Kinetic modeling of bioleaching of copper sulfide concentrates in conventional and electrochemically controlled systems

Hydrometallurgy 127–128 (2012) 16–23

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Kinetic modeling of bioleaching of copper sulfide concentrates in conventional and electrochemically controlled systems Ali Ahmadi a, e,⁎, Mohammad Ranjbar b, Mahin Schaffie c, Jochen Petersen d a

Department of Mining Engineering, Isfahan University of Technology, Isfahan, Iran Department of Mining Engineering, Shahid Bahonar University, Kerman, Iran Department of Chemical Engineering, Shahid Bahonar University, Kerman, Iran d Centre for Bioprocess Engineering Research, University of Cape Town, South Africa e Mineral Bioprocessing Research Group (MBRG), Biotechnology and Bioengineering Research Institute, Isfahan University of Technology, Isfahan, Iran b c

a r t i c l e

i n f o

Article history: Received 22 December 2011 Received in revised form 19 June 2012 Accepted 27 June 2012 Available online 6 July 2012 Keywords: Kinetic modeling Bioleaching Copper concentrate Stirred reactor Electrochemistry

a b s t r a c t In this paper a model of conventional and electrochemical bioleaching of high grade complex copper sulfide ores or flotation concentrates in isothermal stirred tank reactors is presented and compared to experimental data. Experiments were conducted in an electrobioreactor using a mixed culture of moderate thermophile microorganisms at pulp density 20% (w/v), leaching time 10 days, stirring rate 600 rpm and temperature 50 °C. The behavior of conventional and electrochemical bioleaching processes was described with a combined reaction-based kinetic model. The model considers the effects of mineralogical composition of the feed, the properties of the initial solution, the presence of iron- and sulfur oxidizing microorganisms and both the passivation and electroreduction of chalcopyrite on the values of copper recovery, pH and redox potential during the processes. Comparing the values obtained from the integrated semi-empirical model with the experimental data showed that the model results are in good agreement with the real leaching data of copper recovery, ORP (oxidation reduction potential) and pH for the mentioned processes under different experimental conditions. © 2012 Elsevier B.V. All rights reserved.

1. Introduction The modeling of reaction kinetics is an important step toward understanding the nature and the mechanism of leaching processes. Kinetic models can be used for plant design, optimization of operating conditions of an existing plant and real-time optimization including automatic control and maximization of the metallurgical efficiency (Habashi, 2007). Bioleaching systems constitute two interacting subsystems: an abiotic system, which is a mineral suspension in a solution of chemical compounds and gases, and a biological system which is composed of a mixed culture of microorganisms. The leaching kinetics of metals in solution are driven by mass transfer of reactants and products in the solution phase and chemical reaction at the solid/liquid interface, therefore for mathematical modeling of this process, mass transfer between different phases i.e. solid, gas and liquid must be taken into account (Han, 1981; Rossi, 1990). The rate of reaction at the interface mainly depends on the nature of the minerals and on the type and concentration of the reactants, such as ferric. ⁎ Corresponding author at: Department of Mining Engineering, Isfahan University of Technology, Isfahan, Iran. Tel.: +98 311 3915113; fax: +98 3912776. E-mail address: [email protected] (A. Ahmadi). 0304-386X/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.hydromet.2012.06.010

During the last three decades, several models have been proposed to describe the bioleaching process. Miller (1990) and Hansford and Chapman (1992) described the bioleaching of pyrite flotation concentrates from Fairview and Crown Mines (both in South Africa), respectively. Huberts (1994) has derived rate equations based on Ingledew's chemiosmotic theory. Crundwell (1998, 2000) modeled mathematically the leaching of sulfide minerals assuming indirect mechanism. He considered indirect mechanism of bioleaching and described the chemical leaching of sphalerite and the bacterial oxidation of ferrous ions (Crundwell, 1998). He also presented a model for bioleaching of pyritic concentrates which showed a pseudo-stoichiometric relationship between bacterial growth and mineral leaching. In some recently published papers (Bouffard, 2003; Bouffard and Dixon, 2009; Petersen and Dixon, 2006) the conventional bioleaching of low grade sulfide minerals in the presence of various microorganisms have been mechanistically modeled, mostly in isothermal whole ore columns. Electrochemical bioleaching (bioleaching by electrochemical control of oxidation reduction potential (ORP)) was recently explored to extract copper from chalcopyrite concentrates by authors (Ahmadi et al., 2010, 2011) and it was found that this new process has better potential for application in the treatment of such refractory concentrates compared to conventional bioleaching. A fundamental model that would jointly consider biological, chemical and electrochemical phenomena in this complex system is still lacking.

A. Ahmadi et al. / Hydrometallurgy 127–128 (2012) 16–23

Therefore, this study was initiated to develop and formulate a mechanistic model for simulating the conventional and electrochemical bioleaching of copper concentrates in stirred tank reactors with a view to use this model to develop a larger scale application.

17

In this study, experiments were conducted in a constant temperature (50 °C) during the processes, hence the thermal function can be lumped as a constant value. 3.2. Chemical function

2. Experimental The (electro)-bioleaching data used for this research were obtained from an experimental project described in detail in a previous paper (Ahmadi et al., 2011). These experiments were conducted in an electrobioreactor using a mixed culture of moderately thermophile iron- and sulfur oxidizing microorganisms at pulp density 20% (w/v), leaching time 10 days, stirring rate 600 rpm, Norris nutrient medium (0.4 g/l (NH4)2SO4, 0.4 g/l K2HPO4, 0.5 g/l MgSO4.7H2O) and temperature 50 °C. In the electrochemical tests, a current was applied to the working electrode in order to control the solution ORP, which was regulated in two different ranges, i.e. 400–430 mV and 440–480 mV (vs. Ag/AgCl). The amount of current passing through the reactor varied from 100 to 450 mA. A copper flotation concentrate from the Sarcheshmeh Copper Complex, containing 44.0% chalcopyrite (CuFeS2), 24.0% pyrite (FeS2), 6.9 %covellite (CuS), 5.8 % chalcocite (Cu2S), 13.6% non-metallic minerals and 4.8% copper oxide minerals was used during the experiments. The results showed that the electrochemical bioleaching process at low ORP levels (around 400–430 mV vs. Ag/AgCl) has a high potential to extract copper from the concentrate with about 80% Cu leached during the process, relative to about 50% in the conventional bioleaching process (no ORP control). 3. Fundamentals of modeling The overall kinetics of conventional and electrochemical bioleaching are usually related to the kinetics of dissolution for individual minerals, which in turn are determined by the chemical and electrochemical conditions of the environment, the growth and activity of iron and sulfur oxidizing microorganisms, the formation of precipitates such as jarosite and the acidity of solution. Based on the recent studies (Bouffard, 2003; Petersen and David, 2007) the general form of leaching kinetics for each mineral species can be described by thermal, chemical and topological functions as represented by the following equation: rj ¼


 dX j ¼ K j ðT Þf j ðC Þg j d0 ; X j dt

ð1Þ

where the subscript “j” refers to mineral species (covellite, chalcocite, bornite, chalcopyrite and pyrite), X is mineral conversion, K(T) is a rate constant which is a function of temperature and initial mineral grain size, f(C) is a function of solution composition such as the concentrations of ferric iron, ferrous iron, proton and etc. and g(X) is a semi-empirical function of the fraction of unreacted mineral, which represents the changing topology of the mineral surface over the course of leaching. In the following subsections each of these three functions is described in detail. 3.1. Thermal function At a definite size distribution, the thermal function K(T) in Eq. (1) is expressed by the Arrhenius equation as follows: K ðT Þ ¼ kref exp −

Ea R

1 1 − T T ref

Generally, metallic sulfide minerals are dissolved by the oxidative action of ferric iron in solution as follows: 3þ

MS þ 2Fe

→M

2þ

2þ

þ 2Fe

þS

ð3Þ

where M is a divalent metal ion such as Cu 2+. The leaching reaction of metallic sulfide minerals is assumed to be electrochemical in nature and Eq. (3) is the result of two half-cell reactions presented in Eqs. (4) and (5) which take place simultaneously on the surface of the mineral at mixed potential, E. MS↔M 3þ

Fe

2þ

−

þ S þ 2e

−

2þ

þ e ↔Fe

ð4Þ ð5Þ

3.3. Topological factor The topological function used here is a simple power-law expression of the fraction unreacted (Petersen and Dixon, 2006): φ

g ðX Þ ¼ ð1−X Þ

ð6Þ

Depending on the value of φ, Eq. (5) can represent the leaching of any grain topology from uniform spheres to a broad range of grain sizes. If mineral particles are assumed to be spherical and to shrink at a rate proportional to the progress of the leaching, it can be equal to 2/3 (shrinking sphere model). It may also be as high as 3 when the distribution of the effective grain size is particularly wide (Dixon and Hendrix, 1993). Particle size is a critical parameter in describing the topology as well, and Bouffard (2003) has shown how this can be integrated into the topological term, by adjusting the overall rate constant kj (in Eq. (1)) such that: kj ¼ k0 ⋅ aðd0 Þ

ð7Þ

In the modeling of a given particle size distribution, the rate parameter kj is calibrated for this distribution and does not need to be determined as a function of particle size, if no experimental data is available for other distributions. This of course then also limits the ability of the resulting model to describe any other particle size distribution other the one it has been calibrated for. 4. Modeling of ındividual minerals Based on the mineralogical analysis (Section 2) several copper bearing minerals i.e. chalcopyrite, chalcocite, covellite and copper oxides contribute to leaching. These minerals have different behaviors and the overall metal recoveries are the combination of these individual minerals. Pyrite is a major phase which affects both chemical and bacterial subsystems.

!! ð2Þ

where Tref and kref refer to reference temperature and kinetic constant values, Ea is the activation energy (kJ/mol), and R is the gas constant (kJ/kmol/K).

4.1. Copper oxides It has widely been accepted that copper oxide minerals are rapidly leached by sulfuric acid (in the first hour) in ambient conditions. So, the leaching of this fraction of copper was considered in the model as instantaneous release.

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A. Ahmadi et al. / Hydrometallurgy 127–128 (2012) 16–23

4.2. Chalcocite It has widely been accepted that the leaching of chalcocite, Cu2S, in ferric sulfate solutions take places in two distinct stages according to the following equations: 3þ

Cu2 S þ 2Fe →Cu 3þ

CuS þ 2Fe →Cu

2þ

2þ

2þ

þ 2Fe

2þ

þ 2Fe

þ CuS

ð8Þ



ð9Þ

þS

gin, j is the initial grade of mineral species j. The unit of rate for mineral leaching is taken as (mol mineral)/(kg concentrate·min). Covellite grade in the solid phase (mol/kg concentrate) is:
 g CuS ¼ g in; CuS þ g in;Cu2 S ð1−X CuS Þ The grade of covellite at time t + Δt is expressed as follows: tþΔt

The first stage proceeds readily even at room temperature, whereas the produced covellite is rather recalcitrant and the second stage (Eq. (9)) requires a high ratio of ferric iron to ferrous iron (Petersen and David, 2007) to proceed more rapidly. Indeed, the first stage consists of a series of steps in which the reaction products may or may not be observed experimentally depending on the rate of transformation of the successive phase (Bolorunduro, 1999). In the first stage, reaction proceeds rapidly even at low temperatures (Petersen and Dixon, 2006) and is controlled by the diffusion of ferric iron with the power of 0.42–0.6 as confirmed by Bolorunduro (1999), while the second stage reaction corresponds to leaching type III (Nicol, 1993), chemically controlled shrinking sphere model, where the anodic mineral dissolution is a much slower reaction than the cathodic reduction of ferric to ferrous iron. It proceeds slowly at low ratio of [Fe 3+]/[Fe2+] (low solution ORP) especially at ambient conditions, but the rate increases to the half power with an increase of that ratio. The dissolution rate of the first stage is described by the following expression which is derived from leaching Type I (Nicol, 1993).   dX Cu2 S α r Cu2 S ¼ − g in; Cu2 S þ g CuFeS2 1þα   dt h i
2 α 3þ 0:5 g CuFeS2 kCu2 S Fe ¼ − g in; Cu2 S þ 1−X Cu2 S 3 1þα


 g Cu2 S ¼ g in; Cu2 S 1−X Cu2 S tþΔt g Cu2 S

dX Cu2 S t g Cu2 S −

Δt ⋅ g in; Cu2 S dt α t r ¼ g Cu2 S þ r Cu2 S Δt− Δt 1 þ α CuFeS2 ¼

 dX CuS
t Δt g in; CuS þ g in;Cu2 S ¼ g CuS þ r CuS ⋅ Δt dt

t

g CuS ¼ g CuS −

4.4. Bornite Like chalcocite, bornite (Cu5FeS4) is also oxidized in the presence of ferric in two distinct stages according to the following equations (Pesic and Olson, 1984). 3þ

2þ

3þ

2þ

Cu5 FeS4 þ 4Fe →2Cu þ Cu3 FeS4 þ 4Fe Cu3 FeS4 þ 8Fe →3Cu þ 9Fe

2þ

2þ

ð16Þ

þ 4S

ð17Þ

The first stage (Eq. (16)) rapidly proceeds at ambient temperatures and depends on the concentration of ferric ions to the power of 0.5 (leaching type I ((Nicol, 1993) is considered). dX Cu5 FeS4

dt h i
2 3þ 0:5 ¼ −g in; Cu5 FeS4 kCu5 FeS4 Fe 1−X Cu5 FeS4 3

ð10Þ

ð11Þ

ð15Þ

In this research, Δt is taken to be 1 min.

r Cu5 FeS4 ¼ −g in; Cu5 FeS4

where α is a coefficient related to the electroreduction of chalcopyrite described in the next subsection. Bolorunduro (1999) found that at low concentrations of iron (below 0.058 mkl/L), the leaching rate of first stage of chalcocite was directly proportional to the ferric concentration (first order with respect to ferric concentration) in which the rate was limited by the mass transfer of ferric to the mineral surface (leaching type III), while at high concentrations such as our work, the order of reaction decreased to 0.5 with respect to ferric concentration. In the solid phase:

ð14Þ

ð18Þ

In the solid phase:
 g Cu5 FeS4 ¼ g in; Cu5 FeS4 1−X Cu5 FeS4 tþΔt

t

g Cu5 FeS4 ¼ g Cu5 FeS4 −

dX Cu5 FeS4 dt

ð19Þ t

Δt ⋅ g in;Cu5 FeS4 ¼ g Cu5 FeS4 þ r Cu5 FeS4 Δt

ð20Þ

while the remaining 60% of copper is leached in the second stage (Eq. (17)) which is slowly dissolved at ambient conditions. It depends on the ratio of [Fe 3+]/[Fe 2+] in the power of 0.5 which is described according to Eq. (21) (leaching type III (Nicol, 1993) is considered). r Cu3 FeS4 ¼ −g in; Cu5 FeS4

dX Cu3 FeS4 dt 0h

i10:5 3þ
2 Fe ¼ −g in; Cu5 FeS4 kCu3 FeS4 @  2þ  A 1−X Cu3 FeS4 3 Fe

ð12Þ

ð21Þ

In the solid phase:
 g Cu3 FeS4 ¼ g in; Cu5 FeS4 1−X Cu3 FeS4

4.3. Covellite Covellite can originally be present in the concentrate and can also be produced as a secondary product of chalcocite leaching as explained in Eq. (8). The rate expression for covellite leaching, assuming shrinking sphere kinetics is hence given as follows: r CuS


 dX CuS ¼ − g in; CuS þ g in;Cu2 S dt 0h 3þ i10:5
 Fe 2 ¼ − g in; CuS þ g Cu2 S kCuS @  2þ  A ð1−X CuS Þ3 Fe

tþΔt

t

g Cu3 FeS4 ¼ g Cu5 FeS4 −

dX Cu3 FeS4 dt

ð22Þ t

Δt ⋅ g in;Cu5 FeS4 ¼ g Cu3 FeS4 þ r Cu3 FeS4 Δt

ð23Þ

4.5. Pyrite Pyrite is oxidized in the ferric sulfate medium according to Eq. (24).

ð13Þ

3þ

FeS2 þ 14Fe

2þ

þ 8H2 O→15Fe

2−

þ 2SO4 þ 16H

þ

ð24Þ

A. Ahmadi et al. / Hydrometallurgy 127–128 (2012) 16–23

Bouffard et al. (2006) investigated the kinetics and stoichiometry of pyrite oxidation in acid ferric sulfate media and found that elemental sulfur and sulfate are two most stable end-products. In this work, for simplification purposes, the complete oxidation to sulfate (100% sulfate yield) was considered, however it should be modeled as a function of ORP in our future works. It was supposed that the produced sulfur is converted to sulfate in the presense of sulfur oxidizing microorganisms. The dissolution rate of pyrite with ferric iron is described with the leaching type III (Nicol, 1993) as given by Eq. (25):

both the passivation of chalcopyrite at high solution potentials and the electroreduction of the mineral.

h

r CuFeS2 ¼ −gin;CuFeS2 0

:

i

0h

r FeS2 ¼ −g in; FeS2

dt

i10:5 3þ
2 Fe ¼ −g in; FeS2 kFeS2 @  2þ  A 1−X FeS2 3 Fe

tþΔt

t

g FeS2 ¼ g FeS2 −

dX FeS2 dt

t


2 þ αγI 1−X CuFeS2 3

where φA, φB and φC are constants, kCuFeS2 and AcuFeS2 are factors related to temperature effect, Rcrit is the critical ratio of ferric to ferrous concentrations and γ is an coefficient proportional to the current efficiency for Eq. (29). In the solid phase: ð26Þ

Δtg in;FeS2 ¼ g CuS þ r FeS2 Δt

ϕC

ð31Þ

ð25Þ

In the solid phase:
 g FeS2 ¼ g in; FeS2 1−X FeS2

dX CuFeS2 ¼ −g in;CuFeS2 dt

0 0h 3þ i111 Fe B h i h i B @ 0 1 0 1  ACC φA φB C B 3þ 3þ B B Fe2þ C Fe Fe CC B B CC B @ A @ A þ ACuFeS2  2þ  expB− C BkCuFeS2  2þ  C B Rcrit Fe Fe CC B B AC @ A @

×ð1−X Þ

dX FeS2

19

ð27Þ


 g CuFeS2 ¼ g in;CuFeS2 1−X CuFeS2 tþΔt

t

g CuFeS2 ¼ g CuFeS2 −

dX CuFeS2 dt

ð32Þ t

Δtg in;CuFeS2 ¼ g CuFeS2 þ r CuFeS2 Δt

ð33Þ

4.7. Biological oxidation of ferrous iron and elemental sulfur 4.6. Chalcopyrite The leaching of chalcopyrite is more complicated than that of above mentioned sulfide minerals. It is assumed that in ferric sulfate solutions, chalcopyrite is dissolved according to the Eq. (28).

Oxidation of ferrous iron (Eq. (34)) and elemental sulfur (Eq. (35)) are the only biological reactions considered in this research, since indirect mechanisms have been taken into account. 2þ

4Fe 3þ

CuFeS2 þ 4Fe →5Fe

2þ

2þ

þ Cu

þ 2S

ð28Þ

As explained in a previous work (Ahmadi et al., 2011), chalcopyrite would be passivated at high ratios of [Fe 3+]/[Fe 2+]. When experiments are electrochemically controlled, i.e. in the presence of a cathode, it can be supposed that a part of chalcopyrite can be reduced to chalcocite according to the following equation:
 þ − 2þ α: CuFeS2 þ 3H þ e →0:5Cu2 S þ Fe þ 1:5H2 S

ð29Þ

where α is described as the portion of reduced chalcopyrite and is a function of operating current and takes values between 0 and 1. Eq. (29) accords with electrochemical leaching tests at which microscopic observation revealed chalcocite and covellite on the surface of chalcopyrite residues in both abiotic and biotic tests (Ahmadi et al., 2011). It can be assumed that the covellite produced is formed as a result of chalcocite dissolution (Eq. (8)). The overall reaction of chalcopyrite can be written as follows: CuFeS2 þ

4 6α 6α − α 3þ þ Fe þ H þ e → Cu S 1þα 1þα 1þα 1þα 2

þ

ð30Þ

þ 2H2 O

3 S þ H2 O þ O2 →H2 SO4 2

ð34Þ ð35Þ

The oxidation rate of ferrous iron is modeled as a form of the Monod expression which was proposed by Petersen and Dixon (2003).

r Bac;Fe

h i 2þ Fe K Y;Fe ½O 2   ⋅ ⋅ ¼ Y Fe f g;Fe ðT Þ K O;Fe þ ½O2  K Fe2þ þ Fe2þ K Y;Fe þ Y Fe " !# ! kg; Fe ½H SO  ⋅ 1− exp − 2 4 þ km; Fe K H;Fe yg; Fe

ð36Þ

where rBac,Fe is the ferrous iron oxidation rate (mol Fe/l/min), Y is the cell density (teracells/l), y is the yield (teracells/mol Fe), KFe(II) is the ferrous saturation constant (mmolFe (II)/l), KO,Fe is the oxygen saturation constant (mmol O2/l), KY is the growth inhibition factor (teracells/kg water), KH is acid growth limiting factor (molal), kg,Fe is the growth rate constant (1/min), km is the maintenance rate constant (moles/teracells/ min), f (T) is a temperature function taking a value between 0 and 1. The rate of elemental sulfur oxidation is also modeled using a Monod equation (Eq. (37)) as proposed by Petersen and Dixon (2003). r Bac;S ¼ −

3α 5 þ 2α 2þ 1 2 2þ H Sþ Fe þ Cu þ S þ 1þα 2 1þα 1þα 1þα

3þ

þ O2 þ 4H →4Fe

dg S dt

kg;S K Y;S ½O 2  gS ¼ 2Y S ⋅ f g;S ðT Þ: þ km;S ⋅ ⋅ ⋅ K O;S þ ½O2  K S þ g S K Y;S þ Y S yg;S

!

ð37Þ The leaching rate of chalcopyrite is expressed as Eq. (31) which is a form developed from the Petersen and Dixon (2006) model. It should be noted that the model assumes that chalcopyrite kinetics is described as the sum of two parallel reactions, which replace each other around some critical ferric to ferrous ratio. The model considers

where r is the sulfur oxidation rate (mol S/kg/min), gS is the concentration of elemental sulfur (mol S/kg concentrate), Y is the cell density (teracells/l), y is the yield (cells/mol Fe), KS is the sulfur saturation constant (mol S/kg concentrate), KO is the oxygen saturation constant (mmol O2/l) and kg,S is the growth rate constant (1/min).

20

A. Ahmadi et al. / Hydrometallurgy 127–128 (2012) 16–23

Fig. 1. Left) Prediction of conversion for various mineral phases present in Sarcheshmeh copper concentrate and comparison of model predictions of copper recovery (conversion) with the experimental data, right) comparison of model predictions of pH and ORP with the experimental data obtained from bioleaching experiment of the concentrate using moderate thermophiles at 20% (w/v) pulp density.

4.8. Electroreduction of ferric iron

4.10. Jarosite precipitation

In the electrochemical leaching experiments, ferric iron is electrochemically reduced to ferrous iron in the main chamber where the working electrode is the cathode.The rate of electrochemically produced ferrous iron is considered to be proportional to the DC current which is written as the following equation: r Fe2þ ¼ μI

ð38Þ

Jarosite is precipitated according to Eq. (41). 3þ

3Fe

−

þ

ð41Þ

The extent of jarosite is approximated by assuming a linear equilibrium between free acid and ferric iron (Bouffard and Dixon, 2009), thus: K jar ¼

where μ is the current efficiency for ferric reduction.

þ

þ X þ 2HSO4 þ 6H 2 O→XFe3 ðSO4 Þ2 ðOH Þ6 þ 8H

½H2 SO4  ½FeðIII Þ

ð42Þ

4.9. The consumption of sulfuric acid 4.11. Gas–liquid mass transfer Protons (sulfuric acid) are mainly consumed by copper oxides and unspecified gangue minerals according to the following equation: þ

2þ

MO þ 2H →M

þ H2 O

ð39Þ

Acid consumption is modeled with a simple first-order rate law in the concentration of protons as previously reported by Petersen and Dixon (2003), thus: h i þ r cons:;Hþ ¼ kacid H

ð40Þ

The rate of oxygen gas–liquid mass transfer: O2 ðg Þ→O2 ðaÞ

ð43Þ

is conventionally modeled by the following equation:   r O2 ¼ kL a ½O2 L −½O2 L

ð44Þ

where kL is the overall gas–liquid mass transfer coefficient (m/min), a is the interfacial area per unit volume of stagnant solution (m2 interfacial area/m 3 stagnant solution), [O2]L* is the equilibrium concentration of

Fig. 2. Left) Prediction of conversion for various mineral phases present in Sarcheshmeh copper concentrate and comparison of model predictions of copper recovery (conversion) with the experimental data, right) comparison of model predictions of pH and ORP with the experimental data obtained from electochemical bioleaching experiment of the concentrate using moderate thermophiles at 20% (w/v) pulp density and potential range of 400–430 mV.

A. Ahmadi et al. / Hydrometallurgy 127–128 (2012) 16–23

21

Fig. 3. Left) Prediction of conversion for various mineral phases present in Sarcheshmeh copper concentrate and comparison of model predictions of copper recovery (conversion) with the experimental data, right) comparison of model predictions of pH and ORP with the experimental data obtained from electochemical bioleaching experiment of the concentrate using moderate thermophiles at 20% (w/v) pulp density and potential range of 440–480 mV (data of this experiment were not used to obtain model constants).

oxygen in solution and [O2]L is the bulk solution concentration of oxygen. According to Henry's law: 

½O2 L ¼

P O2

ð45Þ

H O2

where H is known as the Henry coefficient which is a function of temperature and solution composition (Tromans, 1998). On the other hand, the consumption rate of oxygen is related to the bacterial oxidation of ferrous iron (Eq. (35)) and elemental sulfur (Eq. (35)). At steady-state conditions: r O2 ðaÞ ¼ ∑ ν O2 ðaÞ;j r j ¼ r R42 −r R33 −3r R35 ¼ 0

ð46Þ

j

It means that the rate of oxygen transferred into the pulp by gas bubbles equals the rate of consumption by cells, assuming any direct reaction between dissolved oxygen and ferrous iron or sulfide minerals is negligible. In order to simplify the modeling, in this study the concentration of oxygen in the solution was considered as a constant (steady state) value during the process.

5. Combining rate equations and modeling results The concentration of species i at time t + Δt is calculated according to the following equation: Ci

tþΔt

t

¼ Ci þ

r i Δt V sol

ð47Þ

where C is the concentration of species i (mol/l), Vsol is the volume of solution in the reactor (l) and ri is the production rate of species i which is calculated as follows: j¼n

r i ¼ ∑j¼1 ν i;j r i;j SLR

ð48Þ

where δ is the solid to liquid mass ratio and ν is the stoichiometric coefficient for species i in reaction j. According to Eq. (47) and by considering the reactions stated in Section 3, the rate expression for each species can be written as Eqs. (49) to (53). r Fe3þ ¼

 2r Cu2 S þ 2r CuS þ

4 r þ 4r Cu5 FeS4 þ 8r Cu3 FeS4 2 1 þ α CuFeS þ14r FeS2 −μI þ 4r Bac;Fe −6r J δ

ð49Þ

Table 1 Input variables of the model. Parameter

Description

Mineralogical parameters X Cu as CuO gin,Cu2S gin,CuS gin,CuFeS2 gin,Cu5FeS4 gin,FeS2 gS

Fraction of copper as oxide Initial grade of chalcocite Initial grade of covellite Initial grade of chalcopyrite Initial grade of bornite Initial grade of pyrite Initial elemental sulfur grade

Initial slurry parameters pHin [Fe (III)]in [Fe (II)]in [Cu (II)]in [O2] Vsol δ T Rcrit (at ORP 420 mV vs. Ag·AgCl)

Initial pH Initial concentration of ferric iron Initial concentration of ferrous iron Initial concentration of cupric ion Concentration of dissolved oxygen Volume of solution Solid: liquid ratio Temperature [Fe(III)]/[Fe(II)]crit

Value 9.84 5.84 6.78 44.1 0.89 23.99 0

1.7 0.0193 0.0276 0.1566 0.005 1 0.2 323 0.7

Unit % % % % % % Mol S/kg concentrate

Molar Molar Molar mmol/l solution l Kg/l K

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A. Ahmadi et al. / Hydrometallurgy 127–128 (2012) 16–23

Table 2 Kinetics parameters for conventional and electrochemical bioleaching at 323 K. Parameter

Value

Unit

kCu2S kCuS kCu5FeS4 kCu3FeS4 kFeS2 kacid (acid consumption)

10 0.12 10 0.3 0.007 3 0.3 0.0002 0.004 0.1 0.7 0.1 0.3

1/min 1/min 1/min 1/min 1/min 1/min

BL ELB

kjar kCuFeS2 φA φB A(CuFeS2) φC

1/min 1/min

Table 3 Electrochemical parameters for electrochemical bioleaching at 323 K. Parameter Μ γCuFeS2 Α

r Fe3þ ¼

Value Current efficiency of ferric reduction Current efficiency of chalcopyrite reduction The portion of reduced chalcopyrite

2r Cu2 S þ 2r CuS þ

0.15 0.0025 0.07

4 r þ 4r Cu5 FeS4 þ 8r Cu3 FeS4 1 þ α CuFeS2 !

ð50Þ

þ14r FeS2 −μI þ 4r Bac;Fe −6r J δ  r Cu2þ ¼ rS ¼

r Hþ

−r Cu2 S −r CuS −

 −r CuS −

 1 r CuFeS2 −2r Cu5 FeS4 −3r Cu3 FeS4 δ 1þα

ð51Þ

 2 r CuFeS2 −4r Cu3 FeS4 −2r S;Bac δ 1þα

ð52Þ

  h i 6α þ r CuFeS2 þ 2r Bac;S −kacid H þ 10r j δ ¼ −16r FeS2 −r Bac;Fe þ 1þα ð53Þ

The above mentioned equations were integrated to obtain a combined semi-empirical model. Calculations were done on an Excel spreadsheet. Figs. 1 to 3 show the predicted values of copper recovery and the conversion of various sulfide minerals, as well as the variation of ORP and pH over the course of conventional and electrochemical bioleaching at 20% pulp density in the stirred electrobioreactor. The model parameters are presented in Tables 1 to 4. Parameters presented in Table 1 are system parameters which should be introduced to the model, while kinetic and electrochemical parameters (Tables 2 and 3) were determined by the minimizing of

square error between experimental data of conventional bioleaching and electrochemical bioleaching at 400–430 mV, and the model prediction values. Conceptually these parameters are meaningful; for example, as can be expected, the rate constant of first stage of chalcocite and bornite leaching (around 10/min) are significantly more than those of their second stage (around 0.2/min) and also are much higher than those of refractory minerals i.e. chalcopyrite and pyrite (much less than 0.01/min). However, the biological parameters (Table 4) are in the range of previously published data for heap bioleaching by Petersen and Dixon (2003). Validity of the model was assessed by comparing the values obtained from the model with the experimental data of electrochemical bioleaching at 440–480 mV, the data of which were not used to obtain model parameters (Fig. 3). The model considers the effects of mineralogical composition of feed, the initial parameters of solution such as pH, concentrations of ferric and ferrous iron, set point potential, the presence of iron and sulfur oxidizing microorganisms and jarosite precipitation on the values of copper recovery, pH and ORP during conventional and electrochemical bioleaching processes. It can be concluded that the model is well able to predict the leaching behavior of the mentioned processes at different experimental conditions. The model can take into account both the passivation of chalcopyrite at high solution ORPs (Fig. 1) and the increasing leach rate of chalcopyrite in the ORP range of 400–430 mV (Fig. 2). In the case of other minerals, the leaching behavior predicted by the model accords with published findings — for example it exhibits the competitive dissolution of pyrite and chalcopyrite at different ORPs (Fig. 1) as described by Petersen and Dixon (2006). However, it does not take into account the galvanic interactions between various mineral phases. It can be concluded that the bioleaching of the concentrate can be predicted reasonably well, and thus the model can be used as a design tool in scale-up of conventional and electrochemical bioleaching of copper concentrates in stirred tank reactors.

6. Conclusions Conventional and electrochemical bioleaching processes were described with a combined reaction based kinetics model. The model considers the effects of the mineralogical composition of feed, the initial pH of solution, the initial concentrations of ferric and ferrous iron, set point potential, the presence of iron and sulfur oxidizing microorganisms and jarosite precipitation on the values of copper recovery, pH and ORP during the processes. Comparing the values obtained from the calibrated model with independent experimental data showed that the model can well predict the target variables. The model can take into account both the passivation of chalcopyrite at high solution ORPs and the increasing leach rate of the mineral at low ORPs. It also shows the competitive dissolution of various sulfide minerals such as pyrite and chalcopyrite at different levels of ORP. The model has thus been validated as a tool for the prediction of the

Table 4 Biological parameters for conventional and electrochemical bioleaching at 323 K. Values are in the range of work done by Petersen and Dixon (2003). Parameter

Description

Unit

Y

Cell density

(teracells/l)

fg (T) KO KFe or KY kg

Temperature function Growth Monod factor for oxygen Growth Monod factor for ferrous ion or sulfur Growth inhibition factor Growth rate constant

Molal Molal for iron oxidizer and mole/kg concentrate for sulfur oxidizer teracells/kg water 1/min

km yg KH

Maintenance rate constant Cell yield per mole Fe or S° Acid growth limiting factor

Moles/teracells/min ×1012 cells/mol Fe or S° Molal

S

Iron oxidizers

Sulfur oxidizers

25

2

1 0.00005 2.00E−05

0.815 5 × 10−5 0.05

0.93201 BL ELB 0 1.6 0.001

0.095 0.2

1 0.37 0 1.5 –

A. Ahmadi et al. / Hydrometallurgy 127–128 (2012) 16–23

performance of the proposed electro-bioleach reactor and could find application in the design of this process at larger scale. Acknowledgments This work was supported by the National Iranian Copper Industries Company (NICICO). The authors are especially grateful to Mr. Reza Atashdehghan, Mr. Saeid Ghasemi and Mrs. Zahra Manafi for their support. References Ahmadi, A., Schaffie, M., Manafi, Z., Ranjbar, M., 2010. Electrochemical bioleaching of high grade chalcopyrite flotation concentrate in a stirred tank reactor. Hydrometallurgy 104, 99–105. Ahmadi, A., Schaffie, M., Petersen, J., Schippers, A., Ranjbar, M., 2011. Conventional and electrochemical bioleaching of chalcopyrite concentrates by moderately thermophile bacteria at high pulp density. Hydrometallurgy 106 (1–2), 84–92. Bolorunduro, S.A., 1999. Kinetics of leaching of chalcocite in acid ferric sulphate media: Chemical and bacterial leaching. M.Sc. thesis, University of British Columbia, Canada. Bouffard, S.C., 2003. Understanding the heap biooxidation of sulphidic refractory gold ores. Ph.D. thesis, University of British Colombia, Canada. Bouffard, S.C., Dixon, D.G., 2009. Modeling pyrite bioleaching in isothermal test columns with the HeapSim model. Hydrometallurgy 95 (3–4), 215–226. Bouffard, S.C., Rivera-Vasquez, B.F., Dixon, D.G., 2006. Leaching kinetics and stoichiometry of pyrite oxidation from a pyrite-marcasite concentrate in acid ferric sulfate media. Hydrometallurgy 84, 225–238. Crundwell, F.K., 1998. The indirect mechanism of bacterial leaching. Miner. Process. Extr. Metall. Rev. 19, 117–128. Crundwell, F.K., 2000. Modeling, simulation, and optimization of bacterial leaching reactors. Biotechnol. Bioeng. 71 (4), 255–265.

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