Predicting Cyanide Consumption in Gold Leaching: a Kinetic and Thermodynamic Modeling Approach

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Article Predicting Cyanide Consumption in Gold Leaching: A Kinetic and Thermodynamic Modeling Approach

Yaser Kianinia 1, Mohammad Reza Khalesi 1,*, Mahmoud Abdollahy 1, Glenn Hefter 2, Gamini Senanayake 2, Lubomir Hnedkovsky 2, Ahmad Khodadadi Darban 1 and Marjan Shahbazi 3

1 Department of Mining Engineering, Tarbiat Modares University, Tehran 1411713116, Iran; [email protected] (Y.K.); [email protected] (M.A.); [email protected] (A.K.D.) 2 Department of Chemical & Metallurgical Engineering & Chemistry, Murdoch University, Murdoch, WA 6150, Australia; [email protected] (G.H.); [email protected] (G.S.); [email protected] (L.H.) 3 Department of Mining Engineering, Yazd University, Yazd 8915818411, Iran; [email protected] * Correspondence: [email protected]; Tel.: +98-21-8288-4365

Received: 18 January 2018; Accepted: 5 March 2018; Published: 8 March 2018

Abstract: The consumption of cyanide during processing operations is a major economic cost in the extraction of gold from its ores, while the discharge of cyanide wastes may result in signiﬁcant environmental pollution. Many factors inﬂuence the levels of consumption and discharge of cyanide, including ore mineralogy and lixiviant solution chemistry. This paper proposes a robust methodology to estimate leaching cyanide consumption due to oxidation and reactions with gold, chalcopyrite and pyrite minerals forming various cyanide complexes, cyanate, thiocyanate and hydroxide precipitates of copper and iron. The method involves concurrent modelling of both the oxidation and leaching kinetics of minerals and the chemical speciation of the lixiviant solutions. The model was calibrated by conducting cyanide leaching experiments on pyrite, chalcopyrite, pyrite + chalcopyrite, pyrite + chalcopyrite + gold and pyrite + chalcopyrite + gold + quartz systems and determining the total Cu, Fe, Au and CN− concentrations in solution. We show that this model can successfully estimate the formation of cyanide complexes and, hence, the consumption of cyanide.

Keywords: leaching; gold ores; cyanide; modelling; consumption; kinetics; speciation

1. Introduction Gold is mainly extracted from its ores or concentrates by leaching with oxygenated cyanide solutions [1,2]. Cyanide consumption during leaching, and the discharge of excess cyanide in wastewater, respectively constitute major economic [3,4] and environmental [5] costs in the gold industry. Cyanide losses in the leaching stage mainly occur via the action of “cyanicides”: minerals, such as the sulﬁdes of copper and iron that dissolve via the formation of strong cyanide complexes, or conversion of CN− to other species such as cyanate (OCN−) and thiocyanate (SCN−). On the other hand, cyanide pollution, through wastewater discharge and mine residues, is of major concern due to the acute toxicity of many cyanide compounds towards animal (including human) life [5]. Wastewater streams of gold processing plants typically have to be treated to lower the concentration of cyanide and related species below regulatory limits [6]. While many workable treatments have been developed there is an inevitable cost; a much better strategy is to minimize such discharges in the ﬁrst place. Various methods have been proposed to minimize cyanide consumption. For example, Deschênes et al. [7] showed that use of lead nitrate and oxygen (200 and 16 mg·L−1, respectively) with high pyrite or chalcopyrite ores lowered cyanide consumption threefold and enhanced the

Minerals 2018, 8, 110; doi:10.3390/min8030110 www.mdpi.com/journal/minerals Minerals 2018, 8, 110 2 of 13 gold leaching rate by 20%. There have also been many experimental investigations of the effects of varying solution chemistry and ore mineralogy on cyanide consumption [8]. On the other hand, there have been rather fewer efforts to develop models for estimating cyanide consumption under real leaching conditions. For example, Adams [9,10] studied the effects of activated carbon on the kinetics of cyanide consumption in gold processing plants and showed it to be ﬁrst order with respect to cyanide concentration, and that a carbon-catalyzed oxidation reaction was responsible for high cyanide losses. Bellec et al. [11] proposed an empirical model that included ore particle size distribution, and cyanide, copper and sulfur concentrations, while De Andrade Lima and Hodouin [8] developed an empirical model that took into account ore particle size, cyanide concentration and the dissolution of sulfur-bearing minerals. However, these models were purely empirical, contained many parameters and were heavily case-dependent. They mentioned that, with decreasing the particle size, gold liberation in the ore increases but the cyanide consumption also increases because of liberation of Cu and Fe minerals [8]. Adams [12] presented a methodology for determining cyanide deportment in gold plants using thermodynamic constants and solution analyses. He was able to avoid considerations of non-ideality, because of the low concentrations of dissolved species, which allowed the use of concentrations instead of activities. A ﬁrst-order rate equation was used to estimate HCN losses by volatilization [12]. Lotz et al. [13] investigated gold leaching kinetics and used experimental arsenic and sulfur speciation information; however, no model was developed in their work. The purpose of the present work is to develop a robust methodology to estimate cyanide consumption during gold leaching over a period of about 30 h with integrated modeling of leaching kinetics and chemical speciation. The amount of cyanicide in the slurry, and solution conditions, such as the concentration of free cyanide (CN−) and pH, are included in the model. With such a model, consumption of cyanide can be optimized and lowered by manipulating the key factors. While a slurry containing gold, pyrite and chalcopyrite was investigated in this work, the proposed approach can be easily extended and tested with ores or concentrates of quite different mineralogy.

2. Theory Gold leaching in cyanide solutions can be described [3] by the electrochemical reactions:

− − − Au(s) + 2CN → Au(CN)2 + e (1)

− − O2(g) + 2H2O + 4e → 4OH (2) 4− In aerated cyanide solutions pyrite, FeS2, dissolves forming the complex Fe(CN)6 [14]:

− 4− 2− FeS2(s) + 6CN → Fe(CN)6 + S2 (3)

The dissolution of chalcopyrite, CuFeS2, can be described [14] by:

− 3− 4− 2− CuFeS2(s) + 10CN → Cu(CN)4 + Fe(CN)6 + 2S (4)

However, these reactions are simpliﬁcations: various copper and iron cyanide complexes form and their distribution in a cyanide solution depends on the EH and pH of the solution and the cyanide-to-copper mole ratio [15]. Since pyrite and chalcopyrite are leached under oxidizing conditions, any sulﬁde ions produced may be oxidized in the sequence [14]:

2− 2− 0 2− 2− 2− S → S2 →S → S2O3 →SO3 → SO4 (5)

The reactions of cyanide with reduced sulfur species are brieﬂy described by Luthy and Bruce (1979) [16], while the oxidation of cyanide can be thought of as [9,10]:

− − − CN → (CN)2 → OCN (SCN ) (6) Minerals 2018, 8, 110 3 of 13

The dissolution kinetics and equilibria of copper, iron and gold species in cyanide solutions are closely related to the concentration of free cyanide, [CN−], and pH. At low free cyanide, low cyanide-to-copper ratios, and high pH, the precipitation of copper as Cu(OH)2 [14] can occur [17]:

− − − 4Cu(CN)2 + O2 + 4OH + 2H2O → 4Cu(OH)2(s) + 8CN (7)

In an analogous way iron may precipitate as goethite, FeOOH(s) [14].

− − − 2− CuFeS2(s) + 2CN + 3OH → Cu(CN)2 + FeOOH(s) + 2S (8)

When the cyanide-to-copper molar ratio drops to 2.5 and a large proportion of copper is present − 2− as Cu(CN)2 , the gold leaching rate is extremely low [18]. This suggests that Cu(CN)3 can provide sufﬁcient cyanide ions for the leaching of gold or other minerals according to Equation (9) [18].

2− − − − 4Au + 8Cu(CN)3 + O2 + 2H2O → 4Au(CN)2 + 8Cu(CN)2 + 4OH (9)

As the leaching of the ore proceeds, the concentrations of the major species change and so does the ionic strength and, consequently, all the activity coefficients and conditional equilibrium constants [19,20]. To model the chemical speciation during the leaching process, it is necessary to quantify the formation of each significant species. This requires answers to three questions: (a) what species are likely to be present? (b) What are their total concentrations? and (c) how do they interact? These questions can be answered by modeling mineral leaching kinetics concurrently with reliable thermodynamic data covering the range of conditions (ionic strength, temperature, and species) of interest. The kinetic and thermodynamic data can be obtained from various databases attached to speciation programs such as PHREEQC (U.S. Geological Survey, Denver, CO, USA) [21–25] and MINTEQ (KTH, Stockholm, Sweden) [26]. For example, the dissolution of Pb, Cd, As, and Cr from cementitious waste [24] and dissolution of the major elements and heavy metals [23] have been simulated by PHREEQC. Unfortunately, incomplete databases, limited information on the ionic strength of the solution, and lack of flexibility in kinetic modeling, limit the applicability of some programs to the estimation of speciation during the leaching of real systems.

3. Methodology In this work, modeling the experimental kinetic parameters of iron, copper and gold leaching from pure minerals and mixtures, and determining the predominant chemical species in solution, were employed as a means of determining free cyanide concentrations. As such, this model creates a tool for optimizing the use of cyanide in gold processing plants.

3.1. Leaching Modeling A kinetic model based on the law of mass action is used to describe the leaching process. For a batch system, this model can be written in the simpliﬁed form:

α β ∂CM(t)/∂t = k CM(t) CCN(t) (10)

1 − (α + β) (α + β) − 1 −1 where, k is the reaction rate constant (mol m ·s ), CM is the concentration of mineral –1 –1 or gold (mmol·L ), CCN is the concentration of free cyanide in solution (mol·L ) and α and β are the reaction order of the model with respect to gold, mineral and cyanide concentrations. It should be noted that the effect of dissolved oxygen concentration was not considered, as in most gold processing plants the concentration of oxygen is kept at the saturation limit. Accordingly, all the test solutions were continuously oxygenated during leaching. Minerals 2018, 8, 110 4 of 13

3.2. Speciation Modeling Based on ion association and complexation reactions in aqueous solution, the equilibrium position of a set of simultaneous reactions in the solution phase, subject to the constraints of mass action and mass balance, was solved using MATLAB software (Mathworks, Natick, MA, USA). For the leaching of each mineral system, possible species were determined from relevant papers and the PHREEQC database [14,19,23]. The most signiﬁcant of these species and their equilibrium constants are shown in Table1. Using these data, the stoichiometric coefﬁcients were coded for the Au-Cu-CN-Fe-S-O-H system in MATLAB. The concentration of each element was determined by summing its total value using all relevant equilibria. Total cyanide (CCN,T) was then calculated as:

− − 2− 3− 4− CCN,T = C(CN ) + 2C(Cu(CN)2 ) + 3C(Cu(CN)3 ) + 4C(Cu(CN)4 ) + C(HCN) + 6C(Fe(CN)6 )+ . . . (11)

In view of the moderate ionic concentrations, the Davies Equation (12) was used to calculate the activity (ai) of each dissolved species via the usual deﬁnitions:

2 √ √ −lnγi = Azi ( I/(1 + I) − 0.3I) (12)

2 I = 1/2∑mizi (13)

ai = γi·mi (14) −1 0.5 where, γi is the activity coefﬁcient, A = 0.5397 (kg·mol ) is the Debye–Hückel constant for activity −1 coefﬁcients, zi is the ionic charge number and I (mol·kg ) is the ionic strength of the electrolyte media −1 and mi is the mollity concentration of ion i (mol·kg ).

Table 1. Main equilibria of the Cu-CN-Fe-Au-S-O-H system (25 ◦C, 1 atm and I = 0).

Equilibrium log K Ref. CN− + H+ = HCN 9.21 [14,19] + − − Au + 2CN = Au(CN)2 39.3 [2,27] + − H2O = H + OH −13.98 [14] Au+ + CN− = AuCN(s) 38.9 [14] 2+ − 4− Fe + 6CN = Fe(CN)6 35.4 [14] S + CN− = SCN− 0.9 [28] 1 − − 2 O2 + CN = OCN 3.5 [28] + − − Cu + 2CN = Cu(CN)2 23.7 [29] + − 2− Cu + 3CN = Cu(CN)3 28.5 [29] + − 3− Cu + 4CN = Cu(CN)4 30.6 [29] 2+ + Cu + 2H2O = Cu(OH)2 + 2H −16.24 [14] 2+ − + Fe + 3H2O = Fe(OH)3 + 3H −32 [14] 3+ + Fe + 2H2O = FeOOH + 3H −0.5 [14] − − Cu(CN)2 = CuCN(s) + CN −4.91 [14]

The activity coefﬁcient for non-ionic species, was obtained by the Setschenow relation [30]:

lnγi = bi·I (15) where, bi is the Setschenow coefﬁcient. A value of bi = 0.1 was used throughout, following [21].

3.3. Integrated Modeling of Leaching Kinetics and Chemical Speciation with MATLAB Mineral leaching and the formation of all plausible complexes was simulated with two m-ﬁles in MATLAB named “Leachingkinetics.m” and “speciationmodel.m” which were linked as shown in Figure1. The ﬁrst simulates the kinetics of gold/mineral leaching and estimates the total concentration of each element in solution during the leaching process. These total concentrations (for Cu, S, free Minerals 2018, 8, 110 5 of 13 cyanide, Fe, and Au) are the inputs for the speciation model, along with temperature and the initial pH, assuming the dissolved ions are in equilibrium. The inputs for the kinetic model are the reaction rate constants α and β for gold, each mineral, (should be estimated by calibration; see Section 3.5), and free cyanide. Outputs of “Leachingkinetics.m” are the total solution concentrations of Cu, Fe, S, andMinerals Au. 2018 The, 8 kinetic, x FOR PEER model REVIEW only uses the free cyanide concentration from the speciation model. 5 of 13

FigureFigure 1. Methodology1. Methodology used used for the for modeling the modeling of mineral of leaching, mineral speciation leaching, and speciation cyanideconsumption. and cyanide consumption. 3.4. Experimental 3.4. Experimental Since cyanide consumption mainly depends on the cyanicide (mainly pyrite and chalcopyrite) contentSince in gold cyanide ores consumption (Equations (3) mainly and (4)), depends individual on the minerals cyanicide and (mainly combination pyrite ofand these chalcopyrite) minerals werecontent subjected in gold to ores leaching (Equations in the absence(3) and (4)), or presenceindividual of gold.minerals It should and combination also be noted ofthat these dissolved minerals oxygenwere subjected and Cu(II)-species to leaching enhance in the absence the oxidation or presence of cyanide of gold. [18 It]. Pyriteshould and also chalcopyrite be noted that were dissolved from theoxygen Sarcheshmeh and Cu(II)-species copper complex, enhance southwest the oxidation of Kerman,of cyanide Iran, [18]. (with Pyrite grades and chalcopyrite of 98.85% and were 95.6% from respectively,the Sarcheshmeh Table 2copper) and gold complex, foils (99.99% southwest Au, of thickness Kerman, 0.2 Iran, mm) (with were grades used forof the98.85% experiments. and 95.6% Forrespectively, model validation Table 2) and gold parameter foils (99.99% estimation, Au, thickness ﬁve mineral 0.2 mm) systems were wereused considered;for the experiments. pyrite, chalcopyrite,For model validation pyrite + chalcopyrite, and parameter gold estimation, + chalcopyrite five +mineral pyrite andsystems gold were + chalcopyrite considered; + pyritepyrite, +chalcopyrite, quartz. For the pyrite pyrite + chal andcopyrite, chalcopyrite, gold + 20 chalcopyri g of eachte mineral + pyrite was and brought gold + intochalcopyrite contact with + pyrite 1.0 L + ofquartz. 600 mg For·L− the1 cyanide pyrite solution.and chalcopyrite, For chalcopyrite 20 g of each + pyrite mineral and was gold brought + chalcopyrite into contact + pyrite with systems, 1.0 L of −1 10600 g ofmg·L pyrite cyanide and 10 solution. g of chalcopyrite For chalcopyrite were used. + pyrite For the and systems gold + containingchalcopyrite gold, + pyrite 0.01 systems, g pure gold 10 g wasof pyrite added. and For 10 the g of last chalcopyrite system, the were % solid used. was For adjusted the systems to 42% containing with quartz. gold, For0.01all g pure experiments, gold was added. For the last system, the % solid was adjusted to 42% with quartz. For all experiments, the pH the pH and the solution concentrations of copper, iron, free cyanide and gold were determined over and the solution concentrations of copper, iron, free cyanide and gold were determined over an an appropriate period of time. The initial pH was set to 11 but was controlled at 10.4 during the appropriate period of time. The initial pH was set to 11 but was controlled at 10.4 during the experiments by addition of sodium hydroxide. The temperature was controlled to 25 ± 0.1 °C and stirring speed was held at 250 rpm. The initial cyanide concentration was 600 mg·L−1 but was allowed to degrade over time. Particle size distribution was −75 + 53 μm (the effects of particle size on leaching are not taken into account in this paper) and the oxygen concentration was 8 mg·L−1. Liquid samples of 30 mL were taken for analysis at specific times (the mass of metals in the samples was considered in the calculations). After sampling, the same amount of water with pH = 10.4 was added to maintain the liquid volume constant. At the end of each experiment, the mass of residual solid was washed, dried and used in establishing the mass balance. Solutions were analyzed by atomic absorption

Minerals 2018, 8, 110 6 of 13 experiments by addition of sodium hydroxide. The temperature was controlled to 25 ± 0.1 ◦C and stirring speed was held at 250 rpm. The initial cyanide concentration was 600 mg·L−1 but was allowed to degrade over time. Particle size distribution was −75 + 53 µm (the effects of particle size on leaching are not taken into account in this paper) and the oxygen concentration was 8 mg·L−1. Liquid samples of 30 mL were taken for analysis at speciﬁc times (the mass of metals in the samples was considered in the calculations). After sampling, the same amount of water with pH = 10.4 was added to maintain the liquid volume constant. At the end of each experiment, the mass of residual solid was washed, dried and used in establishing the mass balance. Solutions were analyzed by atomic absorption spectrometry (AAS) with a Varian SpectrA A-300 for total Au, Cu and Fe [31]. Cyanide concentration was determined by titrating against silver nitrate, using rhodanine as an indicator and potentiometric end-points [32]. Because of the limited number of analyses, the concentration of free cyanide and the total element concentrations (Fe, Cu, Au) were used for validating the model and for determining the model parameters.

Table 2. Composition of chalcopyrite and pyrite.

Elemental Composition (wt %) Mineral Zn Si Sb S Pb Fe Cu Ca As Al Chalcopyrite 0.26 2.86 0.02 33.44 0.01 29.26 33.18 0.01 0.012 0.01 Pyrite 0.01 0.19 0.02 52.71 0.02 46.13 0.02 0.01 0.01 0.19

3.5. Model Calibration For each leaching system, the model parameters (Table3) were estimated by a non-linear least squares optimization method that minimized the sum of squared differences between the Au, Fe, Cu, and free cyanide concentrations in solution obtained by simulations and experiments. Model parameters of the pyrite + chalcopyrite + gold system were used for validation of the method and are discussed in Section 4.6.

Table 3. Calibrated parameters of the kinetic model.

System * Mineral k ** α β Py. Py. 6.8 1.01 1.1 Ch. Ch. 0.58 0.86 1.15 Py. 4.71 0.31 1.82 Py. + Ch. Ch. 0.62 0.61 1.16 Py. 5.96 0.28 2.14 Au + Py. + Ch. Ch. 0.73 0.71 1.25 (±Qtz.) Au 14.99 0.91 1.13 * Abbreviations: Py. (pyrite), Ch. (chalcopyrite), Au (gold) and Qtz. (quartz), ** unit: mol1 − ( α + β ) m(α + β) − 1·s−1.

4. Results and Discussion Table2 shows the calibrated parameters of the kinetic model (Equation (10)) for the ﬁve mineral systems studied.

4.1. Pyrite Leaching The simulation of pyrite leaching in cyanide solution, based on the estimated parameters, is compared with the experimental data in Figure2. The concentrations of iron and free cyanide in solution are well-predicted by the concurrent model. However, the good ﬁt is not the only merit of the present approach. Another important outcome of the proposed methodology is that the concentration of free cyanide is predicted via calculation of all cyanide complexes formed during the leaching process. Minerals 2018, 8, 110 7 of 13 Minerals 2018, 8, x FOR PEER REVIEW 7 of 13

Minerals 2018, 8, x FOR PEER REVIEW 7 of 13 Minerals 2018, 8, x FOR PEER REVIEW 7 of 13

Figure 2.FigureIron 2. and Iron free and cyanidefree cyanide concentrations concentrations inin solution for for the the pyrite pyrite leaching leaching system. system.

4.2. Chalcopyrite Leaching 3− 2− 3− 4− − − In this particular case, HCN, HFe(CN)6 ,H2Fe(CN)6 , Fe(CN)6 , Fe(CN)6 , SCN and OCN Like the pyrite system, equations for sulfide oxidation were considered in the speciation model are formed and the free cyanide is predicted by subtracting protonated or complexed cyanide from the and the parameters of the leaching kinetics model were estimated from the data in Table 2. The results total cyanide concentration. In this system, the predominant iron species in solution was Fe(CN) 4−. of the simulations are compared with the experimental data in Figures 3 and 4, where iron, copper 6 and free cyanideFigure 2.concentrations Iron and free cyanide in the liquidconcen trationsphase were in solution measured for the and pyrite predicted. leaching Insystem. this system the 4.2. Chalcopyritemain complexes LeachingFigure 2.formed Iron and were free Fe(CN)cyanide6 4concen−, Cu(CN)trations32− and in solution Cu(CN) for43 −the. pyrite leaching system. 4.2. Chalcopyrite Leaching Like4.2. the Chalcopyrite pyrite system, Leaching equations for sulﬁde oxidation were considered in the speciation model and the parametersLike the ofpyrite the system, leaching equations kinetics for model sulfide were oxidation estimated were considered from the in data the speciation in Table2 model. The results Like the pyrite system, equations for sulfide oxidation were considered in the speciation model of the simulationsand the parameters are compared of the leaching with the kinetics experimental model were data estimated in Figures from the3 and data4 in, where Table 2. iron, The results copper and andof the the simulations parameters areof the compared leaching with kinetics the modelexperiment wereal estimated data in Figures from the 3 dataand in4, Tablewhere 2. iron, The resultscopper free cyanideofand the free concentrations simulations cyanide concentrations are compared in the liquid in with the phase theliquid experiment werephase measuredwereal data measured in andFigures and predicted. predicted.3 and 4, where In In thisthis iron, system copper the the main and free cyanide concentrations4− in the liquid2 −phase were measured3− and predicted. In this system the complexesmain formed complexes were formed Fe(CN) were6 Fe(CN), Cu(CN)64−, Cu(CN)3 and32− and Cu(CN) Cu(CN)4 43−. main complexes formed were Fe(CN)64−, Cu(CN)32− and Cu(CN)43−.

Figure 3. Iron and copper concentrations in solution for the chalcopyrite leaching system.

Figure 3. Iron and copper concentrations in solution for the chalcopyrite leaching system. Figure 3.FigureIron 3. and Iron copper and copper concentrations concentrations in in solutionsolution for for the the chalcopyrite chalcopyrite leaching leaching system. system.

Figure 4. Free cyanide concentrations in solution for the chalcopyrite leaching system.

Figure 4. Free cyanide concentrations in solution for the chalcopyrite leaching system. Figure 4. Free cyanide concentrations in solution for the chalcopyrite leaching system. Figure 4. Free cyanide concentrations in solution for the chalcopyrite leaching system.

Minerals 2018, 8, 110 8 of 13 Minerals 2018, 8, x FOR PEER REVIEW 8 of 13 Minerals 2018, 8, x FOR PEER REVIEW 8 of 13 4.3.4.3. Pyrite Pyrite + + Chalcopyrite Chalcopyrite Leaching Leaching 4.3. Pyrite + Chalcopyrite Leaching FiguresFigures5 and 5 and6 show 6 show the results the results for iron, for copper iron, copper and cyanide. and cyanide. During the During first 240 the min first of 240 leaching, min of Figures 5 and 6 show the results for iron, copper and cyanide. During the first 240 min of theleaching, cyanide the rapidly cyanide dissolves rapidly most dissolves of the reactive most pyriteof the and reactive chalcopyrite, pyrite formingand chalcopyrite, complexes suchforming as leaching,4− the cyanide3− rapidly 2dissolves− most− of the reactive pyrite and chalcopyrite, forming Fe(CN)complexes6 , Cu(CN) such as4 Fe(CN), Cu(CN)64−, 3Cu(CN)and4 Cu(CN)3−, Cu(CN)2 .3 However,2− and Cu(CN) during2−. leachingHowever, free during cyanide leaching decreases free complexes such as Fe(CN)64−, Cu(CN)4−43−, Cu(CN)32− and Cu(CN)2−. However, during leaching free andcyanide iron, decreases mostly present and iron, as Fe(CN) mostly6 present, can precipitateas Fe(CN)64 as−, can FeOOH(s) precipitate [33 ]as thereby FeOOH(s) decreasing [33] thereby the cyanide decreases and iron, mostly present as Fe(CN)64−, can precipitate3− as FeOOH(s) [33] thereby concentrationdecreasing the of concentration iron in solution of (Figureiron in5 solution). It is reported (Figure that5). It Fe(CN) is reported6 can that also Fe(CN) facilitate63− can gold also decreasing the concentration of iron in solution (Figure3− 5). It is reported that Fe(CN)63− can also leachingfacilitate [34 gold,35] leaching but here [34,35] the concentration but here the of concentration Fe(CN)6 was of veryFe(CN) low.63− was very low. facilitate gold leaching [34,35] but here the concentration of Fe(CN)63− was very low.

Figure 5. Iron and copper concentrations in solution for the pyrite + chalcopyrite leaching system. FigureFigure 5. 5.Iron Iron and and copper copper concentrations concentrations in in solution solution for fo ther the pyrite pyrite + + chalcopyrite chalcopyrite leaching leaching system. system.

FigureFigure 6. 6.Free Free cyanide cyanide concentrations concentrations in in solution solution for for the the pyrite pyrite + + chalcopyrite chalcopyrite leaching leaching system. system. Figure 6. Free cyanide concentrations in solution for the pyrite + chalcopyrite leaching system. 4.4.4.4. Gold Gold + + Pyrite Pyrite + + Chalcopyrite Chalcopyrite Leaching Leaching 4.4. Gold + Pyrite + Chalcopyrite Leaching TheThe results results for for gold, gold, iron iron and and copper copper leaching leaching and and cyanide cyanide for for this this system system are are shown shown in Figuresin Figures7 The results for gold, iron and copper leaching and cyanide for this system are shown in Figures and7 and8. 8. 7 and 8. To calculate the free cyanide in this system during the leaching process (Figure 8), the formation To calculate the free cyanide in this system during the leaching process (Figure 8), the formation of all plausible complexes was considered. The formation of such complexes changes the ionic of all plausible complexes was considered. The formation of such complexes changes the ionic strength of the solution and therefore the activities of all species present. Thus, the concentrations strength of the solution and therefore the activities of all species present. Thus, the concentrations must be calculated by a recursive algorithm (Figure 1). In addition, the calculated species must be calculated by a recursive algorithm (Figure 1). In addition, the calculated species concentrations should fit the total element concentrations predicted by the kinetic model. Figure 9 concentrations should fit the total element concentrations predicted by the kinetic model. Figure 9 shows the concentrations of the main cyanide complexes formed in solution. For this system, shows the concentrations of the main cyanide complexes formed in solution. For this system,

Minerals 2018, 8, x FOR PEER REVIEW 9 of 13

Fe(CN)64−, Cu(CN)32− and Au(CN)2− are predominant (Figure 9a), which agrees with previous studies [15].

Minerals 2018, 8, x FOR PEER REVIEW 9 of 13

Fe(CN)Minerals 620184−, ,Cu(CN)8, 110 32− and Au(CN)2− are predominant (Figure 9a), which agrees with previous9 of 13 studies [15].

Figure 7. Iron and copper concentrations in solution for the gold + pyrite + chalcopyrite leaching system.

With decreasing free cyanide in solution, the concentration of Cu(CN)43− decreases while that of Cu(CN)32− increases. The concentrations of other cyanide-containing species (HCN, CN−, CNO− and SCNFigure−) are 7.7.shown IronIron and andin copperFigure copper concentrations 9b. concentrations The HCN in and solutionin solution CN− for concentrations thefor gold the +gold pyrite + show pyrite + chalcopyrite similar + chalcopyrite behavior. leaching leaching system. system.

FigureFigure 8. 8.Free Free cyanide cyanide and and gold gold concentrations concentrations in in solution solution for for the the gold gold + + pyrite pyrite + + chalcopyritechalcopyrite system.system.

The predicted concentrations of iron in Figures 5 and 7 show much larger deviations (R2 = 0.89 To calculate the free cyanide in this system during the leaching process (Figure8), the formation and 0.81, respectively) from the measured values, compared with other systems. This may be due to of all plausible complexes was considered. The formation of such complexes changes the ionic strength the use of a higher precipitation rate of iron as FeOOH(s) in the model. Whilst prediction of the of the solution and therefore the activities of all species present. Thus, the concentrations must be precipitationFigure 8. Free of iron cyanide was and not gold the concentrataim of thisions project, in solution the absencefor the gold or +presence pyrite + chalcopyrite of gold appears system. to affect calculated by a recursive algorithm (Figure1). In addition, the calculated species concentrations should the cyanide consumption in Figures 4 and 6. For example, the residual free cyanide in the absence of ﬁt the total element concentrations predicted by the kinetic model. Figure9 shows the concentrations −1 −1 2 goldThe decreases predicted from concentrations 200 mg·L ofto iron100 inmg·L Figures over 5 and the 7time show period much 1000–2000larger deviations4− min in ( RFigure2 −= 0.89 6. of the main cyanide complexes formed in solution. For this system, Fe(CN)6 , Cu(CN)3 and andHowever, 0.81, −respectively) in Figure 8, from the thefree measured cyanide concentrationvalues, compared is lowered with other below systems. 100 mg·L This−1 mayafter be 1000 due min to Au(CN)2 are predominant (Figure9a), which agrees with previous studies [15]. theindicating use of a higher higher cy precipitationanide consumption. rate of iron as FeOOH(s) in the model. Whilst prediction of the With decreasing free cyanide in solution, the concentration of Cu(CN) 3− decreases while that of precipitation of iron was not the aim of this project, the absence or presence4 of gold appears to affect Cu(CN) 2− increases. The concentrations of other cyanide-containing species (HCN, CN−, CNO− and the cyanide3 consumption in Figures 4 and 6. For example, the residual free cyanide in the absence of SCN −) are shown in Figure9b. The HCN and CN − concentrations show similar behavior. gold decreases from 200 mg·L−1 to 100 mg·L−1 over the time period 1000–2000 min in Figure 6. The predicted concentrations of iron in Figures5 and7 show much larger deviations ( R2 = 0.89 However, in Figure 8, the free cyanide concentration is lowered below 100 mg·L−1 after 1000 min and 0.81, respectively) from the measured values, compared with other systems. This may be due indicating higher cyanide consumption. to the use of a higher precipitation rate of iron as FeOOH(s) in the model. Whilst prediction of the precipitation of iron was not the aim of this project, the absence or presence of gold appears to affect

Minerals 2018, 8, x FOR PEER REVIEW 10 of 13

4.5. Gold + Pyrite + Chalcopyrite + Quartz Leaching The presence of gangue minerals such as silicates may inhibit the action of cyanicides, therefore, the liberation of cyanicides from the hosting gangue minerals should be considered [36–38]. This phenomenon has been considered for a real gold ore elsewhere [38]. The results, after the addition of quartz to the pyrite + chalcopyrite + gold system to make up a slurry of 42% solids, showed no effect of quartz on cyanide consumption. If metal ions from other minerals capable of forming complexes with cyanide were present in the ore, their equilibrium indices should also be considered in Table 1. However, the modeling methodology would remain the same.

4.6. Cross Validation: Effect of pH

MineralsAs2018 pH, 8 ,affects 110 HCN formation [29], ferric ion precipitation and pyrite oxidation kinetics [39],10 of 13its variation was chosen to validate the method. Accordingly, cyanide consumption was predicted using the model developed for the system pyrite + chalcopyrite + gold with the calibrated parameters of Table 2 and theinitial cyanide pH values consumption of 9.5 and in 11.5 Figures (controlled4 and6. to For 9 example,and 11 respectively). the residual Figure free cyanide 10 compares in the the absence results − − ofpredicted gold decreases by the model from 200and mg the·L measured1 to 100 mgconcentratio·L 1 overns the of free time cyanide. period 1000–2000Decreasing min the insolution Figure pH6. − However,(from 11 to in 9)Figure lowered8, the concentration free cyanide concentrationof free cyanide because is lowered of HCN below evolution. 100 mg Except·L 1 after in the 1000 first min few indicatingminutes of higher the reaction, cyanide there consumption. is a good agreement between the model and the experimental data.

(a)

(b)

FigureFigure 9.9. ConcentrationConcentration ofof thethe mainmain cyanidecyanide complexescomplexes formedformed inin solutionsolution forfor thethe goldgold ++ pyritepyrite ++ chalcopyrite system at pH = 10.4; (a) Fe, Cu or Au (mg/L) as Fe(CN)64−, Cu(CN)4− 32−, Cu(CN)2− 43−, Cu(CN)3−2− chalcopyrite system at pH = 10.4; (a) Fe, Cu or Au (mg/L) as Fe(CN)6 , Cu(CN)3 , Cu(CN)4 , and Au(CN)− 2−; (b) CN (mg·L− −1) as HCN, CN−−1, CNO− and SCN−−, 0.1 × CN− − and 0.1 ×− SCN− concentration− Cu(CN)2 and Au(CN)2 ;(b) CN (mg·L ) as HCN, CN , CNO and SCN , 0.1 × CN and 0.1are× plottedSCN− onconcentration the same scale. are plotted on the same scale.

4.5. Gold + Pyrite + Chalcopyrite + Quartz Leaching The presence of gangue minerals such as silicates may inhibit the action of cyanicides, therefore, the liberation of cyanicides from the hosting gangue minerals should be considered [36–38]. This phenomenon has been considered for a real gold ore elsewhere [38]. The results, after the addition of quartz to the pyrite + chalcopyrite + gold system to make up a slurry of 42% solids, showed no effect of quartz on cyanide consumption. If metal ions from other minerals capable of forming complexes with cyanide were present in the ore, their equilibrium indices should also be considered in Table1. However, the modeling methodology would remain the same. Minerals 2018, 8, 110 11 of 13

4.6. Cross Validation: Effect of pH As pH affects HCN formation [29], ferric ion precipitation and pyrite oxidation kinetics [39], its variation was chosen to validate the method. Accordingly, cyanide consumption was predicted using the model developed for the system pyrite + chalcopyrite + gold with the calibrated parameters of Table2 and initial pH values of 9.5 and 11.5 (controlled to 9 and 11 respectively). Figure 10 compares the results predicted by the model and the measured concentrations of free cyanide. Decreasing the solution pH (from 11 to 9) lowered the concentration of free cyanide because of HCN evolution. Except in the ﬁrst few minutes of the reaction, there is a good agreement between the model and the experimentalMinerals 2018, data.8, x FOR PEER REVIEW 11 of 13

FigureFigure 10. 10.Prediction Prediction vs. vs. measurement measurement of of cyanide cyanide concentrations concentrations in in solution solution for for the the gold gold + pyrite+ pyrite + + chalcopyritechalcopyrite system system at pHat pH = 9= and9 and 11. 11.

5.5. Conclusions Conclusions AnAn integrated integrated kinetics kinetics + + speciation speciation model model for for simulation simulation of of gold gold ore ore leaching leaching and and cyanide cyanide consumptionconsumption has has been been presented presented here. here. The code,The code, developed developed in MATLAB, in MATLAB, takes into takes account into theaccount effects the ofeffects solution of solution pH and pH ionic and strength, ionic strength, along along with thewith type the type and and amount amount ofsulﬁde of sulfide minerals minerals present present onon cyanide cyanide consumption consumption asas a function function of of time. time. Except Except in the in thefirst ﬁrstfew minutes few minutes of theof leaching the leaching process, process,calculated calculated cyanide cyanide concentrations concentrations and cyanide and cyanide consumption consumption were were in excellent in excellent agreement agreement with withexperiments experiments over over ~30 ~30 h h(Figure (Figure 10). 10). Considering Considering th thee nature nature of thethe modelmodel andand the the relatively relatively small small numbernumber of of empirical empirical parameters parameters it requires,it requires, it canit can be be concluded concluded that that integrated integrated kinetics kinetics + speciation+ speciation modelsmodels provide provide a tool a tool for predicting for predicting gold oregold leaching ore leaching behavior behavior and cyanide and consumptioncyanide consumption as a function as a 4− offunction time with of reasonabletime with accuracy.reasonable The accuracy. present The results present showed results that showed for pyrite that leaching for pyrite Fe(CN) leaching6 wasFe(CN) the predominant64− was the predominant complex formed. complex For formed. the chalcopyrite, For the chalcopyrite, and pyrite +and chalcopyrite pyrite + chalcopyrite systems, 4− 2− Fe(CN)systems,6 andFe(CN) Cu(CN)64− and3 Cu(CN)were predominant,32− were predominant, while for while the gold for +the pyrite gold ++ chalcopyritepyrite + chalcopyrite and gold and + 4− 2− − pyritegold + + chalcopyrite pyrite + chalcopyrite + quartz systems, + quartz Fe(CN) systems,6 , Cu(CN) Fe(CN)3 64and−, Cu(CN) Au(CN)32−2 andwere Au(CN) the predominant2− were the ions,predominant at least at ions, high at CN/Cu least at molar high CN/Cu ratios. molar The model ratios. can The be model utilized can forbe utilized optimization for optimization of cyanide of consumptioncyanide consumption in different in mineralogical different mineralogical and solution and conditions, solution conditions, resulting resulting in the generation in the generation of less hazardousof less hazardous species in species discharge in discharge liquors. liquors.

Acknowledgments:Acknowledgments:The The authors authors acknowledge acknowledge Tarbiat Tarbiat Modares Modares University University for for ﬁnancing financing this this study. study. Author Contributions: Yaser Kianinia and Mohammad Reza Khalesi had the idea and designed the experiments; Author Contributions: Yaser Kianinia and Mohammad Reza Khalesi had the idea and designed the experiments; Yaser Kianinia and Marjan Shahbazi performed the experiments (this paper was based on Yaser Kianinia’s Ph.D. thesis);Yaser Mohammad Kianinia and Reza Marjan Khalesi Shahbazi directed performed the Ph.D. the thesis, experiments Mahmoud (this Abdollahy paper was co-directed based on theYaser Ph.D. Kianinia’s thesis, andPh.D. Ahmadthesis); Khodadadi Mohammad Darban Reza consultedKhalesi directed the Ph.D. the thesis, Ph.D. Yaserthesis, Kianinia Mahmoud and Abdollahy Mohammad co-directed Reza Khalesi the Ph.D. wrote thesis, the ﬁrstand draft Ahmad of the Khodadadi paper, Glenn Darban Hefter, consulted Gamini the Senanayake Ph.D. thesis and, Yaser Lubomir Kianinia Hnedkovsky and Mohammad analyzed Reza the Khalesi results andwrote editedthe first the paperdraft of and the gave paper, suggestions Glenn Hefter, for improvements Gamini Senanayake which Yaser and Kianinia Lubomir performed Hnedkovsky and addedanalyzed to the the paper. results and edited the paper and gave suggestions for improvements which Yaser Kianinia performed and added to the paper.

Conflicts of Interest: The authors declare no conflict of interest.

References

1. Marsden, J.; House, I. The Chemistry of Gold Extraction, 2nd ed.; SME: Littleton, CO, USA, 2006. 2. Riveros. P.A. Selectivity aspects of the extraction of gold from cyanide solutions with ion exchange resins. Hydrometallurgy 1993, 33, 43–58. 3. Anderson, C.G. Alkaline sulfide gold leaching kinetics. Miner. Eng. 2016, 92, 248–256. 4. Muir, D. A review of the selective leaching of gold from oxidised copper-old ores with ammonia-cyanide and new insights for plant control and operation. Miner. Eng. 2011, 24, 576–582.

Minerals 2018, 8, 110 12 of 13

Conﬂicts of Interest: The authors declare no conﬂict of interest.

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