Hydrometallurgy 127–128 (2012) 16–23

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Kinetic modeling of bioleaching of copper sulfide concentrates in conventional andelectrochemically 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, Iranb Department of Mining Engineering, Shahid Bahonar University, Kerman, Iranc Department of Chemical Engineering, Shahid Bahonar University, Kerman, Irand Centre for Bioprocess Engineering Research, University of Cape Town, South Africae Mineral Bioprocessing Research Group (MBRG), Biotechnology and Bioengineering Research Institute, Isfahan University of Technology, Isfahan, Iran

⁎ Corresponding author at: Department of Mining EngTechnology, Isfahan, Iran. Tel.: +98 311 3915113; fax:

E-mail address: a.ahmadi@cc.iut.ac.ir (A. Ahmadi).

0304-386X/$ – see front matter © 2012 Elsevier B.V. Aldoi:10.1016/j.hydromet.2012.06.010

a b s t r a c t

a r t i c l e i n f o

Article history:Received 22 December 2011Received in revised form 19 June 2012Accepted 27 June 2012Available online 6 July 2012

Keywords:Kinetic modelingBioleachingCopper concentrateStirred reactorElectrochemistry

In this paper a model of conventional and electrochemical bioleaching of high grade complex copper sulfideores or flotation concentrates in isothermal stirred tank reactors is presented and compared to experimentaldata. Experiments were conducted in an electrobioreactor using a mixed culture of moderate thermophilemicroorganisms at pulp density 20% (w/v), leaching time 10 days, stirring rate 600 rpm and temperature50 °C. The behavior of conventional and electrochemical bioleaching processes was described with a com-bined reaction-based kinetic model. The model considers the effects of mineralogical composition of thefeed, the properties of the initial solution, the presence of iron- and sulfur oxidizing microorganisms andboth the passivation and electroreduction of chalcopyrite on the values of copper recovery, pH and redox po-tential during the processes. Comparing the values obtained from the integrated semi-empirical model withthe experimental data showed that the model results are in good agreement with the real leaching data ofcopper recovery, ORP (oxidation reduction potential) and pH for the mentioned processes under different ex-perimental conditions.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

The modeling of reaction kinetics is an important step toward un-derstanding the nature and the mechanism of leaching processes. Ki-netic models can be used for plant design, optimization of operatingconditions of an existing plant and real-time optimization includingautomatic control and maximization of the metallurgical efficiency(Habashi, 2007).

Bioleaching systems constitute two interacting subsystems: anabiotic system, which is a mineral suspension in a solution of chem-ical compounds and gases, and a biological systemwhich is composedof a mixed culture of microorganisms. The leaching kinetics of metalsin solution are driven by mass transfer of reactants and products inthe solution phase and chemical reaction at the solid/liquid inter-face, therefore for mathematical modeling of this process, mass trans-fer between different phases i.e. solid, gas and liquid must be takeninto account (Han, 1981; Rossi, 1990).

The rate of reaction at the interface mainly depends on the natureof the minerals and on the type and concentration of the reactants,such as ferric.

ineering, Isfahan University of+98 3912776.

l rights reserved.

During the last three decades, several models have been proposedto describe the bioleaching process. Miller (1990) and Hansford andChapman (1992) described the bioleaching of pyrite flotation concen-trates from Fairview and Crown Mines (both in South Africa), respec-tively. Huberts (1994) has derived rate equations based on Ingledew'schemiosmotic theory. Crundwell (1998, 2000) modeled mathemati-cally the leaching of sulfide minerals assuming indirect mechanism.He considered indirect mechanism of bioleaching and described thechemical leaching of sphalerite and the bacterial oxidation of ferrousions (Crundwell, 1998). He also presented a model for bioleaching ofpyritic concentrates which showed a pseudo-stoichiometric relation-ship between bacterial growth and mineral leaching.

In some recently published papers (Bouffard, 2003; Bouffard andDixon, 2009; Petersen and Dixon, 2006) the conventional bioleachingof low grade sulfide minerals in the presence of various microor-ganisms have been mechanistically modeled, mostly in isothermalwhole ore columns. Electrochemical bioleaching (bioleaching by elec-trochemical control of oxidation reduction potential (ORP)) was re-cently explored to extract copper from chalcopyrite concentrates byauthors (Ahmadi et al., 2010, 2011) and it was found that this newprocess has better potential for application in the treatment of suchrefractory concentrates compared to conventional bioleaching. A fun-damental model that would jointly consider biological, chemical andelectrochemical phenomena in this complex system is still lacking.

17A. Ahmadi et al. / Hydrometallurgy 127–128 (2012) 16–23

Therefore, this study was initiated to develop and formulate a mech-anistic model for simulating the conventional and electrochemicalbioleaching of copper concentrates in stirred tank reactors with aview to use this model to develop a larger scale application.

2. Experimental

The (electro)-bioleaching data used for this research were ob-tained from an experimental project described in detail in a previouspaper (Ahmadi et al., 2011). These experiments were conducted inan electrobioreactor using a mixed culture of moderately thermophileiron- 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 temper-ature 50 °C. In the electrochemical tests, a current was applied to theworking electrode in order to control the solution ORP, which wasregulated in two different ranges, i.e. 400–430 mV and 440–480 mV(vs. Ag/AgCl). The amount of current passing through the reactor var-ied from 100 to 450 mA.

A copper flotation concentrate from the Sarcheshmeh Copper Com-plex, containing 44.0% chalcopyrite (CuFeS2), 24.0% pyrite (FeS2), 6.9%covellite (CuS), 5.8 % chalcocite (Cu2S), 13.6% non-metallic mineralsand 4.8% copper oxide minerals was used during the experiments. Theresults showed that the electrochemical bioleaching process at lowORP levels (around 400–430 mVvs. Ag/AgCl) has a high potential to ex-tract copper from the concentratewith about 80% Cu leached during theprocess, relative to about 50% in the conventional bioleaching process(no ORP control).

3. Fundamentals of modeling

The overall kinetics of conventional and electrochemical bio-leaching are usually related to the kinetics of dissolution for individu-al minerals, which in turn are determined by the chemical andelectrochemical conditions of the environment, the growth and activ-ity of iron and sulfur oxidizing microorganisms, the formation of pre-cipitates 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 speciescan be described by thermal, chemical and topological functions asrepresented by the following equation:

rj ¼dXj

dt¼ K

jTð Þf j Cð Þgj d0;Xj

� �ð1Þ

where the subscript “j” refers to mineral species (covellite, chalcocite,bornite, chalcopyrite and pyrite), X is mineral conversion, K(T) is arate constant which is a function of temperature and initial mineralgrain size, f(C) is a function of solution composition such as the con-centrations of ferric iron, ferrous iron, proton and etc. and g(X) is asemi-empirical function of the fraction of unreacted mineral, whichrepresents the changing topology of the mineral surface over thecourse of leaching. In the following subsections each of these threefunctions 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 Tð Þ ¼ kref exp −EaR

1T− 1

Tref

! !ð2Þ

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

In this study, experiments were conducted in a constant tempera-ture (50 °C) during the processes, hence the thermal function can belumped as a constant value.

3.2. Chemical function

Generally, metallic sulfide minerals are dissolved by the oxidativeaction of ferric iron in solution as follows:

MSþ 2Fe3þ→M2þ þ 2Fe2þ þ S ð3Þ

where M is a divalent metal ion such as Cu2+.The leaching reaction of metallic sulfide minerals is assumed to be

electrochemical in nature and Eq. (3) is the result of two half-cell re-actions presented in Eqs. (4) and (5) which take place simultaneouslyon the surface of the mineral at mixed potential, E.

MS↔M2þ þ Sþ 2e− ð4Þ

Fe3þ þ e−↔Fe2þ ð5Þ

3.3. Topological factor

The topological function used here is a simple power-law expres-sion of the fraction unreacted (Petersen and Dixon, 2006):

g Xð Þ ¼ 1−Xð Þφ ð6Þ

Depending on the value of φ, Eq. (5) can represent the leaching ofany grain topology from uniform spheres to a broad range of grainsizes. If mineral particles are assumed to be spherical and to shrinkat a rate proportional to the progress of the leaching, it can be equalto 2/3 (shrinking sphere model). It may also be as high as 3 whenthe distribution of the effective grain size is particularly wide (Dixonand Hendrix, 1993).

Particle size is a critical parameter in describing the topology aswell, and Bouffard (2003) has shown how this can be integratedinto the topological term, by adjusting the overall rate constant kj(in Eq. (1)) such that:

kj ¼ k0 ⋅a d0ð Þ ð7Þ

In the modeling of a given particle size distribution, the rate pa-rameter kj is calibrated for this distribution and does not need to bedetermined as a function of particle size, if no experimental data isavailable for other distributions. This of course then also limits theability of the resulting model to describe any other particle size distri-bution other the one it has been calibrated for.

4. Modeling of ındividual minerals

Based on the mineralogical analysis (Section 2) several copperbearing minerals i.e. chalcopyrite, chalcocite, covellite and copper ox-ides contribute to leaching. These minerals have different behaviorsand the overall metal recoveries are the combination of these individ-ual minerals. Pyrite is a major phase which affects both chemical andbacterial subsystems.

4.1. Copper oxides

It has widely been accepted that copper oxide minerals are rapidlyleached by sulfuric acid (in the first hour) in ambient conditions. So,the leaching of this fraction of copper was considered in the modelas instantaneous release.

18 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 accordingto the following equations:

Cu2Sþ 2Fe3þ→Cu2þ þ 2Fe2þ þ CuS ð8Þ

CuSþ 2Fe3þ→Cu2þ þ 2Fe2þ þ S� ð9Þ

The first stage proceeds readily even at room temperature, whereasthe produced covellite is rather recalcitrant and the second stage(Eq. (9)) requires a high ratio of ferric iron to ferrous iron (Petersenand David, 2007) to proceed more rapidly. Indeed, the first stageconsists of a series of steps in which the reaction products may ormay not be observed experimentally depending on the rate of transfor-mation of the successive phase (Bolorunduro, 1999). In the first stage,reaction proceeds rapidly even at low temperatures (Petersen andDixon, 2006) and is controlled by the diffusion of ferric iron with thepower of 0.42–0.6 as confirmed by Bolorunduro (1999), while the sec-ond stage reaction corresponds to leaching type III (Nicol, 1993), chem-ically controlled shrinking sphere model, where the anodic mineraldissolution is amuch slower reaction than the cathodic reduction of fer-ric to ferrous iron. It proceeds slowly at low ratio of [Fe3+]/[Fe2+] (lowsolution ORP) especially at ambient conditions, but the rate increases tothe half power with an increase of that ratio.

The dissolution rate of the first stage is described by the followingexpression which is derived from leaching Type I (Nicol, 1993).

rCu2S ¼ − gin;Cu2Sþ α1þ α

gCuFeS2

� � dXCu2S

dt

¼ − gin;Cu2Sþ α1þ α

gCuFeS2

� �kCu2S

Fe3þh i0:5

1−XCu2S

� �23 ð10Þ

where α is a coefficient related to the electroreduction of chalcopyritedescribed in the next subsection.

Bolorunduro (1999) found that at low concentrations of iron (below0.058 mkl/L), the leaching rate of first stage of chalcocite was directlyproportional to the ferric concentration (first order with respect to fer-ric concentration) in which the rate was limited by the mass transfer offerric to themineral surface (leaching type III), while at high concentra-tions such as our work, the order of reaction decreased to 0.5 with re-spect to ferric concentration.

In the solid phase:

gCu2S ¼ gin; Cu2S 1−XCu2S

� �ð11Þ

gtþΔtCu2S

¼ gtCu2S−dXCu2S

dtΔt ⋅gin; Cu2S

¼ gtCu2S þ rCu2SΔt− α

1þ αrCuFeS2Δt

ð12Þ

4.3. Covellite

Covellite can originally be present in the concentrate and can also beproduced as a secondary product of chalcocite leaching as explained inEq. (8).

The rate expression for covellite leaching, assuming shrinkingsphere kinetics is hence given as follows:

rCuS ¼ − gin;CuS þ gin;Cu2S� �dXCuS

dt

¼ − gin;CuS þ gCu2S� �

kCuSFe3þh iFe2þ� �

0@

1A

0:5

1−XCuSð Þ23 ð13Þ

gin, j is the initial grade of mineral species j. The unit of rate for mineralleaching is taken as (mol mineral)/(kg concentrate·min).

Covellite grade in the solid phase (mol/kg concentrate) is:

gCuS ¼ gin; CuS þ gin;Cu2S� �

1−XCuSð Þ ð14Þ

The grade of covellite at time t+Δt is expressed as follows:

gtþΔtCuS ¼ gtCuS−

dXCuS

dtΔt gin;CuS þ gin;Cu2S� �

¼ gtCuS þ rCuS ⋅Δt ð15Þ

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

4.4. Bornite

Like chalcocite, bornite (Cu5FeS4) is also oxidized in the presenceof ferric in two distinct stages according to the following equations(Pesic and Olson, 1984).

Cu5FeS4þ 4Fe3þ→2Cu2þþ Cu3FeS4 þ 4Fe2þ ð16Þ

Cu3FeS4þ 8Fe3þ→3Cu2þþ 9Fe2þ þ 4S ð17Þ

The first stage (Eq. (16)) rapidly proceeds at ambient tempera-tures and depends on the concentration of ferric ions to the powerof 0.5 (leaching type I ((Nicol, 1993) is considered).

rCu5FeS4 ¼ −gin; Cu5FeS4dXCu5FeS4

dt¼ −gin; Cu5FeS4kCu5FeS4 Fe3þ

h i0:51−XCu5FeS4

� �23 ð18Þ

In the solid phase:

gCu5FeS4 ¼ gin; Cu5FeS4 1−XCu5FeS4

� �ð19Þ

gtþΔtCu5FeS4

¼ gtCu5FeS4−dXCu5FeS4

dtΔt ⋅gin;Cu5FeS4 ¼ gtCu5FeS4 þ rCu5FeS4Δt ð20Þ

while the remaining 60% of copper is leached in the second stage(Eq. (17)) which is slowly dissolved at ambient conditions. It dependson the ratio of [Fe3+]/[Fe2+] in the power of 0.5 which is describedaccording to Eq. (21) (leaching type III (Nicol, 1993) is considered).

rCu3FeS4 ¼ −gin; Cu5FeS4dXCu3FeS4

dt

¼ −gin; Cu5FeS4kCu3FeS4Fe3þh iFe2þ� �

0@

1A

0:5

1−XCu3FeS4

� �23 ð21Þ

In the solid phase:

gCu3FeS4 ¼ gin; Cu5FeS4 1−XCu3FeS4

� �ð22Þ

gtþΔtCu3FeS4

¼ gtCu5FeS4−dXCu3FeS4

dtΔt ⋅gin;Cu5FeS4 ¼ gtCu3FeS4 þ rCu3FeS4Δt ð23Þ

4.5. Pyrite

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

FeS2 þ 14Fe3þ þ 8H2O→15Fe2þ þ 2SO2−4 þ 16Hþ ð24Þ

19A. Ahmadi et al. / Hydrometallurgy 127–128 (2012) 16–23

Bouffard et al. (2006) investigated the kinetics and stoichiometryof pyrite oxidation in acid ferric sulfate media and found that elemen-tal 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 afunction of ORP in our future works. It was supposed that the pro-duced sulfur is converted to sulfate in the presense of sulfur oxidizingmicroorganisms.

The dissolution rate of pyrite with ferric iron is described with theleaching type III (Nicol, 1993) as given by Eq. (25):

rFeS2 ¼ −gin; FeS2dXFeS2

dt¼ −gin; FeS2kFeS2

Fe3þh iFe2þ� �

0@

1A

0:5

1−XFeS2

� �23 ð25Þ

In the solid phase:

gFeS2 ¼ gin; FeS2 1−XFeS2

� �ð26Þ

gtþΔtFeS2

¼ gtFeS2−dXFeS2

dtΔtgin;FeS2 ¼ gtCuS þ rFeS2Δt ð27Þ

4.6. Chalcopyrite

The leaching of chalcopyrite is more complicated than that ofabove mentioned sulfide minerals. It is assumed that in ferric sulfatesolutions, chalcopyrite is dissolved according to the Eq. (28).

CuFeS2 þ 4Fe3þ→5Fe2þ þ Cu2þ þ 2S ð28Þ

As explained in a previous work (Ahmadi et al., 2011), chalcopy-rite would be passivated at high ratios of [Fe3+]/[Fe2+]. When exper-iments are electrochemically controlled, i.e. in the presence of acathode, it can be supposed that a part of chalcopyrite can be reducedto chalcocite according to the following equation:

α: CuFeS2 þ 3Hþ þ e−→0:5Cu2Sþ Fe2þ þ 1:5H2S� �

ð29Þ

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

CuFeS2 þ4

1þ αFe3þ þ 6α

1þ αHþ þ 6α

1þ αe−→

α1þ α

Cu2S

þ 3α1þ α

H2Sþ5þ 2α1þ α

Fe2þ þ 11þ α

Cu2þ þ 21þ α

S ð30Þ

The leaching rate of chalcopyrite is expressed as Eq. (31) which isa form developed from the Petersen and Dixon (2006) model. Itshould be noted that the model assumes that chalcopyrite kineticsis described as the sum of two parallel reactions, which replace eachother around some critical ferric to ferrous ratio. The model considers

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

rCuFeS2 ¼ −gin;CuFeS2dXCuFeS2

dt¼ −gin;CuFeS2

:

hkCuFeS2

Fe3þh iFe2þ� �

0@

1A

φA

þ ACuFeS2

Fe3þh iFe2þ� �

0@

1A

φB

exp −

Fe3þh iFe2þ� �

0@

1A

Rcrit

0BBBBBB@

1CCCCCCA

0BBBBBBB@

1CCCCCCCA

× 1−Xð ÞϕC þ αγI 1−XCuFeS2

� �23

i ð31Þ

where φA, φB and φC are constants, kCuFeS2 and AcuFeS2 are factors relat-ed to temperature effect, Rcrit is the critical ratio of ferric to ferrousconcentrations and γ is an coefficient proportional to the current effi-ciency for Eq. (29).

In the solid phase:

gCuFeS2 ¼ gin;CuFeS2 1−XCuFeS2

� �ð32Þ

gtþΔtCuFeS2

¼ gtCuFeS2−dXCuFeS2

dtΔtgin;CuFeS2 ¼ gtCuFeS2 þ rCuFeS2Δt ð33Þ

4.7. Biological oxidation of ferrous iron and elemental sulfur

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

4Fe2þ þ O2 þ 4Hþ→4Fe3þ þ 2H2O ð34Þ

SþH2Oþ 32O2→H2SO4 ð35Þ

The oxidation rate of ferrous iron ismodeled as a form of theMonodexpression which was proposed by Petersen and Dixon (2003).

rBac;Fe ¼ YFef g;Fe Tð Þ O2½ �KO;Fe þ O2½ � ⋅

Fe2þh i

KFe2þ þ Fe2þ� � ⋅ KY ;Fe

KY;Fe þ YFe

⋅ 1− exp − H2SO4½ �KH;Fe

!" #kg; Feyg; Fe

þ km; Fe

!ð36Þ

where rBac,Fe is the ferrous iron oxidation rate (mol Fe/l/min), Y is the celldensity (teracells/l), y is the yield (teracells/mol Fe), KFe(II) is the ferroussaturation constant (mmolFe (II)/l), KO,Fe is the oxygen saturation con-stant (mmol O2/l), KY is the growth inhibition factor (teracells/kgwater), KH is acid growth limiting factor (molal), kg,Fe is the growth rateconstant (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 aMonod equation (Eq. (37)) as proposed by Petersen andDixon (2003).

rBac;S ¼ −dgSdt

¼ 2YS ⋅ f g;S Tð Þ: O2½ �KO;S þ O2½ � ⋅

gSKS þ gS

⋅KY;S

KY;S þ YS⋅

kg;Syg;S

þ km;S

!

ð37Þwhere r is the sulfur oxidation rate (mol S/kg/min), gS is the concen-tration 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 saturationconstant (mol S/kg concentrate), KO is the oxygen saturation constant(mmol O2/l) and kg,S is the growth rate constant (1/min).

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 mod-erate thermophiles at 20% (w/v) pulp density.

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

4.8. Electroreduction of ferric iron

In the electrochemical leaching experiments, ferric iron is electro-chemically reduced to ferrous iron in the main chamber where theworking electrode is the cathode.The rate of electrochemically pro-duced ferrous iron is considered to be proportional to the DC currentwhich is written as the following equation:

rFe2þ ¼ μI ð38Þ

where μ is the current efficiency for ferric reduction.

4.9. The consumption of sulfuric acid

Protons (sulfuric acid) are mainly consumed by copper oxides andunspecified gangue minerals according to the following equation:

MOþ 2Hþ→M2þ þ H2O ð39Þ

Acid consumption is modeled with a simple first-order rate law inthe concentration of protons as previously reported by Petersen andDixon (2003), thus:

rcons:;Hþ ¼ kacid Hþh ið40Þ

Fig. 2. Left) Prediction of conversion for various mineral phases present in Sarcheshmeh copwith the experimental data, right) comparison of model predictions of pH and ORP with thcentrate using moderate thermophiles at 20% (w/v) pulp density and potential range of 40

4.10. Jarosite precipitation

Jarosite is precipitated according to Eq. (41).

3Fe3þ þ Xþ þ 2HSO−4 þ 6H2O→XFe3 SO4ð Þ2 OHð Þ6 þ 8Hþ ð41Þ

The extent of jarosite is approximated by assuming a linear equilib-riumbetween free acid and ferric iron (Bouffard andDixon, 2009), thus:

Kjar ¼H2SO4½ �Fe III Þ�ð½ ð42Þ

4.11. Gas–liquid mass transfer

The rate of oxygen gas–liquid mass transfer:

O2 gð Þ→O2 að Þ ð43Þ

is conventionally modeled by the following equation:

rO2¼ kLa O2½ ��L− O2½ �L

� ð44Þ

where kL is the overall gas–liquidmass transfer coefficient (m/min), a isthe interfacial area per unit volume of stagnant solution (m2 interfacialarea/m3 stagnant solution), [O2]L* is the equilibrium concentration of

per concentrate and comparison of model predictions of copper recovery (conversion)e experimental data obtained from electochemical bioleaching experiment of the con-0–430 mV.

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 con-centrate 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).

21A. Ahmadi et al. / Hydrometallurgy 127–128 (2012) 16–23

oxygen in solution and [O2]L is the bulk solution concentration ofoxygen.

According to Henry's law:

O2½ ��L ¼PO2

HO2

ð45Þ

where H is known as the Henry coefficient which is a function of tem-perature and solution composition (Tromans, 1998).

On the other hand, the consumption rate of oxygen is related tothe bacterial oxidation of ferrous iron (Eq. (35)) and elemental sulfur(Eq. (35)). At steady-state conditions:

rO2 að Þ ¼ ∑jνO2 að Þ;jrj ¼ rR42−rR33−3rR35 ¼ 0 ð46Þ

It means that the rate of oxygen transferred into the pulp by gasbubbles equals the rate of consumption by cells, assuming any directreaction between dissolved oxygen and ferrous iron or sulfide min-erals is negligible. In order to simplify the modeling, in this studythe concentration of oxygen in the solution was considered as a con-stant (steady state) value during the process.

Table 1Input variables of the model.

Parameter Description

Mineralogical parametersX Cu as CuO Fraction of copper as oxidegin,Cu2S Initial grade of chalcocitegin,CuS Initial grade of covellitegin,CuFeS2 Initial grade of chalcopyritegin,Cu5FeS4 Initial grade of bornitegin,FeS2 Initial grade of pyriteg S Initial elemental sulfur grade

Initial slurry parameterspHin Initial pH[Fe (III)]in Initial concentration of ferric ir[Fe (II)]in Initial concentration of ferrous[Cu (II)]in Initial concentration of cupric i[O2] Concentration of dissolved oxyVsol Volume of solutionδ Solid: liquid ratioT TemperatureRcrit (at ORP 420 mV vs. Ag·AgCl) [Fe(III)]/[Fe(II)]crit

5. Combining rate equations and modeling results

The concentration of species i at time t+Δt is calculated accordingto the following equation:

CitþΔt ¼ Ci

t þ riΔtVsol

ð47Þ

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

ri ¼ ∑j¼nj¼1νi;jri;jSLR ð48Þ

where δ is the solid to liquid mass ratio and ν is the stoichiometric co-efficient for species i in reaction j. According to Eq. (47) and by con-sidering the reactions stated in Section 3, the rate expression foreach species can be written as Eqs. (49) to (53).

rFe3þ ¼�2rCu2S þ 2rCuS þ

41þ α

rCuFeS2 þ 4rCu5FeS4þ 8rCu3FeS4

þ14rFeS2−μI þ 4rBac;Fe−6rJ

�δ

ð49Þ

Value Unit

9.84 %5.84 %6.78 %

44.1 %0.89 %

23.99 %0 Mol S/kg concentrate

1.7on 0.0193 Molariron 0.0276 Molaron 0.1566 Molargen 0.005 mmol/l solution

1 l0.2 Kg/l

323 K0.7

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

Parameter Value Unit

kCu2S 10 1/minkCuS 0.12 1/minkCu5FeS4 10 1/minkCu3FeS4 0.3 1/minkFeS2 0.007 1/minkacid (acid consumption) BL 3 1/min

ELB 0.3kjar 0.0002 1/minkCuFeS2 0.004 1/minφA 0.1φB 0.7A(CuFeS2) 0.1φC 0.3

Table 3Electrochemical parameters for electrochemical bioleaching at 323 K.

Parameter Value

Μ Current efficiency of ferric reduction 0.15γCuFeS2 Current efficiency of chalcopyrite reduction 0.0025Α The portion of reduced chalcopyrite 0.07

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

rFe3þ ¼ 2rCu2S þ 2rCuS þ

41þ α

rCuFeS2 þ 4rCu5FeS4 þ 8rCu3FeS4

þ14rFeS2−μI þ 4rBac;Fe−6rJ

!δ

ð50Þ

rCu2þ ¼ −rCu2S−rCuS−1

1þ αrCuFeS2−2rCu5FeS4

−3rCu3FeS4

� �δ ð51Þ

rS ¼ −rCuS−2

1þ αrCuFeS2−4rCu3FeS4−2rS;Bac

� �δ ð52Þ

rHþ ¼ −16rFeS2−rBac;Fe þ6α

1þ αrCuFeS2 þ 2rBac;S−kacid Hþh i

þ 10rj

� �δ

ð53Þ

The above mentioned equations were integrated to obtain a com-bined semi-empirical model. Calculations were done on an Excelspreadsheet. Figs. 1 to 3 show the predicted values of copper recoveryand the conversion of various sulfide minerals, as well as the variationof ORP and pH over the course of conventional and electrochemicalbioleaching at 20% pulp density in the stirred electrobioreactor. Themodel parameters are presented in Tables 1 to 4.

Parameters presented in Table 1 are system parameters whichshould be introduced to the model, while kinetic and electrochemicalparameters (Tables 2 and 3) were determined by the minimizing of

Table 4Biological parameters for conventional and electrochemical bioleaching at 323 K. Values ar

Parameter Description Unit

Y Cell density (teracells/l)

fg (T) Temperature functionKO Growth Monod factor for oxygen MolalKFe or S Growth Monod factor for ferrous

ion or sulfurMolal for iron oxiconcentrate for su

KY Growth inhibition factor teracells/kg waterkg Growth rate constant 1/min

km Maintenance rate constant Moles/teracells/myg Cell yield per mole Fe or S° ×1012 cells/mol FKH Acid growth limiting factor Molal

square error between experimental data of conventional bioleachingand electrochemical bioleaching at 400–430 mV, and the model pre-diction values. Conceptually these parameters are meaningful; for ex-ample, as can be expected, the rate constant of first stage of chalcociteand bornite leaching (around 10/min) are significantly more thanthose of their second stage (around 0.2/min) and also aremuch higherthan those of refractory minerals i.e. chalcopyrite and pyrite (muchless than 0.01/min). However, the biological parameters (Table 4)are in the range of previously published data for heap bioleaching byPetersen and Dixon (2003).

Validity of the model was assessed by comparing the valuesobtained from the model with the experimental data of electrochem-ical bioleaching at 440–480 mV, the data of which were not used toobtain model parameters (Fig. 3). The model considers the effects ofmineralogical composition of feed, the initial parameters of solutionsuch as pH, concentrations of ferric and ferrous iron, set point poten-tial, the presence of iron and sulfur oxidizing microorganisms andjarosite precipitation on the values of copper recovery, pH and ORPduring conventional and electrochemical bioleaching processes. Itcan be concluded that the model is well able to predict the leachingbehavior of the mentioned processes at different experimental con-ditions. The model can take into account both the passivation of chal-copyrite at high solution ORPs (Fig. 1) and the increasing leach rate ofchalcopyrite in the ORP range of 400–430 mV (Fig. 2). In the case ofother minerals, the leaching behavior predicted by the model accordswith published findings — for example it exhibits the competitivedissolution of pyrite and chalcopyrite at different ORPs (Fig. 1) as de-scribed by Petersen and Dixon (2006). However, it does not take intoaccount the galvanic interactions between various mineral phases.

It can be concluded that the bioleaching of the concentrate can bepredicted reasonably well, and thus the model can be used as a designtool in scale-up of conventional and electrochemical bioleaching ofcopper concentrates in stirred tank reactors.

6. Conclusions

Conventional and electrochemical bioleaching processes were de-scribed with a combined reaction based kinetics model. The modelconsiders the effects of the mineralogical composition of feed, the ini-tial pH of solution, the initial concentrations of ferric and ferrous iron,set point potential, the presence of iron and sulfur oxidizing micro-organisms and jarosite precipitation on the values of copper recovery,pH and ORP during the processes. Comparing the values obtainedfrom the calibrated model with independent experimental datashowed that the model can well predict the target variables. Themodel can take into account both the passivation of chalcopyrite athigh solution ORPs and the increasing leach rate of the mineral atlow ORPs. It also shows the competitive dissolution of various sulfideminerals such as pyrite and chalcopyrite at different levels of ORP.The model has thus been validated as a tool for the prediction of the

e in the range of work done by Petersen and Dixon (2003).

Iron oxidizers Sulfur oxidizers

25 2

1 0.8150.00005 5×10−5

dizer and mole/kglfur oxidizer

2.00E−05 0.05

0.93201 1BL 0.095 0.37ELB 0.2

in 0 0e or S° 1.6 1.5

0.001 –

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

performance of the proposed electro-bioleach reactor and could findapplication in the design of this process at larger scale.

Acknowledgments

This workwas supported by the National Iranian Copper IndustriesCompany (NICICO). The authors are especially grateful to Mr. RezaAtashdehghan, Mr. Saeid Ghasemi and Mrs. Zahra Manafi for theirsupport.

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