicates that with increasing electrical current density, natural convection increases. Consequently, mass transportation and the production efficiency of the cell increases. However, as the applied current density increases, the surface concentration of copper cations as discussed by Leahy and Schwarz,
ACCEPTED MANUSCRIPT 2014 approaches to zero. The value of current density at which the surface concentration is zero is known as the limiting current, iL. The limiting current D
C
(24)
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i L nF
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density of any reducible species such as Cu2+ is given by (Joy et al.,2010):
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where iL , D, , C are limiting current density of Cu2+, effective diffusivity of Cu2+, thickness of Nernst diffusion boundary layer, and bulk electrolyte of Cu 2+
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respectively. Increasing the current density above iL results in a nodular deposit, which can trap impurities. Therefore, it is necessary to determine the limiting
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current density for the cell. The copper mass transfer rate predicted by the CFD model can be used for this purpose (Leahy and Schwarz, 2014). Decreasing the
D
boundary layer thickness, , increases the limiting current. This can be achieved by
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increasing the velocity past the cathode, or by introducing flow instabilities. To determine the limiting current density for this study, further investigation by
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applying a zero concentration boundary condition at the cathode needs to be done. Fig. 9 shows the effect of the electrical current density on gas vertical velocity distribution between the electrodes in the middle of the cell. This profile is similar to the vertical velocity of the electrolyte in Fig. 8. In this study, the size of bubbles was 50 µm (Filzwieser et al., 1999; Leahy and Schwarz, 2010). For bubbles with 50 µm diameter, the bubble Reynolds number is 0.5 (see Eq. 18). This causes drag coefficient (i.e. CD) to be large, which means that the Stokes drag regime is prevalent, where the drag is so high the two phases have almost the same velocity. This finding is in accordance with Leahy and Schwarz (2010). Fig. 10 illustrates the effect of electrical current density on the gas volume fraction between an anode and a cathode. As one can see from this figure, with increasing electrical current density, oxygen volume fraction between electrodes
ACCEPTED MANUSCRIPT increases because the generated oxygen on the anode increases. This is in
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accordance with Faraday′s Law.
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7.4. Effect of volumetric flow rate
The effects of volumetric flow rate on the vertical velocity of the electrolyte and
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gas, the distribution of copper concentration and the oxygen volume fraction were
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studied. Three flow rates, namely 8, 9.5 and 11 m3/hr were used. The results are shown in Fig. 11. This figure shows that by increasing the flow rate, the maximum vertical velocity near the cathode and the anode increased by about 5.8 and 4%
D
respectively, and the electrolyte moves downward with a lower velocity in the
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middle of the cell. This is due to increasing the forced convection and the velocity
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of the electrolyte at the entrance; consequently, the velocity of fluid that moves between the electrodes increases. Fig. 12 shows the effect of increasing volumetric flow rate on gas velocity distribution. By increasing the volumetric flow rate, the gas velocity increases slightly at distance closest to the cathode. Figs. 13 and 14 illustrate how the volumetric flow rate of the entering electrolyte to the electrowinning cell affects the concentration distribution of copper between the electrodes and the variation of copper concentration at different heights from the bottom of the cathode 5 respectively. These figures show that by increasing the volumetric flow rate, the copper mass concentration increases by about 0.2%. By increasing the flow rate the entering copper ions to the cell increase whereas in our calculation the electrical current density is equal for different flow rates; therefore, according to Faraday's Law, deposited copper on the cathode is the same. As a result for higher flow rate the remaining copper ions
ACCEPTED MANUSCRIPT in electrolyte that cannot precipitate on the cathode increase and the copper mass concentration between the electrodes increases. It would be expected that increased
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flow velocity would improve mass transfer, so improve plating quality, because with increasing flow rate, the boundary layer thickness near the cathode plate
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decreases. In the present study, the amount of copper deposited on the cathode (see
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Eq. 22) is calculated by Faraday's Law. However, this law does not consider the effect of forced convection on deposition rate. Therefore, to define Faraday's Law
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as a suitable boundary condition with considering the effect of forced convection on the boundary layer thickness and copper deposition rate, more studies need to
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be done.
Fig. 15 shows increasing the volumetric flow rate does not affect the oxygen
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volume fraction between the electrodes. 7.5. Effect of change of the distance between the electrodes of the
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electrowinning cell
The distance (D) between electrodes was another important parameter investigated in this simulation. The real distance between electrodes was 42.8 mm and we modelled the flow with another two distances, namely 38 and 34 mm, for electrical current density of 191 A/m2 and volumetric flow rate of 8 m3/hr. Because of these reductions in the distance between electrodes, the length of the electrowinning cell was 86 and 158 mm shorter than that of the real cell, respectively. Fig. 16 shows electrolyte vertical velocity for three distances between electrodes. As one can see from this figure, by decreasing the distance between the electrodes the maximum velocity near the cathode and the anode increases by about 19 and 16% respectively, and in the middle of the cell the electrolyte moves downward with faster velocity.
ACCEPTED MANUSCRIPT Fig. 17 shows the effect of decreasing the distance between electrodes on the gas velocity distribution. This figure indicates that by decreasing the distance the
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maximum velocity near the anode increases and in the middle of the cell gas moves faster downward.
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Figs. 18 and 19 show how changing the distance between electrodes affects the
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concentration distribution between electrodes and the variation of copper concentration at different heights from the bottom of the cathode 5 respectively. By
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decreasing the distance between the electrodes from 42.8 to 34 mm, the copper
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mass concentration decreases by about 0.15%. These little changes in concentration show reducing the distance between the electrodes does not affect the amount of copper deposited on the cathode. The amount of copper entering the
D
area between the electrodes is the product of velocity and area. With reducing the
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distance between the electrodes, the cross-sectional area between the electrodes
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reduces. As a result the velocity of electrolyte increases, but the volumetric flow rate of electrolyte entering the area between the electrodes is probably constant. Therefore, at constant overall flow rate and constant boundary condition for deposition of copper on the cathode, the overall concentration changes is not considerable.
Fig. 20 illustrates how the distance between the electrodes affects the oxygen volume fraction. Since the electrical current density is the same for all the different distances, the generated oxygen for different distances are the same. However, with decreasing distance between the electrodes, oxygen disperses in a smaller volume; therefore, the volume fraction of oxygen increases.
ACCEPTED MANUSCRIPT 8. Conclusions and recommendations In this study, a three-dimensional CFD simulation was applied together with
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experimental field measurements to study the performance of an industrial electrowinning cell in the Sarcheshmeh copper complex, Iran. To validate the
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model, the CFD results were compared by the experimental data. After the
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validation of the model, the effects of different parameters on the performance of the cell were investigated. On increasing electrical current density, from 191 to 300
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A/m2, more copper deposited on the cathode and the electrolyte copper ion
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concentration between the electrodes decreased by about 0.3% (i.e. from 33.49 to 33.4 g/L). Thus, increasing the electrical current density leads to an increase in cell
D
production efficiency, which corresponded with Faraday's Law.
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Increasing the volumetric flow rate from 8 to 11 m3/hr at constant electrical current density, increases the electrolyte vertical velocity at all points between the
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electrodes. On increasing the flow rate, the entering copper ions to the cell increases, so the mass concentration between the electrodes increases. To improve mass transfer to the cathode with increasing flow rate, electrical current density must be also increased. Because as flow rate increases the Nernst boundary layer thickness decreases, this causes the limiting current density to increase. On reducing the distance between the electrodes from 42.8 to 34 mm, the copper mass concentration on the cathode decreases by about 0.15 %. This is due to a decrease in the amount of copper entering to the volume between the electrodes. Decreasing the distance from 42.8 to 38 mm, the copper mass concentration between the electrodes does not change considerably. In this CFD simulation, the effect of forced convection on limiting current density was not investigated. Moreover, in an industrial electrowinning cell, the presence of other ions such as iron affects the copper deposition on the cathode;
ACCEPTED MANUSCRIPT therefore, detailed studies using CFD will be needed to further evaluate the
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performance of an electrowinning cell.
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Acknowledgments
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The authors would like to express their appreciation to the Sarcheshmeh copper complex in allowing them to access the experimental data. Also, reviewers are
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acknowledged for their valuable comments.
ACCEPTED MANUSCRIPT References Al Shakarji, R., He, Y., Gregory, S., 2011. The sizing of oxygen bubbles in copper
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electrowinning, Hydrometallurgy 109, 168-174.
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ANSYS CFX-Solver Theory Guide, Release 12, 2009 ANSYS, Inc.
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ANSYS CFX 12 User's Guide, copyright 1996–2009, ANSYS, Ltd.
Davenport, W.G., King, M., Schlesinger, M., 2002. Extractive metallurgy of copper, fourth ed.
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Elsevier Science Ltd. 327-338.
Filzwieser, A., Hein, K., Hanko, G., 1999. Application of a two phase hydrodynamic modeling
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to an electrowinning cell, Copper 99- Cobre 99, Proc. Of the 4th Intl. Conference Vol. III, Phoenix, Arizona, USA, pp. 695-709. Harlow, F, and P. Nakayama: Transport of Turbulence
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Energy Decay Rate. Report LA-3845, Los Alamos Science Lab, University of California.
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Filzwieser, A., Hein, K., Mori, G., 2002. Current density limitation and diffusion boundary layer
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calculation using computational fluid dynamics, JOM, 54, 28-31. Gamburg, Y.D., Zangari, G., 2011. Theory and Practice of Metal Electrodeposition. Springer Science, New York 1–4.
Hemmati, H., Mohebbi, A., Soltani, A., 2013. CFD modeling of the electrolyte flow in the copper electrorefining cell of Sarcheshmeh copper complex. Hydrometallurgy 139, 54-63. Joy, S., Staley, A., Moats, M., Perkins, C., Uhrie, J., Robinson, T., 2010. Understanding and improvement of electrowinning current efficiency at FMI Bagdad, Proceedings of Copper 2010, 4, 1379-1392. Leahy, M.J., Schwarz, M.P., 2010. Experimental validation of a computational fluid dynamics model of copper electrowinning, Metall and Mater Trans B, 41, 1247-1260. Leahy, M.J., Schwarz, M.P., 2011. Modelling natural convection in copper electrorefining: describing turbulence behavior for industrial sized systems. Metall. Mater. Trans. B, 42, 875– 890. Leahy, M.J., Schwarz, M.P., 2014. Flow and mass transfer modelling for copper electrowinning: development of instabilities along electrodes. Hydrometallurgy 147–148, 41–53.
ACCEPTED MANUSCRIPT Menter, F.R., 1993. Zonal two equation k–ω turbulence models for aerodynamic flows. AIAA 93–2906.
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Nieminen, V., Virtanen, H., Ekman, E., 2010. Copper electrowinning with high current density, Proceedings of Copper, 4, 1545-1557.
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Sadeghi, R., Mohebbi, A., Baniasadi, M., 2011a. CFD modeling of the launder of settler of an
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industrial copper solvent extraction plant: A case study on Sarcheshmeh copper complex, Iran. IJMP 98, 55-65.
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Sadeghi, R., Mohebbi, A., Sarrafi, A., Soltani, A., Salmanzadeh, M., Daneshpojooh, Sh., 2011b. CFD simulation and optimization of the settler of an industrial copper solvent extraction plant: A
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case study, Hydrometallurgy 106, 148-158.
Ziegler, D., Evans, J., 1986. Mathematical modeling of electrolyte circulation in cells with planar
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vertical electrodes, J. Electrochem. Soc, 133, 567–576.
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(a)
(b)
Fig. 1. (a) Electrowinning cell geometry, inlet and outlet geometry and the cathode 1, 2, 3 and 4. (b) Mesh geometry between an anode and a cathode.
33.52 33.515
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33.51 33.505
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33.5
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33.495 33.49
Experimental data
33.485
CFD model
33.48 33.475 0.01
0.02
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Copper mass concentration (g/L)
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Distance from cathode 5 (cm)
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Fig. 2. Comparison of measured copper mass concentration with those predicted by the CFD model.
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1
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0.8
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0.6
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Experimental data CFD model
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0.2
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Height from the bottom of the cathode 5 (m)
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Fig. 3. Comparison of measured copper mass concentration at different heights from the bottom of the cathode with those predicted by the CFD model.
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Anode
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Cathode
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Fig. 4. Velocity vectors between an anode and a cathode.
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At the height of 50cm from the bottom of the cathode At the height of 30cm from the bottom of the cathode
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Electrolyte vertical velocity (cm/s)
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Fig. 5. Electrolyte vertical velocity versus distance from the cathode 5 at different heights.
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Current density 250 (A.m^-2) Current density 300 (A.m^-2)
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Fig. 6. Effect of electrical current density on the copper mass concentration between an anode and a cathode at the middle of the electrowinning cell.
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Current density 191 (A.m^-2) Current density 250 (A.m^-2)
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Fig. 7. Effect of electrical current density on the copper mass concentration between an anode and a cathode in vertical direction.
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Fig. 8. Effect of electrical current density on the electrolyte vertical velocity between an anode and a cathode.
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Fig. 10. Effect of electrical current density on the gas volume fraction between an anode and a cathode.
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flow rate 9.5 (m^3/hr)
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34.95
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Copper mass concentration (g/L) Fig. 14. Effect of volumetric flow rate on the copper mass concentration between an anode and a cathode at different heights from the bottom of the cathode 5.
ACCEPTED MANUSCRIPT
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0.03 0.025
RI
0.02
Volumetric flow rate 9.5 (m^3/hr)
SC
0.015 0.01
Volumetric flow rate 8 (m^3/hr)
Volumetric flow rate 11 (m^3/hr)
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Oxygen volume fraction
0.035
0.005
1 2 3 4 Distance from cathode 5 (cm)
D
0
MA
0
5
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Fig. 15. Effect of volumetric flow rate on gas volume fraction between an anode and a cathode.
ACCEPTED MANUSCRIPT 10.5 9.5
PT RI
7.5 6.5
NU
4.5
3.5 2.5 1.5
1
1.5
TE
-1.5
0.5
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-0.5 0
D
0.5
2
2.5
Current density 191 A/m2 Volumetric flow rate 8 m3/hr
Distance between electrodes 34 mm
SC
5.5
Distance between electrodes 38 mm
MA
Electrolyte vertical velocity (cm/s)
8.5
Distance between electrodes 42.8 mm
3
3.5
4
4.5
Distance from cathode 5 (cm)
Fig. 16. Effect of decrease of the distance between the electrodes on the electrolyte vertical velocity between them.
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PT RI
8
SC
6
2
0
Distance between electrodes 42.8 mm
2
D
1
3
4
5
TE
0 -2
Distance between electrodes 34 mm Distance between electrodes 38 mm
NU
4
Current density 191 A/m2 Volumetric flow rate 8 m3/hr
MA
Gas vertical velocity (cm/s)
10
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Distance from the cathode 5 (cm) Fig. 17. Effect of decrease of the distance between the electrodes on the gas vertical velocity between them.
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PT
33.53 33.52
RI
33.51
33.49
Distance between electrodes 38 mm
NU
33.48 33.47 33.46 33.45 33.44 0.5
1
1.5
2
D
0
2.5
3
Current density 191 A/m2 Volumetric flow rate 8 m3/hr Distance between electrodes 34 mm
SC
33.5
Distance between electrodes 42.8 mm
MA
Copper mass concentration (g/L)
33.54
3.5
4
4.5
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Distance from cathode 5 (cm)
Fig. 18. Effect of decrease of the distance between the electrodes on the copper mass concentration between them.
ACCEPTED MANUSCRIPT
Current density 191 A/m2 Volumetric flow rate 8 m3/hr
RI
PT
0.8
SC
0.6
33.6
D
0.2
0 33.4
Distance between electrodes 34 mm Distance between electrodes 38 mm Distance between electrodes 42.8 mm
MA
NU
0.4
33.8
TE
Height from the bottom of the cathode 5 (m)
1
34
34.2
34.4
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Copper mass concentration (g/L)
Fig. 19. Effect of decrease of the distance between the electrodes on the copper mass concentration between them at different heights from the bottom of the cathode 5.
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0.045 0.04
RI
0.035 0.03
SC
0.025 0.02 0.015
0.01 0 0
1
2
MA
0.005
3
Current density 191 A/m2 Volumetric flow rate 8 m3/hr
Distance between electrodes 34 mm Distance between electrodes 38 mm
NU
Oxygen volume fraction
0.05
Distance between electrodes 42.8 mm
4
5
TE
D
Distance from cathode 5 (cm)
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Fig. 20. Effect of decrease of the distance between the electrodes on the oxygen volume fraction between them.
ACCEPTED MANUSCRIPT
Parameter
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TE
D
MA
NU
SC
RI
Current density (A/m2) Flow rate in inlet (m3/hr) Electrolyte density (kg /m3) Electrolyte kinematic viscosity (m2/s) Dimensions of cathode (height thickness depth) (mm) Dimensions of anode (height thickness depth) (mm)
PT
Table 1 Measured parameters and dimensions of an anode and a cathode in Sarcheshmeh copper complex electrowinning cell.
191 8 1220 1.34e-6 1015 3.2 1052 943 6 920
ACCEPTED MANUSCRIPT Highlights
A three-dimensional CFD simulation for an industrial copper electrowinning cell was
PT
done. The CFD model results were compared with measured data.
A large number of electrodes instead of one pair of electrodes for simulation were used.
The effects of operating parameters such as current density on the performance of the cell
RI
TE
D
MA
NU
The k-ω turbulence flow model was used to calculate liquid velocity profile.
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SC
were studied.