Lecture 8 Flotation 1. CHAPTER 10 - Flotation Machines. Contents: Residence time. Mixing. Unit cells. Flotation banks. Columns. New types of cells.

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1 Lecure 8 Floaion 1 CHAPTER 10 - Floaion Machines Conens: Residence ime. Mixing. Uni cells. Floaion banks. Columns. New ypes of cells. Inroducion Floaion is a rae process. We can invesigae floaion raes in he laboraory, bu we need o know he equipmen characerisics before we can ranslae hese resuls o a full scale plan. The mixing characerisics of he pulp in he floaion machines is paricularly imporan. How long does i spend on average in he cell (mean residence ime)? And does i all spend he same ime here or does some pass hrough quickly (bypass) and some say for a long ime (dead space)? This disribuion of residence ime is used o describe he mixing paern wihin he equipmen. Residence Time Disribuion A full descripion of he residence ime disribuion requires a deailed knowledge of he pah of each elemen of he pulp hrough he vessel. This is generally no pracicable or necessary. All we need o know is how long differen elemens say wihin he cell. The paricles will be floaing for his lengh of ime so ha we can calculae how much floas in his ime. By inegraing over all he elemens in he pulp we can esimae he combined behaviour. Definiions V, v v V = volume of cell or ank (m 3 ) v = volumeric feed flow rae (m 3 / s) = mean residence ime (s) = V / v E() = disribuion of residence ime of maerial wihin he cell or ank (his is he exi age disribuion funcion of maerial leaving he cell where he age is he ime spen in he cell) E = he fracion of maerial in he exi sream wih an age beween and + The fracion of maerial in he exi sream which has spen ime less han 1 in he cell (ie is younger han 1) is given by 1 0 E()d The fracion of maerial in he exi sream which has spen ime more han 1 in he cell (ie is older han 1) is given by 1 1 E()d = 1-0 E()d

2 Lecure 8 Floaion 2 The oal area under he curve = 1 = 0 E()d E() Toal area under curve = 1 Ideal Flow Cases 1. Plug Flow This is he ideal case where all maerial spends he same ime in he cell, eg flow in a pipe. I is he same as a bach operaion. Area = 1 E() 0 T 2. Perfecly Sirred Cell or CSTR (Coninuous sirred ank reacor) This is he opposie ideal case. Mixing is perfec so ha all maerial in he cell is equally likely o leave. Hence fresh feed ha has jus enered is jus as likely o leave as maerial ha has been in he cell for a long ime.

3 Lecure 8 Floaion 3 1/T (exp(-/t))/t Or on a log-linear plo loge() E() Area = CSTR s in series Arranging perfecly sirred cells in series enables inermediae (more realisic) siuaions o be modelled. E() ((/T)exp(-/T))/T 0 0 Area = 1

4 Lecure 8 Floaion 4 By connecing more and more CSTR s ogeher in series he resuling behaviour ends owards plug flow. 3. Shor Circuiing and Dead Space These can be modelled by wo regions in parallel T 1 T 2 If τ1 << τ2 We say ha maerial shor circuis he vessel If τ2 We say we have dead sapce in he vessel, eg a floaion cell may be poorly mixed and sanding-up. Measuremen of Residence Time Disribuion To measure he acual residence ime disribuion of a cell, ank or oher iem of equipmen racer echniques are used. The racer which is added should be easily deeced and measured, bu should oherwise behave in exacly he same manner as he maerial ha is being sudied. For liquids as racer use some easily analysed solue which is no presen in he plan waer fluorescene, lihium chloride, poasium bromide, ec Solids are much more difficul. The bes possible way is o irradiae he solids and measure radioaciviy. I is quie common o race he liquid and assume ha he liquid response is also rue for solids. This may or may no be rue, depending on he size of he solids and he flow regime. In principle i is possible o measure he response of he racer o any inpu signal cyclic, random, impulse. In pracice he impulse es is he mos convenien o do and o analyse. Impulse Tes A ime 0 a quaniy of racer G (kgm) is added as rapidly as possible o he feed o he vessel. Samples are hen aken of he oule sream a paricular subsequen imes and analysed for he level of racer.

5 Lecure 8 Floaion 5 v Tracer Concenraion V,T v Thus Bu G = 0 vcd where c is he concenraion of racer G/v = 0 cd = Area under he curve (v consan) τ = V/v and c0 = G/V Thus Area under curve = c0τ This enables he racer concenraion curve o be scaled o he E curve c E or c/c 0T Area = c 0 T Area = 1 Mean Residence Time τ may be measured from he c curve τ = 0 cd / 0 cd These inegrals can be esimaed from an experimenal curve aking special care wih he ail of he curve. Noes: 1. I is imporan o carryou a mass balance on he racer o ensure ha i is all accouned for, ie esimae v hen check ha G = v. Area under c curve. 2. Seady sae condiions have been assumed 3. We have assumed only one oule. This is OK for a ball mill or condiioner, bu care mus be aken wih floaion cells.

6 Lecure 8 Floaion 6 4. Wach ou for recycles. This can lead o racer reurning o he feed sream and upseing he simple approach. 5. Residence imes of solids, paricularly coarse solids, can differ significanly from hose in liquids. Mixing Models I is generally difficul o incorporae an experimenal residence ime curve ino a mahemaical model. I is beer o choose an ideal flow model ha approximaes he real siuaion, hen carryou calculaions using he flow model. Experimenal curve c 2 CSTR's in series 0 0 An approximae fi o he reidence ime disribuion curve is generally adequae for mineral processing operaions. Floaion Cells and Floaion Banks A floaion cell is an approximaion o a perfecly sirred ank (CSTR). I is imporan ha mixing is good and he solids are suspended. There should be a calmer region a he op of he cell for froh drainage, bu major pulp flow should be well mixed. Problems can arise wih inadequae mixing. Solids can sele ou providing dead regions of he cell. This will reduce he effecive cell volume and he pulp residence ime. Residence disribuion ess can esablish wheher mixing in he cell is saisfacory. Recovery from a single cell V,c C,c c F,c f T,c

7 Lecure 8 Floaion 7 A oal mass balance and componen balance of flows around he cell gives F = C + T (1) And F. cf = C. cc + T. c (2) Mean residence ime for he cell τ is τ = V/T (3) If he floaion rae consan of he mineral species is k (min -1 ) C. cc = k. V. c (4) The recovery of mineral R = C. cc / F. cf (5) Using (1), (2), (3), (4) and (5) gives R = 1-1/(1 + k τ) = k τ /(1 + k τ) (6) The equivalen resul for a bach floaion cell is R = 1 - exp(-k τ) The following able indicaes he inefficiency of a sirred cell. The problem is mos imporan for he fas floaing maerial (high k τ). Easily recovered maerial is los as i passes rapidly from feed o ailing. k τ Single Sirred Cell Recovery % Bach Cell Recovery % Recovery from a Bank of Cells The general way o overcome his problem is o connec he cells ogeher in series o make a floaion bank. Using (6) above we can esimae he recovery for he bank. If we assume ha he single cell volume is disribued beween n equal cells arranged in series R = 1 - (1/(1 + k τ/n)) n As n, R 1 - exp(-k τ) he recovery for a bach cell or plug flow reacor. k τ Single Sirred Cell Recovery % Sage recovery 3 cells in bank % Sage recovery 5 cells in bank % Sage recovery 10 cells in bank % Bach Cell Recovery %

8 Lecure 8 Floaion 8 I can be seen ha here is a recovery advanage in arranging cells in series and ha his is more marked wih he faser floaing maerials. A few cells in series is generally sufficien o gain mos of he advanage of he ideal plug flow reacor. A similar small advanage in concenrae grade is expeced from a series of cells. Consider he floaion o be separaing values from gangue. Assume ha he feed is 10% values and 90% gangue. Take he case of recovery of 50% values, ie k τ = 1 for values. The sage concenrae can be calculaed as follows for a range of rae differences beween values (kv) & gangue (kg) kv / kg Single Sirred Cell Concenrae Grade % cells in bank Concenrae Grade % cells in bank Concenrae Grade % cells in bank Concenrae Grade % Bach Cell/Plug Flow Concenrae Grade % This simplified case suggess some advanage in arranging he cells in series, bu mos of he advanage is achieved by he firs few cells. Arrangemens for Floaion Banks Floaion banks can vary considerably. A one exreme he cells are quie separae so ha pulp can only flow forward, for example by overflowing a weir. This is closes o CSTR s in series bu mos complex o build and operae. Also bank volume is wased beween he cells A he oher exreme here may be no dividers beween he cells. The bank is a rough someimes called a hog rough - wih several agiaors along he lengh. Back mixing can occur so ha he bank mixing ends o rever o a single CSTR. This is very simple o build and operae bu will be less efficien In beween here may be parial divisions skirs beween he cells ha preven mos bu no all of he back mixing. This is he more usual compromise Residence ime measuremens can show he mixing paerns in any paricular bank. They may also show wheher agiaion is adequae or wheher here is dead space in he bank. Minor changes have been made o he designs of he basic cells aimed a increasing efficiency. Improvemens claimed for mixing, air dispersion, mainenance, conrollabiliy. The major rend in recen years is he scale-up of floaion cells o cope wih he massive onnages possible in SAG mills. Sizes are now up o abou 200m 3. To cope wih he size here are some changes o he froh collecion sysems. Discharge is someimes from boh sides of he cell. Someimes anular launders are used o increase he available lip lengh and reduce he disance ha froh has o flow. Major cos adavanages resul from hese big unis. This is parly from economies of scale in cell manufacure, bu also lower insallaion and mainenance coss, and easier conrol.

9 Lecure 8 Floaion 9 Alernaive Floaion Equipmen Floaion Column Floaion columns were originally considered in he 60 s bu did no achieve accepance unil abou 15 years ago. The arrangemen aims a a rue counercurren separaion. High froh dephs are also possible making columns paricularly suiable for cleaning duies. The general arrangemen is as shown below. Columns are ypically abou 10m high. Applicaions were originally in base meals, bu hey are now very widely used for boh meallic and indusrial minerals. Effecive froh washing and process conrol were imporan aspecs in he developmen of he sysems. There are a number of opions o improve he plug flow behaviour in he column wih inernal packing and baffles. Residence ime disribuion and flow paerns of bubbles and paricles are criical o he efficien operaion of hese unis. Bubble generaion is someimes done ouside he column, eg in he Microcell column. This is designed o generae very small bubbles ( mm) paricularly argeed a he floaion of fine paricles.

10 Lecure 8 Floaion 10 Jameson Cell A novel sysem ha has gained considerable accepance in a wide range of applicaions. Air and feed are fed o he cell in a verical je ha enrains air and generaes a froh. This provides a good environmen for paricle capure and separaion. The equipmen is much smaller han a full column and so is claimed cheaper o insall and operae. EKOF The differen asks of paricle suspension, pulp ranspor, and producion of small air bubbles are done in exernal unis conneced o he cell. As he uni ges larger more of hese aeraors are needed.