Continuous bioleaching of chalcopyrite using a novel extremely thermophilic mixed culture

Continuous bioleaching of chalcopyrite using a novel extremely thermophilic mixed culture

Int. J. Miner. Process. 66 (2002) 107 – 119 www.elsevier.com/locate/ijminpro Continuous bioleaching of chalcopyrite using a novel extremely thermophi...

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Int. J. Miner. Process. 66 (2002) 107 – 119 www.elsevier.com/locate/ijminpro

Continuous bioleaching of chalcopyrite using a novel extremely thermophilic mixed culture P. d’Hugues *, S. Foucher, P. Galle´-Cavalloni, D. Morin Biotechnology Unit, Environment and Process Division, Bureau de Recherches Ge´ologiques et Minie`res (BRGM), Avenue Claude Guillemin, B.P. 6009-45060 Orle´ans cedex 2, France Received 6 November 2001; received in revised form 20 December 2001; accepted 11 February 2002

Abstract Continuous bioleaching of chalcopyrite using a novel extremely thermophilic microbial mixed culture (78 jC) was carried out in a laboratory unit using one 50-l operating capacity tank and two 21-l total capacity tanks in series. The following operating conditions were studied: solids’ concentration, agitation – aeration, oxygen and carbon dioxide requirements, nutrient requirements, residence time and pH regulation. The general operability of the bioleach step was shown to be better than expected, with a copper recovery greater than 90% being achieved in a 5-day residence time using a continuous slurry feed at 12% (w/w) solids’ concentration. Nevertheless, some potentially limiting factors, such as bacterial sensitivity, nutrient concentrations, and oxygen transfer efficiency, were also identified. The work formed part of a European project (HIgh-temperature bacterial OXidation, HIOXR) for which the final industrial objective was to propose a complete new method for copper recovery on the basis of an economically and environmentally friendly process. D 2002 Elsevier Science B.V. All rights reserved. Keywords: bioleaching; extreme thermophile; chalcopyrite

1. Introduction Sulphide concentrate processing involving bioleaching in agitated tanks has emerged as a serious alternative to conventional treatment for mineral sulphides. Ten industrial plants using this technique have been commissioned in the last 18 years, of which nine

* Corresponding author. Fax: +33-2-38-64-36-80. E-mail address: [email protected] (P. d’Hugues). 0301-7516/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 7 5 1 6 ( 0 2 ) 0 0 0 0 4 - 2

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were built for a biooxidation pretreatment of refractory sulphidic gold ores or concentrates and the tenth was designed for extracting cobalt from a pyritic concentrate. The processes use mesophilic or moderate thermophilic mixed cultures at approximately 40– 50 jC. These types of bacterial culture, however, are inefficient for leaching chalcopyrite, the major copper sulphide of commercial interest. Bioleaching chalcopyrite with mesophilic cultures gives very slow kinetics and limited copper recovery (Norris, 1997; Third et al., 2000). Several studies carried out at laboratory scale have demonstrated that extreme thermophile cultures containing Sulfolobus-like organisms could successfully bioleach chalcopyrite concentrates (Marsh et al., 1983; Norris and Parrott, 1986; Duarte et al., 1993; Escobar et al., 1993; Clark and Norris, 1996). Although most of the work conducted before 1996 was focused on evaluating the potentialities of the thermophiles rather than developing new processes, some continuous bioleaching tests were nevertheless undertaken at laboratory scale with extremely thermophilic bacteria growing at 65 –70 jC. Tests carried out on gold-bearing sulphides using Sulfolobus acidocaldarius (Lindstro¨m and Gunneriusson, 1990; Sandstro¨m and Petersson, 1997) showed that this strain can achieve good biooxidation performances at 10% (w/w) solids and tolerate a feed solids of up to 20% (w/w) concentration. A Sulfolobus BC strain was also successfully used in a continuous culture for the bioleaching of a chalcopyrite concentrate at 70 jC (Le Roux and Wakerley, 1988); high copper recoveries were obtained although with a relatively long residence time (14 days). The preliminary studies at laboratory scale thus showed that extremely thermophilic bacteria were able to overcome the inhibition encountered with the mesophilic bacterial cultures (Norris, 1997) and that, consequently, biohydrometallurgical processing of chalcopyrite concentrates using these bacteria should be considered. However, it was also put forward that thermophilic bacteria could be more sensitive than mesophilic bacteria to stress generated by high solids’ concentrations and agitation (Escobar et al., 1993; Garcia et al., 1993; Clark and Norris, 1996; Norris, 1997). Moreover, due to a lower solubility of oxygen and carbon dioxide in water at elevated temperature, gas –liquid transfer limitation could have a negative impact on bioleaching efficiency (Boogerd et al., 1990; Boon and Heijnen, 1998). Since 1999, Billiton and Mintek/Bactech, two leading companies involved in the development of bioleaching processes in agitated tanks, have been publishing results concerning continuous bioleaching testwork on chalcopyrite concentrates with thermophilic bacteria (Dew et al., 1999; Miller et al., 1999; Gericke and Pinches, 1999; Gericke et al., 2001). Copper recoveries higher than 90% were achieved at 10% (w/w) solids’ concentration. Very little information on the operating conditions tested is available from the work carried out by Billiton (Dew et al., 1999), whereas detailed data is available from Mintek pilot studies carried out at only 70 jC (Miller et al., 1999; Gericke and Pinches, 1999; Gericke et al., 2001). In the framework of a European Union Research Programme, a consortium of European partners (BRGM, France; University of Warwick, UK; Boliden, Sweden; Cognis, Germany; MIRO, UK) conducted a project called HIgh-temperature bacterial OXidation (HIOXR) from 1996 to 1999. The project was dedicated to implementing a new thermophilic bacterial culture for bioleaching chalcopyrite concentrates.

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The major task of the HIOXR project, which is the work described in this paper, focused on continuous bioleach testing in a laboratory-scale unit with a new thermophilic culture able to bioleach chalcopyrite concentrate at 78 jC. It tested the following operating conditions: solids’ concentration, agitation – aeration, oxygen – carbon dioxide requirements, nutrient requirements, residence time, and pH control. The sensitivity of the culture to process breakthrough was also investigated as an important parameter of the process operability at industrial scale.

2. Materials and methods 2.1. Bacterial inoculum Paul Norris (University of Warwick, UK) provided the extremely thermophilic mixed culture used as an inoculum. This culture (named ICHT) originates from a hot spring in Iceland. Its optimum growth temperature is in the range between 75 and 85 jC. Its tolerance to copper was brought up to 45 g/l by serial culture with chalcopyrite and by gradually increasing concentrations of copper in solution. From 16S rRNA gene sequences determination, it was determined that the culture comprises a novel unclassified strain, a Sulfolobus B6-2-like organism and Acidianus infernus. 2.2. Sulphide materials The continuous study was carried out using a chalcopyrite concentrate originating from an old stockpile of the Kilembe mine (Uganda). The main chemical and physical characteristics of this copper sulphide concentrate are shown in Table 1. The modal composition determination of the concentrate gave a chalcopyrite content of approximately 77%, whereas pyrite was in the range of 7% to 8%. 2.3. Nutrients The standard composition of the nutritive medium used during testwork was in g/l: (NH4)2SO4 0.4; MgSO47H2O 0.50; K2HPO4 0.20. 2.4. Continuous mini pilot plant The laboratory-scale unit consisted of three tanks in series: one 50-l and two 21-l operating capacity tanks, all made of 304-l stainless steel and with a height:diameter ratio equal to 1. The pulp passed from one tank to the next by overflowing. The feed was made Table 1 Main chemical and physical characteristics of the copper sulphide concentrate Cu (%)

Fe (%)

Sj (%)

S2 (%)

SiO2 (%)

SO24

26.5

27.9

0.4

31.1

8.9

1.8

(%)

d80 (Am) 44

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up of a sulphide concentrate slurry with a high solids’ concentration and a concentrated nutritive medium solution. The operating temperature was maintained constant at 78 jC. The reactors were hermetically sealed at the top and connected to a condenser system to minimise evaporation. The bioleach slurry was mechanically stirred by a mixed (axial– radial) system mounted on a rotating shaft. Air enriched with carbon dioxide was injected beneath the turbine at the bottom of the tanks. The initial operating conditions were as follows: solids’ concentration 4% (w/w); air flow 1000 Nl/h in the first reactor and 600 Nl/h in the others; carbon dioxide concentration in the air of 1% (v/v); agitation rate of 350 rpm; residence time of 3 days in the first reactor. The pH value in the first tank was maintained above 1.3 by adjusting the pH in the feed slurry. Fourteen different operating conditions were investigated over a period of 6 months; they can be divided into three main periods corresponding to a stepwise increase in the solids’ concentration. All the tested operating conditions are presented in Table 2. 2.5. Analytical techniques Copper and total iron concentrations in solution were measured by atomic absorption spectrophotometry (Varian SpectrAA-300). The ferrous iron concentrations in the solution were monitored by titration with ceric sulphate and phenantroline – ferrous sulphate as indicator. The pH of the supernatant at ambient temperature was also measured with a WTW pH meter. Free bacteria in solution were counted using a Thoma counting cell under an optical microscope (  400). The oxygen and carbon dioxide concentrations in the inlet and outlet gas of each reactor were measured by means of a paramagnetic analyser and an infrared analyser, respectively (ADC 7000-Analytical Development). Dissolved oxygen measurements in the pulp were carried out using a Heito oxygen meter equipped with an electrochemical probe adapted to high temperature. When the unit was operating at steady

Table 2 Steady-state operating conditions used during the continuous culture testwork Stage 1—Period at 4% (w/w) solids (1) Initial operating conditions (2 – 3) Agitation speed from 350 to 400 rpm, then 450 rpm (4) Residence time from 3 to 2.5 days in first reactor (5 – 6) Air flow rate from 1000 to 1200 and 1500 Nl/h Stage 2—Period at 8% (w/w) solids (7) Solids’ concentration from 4% to 8% (8 – 9) O2 content in air from 21% to 25% (v/v), then 30% (v/v) (10) CO2 content from 1% to 2% (v/v) (11) Air flow rate at 1200 Nl/h and agitation speed at 350 rpm Stage 3—Period at 15 – 12% (w/w) solids (12) Solids’ concentration at 15% (w/w) (13) Solids’ concentration at 12% (w/w) (14) Increase in concentration of the nutrients (  4) and pH regulation.

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state, copper dissolution rates and final copper recovery were calculated by material balance using the feed flow of copper and the copper concentration in solution. The complete material balance was obtained by pulp sampling after each tank.

3. Results and discussion 3.1. Daily follow-up of the operation A general overview of the results obtained in terms of copper are presented in Fig. 1. The vertical lines separate the 14 sets of operating conditions tested, with the bold lines separating the three main stages. During the first stage tests at 4% (w/w) solids’ concentration, the copper concentration profiles show that a satisfactory steady state of the unit was obtained until Test 5. Problems of pulp feed and evaporation control were encountered with Test 6. Increasing the solids’ concentration from 4% to 8% (w/w) for the second stage tests resulted in a rapid increase in the copper concentration and a stabilisation of the unit after 20 days (Test 7). Nevertheless, problems of evaporation were encountered during Tests 8 and 9, which resulted in relative instability of the unit. The unit was at a satisfactory steady state during Tests 10 and 11. For the third stage at a much higher solids’ concentration (15% w/w), it was not possible to obtain a satisfactory steady state in the bioleaching unit. From the gas analysis results (Fig. 2), it was concluded that the abrupt change of the solids’ concentration from

Fig. 1. Dissolved copper concentration vs. time.

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Fig. 2. Oxygen and carbon dioxide uptake rates in the first reactor vs. time.

8% to 15% (w/w—Test 12) had a detrimental affect on both the bacterial activity and the oxidation efficiency. The solids’ concentration was, therefore, reduced to 12% (w/w—Test 13), but even then a satisfactory steady state in terms of copper concentration was not obtained before starting Test 14. After 160 h of culture, a failure in the air feed (lasting 10 h) had a dramatic detrimental effect on the bacterial culture in the first reactor. This effect, mainly observed through the gas analysis, was confirmed by microscopic observation. A new culture was, therefore, prepared using a batch procedure. A sample of the bioleached pulp previously collected and stored for 7 days at ambient temperature was used as an inoculum. In batch tests, the extreme thermophiles proved difficult to reactivated after a prolonged period (longer than 1 week) in nonoptimal conditions. Once the culture was established, however, the continuous feed of the unit started at 12% (w/w) solids and 10-day residence time. The residence time in the first tank was reduced in two steps; from 10 to 5 days and then from 5 to 2.5 days. Two weeks were necessary to reestablish a healthy ICHT culture. Gas analysis in real time was shown to be an efficient way to monitor the process. In particular, it was demonstrated that the sulphide oxidation efficiency, when using a bioleaching process at high temperature, was very sensitive to the smallest changes in operating conditions. In this case, the gas analysis system provided a much faster response than the follow-up of dissolved copper concentrations. The copper:iron grades ratio in the concentrate was estimated at 0.95 g of copper/1.0 g of iron. The stoichiometric ratio in chalcopyrite (77% of the concentrates) is 1.14 (g copper/g iron). The iron concentration in solution profile was very similar to that of copper (results not shown). During all the tests, the copper:iron ratio was observed to be greater

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than 1.4 in all the reactors. This result shows that at least 20% to 30% of the iron from the concentrate was involved in precipitate formation, depending on whether or not it could be assumed that the pyrite was totally degraded. The pH in each tank was not regulated by carbonate addition during the tests (except at the end of Test 14). A pH control of the feed pulp was carried out and was sufficient to maintain the pH in the first reactor between 1.5 and 1.3. 3.2. Tests at 4% (w/w) solids’ concentration The results obtained in terms of copper dissolution during the first stage bioleaching operation at 4% (w/w) solids’ concentration are presented in Fig. 3. The first operating parameter tested was the rotational speed of the agitation system in the first tank (Tests 1, 2, and 3). The aim was to determine whether the bacterial culture was sensitive to the shear effect or to the turbulence generated by the agitation system. Each of the three tests gave a similar copper dissolution efficiency of approximately 75% in the first tank, with a calculated residence time of 3 days in that tank, showing no major detrimental effect of the agitation at 4% (w/w) solids. The feed rate of the unit was then increased in order to reduce the residence time in the first reactor from 3 to 2.5 days (Test 4), following which the air flow rate in the first tank was increased in two steps from 1000 to 1500 Nl/h (Tests 5 and 6) in order to evaluate the oxygen availability influence. It had been feared that oxygen transfer into the pulp could

Fig. 3. Copper dissolution kinetics at 4% (w/w) solids.

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be a limiting factor at 80 jC, and no efficient probe able to measure dissolved oxygen at 80 jC was available at the time of the test. The results at 4% (w/w) solids showed very similar copper dissolution kinetics for the different operating conditions tested. The increase in agitation speed and airflow rates did not help to significantly improve the kinetics, and the decrease in residence time did not affect the overall copper dissolution kinetics. The best copper leaching rates obtained during this first stage were approximately 100 mg/l/h in the first reactor. At 4% (w/w) solids, a copper extraction of approximately 85% was obtained for the whole unit with a total 4-day residence time. As no major limitation (agitation and oxygen transfer efficiency) was identified at 4% (w/w) solids, it was decided to increase the solids’ concentration to 8% (w/w) in order to increase the amount of substrate available for the bacteria. 3.3. Tests at 8% (w/w) solids’ concentration The copper dissolution kinetics results obtained during the second stage bioleaching operation at 8% (w/w) solids are shown in Fig. 4. The solids’ concentration was first increased from 4% to 8% (w/w—Test 7) and then, assuming that the increase in sulphide substrate concentration would lead to an increase of the oxygen requirement, the air was enriched with pure oxygen in two steps from 21% to 25% and from 25% to 30% (Tests 8 and 9, respectively). It is known that the dissolved concentration of oxygen at equilibrium decreases with increasing temperature (Boogerd et al., 1990). Moreover, some authors also indicate that, at 80 jC, carbon dioxide limitation was more likely to occur than oxygen

Fig. 4. Copper dissolution kinetics at 8% (w/w) solids.

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limitation (Boogerd et al., 1990; Boon and Heijnen, 1998). Consequently, the influence of an increase in the carbon dioxide content from 1% to 2% (v/v) was also tested (Test 10). Reliable measurements of oxygen and carbon dioxide concentrations were obtained in both the inlet and outlet gas of each reactor for this 8% (w/w) solids’ concentration. Moreover, an oxygen probe capable of measuring the dissolved oxygen concentration in the pulp at 80 jC was developed and successfully used (Test 10). The increase of the oxygen content from 21% to 25% (v/v) in the feed gas phase of the first reactor at 8% (w/w) solids led to an improved bioleaching efficiency in the first reactor and a slightly faster overall kinetics; copper leaching rates increased from 170 mg/ l/h (Test 7) to 190 mg/l/h (Test 8). Once the air was enriched with oxygen, the dissolved oxygen concentration was measured in the range of 4 to 5 mg/l. This result demonstrates that there was no oxygen limitation in the first reactor. The increase in the carbon dioxide content from 1% to 2% (v/v) in the feed gas phase of the first reactor, however, did not improve the bioleaching efficiency (Test 10). As excessive hydrodynamic turbulence caused by agitation and aeration combined with an increase in the solids’ concentration is sometimes suspected as being a stress factor for the bacteria (Bailey and Hansford, 1993), the air flow rate and agitation speed in the first reactor were reduced (Test 11). Although these changes did not improve the overall copper solubilisation kinetics, a slight increase in bioleaching efficiency was noted in the first reactor; the copper leaching rates obtained during this test increased to 210 mg/l/h. This result showed that excessive agitation – aeration conditions combined with an increase in the solids’ concentration could lead to a limitation of the bioleaching efficiency. At 8% (w/w) solids’ concentration, a copper recovery of approximately 85% was obtained with a 5-day residence time. Considering the industrial objectives of the study, the solids’ concentration was increased from 8% to 15% (w/w—Test 12). 3.4. Tests at 15% and 12% (w/w) solids’ concentration The results obtained during the third stage continuous bioleaching operation at 15% and 12% (w/w) solids are presented in Fig. 5. At 15% (w/w) solids, a fall in the OUR from 820 mg/l/h to 450 mg/l/h was observed in 4 days (Fig. 2), showing that the abrupt change of the solids’ concentration had a detrimental effect on oxidation efficiency. A comparable fall was also observed with bacterial activity (CUR). The solids’ concentration was, therefore, reduced to 12% (w/w—Test 13). Some difficulties were encountered in obtaining steady state operating conditions at 12% solids. The ferrous iron concentration in solution was very unstable (results not shown) with very high ferrous iron concentrations being measured (over 5 g/l in the first reactor and up to 14 g/l in the third reactor). These concentrations are well known to have a very negative effect on the efficiency of the downstream process (solvent extraction). Moreover, it has recently been demonstrated that a ferrous iron concentration above 7.5 g/l could inhibit the growth of Acidianus brierleyi, an extreme thermophilic archaeon (Nemati and Harrison, 2000). The assessment of the bioleaching performances of Test 13 was, therefore, carried out in the last days of the test where the ferrous iron concentrations remained below 1 g/l in all the reactors. A copper extraction of 80% was obtained with a 5day residence time, with the copper leaching rate for the first reactor being evaluated at

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Fig. 5. Copper dissolution kinetics at 15 – 12% (w/w) solids.

approximately 270 mg/l/h. With 30% (v/v) oxygen in the air, the dissolved oxygen concentration was measured in the range of 3 to 4 mg/l, indicating no oxygen limitation. The limiting dissolved oxygen concentrations stated in the literature concerning bioleaching with mesophilic cultures are generally in the range 0.1 to 1.1 mg/l (Bailey and Hansford, 1993). As the nutrient concentration had been defined for a 4% (w/w) solids batch culture, it was suspected that the nutrient availability might have limited the bioleaching efficiency at 12% (w/w) solids’ concentration. A test was, therefore, carried out using a medium that was four times more concentrated in terms of nutrients (Test 14). This gave a significant improvement of the bioleaching efficiency with, in the first reactor, an increase of almost 10% of the copper leaching rate (up to 300 mg/l/h) and oxygen consumption (up to 810 mg/l/h). The improvement of bioleaching efficiency during Test 14 seemed to be linked to an enhancement of the bacterial productivity (increase in CUR). The bacterial concentration in solution also increased from 1.6  109 to 2.4  109 bacteria/ml. The ferrous iron concentrations in the reactors were more stable during Test 14 and most of the time remained below 1 g/l. The pH values in the first reactor during this test tended to fall below 1.3, and so a pH control to maintain a value above 1.4 was tested, first in the second reactor and then, a couple of days later, in the first reactor. No major influence was identified by gas analysis. Even though the increased ammonium in the more concentrated nutrient solution was liable to react with ferric iron to form jarosite precipitates, it can, nevertheless, be assumed that it helped to enhance ammonium availability for bacterial growth. Moreover, it seems

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that the increase in precipitate formation (results not shown), probably through jarosite formation, did not affect the overall efficiency of the process. When bioleaching chalcopyrite at high temperature, it was observed by Gomez et al. (1996) that strong jarosite precipitation at the surface of the mineral hindered the bacterial attack. Nevertheless, the positive or negative impact of this phenomenon in the bioleaching processes is still controversial and under discussion in the literature (Boon and Heijnen, 1993; Southam and Beveridge, 1993; Stott et al., 2001). The influence of precipitate formation is probably linked to the operating conditions in terms of sulphide mineral characteristics, solids’ concentration, agitation conditions, and ferric iron concentration. At 12% (w/w) solids, a copper recovery of 90% was obtained with a 5-day residence time. The calculated copper leaching rate was approximately 300 mg/l/h and was the best copper solubilisation rate obtained during the continuous operation. 3.5. Main technical results The critical technical information collected during the continuous bioleaching testwork can be summarised as follows. The optimal solids’ feed concentration was determined at 12% (w/w). This solids’ concentration is sufficient to provide a copper-rich solution fitted to the downstream steps. An increase of the value of this parameter may be expected if a tight control of the operating conditions and a gradual increase in the solids’ concentration can be ensured. The composition of the very simple nutrient medium was shown to be well adapted to the continuous operation at 12% (w/w) solids. The mechanical mixing system developed for bioleaching with mesophilic bacteria also proved suitable for bioleaching with thermophilic bacteria. Whereas the destruction of bacterial cells due to mechanical shearing was feared to be a major issue as regards thermophilic bacteria, no major detrimental effect due to the agitation system was observed during the testwork. Nonetheless, it was observed that hydrodynamic turbulence caused by agitation (and aeration) could still be a potentially limiting factor if they are combined with a relatively high solids’ concentration. The partial pressure of oxygen in the air (21%) was sufficient to provide a satisfactory oxidation rate of the sulphides. Although a higher oxygen concentration improved the bioleaching efficiency, the technical and economic implications of implementing an oxygen enrichment system were not examined. Bioleaching with the ICHT culture at high temperature was shown as being more sensitive to variations in operating conditions than bioleaching with mesophilic cultures. Finally, optimisation of the particle size distribution of the concentrate was not investigated; optimisation of this parameter could help to improve the bioleaching performances of HIOXR process. It has already been demonstrated that particle size distribution can dramatically affect the bioleaching efficiency when using extreme thermophilic bacteria (Lindstro¨m et al., 1993; Gericke and Pinches, 1999; Nemati et al., 2000).

4. Conclusion The work achieved during the HIOXR project has shown that the treatment of a chalcopyrite concentrate with an extreme thermophilic bacterial culture like the ICHT

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mixed culture is technically feasible. A copper recovery greater than 90% was achieved with a 5-day residence time at 12% (w/w) solids’ concentration. The copper leaching rate in the first reactor stage reached a value of approximately 300 mg/l/h with a residence time of 2.5 days. It is important to note that the bioleaching work carried out within the tests was focused on the performance of the first reactor of the unit. A better optimisation of the culture conditions in the other reactors would improve the overall bioleaching performances. A preliminary cost estimation, based on the experimental data obtained during this work and on results of an additional study on the downstream processing steps, shows that the ranges of both capital and operating costs are such that a plant using the process is likely to be profitable (Morin et al., 2001). The capital and operating costs per pound of pure copper produced, based on a 27,300 tonnes copper production/year, are 0.88 and 0.15 Euro/lb Cu, respectively. All the information that was acquired during the project in terms of technical equipment, operating experience, and simulation tools is now ready to be tested on real cases and for feasibility studies.

Acknowledgements This paper is published with the permission of BRGM as scientific contribution BRGM-CORP-001692. The HIOX project was funded by the European Commission (DG XII) under the Industrial and Materials Technologies Programme, contract no. BRPRCT96-0250. The authors are grateful to the partners of HIOX project for their technical and financial collaboration (Miro, University of Warwick, Cognis, Boliden, Normandy La Source, Rio Tinto, Anglo-American and Greenwich). The authors would also like to thank Patrick Skipwith for reviewing the English.

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