Modelling the Electrolyte Flow in a Full-scale Copper Electrorefining Tankhouse Cell

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1 Modelling the Eletrolyte Flow in Full-sle Copper Eletrorefining Tnkhouse Cell Andres Kemminger, Andres Ludwig Montnuniversitet Leoben Deprtment Metllurgy, Chir of Simultion nd Modelling of Metllurgil Proesses Leoben, Austri Keywords: Hydrometllurgy, eletrolysis, CFD simultion, opper Abstrt A omputtionl fluid dynmi simultion of the eletrolyte flow in full-sle opper eletrorefining tnkhouse ell hd been performed. The dissolution of opper ions t the impure nodes nd their plting onto the thodes leds to lol density vrition long the eletrodes nd thus to buoyny-driven flow between nodes nd thodes. Corresponding Cu ++ onentrtion fields together with the resulting nturl onvetion pttern were simulted by mens of lol simultion. As the predited onentrtion nd veloity fields within the gps were minly independent of globl flow phenomen, representtive results were used s inlet informtion for 120 interfes tht link the lol simultion to globl simultion. With suh hybrid-pproh it ws possible to simulte both smll-sle flow phenomen between the eletrodes nd lrge-sle flow phenomen in the full-sle industril tnkhouse ell. The results suggest tht fresh eletrolyte is first pushed down by the flow leving the eletrode gps, nd then guided to the side of the tnkhouse ell from where it is suked into the upper prt of the eletrode gps. 1 Introdution The opper refining eletrolysis proess is essentil to produe high purity opper t industril sle. High purity opper is needed in eletril pplitions like ondutors, where high eletri ondutivity is neessry [1]. The fundmentl steps of opper refining re: 1. eletrohemil dissolving opper from impure nodes into CuSO 4 -H 2 SO 4 -H 2 O eletrolyte; 2. eletrohemil plting pure opper (without the node impurities) from the eletrolyte onto stinless steel opper thodes. The min purpose is not only to produe pure opper tht is essentilly free of hrmful impurities but lso to seprte vluble impurities (e. g. gold nd silver) from the nodi opper for lter reovery [2]. Proeedings of EMC

2 Kemminger, Ludwig 2 Numeril model A numeril lultion of fluid flow or het flow is only possible if the physil lws n be trnsformed into mthemtil equtions, normlly into differentil equtions. Eh single differentil eqution is linked to ertin onservtion lw nd onsists of one physil vlue s depended vrible. It is ssumed tht the different ftors influening the physil vlue re in equilibrium. The dependent vrible of these differentil equtions re used s speifi vlue, whih mens tht it is lulted for one ontrol volume. Exmples re the veloity (momentum per ontrol volume), mss nd speifi enthlpy/energy [3]. With the ontinuity eqution (1) nd the momentum onservtion eqution (2) the flow of the eletrolyte nd with the speies onservtion eqution (3) the vrition in Cu ++ tions onentrtion ws lulted. t t t v 0 (2) v vv p g F (3) v D Q In the formul is the density of the eletrolyte, p the stti pressure, the stress tensor nd g nd F re the grvittionl body fore nd externl body fores tht rise from dissolving nd plting of opper s used by Lehy [4]. The externl body fore given by eqution (4) represents boussinesq pproximtion [5]. By using this pproh the density n be onsidered onstnt in the onservtion equtions (1) nd (2). D is the diffusion oeffiient. The quntity (1) Q represents the rte of dissolution nd plting of the Cu ++ tions. The dissolution hppens t the node where the opper tions enter the numeril domin. Ctions re trnsported to the thode by diffusion nd onvetion where they re plted i.e. tken out of the numeril domin. Therefore, Q hs positive vlue on the node nd negtive vlue t the thode. In the rest of the numeril domin it is set to zero. As shown in eqution (5), F g 0 Q is governed by the urrent density j. j mcu with ( ) on thode nd (-) on node Q z F (5) 0 elsewhere The urrent density is lulted only t the surfe of every thode nd node by using the Butler- Volmer eqution [6] s shown in eqution (6). (4) 796 Proeedings of EMC 2013

3 Modelling the Eletrolyte Flow in Copper Eletrorefining Cell j j z F exp( R T ) j z F exp( R 0 T ) (6) The equtions re losed with set of model prmeters, given in Tble 1. The CFD model is set up within the ANSYS Fluent 14.5 frmework [7]. Tble 1: Model prmeters Prmeter Vlue Unit density 1220 kg m -3 0 initil Copper onentrtion 45.5 kg m -3 solutl expnsion oeffiient m³ kg -1 D diffusion oeffiient kg m -1 s -1 m Cu molr mss of Cu kg mol -1 z Current number (No. of eletrons per Cu ++ tion) 2 - F Frdy onstnt C mol -1, nodi, thodi trnsfer oeffiient 0.6, 0.4 -, nodi; thodi overpotentil 0.01, 0.08 V T eletrolyte temperture K j, j nodi, thodi exhnge urrent 258 A m -2 3 Simultion strtegy nd problem desription The simultion of opper eletrolysis hs been the topi of number of reserh ppers. While most frequently the nturl onvetion is simulted in smll-sle test domins ([6], [8], [9] nd [10]) or in lrge-sle 2D domins ([11] nd [12]), this pper tkles the simultion of the flow pttern used by the intertion of nturl nd fored onvetion in full-sle opper eletrorefining tnkhouse ell. Industril tnkhouse ells n reh n overll length of severl meters. They usully onsist of up to 60 thodes nd 61 nodes. Sine the nturl onvetion is bsed on onentrtion vrition in the viinity of the eletrodes, the numeril grid must be very fine in these res in order to hieve suffiient urte solution. On the other hnd, the lrge size of n industril eletrolysis tnkhouse ell (see Figure 1) would mke more thn billion numeril volume elements neessry nd thus, onsidering the tody s omputer tehnology, simultneous lultion of nturl nd fored Proeedings of EMC

4 Kemminger, Ludwig onvetion in full-sle simultion domin is unprtil, if not impossible. Therefore, the simultion hd to be seprted into two steps. First, the flow of the eletrolyte used by nturl onvetion in typil node-thode gp ws simulted with so-lled lol simultion. Here, very fine meshing of the numeri grid t the node nd thode ws pplied in order to get suffiient resolution of the solutl nd momentum boundry lyers (see Figure 2). The simultion of the fored onvetion is then done s so-lled globl simultion, where the simultion domin onsisted of the whole tnkhouse ell prt from the gps between nodes nd thodes. These were bloked off in order to keep the size of the numeri grid t mintinble level. The link between the lol simultion of nturl onvetion between the eletrodes nd the globl simultion of the fore onvetion in the full-sle tnkhouse ell ws done by introduing series of interfes llowing the trnsfer of veloity- nd onentrtion profiles from the lol to the globl simultion (see Figure 3). Figure 1: Geometry of n industril used tnkhouse ell with the lternting ssembly of nodes nd thodes. Figure 2: The lol simultion domin overed the re between two thodes. Beuse of the symmetry only hlf of the domin ws modelled. A very fine mesh ws used in order to get n dequte solution of onentrtion- nd veloity grdients t the eletrodes. The veloity- nd opper profiles t the interfes defined to link lol nd globl simultion re lter used s inlet informtion for the globl simultion. 798 Proeedings of EMC 2013

5 Modelling the Eletrolyte Flow in Copper Eletrorefining Cell Figure 3: The globl simultion domin overed the whole tnkhouse ell exept for the gps between nodes nd thodes. Here, interfes were defined with whih the dynmi of the nturl onvetion ourring between the eletrodes were trnsferred from the lol to the globl simultion. 4 Simultion results 4.1 Lol simultion In order to study the nturl onvetion ourring long the eletrodes so-lled lol simultion of the Cu ++ onentrtion nd the 3D veloity field between the eletrodes were done. The lol simultion domin inluded one node nd two thodes (with the tthed edge strips). The geometry for the detiled thode-thode simultion is shown in Figure 2. To hieve better solution of the onentrtion nd veloity boundry lyers the size of the volume elements t the eletrodes ws set to 500 µm. To derese the totl number of volume elements in the domin nd therefore derese the omputtion time, only hlf of the symmetri node-thode pir ws simulted. A trnsient simultion ws performed until stedy-stte veloity profile t the interfes mentioned in the lst setion were found. The boundry onditions for the flux of opper t the node nd thode ws bsed on the Frdy lw s given by eqution (5). A positive flux is pplied on the node nd negtive flux on the thode. At the wlls no slip boundry onditions re pplied while on the free top surfe no frition boundry ondition ws pplied. The eletrohemil retions use the dissolution of Cu ++ tions t the node nd their deposition t the thode. Therefore, grdient of onentrtion forms between the eletrodes. Figure 4 shows detiled view of the Cu ++ onentrtion in the node-thode gp t different heights. Proeedings of EMC

6 Kemminger, Ludwig () (b) () (d) Figure 4: Conentrtion distribution in the gp between thode (left) nd node (right) () 60 mm bove the lower end of the node, (b) 500 mm, () 1000 mm nd (d) digrm plot of Cu ++ onentrtion profile ross the gp. Note tht (), (b) nd () hd to be sled by ftor of 4 to better visulize the onentrtion distribution. This onentrtion grdient leds to onvetive eletrolyte flux s shown in Figure 5. The low density in front of the thode uses n upwrd movement while the higher density t the node leds to downwrd movement of the eletrolyte. The veloity of the eletrolyte hnges with height. At the top of the node only smll mount of Cu ++ hs been dded to the eletrolyte lredy nd the downwrd movement is very slow. While moving downwrd long the node more Cu ++ is dded to the eletrolyte using stronger buoyny fore nd fster movement. Therefore, the highest downwrd veloity n be found t the bottom of the node where lso the onentrtion of Cu ++ rehes its highest numbers. At the thode the opposite mehnism hppens. () (b) () (d) Figure 5: Veloity vetors in the gp () 60 mm bove the lower end of the node, (b) 500 mm, () 1000 mm nd (d) digrm plot of vertil veloity over the gp width. Note tht (), (b) nd () hd to be sled by ftor of 4 to better visulize the results. Figure 6 shows the opper onentrtion diretly in front of the node nd thode. Clerly visible is the stking of lyers with different onentrtions. The downwrd movement of eletrolyte t 800 Proeedings of EMC 2013

7 Modelling the Eletrolyte Flow in Copper Eletrorefining Cell the node trnsports the tions to the lower prt of the node. While moving, more nd more tions re loded into the eletrolyte resulting in high onentrtion t the bottom prt of the node. The opposite n be seen t the thode. While moving upwrd, more tions re removed from the eletrolyte leding to low onentrtion of Cu ++ t the top. () (b) Figure 6: Cu ++ onentrtion in kg m -3 djent to the thode (), nd djent to the node (b). () (b) Figure 7: Veloity profile t the interfe linking lol nd globl simultions in m s -1 () the integrl of the mss flow equls zero nd thus the mss is onserved long the interfe, (b) Detiled view of the interfe t the bottom; the downwrd movement long the node is stronger thn the upwrd movement t the thode. Proeedings of EMC

8 Kemminger, Ludwig We hve performed severl lol simultions by ssuming different in- nd outlet onditions t the front nd bk fes of the domin. It turned out tht the flow between the eletrodes ws only little influened by the in- nd outlet onditions, espeilly for the flow t some distne from the edges of the eletrodes. Thus, the flow field t the interfe linking lol nd globl simultions, shown in Figure 7, seems to be universl one, whih minly depends on the phenomen hppening between the node nd thode, nd whih is mrginlly ffeted by the globl flow. Although it seems tht the downwrd movement t the node domintes the flow, the totl mss rossing the interfe is zero. Veloity profiles s the ones shown in Figure 7 were tken s inlet profiles for the globl simultions t the 120 interfes linking lol nd globl simultions. 4.2 Globl Simultion With the globl simultion the flow field in the whole tnkhouse ell governed by both fore onvetion vi n in- nd outlet nd nturl onvetion vi the 120 gp inlets were estimted. As mentioned bove, the veloity profiles gined from the lol simultion were used t these inlets. The orresponding interfes linking globl nd lol simultions were loted 50 mm bove the lower end of the nodes. This position ws hosen beuse numerous simultion trils showed tht the flow between the eletrodes were negligibly ffeted by ny globl flow detils. Therefore, the ssumed one-wy oupling between the lol nd globl simultion is justified nd the sme veloity profiles n be used for ll node-thode gp inlets. Figure 8 shows the input vlues for the gp interfes gined by the lol simultion. The fored onvetion used by the pumping of fresh eletrolyte in nd out of the tnkhouse ell forms free jet t the inlet. This free jet interts with the nturl onvetion from between the node-thode gps nd is thus pushed down, see Figure 8b) nd 9. The flow ptterns underneth the eletrodes re shown in Figure 10 in detils. It n be seen tht the eletrolyte flows from the bottom to the side of the tnkhouse ell, where it moves up nd is then drwn into the upper prt of the gp between the eletrodes. 802 Proeedings of EMC 2013

9 Modelling the Eletrolyte Flow in Copper Eletrorefining Cell () b) Figure 8: () Veloity profile gined from the lol simultion nd used s boundry onditions for the globl simultion t the 120 gp interfes, nd (b) the fresh eletrolyte jet strem from the inlet of the tnkhouse ell interts with the nturl onvetion from the nodethode gps (veloity vetors in m s -1 ). Figure 9: Contour plots (in m s -1 ) of the globl flow field plotted on different plnes in the tnkhouse ell. High veloities n be found in the bulk re underneth the eletrodes lose to the inlet s well s between the eletrodes nd the outer wlls. Proeedings of EMC

10 Kemminger, Ludwig () (b) () Figure 10: Veloity vetors (in m s -1 ) t three plnes in the tnkhouse ell () t the first nodethode gp, (b) t the 5th node-thode gp, () t the 10th node-thode gp. The dotted line shows the position of the interfe used to link lol nd globl simultions. Besides to some disturbnes t the first gp, the eletrolyte moves from the bottom of the eletrodes to the sides, where it is drwn into the upper prt of the gp between the eletrodes. 5 Conlusion The presented simultion pproh enbles the CFD simultion of full sle opper eletrorefining tnkhouse ell inluding the nturl onvetion in between two representtive node-thode gps. The density hnges tht re responsible for the ourring onvetive eletrolyte movement re tking ple just in front of the node nd thode surfes. Due to the size differene between orresponding boundry lyers nd the dimensions of industril opper eletrorefining tnkhouse ells, diret numeril simultion ombining nturl nd fored onvetion in one singe simultion is priniplly oneivble but beuse of vilble hrdwre power still impossible. These limittions n be overome by seprting the simultion into two distintive steps. First, the eletrolyte flow used by nturl onvetion in the gp between the eletrodes n be modelled with lol simultion using very fine numeril grid. In seond step globl simultion n be pplied to simulte the intertion of nturl nd fored onvetion in the full-sle industril tnkhouse ell. The present results show tht (i) the flow in the gp between the eletrode is minly governed by nturl onvetion used by density hnges of the eletrolyte, nd (ii) the inlet jet into the full- 804 Proeedings of EMC 2013

11 Modelling the Eletrolyte Flow in Copper Eletrorefining Cell sle tnkhouse ell is pushed downwrds by the flow from the rry of eletrode gps nd then guided to the tnkhouse ell sides from where it is drwn into the eletrode gps. The lst finding suggests tht fresh inhibitor generlly enters the eletrode gps from upper side res. Further studies inluding experimentl verifitions re required to understnd the influene of fresh eletrolyte intke on the distribution of these surfe tive gents in more detils. Referenes [1] DAVENPORT W.G., M. KING, M. SCHLESINGER AND A.K. BISWAS, Extrtive Metllurgy of Copper, 4 th edition, Pergmon publishing (2002), 265. [2] PAWLEK F., Metllhüttenkunde, Wlter de Gruyter, Berlin - New York, (1983), [3] PATANKAR S.V, Numeril Het Trnsfer nd Fluid Flow, Series in Computtionl Methods in Mehnis nd Therml Sienes, Hemisphere Publishing Corportion, (1980), [4] LEAHY M.J. & P. SCHWARTZ, Experimentl vlidtion of omputtionl fluid dynmis model of opper eletrowinning, Metllurgil nd Mterils Trnstions B 41, (2010) No. 6, [5] PLAWSKY J., Trnsport Phenomen Fundmentls, 2 nd Edition, CRC Press Tylor nd Frnis Group, (2010), [6] DOCHE O., F. BAUER & S. TARDU, Diret simultion of n eletrolyte deposition under turbulent flow A first pproh, Journl of Eletrohemil Chemistry 664 (2012), 1-6. [7] ANSYS, FLUENT 14.5, ANSYS In., Cnonsburg, USA, (2012), website [8] KONISHI Y., Y. TANAKA, Y. KONDO & Y. FUKUNAKA, Copper dissolution phenomen long vertil plne node in CuSO4 solution, Eletrohemi At 46 (2000), [9] KAWAI S., K. NISHIKAWA, Y. FUKUNAKA, S. KIDA, Numeril simultion of trnsient nturl onvetion indued by eletrohemil retions onfined between vertil plne Cu eletrodes, Eletrohemi At 53 (2007), [10] XUEGENG Y., K. ECKERT, K. SEIDEL & M. UHLEMANN, The strtup of nturl onvetion during opper eletrolysis in the presene of n opposing Lorentz fore, Eletrohemi At 54 (2008), [11] LEAHY, M.J. & P. SCHWARZ, Modelling nturl onvetion in opper eletrorefining: Desribing turbulene behviour for industril-sized-systems, Metllurgil nd Mterils Trnstion B 42 (2011), [12] FILZWIESER, A., A. LACKNER & K. HEIN, Möglihkeiten zur Strömungsberehnng in Elektrolysezellen unter besonderer Berüksihtigung des Stofftrnsportes, Heft 81 der Shriftreihe der GDMB (1998), Proeedings of EMC

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