MODELLING HEAT TRANSFER IN THE DRIPPER ZONE OF A HEAP LEACHING OPERATION

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1 Fifth Interntionl Conference on CFD in the Process Industries CSIRO, Melbourne, Austrli December 006 MODELLING HEAT TRANSFER IN THE DRIPPER ZONE OF A HEAP LEACHING OPERATION Simon C. T. TRANG, Drrin W. STEPHENS nd M. Philip SCHWARZ CSIRO Minerls, Clyton, Victori 3169, AUSTRALIA ABSTRACT A computtionl fluid dynmics (CFD) solver ANSYS- CFX is used to model the het trnsfer in the region ner the surfce of lech hep when drippers re buried. The potentil for nturl convection to occur bove the dripper level, thus substntilly incresing het loss from the hep, is investigted. A prmeter nlysis is performed which shows tht the fctors tht my be importnt to the initition of nturl convection re permebility, the depth t which the drippers re buried nd the spce between ech dripper. The current study shows tht permebility is the only prmeter which hs profound effect on het loss by nturl convection. NOMENCLATURE b dripper spcing, (m) B body force vector, (N/m 3 ) C 1 het trnsfer coefficient between hep surfce nd top ir, (W/m 3 ) C het trnsfer coefficient between ir nd the mteril surrounding the dripper, (W/m 3 ) d hep prticle size, (m) g grvittionl constnt vector, (m/s ) h sttic enthlpy, (J/kg/s) H dripper buried depth, (m) k eff effective therml conductivity, (W/m/K) K bed permebility, (m ) Nu Nusselt number for ir/prticle inter-phse het trnsfer, (-) p ir pressure, (N/m ) q comb het flux loss due to the combintion of nturl convection nd conduction, (W/m ) R resistivity due to porous medi, (kg/m 3 /s) S source or sink of energy, (W/m 3 ) S drip source vlue t ech dripper, (W/m 3 ) S top source vlue bove the hep surfce, (W/m 3 ) T ir temperture, (K) T drip cid solution feed temperture, (K) T top fixed temperture bove the hep surfce, (K) T 0 buoyncy reference temperture, (K) u ir velocity vector, (m/s) (x, z) two-dimensionl sptil coordinte system, (m) α volume frction of hep prticles (1- ε), (-) γ therml expnsion coefficient of ir, (1/K) ε bed porosity, (-) λ ir therml conductivity, (W/m/K) dynmic ir viscosity, (kg/m/s) μ ρ ir density, (kg/m 3 ) ρ,0 ir density t tmospheric conditions, (kg/m 3 ) INTRODUCTION Hep leching is ppeling for processing low-grde metl bering ores (both sulphides nd oxides) due to its low cpitl nd opertion costs. However there re still spects of the process tht need to be improved, for exmple the recovery nd leching rte for chlcopyrite, nd cid consumption in the leching of nickel lterites. Therml blnce within the hep is thought to be criticl to mny of the issues fcing opertors of hep leching. Some believe tht bio-leching rtes of sulphide ores might be enhnced by incresing the temperture within the hep, nd work hs been crried out to investigte the use of thermophiles nd moderte thermophiles (Petersen nd Dixon, 00). On the other hnd, work by Lehy et l (Lehy et l, 005 & 006) suggests tht one of the mechnisms limiting the bio-leching rte is overheting within the hep. In the cse of nickel lterites, the het of rection is quite smll, so tht if one wishes to mintin the hep temperture t level significntly higher thn mbient, het loss of hep should be minimised. The solution used for leching is typiclly fed to the hep vi drippers which re lid on the surfce of the hep or buried smll distnce below the surfce. If the solution is t mbient temperture, its ppliction is mjor fctor in cooling the hep (Dixon, 000), wheres if the hep is being heted by solution t temperture bove mbient, het loss t the top of the hep my be significnt, which my be driver for burying the drippers. Drippers my lso be buried to reduce evportion. Suppression of het loss nd evportion by buril of drippers could be compromised if nturl convection cells form in the region bove the drippers, becuse these could substntilly increse the het nd mss trnsfer from the dripper level to the surfce of the hep. In this pper we investigte the loss of het from hep in sitution where the drippers re buried beneth the surfce, nd, for simplicity, where no ir is sprged from the bottom of the hep. To do this we simulte the region between the surfce nd the buried drippers, which will herefter be referred to s the dripper zone. Previous models of hep nd dump leching/bioleching, nd cid mine dringe hve ttempted to tret the whole depth of the bed, with pproximte, lbeit resonble, submodels to tret the detiled mechnisms occurring in vrious zones within the hep. The models hve ccounted for het nd mss trnsfer occurring in three phse system consisting of the ore prticles in the hep, cid solution nd ir (Css et l., 1998; Lehy et l., 003; Pntelis nd Ritchie, 199; Dixon nd Hendrix, 1993; Brtlett nd Prisbrey, 1996; Lu nd Zhng, 1997). A more comprehensive review of the current stte of hep leching 1

2 models reported in literture ws given by Dixon (003) nd Lehy (006). To the uthors knowledge, none of the models mentioned bove hs included study of the detiled het trnsfer mechnisms in the dripper zone. The im of this work therefore is n ttempt to fill the gp in the literture by developing preliminry twodimensionl (-D) CFD model for simulting the het trnsfer in the dripper zone. Het trnsfer in the dripper zone is very complex process in tht het loss cn be due to forced convection, nturl convection or conduction or combintion of ll three. There will be temperture grdients both within the hep bed nd the ir lyer flowing over the bed. A multi-dimensionl CFD model is required to investigte these issues. The CFD model will lso be ble to investigte the effect of bed permebility, the depth t which the drippers re buried (herefter referred to dripper buried depth) nd the distnce between ech dripper (herefter referred to dripper spcing) on the het trnsfer in the surfce ner the hep. MODEL DESCRIPTION Assumptions The geometry used for simulting the dripper spce is two-dimensionl porous medium of rectngulr shpe s shown in Figure 1 with the hep shown in bold nd the extent of the computtionl domin shown by the dshed line. The following key ssumptions hve been mde in conducting the CFD simultion: The hep is ssumed to be two-dimensionl: it is likely tht the distnce between holes long the dripper lines is much less tht the spcing between dripper lines (i.e. dripper spcing); Flow field symmetry hs been ssumed: just hlf of the zone between drippers is simulted; Permebility nd porosity re ssumed to be uniform through the hep bed; The het loss due to wter evportion ws neglected in the current study; Conductive het trnsfer through the bed mteril ws neglected; hence the simultion cn be treted s single phse gs flow through porous medi; It ws ssumed tht there is no irflow cross the top of the hep t this stge. Figure 1: Schemtic Hep Dripper Zone Air flow The stedy stte ir flow occurring in the porous hep cn be described by the eqution of continuity nd the stedy stte Nvier-Stokes equtions s below: u = 0 (1) ρ ( uu) = p + μ u + B () where p, u, B, μ nd ρ re the pressure, velocity, body forces, ir viscosity nd density respectively. The body force B ccounts for the Drcy resistnce to flow in the porous medium nd grvity by tking the form B = Ru + ρ g (3) where g is the grvittionl vector nd R is the porous resistivity (Al-Khlift nd Arstoopour, 1997) given by εμ R = (4) K Here ε nd K re the porosity nd permebility of the hep respectively. The buoyncy effect induced by the ir density ρ vrition due to differences in the ir temperture is incorported into the model using the Boussinesq pproximtion. In the body force term for ρ in eqution (3), the ir density is tken to be ρ = ρ, ( 1 γ ( T T )) (5) 0 0 where γ is the therml expnsion coefficient of ir, ρ,0 is constnt nd equl to the ir density t the tmospheric conditions, nd T 0 is the buoyncy reference temperture. The density on the left hnd side of eqution () is set equl to the tmospheric vlue so tht the momentum eqution is given by ρ ( uu) = p + μ u,0 Energy blnce εμ u + ρ,0 (1 γ( T T )) g 0 K The temperture is described by the stedy stte het eqution given by ρ ( u h) = λ T + S (7) where h is the sttic enthlpy, λ is the therml conductivity of ir nd S represents sources or sinks of energy. Boundry Conditions The conditions imposed t the boundries of the computtionl domin (see Figure 1) re s follows: u( x,0 ) T( x,0) = 0, = 0 (8) u( xb, ) T( xb, ) = 0, = 0 (9) u( H, z) T( H, z) = 0, = 0 (10) p 0, z = 1tm for 0 z b (11) ( ) (6)

3 A source/sink of energy ws used in the region bove the hep surfce to mimic fixed temperture boundry condition for the ir (Lu nd Zhng, 1997). The source term pplied in eqution (7) ws evluted using the following expression Stop = C1( T Ttop ) (1) where T is the locl ir temperture, T top is the required fixed temperture (ssumed to be 0 C) nd C 1 is constnt with vlue set lrge enough to ensure the locl ir temperture chieves the desired fixed temperture. A typicl vlue for C 1 ws 1000 W m -3 K -1. The effect of the hot liquid t ech dripper ws included s point source in eqution (7) with the source vlue being given by Sdrip = C ( T Tdrip ) (13) where T drip is the cid solution feed temperture (ssumed to be 60 C) nd C is het trnsfer coefficient between the ir nd the mterils (ore prticles nd liquid) surrounding the dripper. The coefficient C is estimted by nlogy with interphse het trnsfer in multi-phse prticle model nd its vlue cn be determined by (ANSYS, 005) 6λ Nu α C = (14) d where Nu is the Nusselt number for ir/prticle interphse het trnsfer nd ws ssumed to be.0 in this study bsed on the expected lminr flow within the hep (ANSYS, 005); α is volume frction of hep prticles (1- ε) nd d is the hep prticle size ssumed to be 1 cm in this study bsed on dt reported in literture (Bouffrd, 005). NUMERICAL METHOD The stedy stte equtions (1)-(7) were solved using ANSYS CFX 10. A -D extruded mesh consisting of prisms nd hexhedrons ws used for ll simultions. A mesh independence study ws conducted for one of the simultion configurtions nd the mesh spcings required for mesh independent solution were determined. This mesh spcing ws used on ll subsequent simultions. The results were ssumed converged when the normlized residuls for ll vribles were less thn As ANSYS-CFX uses flse time-stepping method when solving stedy stte problems different flse timesteps were used to solve the momentum nd energy equtions. RESULTS The key prmeters used in the CFD simultion re shown in Tble 1. In order to simplify the nlysis, wll boundry condition ws imposed t the hep level where the drippers re buried. The totl het loss hence is not n pproprite prmeter to quntify the enhncement of het trnsfer due to nturl convection. keff / λ Hep porosity 3 3 ε = 0.3 m /m Hep permebility 10 K = 1 10 m (bse cse) Air density 3 ρ = kg/m Air viscosity 5 μ = kg/m/s Air conductivity Prticle dimeter λ = W/m/K d = 1 [cm] Tble 1: Prmeters for the CFD simultions The quntity of het loss due to the combintion of nturl convection nd conduction cn be expressed indirectly vi n effective therml conductivity k eff which is derived ΔT from qcomb = keff where H is the depth of the dripper, H ΔT is the verge temperture difference between the hep surfce nd the dripper depth nd q comb is net het flux leving the hep surfce. A rtio of to λ which keff is the therml conductivity for the het loss due to pure conduction should give n indiction of the enhncement of het trnsfer provided by nturl convection. This rtio will be used to investigte the effects of dripper spcing, dripper buried depth nd hep permebility on the het trnsfer in the dripper spce throughout the results section. The effect of the dripper spcing on the nturl convective het trnsfer for the bse cse (K=10-10 m ) is shown in Figure. From Figure it cn be seen tht the rte of het trnsfer enhncement by nturl convection does increse slightly s the dripper spcing increses from 0.3 to 1 m per dripper, nd remins reltively constnt s the dripper spcing increses further. Nevertheless, over the whole rnge of dripper spcing investigted (from 0.3m to 3m per dripper), the enhncement on het trnsfer provided by nturl convection is very smll, less thn 1%. The effect of dripper buried depth on het trnsfer enhncement for the bse cse (K=10-10 m ) is shown in Figure 3. Over the rnge dripper buried depth investigted (from 0.3 m to 1.5 m), the het trnsfer enhncement offered by the nturl convection is negligible Dripper spcing (m per dripper) Figure : Effect of dripper spcing on het trnsfer enhncement, H = 0.3m, K = m 3

4 keff / λ Dripper buried depth (m ) Figure 3: Effect of dripper buried depth on het trnsfer enhncement, b = 0.7m/dripper, K = m The bove observtions re somewht t odds with the expecttion tht the strength of nturl convection should vry with the rtio of dripper buried depth to dripper spcing. One possible explntion is tht the resistivity of the hep bed my substntilly dmpen the formtion of nturl convection cells within the hep. To test this, the effect of dripper spcing nd dripper buried depth hve been determined for two lrger vlues of K (1 nd orders of mgnitude lrger respectively). The flow fields for the three K vlues re shown in Figures 4, 5 nd 6. From these figures, it cn be seen tht the strength of the nturl convection flow intensifies drmticlly t K = 10-8 m. keff / λ Figure 6: Flow field (m/s) for K = 1e-8 m The effects of vrious vlues of K on k eff /λ over rnge of dripper spcing nd dripper buried depth re shown in Figures 7 nd 8 respectively Dripper spcing (m per dripper) K=1e-10 K=1e-9 K=1e-8 Figure 7: Effect of dripper spcing on het trnsfer enhncement for vrious K, H = 0.3m Figure 4: Flow field (m/s) for K = m Figure 5: Flow field (m/s) for K = 10-9 m keff/ λ Dripper buried depth (m ) K=1e-10 K=1e-9 K=1e-8 Figure 8: Effect of dripper buried depth on het trnsfer enhncement for vrious K, b = 0.7 m / dripper From Figures 7 nd 8, it cn be seen tht t K = 10-9 m, the effect of the dripper spcing on the het trnsfer enhncement becomes noticeble. The effect of the dripper buried depth however is less obvious. As K increses further to 10-8 m, the effect of both dripper spcing nd dripper buried depth chnge drmticlly. The pronounced effect of permebility on the nturl convection flow is consistent with findings reported in the literture (Lehy et l, 003, Lu nd Zhng, 1997). From Figure 7, it cn be seen tht t K = 10-8 m, s dripper spcing increses from 0.3 to 1.5 m per dripper, the het trnsfer enhncement by nturl convection increses from bout 3% to 60%. As with K = m, the het trnsfer is not enhnced ny further with increse of dripper spcing beyond 1.5 m. The dependence on the strength of nturl convection with dripper spcing nd depth is understndble: it is well known from the nturl 4

5 convection literture tht there re preferred spect rtios for nturl convection cells. The effect of dripper buried depth for K = 10-8 m is shown in Figure 8. From Figure 8, it cn be seen tht s dripper buried depth increses from 0.3 m to 1 m, the het trnsfer enhncement by nturl convection decreses substntilly from bout 35% to 8%. After tht, the decrese of the het trnsfer enhncement becomes moderte with further increse of dripper buried depth. The trend shown in Figure 8 is consistent with the trend shown in Figure 7, i.e, for given het source, the strength of nturl convection increse with the decrese of the dripper spce spect rtio. Permebility is n intrinsic function of the porous medi nd is expected to depend on prmeters such s rock prticle size nd porosity. By ssuming lminr flow in the pore spce (so tht the Hgen-Poiseuille eqution cn be pplied), n eqution for clculting permebility for n ssemblge of uniform spheres s function of porosity, rock prticle size nd tortuosity cn be derived theoreticlly from Drcy s lw (Lke, 1989): 3 ε d K = (15) 7τ (1 ε) Eqution (15) is known s the Crmn-Kezeny eqution where τ, the tortuosity is defined s the squred rtio of the men flow pth length to the prticle size. Tortuosity is n indictor of the geometry of prticles nd pore chnnels. The vlue of τ is lwys greter thn 1 nd cn be greter thn 10, with generl verge vlue of 3.3 (Slem nd Chilingrin, 000). For n ssemblge of regulrly pcked spheres the vlue is.08 (Lke, 1989). Relible mesurements of ore hep permebilities re rrely vilble t operting mines. The permebility for the bse cse (K = m ) ws estimted from vlues widely reported in the literture (Css et l., 1998; Lehy et l., 003, Pntelis nd Ritchie, 199; Lu nd Zhng, 1997, Brtlett, 1998). Brtlett (1998) reported tht even though eqution (15) is vlid for uniform size porous medi but cn still be used to estimte the intrinsic permebility if the prmeter d in eqution (15) is n effective prticle dimeter, which is chosen to be the lrgest prticle dimeter of the 10% cumultive pssing, d 10, nd with n effective prticle dimeter of bout 1.5 mm, τ = nd porosity of 0.07 to 0.5, the permebility estimted from eqution (15) rnges from to 10-9 m. It is of interest to investigte wht effective prticle dimeters nd porosities will yield permebility of the order of 10-8 m. Tble shows vrious permebilities clculted from eqution (15) for effective prticle dimeter rnges from 1 mm to 0 mm nd porosity from 0.3 to 0.5. Most hep construction prctices usully end up with mny fine prticles. It is therefore tht the effective prticle dimeter of most of these heps my not exceed 5 mm. The clcultions presented in Tble show tht for size distributions with effective prticle dimeter lrger thn 5 mm, it is possible tht enhnced het (nd mss trnsfer) through nturl convection could occur bove buried drippers. If it is desired to suppress this effect, lower permebility lyer could be dded bove the drippers. ε Effective K prticle dimeter (m) (m ) E E E E E E E E E E E E E E E-06 Tble. Permebility estimted from Crmen-Kozeny eqution. CONCLUSION A CFD model hs been developed to investigte the het trnsfer in the dripper zone of hep leching. It ws found tht for the permebility of hep bed reported in literture, the nturl convection flow is very wek nd the het trnsfer in the dripper zone is dominted by conduction over the rnge of dripper spcing nd dripper buried depth investigted. ACKNOWLEDGEMENTS The uthors would like to cknowledge the help of Mrtin Lehy in discussing vrious spects of hep leching modeling, nd Peter Witt on severl issues in setting nd running ANSYS-CFX. REFERENCES AL-KHLAIFAT, A. nd ARASTOOPOUR, H., (1993), Simultion of two-phse flow through low-permebility porous medi, AEA technology interntionl user conference 97. ANSYS Inc (005). ANSYS-CFX Version 10.0 Documenttion. Pittsburgh, Pennsylvni, United Sttes of Americ BARTLETT, R. W., (1998), Solution mixing, leching nd fluid recovery of mterils, nd ed., Gordon nd Brech Science Publishers,, BARTLETT, R.W. nd PRISBREY, K.A., (1996), Convection nd diffusion limited ertion during bioxidtion of shllow ore heps, Int. J. Miner. Process., 47, BOUFFARD, S.V., (005), Review of gglomertion prctice nd fundmentls in hep leching, Minerls processing & Extrctive Metll. Rev., 6: CASAS, J.M., MARTINEZ, L. MORENO, L. nd VARGAS, T., (1988), Bioleching model of coppersulfide ore bed in hep nd dump configurtions, Met. Mt. Trns., 9B, Aug. 1988, τ 5

6 DIXON, D.G. nd HENDRIX, J.L., (1993), A generl model for leching of one or more solid rectnts from porous ore prticles, Met. Mt. Trns., B, Feb. 1993, DIXON, D.G., (000), Anlysis of het conservtion during copper sulphide hep leching, Hydrometllurgy, 58, 000, LAKE, L. W., 1998, Enhnced oil recovery, Prentice Hll, Englewood Cliffs, 1998, LEAHY, M.J., (006), Temperture nd ir flow effects in the modelling of bcteri in hep bioleching of chlcocite, PhD Thesis, University of Melbourne, 006. LEAHY, M.J., SCHWARZ, M.P. nd DAVIDSON, M.R., (003), An ir sprging CFD model for hep bioleching of copper-sulphide, 3 rd Interntionl Conference on CFD in the Minerls nd Process Industries, 003, LEAHY, M.J., SCHWARZ, M.P. nd DAVIDSON, M.R., (003), An ir sprging CFD model for hep bioleching of copper-sulphide, 3 rd Interntionl Conference on CFD in the Minerls nd Process Industries, 003, LEAHY, M.J., DAVISON, M.R. nd SCHWARZ, M.P. (005), A model for hep bioleching of chlcocite with het blnce: bcteril temperture dependence, Minerls Engineering, 18, LEAHY, M.J., DAVIDSON, M.R., SCHWARZ, M.P., (006), A model for hep bioleching of chlcocite with het blnce: mesophiles nd moderte thermophiles, Hydrometllurgy, (ccepted). LU, N. nd ZHANG, Y., (1997), Onset of thermlly included ir convection in mine wstes, Int. J. Het Mss Trnsfer, 40(11), PANTELIS, G. nd RICHIE, A.I.M., (199), Rtelimiting fctors in dump leching of pyritic ores, Appl. Mth. Modelling, 15, PETERSEN, J., J. nd Dixon, D., 00, Thermophilic hep leching of chlcopyrite concentrte, Minerls Engineering, 15, SALEM, H. S. nd CHILINGARIAN, G.V., 000, Physicl nd mthemticl spects of tortuosity in regrd to the fluid flow nd electric current conduction in porous medi, Energy Sources,,

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