Cyanidation kinetics of silver sulfide

Hydrometallurgy 56 Ž2000. 171–188 www.elsevier.nlrlocaterhydromet

Cyanidation kinetics of silver sulfide R.M. Luna, G.T. Lapidus ) Departamento de Ingenierıa UniÕersidad Autonoma Metropolitana-Iztapalapa, AÕ. ´ de Procesos e Hidraulica, ´ ´ Michoacan sr n, Apartado Postal 55-532, Mexico, D.F., 09340, Mexico ´ y Purısima ´ Received 27 September 1999; received in revised form 21 January 2000; accepted 4 February 2000

Abstract In the present study, silver sulfide cyanide leaching was initially studied using synthetic Ag 2 S and oxygen. Qualitative and quantitative chemical analyses were employed to determine which species ŽS 2y, S 2 O 32y, SO 32y, SO42y, H 2 O 2 , or SCNy . were present in solution. The results made it possible to establish the stoichiometric relationships of the reactions under consideration. It was found that thiosulfate ion is the dominant sulfur species. In the second part, the kinetics of silver extraction were determined for a mineral concentrate. The sodium cyanide and oxygen concentrations were varied to define the diffusional and reaction phenomena that occur during leaching at constant temperature and pressure. A mathematical model for silver leaching by cyanidation, which considers the redox reaction and complex equilibria in the solution phase, was developed. Silver sulfide leaching from mineral particles was found to be a kinetically controlled process, strongly influenced by solubility phenomena. The experimental results agreed with those predicted by the proposed model. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Leaching; Silver sulfide; Cyanidation; Mathematical modeling

1. Introduction Cyanidation has been used for over 100 years to extract precious metals from sulfide ores. Despite this fact, the reactions involved are not fully understood. The chemical reactions that take place during the cyanidation of concentrate for ores can be very complex. The extraction of a specific metal depends on its oxidation state, nature and mineral composition w1x. Although there has been much research performed with other )

Corresponding author. Fax: q52-5-804-4900. E-mail address: [email protected] ŽG.T. Lapidus..

0304-386Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 6 X Ž 0 0 . 0 0 0 7 2 - 4

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chemical systems for precious metal leaching from sulfide ores or concentrates, at present, the cyanidation method yields the highest extractions at the lowest cost for the majority of minerals. Most of the studies related to the cyanidation process focus on the electrochemical nature of the reaction. The optimum concentration ratio between cyanide and oxygen was determined by Habashi w2x for pure gold dissolution. Osseo-Asare et al. w1x undertook a thermodynamic study using Habashi’s results and presented Eh–pH diagrams that define the silver cyanide complex regions at different cyanide concentrations. Wadsworth w3,4x developed a kinetic model for gold cyanidation on a rotating disc. He determined the diffusional regimes with respect to the cyanide and oxygen concentrations, and assumed a similar behavior for metallic silver. Despite the extensive electrochemical studies realized and the major contributions made in this field, there is neither a precise knowledge of the chemical reactions involved nor of the secondary reactions occurring in the leaching of sulfide ores. Zhang et al. w5x carried out a thermodynamic study, which presents a series of possible reactions that may occur during silver sulfide cyanidation. However, these results were developed only on the basis of calculated predominance area diagrams for pure silver. Specifically regarding silver sulfide, Shoemaker and Dasher w6x argue that silver leaching takes place when the sulfide ion is slowly and reversibly converted into thiosulfate, but only at high free cyanide concentrations. To date there is insufficient published information about the reactions and their limitations to allow optimization of the process. For that reason, in this work, the stoichiometric relations of the leaching reaction were determined in order to explain the nature of silver sulfide cyanidation. A particulate model was also developed, and confirmed by experiment, for silver leaching from a sulfide concentrate at different cyanide and oxygen concentrations.

2. Theoretical aspects 2.1. Cyanidation reactions Two types of reaction are involved in the cyanidation process: a redox reaction at the mineral–solution interface and complex formation in the fluid. The possible reactions between silver sulfide and the oxidizing agent in aqueous media may be represented as follows: Ag 2 S q 2 ÕCNyq z H 2 O q xO 2

™ 2C q SO q wOH

y

y

Ž 1.

w x 2y and AgwCNx 43y; SO y s S 2y, SO 32y, SO42y, S 2 O 32y; where: C s AgwCNxy 2 , Ag CN 3 y y andror SCN ; OH s OH or H 2 O 2 . The detection and quantification of the species produced during the cyanidation process were carried out in the first part of the experimentation to establish the stoichiometric relations of the reaction. The possible chemical species present during

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Table 1 Silver reactions with cyanide, sulfite, sulfate and thiosulfate Complex reactions

log 10 K

Agq q2CNy AgŽCN.y 2 Agq q3CNy AgŽCN. 32y q y Ag q4CN AgŽCN.43y q 2y Ag qSO 3 AgŽSO 3 .y Agq q2SO 32y AgŽSO 3 . 23y Agq q3SO 32y AgŽSO 3 . 35y Agq qS 2 O 32y AgŽS 2 O 3 .y Agq q2S 2 O 32y AgŽS 2 O 3 . 23y Agq q3S 2 O 32y AgŽS 2 O 3 . 35y 2Agq q4S 2 O 32y Ag 2 ŽS 2 O 3 .46y 3Agq q5S 2 O 32y Ag 3 ŽS 2 O 3 .7y 5 6Agq q8S 2 O 32y Ag 6 ŽS 2 O 3 .10y 8 q y Ag qSCN AgŽSCN. Agq q2SCNy AgŽSCN.y 2 Agq q3SCNy AgŽSCN. 32y Agq q4SCNy AgŽSCN.43y

20 20.3 20.8 5.6 7.8 9.0 8.82 12.63 12.8 26.3 39.8 78.6 4.8 8.2 9.5 9.7

Redox reactions 2S 2y q3H 2 O S 2 O 32y q6Hq q8ey 2S 2y q3O 2 2SO 32y S 2y q2O 2 SO42y S 2y qCNy SCNy q2ey 2O 2 q4H 2 Oq8ey 8OHy O 2 q2H 2 Oq2ey H 2 O 2 q2OHy

E 0 ŽV. 0.006 1.511 2.451 0.002 0.401 0.88

m m m m m m m m m m m m m m m m

m m m m

m m

leaching, according to the electrochemical potentials w7,8x and equilibrium constants w9x reported in the literature are expressed in Table 1. To facilitate data manipulation, the numerous chemical entities, which may be present during leaching, were grouped into total chemical species groups. Using the numeration as expressed in Table 2, the following groups are formed:

Total sulfur s wSx T s C 1 q 2C 3 q C 4 q C 5 q C 11 q 2C 12 q 3C 13 q 2C 14 q 4C 15 q 6C 16 q 8C 17 q 10C 18 q 16C 19 q C 22 q C 23 q 2C 24 q 3C 25 q 4C 26

Table 2 Chemical species that may be present in the solution during silver sulfide leaching by cyanide 1sS 2y 2 sO 2 3sS 2 O 32y 4 sSO 32y 5sSO42y 6 s Agq 7sCNy

8s AgŽCN.y 2 9s AgŽCN. 32y 10 s AgŽCN.43y 11s AgŽSO 3 .y 12 s AgŽSO 3 . 23y 13s AgŽSO 3 . 35y 14 s AgŽS 2 O 3 .y

15s AgŽS 2 O 3 . 23y 16 s AgŽS 2 O 3 . 35y 17s Ag 2 ŽS 2 O 3 .46y 18s Ag 3 ŽS 2 O 3 .7y 5 19s Ag 6 ŽS 2 O 3 .10y 8 20 s H 2 O 2 y 21sOH

22 sSCNy 23s AgŽSCN. 24 s AgŽSCN.y 2 25s AgŽSCN. 32y 26 s AgŽSCN.43y

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Total silver s wAgx T s C 6 q C 8 q C 9 q C 10 q C 11 q C 12 q C 13 q C 14 q C 15 q C 16 q 2C 17 q 3C 18 q 6C 19 q C 22 q C 23 q 2C 24 q 3C 25 q 4C 26 Total cyanide s wCNx T s C 7 q 2C 8 q 3C 9 q 4C 10 q C 22 q C 23 q 2C 24 q 3C 25 q 4C 26 Total oxidizing agent s wO 2 x T s C 2 Total hydroxyls wOHx T s 2C 20 q C 21

3. Mathematical model The unsteady state shrinking core concept w10x was employed in the mathematical model developed to describe silver sulfide leaching. This model makes the following assumptions, which are applicable to concentrate leaching: Ø The system is isothermal. Ø The silver sulfide initially has a uniform distribution throughout the particle and the other species present are considered to be inert with respect to the cyanidation reaction. Of course this is not the case for gold and for some reactive copper and iron species, such as chalcopyrite and pyrrhotite. However, when these species are found in small quantities, their effect on the model is limited. Ø The particle is spherical and conserves its size and shape during the leaching process. Ø The complexation Žhomogeneous. reactions in the aqueous solution are instantaneous, compared to the leaching Žheterogeneous. reactions. Ø The reaction boundary is well defined and the diffusion and reaction resistances act in series. Because of the mixing in the reactor, the external mass transfer resistance is considered to be negligible. The diffusion of the chemical species j in the inert layer may be expressed using Fick’s second law in spherical coordinates:

´

E Cj

s

Et

Dj E 2

R ER

½

R2

E Cj ER

5

Rc - R - Rp .

Ž 2.

Since the complexes formed within a total species group balance those destroyed in the diffusion region, there is no net reaction and Eq. Ž2. therefore may be used to describe the diffusion of each total chemical species group through the inert layer w11x. For example, for the total cyanide Eq. Ž2. may be expressed as follows:

´

E w CN x T Et

1 s

2

E

R ER

½ ž

R2 D7

EC 7 ER

q2 D 8

EC8 ER

q3D 9

EC9 ER

q4D 10

EC10 ER

q

/5

.

Ž 3.

For the other four differential equations, the diffusion equations are analogous. At the beginning of the process, the redox reaction takes place at the particle surface. The initial condition for each total chemical group reflects the composition of the bulk solution before cyanidation takes place.

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3.1. Initial conditions @ t s 0,

Rp s Rc ,

0

Cj s Cj .

For each total chemical species:

w S x T s 0 s Total sulfur in solution w CNx T s w CNx

0 T s Total cyanide

Ž 4. Ž 5.

w O 2 x T s w O 2 x T0 s Total oxidizing agent w Agx T s 0 s Total silver in solution

Ž 6. Ž 7.

w OHx T s w OH x T0 s Total hydroxyl Ž initial bulk solution pH.

Ž 8.

3.2. Boundary conditions 3.2.1. At the particle surface (R p ) As was mentioned previously, agitation within the reactor was such that the external mass transfer resistance may be considered negligible and, therefore, the concentration of each total species group at the particle surface at any time may be equaled to that of the bulk. To update these concentrations as the leach progresses, material balances must be made in the bulk solution for the consumption or production of each chemical species. These balances are related to the stoichiometry of the reaction. The silver concentration in the bulk solution is proportional to the fractional conversion of the original quantity of silver in the concentrate and the percent solids in the leach system. @ t ) 0, R s R p

w Agx T s a X

Ž 9.

where: a s material balance constant factor in the solution Ž r L W .rŽ r M .. For total sulfur, the silver sulfide stoichiometry dictates that the quantity is related to half of the silver fraction converted: 1 wSx T s a X . Ž 10 . 2 The total hydroxyl ion is referred to the initial pH in the bulk solution plus the stoichiometric quantity that is formed during reaction. w w OHx T s w OH x T0 q a X Ž 11 . 2 The total concentrations of the other chemical species remain constant in the bulk solution. In the case of cyanide, this occurs because all of the complexes, reactants and products, are included in the group. Oxygen is considered constant because, even though there is consumption, its concentration is continuously replenished.

w CNx T s w CNx T0

Ž 12 .

w O 2 x T s w O 2 x T0

Ž 13 .

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3.2.2. At the reaction boundary (R c ) The establishment of the conditions for each total chemical species was made on the basis of the experimental results Žsee Results and discussion. and is related to the stoichiometric fluxes of the total species groups. The sulfur flux is dictated by the total flux of the silver, according to the stoichiometry of the mineral ŽAg 2 S.: NwS x T s

1 2

Nw Ag x T

Ž 14 .

The oxygen reduction and sulfur oxidation reactions, that are described by Eq. Ž1., will be experimentally established Žsee Results and discussion.. In this manner, the total oxidizing agent flux is stoichiometrically related to that of total silver, but of opposite sign. x NwO 2 x T s y Nw Ag x T Ž 15 . 2 The hydroxyl ion flux may be expressed as: w NwOH x T s y NwO 2 x T . x

Ž 16 .

For the total cyanide, the flux is considered equal to zero since there is no consumption in the system. NwCN x T s 0

Ž 17 .

For the boundary condition relative to the oxidation reaction, there exist two possibilities: 1. That this is so fast that it reaches equilibrium or 2. That its kinetics are slow compared to diffusional phenomena The election of the correct boundary condition must be based on the experimental results. In the case where the reaction reaches equilibrium, using Eq. Ž1., the boundary condition may be expressed as follows: y 2

K EQ s

w

w SO Y xw OHy x . x w CNy x 2 Õ w O 2 x

Ag Ž CN . V

Ž 18 .

On the other hand, if the sulfur oxidation reaction proves to be slow and the process is controlled by the reaction kinetics, then the boundary condition may be represented as: b

r SO Y s k c w S 2y x w O 2 x

g

Ž 19 .

where, b and g are the reaction orders of the sulfide ion and oxygen, respectively. The above reaction poses a problem since a non-diffusing species, the sulfide ion, is located only at the reaction core. In order to circumvent this difficulty, the sulfide ion

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concentration was calculated indirectly using the silver sulfide solubility product, as shown below: r SO Y s k c

b

K ps

g

wO2 x .

q 2

Ž Ag .

Ž 20 .

In this manner, the rate expression actually includes the solubility limitation. The core shrinkage rate may be described by a material balance with respect to the flux of the total silver at R c : d Rc

s

dt

DAg ECAg

rM

ER

.

Ž 21 .

Rs R c

The conversion of silver extracted from the concentrate is related to the position of the unreacted core by the following expression: Xs1y

Rc

ž / Rp

3

.

Ž 22 .

The diffusion equations with their initial and boundary conditions were converted to dimensionless parameters using the same change of variables presented by Taylor et al. w12x. The dimensionless differential equations and their respective initial and boundary conditions were discretized using the orthogonal collocation and implicit Euler methods in radial and temporal co-ordinates, respectively. The entire system was solved for progressive times using a Newton–Raphson type algorithm.

4. Experimental method This section was developed in two parts: in the first, a set of experiments was realized to determine the nature of the sulfur species present during the leaching and the mechanism of the reaction; in the second, leaching experiments were performed on a sulfide concentrate. A mass balance was effected for the bulk solution to calculate the species distributions, considering the reactions that take place during leaching Žsee Table 1.. For the first part, silver sulfide was prepared in the laboratory from sodium sulfide and silver nitrate. One experiment was performed using nitrogen as an inert gas. In the other experiments, oxygen was used as an oxidizing agent at two concentrations, 21% and 100% Žair and oxygen.. To prepare the cyanide solutions, water was placed in a vessel and the pH was adjusted to 10.6 with NaOH. The cyanide salt was then dissolved and the flow of the oxidizing agent initiated. After 30 min, the reaction was started by introducing the silver sulfide. The reaction lasted 8 h in each case. Samples of the solution were extracted at pre-established time intervals and analyzed for silver by atomic absorption spectrometry ŽAAS.. In the reaction that employed pure oxygen, silver sulfide was placed in contact with a 0.01-M cyanide solution during 24 h,

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qualitative and quantitative analyses were performed on the final solution to identify the species of sulfur present in the reaction Ž1.. In the qualitative analysis the thiosulfate, thiocyanate, sulfate, sulfite ions and hydrogen peroxide were tested for using iodine– iodide, ferric chloride, barium sulfate, acidic fuchsine and titanium tetrachloride, respectively. Since only thiosulfate was identified, it was quantified with the iodometric method. Kinetic experiments were realized on a sulfide concentrate provided by Companıa ˜´ Real de Monte y Pachuca, Hidalgo, Mexico. For this study the y200 q 300 mesh ´ fraction Ž52–74 mm. was employed, which contained 1.2% Ag, 0.27% Cu, 0.92% Pb, 21.4% Fe and 3.04% Zn as sulfides and 7.25 grton metallic Au. Leaching tests were carried out in a standard 1 L Pyrex reactor fitted with four ports: one for sampling, another for the introduction of the oxidizing agent, the third for the gas purge and the last for the agitator. The system temperature was established at 208C. Samples of the solution taken were at pre-established intervals as in the first part. At the end of each experiment, the residues were filtered, dried and analyzed for gold, silver and copper to complete the metallurgical balance.

5. Results and discussion 5.1. Determination of the chemical species present and the stoichiometric relations between synthetic Ag 2 S and oxygen The objective of this section was to determine the chemical species of sulfur produced and the stoichiometric relations of the oxidation reaction. For this purpose, pure silver sulfide was placed in contact with a 0.01-M cyanide solution during 24 h. After this time, the filtered solution was analyzed qualitatively and quantitatively using established methods w13,14x. The only sulfur species identified was the thiosulfate ion. On the basis of this result, the complex reactions involving silver in the bulk solution were established. The formation values of the complexes shown in Table 1 allowed the calculation of the cyanide complex distribution as the silver was extracted. Table 3 shows the most representative silver complexes, which contain cyanide and thiosulfate. It should be noted that, according to the mineral stoichiometry, the total thiosulfate ion concentration is four times less than that of the silver. Together with the reduced complex stability of the thiosulfate ion with silver, this explains the low concentration of these complexes in solution. With respect to oxygen reduction, hydrogen peroxide was not detected by the qualitative methods. This could imply that the oxygen undergoes complete reduction to form hydroxyl ion, although this assumption was further tested in the concentrate leach experiments. With the above results, the oxidation reaction ŽEq. Ž1.. was established as follows: Ag 2 S q 4CNyq O 2 q 1r2H 2 O

™ 2AgŽ CN.

y 2y y 2 q 1r2S 2 O 3 q OH .

Ž 23 .

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Table 3 Values of the most representative silver complex concentrations for the reaction between silver sulfide and oxygen Time Žmin.

4 wAgŽCN.y x 2 =10

wAgŽCN. 32y x=10 6

wAgŽCN.43y x=10 7

wAgŽS 2 O 3 . 23y x=10 14

15 60 75 90 105 150 180 360 480 1440

4.60 4.70 4.80 4.90 5.00 5.10 5.20 5.37 6.13 7.12

8.4 8.5 8.6 8.7 8.8 8.9 9.2 9.5 10.7 12.1

2.39 2.43 2.45 2.47 2.51 2.54 2.60 2.68 2.95 3.27

3.7 3.9 4.0 4.2 4.5 4.7 5.2 5.9 9.1 14.9

5.2. Concentrate leaching at different conditions The objective of this section was to determine the nature and velocity of the heterogeneous redox reaction at the unreacted core boundary. This information was later integrated into the particle leaching model. To further confirm that oxygen reduction does not proceed through the production of hydrogen peroxide, a sequestering agent was employed, CaŽOH. 2 . The scientific contributions related to the behavior of calcium hydroxide as a pH regulator in cyanidation, show that during gold leaching, this compound reduces the extraction rate of the metal w15x. It was observed that at the instant hydrogen peroxide is formed as an intermediary product, the calcium ion reacts with it to form calcium peroxide, which does not allow further oxidation of the metal w16x. In order to investigate the mechanism of oxygen reduction, two leaching experiments of the concentrate were carried out at the same conditions ŽpH s 10.6, T s 208C, agitation rate s 520 rpm, and 10 g concentraterliter solution., only that in one of them, CaŽOH. 2 was used to adjust the pH, while in the other NaOH was employed. Fig. 1 shows the behavior of these two experiments, where a similar tendency is observed. This confirms that hydrogen peroxide is not produced as an intermediate during the leaching of silver sulfide. In the following set of experiments, NaOH was used to adjust the pH. In Fig. 2 the results of concentrate leaching at different cyanide concentrations are presented using oxygen as the oxidizing agent. It may be observed that the extraction rate increases when the cyanide concentration is raised, unlike the case for the pure metals w4x where a maximum stable extraction value is reached at a relatively low cyanide concentration. Although the silver sulfide conversions at low cyanide concentrations are not negligible as had been mentioned by Shoemaker and Dasher w6x, they are very limited. The experiments at higher cyanide concentrations show that the extraction does not reach 100%. There seems to be a quantity of silver that is not leachable by cyanide. The reasons for this behavior may be that either this silver may be occluded in the ore

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Fig. 1. Silver concentration in the bulk solution versus time for concentrate leaches adjusting pH with Ca ŽOH. 2 and NaOH. wNaCNx s 0.01 M.

particles or it may be present as another more refractory mineral phase such as Ag 2 Se or Ag 2Te w7x. In subsequent figures, the unleachable silver is deducted.

Fig. 2. Silver fractional conversion versus time obtained for concentrate leaches at different cyanide concentrations. Pure oxygen was used in all experiments.

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Controlled experiments were performed at 0.1 M cyanide using oxygen at two different concentrations, pure oxygen Ž100%. and air Ž21%., and the results are shown in Fig. 3. It may be observed that although the difference between initial extraction velocities with air and oxygen is large, it is not proportional to the oxygen concentration. It was demonstrated by Wadsworth w4x and Habashi w2x that in the case of pure metals, where two fluid reagents are necessary, diffusion controlled kinetics are governed by only one reactant at a time over most of the concentration range. This means that cyanidation is limited by either cyanide or oxygen diffusion. These authors found that the transition point between oxygen and cyanide diffusion control is determined by the stoichiometry of the oxidation reaction and the relative diffusivity ratio. For gold, this relation was estimated to be CCN yrCO 2 s 4, DO 2rDCN ys 6, which closely resembled that found with experimental measurements w4x. According to the stoichiometry of Eq. Ž23., the transition from cyanide to oxygen diffusion control should occur at a cyanide concentration six times the oxygen concentration or 0.005 M cyanide for the pure oxygen case. This implies that if silver leaching kinetics were controlled solely by diffusional phenomena, identical extraction rates would be expected for cyanide concentrations greater than approximately 0.025 M. This is not the case for the experiments shown in Fig. 2 and, for that reason, pure diffusion control is doubtful. The leach experiments shown in Fig. 4 were performed at 0.1 M cyanide with different concentrate quantities. The objective of these experiments was to detect a possible reversibility in the reaction or silver saturation in the solution. It may be observed from the figure that the experiment with the larger quantity of concentrate produced less fractional silver conversion. This finding points to the fact that the

Fig. 3. Silver fractional conversion versus time for mineral concentrate leaches carried out during 8 h at two different oxygen concentrations. wNaCNx s 0.1 M.

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Fig. 4. Silver fractional conversion versus time for concentrate leaches with different quantities of solid. wNaCNx s 0.1 M.

reaction may be approaching equilibrium or solution saturation when the mineral concentration, and therefore silver content, are higher. 5.3. Mathematical model The mathematical model was solved for both cases: reaction equilibrium and slow kinetics at the core boundary. The only adjusted parameter for each case was the pore tortuosity since all of the other parameter values were reported or estimated. When reaction equilibrium was assumed ŽEq. Ž18.., the simulations for all of the cyanide concentrations show that the oxygen concentration at the core boundary must be near zero Ž10y8 0 M. in order to satisfy that equation, due to the very large value of the equilibrium constant. Because of this, the equilibrium condition essentially implies oxygen diffusion control. Fig. 5 shows the simulation results for different cyanide concentrations using the reaction equilibrium boundary condition. It may be appreciated that the model predicts the same extraction rate at all cyanide concentrations, contrary to the experimental behavior observed in Fig. 2. Consequently, it may be concluded that reaction equilibrium or oxygen diffusion control cannot explain the observed change in the leaching velocity with cyanide concentration. Since the reaction equilibrium assumption and reagent diffusion control do not correctly predict the actual leaching behavior, the second option ŽEq. Ž20.., related to reaction kinetics, was examined. In this part, it was necessary to determine the reaction order for both the sulfide ion and the oxygen concentrations. In Figs. 6 and 7, the results obtained from the model are presented for reaction orders of one. Satisfactory adjustments were achieved for five of the six experiments at different cyanide concentrations

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183

Fig. 5. Model simulations of an oxygen diffusion control mechanism. Cyanide concentrations interval 0.001–0.3 M. The model shows the same behavior for all concentrations.

and both oxygen concentrations. The value of the kinetic rate constant was found to be 0.4847 cm4rmol s. This corresponds to a Damkohler number, in the dimensionless ¨

Fig. 6. Comparison of model and experimental results at different cyanide concentrations. Model results are shown as continuous lines.

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Fig. 7. Comparison of model and experimental results at different oxygen concentrations. Model results are shown as continuous lines. wNaCNx s 0.1 M.

model, of 5 = 10y5 using pure oxygen as the reference compound. The above value very clearly represents a reaction-controlled regime. The porosity value used was experimentally determined on the basis of a totally leached ore Žexperiment with 0.3 M NaCN.. Simple inspection of Eq. Ž20. would seem to indicate that the cyanide concentration should not affect the reaction rate. However, since the boundary condition is expressed as a function of the K ps and free silver ion concentration, the cyanide concentration indirectly affects the rate. Table 4 shows the free silver and corresponding sulfide ion concentrations calculated by the model at the reaction boundary for various cyanide concentrations. The previous results, for 10 g of concentrate per liter of leaching solution, show an excellent fit of model simulations with respect to the experimental tests. However, it may be observed in Fig. 8 that this is not the case for a higher percentage of solids.

Table 4 Free silver and sulfide ion concentrations at the reaction boundary for different cyanide concentrations wCNy x, ŽM.

wAgq x=10 22 , in R c

wS 2y x=10 6 , in R c

0.001 0.003 0.01 0.03 0.10 0.30

4.23 2.45 1.36 0.91 0.50 0.24

0.06 0.17 0.54 1.21 4.00 17.36

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Fig. 8. Model and experimental results for leaching with 100 g concentraterliter. wNaCNx s 0.1 M and wPO x s 0.8 atm. Ž100%.. 2

There is a large difference between the model and experimental results during the first 10 h, probably due to an oxygen gas to liquid mass transfer limitation. In other words, the quantity of oxygen being transferred into the solution by simply bubbling was insufficient to maintain the solution saturated under these conditions. On other hand, the figure shows a stagnation stage after 10 h, which may be attributed to the silver saturation in the bulk solution. It is interesting to note that the model simulates this region very well. This situation may be better understood by analyzing Fig. 9, where the total silver profile is shown at two different conversions. At 11% conversion, which corresponds to a zone within the first 10 h, the silver concentration decreases from R c to R p , as would be expected when diffusion occurs. In the case of 77% conversion, after 15 h reaction, the silver complex profile is almost completely horizontal, showing that the solution within the pores has nearly reached saturation with the bulk solution. The saturation phenomenon, that is present during leaching due to a limited silver solubility, indirectly affects the kinetic expression. This will have a negative effect on the extraction when cyanide concentrations are low or the silver quantity is high. Therefore, a high solids content or using very high-grade material will seriously hamper leaching. Under these conditions, in spite of the advantages and low cost system operation, heap leaching is not recommendable. Consequently, it is important to consider leaching at a higher temperature since the reaction rate is expressed as a function of solubility and reaction constant which both increase exponentially with temperature. Extraction of silver from the concentrate at three different temperatures is shown in Fig. 10 for the same cyanide concentration Ž0.01 M.. The extraction at 428C shows both a higher initial leaching velocity and an

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Fig. 9. Silver concentration profiles at two conversion levels with 100 g concentraterliter. wNaCNx s 0.1 M.

increased level of solubility Žestimated increment was from 1.1 = 10y5 0 at 208C to 6.4 = 10y4 9 at 428C., despite the lower oxygen solubility Žapproximately 20%.. For the experiment at 658C, a saturation plateau is not reached even at over 80% conversion. For that reason, in those operations where high-grade materials are processed, an increase in temperature could avoid the stagnation of the reaction.

Fig. 10. Model and experimental results for leaching at different temperatures. wNaCNx s 0.01 M and wPO x s 0.8 atm. Ž100%.. 2

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6. Conclusions From the results obtained in the first experimental section, the only sulfur species detected in solution was the thiosulfate ion. On the basis of equilibrium calculations, AgŽCN.y 2 was determined to be the most representative silver complex. Also, the mechanism of the reaction was found to follow the direct formation of hydroxyl ions, without proceeding through hydrogen peroxide. With the previous results, the stoichiometric relations were established and the cyanidation reaction may be expressed as follows: Ag 2 S q 4CNyq

1 2

H 2 O q O2

m 2AgŽ CN.

y 2 q

1 2

S 2 O 32yq OHy.

Silver leaching from the concentrate increases as the cyanide concentration is elevated. However, at higher mineral contents, a saturation phenomenon is present. Model simulations obtained from the proposed kinetic model nearly coincided with the experimental results using only one adjustable parameter, except where a large quantity of concentrate was employed. The agreement of the model with respect to experiments proved that silver extraction was kinetically controlled by a second order reaction relative to the local oxygen and sulfide ion concentrations.

7. Nomenclature w Cj x Dj kc K EQ K ps N w C j xT r SO Y Rc Rp R t X Õ,w, x, z

concentration of chemical species jth diffusivity of the chemical species jth kinetic rate constant equilibrium constant solubility product constant flux of the total chemical species jth velocity rate radius of the shrinking core particle radius radius time fractional conversion of silver stoichiometric relationships

Greek letters ´ porosity in the inert layer rL density of the solution rM molar density of silver in the mineral a accumulation of the silver in the bulk solution b reaction order with respect to sulfur g reaction order with respect to oxygen

188

R.M. Luna, G.T. Lapidusr Hydrometallurgy 56 (2000) 171–188

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