Leaching Chalcopyrite Concentrate with Oxygen and Sulfuric Acid Using a Low-Pressure Reactor

: This article presents a copper leaching process from chalcopyrite concentrates using a low-pressure reactor. The experiments were carried out in a 30 L batch reactor at an oxygen pressure of 1 kg/cm 2 and solid concentration of 100 g/L. The temperature, particle size and initial acid concentration were varied based on a Taguchi L9 experimental design. The initial and ﬁnal samples of the study were characterized by chemical analysis, X-ray diffraction and particle size distribution. The mass balance showed that 98% of copper was extracted from the chalcopyrite concentrate in 3 h under the following experimental conditions: 130 g/L of initial sulfuric acid concentration, temperature of 100 ◦ C, oxygen pressure of 1 kg/cm 2 , solid concentration of 100 g/L and particle size of − 105 + 75 µ m. The ANOVA demonstrated that temperature had the greatest inﬂuence on copper extraction. The activation energy was 61.93 kJ/mol. The best ﬁt to a linear correlation was the chemical reaction equation that controls the kinetics for the leaching copper from chalcopyrite. The images obtained by SEM showed evidence of shrinking in the core model with the formation of a porous elemental sulfur product layer.


Introduction
Chalcopyrite is the most abundant sulfide copper mineral in the Earth's crust. Generally, it is associated with other compounds such as galena, sphalerite, pyrite, arsenic, antimony or bismuth sulfides; moreover, it is often bonded with valuable metals such as silver and gold.
From an environmental and economic perspective, further technological developments for obtaining high-grade copper in an efficient and cost-effective manner are desirable. Today, companies such as Beijing Nonferrous Metal, JX Nippon Mining & Metals, Freeport McMoran, Freeport Minerals, Phelps Dodge, Outotec, BHP Billiton, etc. are investing in hydrometallurgical research because of the potential associated economic benefits [1].
Specifically, hydrometallurgical processes have a series of advantages in comparison to pyrometallurgical processes, for example, the required plant capacity is smaller (<10,000 t/y of copper), there is no need for an acid plant, no dust is emitted, etc.
Hydrometallurgical pilot plant projects such as Outotec, Galvanox, Activox and AAC/UBC have implemented some of the latest technology for mineral leaching, and several demo plants have

Material and Equipment
The experiments were carried out in a stainless steel 316 L closed reactor having a volume of 30 liters and being equipped with an agitation system with 4 baffles, a security valve calibrated at 2 kg/cm 2 , a rupture disc calibrated at 3 kg/cm 2 , a pressure transmitter with a chemical seal and a resistance temperature detector (RTD) connected to a data logger. Also, the reactor had a controlled cooling-heating jacket. Figure 1 shows an image of the reactor.

Material and Equipment
The experiments were carried out in a stainless steel 316 L closed reactor having a volume of 30 liters and being equipped with an agitation system with 4 baffles, a security valve calibrated at 2 kg/cm 2 , a rupture disc calibrated at 3 kg/cm 2 , a pressure transmitter with a chemical seal and a resistance temperature detector (RTD) connected to a data logger. Also, the reactor had a controlled cooling-heating jacket. Figure 1 shows an image of the reactor. The chalcopyrite concentrate was supplied by Peñoles (Mexico). Samples of the concentrate were characterized by X-ray diffraction (XRD, Panalytical, Empyrean model), chemical analysis (CA, PerkinElmer 8300, LECO SC230DR) and a backscattered electron (BSE) module in a scanning electron microscope (SEM, FEI, Quanta600 model) for a wider range of the mineralogical species. The chemical analysis is presented in Table 2. The carbonate content was calculated with the difference of total and organic carbon. Table 3 shows the mineralogical reconstruction via XRD and CA expressed in terms of weight percentage (Wt.%). The mineralogy species obtained by BSE-SEM are shown in Table 4 in terms of weight percentage (Wt.%).   The chalcopyrite concentrate was supplied by Peñoles (Mexico). Samples of the concentrate were characterized by X-ray diffraction (XRD, Panalytical, Empyrean model), chemical analysis (CA, PerkinElmer 8300, LECO SC230DR) and a backscattered electron (BSE) module in a scanning electron microscope (SEM, FEI, Quanta600 model) for a wider range of the mineralogical species. The chemical analysis is presented in Table 2. The carbonate content was calculated with the difference of total and organic carbon. Table 3 shows the mineralogical reconstruction via XRD and CA expressed in terms of weight percentage (Wt.%). The mineralogy species obtained by BSE-SEM are shown in Table 4 in terms of weight percentage (Wt.%).  Then, the chalcopyrite concentrate was fractionated to different sizes in a Tyler RO-TAP ® Sieve Shaker using −74, −105 + 74 and −149 + 105 µm. All fractions were characterized, and no significant variation was observed in the mineralogical composition and chemical analysis. The particle size Metals 2019, 9, 189 5 of 16 distribution of the residues was measured in a Horiba LA 950 V2, which expressed the results in terms of the equivalent spherical diameter.

Experimental Method
To clarify the effects of particle size, temperature and initial sulfuric acid concentration on copper extraction, a Taguchi 3 3 experimental design was employed. In addition, a tenth test was done using different temperatures to calculate the activation energy. The following experimental conditions were constant: residence time (7 h), oxygen pressure (1 kg/cm 2 ), solid concentration (100 g/L) and agitation velocity (550 RPM). Table 5 shows the experimental design. The experimental procedure began with the addition of hot water (80 • C) to the reactor and the initiation of the agitation system, which was set at a low revolution speed; then, the chalcopyrite concentrate was fed into the reactor, followed by sulfuric acid. After the addition of these materials, a 2 min air purge was performed; then, the reactor was closed and pressurized to 1 kg/cm 2 with medicinal oxygen. The agitation velocity was set at 550 RPM, and the data logger was then turned on to start recording data.
To determine the kinetics of the copper leaching process, 100 mL samples were taken from a lateral valve of the reactor at different time intervals during the test.

Thermodynamics
The thermodynamics of copper sulfide leaching are based on the interaction of the elements required to carry out the decomposition of chalcopyrite. The main reactions that govern the leaching of copper concentrates are shown as follows: The Pourbaix diagrams in Figure 2 show that a low pH is required to keep copper and iron in sulfate solution. In addition, to ensure that ferric ions are present in the solution, the oxide potential must be above 0.57 V (SHE). This step enables indirect leaching via reaction 2, wherein the oxidation-reduction cycle of iron facilitates the decomposition of chalcopyrite. The Pourbaix diagrams were calculated with the software HSC 8.

Thermodynamics
The thermodynamics of copper sulfide leaching are based on the interaction of the elements required to carry out the decomposition of chalcopyrite. The main reactions that govern the leaching of copper concentrates are shown as follows: CuFeS2 + 2.5O2 + H2SO4 = CuSO4 + FeSO4 + H2O + S° CuFeS2 + 2Fe2(SO4)3 = CuSO4 + 5FeSO4 + 2S° 4FeSO4 + O2 + 2H2SO4 = 2Fe2(SO4)3 + 2H2O (1) (2) (3) The Pourbaix diagrams in Figure 2 show that a low pH is required to keep copper and iron in sulfate solution. In addition, to ensure that ferric ions are present in the solution, the oxide potential must be above 0.57 V (SHE). This step enables indirect leaching via reaction 2, wherein the oxidationreduction cycle of iron facilitates the decomposition of chalcopyrite. The Pourbaix diagrams were calculated with the software HSC 8.

Extraction and Chemical Analysis
The results of the experiment show that the main influential variables in the leaching process were temperature and initial sulfuric acid concentration. Particle size did not significantly affect the process. The results of copper extraction versus time are presented in Figure 3.
The test number 5 presented the best results according to the mass balance. Under the corresponding conditions, 97.99% of copper was extracted in 3 h of reaction. The solid shrink was 61.8% (Wt.%), and the oxygen consumption was 0.662 g O2/g Cu fed. The density of the final solution was 1.15 g/mL, and a final oxidation-reduction potential (ORP) of 0.483V was measured in the suspension with a calomel electrode (Hg/Hg2Cl2).

Extraction and Chemical Analysis
The results of the experiment show that the main influential variables in the leaching process were temperature and initial sulfuric acid concentration. Particle size did not significantly affect the process. The results of copper extraction versus time are presented in Figure 3.
The test number 5 presented the best results according to the mass balance. Under the corresponding conditions, 97.99% of copper was extracted in 3 h of reaction. The solid shrink was 61.8% (Wt.%), and the oxygen consumption was 0.662 g O 2 /g Cu fed. The density of the final solution was 1.15 g/mL, and a final oxidation-reduction potential (ORP) of 0.483V was measured in the suspension with a calomel electrode (Hg/Hg 2 Cl 2 ).
Notably, different authors have reported percentages of copper extraction from chalcopyrite of 70% [11], 65% [12], 60% [13], 83% [14] and up to 95% [15]; in addition to 95% via the arbiter process, 98% via the Freeport McMoran method, 97-98% via the Activox process, 98% via the Albion process and 95% via the Galvanox process [1]. Metals 2019, 9, x 9 of 19 The test 5 was carried out at 100 °C with an initial sulfuric acid concentration of 130 g/L; this concentration of sulfuric acid was sufficient for reaction with species and to keep the iron in solution. Table 6 presents the CA of the residues and the solution along with the percentages of elemental distribution in the liquid phase that were obtained from the mass balance. Table 6. Chemical analysis of the test 5 residue (Wt.%), chemical analysis of the solution (g/L) and the elemental distribution in the liquid phase (%) of the leaching process.

Element
Residue The leaching solution contained a high percentage of zinc, copper and iron because of the solubility of these elements in the utilized sulfate medium (given the temperature and acid concentration). In a global process view, it is important to consider that the solution could be treated in a solvent extraction and electrowinning stages for the production of electrolytic copper. The raffinate from solvent extraction could be neutralized with calcium carbonate to precipitate ferric ions, zinc, arsenic and minor elements; then, the solution could be recycled to the direct leaching stage.
The iron in the residue mainly corresponded with pyrite, which requires higher temperature and pressure for decomposition. Table 7 shows the species present in the solid phase in terms of weight percentages, including elemental sulfur (64.1%), anglesite (19.3%), silica (5%), pyrite (5.7%), unreacted chalcopyrite (3.23%) and gypsum (2.3%). The test 5 was carried out at 100 • C with an initial sulfuric acid concentration of 130 g/L; this concentration of sulfuric acid was sufficient for reaction with species and to keep the iron in solution. Table 6 presents the CA of the residues and the solution along with the percentages of elemental distribution in the liquid phase that were obtained from the mass balance. The leaching solution contained a high percentage of zinc, copper and iron because of the solubility of these elements in the utilized sulfate medium (given the temperature and acid concentration). In a global process view, it is important to consider that the solution could be treated in a solvent extraction and electrowinning stages for the production of electrolytic copper. The raffinate from solvent extraction could be neutralized with calcium carbonate to precipitate ferric ions, zinc, arsenic and minor elements; then, the solution could be recycled to the direct leaching stage.
The iron in the residue mainly corresponded with pyrite, which requires higher temperature and pressure for decomposition. Table 7 shows the species present in the solid phase in terms of weight percentages, including elemental sulfur (64.1%), anglesite (19.3%), silica (5%), pyrite (5.7%), unreacted chalcopyrite (3.23%) and gypsum (2.3%). From an economic perspective, the recovery of valuable minerals in residues following the hydrometallurgical treatment of chalcopyrite concentrates is important. The high content of elemental sulfur could reduce the profitability of recovering valuable metals by cyanidation or melting processes. Table 8 presents the final particle size distribution of the P5 test. As expected, the particle size decreased considerably from 100% +74 µm to 90% −16.92 µm because of the leaching of chalcopyrite particles and the formation of elemental sulfur.   From an economic perspective, the recovery of valuable minerals in residues following the hydrometallurgical treatment of chalcopyrite concentrates is important. The high content of elemental sulfur could reduce the profitability of recovering valuable metals by cyanidation or melting processes. Table 8 presents the final particle size distribution of the P5 test. As expected, the particle size decreased considerably from 100% +74 μm to 90% −16.92 μm because of the leaching of chalcopyrite particles and the formation of elemental sulfur. 11.00 6.99 Figure 4 shows electron images obtained by SEM-BSE of unreacted chalcopyrite and galena particles, which were identified by SEM-EDS. The porous layer of elemental sulfur surrounding the particles can be observed. These particles are indicative of the shrinking core model, wherein a layer of elemental sulfur is formed as a product. However, the high extraction percentage of copper obtained in a short time (3 h) indicates that the elemental sulfur layer does not passivate the leaching of the chalcopyrite concentrate. Figure 5 shows the microstructure and the X-ray mapping by SEM-EDS for sulfur, copper and iron of the unreacted chalcopyrite particle.     In Figure 6, the temperature profile, in addition to the partial and accumulated oxygen consumption, are shown. At 2 h, oxygen consumption reaches its maximum and then decreases after this point. In Figure 6, the temperature profile, in addition to the partial and accumulated oxygen consumption, are shown. At 2 h, oxygen consumption reaches its maximum and then decreases after this point. A similar finding was observed for the iron concentration in solution; ferrous ions reached their maximum concentration at 2 h and then decreased. This could explain the chalcopyrite leaching as a two steps process.
Specifically, the first step occurred within the initial 2 h of the test, wherein most of the chalcopyrite was decomposed at temperatures above 95 °C. The second step occurred when the remaining ferrous ions were oxidized to ferric iron. Depending on the next stages, which are related with the liquid phase (iron purification or solvent extraction), the Fe 3+ /Fe 2+ relation must be as high as possible to ensure that the process is not affected. In Figure 7, the concentration profile of iron and ferrous ions during leaching is shown. A similar finding was observed for the iron concentration in solution; ferrous ions reached their maximum concentration at 2 h and then decreased. This could explain the chalcopyrite leaching as a two steps process.
Specifically, the first step occurred within the initial 2 h of the test, wherein most of the chalcopyrite was decomposed at temperatures above 95 • C. The second step occurred when the remaining ferrous ions were oxidized to ferric iron. Depending on the next stages, which are related with the liquid phase (iron purification or solvent extraction), the Fe 3+ /Fe 2+ relation must be as high as possible to ensure that the process is not affected. In Figure 7, the concentration profile of iron and ferrous ions during leaching is shown.
A similar finding was observed for the iron concentration in solution; ferrous ions reached their maximum concentration at 2 h and then decreased. This could explain the chalcopyrite leaching as a two steps process.
Specifically, the first step occurred within the initial 2 h of the test, wherein most of the chalcopyrite was decomposed at temperatures above 95 °C. The second step occurred when the remaining ferrous ions were oxidized to ferric iron. Depending on the next stages, which are related with the liquid phase (iron purification or solvent extraction), the Fe 3+ /Fe 2+ relation must be as high as possible to ensure that the process is not affected. In Figure 7, the concentration profile of iron and ferrous ions during leaching is shown.

Statistical Analysis
As mentioned in Table 5, this study is based on a modified Taguchi L9 experimental design with three levels for three independent variables or parameters. An additional experiment was realized (Test 10): analysis of variance (ANOVA) of the experimental tests data at different conditions was used to evaluate the effect of each individual variable. The results of Test 10 were not included in ANOVA due the difference of temperature between the lowest and the average and the small amount of Cu extraction observed. Table 9 shows the effects of each parameter using the ANOVA module of the Minitab 15 software. The table shows the values of degree freedom (DF), sum of squares (SS), media of squares (MS), Fisher ratio (F), probability level (Prob Level) and the probability that a false null hypothesis can be rejected (Power) with a 95% confidence level (α = 0.05). According to F, Prob Level and Power values, ANOVA shows that under the studied conditions, temperature is the most important factor for copper extraction and oxygen consumption. The results also indicated that within the analyzed range, the other two variables studied (initial acid and particle size) did not have a statisticallysignificant effect.

Statistical Analysis
As mentioned in Table 5, this study is based on a modified Taguchi L9 experimental design with three levels for three independent variables or parameters. An additional experiment was realized (Test 10): analysis of variance (ANOVA) of the experimental tests data at different conditions was used to evaluate the effect of each individual variable. The results of Test 10 were not included in ANOVA due the difference of temperature between the lowest and the average and the small amount of Cu extraction observed. Table 9 shows the effects of each parameter using the ANOVA module of the Minitab 15 software. The table shows the values of degree freedom (DF), sum of squares (SS), media of squares (MS), Fisher ratio (F), probability level (Prob Level) and the probability that a false null hypothesis can be rejected (Power) with a 95% confidence level (α = 0.05). According to F, Prob Level and Power values, ANOVA shows that under the studied conditions, temperature is the most important factor for copper extraction and oxygen consumption. The results also indicated that within the analyzed range, the other two variables studied (initial acid and particle size) did not have a statistically-significant effect.  Figure 8 shows the correlations of temperature, initial acid concentration and particle size with percentage of copper extraction. As observed, temperature had the greatest effect on the process of leaching copper from chalcopyrite concentrates. Figure 9 shows the correlations of temperature, initial acid concentration and particle size with oxygen consumption. As expected, temperature once again had the greatest effect on oxygen consumption, whereas particle size and initial acid concentration had no clear influence.
* α = 0.05. Figure 8 shows the correlations of temperature, initial acid concentration and particle size with percentage of copper extraction. As observed, temperature had the greatest effect on the process of leaching copper from chalcopyrite concentrates. Figure 9 shows the correlations of temperature, initial acid concentration and particle size with oxygen consumption. As expected, temperature once again had the greatest effect on oxygen consumption, whereas particle size and initial acid concentration had no clear influence. Figure 8. Correlations of temperature, initial acid concentration and particle size with extraction of copper. Figure 9. Correlations of temperature, initial acid concentration and particle size with oxygen consumption.
According to the above results the copper extraction can be calculated with the following multiple regression equation: Copper extraction (%) = − 146.382 + 2.253 T + 0.0957 Acid − 0.0554 Size (4) Figure 8. Correlations of temperature, initial acid concentration and particle size with extraction of copper. Figure 8 shows the correlations of temperature, initial acid concentration and particle size with percentage of copper extraction. As observed, temperature had the greatest effect on the process of leaching copper from chalcopyrite concentrates. Figure 9 shows the correlations of temperature, initial acid concentration and particle size with oxygen consumption. As expected, temperature once again had the greatest effect on oxygen consumption, whereas particle size and initial acid concentration had no clear influence. Figure 8. Correlations of temperature, initial acid concentration and particle size with extraction of copper. Figure 9. Correlations of temperature, initial acid concentration and particle size with oxygen consumption.
According to the above results the copper extraction can be calculated with the following multiple regression equation: Copper extraction (%) = − 146.382 + 2.253 T + 0.0957 Acid − 0.0554 Size (4) Figure 9. Correlations of temperature, initial acid concentration and particle size with oxygen consumption.
According to the above results the copper extraction can be calculated with the following multiple regression equation: Copper extraction (%) = −146.382 + 2.253 T + 0.0957 Acid − 0.0554 Size (4) where T is the temperature expressed in • C; Acid is the initial acid concentration in g/L and size is the particle size of the chalcopyrite concentrate in µm.

Effect of Temperature
As observed in Figure 3, the different tests can be categorized into three groups with differing rates of reaction that were principally determined by temperature. The tests of the first group were carried out at 100 • C (tests 3, 5 and 7) and resulted in 97% copper extraction within 3 h. The second group (tests 2, 4 and 9) resulted in 55-77% copper extraction within 7 h. The tests of the final group were carried out at 80 • C (tests 1, 6 and 8) and resulted in 10-20% copper extraction within 7 h.
To highlight the required temperature for activating the decomposition of chalcopyrite concentrates, test 5 was replicated with a slowly-increasing temperature. Figure 10 shows the percentage of copper extraction and temperature versus time. As observed, the temperature had to reach 92-95 • C to decompose the chalcopyrite in the concentrate.

Effect of Particle Size
In the three groups that formed with respect to different reaction temperatures (Figure 3), the reactions were also faster for concentrates of small particle size; nevertheless, in the group that reacted at 100 • C, the −149 + 105 µm chalcopyrite concentrate reacted more rapidly than the concentrate filtered by −75 µm. The reactions in this group could have been slowed by the heat transfer from the jacket of the reactor to the suspension, resulting in different rates of reaction.
Thus, even when the chalcopyrite concentrate was a larger particle size (−149 + 105 µm), the copper extraction was not affected at 100 • C, and a similar level of extraction of copper was obtained. group (tests 2, 4 and 9) resulted in 55-77% copper extraction within 7 h. The tests of the final group were carried out at 80 °C (tests 1, 6 and 8) and resulted in 10-20% copper extraction within 7 h.
To highlight the required temperature for activating the decomposition of chalcopyrite concentrates, test 5 was replicated with a slowly-increasing temperature. Figure 10 shows the percentage of copper extraction and temperature versus time. As observed, the temperature had to reach 92-95 °C to decompose the chalcopyrite in the concentrate.

Effect of Particle size
In the three groups that formed with respect to different reaction temperatures (Figure 3), the reactions were also faster for concentrates of small particle size; nevertheless, in the group that reacted at 100 °C, the −149 + 105 μm chalcopyrite concentrate reacted more rapidly than the concentrate filtered by −75 μm. The reactions in this group could have been slowed by the heat transfer from the jacket of the reactor to the suspension, resulting in different rates of reaction.
Thus, even when the chalcopyrite concentrate was a larger particle size (−149 + 105 μm), the copper extraction was not affected at 100 °C, and a similar level of extraction of copper was obtained.

Effect of Acidity
The initial sulfuric acid concentration in the suspension must be calculated based on the stoichiometry of the compounds that consume acid and the final acid concentration required to keep iron and copper in solution.
According to Figure 8, the initial sulfuric acid concentration is not significant for copper extraction. But in other exploratory tests carried out with the same copper concentrates at 100 °C under the same conditions, the suspension was found to require at least 15 g/L of sulfuric acid in solution to avoid the precipitation of iron as plumbojarosite in the residue. Thus, to prevent any problems in the recovery of valuable metals resulting from the presence of elemental sulfur and plumbojarosite in residues, and to avoid any potential impact on the profitability of operations, the initial sulfuric acid concentration is important to consider. 3Fe2(SO4)3 + 12H2O + PbSO4 = 2Pb0.5Fe3(SO4)2(OH)6 + 6H2SO4 (4) Figure 11 shows the iron and acid concentrations in solution, the percentage of plumbojarosite in the residue and the percentage of copper extraction versus time in an exploratory test. The initial

Effect of Acidity
The initial sulfuric acid concentration in the suspension must be calculated based on the stoichiometry of the compounds that consume acid and the final acid concentration required to keep iron and copper in solution.
According to Figure 8, the initial sulfuric acid concentration is not significant for copper extraction. But in other exploratory tests carried out with the same copper concentrates at 100 • C under the same conditions, the suspension was found to require at least 15 g/L of sulfuric acid in solution to avoid the precipitation of iron as plumbojarosite in the residue. Thus, to prevent any problems in the recovery of valuable metals resulting from the presence of elemental sulfur and plumbojarosite in residues, and to avoid any potential impact on the profitability of operations, the initial sulfuric acid concentration is important to consider. A comparison of the copper extractions with low and high acid concentrations in the reaction solution shows that passivation was promoted by a lack of acid in the solution, which, in turn, produced a plumbojarosite layer on the chalcopyrite surface (see Figure 12). Figure 11. Results of an exploratory test with a low acid concentration in the reaction solution. Figure 11. Results of an exploratory test with a low acid concentration in the reaction solution.
A comparison of the copper extractions with low and high acid concentrations in the reaction solution shows that passivation was promoted by a lack of acid in the solution, which, in turn, produced a plumbojarosite layer on the chalcopyrite surface (see Figure 12).  The mass balance demonstrated that the ratio of sulfuric acid consumed (real) to that calculated by stoichiometry is given by equation 5.

Kinetics
To determine the kinetics of the leaching process described herein, the shrinking core (product layer) model was applied to the real batch process considering the scanning electron microscopy (SEM) images of partly-reacted particles (Figure 4). The controlling step of the reaction was based on a comparison of the experimental data and assessment of which controlling model gives the best fit to the data. If the chemical reaction mechanism is assumed to be the controlling step, 1 − (1 − X) 1/3 (X = conversion) is plotted as a function of time for the experimental data, and if the plot gives a linear correlation, the assumption is considered to be correct. Analogously, 1 − 3(1 − X) 2/3 + 2(1 − X) (diffusion as controlling mechanism) can be plotted for the data when a non-porous product layer is formed [16,17].
The results show that the chemical reaction is the controlling stage for leaching copper from chalcopyrite concentrate. Figure 13 shows the linear regressions of the 9 tests. The equation of the chemical reaction as the controlling step is also shown as follows (Equation 6). The mass balance demonstrated that the ratio of sulfuric acid consumed (real) to that calculated by stoichiometry is given by Equation (6)

Kinetics
To determine the kinetics of the leaching process described herein, the shrinking core (product layer) model was applied to the real batch process considering the scanning electron microscopy (SEM) images of partly-reacted particles (Figure 4). The controlling step of the reaction was based on a comparison of the experimental data and assessment of which controlling model gives the best fit to the data. If the chemical reaction mechanism is assumed to be the controlling step, 1 − (1 − X) 1/3 (X = conversion) is plotted as a function of time for the experimental data, and if the plot gives a linear correlation, the assumption is considered to be correct. Analogously, 1 − 3(1 − X) 2/3 + 2(1 − X) (diffusion as controlling mechanism) can be plotted for the data when a non-porous product layer is formed [16,17].
The results show that the chemical reaction is the controlling stage for leaching copper from chalcopyrite concentrate. Figure 13 shows the linear regressions of the 9 tests. The equation of the chemical reaction as the controlling step is also shown as follows (Equation (7)).
where t is time and k is the apparent velocity constant. Table 10 shows the apparent velocity constants (k) and the determination coefficient (R 2 ) of the linear regression of the chemical reaction model for all 10 tests. To calculate the activation energy, logarithms were applied to the Arrhenius equation (Equation (8)) to reformulate it as a linear equation. Accordingly, the logarithm of the apparent velocity constants versus the inverse of temperature of tests P3, P8, P9 and P10 is shown in Figure 14.
An activation energy of 61.93 kJ/mol was determined from the slope of the straight line in Figure 14. According to Habashi (1999), a chemically-controlled process is usually greater than 41.8 kJ/mol [18]. where t is time and k is the apparent velocity constant.  Table 10 shows the apparent velocity constants (k) and the determination coefficient (R 2 ) of the linear regression of the chemical reaction model for all 10 tests.
To calculate the activation energy, logarithms were applied to the Arrhenius equation (Equation  7) to reformulate it as a linear equation. Accordingly, the logarithm of the apparent velocity constants versus the inverse of temperature of tests P3, P8, P9 and P10 is shown in Figure 14.  An activation energy of 61.93 kJ/mol was determined from the slope of the straight line in Figure  14. According to Habashi (1999), a chemically-controlled process is usually greater than 41.8 kJ/mol [18].
In order to compare the activation energy with similar processes, Table 11 shows the results reported by some authors in literature. It can be observed that the activation energy for processes that use sulfuric acid, ferric ions and/or oxygen is similar to the obtained in this work that use sulfuric acid and oxygen. In the work reported by Padilla et al (2008), they use also only sulfuric acid and oxygen in a pressure reactor and a copper extraction of 95% was obtained at an oxygen pressure of 5   Table 10 shows the apparent velocity constants (k) and the determination coefficient (R 2 ) of the linear regression of the chemical reaction model for all 10 tests.
To calculate the activation energy, logarithms were applied to the Arrhenius equation (Equation  7) to reformulate it as a linear equation. Accordingly, the logarithm of the apparent velocity constants versus the inverse of temperature of tests P3, P8, P9 and P10 is shown in Figure 14.  An activation energy of 61.93 kJ/mol was determined from the slope of the straight line in Figure  14. According to Habashi (1999), a chemically-controlled process is usually greater than 41.8 kJ/mol [18].
In order to compare the activation energy with similar processes, Table 11 shows the results reported by some authors in literature. It can be observed that the activation energy for processes that use sulfuric acid, ferric ions and/or oxygen is similar to the obtained in this work that use sulfuric acid and oxygen. In the work reported by Padilla et al (2008), they use also only sulfuric acid and oxygen in a pressure reactor and a copper extraction of 95% was obtained at an oxygen pressure of 5 In order to compare the activation energy with similar processes, Table 11 shows the results reported by some authors in literature. It can be observed that the activation energy for processes that use sulfuric acid, ferric ions and/or oxygen is similar to the obtained in this work that use sulfuric acid and oxygen. In the work reported by Padilla et al. (2008), they use also only sulfuric acid and oxygen in a pressure reactor and a copper extraction of 95% was obtained at an oxygen pressure of 5 kg/cm 2 , 125 • C in 4 h [19]. In our work, we obtained 98% Cu extraction under less extreme conditions: oxygen pressure of 1 kg/cm 2 , 100 C and only 3 h. Padilla et al. (2008) required a higher activation energy than the present work; this is due to the design of reactor used. The reactor used in the present work promotes a high interaction between the solid-gas-liquid phases, improving the mass transport at the gas-solid interface. Thus, the activation energy required for the leaching of chalcopyrite decreases.

Conclusions
In the present study, the copper leaching of chalcopyrite concentrate in a 30-L batch reactor was described. The experimental results showed that it is possible to extract 98% of copper in only 3 h. This result indicates a fast process compared with others reported in literature.
The best result (98% in 3 h) was obtained under the following reaction conditions: 130 g/L of initial sulfuric acid concentration, temperature of 100 • C, oxygen pressure of 1 kg/cm 2 , solid concentration of 100 g/L and concentrate particle size of −104 + 75 µm.
The copper leaching is controlled chemically. Then, the elemental sulfur layer exposed on the unreacted particles of chalcopyrite does not interfere with the mass transport or the interactions between phases.
A statistical analysis showed that temperature is the most important variable influencing the extraction of copper and oxygen consumption. A temperature of at least 92 • C (61.93 kJ/mol) is necessary to activate the decomposition of chalcopyrite.
The initial sulfuric acid concentration must also be considered as an important variable from an economic perspective. An excess of sulfuric acid will increase the neutralizing agent in the posterior stages of the leaching process, whereas a lack of sulfuric acid could result in the precipitation of iron as plumbojarosite, and could therefore create difficulties in the recovery of valuable metals at later stages.