Avesti Publishing Journl of Fluid Flow, Het nd Mss rnsfer Volume 3, Yer 2016 ISSN: 2368-6111 DOI: 10.11159/jffhmt.2016.008 Indirect Drying of Copper Concentrte in Rotting-Coil Dryer Rolndo E. Veg 1*, Pblo Zúñig 1, Jules hibult 2, Rmón Blsco 1, Pedro I. Álvrez 1 1Deprtmento de Ingenierí Químic, Universidd de Sntigo de Chile Sntigo Sntigo, Chile rolndo.veg@usch.cl; pblo.zunigm@usch.cl; rmon.blsco@usch.cl; pedroivn.lvrez@usch.cl 2Deprtment of Chemicl nd Biologicl Engineering, University of Ottw Ottw, Ontrio, Cnd K1N 6N5 Jules.hibult@uottw.c Abstrct- he Schlünder nd Mollekopf [1] penetrtion model ws used to simulte the drying of copper concentrte in continuous indirect rotting-coil dryer locted t Chilen industril copper smelter. he dryer consists of 8.48 m long pn with cylindricl bottom corresponding to n inner dimeter of 2.77 m nd mximum depth of 1.66 m. Heting is provided by system of coils mounted on centrl rotting shft inside the dryer, with pproximtely 237 m 2 of effective heting surfce in contct with the concentrte out of totl vilble coil surfce re of 460 m 2. he dryer opertion ws simulted with flow equivlent to 41.34 tons per hour of dry concentrte. he initil nd finl moisture contents were 10.5% nd 0.2% (wet weight bsis), respectively. Simultion results (solid moisture content nd temperture profiles, nd drying curve) for the drying of the copper concentrte were obtined in terms of the mixing number, N mix. he mixing number is fundmentl empiricl prmeter of the penetrtion model. Due to the bsence of experimentl dt for the chrcteriztion of the drying curves, the fitting of N mix ws obtined s function of the concentrte's outlet moisture content, yielding vlue of 2.41, in greement with typicl vlues reported in the literture. Keywords: Copper concentrte, penetrtion model, mixing number, indirect drying, rotting-coil dryer. Copyright 2016 Authors - his is n Open Access rticle published under the Cretive Commons Attribution License terms (http://cretivecommons.org/licenses/by/3.0). Unrestricted use, distribution, nd reproduction in ny medium re permitted, provided the originl work is properly cited. Nomenclture Symbol Definition Units Reltive coordinte of the height m Dte Received: 2015-07-19 Dte Accepted: 2016-01-13 Dte Published: 2016-04-26 62 of solid concentrte A EF Effective Surfce re for Het trnsfer m 2 Position of the drying front m,1 Position of the drying front t the end of the first contct period m,2 Position of the drying front t the end of the second contct period m A DC otl surfce re for het trnsfer m 2 z A EF Effective surfce re for het trnsfer for section of the bed m 2 c pef Effective het therml cpcity of the bed t constnt pressure J kg 1 K 1 c pl Het therml cpcity of the liquid J kg 1 K 1 h dry Overll Het trnsfer coefficient of the dry bed h vg Het trnsfer coefficient t the evportion front h p Het trnsfer coefficient between solid prticles h sb penetrtion within the bed h sb,dry penetrtion within the dry bed h sb,wet penetrtion within the wet bed h vw Het trnsfer coefficient between the gs phse with the wll h wll wll h wet penetrtion of the wet bed h ws first solid lyer with the wll
k ef Effective therml conductivity with the bed W m 1 K 1 L S Length of the dryer m M SS Mss of dry solid kg SS z M SS Mss of dry solid for ech section of the bed kg SS N mix Mixing number - N v Drying rte per unit re kg s 1 m 2 PH Number of phse chnge - q =0 Het flux density t the heting surfce W m 2 q = Het flux density t the drying front W m 2 Het flux density entering the bed of prticles W m 2 Q in Net Het flow entering the bed of prticles W t ime s t ret Residence time s emperture K b Bed temperture K b,1 Bed temperture t the end of the first contct period K b,2 Bed temperture t the end of the second contct period K b,in Inlet bed temperture K h Interfce temperture between the heting Surfce nd the bed K t mix ime constnt of the stirring device s t R Imginry of fictitious contct time s w emperture of the heting surfce K v con Axil velocity of the solid concentrte m s 1 W con Mss flow rte of the dry concentrte kg s 1 X Concentrte moisture content (dry bsis) kgh 2O kgss 1 X 1 Moisture content fter the first contct period kgh 2O kgss 1 X 2 Moisture content fter the second contct period kgh 2O kgss 1 X in Initil moisture content of the bed of the contct period (dry kgh 2O kgss 1 bsis) X out Exit moisture content of the bed (dry bsis) kgh 2O kgss 1 x wet Moisture content of the bed (wet bsis) kgh 2O kgsh 1 z Axil coordinte m Greek Symbols α ef Effective therml diffusivity of m 2 s 1 the dry bed β p Permetion coefficient of the solid prticles m s 1 β sb Permetion coefficient of the solid bed m s 1 Δ Difference - λ v Ltent het of vporiztion of wter J kg 1 ξ Reduced position of the drying front - ρ ef Effective density of the bed kg m 3 ψ Bed hold-up - 1. Introduction Indirect contct drying is unit opertion in which the wet mteril to be dried is not in direct contct with the heting medium but seprted by conducting surfce. One pproch to model the behvior of this type of drying opertion is through the use of the penetrtion model developed by Schlünder [2], which is bsed on fundmentl physicl principles. In its origin, the penetrtion model ws developed to describe het trnsfer from hot surfce to solid bed of prticles t rest occurring in two sequentil stges [1]. In the first stge, het is trnsferred from the heted surfce to the first lyer of prticles djcent to the surfce, resulting in contct resistnce. In the second stge, het is conducted progressively inside the bed of prticles, cusing penetrtion resistnce of the solid bed [2], [3], [4]. his concept ws dpted to represent the indirect drying of solids, subjected to some mixing ction, by introducing geometricl prmeter to include the rndom motion of the prticles. he penetrtion model hs been used to describe the drying process under different operting conditions such s vcuum [1], [5] nd in the presence of n inert gs tmosphere [6]. sotss nd Schlünder [7] hve included the solid hygroscopic ffinity to the model with the ddition of n dsorption curve in the development of the model. hey hve studied the influence of the solid prticle size distribution on the model prediction. Even though the penetrtion model ws developed for the drying of bed of solid prticles resting on heted horizontl flt surfce, it ws possible to use it to model the drying of solid bed occurring in vrious types of dryers: moving discs, rotting cylinders equipped with lifters, fixed cylinders with rotting bldes. Intelvi [8] nd Intelvi et l. [9] modelled the drying of phrmceuticl products in rotting-disc btch dryer, under both vcuum nd tmospheric 63
pressure with very stisfctory results. hey used discrete element method (DEM) model for their simultion nd compred their results with the experimentl results published by Schlünder nd Mollekopf [1] where it ws determined tht the results were very well simulted except t very high RPM (> 45) nd very low moisture content (< 0.1%) where the internl mss trnsfer resistnce becomes nonnegligible. Osmn et l. [10] lso used the DEM model where they dded the het trnsfer phenomen nd obtined good results. Jorquer [11] nd Veg [12] hve pplied the penetrtion model to describe the btch drying of different types of solids in rotting-tube dryer, much more complex geometry thn disc dryers. hey obtined results tht were consistent with experimentl dt. Shene et l. [13] introduced the concept of continuous opertion to the penetrtion model. his concept ws subsequently implemented by Riquelme [14], who obtined very good results when compred with experimentl results. sotss et l. [15] proposed new pproch in order to identify the missing elements in the conventionl penetrtion model, such s the mechnicl nd sttisticl properties of solid prticles. However, the penetrtion model hs been mostly tested t the lbortory scle with dryer prototypes (discs, rotting drums nd rotting drum with flights) of reltively low cpcity, which rises the question on the predictive bility of the penetrtion model for the indirect drying of solids t n industril-scle opertion using rotry-tubes, rotting-coils nd rotting-discs dryers. One reserch group hs, however, extended the penetrtion theory to compute the drying kinetics of municipl sewge sludge [16][17]. he min objective of this pper is to model the continuous indirect drying of copper concentrte in rotting-coil dryer t n industril scle where stem condensing within the rotting coils serves s the het source. his is in contrst with the pplictions reported in the literture where modeling nd simultion re performed with prototypes of indirect dryers of low cpcity most often operting in btch mode. In this pper, it is therefore desired to model nd simulte the drying behvior of n industril copper concentrte rotting-coil dryer using the penetrtion model of [1]. 2. Model Description he penetrtion model of Schlünder nd Mollekopf [1] ws developed for indirect drying opertion in rotting disk dryer in which the heting surfce hd circulr geometry. he solid bed of prticles is distributed over the surfce of the heted disks where it bsorbs het such tht the solid moisture eventully reches the sturtion temperture nd the evportion process begins. While the bed is sttic, the contct time between the hot disk surfce nd the solid prticles is known nd equl to the residence time. However, in order to improve het trnsfer, the solid bed is gitted using series of mixers. As result, the time for which the solid is in direct contct with the heting medium is not known nd, to include this mixing effect in the model, geometric prmeter known s the mixing number N mix is used. he mixing number correltes the estimted time (t R) during which the solid prticles re in contct with the heting surfce nd the time constnt or the inverse ngulr velocity of the stirring device (t mix): t R t mixnmix (1) In this model (Figure 1), it is ssumed tht the sttionry mixing process cn be viewed s sequence of unstedy mixing steps. Ech step hs durtion t R which corresponds to n imginry or fictitious time tht the solid to be dried is in sttic contct with the heting surfce (contct surfce re between prticles nd heting surfce for rotting disk dryers, rotry cylinder dryers equipped with lifters, cylindricl dryers with rotting bldes or others). At t = 0, the bed hs n initil moisture content X in nd n initil temperture b,in. A drying front coming from the heting surfce ( = 0) penetrtes the bed to n rbitrry distnce,1. In the region between 0 < <,1, the solid prticles re completely dry (X = 0) under the ssumption tht there is no bound moisture (non-hygroscopic bed), s schemticlly represented by the light color prticles of Figure 1(b). In this zone, temperture profile hs developed nd the bed properties cn be pproximted by treting the bed s qusi-continuous medium. Beyond the moving drying front, for >,1, the solid prticles re still t the sme initil moisture content (X in) nd t temperture b,in, s schemticlly represented by drk color prticles of Figure 1(b). At the end of the sttic period (t = t R), the bed is mixed instntneously nd perfectly. his step results in uniform bed moisture X 1 nd bed temperture b,1. his step mrks the completion of the first period of contct nd the initilistion of second 64
contct period. his process is repeted in the sme mnner until the bed of prticles becomes completely dry. Figure 1 illustrtes schemticlly the progressive drying of bed of solid prticles vi the repeted drying-mixing cycles. In this work, it is ssumed tht the control of the drying process depends solely on het trnsfer nd thus the mechnisms by which het is trnsferred. In indirect dryers such s rotting discs, rotry cylindricl equipped with lifters, sttic rotry drum with rotting bldes, rotting coils nd others, it is possible to observe the presence of severl het trnsfer resistnces. hese resistnces, going from the heting medium to the gseous phse contining wter vpor coming from the drying bed, re in series: (1) 1/h vw is the resistnce previling between the heting medium nd the conductive wll (typiclly negligible compred to other resistnces if the heting medium is stem), (2) 1/h wll is the resistnce due to conduction through the wll (negligible for metl wll), (3) 1/h ws is the contct resistnce between the heting wll nd the solid bed of prticles, (4) 1/h sb is the resistnce due to het penetrtion into the bed of prticles, (5) 1/h p is the internl prticle het resistnce (considered negligible for copper concentrte prticles becuse of the smll prticle dimeter of the order of tenths of microns, negligible porosity nd high therml conductivity) nd (6) 1/h vg is the resistnce t the evportion surfce (considered negligible in this work). Even though there re severl resistnces in series, only two resistnces re considered importnt: the contct resistnce between the heting wll nd the solid bed of prticles nd the penetrtion het resistnce of the solid bed [18]. he contct het trnsfer coefficient (h ws) cn be estimted using the mthemticl model developed by Mollekopf nd Mrtin [19] while the bed penetrtion trnsfer coefficient (h sb) is determined bsed on the properties of the prticles for the dried bed. In ddition, there re two mss trnsfer resistnces: one for the bed permetion (1/β sb) nd nother one for prticle permetion (1/β p). Studies hve shown tht the bed permetion resistnce for sttic solid beds is very smll nd, for mixed solid beds, it is roughly zero such tht it cn be sfely neglected [1]. he prticle permetion resistnce cn lso be neglected for non-porous prticles, which is the cse in this investigtion for copper concentrte. In summry, the penetrtion model proposes tht the drying rte is property of the solid bed insted of property of the prticles, which is the reson why the resistnces due to solid prticles re neglected. his is mply justified in this investigtion due to the specific properties of copper concentrte prticles. herefore, the model proposed by Schlünder nd Mollekopf [1] is used s simplifiction of the rel continuous drying process. Figure 1. Penetrtion model pplied to indirect contct drying. Performing n energy blnce on qusicontinuous medium with respect to the temperture grdient, the het diffusion eqution is obtined [20]: 2 1 2 αef t where α ef represents the effective therml diffusivity of the bed, defined s: α () Initition of drying (t = 0) w,in k X = X in w w,in (d) Penetrtion of the drying front (t = 2t R ) b1 (b) Penetrtion of the drying front (t = t R ) X = X 1 X = 0,2 h w X = X in X = 0 h w (e) Perfect instntneous mixing (t = 2t R ) (2) ef ef (3) ρef cp,ef k ef is the therml conductivity of the bed, ef is the bed density nd c p.ef is the therml cpcity of the solid bed. he initil nd boundry conditions for the section of the bed in the vicinity of the heting surfce cn be defined s follows (Figure 1):,l b2 (c) Perfect instntneous mixing (t = t R ) X = X 2 w b,1 X = X 1 w 65
IC: t < 0 = b BC1: = 0 = h BC2: = = b By introducing these boundry conditions in Eq. (2), it is possible to describe the temperture profile of the bed t ech instnt within the time intervl 0 < t < t R: erf 4α b ef t 1 erf ξ h b where ξ is the normlized drying front position, defined by: ξ (4) (5) 4α t ef he reduced drying front position cn be estimted from the following expression [1]: h h 1 h h PH 2 ws ws ξ π exp ξ 1 1 erf ξ 1 dry dry where PH is the phse chnge number tht represents mesure of the intensity of the ltent het of vporiztion compred to the sensitive het. It is defined s: X λ PH v c p,ef w b (6) (7) An verge individul het trnsfer coefficient, h sb,wet, for the penetrtion of the moist bed cn be defined s: h sb,wet t k R ef 1 t R 0 h b 0 (8) Evluting / 0 nd substituting it in Eq. (8), the following eqution is obtined for the verge penetrtion het trnsfer coefficient for the wet bed: h 2 k ρ c 1 ef ef p,ef sb,wet π tr erf ξ (9) On the other hnd, the individul het trnsfer coefficient, h sb,dry, for the penetrtion of the dry bed cn be obtined from Eq. (9) becuse when the moisture content X tends to zero, ξ tends to infinity nd erf ( ξ ) tends to unity giving rise to Eq. (10): h 2 k ρ c ef ef p,ef sb,dry π t (10) R Combining the two individul het trnsfer resistnces in series (1/h ws nd 1/h sb), it is possible to determine the overll het trnsfer resistnce to the flow of het for both the dry bed (h dry) nd the wet bed (h wet): 1 1 1 (11) h h h dry ws sb,dry 1 1 1 (12) h h h wet ws sb,wet Knowing the overll het trnsfer coefficient h wet, it is possible to determine the het flux both t the heting surfce ( = 0) nd the loction of the drying front ( = ): q 0 hwet w (13) b = wet w b 2 q h exp ξ (14) Assuming tht the het bsorbed by the moisture t the drying front of the solid bed is only ltent, tht is the het required to chnge the moisture from liquid to vpor without incresing the temperture, the rte of evportion of the moisture from the bed cn therefore be clculted s: N v 2 hwet w b exp ξ (15) λ v he chnge in the moisture content of the bed during the time period 0 < t < t R is given by 66
ΔX N t A M v R EF (16) SS where A EF is the totl effective surfce re for het trnsfer (totl contct surfce between the solid prticles nd the heting surfce) nd M SS is the totl mss of the dry solid. Performing n energy blnce on the bed, during the time period of the imginry or fictitious sttic contct, the verge increse in temperture of the bed (Δ b) cn be determined by the following eqution: λ 1exp ξ ΔX c Xc exp ξ v b 2 p,ef p,l 2 (17) 2.1. Model dpttion to continuous drying opertion he penetrtion model ws developed t the lbortory scle on btch dryers (rotting disks, rotry drum nd fixed drum with rotting bldes). For the modeling of continuous indirect dryer such s rotrycoil dryers, it is ssumed tht ll the prticles move s plug flow system with uniform nd constnt speed throughout the dryer. herefore, the xil movement during ech imginry or fictitious contct period t R is the distnce trveled by the prticles long the length of the dryer. According to Shene et l. [13], this distnce is given by: Δz Vcon tr (18) where V con represents the verge velocity of the copper concentrte prticles in the xil direction nd is given by the following expression: W con V con = (19) ρ ef S con W con is the mss flow rte of the dry concentrte within the dryer, ρ ef is the effective density of the bed of dry concentrte nd S con is the cross sectionl re of the flow of concentrte, which is obtined s function of the internl geometry of the dryer nd the solid holdup [21]. During the time period t R, both the mss of solid z M SS nd z the effective het trnsfer re ( A EF ) re given by the following expressions [14]: z z M SS M LS z z A EF A LS SS EF (20) (21) where L S is the length of the dryer. Moreover, the residence time of the concentrte within the dryer cn be clculted using n expression similr to Eq. (18). L S t res = (22) V con It is lso possible to relte the section of the dryer z clculted using Eq. (18) nd the overll length of the dryer L S: S N i = 1 L = z = N z (23) i where N is the number of sections of the dryer of length z tht the concentrte trvels during ech time intervl t R, s discussed before. Likewise, similr expression cn be estblished between the residence time t res nd the imginry od fictitious contct time t R: N res Ri R i = 1 t = t = N t (24) 3. Mterils nd Methods he rotry-coil dryer is enclosed in fixed metl chmber. he bottom portion of the drying chmber is cylindricl wheres the top of the drying chmber hs rectngulr shpe. he coils, serving s the het trnsfer surfce, re mounted on hollow centrl shft nd supplied with stem. he centrl shft nd the coils re ttched to drive unit which is rotted to provide mixing nd het trnsfer. Figure 2 gives the schemtic digrm of the lterl nd trnsversl cut-out views of the rotry-coil dryer showing the min components of the dryer. he heting system consists of centrl cylindricl rotor to which heting coils re ttched. he heting coils consist of series of concentric rings connected through tube mnifolds s shown in Figure 3. 67
Input Vpour (Heting medium) Condenste Output minerl concentrte Drying chmber Heting system (Rotry coils) Output Moist Gs Heting system (Rotry coils) () Input minerl concentrte Output minerl concentrte Purge gs (Air) Rottion drive system (b) Figure 2. Schemtic digrm of longitudinl () nd perpendiculr (b) cross-sectionl view of the rotting-coil dryer. Stem is the heting medium nd is supplied from boiler to the centrl rotting shft of the dryer nd subsequently distributed to the surrounding coils. Due to the rottion of the heting system, the condenste produced when het is trnsferred to the concentrte is withdrwn through the tube mnifolds to the rotor nd then recirculted to the boiler. Figure 3. Side view of the heting system of the rotting-coil dryer. ble 1. Min dimensions of the industril rotting-coil dryer. Dimensions Length Mgnitude [units] 8.480 [m] Dimeter (circulr bottom section) 2.772 [m] Height bove shft (rectngulr section) 1.664 [m] otl het trnsfer surfce re 460 [m 2 ] otl effective re for het trnsfer 237 [m 2 ] otl het trnsfer volume 16.2 [m 3 ] Internl volume of the dryer shell 64.7 [m 3 ] he concentrte inlet port of the dryer is locted t one end of the dryer. he inlet port is equipped with double-gte vlve used to regulte the mount of moist concentrte entering nd to prevent t the sme time undesired ir intke. he dry concentrte is dischrged through n djustble dmper t the opposite end of the dryer which llows controlling the solid holdup within the dryer. Moisture tht evportes during the drying process is driven by the purge ir flowing co-currently with the concentrte. he gseous mixture is dischrged to the tmosphere through n exhust gs fn then directed to stck. Dimensions of the dryer nd the heting system re given in ble 1. 3.1. Effective re for het trnsfer Schlünder nd Mollekopf [1] performed their investigtion with btch rotting disk dryers of different dimeters in which the solid ws in contct with the entire heting surfce. hey lso investigted dryers of different geometry such s rotry drum with lifters nd sttionry cylinder with rotting bldes. Unlike rotting disc dryers, these dryers re not completely filled with solids such tht only portion of the heting surfce is in contct with the solid. his frction of the heting surfce, clled the effective heting surfce A EF, is ssumed equivlent to the heting surfce tht would hve rotting disk dryer nd this is the surfce re tht is used in the model of the dryer presented in Figure 1. In this work, the sme concept pplies to the continuous rotry-coil dryer which possesses greter geometric complexity. herefore, the solution is to consider the rotry-coil dryer s rotry-disk dryer. A detiled study on the industril copper concentrte dryer llowed determining the re nd the volume of both the inner shell of the dryer nd the heting mechnism of the rotry-coil dryer [21]. As mentioned bove, the solid concentrte trvels distnce z during ech time intervl t R nd is in 68
Δz contct with frction of the totl heting re A, s EF indicted in Eq. (21). herefore, for the purpose of the model, the rotry-coil dryer from ntionl foundry cn be represented by N rotting disk dryers connected in series, where N is the number of sections of the dryer of length z. Unlike btch rotting-disk dryers where the solid is in contct with the entire heting surfce re, the pn of the industril copper concentrte continuous rotry-coil dryer is not completely filled such tht frction of the heting surfce is bove the concentrte bed nd exposed to the flow of hot gs. According to the dryer mnufcturer's specifictions, the optimum utiliztion of the heting surfce occurs when the level of concentrte bove the centrl rotor is bout meter, resulting in solid holdup percentge volume frction (ϕ) of pproximtely 56%. he effective het trnsfer surfce re of the industril rotry-coil dryer used for the copper concentrte, estimted using the geometricl dimensions of the industril dryer, ws estimted to be 237 m 2 [21]. 3.2. Simultion Dt Dt presented in ble 2 correspond to verge vlues obtined during norml opertion of the industril dryer over period of severl months. hese vlues were provided by engineers tht were in chrge of the process. ble 3 presents the physicl nd thermodynmic properties of typicl copper concentrte of Chilen foundry tht collborted in this investigtion nd s n end-user of this model. he chrcteriztion of the concentrte smples includes the following properties: the verge prticle dimeter, the verge density of the solid prticles of the dry concentrte, the effective density of the dry concentrte, nd the specific het therml cpcity of the dry concentrte. he therml conductivity of the dry bed ws determined experimentlly using current metre (C MERE), which consists of controller (setting of prmeters, progrmming nd executing the desired mesurement), solid immersion mesurement probe (interfce between the controller nd the solids smple) nd rectngulr continer which receives the smples for which therml conductivity is required. ype Opertionl Chrcteristics of concentrte ble 2. Opertionl dt. Prmeters Mgnitude [units] Pressure 1 [tm] Stem pressure in coils 11.74 [tm] Coil surfce temperture 186 [ C] Rotting speed 4 [rpm] Concentrte hold-up 55.6 [%] Mss flow rte (dry) 41.3 [t d/h] Initil moisture (wet) 10.5 [%] Exit moisture (wet bsis) 0.2 [%] Initil solid temperture 20 [ C] Exit solid temperture 148 [ C] ble 3. Physicl nd thermodynmic properties of the concentrte. Mgnitude Properties [units] Suter men prticle dimeter 21.9 [μm] Prticle density 4252 [kg/ m 3 ] Effective density of dry concentrte 2030 [kg/ m 3 ] Het cpcity of dry concentrte (100 C) 500 [J/kg K] Effective therml conductivity of dry bed 0.28 [W/m K] 4. Results nd Discussion Model simultions were performed using Visul Bsic for Applictions (VBA - Version 7 in Excel 2010). Bsiclly, the process model itertively clcultes the vlue of the mixing number (N mix) such tht the vlue of finl moisture content of the concentrte (0.2% wet bsis) is chieved. When convergence hs been chieved, summry of the most relevnt simultion results re recorded into n Excel spredsheet. he process model includes model equtions, initil dt, nd correltions to clculte the physicl, thermodynmic nd effective properties involved in the process. ble 4 shows the most relevnt results obtined with the simultion model. ble 4. Summry of simultion results. Prmeter/Vrible Mgnitude [units] Mixing number, N mix 2.41 Concentrte exit temperture Fictitious or imginry time of contct, t R 148.2 [ C] 36 [s] Number of sections of the dryer 76 Length of ech section of the dryer, z 0.11 [m] 69
4.1. Purge ir flow rte A purge strem of hot ir is fed to the dryer to remove the evported liquid from the surfce of the prticles. he purge ir strem is in fct strem of mbient ir tht is used to pneumticlly trnsport the hot solid concentrte from the exit of the dryer to the solid silos nd to recover portion of the sensible het from the hot solid concentrte. he heted mbient ir is then sent to cyclone prior to be fed to the dryer. he purge ir cn be considered s resistnce to mss trnsfer of the liquid from the interfce of the prticle to the gs phse. his mss trnsfer resistnce is ssumed to be negligible in this study. he purge ir strem enters t temperture of pproximtely 120 C nd, becuse it is in contct with the heting surfce bove the bed of solid concentrte, its exit temperture reches 135 C. Under these therml conditions, the purge ir will not rech sturtion conditions nd its temperture will lwys be bove the dew point temperture, thus llowing for proper opertion for the filter bg nd thus minimizing concentrte prticle losses to the tmosphere. 4.2. Mixing number he mixing number (N mix) is n empiricl prmeter nd, ccording to the definition given by Schlünder nd Mollekopf [1], cn be viewed s the number of revolutions of the mixing device required to completely mix the bed of prticles once, i.e. homogenizing the bed of prticles such tht the humidity nd the temperture rech uniform conditions. he mixing number is considered s purely geometricl nd mechnicl prmeter nd is identicl for both wet nd dry beds. A vlue of 2.41 ws obtined in this investigtion for the mixing number. his vlue is relted on the one hnd to the output moisture of the concentrte (0.2 % wet bsis) nd to the totl length of the dryer (L S = 8.48 m) on the other hnd. here exists unique vlue of the mixing number N mix tht stisfies the operting output conditions. Hoekstr et l [22] used bench-scle dryer to determine by regression nlysis the unknown mixing prmeters tht llowed them to determine the drying curve t n industril production scle with excellent results. hey concluded tht the mixing number could be used to scle up the dryer provided the solids do not exhibit extreme stickiness. 4.3. Anlysis of the moisture content nd temperture profiles of the copper concentrte Figure 4 presents the profiles of the temperture nd the bed moisture content long the length of the dryer predicted by the model. With respect to the reltive moisture content profile, the model predicts the typicl decy normlly observed in concentrte moisture content long the length of the dryer. A close look t the moisture content profile, it is possible to observe tht the solid concentrte hs lost more thn three qurters of its initil moisture content prior to reching the midpoint loction of the dryer (L = 4.24 m). his profile cn be explined by considering the model of vcuum drying where there is negligible resistnce to mss trnsfer in ddition to the ssumption tht the solid is sturted from the beginning of the drying process. herefore, the het trnsfer is equivlent to the bsorption of the ltent het of evportion, resulting in higher drying rtes such tht the moisture content decys fster. With respect to the temperture profile of the solids long the bed, rpid nd sustined increse in temperture is observed. he decrese in the solid moisture content cuses the nerly dried prticles to rech tempertures beyond the sturtion temperture of wter. In ddition, the concentrte outlet temperture simulted by the model is 148.2 C, which is very close to the ctul exit concentrte temperture of 148 C. he temperture chnges more rpidly in the center portion of the bed. he rte of chnge t the entrnce of the dryer is slightly smller becuse of the colder entering solid nd its sensible het. In the lst section of the dryer, the temperture increse more slowly of the decrese of temperture driving force. he net het flow into the bed cn be clculted bsed on the sum of the fluxes of het estimted using Eq. (13): N Δz in EF = 0 i i = 1 Q = A (q ) (25) Furthermore, the net flow of the ltent het bsorbed by the bed is estimted similrly to Eq. (25) using het flux densities estimted using Eq. (14): N Δz lt EF = i i = 1 Q = A (q ) (26) 70
It is estimted vi the simultion tht the net het flow (Q in) is pproximtely equl to 4663 kw wheres the het flow ssocited with the ltent het of evportion (Q lt) is 3564 kw. By performing n energy blnce using the ctul industril conditions of the copper concentrte drying process, vlue of Q in of 4253 kw nd n estimted vlue Q lt of 3409 kw were clculted. herefore, there is reltive good mtch between the simulted nd the ctul het flow vlues. Figure 5 presents the profiles of the drying rte of the bed of concentrte s function of the reltive moisture content. he drying curve of Figure 5 is mximum t the beginning of the drying process (X/X in = 1) becuse t the inlet end of the dryer the solid moisture content is t sturtion temperture nd, therefore, does not require het to be used for heting the bed moisture. hen, continuous decrese in the drying rte is observed until the rtio X/X in finlly pproches zero towrds the end of the dryer. In this prticulr opertion, constnt-rte period is not observed. he fct tht the feed moisture content is reltively low lso contributes to the bsence of constnt-rte period. Figure 4. Moisture content nd temperture profiles long the drying bed. he drying rte profile hs been plotted s function of the dimensionless moisture content (X/X in) such tht its vlue vries between 0 (finl moisture) nd 1 (initil moisture). Applying the penetrtion model, it is possible to obtin the drying curve s function of the moisture content of the bed nd to solve the following integrl eqution: A EF Xin dx W N X (27) con Xout v where W con denotes the mss flow rte of the dry concentrte. he estimted residence time of the concentrte in the dryer is 2751 s, which cn be obtined both using Eq. (22) nd Eq. (24). Figure 5. Plot of the solids drying rte. 5. Conclusion In this investigtion, n industril rotry-coil dryer used for drying copper concentrte ws simulted successfully bsed on the model proposed by Schlünder nd Mollekopf [1]. In this model, the fct tht the resistnce to mss trnsfer is negligible llows the development of model to simulte vcuum opertion with presence of n inert purge gs. Due to the lck of experimentl dt internl to the solid bed, the determintion of the mixing number ws performed bsed on the inlet nd outlet moisture contents of the solid bed. Simultion results for the continuous drying opertion of Chilen foundry were quite stisfctory. For obvious resons, it ws not possible to compre the simulted temperture nd moisture content profiles long the length of the dryer with experimentl dt. Nevertheless, the predicted solid moisture content nd temperture profiles re quite representtive of profiles typiclly observed in drying opertion. In this investigtion, mixing number of 2.41 ws determined. Since the mixing number is identicl for wet nd dry solid beds, it cn be used for the industril copper concentrte bed even though the initil moisture content vries provided tht the ngulr frequency of the mixing device remins the sme. Acknowledgement he uthors cknowledge the finncil support of DICY-USACH - Number 051311 AG. 71
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