APPLICAZIONE DI HDSM

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    J. S. A fr. Inst. M in. M etal/., vol. 91, no. 3.Mar. 1 99 1. p p. 9 5-1 ,0 3.

    A comparison of several kinetic models for theadsorption of gold cyan ide on to activated carbonby J.O . LE ROUX*, A.W . BRYSONt, and B.O. YOUNGt

    SYNOPSISSeveral rate models for the adsorption of gold cyanide from aqueous solution onto activated carbon are givenin the literature. The purpose of this study is to critically examine their ability to sim ulate the adsorption processover a wide range of conditions.An account is given of a com prehensive set of experim ental work on the kinetics of gold adsorption onto a coconut-shell-based activated carbon. Equilibrium isotherm s were also determ ined.It is concluded that the homogeneous surface-diffusion model fits the experimental data reasonably well andprovides a good balance between simplicity and descriptive accuracy. The m odel contains two parameters: thee xtr a- pa rtic le mas s- tr an sfe r c oe ffic ie nt a nd a n e ffe ctiv e in tr ap ar tic le s urfa ce -d iffu sio n c oe ffic ie nt. B oth c an b e e va lu ate drea dily fro m sim ple ad so rp tio n e xp erim ents.SAMEVATTINGDaar word verskeie tem pomodelle vir die adsorpsie van goudsianied uit 'n w ate rig e o plo ssin g o p g ea ktive erd ekoolstof in die literatuur aangegee. Die doel van hierdie studie is om hul vermoe aan die adsorpsieproses in 'ngroot verskeidenheid om standighede te sim uleer, krities te ondersoek.Daar word verslag gedoen oor 'n om vattende stel eksperim ente in verband m et die kinetika van goudadsorpsieop geaktiveerde koolstof wat van klapperdoppe b~rei is. Daar is ook ewewigsisoterme vasgestel.Die gevolgtrekking word gem aak dat die hom ogene oppervlakdiffusiem odel die eksperim entele data redelik goedpas en 'n goeie balans tussen eenvoudige en beskrywende akkuraatheid gee. Die m odel het twee parameters:d ie e ks tr ap ar tik el-ma ss ao or dra gk oe ffis ie nt e n 'n e ffe ktiewe in tr ap artik el-o pp er vla kd iffu sie ko effis ie nt. A lb ei k an mak likaan die hand van eenvoudige adsorpsie-eksperimente ge-evalueer word.

    INTRODUCTIONT he recovery of gold by the adsorption of aurocyanidecom plexes onto activated carbon is a w ell-establishedc ommerc ial m eta llu rg ic al p ro ce ss !. It h as fo un d ap plic a-tion in c ou nte rc urre nt s tirre d-ta nk sy stem s (th e ca rb on -in-pulp or C IF process), in packed adsorption colum n~ ,and in fluidized-bed reactors3. A fter the gold species hasbeen eluted from the activated carbon w ith a hot causticc yanid e solu tio n, th e g old is r ec ov er ed by e le ctrow in nin gor zinc precipitation and, finally, by sm elting!.The d es ig n o f such a ctiv ate d-c arb on adsor ptio n sys temsm ay be based on inform ation gained from pilot-plant testprogrammes. A lthough this approach considers m anypractical aspects of a particular application, the tests arehighly specific and tim e-consum ing, and do not readilyl en d t hemse lv es to g en era liz atio n, a nd h en ce to t he p re dic -tion of system variables other than those em ployed in thep artic ula r te st. O n th e o th er h an d, w ell-c on tro lle d b en ch -s ca le la bo ra to ry adsor ptio n exp eriments c an b e emplo yedfo r th e d ev elo pmen t o f m ath ematic al p ro ce ss mod els th atcan be used to elucidate adsorption and adsorber designp rin cip le s, a nd w ill p erm it the d ire cted u se o f p ilo t-sc aletests to verify the design of adsorption system s4.L abora to ry -s ca le a dsorp tio n s tu die s c ou ld t yp ic ally in -volve equilibrium or kinetic experim ents. R esearchersh av e re po rte d tha t eq uilib rium b etw ee n g old cy an id e a ndactivated carbon had not been achieved after three

    * D iv is io n o f Wate r T ec hn olo gy , C SIR , P .O . B ox 3 90 , P re to ria 0 00 1.t D epartm ent of C hem ical Engineering, U niversity of the W itw aters-rand, P .O . W its, 20 50 T ransvaal. (A ll correspo nden ce sho uld b ea dd re ss ed to th ese a uth ors .)@ The South A frican Institute of M ining and M etallurgy, 1991. SAISSN 0038-223X /3.00 + 0.00. Paper received 7th M arch, 1990;m od ified pap er received 2 2nd O cto ber, 199 0.

    m onths5 and, in another case, after six m onths6. Sincepractical retention times in a CIF adsorber are of theorder of one houe, it appears reasonable to focus onadsorption kinetics as a m eans of describing and com -p arin g diffe re nt g old -a dso rp tio n sy stem~. In this re ga rd ,m any of the rate m echanism s are studied m ore easily byth e u se o f a gita ted fin ite -b ath ba tc h a ds orp tio n sy stem s8 .A major objective of the study reported here was toevaluate and com pare a num ber of adsorption m odels interm s of their adequacy in describing the adsorption ofaurocyanide species from a suitable background solu-tion. B oth em pirical and fundam ental kinetic m odels ofmod erate comp le xity w ere co ns id ered .K IN ET IC MODEL S

    As is the case with all kinetic processes, the rate ofadsorption is a function of the state of the system ; thatis, the rate is dependent on intensive properties only. Insom e of the m odels that have been proposed, tim e is in-cluded in the expressions. How ever, this variable is anextensive property and therefore has no place in suchm odels. In batch experim ents, tim e appears in the m odelas a consequence of mass balances, and not kineticexpressions.R ate m odels can generally be classified as em pirical,mechanistic, or a combination of the two. In the first,an attem pt is m ade to fit the experim ental data to a sim plefunctional form , w hich need not possess any theoreticalbasis. M echanistic m odels, on the other hand, attem ptto use detailed physicochem ical concepts to describe theprocess. H ow ever, this m ay lead to prohibitively com -plex m odels that m ay be difficult to apply in practice.

    JO URNAL O F TH E SOUTH AFR IC AN IN STITU TE O F M IN IN G A ND META LLURGY MARCH 1991 95

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    A good m odel should therefore strike a balance betw eensimp lic ity a nd d esc rip tiv e a cc ura cy .Empirica l R ate Mod elsT he sim plest m eans of linearizing the data from batchk in etic e xp erimen ts is to p lo t th e c on ce ntra tio n o f re sid ua ladsorbate in the liquid phase against the square root ofthe tim e9. T his m ethod w as em ployed w ith good resultsby Weber and MorrislO, who compared the rates ofadsorption of a range of alkyl benzene sulphonates overtime ranges of several hours. However, the methodproved inadequate to linearize kinetic data for p-nitro-phenol9.M any of the other em pirical rate m odels that have beenused to describe the adsorption of gold from solutionhave been reviewed, although not exhaustively, byJ o hn sl1 , L a B ro oy et al. 12 ,and Van Deventef. The m ostrelevant of these m odels are listed below.

    F irst-o rd er ra te mod el1 1:r = kl C - k2 q , (1 )

    M odel of Dixon e t a l.l3 :r = k3 C(q+ - q) - k4 q (2 )

    M odel of Nicol e t a l.2 :r = ks (K C - q) (3 )

    M odel of Flem ing et al. 14 :q = k6 Co tn " (4 )

    Model of La Brooy et al. 12 :q = k7 C tn , " (5 )

    where r = rate of gold adsorption (m g A u/s'dm 3)C = concentration of gold in solution (m g Au/dm3)q = mass of gold on the carbon (mg Au/g car-bon)t = tim e elapsed from start of batch experim ent(s )Co = ini ti al concentr at ion o f gold in solution (mgAu/dm3)q+ = mass of gold on carbon w hen it is com plete-ly loaded (m g Au/ g carbon)kl . . . . k7, K, n = cha ra cte ristic c on sta nts.

    These m odels are all subject to lim itations, either inregard to adequacy of fit or in terms of the time spano ver w hich th ey accurately de sc rib e the gold co ncen tra-tion in solution. Thus, the first-order rate m odel whentested by J o hns7 w as rejected in favour of a m ore sophis-ticated non-linear m odel (to be considered later) on thegrounds that the rate constants are dependent upon thep artic le siz e o f th e a ctiv ate d c arb on , a nd a re a lso d iffic ultto calculate accurately since they differ by som e fiveo rd ers of m ag nitude .L a B rooy e t a l.1 2 found both the m odel of Fleming,equation (4), and that of N icol e t al., equation (3), tobe adequate for only the first hour of batch adsorption.The y c on se qu en tly a da pte d th e fo rmer mod el b y re pla cin gthe initial conc entration, C o, by the tim e-d epen den t con-centration, C (equation (5, and reported a good fit overthe first 4 hours of their kinetic batch adsorption96 MARCH 1991 JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY

    experiments.The sim plicity and apparent usefulness of this two-param eter model over an extended adsorption periodm ake it attractive for describing the rate of gold adsorp-tion. A s w ith all em pirical m odels, its value is lim ited tothe range of experim ental variables used. In addition,tim e appears in equation (5) and, as pointed out earlier,this expression is valid only for batch system s.Mechan is ti c Mode lsPossib le T ra nsp ort Mec ha nism sFrom a m echanistic point of view, the rate of adsorp-tion of an adsorbate on to activ ated carb on can be describ -ed by the follow in g series of transpo rt m echan ism sI5 .16 :

    (1) film diffusion, i.e. diffusion from the bulk liquidphase through a hypothetical hydrodynam ic boun-dary layer or film surrounding the particle;(2) pore diffusion, i.e. diffusion w ithin the pore fluid ofthe par ti cl e;(3) surface diffusion, i.e. m igration of adsorbed m ole-cules along the internal pore wall; and'(4) adsorption onto the internal surface of the carbon.The se ste ps e ac h re pre se nt a re sista nc e in th e tra nsp ortm echanism . Adsorption step (4) is considered to be sorapid as n ever to c onstitu te the rate-lim iting step a nd, forstro ng ly a dso rb ed mole cu le s, th e p ore -d iffu sio n flu x h asbeen shown to be orders of magnitude lower than thato f surfa ce diffu sion l7 . T hese tw o step s can conseq uen t-ly be neglected in m ost adsorbate-adsorbent system s15w ithout undue loss of accuracy. T hus, the rate of adsor-bate removal from a liquid can often be adequatelydescribed by the assum ption of initial film-transferd om in ance, eve ntu al surface-d iffu sion d om ina nce, and

    a transition period during which both mechanisms in-fluence the adsorption rate18. V an L ie~, com paring thes urf ac e- dif fu sion and por e- dif fu sion mode ls , s howed th atthey h ave very sim ilar cha racteristics, and th at it is th ere-fore difficult to separate the tw o m echanism s. H e ulti-m ately show ed that it is adequate to com bine the effectsof intraparticle diffusion by m eans of an effective sur-f ac e- dif fu sion coe ff ic ient . Thi s coe ff ic ient i s t he re fo re notnecessarily the true surface-diffusion coefficient, butrather a m easure of intraparticle diffusion.Film transfer can be assum ed to determ ine the adsorp-tion rate in the early stages of a batch adsorption experi-m ent, and the film theory postulates a linear concentra-

    tion gradient from the bulk liquid to the surface ofthe adsorbent particle. If diffusion through the film isdescribed by Fick's first law , and if spherical-particleg eom etry is assum ed, the flu x, iT , of the diffusin g speciesis given byiT = kf (Cb - C,), (6 )

    where kf is th e film c oeffic ient, C b is the conc entrationof the bulk liquid phase of the adsorbate species, and Csis th e c on ce ntra tio n o f th e sp ec ie s a t th e in te rfa ce b etw ee nth e b ulk liq uid a nd th e p artic le su rfa ce . The film -tra nsfe rm odel assum es equilibrium betw een C s and the averageads or bent l oadi ng o r s oli d- phas e concentr ati on , ij , of th eadso rbate species . Th is e ff ec tive ly means tha t int rapar ti cl ediffusion is assumed to be rapid. From a m ass balanceo ver th e batch reacto r on the b asis o f sph erical-particle

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    geom etry, the batch rate equatio n fo r film -diffusion con-trol is found to bedC bTt = - kr {3(Cb - Cs), """""""""""""" (7 )

    where{3 = ~ """"""""""""""""""""""" (8 )V pprp

    and Pp i s the density of the dry adsorbent in air (i.e. thed en sity o f th e a ds orb en t p artic le ), r is the radius of theparticle, m is the mass of the ads6rbent, and V is thevolum e of the batch reactor.L in ea r F ilm -tra nsfe r Mod elT he linear film -transfer m odel assum es that the con-centration of the adsorbate at the particle surface, C s, isnegligible at sm all v alues of tim e in a b atch reactor, com-pared with the concentration of the bulk liquid, Cb,Thus, equation (8) can be integrated to yield

    In(~:Jlt-o = -k r {3 t """"""""""""""'" (9 )Experimentally kr is determ ined from the initial slopeof a plot of In C/ Cbo against t fo r a given adsorbent-particle diam eter since {3 is a function of r .

    Non -lin ea r F ilm -tra nsfe r Mod elT he linear film -transfer m odel is applicable only overthe initial portion of the kinetic curve, insofar as it islinear and can be described by equation (9). The film -transfer m odel can be refined by the introduction of ane xp re ss io n to d esc rib e th e c on ce ntra tio n o f th e a ds orb ateat the particle surface, C s in equation (7). The concen-tra tio n o f th e liq uid p ha se a t th e p artic le -liq uid in te rfa ceis assum ed to be in equilibrium w ith the concentrationof the solid adsorbate at the interface, and can thereforebe described by an appropriate isotherm m odel. In thep resent stud y, the F reundlich isoth erm w as found to ade-q ua te ly d es crib e th e e xp erim en ta l e qu ilib rium d ata . T hisisotherm has the formq = A C\ """"""""""""""""""""""" (10)where A is the Freundlich constant and "I is the Freundlichex ponent. T he combination of equations (7) and (10) w ithth e b atc h rea cto r m ass -b ala nc e e qu atio n y ie ld s th e fo llow-ing differential rate equation in the variable C b:d~b= -{3kr[C b- (V(C,;;;Cb}/"tl (11)

    w hich, upon integration, results inrCbo dCbJc b [Cb r

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    a uro cy an id e sp ec ie s, a s a dso rb ed b y a p artic ula te a dso rb -ent in a stirred batch reactor or finite bath. In the con-struction of an adsorption model for this system , them ic ro - a nd mac ro -e nv iro nmen ts a re c on sid ere d se pa ra te -ly, and the concentrations of the solid and liquid phasesa re th en a ss oc ia ted by a s uit ab le equ il ib rium re la ti on sh ip .T he follow ing initial assum ptions w ere m ade:. spherical geom etry is assum ed for the adsorbent par-

    ticlesl9. the particles of adsorbent are considered to be iso-trop ic o r un iform16. adsorption is considered to take place under isother-ma l condit io ns. diffusion of the adsorbate in the bulk liquid is assum -ed to have a negligible influencel6.A s discu ssed earlier, in th is stud y intra p artic le d iffu -sion is regarded as a single m echanism . It is referred toas surface diffusion, and is characterized by the effec-t iv e s ur fa ce -d if fu sion coe ff ic ient .General expositions of the HSDM are given else-where1s,zo. A detailed derivation of the form of the

    model used in this study has been given by Le Rouxz1.The governing equations in dim ensionless form are asfollows:T he particle m ass-balance equation is

    ~~ = ;z % (rz~;) (15)wi th ini tial condit ion

    if> (r , r = 0) = 0 (16)an d bou nd ary co ndition s

    ~~ I!=o = 0, (17)and

    ~~ I!=I = Shb (X - XJ """""""""""'" (18)

    Sh kfroCbO , ( Cb O )= D - Bl - (19)Pp sqo ppqoB i = ~ (20)ppDs'

    The d im ension less v ariab les areif> = !Lqo

    CsX =- Cb o

    CbX= -Cb oillsr= - ~

    rr = -. (21)roSh b is th e S herw ood n umbe r base d on the su rface -d iffu -s ion coeff ic ient (D J for a batch reactor system , and Biis the Biot num ber, w hich represents the ratio betw eenthe film - and the surface-diffusion coefficients for aspec if ic par ti cl e r ad ius1s; qo is the solid concentration ineq uilib rium w ith the in itial liq uid con cen tratio n Cbo'The reactor m ass-balance equation isrl zx(r) = 1 - a J o r if>(r,r) dr, (22)98 MARCH 1 99 1 JOURNA L O F THE SOU TH A FR IC AN IN ST ITU TE O F M IN ING AND META LLURGY

    where3 m q oa = - . VCbo

    The F reundli ch is oth erm in d imens ionl es s f orm becomesif> = xr. , (23)T he H SD M eq uation s w ere solv ed nu merically. E qu a-

    tion (15) was solved by use of the NAG FORTRANso ftw are -lib ra ry ro utin e D03PGF, while th e in te gra tio nof equation (22) was perform ed by the IM SL softw are-library routines D CSIN T and D CSITG.EXPERIMENTAL

    Activated carbons m ade from coconut shell are con-sidered to be well-suited to the recovery of gold6,1l,zz,and the brand G210 AS, which is m anufactured by PicaSA (France), w as consequently selected for the presentstudy. An analysis of som e of the properties of this ac-tivated carbon is given in Table I. The skeletal densitywas determ ined by use of a M icrom eritics Autopycno-meter M odel 1320, the BET internal-surface area wasmeasured with a M icromeritics Rapid Surface AreaA nalyzer M odel 2200A , and the pore-volum e distribu-tio ns an d particle d en sities w ere de term ine d b y mercuryporisom etry on a M icrom eritics A utopore M odel 9200.The iodine numbers, methylene blue numbers, andcaram el decolorizing index are standard analyses foradsorbentsZ 3, and are perform ed w ith m olecules of pro-gre ssiv ely in cre asin g mole cular m asses (io dine = 254 am uand methylene blue = 373,9 am u). Thus, they give anindication of the pores accessible to these m olecules.

    T AB LE IP RO PE RT IE S O F A CT IV AT ED -C AR BO N A DS OR BE NT

    Property G 21O A S (Pica)Io din e n um berBET surface area (m2)M ethylene blue num berC ara me l d eco lo riz in g (0/0)P article density (g/ cm J)Skeletal density (g/ cm J)A pparent density (g/cm J)Total pore volum e (cm J/cm J)M acro-pore volum e (cm 3/cm 3)M eso-pore volum e (cm 3/cm 3)M icro-pore volum e (cm 3/cm 3)A sh co nten t (0J0)

    134598 126 277,80,8182,1510,4310,6200,1860,1300,3041,77

    The aurocyanide com plex A u(CN ); has a m olecularm ass of 246 am u, which corresponds closely to the m assof the iodine m olecule.A samp le o f c ommerc ia lly a va ila ble G21Oa ctiv ate d c ar-bon was dry-sieved, and the particle-size fraction plus1,4 mm minus 1,7 mm was selected for the study. Thearithm etic average of 1,55 m m w as used for all the m odelcalculations.P ro perties of th e A dsorbateThe gold solution was prepared according to themethod of AARL 24 for the determ ination of the gold-adso rp tion rate o f activated carb on. A ll the re agen ts w ere

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    I ni ti al g ol dconcentration

    (Cbe) kf D eg re es o f Correlationmg/I 10004cm/s freedom coefficient5,30 7,97 4 0,95958,73 4,85 5 0,992932,00 5,66 3 0,990454,44 5,44 3 0,9785111,11 4,88 3 0,9952

    ClE~ 1 0' .. .. .. .Adso rp tio n E xp erim ents g;All the equilibrium adsorption experiments were con- ~.Qducted using G 21O activated carbon of the fraction plus

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    In itia l g oldconcentration M inimum sum(Coo) kr Degrees of o f s qu ar edmg/I 10-4 cm /s freedom errors

    5,30 5,40 10 2,48 10-25,30 8,10 3 1,08 10-38,73 5,39 3 3,95 10-432,00 5,42 3 5,87 10-454,44 5,26 3 8,33 10-41II,ll 4,18 7,70 10-4

    results. J o hns7 also consid ered th e linear film -transfermodel to be inadequate, and La Brooy e t a l.1 2 found itto be accurate only up to adsorption tim es of 1 hour. Thelatter finding w as confirm ed in the present study for theinitial gold concentrations of 5,3 and 8,7 m g/I.N on -lin ea r F ilm -tra nsfe r Mod elT he non-lin ear film -tran sfer model is co nsidered to be

    m ore sophisticated than the linear film -transfer m odelsince th e form er does not neglect th e gold concentrationof the intraparticle solid phase.The mod el w as a pp lie d u sin g d imen sio nle ss c on ce ntra -tion-tim e profiles that give the solution for each valueof Cbo of equation (3). The profiles for the differentinitial concentrations are depicted in Fig. 1. It is note-w orthy that the initial p ortions of the p rofiles are alm ostlin ea r and independent o f t he in itia l liq uid concentr atio n,C bo, and that this region constitutes an increasing por-tion of the profile as C bo decreases.T he application o f th e non -linear film -tran sfer modelto the kinetic data for an initial gold concentration of8,73 m g/l is illustrated in Fig. 3, and the results for allth e in itia l c on cen tra tio ns emp lo ye d a re g iv en in T ab le Ill.

    1 ,0 - --- -- --- -- ---0,9~ 0,8

    "g 0,78~ 0,6g

    F ilm coefficient: 5,39 x 10-3 cm/s3 degrees of freedom

    ~ 0,5"E0"~ 0,4Cl )

    ~ 0,30,20,1 0 20 0 250 300 350 40050 4500 100

    T im e, m inF ig . 3 -Non -lin ea r fllm -d iffu sio n mod el fo r a n in itia lgold c on ce ntra tion of 8 ,7 3 mg/dm3

    TABLE IIINON-L INEAR FILM-TRANSFER MODEL: F ILM COEFFICIENTS FORDIFFERENT INTIAL GOLD CONCENTRAnONS

    Fig. 4 illustrates the inadequacy of the model at them ost favourable C oo value of 5,3 m g/l by com paring theapplication of the m odel to the whole range of kineticdata ov er 4 80 m in utes w ith th e applicatio n ov er the in itial60 m inutes only. The inadequacy of the model becameconsid erably more pronou nced as the initial con centra-100 MARCH 1991 JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY

    tion of gold increased. T his inadequate perform ance ofthe m odel is at variance w ith the results of J ohns7 sincehe used such a high ratio of carbon to solution that theconcentration of the gold solution was reduced to un-m easureably low levels before intraparticle diffusionbecam e relevant. Therefore, the results of the presentstudy do no t su pport th e assumption of film -tran sfer co n-trol of the adsorption rate over the range of gold con-cen tr at ions conside red.

    Fi lm coeff ic ien t: 5,40 x 10-3 cmis- 1 0 d eg re es o f fr ee dom8,10 x 10-3 cmis- 3 d eg re es o f fr ee dom

    50,78"C

    0,6":;gO,5gjCl)~O ,"0 ;~OEi50, 20,1

    0 35 0 400 450 50000 150 200 250 300T im e, m in50

    Fig. 4-Non-l inear f ilm-t ransfer model : Determinati ono f th e f ilm coe ff ic ient a t d if fe rent d eg rees o f f re edomf rom e ith er th e in itia l o r a ll t he d at a v alu es ( in itia l g ol dc on ce ntra tio n 5 ,3 mg/dm3 )

    50 0

    Th e results obtained from the linear and non-linearfilm -tran sfer models are compared graphically in F ig. 5,from which it appears that the kf values for the twomod els are substan tially sim ilar. Fo r this comparison , itshould be borne in m ind that the m ethods of determin-ing kf in both m odels are insensitive, Le. the num ber ofdegrees of freedom is sm all, and on this basis no signifi-cant relation sh ip app ears to ex ist betw een the v alues o b-ta in ed from th e two mod els. T hu s, th e more so ph istic ate dnon-linear film model does not appear to represent asignificant im provem ent over the sim pler, linear filmmodel.

    Film co efficie nt, 1 0 cm's1086420 5,30 8,73 32,0 54,4

    In it ia l [Au], mg'l- Linearmodel - Non-l inearmodelFig.5 -L in ea r and non -lin ea r f ilm- tr an sf er mode ls : Compar is onof film-transfercoefficientsfor rate studies at differe"t initialgoldconcentrations

    111,1

    Empirical Rate Model of La Brooy et al.T he em pirical m odel suggested by L a B rooy e t a l.1 2asdescribed by eq uatio n (5) w as applied to test its adeq uacy

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    I nitia l g oldconcentration

    (Coo) kf n Correlationmg/I [minlml/ (slope) coefficient5,30 0,327 1,229 0,95808,73 1,052 0,935 0,998532,00 2,189 0,742 0,998854,44 3,177 0,640 0,9985111,11

    I nitia l g old HSDM par am ete rs Mo de l fit:concentration m inim um sum

    (Coo) kf D, o f s qu are d e rr or smg/l 1 0-4 cm/s 10 - 9 cm2/s 10-35,30 3,70 2,10 6,678,73 0,11 3,04 I,ll

    32,00 4,40 9,81 1,6454,44 1,62 15,2 1,02111,11 0,54 22,6 1,60

    at d escrib ing the available kinetic data. T he equation w aslinearized by the plotting of In (q / C ) against In t and thefitting of a linear regression m odel to the m odified datato obtain a slope n and an intercept In k7 ' The resul ti ngvalues of nand k7 are given in Table IV , and the modelequations are compared in Fig. 6.TABLE IV

    EMPIRICAL RATE MODEL OF LA BROOY et al,l2: MODELP AR AM ETE RS F OR D IF FE REN T IN IT IA L G OL D CO NCE NT RA TIO NS

    8

    7I ni tia l g old c on cn , mgll"of." 5,3-9- 8,7-.- 32,0-8- 54,4

    6

    a:I.!: 5

    4

    3

    22 6 7 84 5

    In tF ig . 6 -C om pa ris on o f L a B ro oy m ode l c urve s fo r d iffe re nt in itia lgo ld concent rat ions

    It is apparent that the m odel fits the data w ell over thefull tim e range for all the initial gold concentrationsstudied except 111 m g/l, w here the transform ation w astotally non-linear. U nlike th e findings of L a B rooy e t a l.,the present study did not yield n values close to unity inall cases. H ow ever, their study w as conducted at an initialgold concentration of 10 m g/l, and the n valu e in T ableIV for C oo = 8,73 m g/l is slightly below unity. It appearstherefore that their observation is a special case at theinitial concentration they had selected .

    H om ogeneous S urface-diffusion ModelThe hom ogeneous surface-diffusion m odel (H SDM)w as derived in a form that assum ed constant diffusivity.This assum ption w as m ade to lim it the num ber of m odelparam eters to tw o, since recognition of the concentra-tion dependence of D, would introduce a third para-meter into the HSDM equations25 to describe the in-c re ase in th e e ffe ctiv e s urfa ce d iffu siv ity w ith in cre as in gsurface loading. In this regard, V an D evente~ success-

    fu lly a pp lie d a th re e-p arame te r g old -a ds orp tio n mod el inw hich he assum ed that the surface concentration w asd ep en dent on the surface diffusivity. A residen ce tim e o fabout 1 hour in a typical CIF reactor underlies theassum ption of the present stu dy that the tw o-param eterm odel is justified w hen applied to kinetic data that havebeen collected at relatively low loadings. If the goldloading approaches the equilibrium loading, a m oresophisticated m odel is required , as shown by V an D even-te~.The application of the HSDM to the experimentalkinetic data is illustrated in Fig. 7 for an initial gold con-centration of 8,73 mg/I. The values of the fitted para-m eters for the other initial concentrations are providedin T able V and illustrated in Fig. 8. T he results indicatea good fit of the H SDM over the tim e range studied. Fig.8 shows an increase in D, w ith increasing initial goldconcentration, but no particular trend for the kf values.1,

    F ilm c oe ffic ie nt: 7 ,8 0 x 1 0-8 c mlsSurface d if fus ion coef fi ci en t :3,27 x 10-9 cm 'ls

    0,9iJ~ 0,8c:"80,7'C~ 0,6~ 0, 5c0.~ 0,0)EC 0,30, 20, 10 50 10 0 150 200 250 300T im e, m in 350 400 450 500

    Fig. 7 -Homoge ne ou s s urfa ce -d iffu sio n mode l fo r a ninitial gold concentration of 8,73 mg/dm3TABLE V

    HOMOGENEOUSSURFACE-DIFFUSIONMODEL: MOD ELPA RAMETE RSFOR DIFFERENT INIT IAL GOLD CONCENTRATIONS

    T he absence of a sim ple relation betw een [A u]o and kfm ay be attributable to a com bination of tw o factors, vizth e relativ e in ac cu ra cy o f th e a na ly tic al d ete rm in atio n o fthe residual-gold concentration as d iscussed abo ve, andthe insensitivity of the HSDM to variation in the kfvalue. Since the film coefficient is determ ined m ainlyfrom th e in itia l p ortio n o f th e ra te c urv e, sma ll v aria tio nsin the analytical accuracy of the first few data pointscould have a significant im pact on its m agnitude. O n thew hole, the m odel can be considered to b e satisfacto ry fora time range of about 300 m inutes for initial gold con-centrations of up to about 110 mg/I.

    JO URNA L O F TH E SOUTH A FR IC AN IN STIT UTE O F M IN IN G AND MET ALLU RGY MARCH 1991 10 1

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    24

    20

    f 160c~ Je12E00c 8O '

    4

    00

    Mode l parameters:-e - D. (10-9 cm'l s). k, (10-9 cmls )

    .. .

    40 60Initial [Au], mg/I

    Fig. 8-Comparlson of k, an d D. for different Initial go ldconcentrations

    800 10 0 12 0

    HSDM Sens itiv ity AnalysisThe sensitivity of the HSDM was analysed at an ini-tial gold concentration of 8,73 m g/l since that case gavea good description of the experim ental data and has som epractical s ignif icance.Fig. 9 contains the m odel curves for film coefficientsof 50, 75, 125, 150, and 200 per cent of the optimumparam eter value, and compares these resp onses w ith thatof the m odel that best fits the data. It appears that fairlyl arg e in cr ea se s in kf have only a slight effect on the m odelup to tim es of 200 m inutes, but that a reduction in kf ha sm ore m arked effects. This shows that the accurate de-te rm in atio n o f kf is no t p ossible from the present experi-m ents. G enerally, the effect o f v ariation in kf is to c ha ng ethe initial slope of the model curve up to about 100minutes. Fig. 10 shows the effect of variations in thesurface-dif fus ion coeff ic ient, Ds, by 50, 75, 125, and 150per cent. The effect is sm oother than w hen the m m coeffi-cient is varied, and it is notable that decreases in Ds hadthe effect of decreasing the gold adsorption rate over theentire period of the experim ent.

    CONCLUSIONSK in etic -ra te mod els b ase d o n film -tra nsfe r re sista nc ew ere fou nd to be o f lim ited ap plicab ility in describing th erate of gold adsorption in the adsorbent-adsorbate

    sy stem s studied. A lthoug h these models ten d to describethe rate data better at low er initial gold concen trations,both models were found to be useful only for the firsthour, representing a low gold loading.B oth tw o-param eter models in vestigated in the study ,viz the empirical model of La Brooy et al.12 and thehom ogeneous surface-diffusion m odel (H SD M), w erefound to adequately describe the experim ental kineticd ata o ve r th e p erio d o f 4 80 m in ute s se le cte d fo r th is stu dy .T he form er m odel w as found to be m ost suitable at low erinitial gold concentrations, and could not be applied atthe h ighest co ncentratio n of III m g/l. H ow ev er, concen-trations such as this would not be encountered in prac-tice. A shortcom ing of this m odel is its em pirical basis,which m akes it suitable as a descriptive, rather than asa pred ictiv e or m echanistic, tool. B oth from a fund am en-

    0,9~0,8c:u80,7"~0,6~ 0,50'0;fii0,4Eis 0,3

    1,0

    Optimum k, = 7 ,8 E -6 c mlsOptimum D. = 3 ,2 7 E -9 cm 'l s0, 20 200 250 300T im e , m in 350 400 45 0 50 010 0 15 00

    Fig. 9-HSDM:Sensitivity o f th e m od el to v aria tio nsIn th e film c oe fficie nt k, ( In it ia l go ld concent ra ti on8 ,73 mg /dm3)

    0,20

    0 E xp er im en ta l v alu esMode ls fo r:

    "'- -optimumD.",." ==== 50% optimumD."'" '~ = - = = 7 5% opt im um D:,.,~ ~ === 125%optimumD:",:.~, ' ~ ==: :: :: - ., 150% optimum D.

    ~=~:~~.:::~~~~

    200 250T im e , m in 300 3500 400 45000 50050

    F ig . 10-HSDM: Sen si tiv it y o f th e mode l t o v ar ia tio nsin the surface-diffusion coeff ic ient D. ( in it ia l go ldconcen trat ion 8 ,73 mg/dm3)

    tal and a descriptive point of view, the two-param eterHSDM was found to be adequate for the purpose ofdescribing the rate of adsorption of gold cyanide in abat ch re ac to r.I t is worth noting that these experim ents and m ost ofthe other experim ents conducted to date have used clearsolutions. The effect of slurries on the adsorption per-form ance have been studied by Jordi e t a l.2 6.ACKNOWLEDGEMENTS

    The guidance of Dr B.M . van Vliet of the Division ofW ater T echnology of the C SIR and the laboratory assist-ance of M rs E. Steyn are gratefully acknowledged.REFERENCES

    1. LAXEN, P.A. G eneral introduction. Lecture presented at theC arbon School of the SA l M M , first held at M intek, R andburg,Q ct. 19 85 .2. NICOL, M .J., F LE MIN G,C A., an d C RO M BE RG ,G . T he a ds or ptio nof gold cyanide onto activated carbon. I. The kinetics of adsorp-tion from pulps. J. S. A fr. Inst. M in. M etal/., vo!. 84, no. 2. 1984.p p. 5 0-5 4.

    3. NICOL, D .I. The adsorption of dissolved gold onto activatedcarbon in a NIM CIX contactor. J. S. A fr. Inst. M in. M etal/., vo!.79. 1979. p. 500.4. WEBER, W .J., and SMITH, E.H. Simulation and design models fora ds or ptio n p ro ce ss es. E nviro nm en ta l S cien ce an d T echn olo gy, vo!.21, no. 11. 1987. pp. 1040-1050.

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    5. M cD oU GA LL, G .J., HA NCO CK , R.D ., N ICO L, M .J., W ELLING TON ,O .L., and COPPERTHW AITE, R.G. The mechanism of the adsorp-tion of gold cyanide onto activated carbon. J. S. Afr. Inst. M in.Metall., vol. 80, no. 9. 1980. pp. 344-356.

    6. VAN DEVENTER, J.S.l. Kinetic model for the adsorption of metalcyanides on activated charcoal. PhD thesis, University of Stellen-bosch, 1984.

    7. JOHNS, M .W . The simulation of gold adsorption by carbon usinga film diffusion model. MSc (Eng) dissertation, University of theW itwatersrand, Johannesburg, 1987.

    8. V AN LIER. M ass transfer to activated carbon in aqueous solutions.PhD thesis, Technische Universiteit, Delft (Netherlands), 1989.9. FAUST, S.D ., and ALY, O.M . Adsorption processes for w ater treat-

    ment. Boston (USA), Butterworths, 1986.10. WEBER, W .l., and MORRIS, J.C . Equilibria and capacities for

    adsorption on carbon. J. Sanitary Eng. D iy., ASC E, vo l. 9 0 (S A3 ).1964. pp. 79-107.

    11. JOHNS, M . W . Model applications. Lecture presented at CarbonSchool of the SAIMM , M intek, Randburg, act. 1985.

    12. LA BROOY, S.R ., BAX, A.R., MUIR, D .M ., HOSKING, J.W .,HUGHES, RC., and PARENTICH, A. Fouling of activated carbonb y c ir cu it o rg an ic s. G old lO O, Proceedings of the International C on-ference on Gold. Johannesburg, South African Institute of M iningand M etallurgy, 1986. pp. 123-132.

    13. DIXON, S., CHO, RH., and PITT, c.H . The interaction betweengold cyanide, silver cyanide and high surface area charcoal. AIChESym posium Series, 174 (173). 1978. p. 75.14. FLEMING, c.A ., N ICOL, M .l., and NICOL, DJ. The optimisationof a carbon-in-pulp adsorption circuit based on the kinetics of ex-traction of aurocyanide by activated carbon. Paper presented atthe meeting 'Ion Exchange and Solvent Extraction in Mineral Pro-cessing', M intek, Randburg, Feb. 1980.

    15. CRITTENDEN, J .C . Mathematical modelling of a fixed bedadsorber-single component and multicomponent. PhD thesis,

    University of M ichigan, Ann Arbor (USA), 1976.16. SO NTHEIM ER, H., FRICK , B.R., FETTIG, J., H ORNER, G ., HU BELE,C ., and ZIMMER , G . A dsorptionsverfahren zur W asserreinigung.

    D VGW -Forschungstelle am Engeler-Bunte, Institute der Univer-sitiit Karlsruhe. K arlsruhe (W est G erm any), G. Braun Gm bH , 1985.

    17. NERETNIEKS, I. Analysis of some adsorption experiments w itha ctiv ate d c arb on . Chem . Eng. Sci., vol. 31. 1976. pp. 1029-1035.

    18. LETTERM AN, R.D ., QU ON , J.E., and GEM MEL, R.S. Film transfercoeffiCient in agitated suspensions of activated carbon. J. WaterP ollu tio n C on tr ol F ed er atio n, vol. 46, no. 11. 1974. pp. 2536-2546.

    19. D IGIAN O, F.A., and W EBER, W .l. Sorption kinetics in finite-bathsystems. J. Sanitary Eng. D iy., Proc. ASCE, vol. 98 (SA 6). 1972.p p. 1 02 1-1 03 6.20. LIAPIS, A .I., and RIPPEN, D.W .T. A general model, for the simu-

    lation of multi-component adsorption from a finite bath. Chem.Eng. Sci., vol. 32. 1977. pp. 619-627.

    21. LE Roux, J.D . Modelling of the effect of organic fouling on theadsorption of gold cyanide. MSc Dissertation, University of theW itw atersrand, Johannesburg, 1989.

    22. M cDoUGALL, G .J. The manufacture of activated carbon. CarbonSchool of the SAIMM , M intek, Randburg, act. 1985.

    23. A MERICAN W ATER W ORKS ASSOCIATION (A WWA). Standard forg ran ular ac tiv ate d c arb on . J. Amer. W ater W orks Assoc., v ol. 6 6,no. 11. 1974. pp. 672-681.

    24 . A NG LO AMERIC AN R ES EARCH LABORATOR IE S (AAR L). S tan da rdanalytical procedures for evaluation of activated carbon. J ohan-nesburg, Jul. 1987.25. ANDERSON, P. The modelling and design of an activated carbonadsorber for the recovery of organic components from a cellulose-plant effluent. M Sc D issertation, U niversity of the W itw atersrand,Johannesburg, 1986.

    26. JORD!, R.G ., YOUNG, B.D., and BRYSON, A.W . Gold adsorptionon activated carbon and the effect of suspended solids. C hem. Eng.Commun., 1991.

    Comminution processesThe South A frican Institute of M ining and M etallur-gy w ill be holding a 3-day school devoted to the Practi-

    cal Design of Comminution Processes. The School issch edu led for 14th to 16th M ay , 1991, in Johannesb urg.ObjectiveThe objective of the School is to provide a wide in-sight into the m odern theory and practices em ployed inth e selection of comm inution rates esp ecially, but n ot ex-c lu siv ely , fo r th os e who se e xp erie nc e h as p re vio usly b ee nm ainlr confined to W itw atersrand gold ores.The curriculum w ill be specifically biased tow ardsN orth American practice, and D erek B arratt of W rightEngineers, V ancouver, C anada, has agreed to accept therole of principal lecturer. Support w ill be given by J e nsL ich ter and oth er local experts, w ho w ill provide a S outhAf ri can per spec tive .

    W ho Should A ttendThe School w ill be structured to cater for all activelyinvolved in the m any facets of the design and operationof comminution plants.The Cu rri cu lumBec au se o f th e lo gistic al p ro blems in vo lv ed in a ssemb -ling a timetable for a school where the lecturers are

    situated at opposite sides of the w orld, it is not possibleto publish a tim etable at this stage. H ow ever, the topicsthat w ill be covered include the follow ing:

    . W ork indices. Testworkon impact c ru sh ing. E ffe ct o f m ineralogyon te st resu lts. Inte rpre ta tion of dri ll -coreresul ts. B atch-scale tests. S truc tu rin g o f p ilo t-p lan t testw ork. Interpretation of results and scale-up. C ompariso n o f a ltern ativ e comm in utio n ro utes. P ulp rh eo lo gy a nd its effec t o n g rin din g effic ien cy. C lassificatio n. M ill geom etry. C hoice of ancillary equipm ent

    . F in an cia l a na ly sis. C on tro l a nd optim iz ation. Simulation.Social EventsThe p ro gramme in clu de s a b arb ec ue on 14th May anda h alf-d ay tec hn ical v isit o n 1 6th May .

    Con ta ct Add re ssFor further inform ation, contactPam ela Sm ithSAIMMP .0. Box 61127Marsh alltown 2 10 7.T el.: (011) 834-127 3/7; T elex: 4-86431F ax : (0 11 ) 8 35 -5 92 3.

    JOURNA L O F TH E SOU TH A FR IC AN IN STITU TE O F M IN ING AND META LLURGY MARCH 1991 103