Liebenberg and Van Deventer-1997

7/28/2019 Liebenberg and Van Deventer-1997

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PergamoaSo892-6875(97)99977-9

Minerals Engineering, Vol. 10. No. 9, 959-972 . 1997p.0 1997 Else-via Science LtdRinted in Great Britah AU rights reserved08924875197 $17.00+0.00

THE DYNAMIC SIMU LATION OF IN-PULP SORPTION PROC ESSESUSING THE LUMPING OF COMPETITIVE AND FOULING PHENOMENA

S.P. LIEBENBERG and J.S.J. VAN DEVENTERDepartm ent of C hemical Engineering, The University of M elbourne, Parkville,Victoria 3052, Australia. &nail: jsj.van_deventer@chem _eng.unimelb.edu.au

(Recei ved 27 N ovember 1996; accept ed 28 Februar y 1997)ABSTRACT

For t he (effect i vemo& ll ing of in-pul p sorpt ion processes t he efl ect of competi ti veadsorpti on and ouli ng must be included. A mul t i component reundli ch isotherm w asi ncorporat ed n he branched pore adsorpt i onmodel and appli ed o he batch adsorpt i onof d@erent metal cyani des ont o acti va t ed arbon. A eached ore was al so used n theveri fi cati on f he modell ing t rat egy.As a result of he complexit y f a eached pulp ti s mpossi ble r mpract i cal o consi der he compet i t i ve rfoul i ng efl ect f each ndiv i dualspecies. hrence, compet i t i ve dsorpt i on nd oul i ng w ere efl ecti vely ccount ed or by hel umpi ng of t hese eff ects as a combined compet i t i on oefi cient. The decreased gol dadsorpti on n a complex mult icomponent ystem ompared w it h solut ion f gold on tsow n can be ascri bed concept uall y o compet i t i on y an i maginary component n asimpl i fi ed w o component system. Pseudo equil i bri um sotherms can be used, butcarbon/solut i on ontact i ng imes f ess han 72 hours coul d ead o neffect i vemoakll ing.43 1997 El sev i erSci ence L t dKeywordsGold ores, Activated carbon, Reaction kinetics, Modelling

INTRODUCTIONThe non-ideal beh,aviour of carbon-in-pulp (CIP) circuits and the problems encountered in the modellingof such adsorption systems a re well known. N evertheless, the numerous sub-processes taking place duringadsorption from a leaching pulp have been largely ignored a&have led to simulation models that are unableto predict the behacviour f a CIP system under conditions of changing competition and fouling. With therapid increase in computing power m ore complex and fundamentally correct models can be used in theprediction of in-pulp sorption processes.Existing batch and continuous simu lation mode ls account for one com ponent only and no provision is m adefor the competitive effec t of species such as copper, silver, nickel and other metal cyanides. Foulants suchas calcite (CaCO $, silica precipitates and organic pollutants [1,2] inhibit the rate of adsorption and theequilibrium loading of gold onto activated carbon. Changes in the degree of fouling, and in the cyanide andoxygen concentrations down a ca scade of adsorption tanks can increase the complexity of the simulations.It is im practical to account for other physical effects such as the intrusion of tine particles, and the blockingof active sites and pores in the adsorbent by precipitates and organic substances. In most instances

Presented at Miner&s Engineering 96, Brisbane, Australia, August 26-28, 19%

95 9


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960 S. P. Liebeaberg and J. S. J. van Deventer

the detailed composition of a leached pulp is unknown. To quantify all the factors affecting an industrialadsorption process on an individual basis in a simulation model is impossible. On the other hand, a totalneglect of these factors usually leads to over-simplification and a narrow range of applicability of models.Therefore, the aim of this paper is to develop a fundamental batch adsorption model which incorporatescompetitive effects and which will still be applicable over a broad range of conditions. In order to applyfundamental models to leached pulps the deviation from clear solutions of known composition must bequantified. The competition between gold and a competing species in a complex slurry will be different tothat in a bi-solute system tested in clear, distilled water. In this paper an imaginary component will bepostulated to effectively simulate the combined detrimental effect of competitive and fouling species ongold. The lumping of these unidentilied or indeterminable species in a single competitive species offers theopportunity to effectively model ill-defined non-ideal systems. It will be explained how relative tests suchas the activity tests used in industry can give an indication of the combined competitive effect of the pulpcomponents.

BATCH ADSORPTION MODELVarious batch adsorption models have been proposed through the years and are categorised as eitherempirical [3,4], semi-empirical or mechanistic [5,6,7]. In general the empirical rate models only describethe lirst hours of the adsoiption process whereas mechanistic models are more fundamentally correct andcan be used in batch and dynamic adsorption modelling [5]. Although mechanistic models such as thebranched porn model [6,7] and the homogeneous surface-diision model [5] tend to be complex, increasedcomputing power and simulation speed make these models more sensible to use. Multicomponentequilibrium isotherms can be incorporated in the fundamental models and competition coefficients describethe interaction between species and physical phenomena such as intrusion and fouling.In order to determine the kinetic and equilibrium parameters for a dynamic countercurrencascadeadsorption system, batch tests should be conducted 161.A batch adsorption model incorporating innaparticlediffusion in the macropores and micropores [6] will be used here which could form the basis for acontinuous CIP model. In this paper the model is formulated for the multicomponent case using thecompetitive Freundlich isotherm proposed by Sheindorf et al. [8].A complete summary of this branched pore adsorption model and the model assumptions was given by VanDeventer [6] and Peel et a l . [7]. The carbon pore structure is divided into a loading fraction 01whichconsists of macropores and a fraction (1-o) consisting of micropores. This fraction is usually back-calculatedfrom experimental adsorption data The rate of adsorption is described by film diffusion through the externalliquid film, Fickian surface diffusion of the adsorbed species through the macropores and a linear drivingforce expression which describes diffusion from the macropotes to the micropores. The Fickian surfacediffusion in radial coordinates can be approximated by a quadratic driving force expression which allowsthe problem to be solved as a set of ordinary differential equations instead of a set of partial differentialequations [6].Material Balance Equations [6]The material balance for component j in the liquid phase in a batch stirred tank reactor is:

(1 )

A macropore mass balance for component j leads to the following:


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Dynamic simulation of in-pulp orption rocesses

Performing a mass balance between the macropores and the micropores gives:

The mass balance at the external particle surface is:

96 1

(2 )

(4)

Equilibrium ExpressionsThe equilibrium loading on the surface is expressed as a function of the surface concentration by themulticomponent Freundlich isotherm:

When modelling complex multicomponent systems, the mathematics and computational effort necessary todetermine the equilibrium and interaction parameters can limit the application of such a model. Thesimplicity of the multicomponent Freundlich isotherm is a definite advantage in parameter estimation, asa single parameter can be used to describe the interaction between two species. In earlier papers it has beenshown that Eq. 5 could be used in the modelling of bi-solute metal cyanide systems [9-l 11. n the b&solutecase the competitive Frenndlich isotherm results in the following simplified expressions:

ql =A,C,(C, +h12C~+ (6 )

(7)

The differential equations (Eqs. 1-3) are solved together with Eqs. 4 and 5 in an iterative pn>cedure [6].Conventionally, interaction parameters such as the competition coefficient &iGii>n the Freundlich isothermin Eq. 5 are used1 to d escribe the effect of one species on another. Hence, the higher the nnmber ofadsorbing species present in a system, the more interaction parameters are required. However, if some orall of the species could be lumped it will reduce the number of parameters.Lumping of Competitive and Fouling PhenomenaIn a complex pulp containing numerous dissolved species it is impractical to identify all these species, and


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962 S. P. L&e&erg and J. S. J. van Deventer

in any event, it is unrealistic to determine kinetic and equilibrium parameters for all these species.Furthermore, inorganic precipitates which form in the pores and on thesurface of the activated carbon couldreduce the adsorptivity and be observed a s compe titive species. It is well-kno wn that organic foulants alsoreduce the adsorptivity either through pore blockage or competitive adsorption. Evidently these competitiveeffects cannot be quantified individually in a practical simulation model.There are at least three method s by which the number of competitive species and effects could be reduced.(a) Firstly, if all individual sp ecies have been identified and characterised, some of them could be lumpedtogether by adding their concentrations according to a weigh ting formula. (b) Secondly, if say the adsorptionbehaviour of gold cyanide is known in a pure solution, and then measured again in a pulp, tbe differencein the adsorption profiles c ould be attributed to the collective effect of competitive and fouling spec ies. Thekinetic and equilibrium parameters for a so-called Z wnped maginary compet i t i ve spec ies could then be back-calculated from such data. (c) Thirdly, if the adsorption behaviour of gold cyanide in a pure solution isknown, and then measured in a pulp, a so called tracer componen t such as nickel could be used to representthe collective effect of competition and fouling. In this paper the application of methods (b) and (cl willbc demonstrated, as very little attention has been paid to this complex problem in the literature onadsorption modelling.The incorporation of the compe tition coefficient (b]a> via the Freund lich isotherm in the model allows thequantitication of the effect of non-idealities as a whole. The competition coefficient combines the effectsof fouling an d interaction of the different species on each other. Equation s l-5 can be used to describe thedynamic adsorption behaviour of continuous counter current cascade systems. Bate equations for thesimultaneous leaching a nd preg-robbing that occur in a CIFVClL circuit can be added to the systemequations. In a continuous CIL circuit Eq. 1 is replaced by a continuous flow equation, and a populationbalance approach is used to describe the movement of carbon. In the interest of conciseness, this paper willdemonstrate the effect of competition only in batch reactors.

ADSORPTION DATAAdsorption data from Nieuwoudt [12] were used in this study. A brief overview of the experimentalprocedures is provided below. For the batch adsorption experiments potassium aurocyanide (KAu(C!N)2)ndsilver cyanide were used as pure crystalline salts. Silver cyanide was dissolved using potassium cyanide.Potassium tetracyanonickelate, K2Ni(CN)4.H20, was prepared by adding potassium cyanide to nickelsulphate and crystallising it. The precipitate was washed free of the sulphates. The copper complexes wereformed using Cu2(CN)2 and dissolving a stoichiometric amount of potassium cyanide. The copper wasloaded mainly as CU(CN& ~- and Cu(CN ),3-. The apparent density of the coconut shell carboo wasdetermined as 1004 kg/m3 and the BET surface area as 1246 m2/g.All the batch adsorption tests were performed with distilled water. Equilibrium adsorption experiments wereperformed with oven dried carbon of the size fraction 0.85 - 1.18m m. The carbon was cootacted with a onelitre solutioo for three weeks and mechanically agitated with flat bladed stirrers in baffled reactors. The pHwas maintained at 8.5 by adding small amounts of KOH or HCI. The batch kinetic experiments wereconducted in baffled reactors with volumes of either 4 of 5 litres. The pH was also maintained at 8.5.In order to obtain a real leached pulp, an ore was leached with potassium cyanide in a stirred reactor for24 hours. The leaching was performed at a pH of 11 and the pH adjusted by adding KOH. After leachingthe pulp was filtered to obtain a clear solution. The pH was again adjusted to 8.5, by adding KOH or HCI.

EQUILIBRIUM EXPRJZSSIONSClear solutioo batch adsorption tests (where distilled water and crystalline A.B grade salts were used) wereconducted with the following metal cyanide s: gold, coppe r, silver and .mckel. After the clear solutionadsorption tests, resuits could be compared to adsorption tests cooductcd in a slurry. The different levels


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Dynamic simulation of in-pulp sorption processes 96 3of competition and fouling were investigated and compared in the adsorption m odelling.Bkolute EquilibriaWhen using the Freundlich isotherm, single component parameters are used for the modelling ofmulticom ponent systems. Equilibrium adsorption experime nts for gold, silver, copper and nickel wereconducted and the. following Freundlich single component isotherms were obtain&

Au: q=39.267C:*1m

Ag: q=25 .31X-

cu: q=52.483c?ma18

(8 )

(9 )

(10)

Ni: q = 3 .3 0 8 6c * 30 7 5 ( 1 1 )The loading of copper presented an interesting case where at a pH of 8.5 the copper will be loaded mainlyas CUDS- with some Cu(C.&-. and CU(C N)J~- present [131. Only Cu(C N&- loads appreciably andindicates via the high equilibrium isotherm that most of the copper was loaded as CUE -. This indicatesthat although the copper was at first present as mainly CUDS-, oxidation of the cyanide (CN-) tookplace over the adsorption period of thme weeks and the copper complexes degraded ftom CUDS- toCu(CN)2-. This is possible and a similar effect was observed in the adsorption process of gold [14]. Todetermine the competitive effect of copper, silver and nickel on gold, bi-solute equilibrium experim ents wereconducted yielding the following results:Au and AgqA , 39.267C,,(C, + 0.57C~ .14B8- 1

Au and Cuq*= 39267Q C* +o .055ccJa ~ -

Au and Niq A , 3 9 .2 6 7C , ,( C , +O .O 7 7C &? . -

(12)

(13)

(14)

(15)

(16)(17)

The competition coefficients were determined through regression of the bi-solute data, and must beregarded as empirically fitted constan ts.


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964 S. P. Liebenberg and J. S. J. van DeveaterEquilibrium Expressions for Leached LiquorEquilibrium experiments conducted in clear solutions containing only two species give an indication of thecompetition, while when determining the competition coefficients from a leached ore, the interactions arenumerous and often difficult to isolate. The leached ore contained mainly gold, silver, copper and nickel.It was assumed that the isotherm parametersdetermined from tbe clear solutions still apply and that onlythe competition coefficients will change. It would be impossible to determine the competition coefficientsseparately in a leached ore. The values from the leached liquor were treated as bi-solute data If only goldand silver were to be considered in the system, the competition coefficients would account for the effectof the copper, nickel and other species present such as ultra-fine particles and precipitates in the pores ofthe carbon. By treating the leached liquor as b&solute data the following competition coefficients weredetermined:Au&bAu,*s = 0.25bAg,Au = 2h1Au&hbAu.Cu = 0.25bCu,Au = 2.0Au,Ni

(18)(19)

bAu,Ni = O-7 (22)hNi.Au = 0.015The batch adsorption model can be used for the simulation of the kinetic runs and validation of the approachis given below. With this approach it is clear that the competition coefficient combines or 1~s all theunaccounted effects in one parameter. Evidently, the competition coefficient accounts for the lowering inthe equilibrium.

SIMULATION OF ADSORPTION DAT AThe validity of the branched pore adsorption model was tested on complex multicomponent systems wherethe individual effects were indeterminable. The surface diffusion coefficient, interregional rate coefficientand fraction of pores available as macropores were determined from the experimental data. At high stirringspeeds the film diffusion coefficient has no influence on the simulation results and it should be noted thatthis must be maintained in all experiments to ensure comparable results.Clear Solution ExperimentsThe validity of the model parameters was tested at various experimental conditions and typical singlecomponent simulations of gold, silver, nickel and copper can be seen in Figure 1. The model parametersfor the different metal cyanides are given in Table 1.


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965ynamic imulationof in-pulp sorptionprocessesTABLE 1 Kinetic adsorption parameters.

Thegold-silver system has been studied by Van Deventer [9], while the simulations here are also concernedwith gold-copper and gold-nickel systems. The Au-01 (Figure 2) and Au-Ni (Figure 3) systems weresimulated with the b&solute equilibrium parameters (Eqs. 14-17). The competition coefficients weredetermined by using Eqs. 6-7 and the bi-solute equilibrium data.

1

O.IB

o0.6v0 0.4

02

(3ecu ??g mAu-Model

0 10 20 30 40 50

Time [hrsl80

Fig.1 Batch kinetic model predictions with single component equilibrium parameters.

1

0.8

0.6e0 0.4

0.2

00 10 20 30 40 50 60 70 80

Time [hrsl

Fig.2 Batch kinetic model predictions of bi-solute Au-Cu system.


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966 S. P. Liebeoberg and J. S. J. vao DeveoterLeached Liquor ExperimentsAs stated before, the aim is to determine whethe r the comb ined effect of foulants and competitive speciescan be modelled effectively. To illustrate the difference in adsorption between a clear solution an d theleached liquor, the adsorption of gold from the leached liquor was simulated with and without competition.From Figure 4 it is clear that the deviation from clear solution is substantial and that the adsorption processcan be simula ted effectively only through the introduction of a competition coefficient. In this case thedifference is attributed to competitive adsorption by a lumped imaginary species, with w hich the competitiveeffect of all metal cyanides and possible fouling are taken into account. The model parameters for thisspecies are shown in Table 2, and were determined by empirical fitting of the data. In view of the excessof competitive species relative to gold, it was assume d that gold had no effect on this imagina ry speciesfrom a modelling point of view.

1

0.80.6

50 0.4

0.2

0

1

0.8

0.680 0.4

0.2

0

I I I I I I I

0 10 20 30 40 50 60 76 80Time [hrslFig.3 Batch kinetic model predictions of bi-solute Au-Ni system.

A - Simulated with competition6 - Simulated without competition

.h L0 10 20 30 40 50 60 70 80

Time [hrslFig.4 Leached liquor batch adsorption data simulated with and without competition.


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Dynamic simulation of in-pulp sorptioo processes 967TABLEZKinetic and equilibriumparametersforlumpedmaginarycompetitivespecies

a A II bA~,lm. . 0.307 .The comp etition coefficients determine d from the leached liquor were used in the kinetic simulations an dgold wa s used in combination with nickel, copper an d silver. It must be noted that the results (Figures 5-7)were obtained using the competition coefficients from the leached liquor equilibrium adsorption data. Byfitting empirically fitted compe tition coefficients, su ch as used in Figure 4, more accurate simula tions c anbe obtained . By doing this, the competition coefficient becom es a purely em pirical c onstant, with noexperimen tal determin ation necessary and will give an indication of the overall competitive effect.

1

0.8

0.8s3 0.4

0.2

0

1

0.8

0.2

10

0 10 20 30 40 50 80 70 80Time [hrsl

Fig.5 Batch kinetic adsorption simulations of a multicomponentleached liquor system as a bi-solute Au-Ag system.

0 10 20 30 40 50 60 70 80Time [hrsl

Fig.6 Batch kinetic adsorption simulations of a multicomponentleached liquor system as a bi-solute Au-Cu system.


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968 S. P. J iebcnbergand J . S. J . van Deventer

The simulatiot~s n Figures 5-7 are satisfactory given the complexity of the systems. Using nickel incombination with gold gave the best prediction of leached liquor data. I&iscould be due to the fact thatnickel is the least affected by competing species, as indicated by the low competition coefficient of 0.015(Eq. 23). Nickel adsorbs as Ni(CN)d2-and the low equilibrium adsorption could be the reason why it islargely unaffected by competitive adsorption in the kinetic studies.It is proposed that for practical applications the following strategy sbould be followed in order to quantifythe effect of competition on equilibrium. In an operating plant the composition of a pulp is not constant,so that it is important to use a clear solution of known composition as a point of reference. Such a solutioncould contain a number of other metal,cyanides in addition to gold. Powdered activated carbon should beused so as to accelerate the attainment of equilibrium [6]. Evidently, actual granular carbon should be usedin kinetic tests. In a specific pulp, the combined effect of fouling, competing species, cyanide concentrationand other indeterminable effcompetirivespecies. The parameters of the latter species will change as the nature of the ore changes, whichcould then be used to chamcterise the effect of the total pulp on adsorption. Similarly, if there is a changein the type of activated carbon used, or in the efficiency of the thermal regeneration method, this testingproced& could be used to chamcterise the carbon.

1

0.8

0 IO 20 30 40 50 80 70 80Time hrsl

Fig.7 Batch kinetic adsorption simulations of a multicomponentleached liquor system as a bi-solute Au-Ni system.

PSEUDO EQUILIEEIUM ISOTHERMSIt can take more than 3 weeks to a ttain true equilibrium [6]. This is impmctical for plant simulatious wherequick relative tests are necessary to obtain an indication of equilibrium conditions. Shorter or pseudoequilibrium tests are often used to approximate the real equilibrium. This strategy inevitably leads to lessaccurate models and a more empirical approach where the use of fundamemalmodels ate considered to beimpractical. To illustrate the importance of the solution cont&iug time with carbon in determining pseudoequilibrium isotherms, model simulations were performed for gold cyanide in contact with different massesof carbon. In Figure 8 the differences in values are illustrated and it is clear that the solution contact timeplays a vital role. From these simulations the conespoading pseudo equilibrium isotherms were determinedas shown iu Figure 9.


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Dynamic simulation of in-pulp sorption processes 969

Shorter ontacting times lead to lower pseudo equihbrium isotherms. Single component Freundlich isothermswere fitted to the simulated results in Figure 9 and are shown in Table 3. From a modelling perspective itis obvious that the pseudo equilibrium isotherms cannot be used in adsorption simulations without changingmodel parameters, In order to perform simulations with the pseudo isotherms, it was necessary to changethe fraction of loading capacity available as macropores, which would make sense due to the fact that theinitial adsorption takes place in the macropores. Thii approach was applied to the pseudo isotherm for 72hours. All the other kinetic parameters were the same as in previous modelling. As can be expected, thefraction of macropores increased from 0.26 to 0.65. The simulation results can be seen in Figure 10.

I

0.8

oOA3Y0 0.4

0.:2

00 10 20 30 40 50

Time [hrsl80

Fig.8 Batch kinetic adsorption simulations of gold for the determination of pseudo equilibrium isotherms.

353025

2 2020) 15u

1050

72 hrs

24 hrs

1 hr

0 2 4 6 8 10 12 14Ce bngA1

Fig.9 Pseudo equilibrium isotherms for gold after different solution contacting times.


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970 S. P. Liebenbergand J. S. J. van DeventerTA BLE 3 Freuadlich i&berm param eters for pseudo equilibrium adsorption tests.

0.8

0.6e0 0.4

0.2

00

I I . I I I I

10 20 30 40 50Time [hrsl

60 70 80

Fig.10 Batch kinetic simulation of gold adsorption with 72 hourpseudo equilibrium isotherm (single component in clear solution).

Further modelling soon revealed that it was not beneficial to alter the kinetic parameters further, and thatthe pseudo equilibrium isotherms for 24 hours and lower were impossible to use due to the low equilibriumattained in the time. Fundamental adsorption predictions will only be possible if the pseudo equilibriumparameters are empirically adjusted to values closer to true equilibrium. Equilibrium values determined for72 hours can still be used effectively and the accuracy can be improved by using fine carbon.For the effective fundam ental mo delling of CIPKIL circuits quick relative te sts are required. A s stated, oneand six hour equilibrium data will be ineffective when granular activated carbon is used.

CONCLUSIONS AND SIGNIFTCANCEIn the application of a fundamental model to adsorption of metal cyanides in a plant, quick pseudoequilibrium isotherms cannot be used for modelling purposes. Relative tests to give an indication of thedeviation from clear solution tests can be conducted. This deviation can be a guide for changing thecompetition coefficients in a general fundarpental CIP/cIL sin?ulation pmgram.

The lumping of fouling and competing species is feasible, and any factor decreasing the equilibrium loading


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Dynamic imulation f in-pulpsorption rocesses 971

of gold can be accounted for by the competition coefficients. Althou gh the proposed m odel is fundam entallybased, empirically determined parameters are incorporated in the modelling strategy, which creates a usefultool for predicting changes in adsorption behaviour. The application of this approach will be tested onindustria l scale with the incorporation of the batch kinetic model into a dynam ic countercurrent CIPKILmodel. In such a model other factors such as preg-robbing, simultaneous adsorption, leaching, and a carbonloading distribution can be incorporated. It is well-known that batch kinetics cannot be scaled-up directlyto simulate a large scale CIP/CIL plant in view of differences in hydrodynam ics. Neverthe less, a changein batch behaviour gives a relative indication of changes to be expected on a continuous plant.

1.

2.3.

4.5.

6.7.8.9.10 .11 .

12 .13 .14 .

Macrae, C.M., Sparrow, G.J. & Woodcock, J.T., ,1988, Gold, calcite and other materials onactivated carbons from CIP plants, Proceedings of he Third M il l O perat orsConference, AuslMMCobar Branch, Cobar NSW, Australia, pp. 53-59.La Brooy, S.R, 1988, The fouling of activated carbon in Western Australia, Proceedi ngs of heRand01 nternat i onal old Conference, Perth, Western Australia, October 1988, pp. 264-267.Fleming, C.A., Nicol, M.J. dz Nicol, D.I., 1980, The optimization of a CIP circuit based on thekinetics of the extraction of aurocyanide by activated carbon, Symposi um n I on Exchange an dSolv ent Extr acti on n M ineral Extracti on,Randburg, Mintek, Paper no. 6, pp. l-29.Dixon, S., Cho, E.H. & Pitt, C.H., 1978, The interaction between gold cyanide, silver cyanide andhigh surface area charcoal A .I.Ch.E. Symposium eri es, no. 173, vol. 74, pp. 75-83.Le Roux, J.D., Bryson, A.W. & Young, B.D.,1991, A comparisou of several kinetic models forthe adsorption of gold cyanide onto activated carbon, J. S. Afr. nst. M in. M etal l . , ol. 91, no. 3,pp. 95-103.Van Deventer, J.S.J., 1984 , Kinetic m odel for the adsorption of metal cyanides on activatedcharcoal, Ph.D . Thesis,University of Stellenbosch, South Africa, 337 p.Peel, RGl., Benedek, A. & Crowe, C.M ., 198 1, A branched pore kinetic model for activated carbonadsorption, AIChE J., vol. 27, no.1, pp. 26-32.Sheindonf, C.H., Rebhun, M . & Sheintuch, M., 198 1, A Freundlich-type multicomponent isotherm,Journal ofColloid and nt erf ace Sci ence, vol. 79, no. 1, pp. 136-142.Van Deventer, J.SJ., 1986, Competitive equilibrium adsorption of metal cyanides on activatedcarbon, Separat i on Science and Technology , ol. 21, no.10, pp.1025-1037.Van der Merwe, P.F. & Van Deventer, J.S.J., 1988, The influence of oxygen on the adsorption ofmetal cyanides on activated carbon, Chem. Eng. Commun., ol. 65, pp.121-138.Liebenbe rg, S.P., Van Deven tkr, J.S J. & Lorenzen, L., 19 95, A dynam ic mo del for the competitiveelution of gold and base metals from activated carbon, Proceedi ngs of the X I X nt ernat i onalM i neral Processi ng Congress, Society for Mining, Metallurgy, and Exploration, Inc. (AIME ),Littleton, Co., 1995, vol. 4, Chapter 13, 1995, pp. 61-64.Nieuw oudt, I., 1989, Dynam ic mod el for the competitive adsorption of metal cyanides on activatedcarbon in batch reactors, A4.Eng. Thesis,University of Stellenbosch, South Africa.Ibrado, A.S. & Fuerstenau, D.W., 1989, Adsorption of the cyan0 complexes of Ag(IJ, Cu(I),Hg(II), Cd@) and Zn(II) on activated carbon, M iner. M et alE. rocess., vol. 6, no.1, pp.23-28.Tsuchida, N., Ruane, M. & Muir, D.M., 1984, Studies on the mechanism of gold adsorption oncarbon, Proceedi ngs of M int ek 0: I nt erna t i onal onference on M ineral Science and Technology ,vol. 2, El&or L.F. Haughton, Mintck, South Africa.

LIST OF SYMBOLSA Parameter in Freundlich isothermb Com petition coefficient in Freundlich multicom ponent isothermC Liquid phase concentration [g~1-~]camp Number of components presentD, Effective surface diffusion coefficient [m2.&]dc Carbon particle diameter [m]

REFERENCES


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91 2 S. P. Jiebeaberg and J. S. 1. van Deventer

4J4n9QIIItVW

Inferregioual transport coefficient from macn3pores o miv [s-l]Film tmnsfer coefficient [m.s-1Exponent in Freundlicb isothermLoading on activated carbon [g.kg-1Squared macropoxe loading [g2.kg-2]Time Es]Volume of solution in reactor [m3]Weight of carbon [g]

Greek SymbolsaPC

Fraction of loading capacity available as macroporesApparent carbon particle density Fg.m-3]

Subscriptsb Microporese Equilibriumj Refers to specific metal cyanide sorbateji Refers to competing metal cyanide sorbate (ruuning variable)m MacroporesS Liquid-carbon interface

Liebenberg and Van Deventer-1997

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