Biooxidation of a gold concentrate in a continuous stirred tank reactor: mathematical model and optimal configuration

Biochemical Engineering Journal 19 (2004) 33–42

Biooxidation of a gold concentrate in a continuous stirred tank reactor: mathematical model and optimal configuration Ramon Gonzalez a , Juan C. Gentina b,∗ , Fernando Acevedo b a b

Department of Chemical Engineering, Iowa State University, Ames, IA 50011-2230, USA School of Biochemical Engineering, Catholic University of Valparaiso, Valparaiso, Chile Received 29 January 2003; accepted after revision 22 September 2003

Abstract A model was developed to represent the biooxidation by Acidithiobacillus ferrooxidans of a refractory gold concentrate in a continuous stirred tank reactor (CSTR). The model accounts for the growth of attached and planktonic cells, their role in mineral solubilisation, and the contribution of ferric ions to the process. Predicted solubilisation rates increase with increasing solids dilution rates until a maximum, in agreement with the experimental results. Concentration of suspended cells was more affected by changes in solids dilution rates than attached cells did, behaviour well represented by the model. The model was also able to predict the observed increase in cell growth and mineral solubilisation due to the decrease in particle size and the enrichment of the air with CO2 . Finally, the model was used to predict the optimal configuration of a continuous biooxidation system that minimises the residence time required to attain a defined degree of mineral solubilisation. This configuration was found to be a two-stage system consisting of a CSTR followed by a plug flow reactor. The latter can be replaced by a series of smaller equal-size CSTRs. © 2003 Elsevier B.V. All rights reserved. Keywords: Acidithiobacillus ferrooxidans; Bioreactors; Continuous biooxidation; Heterogeneous biocatalysts; Kinetic parameters; Modelling

1. Introduction Biooxidation of sulphide minerals has become an important method for the pre-treatment of refractory gold ores. This technology is currently used in several countries including Australia, Brazil, Ghana, Peru, and South Africa. In all these commercial plants, bacterial leaching is carried out in a system composed of several continuous stirred tank reactors (CSTR) with a primary CSTR of larger volume followed by a series of smaller and equal-size CSTRs [1,2]. Up to date, large-scale bacterial leaching of gold concentrates is mainly based on the activity of Acidithiobacillus ferrooxidans, Acidithiobacillus thiooxidans and Leptospirillum ferrooxidans. The process takes place through two general mechanisms: (i) the direct mechanism that accounts for the dissolution of reduced or partially reduced sulphur compounds (i.e. sulphide, elemental sulphur, and thiosulphate) by the action of the cells attached to the mineral particles, and (ii) the indirect mechanism, that accounts for the oxidation of the mineral by ferric ions [3,4]. In the indirect mechanism, the bacterial population oxidises the ferrous ions to ferric ions that in turn oxidise the mineral ∗ Corresponding author. Fax: +56-32-273-803. E-mail address: [email protected] (J.C. Gentina).

1369-703X/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.bej.2003.09.007

particles. In the case of pyrite biooxidation direct and indirect bacterial leaching can be described according to the following reactions: • Direct mechanism: 2FeS2 + 7O2 + 2H2 O ⇒ 2FeSO4 + 2H2 SO4

(1)

• Indirect mechanism: FeS2 + Fe2 (SO4 )3 ⇒ 3FeSO4 + 2S0

(2)

The elemental sulphur produced during the oxidation of pyrite by ferric ions is oxidised by attached cells. This step can be represented as follows: S0 + 1.5O2 + H2 O ⇒ H2 SO4

(3)

The ferrous ions produced according to Eqs. (1) and (2) are oxidised to ferric ions by the bacterial population, as shown in the reaction: 4FeSO4 + O2 + 2H2 SO4 ⇒ 2Fe2 (SO4 )3 + 2H2 O

(4)

Several authors have proposed kinetic models for the biooxidation of different sulphide minerals [5–9]. However, in few cases the mathematical characterisation includes the behaviour of free and adsorbed bacteria, and their relation

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R. Gonzalez et al. / Biochemical Engineering Journal 19 (2004) 33–42

Nomenclature A A0 CFe2+ CFe3+ 0 CFe 3+ CSO4 2− D DS EFeS2 Eh Eh0 f F k K KI MFeS2 0 MFeS 2 MT n R rpm SF ST T vL vS vSDM vSIM vvm V W X XS XSM Y YS

surface area (m2 ) surface area in the feed (m2 ) ferrous ion concentration (g l−1 ) ferric ion concentration (g l−1 ) ferric ion concentration in the feed (g l−1 ) sulphate concentration (g l−1 ) liquid dilution rate (=V/F) (per day) solids dilution rate (=MT /W) (per day) pyrite oxidation rest potential (mV) redox potential (mV) standard redox potential (mV) Faraday’s constant liquid flow (l per day) rate constant (g FeS2 l−1 mV−1 m−2 per day) affinity constant (g protein l−1 ) inhibition constant (g Fe3+ l−1 ) actual mass of pyrite in the reactor (g) mass of pyrite in the reactor in the absence of biooxidation (g) total mass of solids in the reactor (g) number of transferred electrons ideal gas constant revolutions per minute concentration of solids in the feed (g l−1 ) total concentration of solids (g l−1 ) absolute temperature (K) growth rate in the liquid (g protein l−1 per day) growth rate on the solid (g protein (g ore)−1 per day) rate of reaction by direct mechanism (g pyrite l−1 per day) rate of reaction by indirect mechanism (g pyrite l−1 per day) volumes of air per volume of liquid per minute volume of liquid (l) outlet solids mass flow rate (g per day) cell protein concentration in liquid phase (g protein l−1 ) cell protein concentration on solid (g protein (g ore)−1 ) maximum cell protein concentration on solid (g protein (g ore)−1 ) cell yield on ferrous iron (g protein (g Fe2+ )−1 ) cell yield on solid compounds (g protein (g oxidised sulphur–sulphide)−1 )

Greek letters µ specific growth rate in liquid phase (per day) µS specific growth rate on solid (per day) µSM maximum specific growth rate on solid (per day)

with the solubilisation of mineral particles: i.e. the growth of attached and suspended cells, the oxidation of ferrous ions, the interaction between ferric ions and the mineral, and the change in particle size. Undoubtedly, the availability of these kinetic models allows the optimisation of the process, including the configuration of a continuous biooxidation system. The objective of this work was to develop a mathematical model that represents the bacterial leaching of a gold concentrate in a CSTR, and its use in the determination of the optimal configuration of the continuous system.

2. Materials and methods 2.1. Microorganism and culture conditions A. ferrooxidans R-2, isolated at El Teniente Mine in Rancagua, Chile, and kindly supplied by Dr. Manuel Rodriguez, Catholic University of Chile, was pre-cultivated in 9 K medium [10] at 33 ◦ C and pH 1.5. The inoculum obtained was then adapted to grow in a modified 9 K medium in which the ferrous sulphate was replaced by a gold concentrate at a pulp density of 6%. The gold concentrate (Minera El Indio, Chile) contained 42 g Au/t, 42.8% pyrite (FeS2 ) and 40.7% enargite (Cu3 AsS4 ) with an elemental composition of 21.1% Cu, 22.6% Fe, 37.8% S, and 7.7% As, the rest being gangue. Mineral particles of two sizes were used: under 35 and 35–75 ␮m. 2.2. Culture system The experiments were conducted in a 5 l continuous stirred tank bioreactor with a working volume of 3 l. The reactor dimensions were 30 cm tall and 14 cm width and it had a rounded bottom. In order to favour the suspension of solids with minimum power consumption, a pumping up marine propeller of 8 cm diameter placed at 9 cm from the bottom of the bioreactor and operated at 860 rpm was used [11]. The aeration rate was 2 vvm, the temperature was 33 ◦ C, and the pH was controlled at 1.5 by the addition of either concentrated sulphuric acid or 5 N sodium hydroxide. Solid and liquid nutrients were continuously fed to the bioreactor. The dry gold concentrate was fed using a syringe pump (Sage Instruments, Cambridge, USA) adapted as metering solid feeder. Liquid medium (9 K without ferrous sulphate) was fed with a peristaltic pump (Masterflex, Cole-Parmer, Vernon Hills, IL). The liquid and solid feed rates were controlled in order to ensure 6% of solids in the feed. The suspension was withdrawn from the reactor by overflow. Each steady state was attained by inoculation of fresh medium and concentrate with adapted cells. The fermentor was initially operated batchwise. Continuous addition of the feed was started once the cells were actively growing. The existence of steady state was verified by measuring ferric iron and total cell concentrations.

R. Gonzalez et al. / Biochemical Engineering Journal 19 (2004) 33–42

2.3. Analytical methods Cell concentration was quantified indirectly by measurement of protein, using alkaline hydrolysis of cell envelopes and the Lowry method [12]. Protein of suspended cells was measured after removing mineral particles by centrifugation at 1000 rpm (77 g). Total protein was measured in a sample without removing the mineral particles [13]. Protein corresponding to attached cells was calculated subtracting the protein of suspended cells from the total protein. Ferrous iron and total iron (after reducing the ferric iron with hydroxylamine hydrochloride) was quantified by the o-phenanthroline method [14]. Ferric iron was estimated as the difference between ferrous and total iron. Sulphate ion was measured by a turbidimetric method [15]. The concentration of mineral particles was quantified by dry weight. Samples were centrifuged at 1000 rpm (77 g) and the solid was washed with acid water (pH 1.5) and dried at 105 ◦ C for 24 h. The concentration of solids inside the bioreactor was quantified by decanting all solids and measuring the volume and density of the sediment. This procedure was carried at every steady-state condition.

3. Development of the model The bacterial leaching of mineral particles involve the physical and chemical interaction between bacterial cells, mineral particles, and components of the liquid medium. The model here developed considers the direct and indirect action of bacterial cells in the solubilisation of mineral particles. Specific aspects or assumptions used in the development of the model are discussed below. 3.1. Experimental evidences Previous experiments performed in batch and continuous systems with A. ferrooxidans have shown a preferential solubilisation of pyrite and almost no solubilisation of enargite [16,17]. Additionally, ferrous iron was never present at levels higher than 1.5 ppm resulting in constant Eh values [16,17]. The concentration of ferrous and ferric iron and the Eh values, can be related by Nernst equation: 

CFe3+ RT Eh = Eh0 + (5) ln nf CFe2+ For the couple Fe3+ /Fe2+ , having an Eh0 of 0.77 V with respect to the hydrogen standard electrode, the magnitude of the Fe3+ /Fe2+ ratio is controlled by the low concentrations of Fe2+ that keep the Eh at nearly constant values. 3.2. Attachment of bacterial cells to mineral particles We have previously characterised the attachment of A. ferrooxidans R-2 to particles of this mineral using the Langmuir

35

isotherm [18]. Therefore, the relation between attached and suspended cells is represented by the following equation: X (6) XS = XSM K+X 3.3. Cell growth A. ferrooxidans is able to use both ferrous iron and reduced sulphur species as energy source. According to the mechanism described in Section 1, we will consider the growth of attached cells using S0 and S2− and the growth of suspended cells using Fe2+ . The growth rate of attached cells is a function of the specific growth rate and the concentration of attached cells: vS = µS XS

(7)

Note that the growth of attached cells will increase the levels of both attached and free cells. Furthermore, we have previously shown that the specific growth rate on S0 and S2− is a function of the ferric iron and CO2 concentrations, but independent of specific surface area [17]: 1 µS = µSM (8) 1 + (CFe3+ /KI ) µSM is a function of the partial pressure of CO2 in the air. The growth rate of suspended cells can be represented as follows: vL = µX

(9)

3.4. Solubilisation of mineral particles by the direct action of the cells Sulphide and elemental sulphur can be oxidised to sulphate by the direct action of attached cells. Considering Eq. (1), the following expression can be established for the rate of solubilisation of pyrite through the direct action of A. ferrooxidans cells: µ S X S ST vSDM = 1.873 (10) YS The coefficient of Eq. (10) is derived from the stoichiometry of reaction (1). 3.5. Solubilisation of mineral particles by the indirect action of the cells The indirect action of suspended cells involves the oxidation of ferrous ions to ferric ions, which can be represented as follows: dCFe3+ dC 2+ µX = − Fe = (11) dt dt Y The oxidation of mineral sulphides to elemental sulphur by ferric ions has been successfully modelled by the following expression [9]: vSIM = kA(Eh − EFeS2 )

(12)

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Considering constant shape and density factors for the mass of pyrite contained in each particle, the surface area can be expressed as a function of the mass of pyrite as follows:  A = A0

MFeS2

3.6. Mass balances Mass balances for individual species were used to represent the operation of the continuous biooxidation system. These include suspended and attached cells, ferric and ferrous ions and sulphate ions. The existence of steady state and homogeneous suspension was assumed in each case. The assumption of steady-state conditions implies dC/dt = 0 for cells, Fe2+ , Fe3+ and SO4 2− . Additionally, concentration of cells, ferrous iron and sulphate in the feed were considered to be zero and the ferrous concentration in the reactor was considered negligible, as stated in Section 3.1. With the above assumptions, the mass balances are as follows:

2/3 (13)

0 MFeS 2

or  A = A0 1 −

CFe3+

2/3 (14)

0 CFe 3+

Combining Eqs. (12) and (14):  vSIM = k Eh A0 1 −

CFe3+

2/3

• Mass balance for ferrous iron: µX = 1.398vSIM + 0.466vSDM Y

(15)

0 CFe 3+

6

(16)

6

3

3

4

2 1 0 0.00

2

5

4

3 0.02

0.04

0.06

0.08

0.10

0.12

3

4

5

2

X (g protein/L)

1

1

0

(A)

Xs·10 (g protein/ g ore)

Xs·103(g protein/g ore)

5

-1

X·30 (g protein/ L) ; µ s (d )

6

0 0.0

0.4

0.8

1.2

1.6

2.0

2.0

3.2

1.6

2.4

1.2

1.6

0.8

0.8

0.4

(B)

0.0

Ferric iron productivity (g/L.d)

4.0

CFe 3+ (g/L); CSO42- (g/L) Sulphate productivity (g/L.d)

Solids dilution rate (d-1)

0.0 0.0

0.3

0.6

0.9

1.2

1.5

Solids dilution rate (d-1) Fig. 1. Effect of solids dilution rate on cell growth and mineral solubilisation: (A) (䊊) cells suspended in the liquid, (䊐) cells attached to the solids, (䉫) specific growth rate on solid. Inserted graph: () attached vs. suspended cells. (B) (䊉) Sulphate concentration, (䊏) sulphate volumetric productivity, (䉬) ferric iron concentration, and (䉱) ferric iron volumetric productivity. Symbols represent experimental data and lines model predictions.

R. Gonzalez et al. / Biochemical Engineering Journal 19 (2004) 33–42

-3 Xs·10 (g protein/g ore)

5 -1

X·10 (g protein/L); µs (d )

12

12

4 3

10

10 8 6

Xs·10 (g protein/g ore)

6

37

8

4 2

6

3

0 0.0

0.5

1.0

2

1.5

2.0

4

X·10 (g /L)

1

2

0

0 0.0

(A)

0.5

1.0 Solids dilution rate (d-1)

1.5

2.0 2.0

-3 Xs·10 (g protein/g ore)

5 -1

4 3

5

5

4 3

4

2

3

1 0

2

3

X·10 (g protein/L); µ s (d )

6

6

0.0

0.5

1.0 X·10 (g protein/L)

1.5

2

2.0

1

1

0

(B)

Xs·10 (g protein/g ore)

6

0 0.0

0.1

0.2

0.3 0.4 0.5 Solids dilution rate (d-1)

0.6

0.7

0.8

10

6 6

7 6 5 4

5

5

4 3

4

2

3

1

3

0 0.0

3

Xs·10 (g protein/g ore)

-3 Xs·10 (g protein/g ore)

8

-1

X·10 (g protein/L); µs (d )

9

0.5

1.0 X·10(g protein/L)

1.5

2.0

2

2 1

1 0

(C)

0 0.0

0.2

0.4

0.6

0.8 1.0 1.2 Solids dilution rate (d-1)

1.4

1.6

1.8

2.0

Fig. 2. Influence of particle size, ferric iron concentration and CO2 levels on the relation of the solids dilution rate to cell growth. Model predictions are presented in panels A (decrease in particle size: from 53–75 to <35 mm), B (5.4 g l−1 Fe3+ in the feed), and C (enrichment of air with CO2 : 2%, v/v). Dotted lines represent the changed conditions of particle size, Fe3+ and CO2 . Solids lines represent the model prediction based on the control experiment run at the particle size of 53–75 mm, no Fe3+ in the feed, and incoming air without CO2 enrichment. For symbols in panels A–C, see Fig. 1A. Symbols are used for curve identification and do not represent experimental points. Panel D presents the experimental results at a solids dilution rate of 0.7 per day.

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R. Gonzalez et al. / Biochemical Engineering Journal 19 (2004) 33–42

Fig. 2. (Continued ).

The coefficient of Eq. (16) is derived from the stoichiometry of reactions (1) and (2). • Mass balance for ferric iron: µXV 0 (17) − 0.932vSIM V F(CFe3+ − CFe 3+ ) = Y The coefficient of Eq. (17) is derived from the stoichiometry of reaction (2). Combining (16) and (17) yields: 0 D(CFe3+ − CFe 3+ ) = 0.466vSIM + 0.466vSDM

(18)

4. Results and discussion 4.1. Determination of the model parameters The parameters of the model were obtained by non-linear regression of Eqs. (6), (8) and (15). In all cases the correlation coefficients were higher than 0.90. The values of the parameters are shown in Table 1. 4.2. Cell growth and mineral solubilisation

• Mass balance for sulphate: D(CSO4 2− ) = 1.602vSDM

(19)

The coefficient of Eq. (19) is derived from the stoichiometry of reaction (1): FX + WXS = µXV + µS XS MT

(20)

• Mass balance for suspended and attached cells: Where the left side represents the cells leaving the system and the right side the cell growth in the liquid phase and on solid particles. Using Eq. (16) and rearranging Eq. (20): DX − Y(1.398vSIM + 0.466vSDM ) = XS (µS − DS )ST (21) In the above equation, ST can be represented as ST = SF − 0.33CSO4 2− − CFe3+

(22)

Eqs. (6), (8), (10), (15), (18), (19), (21) and (22) compose the mathematical model that represents the continuous biooxidation system. The system of equations was solved numerically using the quasi-Newton method and quadratic extrapolation.

Fig. 1 shows cell growth and mineral solubilisation for different solids dilution rates. Panel A also includes the equilibrium curve between suspended and attached cells and the specific growth rate on solid. Cells concentration in the liquid phase decreases more dramatically with increasing solids dilution rates than attached cells do. The model represents very well this behaviour, as well as the saturation of solids surface with the increase in suspended cells concentration. Additionally, model predictions and experimental data show an increase in the specific growth rate on the solid for higher solids dilution rates. This is due to lower ferric ion concentrations in these conditions. Table 1 Parameters of the model Parameter

Value

YS (g protein/g S0 –S2− ) µSM (per day) KI (g Fe3+ l−1 ) Y (g protein (g Fe2+ )−1 ) XSM (g protein (g ore)−1 ) K (g protein l−1 ) k Eh A0 (g pyrite l−1 per day)

0.40 [17] 3.06 0.446 0.003 [20] 5.2 × 10−3 0.0187 1.378

R. Gonzalez et al. / Biochemical Engineering Journal 19 (2004) 33–42

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Fig. 3. Effect of particle size, ferric iron concentration and CO2 levels on mineral solubilisation. Model predictions are presented in panels A (decrease in particle size: from 53–75 to <35 mm), B (5.4 g l−1 Fe3+ in the feed), and C (enrichment of air with CO2 : 2%, v/v). Changes in particle size, Fe3+ and CO2 are represented by dotted lines in panels A–C. Solid lines represent the model prediction based on the control experiment run at particle size of 53–75 mm, no Fe3+ in the feed and incoming air without CO2 enrichment. For symbols in panels A–C, see Fig. 1B. Experimental results at a solids dilution rate of 0.7 per day are presented in panel D.

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R. Gonzalez et al. / Biochemical Engineering Journal 19 (2004) 33–42

Fig. 3. (Continued ).

The amount of sulphur and iron solubilised decreased at higher solids dilution rates as can be judged by the lower concentrations of sulphate and ferric iron (Fig. 1B). Volumetric productivities for the solubilisation of mineral particles (ferric iron and sulphate productivities) exhibited a maximum at solid dilution rates in the range of 0.5–0.7 per day. Again, the model fits the experimental data very well. 4.3. Effect of particle size, concentration of ferric ion, and carbon dioxide levels Figs. 2 and 3 illustrate the effect of particle size, concentration of ferric ion, and carbon dioxide levels on cell growth (Fig. 2) and mineral solubilisation (Fig. 3). The predictions of the model (parts (A) and (C) of Figs. 2 and 3) and the experimental results (part (D) of Figs. 2 and 3) have been included in these figures. The reduction of particle size brings about an increase in the specific surface that results in an increase in the concentration of attached cells and its ratio with respect to suspended cells, as can be seen in model predictions (Fig. 2A) and experimental data (Fig. 2D). However, there is no variation in the specific growth rate on the solid as it is not a function of the specific surface area. The observed increment in total cell concentration (suspended and attached cells) could be interpreted as that of continuous culture (control run) was limited by the energy source. Higher specific surface areas also favoured mineral solubilisation as can be judged by the higher concentrations and volumetric productivities for sulphate and ferric ion (Fig. 3A and D). This is due to an increase in the rate of reaction of both the direct and indirect mechanism (Eqs. (10) and (12)). In the case of the direct action, the higher rate is due to the increase in attached cell concentrations. It is worthwhile noting that model predictions (part (A) of Figs. 2 and 3) and experimental data (part (D) of Figs. 2 and 3) are in good agreement.

Addition of ferric iron had a negative effect on cell growth: there was a decrease in the concentration of suspended and attached cells as well as the specific growth rate on the solid (Fig. 2B and D). However, there was an increase in the ratio of attached to suspended cells due to the positive effect of ferric ion on cell attachment [18]. As would be expected, mineral solubilisation was also negatively affected by the addition of ferric iron to the feed stream. This was predicted by the model (Fig. 3B) and experimentally verified (Fig. 3D). Increase of CO2 content in the incoming air (up to 2%, v/v) had a positive effect on cell growth (suspended and attached cells and specific growth rate on the solid) but did not affect the ratio of attached to suspended cells (Fig. 2C and D). This could be interpreted as a limitation by carbon source (CO2 ) in addition to the already shown limitation by energy source (mineral) in the control run. Enrichment of incoming air with CO2 was also beneficial for the solubilisation of mineral particles (Fig. 3C and D). This is presumably due to higher attached cell concentrations and higher specific growth rate on the solid that in turn produce an increase in the rate of the direct mechanism. Again, the model predictions (part (C) of Figs. 2 and 3) agree very well with experimental results (part (D) of Figs. 2 and 3). 4.4. Optimal configuration of continuous biooxidation system Bioleaching is by definition an autocatalytic system where cells and ferric ions are reactants and products in the global reaction. The process can be simplified as follows: Cells + MeS + Fe3+ + 2O2 ⇒ Cells + Fe3+ + SO4 2− + Me2+ where MeS is a metal sulphide.

R. Gonzalez et al. / Biochemical Engineering Journal 19 (2004) 33–42

41

Fig. 4. Performance curves for a CSTR and a plug flow reactor (PFR) during the biooxidation of a gold concentrate. Panel A shows the fraction of iron solubilised and panel B the fraction of sulphide–sulphur solubilised. Dotted line corresponds to PFR and solid line to CSTR.

It is known that for autocatalytic reactions the CSTR is superior to the PFR at low conversions and that the opposite is true for high conversions. Thus it has been proposed that for these type of reactions at high conversions the optimal reactor configuration that minimises the residence time (or reaction volume) for a defined conversion is a CSTR followed by a PFR [19]. The model developed in this work allows representing the autocatalytic behaviour of a biooxidation system. Using this model, the performance curves for a CSTR and a PFR were obtained and are shown in Fig. 4. With these curves, the ideal configuration of a continuous system could be determined based on the desired fraction of sulphur or iron solubilised. As can be seen in the figure, up to an iron solubilisation of 18% the CSTR requires a smaller residence time, which for a fixed fluid flow implies smaller reaction volume; for higher solubilisations, the PFR will be preferable. So the best configuration would be a CSTR that gives 18% solubilisation followed by a PFR up to the desired conversion. This configuration can be achieved in practice using a primary CSTR followed by a series of smaller and equal-size CSTRs that

would reproduce the behaviour of the PFR. This is the actual configuration used in most commercial mineral biooxidation plants [1,2]. A similar reasoning could be applied to sulphur solubilisation.

Acknowledgements The authors wish to acknowledge support received from projects FONDECYT 1980335 and DGIP-UCV 203.780. One of them (RG) received a AGCI fellowship from the Chilean government. References [1] F. Acevedo, Electron. J. Biotechnol. 3 (2000) 184. http://www. ejbiotechnology.info ISSN 0717-3458. [2] J.A. Brierley, C.L. Brierley, Hydrometallurgy 59 (2001) 233. [3] K. Bosecker, FEMS Microbiol. Rev. 20 (1997) 591. [4] P.R. Norris, N.P. Burton, N.A.M. Foulis, Extremophiles 4 (2000) 71. [5] S. Asai, Y. Konishi, K. Yoshida, Chem. Eng. Sci. 47 (1992) 133.

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[6] F.K. Crundwell, Biotechnol. Bioeng. 71 (2000–2001) 255. [7] D.E. Dew, Comparison of performance for continuous bio-oxidation of refractory gold ore flotation concentrates, in: C.A. Jerez, T. Vargas, H. Toledo, J.V. Wiertz (Eds.), Biohydrometallurgical Processing, vol. II, University of Chile, Santiago, 1995, pp. 239–251. [8] Y. Konishi, Y. Takasaka, S. Asai, Biotechnol. Bioeng. 44 (1994) 667. [9] S. Nagpal, D. Dahlstrom, T. Olman, Biotechnol. Bioeng. 43 (1994) 357. [10] M.P. Silverman, D.G. Lundgren, J. Bacteriol. 77 (1959) 642. [11] R. Gonzalez, M.Sc. Thesis, School of Biochemical Engineering, Universidad Católica de Valpara´ıso, Valpara´ıso, Chile, 1999, p. 88. [12] G. Peterson, Anal. Biochem. 83 (1977) 346. [13] G. Karan, K.A. Natarajan, J.M. Modak, Hydrometallurgy 42 (1996) 169. [14] L. Herrera, P. Ruiz, J.C. Agillon, A. Fehrmann, J. Chem. Technol. Biotechnol. 44 (1989) 171.

[15] Instituto de Hidrolog´ıa de España, Análisis de Aguas Naturales Continentales, Centro de Estudios Hidrográficos, Madrid, 1980, p. 32. [16] C. Canales, F. Acevedo, J.C. Gentina, Process Biochem. 37 (2002) 1051. [17] R. Gonzalez, J.C. Gentina, F. Acevedo, Continuous biooxidation of a refractory gold concentrate, in: R. Amils, A. Ballester (Eds.), Biohydrometallurgy and the Environment Toward the Mining of 21st Century, Part A, Elsevier, Amsterdam, 1999, pp. 309–317. [18] R. Gonzalez, J.C. Gentina, F. Acevedo, Biotechnol. Lett. 21 (1999) 715. [19] O. Levenspiel, Chemical Reaction Engineering, 3rd ed., Wiley, New York, 1998, Chapter 6. [20] F. Acevedo, J.C. Gentina, R. Contreras, T. Muzzio, Kinetics of Thiobacillus ferrooxidans cultivation in defined media, in: R. BadillaOhlbaum, T. Vargas, L. Herrera (Eds.), Bioleaching: From Molecular Biology to Industrial Applications, University of Chile-UNDP, Santiago, 1991, pp. 79–88.