J. S. AIr. Inst. Min. Metal/., vol. 84, no. 3.Mar. 1984. pp! 70-78.

The absorption of gold cyanide ontoactivated carbon. 11. Application of the kineticmodel to multistage absorption circuits

by M. J. NICOL*, C. A. FLEMINGt, and G. CROMBERGE:j:

SYNOPSISA relatively simple rate equation for the kinetics of the absorption of gold from cyanide solutions onto activated

carbon was lI5ed as the basis in the development of a model for multistage carbon-in-pulp and carbon-in-Ieach ab-sorption circuits.

The model was used in the prediction of both the steady-state and the transient behaviour of the absorptionprocess, and the results were found to be in reasonable agreement with those observed in an extended pilot-plantcampaign. A number of practical implications of the model are discussed, and an assessment is made of the economicconsequences of the various process options available for the design of a carbon-in-pulp plant.

SAMEVATTING'n Betreklik eenvoudige tempovergelyking vir die kinetika van die absorpsie van goud uit sianiedoplossings op

geaktiveerde koolstof is gebruik as grondslag vir die ontwikkeling van 'n model vir veeltrapkoolstof-in-pulp- enkoolstof- in-Ioogabsorps iekri nge.

Die model is vir die voorspelling van sowel die vastetoestand- as die oorgangsgedrag van die absorpsieproses ge-bruik en daar is gevind dat die resultate redelik ooreenstem met die wat in 'n uitgebreide proefaanlegkampanjewaargeneem is. 'n Aantal praktiese implikasies van die model word bespreek en die ekonomiese gevolge van dieverskillende prosesopsies wat vir die ontwerp van 'n koolstof-in-pulpaanleg beskikbaar is, word geevalueer.

IntroductionA previous paperl describes a relatively simple kinetic

model for the absorption of gold from cyanide solutionsand pulps onto activated carbon, and illustrates the useof the rate equation in predicting the performance ofsingle-stage continuous and batch absorption tests. Theapplication of this kinetic model to the description,design, and optimization of multistage carbon-in-pulp(CIP) absorption circuits is developed in this paper.

As suggested in the previous paper, the rate at whichactivated carbon absorbs gold is the most importantproperty of the carbon used in this application becausethis factor determines the operating efficiency of a CIPplant, in which true equilibrium between the carbon andthe solution is seldom achieved in any stage. The well-known McCabe-Thiele approach to the description ofmulti stage countercurrent extraction circuits cannot beexpected to yield adequate results when applied to CIPcircuits because it is based on an equilibrium descriptionof the system. For this reason, workers at the UnitedStates Bureau of Mines, in the only published work onthis topic2, adopted a modified McCabe-Thiele approachin which pore diffusion was coupled to a Freudlich iso-therm to describe the equilibrium between silver cyanideand activated carbon.

* Directort Assistant Director:j: Senior Scientist

All of the Mineral and Process Chemistry Division, Council forMineral Technology (Mintek), Private Bag X3015, Randburg,2125 Transvaal.

@ The South African Institute of Mining and Metallurgy, 1984.SA ISSN 0038-223X/S3.00 + 0.00.

70

Continuous Countercurrent ExtractionIn the simplest approach to the modelling of a CIP

circuit, the assumption is made that the flow of pulp andcarbon is continuous but countercurrent, and that asteady-state condition is reached in which the concen-trations of gold in the solution and on the carbon areconstant in each stage of the absorption ciromt. It isfurther assumed that each contactor can be treated as aperfectly mixed reactor with a constant residence timefor both the pulp and the carbon.

In the previous paper it was shown that, under condi-tions of constant gold concentration in solution, thefollowing equation can be used to describe the rateof absorption of gold onto carbon:

d[Au]cjdt = k(K[Au]s - [A'u] c), (1)where [Au]c is the concentration of gold on the carbon atany time t, [Au]s is the concentration of gold in solution,k is a rate constant, and K an equilibrium constant. Bothk and K can be obtained from batch absorption tests asdescribed in the previous paper.

This rate equation can be combined with mass-balanceequations to yield an overall model for a circuit consistingofN stages (shown schematically in Fig. 1) in which pulp(at an equivalent solution flowrate of Vs) enters the firststage with a gold concentration of [Au]~ and carbon (ata flowrate of V c) enters the last stage with a gold concen-tration of [Au]~. As shown, the concentrations of gold insolution and on the carbon in any stage i are representedby [Au]~ and [AU]~-l respectively.

The overall mass balance of gold across the circuitrequires that

Vs ([Au]~-

[Au]~= Vc([Au]~ - [Au]~ ) (2)

MARCH 1984 JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY

20 000

18000

16000

14000

-Cl 12000t:icis 10000III.2c0 8000-eIIICJ

6000

4000

(Aul~~

[Au~

1

[Auf.r--

Slage1 Siege

2

[AUJ:'-1 (Aul~"""""""""""1i~ ~

SI~ge

IAuJ:

[AuJ:'-' [AuJ:'

[AuC

Fig. I-Concentrations of gold in the solution and on thecarbon

N d

NIn general, [Au]a < < [Au]a an [Au]e < < [Au]e so that

this equation can be simplified and rearranged to giveV e = Va[Au]~j[Au]~, . . . . . . . . (3)

which specifies the rate at which carbon must be movedfor the desired loading, [Au]~. Experience has shown thata value of 1500 for the ratio [Au]~j[Au]~ is a reasonableexpectation. This can be seen from the data for actualoperating plants shown in Fig. 2. It is interesting to notethat the results obtained from pilot-plant investigationsinvariably predict better performance than is generallyachieved during full-scale operation. The only variableleft that can be adjusted if the desired performance is tobe achieved is the mass of carbon (M e) in each stage.This determinesthe average residence time of carbon perstage (te

= M ejV e).The following iterative procedure has been found useful

for the derivation of the required amount of carbon.Consideration of the mass balance and reaction accord-

ing to equation (1) occurring in Stage 1 yields the follow-ing well-known form of equation for the performance of astirred- tank reactor:

[Au ] O=

[Au]~ + K[Au]~ kte (4)e l+kte ...,..

It should be pointed out that, because of the form ofequation (1), it is identical whether homogeneous orsegregated reaction is assumed in the stage. (This can beshown quite simply by substitution of the integratedform of equation (1), which applies to a batch reactor,into the expression for a stirred-tank reactor, which incor-porates the exit age distribution function for the segre-gated phase, i.e. the carbon). An initial estimate (say 10hours) is made for te, which is used in the calculation of[Au]~ and [Au]~ from equation (4) and the mass balanceacross the first stage (equation (2) with N = 1). 'fhevalues of [Au]~ and [Au]~ can then be used in the calcu-lation of the corresponding quantities for the secondstage, and so on until the values of [Au];

Test 1, 400 ljh Test 2, 800 ljhGold in solution, gjt Gold on carbon, gjt Gold in solution, gjt Gold on carbon, gjtObserved Predicted Observed Predicted Observed Predicted Observed Predicted

2,02 2,02 0 0 2,26 2,26 0 00,76 0,52 3092 3097 1,12 1,00 6503 65120,24 0,13 1600 793 0,39 0,44 3693 2835

0,039 0,034 168 201 0,15 0,19 1972 11960,015 0,009 I 40 49 0,08 0,08 550 4670,002 0,002 18 10 0,03 0,03 189 141

PREDICTED AND OBSERVED OPERATION OF PILOT PLANT AT WESTERN AREAS GOLD MINE

TABLE I

Stage

Feed12345

Carbon per stage: Observed 10 kgPredicted 6,6 kg

Observed 10 kgPredicted 6,4 kg

Periodic Transfer of CarbonIn practice, carbon is not transferred continuously

countercurrent to the flow of the pulp. Instead, a fractionof the carbon inventory in each stage is removed at fixedtime intervals and transferred to the preceding stage bymeans of airlifts or pumps. In the extreme case, all thecarbon in anyone stage is transferred during a cycle. Ifit is assumed that this transfer is accomplished in a veryshort time compared with the time tha.t the carbonspends in each contactor between transfers, then thefollowing simple analysis enables the periodic perform-ance of an absorption section to be modelled.

The rate of loading of gold onto a batch of carbon(mass M c) transferred into a contactor (containing a massMs of solution) through which pulp containing gold at aconcentration of [Au]~nis passed at a flowrate Vs can bederived if the expression for the mass balance across thecontactor is combined with a suitable rate equation.Thus, for the mass balance,

Mc d[~~]c = Vs([Au]~n- [Au]s)

+ Md[Au]s

s dt . . . . . . . (5)As shown in the previous paperl, the concentration of

gold in solution increases with time, but the termMs d[Au]s/dt is small in relation to the others for reason.able concentrations of carbon. This equation can then besimplified to

d[~~]c= ;: ([Au]~n-[Au]s). (6)

Equation (1) can be combined with this equation toyield the following expression for [AuJs:

[A ] =M ck[Au]c + Vs[Au]~n

Us M ckK + Vs .

Substitution in (6) yieldsd[Au]c

- k (K [A ]In [A ] )~-

A us- Uc,

where kA = kVs/(MckK + Vs).

. . . . . (7)

. . . . . . (8)

For the first stage of a multistage circuit with a con-stant feed concentration [Au]~n= [Au]~, equation (8) can

72 MARCH 1984 JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY

be integrated to yield the following expression for theconcentration of gold on the carbon as a function of timein the first stage:

[Au]~= K[Au]~-

exp( -kAt)(K[Au]~ - [Au]~), . (9)

where [Au]~ is the concentration of gold on the carbonadded to the contactor. Substitution of equation (9) intoequation (7) yields the following expression for the con-centration of gold in solution in the first stage as a func-tion of time:

1 0 kAM COl[Au]s = [Au]s - ~exp( -ht)(K[Au]s-[Au]c). (10)

As shown in the previous paper, these expressions canbe simplified if the absorption reaction is far fromequilibrium. The resulting equations predict a lineardependence of both [Au]~ and [Au]~ with time in thefirst stage after carbon has been transferred into thecontactor.

This procedure cannot be followed for the second orsubsequent stages because the feed to each stage is notconstant and the equation (written for the second stage)

d[Au]~= kA (K[Au]l- [Au]~)

"""

(ll)dt

cannot be simply integrated. The simplest approach hasbeen found to be the following.(i) [Au]~ and [Au]~ are obtained as a function of time

by the procedure previously outlined.(ii) The values of [Au]~ thus obtained are used in a

numerical integration of equation (ll) to give [Au]~.(iii) Values for [Au]: are then obtained by use of equa-

tion (7).(iv) This procedure can be repeatedfor each subsequent

stage.Simulation of the start-up and approach to the steady-

state operation of a circuit can be made if it is assumedthat fresh carbon is added to each stage at the start andall the carbon is transferred at fixed time intervals. Thiscalculation procedure can be carried out after each trans-fer, and Fig. 3 shows the approach to steady-state con-ditions predicted for the first and fourth stages of theMintek pilot plant as detailed in Table 1.

4000--Q

U-::::a

cC-

2000

~0,7-

-Q;,-::::a

cC-

0,5

1,0

0,9

:u 0,8:;~

..":;~ 0,7

0,6 [Au):' is steady-state concentration

0,50 2 3

No. of transfers4 5

Fig. 3-Approach to steady-state operation

Actual plant data are shown in Fig. 4 for the gold onthe carbon over four cycles in the first stage, and the solidlines were calculated according to the above procedure.The agreement between observed and calculated perform-ance is seen to be reasonably good and, if the inaccura-cies associated with the sampling and analysis of both thesolution and the carbon are taken into consideration, theresults demonstrate that the model can adequatelydescribe the performance of a CIP circuit operated in thisperiodic-transfer mode. The calculated periodic variationin the concentration of gold in solution is also shown inFig. 4.

6000'

.

.

t

Some Practical ImplicationsA number of conclusions regarding the design and

operation of an absorption circuit can be made as a resultof the application of this model.Transfer of Carbon

A comparison of the data calculated from the predictedcurves in Fig. 4 with those in Table I shows that there isvery little difference in the expected performance of anabsorption circuit with continuous transfer of carbon,or with periodic complete transfer of all the carbon, fromstage to stage. A full analysis of the relative performancefor the transfer of various fractions of the carbon inven-tory of each stage during each cycle produced the valuesgiven in Table H. It should be emphasized that thesevalues are for an ideal case and do not allow for possible'poisoning' of the carbon or other similar effects.Amount of Carbon per Stage

It has often been suggested, without explanation, thatmore carbon should be added to the latter stages of anabsorption circuit than to the early stages. This is sup-

TABLE IIANALYSIS OF RELATIVE PERFORMANCE FOR THE TRANSFER OF

VARIOUS FRACTIONS

Fraction transferredper cycle

Relative performance

1,000,500,250,10

Continuous

1,000,950,920,900,88

. Observed [Au)cPredicted [Au)c

- -- Predicted [Au)a

0,9

tTransfers of carbon

t0

0 100Time, h

0,3200

Fig. 4--Cycllc behaviour of the CIP pilot plant

JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY MARCH 1984 73

Stage Gold in solution Stage efficiencyg/t %

Feed 6,141 4,09 332 2,91 293 2,09 284 1,40 335 0,86 396 0,47 457 0,15 68

posed to result in a more effective operation with reducedconcentrations of gold in the barren solution. The predic-ted effects of such a non-uniform distribution of carbonin the Mintek pilot plant at Western Areas are shown inFig. 5. It can be seen that, if the carbon is distributeduniformly throughout the plant, the gold in solutiondecreases exponentially with the number of stages, i.e.each stage extracts the same fraction of gold as thatwhich enters the stage. It should be noted that a non-uniform distribution of the carbon in the direction of agreater fraction in either the first or last two contactorsresults in a higher concentration of gold in the barrensolution. The practical implication of this finding is ob-vious in that, for a given performance, the minimumcarbon inventory is realized when the carbon isdistributed uniformly throughout the absorption circuit.It is interesting to note, however, that the amount ofgold 'locked up' in the carbon in a plant has a bearing onthe optimum distribution of carbon.

This can be seen from Table Ill. The amount of carbonrequired and the gold lock-up in the four-stage plant werecalculated from the model for the following possibilities:(a) a uniform distribution of carbon throughout the

plant,(b) three times as much carbon in stages 1 and 2 as in

stages 3 and 4, and(c) three times as much carbon in stages 3 and 4 as in

stages 1 and 2.

10,0

~

iS'S

(!)10kg In .ach stag.

~ 5 kg In stages 1 and 215kg In stag.s 3 and 4

1,0

. 15kg In stag.s 1 and 25kg In stage. 3 and 4

0,10

0,01

0 2Stag.

31

74

Fig. 5-Effect of carbon distribution on CIP performance

MARCH 1984 JOURNAL OF THESOuni AFRICAN INSTITUTE OF MINING AND METALLURGY

TABLE IIIEFFECT OF NON-UNIFORM DISTRIBUTION OF CARBON

ExampleRelative carbon

inventoryRelative gold

lock-up

(a) Uniform(b) Stages 1,2 > Stages 3, 4(c) Stages 1, 2 < Stages 3, 4

11,680,77

11,191,19

Stage EfficiencyThe stage efficiency, i.e. the percentage of gold extract-

ed in each stage, is usually constant if the concentrationof carbon in each stage is the same. This has generallybeen found to be the case on both pilot and full-scaleplants. However, there are exceptions, as shown byTable IV.

TABLE IVSOLUTION PROFILE FOR PLANT TREATING A CALCINE AT THE PRESI-

DENT BRAND GOLD MINE

The decreasing stage efficiency as the carbon progressesthrough the plant is indicative of a cumulative 'poison-ing' effect, and an investigation with a scanning electronmicroscope revealed the presence of a layer of fine hema-tite that had built up on the carbon particles and washindering the mass transport of gold to the carbonsurface.

Carbon InventoryAs in most multistage processes, the total amount of

absorbent material (in this instance carbon) decreases asthe number of stages increases. Calculations similar tothose for Table I for conditions pertaining to the pilotplant at Western Areas Gold Mine produced the valuesthat were plotted in Fig. 6. Here, the carbon inventoryand gold lock-up were normalized to the case in which aninfinite number of stages are used. It is apparent from thecurves that there is a significant advantage to be gainedin terms of reduced inventories of both carbon and gold(on the carbon) by the use of a large number of stages.This is obviously offset by the higher capital and opera-ting costs associated with each additional stage, and itcan be expected that there will therefore be an optimumnumber of stages for each individual application. Thisaspect is treated later in more detail.

4 Application to Carbon-in-LeachThe addition of carbon direct to a gold-leaching circuit

is an attractive alternative to a separate carbon-in-pulp

54

~

0

i 3>.:c0of!III

~2

.~

eGiex:

1 ------------------

04 5 6 7

No. of stagesFig. 6-lnfluence of the number of stages on carbon inventory

and gold lock-up

absorption circuit. This approach has obvious advantagesfrom the point of view of capital costs, but at the sametime presents a number of operational problems. Theseare not discussed here, but the application of the CIPmodel for the absorption process to a typical carbon-in-leach (CIL) application is useful in an assessment of thetechnical feasibility of such an option and the identifica-tion of some of the more important design and operatingparameters. Such a model should also be of value in anestimation of the effects of the additional gold leachingthat can occur during absorption in a conventional CIPcircuit. The derivation of such a model requires that asuitable rate equation should be obtained for the leachingof gold. This equation can then be combined with therate expressions for absorption and the relevant mass-balance equations.

Kinetics of LeachingThe rate of gold leaching from ores such as those

encountered in the present example is a complex kineticproblem involving a number of chemical, mass-transport,and mineralogical factors. However, a relatively simpleexpression has evolved from experience at Mintek with theleaching of a number of local ores. This rate expressionhas the following form:

d[Au]p tA A 2

- dt ' = kp ([ u]p,t - [ u]p,e) , . . (12)

where [Au]p,t is the concentration of gold in the ore attime t and [Au]p,e is the corresponding quantity atinfinite time (Le. the minimum achievable residue grade),while kp is a rate constant.

Examples of the use of this expression to describe thekinetics during batch leaching are given in Fig. 7, in

8

which data for the leaching of a high-grade ore (7 gjt) anda low-grade residue (0,8 gjt) are plotted on a logarithmicscale. The lines were calculated from the integrated formof equation (12), and best-fit values for the parameters

Cl. [Au]p,e and kp were derived from a non-linear least-Z squares treatment of the data. The agreement can be seen6~ to be good, and it is interesting that such an analysis of!! some six different ores yielded values for the rate constant& kp that vary in the rather limited range 0,4 to 1,0 h-l.~ This suggests that most ores are leached at roughly the

4 ]! same rate, and that an average of 0,7 h-l is a reasonable~ estimate for use in the absence of actual values. The finer

grind that is necessary for CIL probably results in some-what faster leaching, and the suggested value of 0,7 h-lis probably a lower limit.

Model for the Multistage OIL ProcessThe methods outlined earlier for a multistage conti-

nuous CIP plant operating at steady state can be simplyextended by the inclusion of the solids in the massbalance for each stage after the concentration profile forthe solids has been calculated from equation (12) withthe average residence time for the pulp in each stage;that is, the assumption is made that the rate of leachingis independent of the presence of acti vated carbon. Batchtests at Mintek have shown this to be the case. Theapplication of this procedure to a typical low-grade ore(such as that used in the Mintek pilot plant at WesternAreas Gold Mine) yields the following performance for asimulated CIL plant designed to achieve the same per-formance as the CIP plant operated under the conditionsof Test I in Table I, viz a pulp flowrate of 400 Ijh with abarren solution of 0,002 gjt gold and a carbon loading ofapproximately 3000 gjt from a head grade of 2 gjt. TheCIL plant has 8 stages with a pulp residence time of 3hours per stage, and the calculations were made on theassumption that activated carbon is present in all thestages or only the last seven, six, five, or four stages of

8

2

2The lines were calculated fromthe leaching-rate equation (12)

..

:;'et:5

.\~ .

H;gh d. ...-1 _...

"',AA. ~ ALA"'b. ~~- b.

-20 ,.0

""""-0~

Low-grade residue

-30 10 20 30

Time,hFig. 7-Leaching rates of two ores from different localities

40 50

JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY MARCH 1984 75

Stage Solids, g/t Solution, g/t Carbon, g/t

---------

---

Feed 0,26 2,021 0,25 0,43 30722 0,25 0,092 6693 0,24 0,022 1584 0,23 0,006 445 0,23 0,002 12

leaching, i.e. with varying numbers ofpreleaching stages.The profiles calculated for the solution and solids (ore)

in the example in which the first three stages do notcontain carbon are shown in Fig. 8. It can be seen thatalmost 90 per cent of the gold is leached in the first stage,implying that carbon could be added to the first stagewithout affecting the achievable loading on the carbonwhile possibly reducing the gold in the barren solution.However, the calculations show that there is an optimumpoint for the addition of carbon. Thus, the amounts ofcarbon required to achieve the same performance and thegold locked.up in the plant (relative to the examplewhere all the stages contain carbon) are plotted in Fig. 9,from which it is apparent that two stages of preleachingwould be optimum. The point of addition of carbon willvary with head grade and the desired barren-solutionvalue. However, only in very exceptional cases are morethan 5 or 6 hours of preleaching required. Thus, calcula-tions in which the desired barren solution in this applica.tion is increased to 0,01 gjt results in an optimumsituation of one preleaching stage, and an increase of thehead-grade to 8 gjt results in the prediction that carbonshould be added to all the stages.

This model permits an assessment of the effect ofso-called 'extra gold dissolution' during CIF absorption.Observations on both pilot-and full-scale plants haveshown that the washed residues after CIF are invariablylower than those obtained by sampling of the feed to

2,4

2,2Carbonadded

~2,0

1,8

1,6

1,4-

'at:; 1,2~

1,0

0,8

0,6

0,4

0,2

00 1 2 3 4

StageFig. 8-Calculated solids and solution profiles for a CIL plant

5 6 7

76 MARCH 1984 JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY

1,2

~

1,10-i 1,0>.5CD~

0,9IQ'iia: 0,8

0,70 3 41 2

No. of pre-Ieaching stagesFig. 9-Effect of number of pre-Ieaching stages on the relative

performance of a CIL plant

CIF. This difference can in some instances amount to anadditional gold recovery of as much as 1 to 2 per cent.However, continued slow leaching of the gold duringCIF absorption can lead to apparent poor performance ofthe circuit, especially if low (less than 0,01 gjt) barrenvalues are desired. This can be seen from the followingfairly typical example in which the pulp produced by theleaching in 8 stages of 3 hours each as described above issubjected to CIP absorption. In the absence of additionalleaching, five-stages of CIF would result in the predietedresults shown in Table I (Test 1), in which 6,6 kg of car-bon per stage would be required to produce a barrensolution containing 0,002 g/t of gold. An allowance forcontinued gold leaching results in the predicted profilesshown in Table V.

TABLE VPREDICTED EFFECT OF ADDITIONAL LEACIDNG OF GOLD ON CIP

ABSORPTION,

Conditions: The same as for Test I in Table I

8

Table V can be compared with Table I and the resultspredicted for a CIL plant (Table VI).

It is apparent that the dissolution occurring duringabsorption can have a significant effect on the amount ofcarbon required, and this results in a higher carbon (andgold) inventory for a CIL plant than for a CIP plant.This would need to be taken into account in any economicevaluation of the alternative circuits.

Carbon GoldLeaching Head CIP Residue inventory lock-up

Plant stages g/t stages g/t kg kg

Leach-CIP 8(3) 2,3 5(1) 0,26 32,9 0,027*Leach-CIP 8(3) 2,3 5(1) 0,23 55,2 0,044CIL 8(3) 2,3 0 0,26 68,5 0,055

The figures in parentheses represent pulp residence times

*Allowance was made for leaching during CIP absorption.

30

;:-010

200It)It)SG)> 10;: G'I 0I '"xc'iij 'aCl C 0I'iii !;~ccas

-10iiZ

-20

TABLE VICOMPARISON OF CIP AND CIL

Application to the Economic Optimization of DesignIt should be apparent from these considerations that

the design of a CIP plant involves decisions on a numberof process options, the most important of which are thedesired extraction (i.e. the maximum concentration ofgold in the barren pulp), the loading of gold on the car.bon, and the number of stages to be employed. Havinga knowledge of the kinetics of extraction and using thismodel, one can show that the correct decisions on theseoptions can lead to economic optimization of the plantdesign. It should be emphasized that the approachsuggested is a simplification of a complex economic-optimization procedure. However, it serves to ilIustratehow the models developed in this paper can be incorpora-ted into such a cost-minimization procedure.

A major consideration is the value of the carbon andthe gold absorbed on the carbon in the absorption circuit.As a first approximation, the value of the carbon and itsassociated gold was considered to be part of the capitalcost of the plant. The following example was based onthe operating characteristics of the Mintek pilot plantat Western Areas Gold Mine, which was fully describedearlier. The calculations were made for a hypotheticalplant to treat pulp containing 200 kt of solution permonth, and the following assumptions were made:

RValue of activated carbon per ton 3000Value of gold per kilogram 15000Cost of elution: and reactivation per ton of

carbon 100Cost of absorption vessel 150 000

As a result of the interdependence of the variousparameters, an iterative procedure was employed inwhich, for example, the number of stages and the desiredconcentration of gold in the barren solution are fixed andan optimum gold loading on the carbon is calculated.This value can then be used in the calculation of theoptimum number of stages, and in the estimation of thebarren-solution value, which can then be used in anothercycle of calculations. In this particular instance, theassumption was made that 6 stages are required toproduce a barren solution containing 0,001 gjt of gold.These values were then substituted into the model to-gether with various possible gold loadings, and' thenecessary amounts of carbon and the gold locked upwere calculated. The results are shown in Fig. 10, inwhich it can be seen that the optimum loading is 4000 gjt.The existence of this optimum is attributed to the oppo.

sing effects of lower operating costs associated with ahigher gold loading (i.e. a slower movement of carbonthrough the plant) and the increase in the amount ofcarbon and gold in the absorption vessels. The intereston these values was calculated for a rate of 15 per centper annum.

It has already been demonstrated that the amount ofcarbon required to achieve a desired extraction and theamount of associated gold decrease with increasing num-bers of stages (Fig. 6). In this example, the decrease incapital associated with the carbon and loaded gold mustbe balanced against the cost of extra absorption vessels.The use of the optimum loading of 4000 gjt and a desiredbarren solution of 0,001 gjt in the model for various num-bers of stages produced the results ilIustrated in Fig. ll,from which it can be seen that the previous estimatedoptimum of 6 stages is correct.

Finally, these values of 4000 gjt loading and 6 stagescan be used in a similar calculation to give an optimumvalue for the gold in the barren solution. In this case,increased recovery is offset by the need for the employ-

(141)

- - - - - - - - - - (103)

Figures in parentheses arethe calculated carbon flow.rates in kg/h

'2500 3500 4500 5500Gold on loaded carbon, g/t

Fig. IO-Optimization of the carbon flowrate and the goldloading in a six-stage CIP plant

JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY MARCH 1984 77

600Cii'CDg)as- 5001/1~0-CD 400>::: ;;-as 0a; ,...:. x 300c'ij "Cg) C

asiii a:-

- 200'0.asu

iii"-CD>0

100

04 5 6 8 97

Number of stagesFig, I I-Optimization of the number of stages in a CIP plant

ment of more carbon with its associated gold, The resultsof these calculations are shown in Fig. 12, from which itcan be seen that the plant should be designed to producebarren values below 0,002 g/t. A comparison of therelative revenues in Figs. 10 and 12 shows that the loss ofgold in the barren pulp is a more important considerationthan the amount of gold locked up in the plant.

ConclusionsA relatively simple rate expression for the absorption

of gold onto activated carbon was used as the basis forthe development of a model for a multi stage CIP absorp-tion circuit, When the model was used in the predictionof both the steady-state and the transient behaviour ofthe absorption process, the results were in reasonableagreement with those observed in an extended pilot-plant campaign.

Extension of the model to the description of a CILprocess was made possible by the inclusion, in the overallCIF model, of a suitable rate equation for leaching. This

78 MARCH 1984 JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY

300~

Cl,..0cS.5!

: 200:::.!!

~! ,... )(1/1as 'g! cU I

.5 S 100ii~

cCIGiz

0

0,0005 0,002 0,004 0,006 0,010,001Gold in barren solution, g/t

Fig. 12-0ptimization of the extraction efficiency in a six-stage CIP plant

enabled the optimum point of addition of carbon to theleaching circuit to be identified, and also allowed for anassessment of the effects of gold dissolution during a nor.mal CIF absorption.

Finally, a brief assessment was made of the economicconsequences of the various process options availablefor the design of a CIF plant.

AcknowledgementThis paper is published by permission of the Council

for Mineral Technology.

1.References

NrcOL, M. J., FLEMING, C. A., and CROMBERGE,G. The ab-sorption of gold cyanide onto activated carbon. I. Thekinetics of absorption from pulps. J. S. Afr. Inst. Min.Metall., vo!. 84, no. 2. Feb. 1984. pp. 50-54.HUSSEY, S. J., SALISBURY,H. B., and POTTER, G. M. Carbon-in-pulp silver absorption from cyanide leach slurries of asilver ore. U.S. Bur. Mines, Report oJ Investigation no. 8268,1978.

2.