Dissolution of Black Copper Oxides from a Leaching Residue

: This article presents the behavior of black copper minerals in reducing acid leaching using FeSO 4 as reducing agent. The original sample, which was a blend of green and black copper minerals, was treated ﬁrst by an oxidizing acid leach using O 3 to dissolve the soluble phase (green copper oxides). The residue (mainly black copper) was evaluated by agitated leaching under three di ﬀ erent solution potentials, with respect to the standard hydrogen electrode (SHE) (450, 500, and 600 mV (SHE)) at 25 ◦ C. The original sample and the leach residue were characterized by scanning electron microscope (SEM) and inductively coupled plasma atomic emission spectroscopy (ICP-AES). The O 3 leach residue was 1.43% copper, with 50% of the insoluble phase associated with copper pitch, copper limonites, and unreacted chrysocolla. The results of leaching using FeSO 4 demonstrate that it is possible to obtain 90% copper extraction using a solution with a potential of 450 mV, while leaching at 600 mV resulted in 65% copper extraction. Acid consumption was 40 kg / t in the test at 450 mV, followed by 30 kg / t in the 500 mV test, and ﬁnally 25 kg / t in the 600 mV test, showing that reactivity decreases with increased solution potential. The results show that retreatment of a leaching residue is possible, considering the presence of copper pitch, copper limonites, and chrysocolla as the main copper contributing minerals. Modeling of copper extraction with nonlinear regression is proposed. The retreatment of residues resulting from conventional acid leaching can be an alternative to make use of the treatment capacity of hydrometallurgical plants.


Materials and Methods
The residue from an oxidizing acid leaching (which initially contained copper oxide mineral, mainly chrysocolla) was used to evaluate the dissolution of black copper ore using a reducing leaching. The original copper oxide mineral and the residue of the acid oxidizing leaching (black copper) were characterized by SEM (JEOL USA Inc., Peabody, MA, USA). The oxidative leaching test employed O 3 at room temperature and 50 g/L of H 2 SO 4 . The residue, containing black copper was dissolved using FeSO 4 following the considerations of [6,11]. The solution potential was controlled by adding O 3 or FeSO 4 , depending on the value to be controlled. The acid consumption obtained in the leaching tests were measured. Copper, iron, and manganese extraction rates are reported.

Sample Characterization
The oxide sample was collected near the La Famosa mine, located in the Third Region of Atacama, Chile. The sample was manually selected according to the criteria of [10,13], considering black streaks, massive habit, earthy luster, and an amorphous character. Feed samples were crushed and milled to a particle size 100% below 1.6 mm. The chemical composition was determined using inductively coupled plasma atomic emission spectroscopy (ICP-AES) model Optima 2000 DV (PerkinElmer, Überlinge, Germany). For the determination of total and soluble copper, the solid sample has been digested in two different ways: soluble copper using a 2.5 g sample in a 50 mL solution with 5% sulfuric acid, and total copper using 1 g sample in 20% aqua regia solution and reaching the boiling point. The morphology was characterized by scanning electron microscopy (SEM) using JEOL 6360-LV equipment (JEOL USA Inc., Peabody, MA, USA) an energy-dispersive X-ray spectroscopy (EDS) microanalysis system (Zeiss Ultra Plus, Zeiss, Jena, Germany) and operated at 30 kV under high vacuum conditions. For SEM analysis, the mineral samples were treated with epoxy resin and metallized with a thin carbon layer to improve their conductivity.

Leaching Experiments
Four leaching tests were conducted. The first test involved acid leaching in an oxidizing media using O 3 in order to remove the oxide minerals while the other three tests were the black copper leaching obtained on the residue of the first test. The first test was performed with a particle size 100% below 1.6 mm at a temperature of 25 • C, a leaching time of 72 h, 50 g/L of H 2 SO 4 , 500 min −1 of mechanical agitation, and 1000 g of sample added in 2 L of leaching solution using 3 L/min of O 3 (at 50%). The O 3 gas was added by injection to the leaching solution until obtaining an Eh of 1000 mV (SHE) using an ozonator model L21 (Pacific Ozone, Benicia, CA, USA) fed with oxygen through an oxygen generator system. The solution potential was controlled at 1000 mV throughout the test. The solid residue obtained in test 1 was divided into three homogeneous samples and leached to three different solution potentials under reducing conditions.
The three tests under reducing conditions were performed using 250 g of sample in 0.3 L of leaching solution at 25 • C, 40 g/L of FeSO 4 , 50 g/L of H 2 SO 4 , with a leaching time of 8 h, and 500 min −1 of mechanical agitation at three different solution potentials: 450, 500, and 600 mV (SHE). FeSO 4 or O 3 was used to control the solution potential as required. All potentials shown are quoted with respect to the standard hydrogen electrode (SHE).
The aliquots obtained at different leaching times were filtered (0.2 µm) and Cu 2+ , Mn 2+ and Fe concentrations were determined by inductively coupled plasma atomic emission spectroscopy (ICP-AES) model Optima 2000 DV (PerkinElmer, Überlinge, Germany). Figure 1 shows a representation of the system. Four leaching tests were conducted. The first test involved acid leaching in an oxidizing media using O3 in order to remove the oxide minerals while the other three tests were the black copper leaching obtained on the residue of the first test. The first test was performed with a particle size 100% below 1.6 mm at a temperature of 25 °C, a leaching time of 72 h, 50 g/L of H2SO4, 500 min -1 of mechanical agitation, and 1000 g of sample added in 2 L of leaching solution using 3 L/min of O3 (at 50%). The O3 gas was added by injection to the leaching solution until obtaining an Eh of 1000 mV (SHE) using an ozonator model L21 (Pacific Ozone, Benicia, CA, USA) fed with oxygen through an oxygen generator system. The solution potential was controlled at 1000 mV throughout the test. The solid residue obtained in test 1 was divided into three homogeneous samples and leached to three different solution potentials under reducing conditions. The three tests under reducing conditions were performed using 250 g of sample in 0.3 L of leaching solution at 25 °C, 40 g/L of FeSO4, 50 g/L of H2SO4, with a leaching time of 8 h, and 500 min -1 of mechanical agitation at three different solution potentials: 450, 500, and 600 mV (SHE). FeSO4 or O3 was used to control the solution potential as required. All potentials shown are quoted with respect to the standard hydrogen electrode (SHE).
The aliquots obtained at different leaching times were filtered (0.2 μm) and Cu 2+ , Mn 2+ and Fe concentrations were determined by inductively coupled plasma atomic emission spectroscopy (ICP-AES) model Optima 2000 DV (PerkinElmer, Ü berlinge, Germany). Figure 1 shows a representation of the system.

Sample Characterization
The sample had a high copper grade, with a high solubility of 92.3%, indicating the presence of highly soluble copper oxides like atacamite or chrysocolla. The non-soluble fraction is associated with the presence of black oxides. The high iron content and low manganese content indicate the presence of copper limonites [11]. The feed sample characterization can be observed in Table 1. The feed sample contained copper oxide minerals like chrysocolla ((Cu,Al)4H4(OH)8Si4O10 ·nH2O)) and dioptase (Cu6Si6O18·6 H2O) (See Figure 2, particles 2 and 3). The distribution of the copper oxide minerals shows a clear relationship with the alteration, so chrysocolla and copper pitch prevail over atacamite in propylitized rock, while atacamite and copper wad predominate in argilized rock

Sample Characterization
The sample had a high copper grade, with a high solubility of 92.3%, indicating the presence of highly soluble copper oxides like atacamite or chrysocolla. The non-soluble fraction is associated with the presence of black oxides. The high iron content and low manganese content indicate the presence of copper limonites [11]. The feed sample characterization can be observed in Table 1.  Figure 2, particles 2 and 3). The distribution of the copper oxide minerals shows a clear relationship with the alteration, so chrysocolla and copper pitch prevail over atacamite in propylitized rock, while atacamite and copper wad predominate in argilized rock [13].
Thus, the presence of copper pitch, Cu-bearing manganese oxyhydrates is evidenced, which concurs with [30], who described the Cu-Mn-Si matrix as a black oxide mineral ( Figure 2, particle 1). Gangue minerals associated with potassium feldspar were also identified ( Figure 2, particle 4). Figure 3 shows the EDS information associated with the particles.
Metals 2020, 10, x FOR PEER REVIEW 4 of 12 [13]. Thus, the presence of copper pitch, Cu-bearing manganese oxyhydrates is evidenced, which concurs with [30], who described the Cu-Mn-Si matrix as a black oxide mineral ( Figure 2, particle 1). Gangue minerals associated with potassium feldspar were also identified ( Figure 2, particle 4). Figure  3 shows the EDS information associated with the particles.

Leaching Test With O3
The copper in the feed mineral was 83% dissolved at 72 h ( Figure 4). Oxidizing conditions were favorable for the dissolution of oxide minerals such as chrysocolla and dioptase [6,11]. The main objective of the first leaching was to remove the soluble phases present in the mineral (chrysocolla and dioptase). It was assumed that the undissolved copper mineral was mainly associated with the Cu-Mn-Si phases. According to [22,31], manganese oxides are relatively insoluble in a conventional Metals 2020, 10, x FOR PEER REVIEW 4 of 12 [13]. Thus, the presence of copper pitch, Cu-bearing manganese oxyhydrates is evidenced, which concurs with [30], who described the Cu-Mn-Si matrix as a black oxide mineral ( Figure 2, particle 1). Gangue minerals associated with potassium feldspar were also identified ( Figure 2, particle 4). Figure  3 shows the EDS information associated with the particles.

Leaching Test With O3
The copper in the feed mineral was 83% dissolved at 72 h ( Figure 4). Oxidizing conditions were favorable for the dissolution of oxide minerals such as chrysocolla and dioptase [6,11]. The main objective of the first leaching was to remove the soluble phases present in the mineral (chrysocolla and dioptase). It was assumed that the undissolved copper mineral was mainly associated with the Cu-Mn-Si phases. According to [22,31], manganese oxides are relatively insoluble in a conventional

Leaching Test With O 3
The copper in the feed mineral was 83% dissolved at 72 h ( Figure 4). Oxidizing conditions were favorable for the dissolution of oxide minerals such as chrysocolla and dioptase [6,11]. The main objective of the first leaching was to remove the soluble phases present in the mineral (chrysocolla and dioptase). It was assumed that the undissolved copper mineral was mainly associated with the Metals 2020, 10, 1012

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Cu-Mn-Si phases. According to [22,31], manganese oxides are relatively insoluble in a conventional acid medium. Under these conditions, the dissolution of soluble copper is nearly total (92.3%). Figure 5 shows that close to 80 kg of sulfuric acid was consumed per ton of mineral, which was due to the high grade of copper in the sample. The presence of k-feldspar, which [32] described as a low reactivity gangue mineral, was identified by SEM. Other low reactivity gangues like quartz, biotite, and muscovite were not found in this sample [33].
The residue from leaching with O 3 was characterized by SEM to identify non-soluble solid phases. A chemical analysis by inductively coupled plasma atomic emission spectroscopy (ICP-AES) model Optima 2000 DV (PerkinElmer, Überlinge, Germany) showed the residue was copper-depleted and that there was an increase in the non-soluble phases (51% soluble), mainly associated with black copper ores or green copper oxide phases that did not react completely. Table 2 shows the chemical composition of the solid residue.
Metals 2020, 10, x FOR PEER REVIEW 5 of 12 acid medium. Under these conditions, the dissolution of soluble copper is nearly total (92.3%). Figure  5 shows that close to 80 kg of sulfuric acid was consumed per ton of mineral, which was due to the high grade of copper in the sample. The presence of k-feldspar, which [32] described as a low reactivity gangue mineral, was identified by SEM. Other low reactivity gangues like quartz, biotite, and muscovite were not found in this sample [33].
The residue from leaching with O3 was characterized by SEM to identify non-soluble solid phases. A chemical analysis by inductively coupled plasma atomic emission spectroscopy (ICP-AES) model Optima 2000 DV (PerkinElmer, Ü berlinge, Germany) showed the residue was copperdepleted and that there was an increase in the non-soluble phases (51% soluble), mainly associated with black copper ores or green copper oxide phases that did not react completely. Table 2 shows the chemical composition of the solid residue.   In addition to the chemical characterization, the solid residue was analyzed by SEM. Image 6 shows the presence of copper pitch that does not react under oxidizing conditions [11] (Figure 6, particle 1). Unreacted chrysocolla is also observed, but in the context of copper depletion ( Figure 6, particle 2). The presence of chrysocolla explains the soluble phase that still evident in the residue. Figure 7 shows the EDS information relating to the particles. acid medium. Under these conditions, the dissolution of soluble copper is nearly total (92.3%). Figure  5 shows that close to 80 kg of sulfuric acid was consumed per ton of mineral, which was due to the high grade of copper in the sample. The presence of k-feldspar, which [32] described as a low reactivity gangue mineral, was identified by SEM. Other low reactivity gangues like quartz, biotite, and muscovite were not found in this sample [33]. The residue from leaching with O3 was characterized by SEM to identify non-soluble solid phases. A chemical analysis by inductively coupled plasma atomic emission spectroscopy (ICP-AES) model Optima 2000 DV (PerkinElmer, Ü berlinge, Germany) showed the residue was copperdepleted and that there was an increase in the non-soluble phases (51% soluble), mainly associated with black copper ores or green copper oxide phases that did not react completely. Table 2 shows the chemical composition of the solid residue.   In addition to the chemical characterization, the solid residue was analyzed by SEM. Image 6 shows the presence of copper pitch that does not react under oxidizing conditions [11] (Figure 6, particle 1). Unreacted chrysocolla is also observed, but in the context of copper depletion ( Figure 6, particle 2). The presence of chrysocolla explains the soluble phase that still evident in the residue. Figure 7 shows the EDS information relating to the particles.  In addition to the chemical characterization, the solid residue was analyzed by SEM. Image 6 shows the presence of copper pitch that does not react under oxidizing conditions [11] (Figure 6, particle 1). Unreacted chrysocolla is also observed, but in the context of copper depletion ( Figure 6, Metals 2020, 10, 1012 6 of 12 particle 2). The presence of chrysocolla explains the soluble phase that still evident in the residue. Figure 7 shows the EDS information relating to the particles.   Figure 8 shows the presence of copper limonites (lim-Cu). This type of contributor, which is associated with black copper oxides, was also reported by [34]. These authors also noted the copper content of limonites is not constant, owing to inclusions and ion exchange, among other causes. Unleached chrysocolla is also identified ( Figure 8, particle 2). The minerals identified in the residue are associated with black copper oxides, according to the classifications of [6,13,34]. Figure 9 shows the EDS information associated with the particles.

Black Copper Leaching Using FeSO4
The residue obtained from O3 with higher insoluble copper content was leached using FeSO4 at three distinct solution potentials: 450, 500, and 600 mV (SHE). The highest copper dissolution of 90% was obtained at 450 mV after 8 h of leaching. The test with 500 mV yielded 77% copper extraction, while the test at 600 mV yielded 65%. The reducing conditions used in these tests (FeSO4) demonstrate the possibility of leaching insoluble copper minerals. This is important considering the age of some deposits and the accumulation of residues, products of oxidizing acid leaching containing insoluble copper. Figure 10 shows the results of the copper dissolution under reducing conditions. According to [11], the authors obtained similar results with reducing conditions (up to 432 mV (SHE)) that favored dissolving copper from black copper oxides. The maximum acid consumption obtained in   Figure 8 shows the presence of copper limonites (lim-Cu). This type of contributor, which is associated with black copper oxides, was also reported by [34]. These authors also noted the copper content of limonites is not constant, owing to inclusions and ion exchange, among other causes. Unleached chrysocolla is also identified ( Figure 8, particle 2). The minerals identified in the residue are associated with black copper oxides, according to the classifications of [6,13,34]. Figure 9 shows the EDS information associated with the particles.

Black Copper Leaching Using FeSO4
The residue obtained from O3 with higher insoluble copper content was leached using FeSO4 at three distinct solution potentials: 450, 500, and 600 mV (SHE). The highest copper dissolution of 90% was obtained at 450 mV after 8 h of leaching. The test with 500 mV yielded 77% copper extraction, while the test at 600 mV yielded 65%. The reducing conditions used in these tests (FeSO4) demonstrate the possibility of leaching insoluble copper minerals. This is important considering the age of some deposits and the accumulation of residues, products of oxidizing acid leaching containing insoluble copper. Figure 10 shows the results of the copper dissolution under reducing conditions. According to [11], the authors obtained similar results with reducing conditions (up to 432 mV (SHE)) that favored dissolving copper from black copper oxides. The maximum acid consumption obtained in  Figure 8 shows the presence of copper limonites (lim-Cu). This type of contributor, which is associated with black copper oxides, was also reported by [34]. These authors also noted the copper content of limonites is not constant, owing to inclusions and ion exchange, among other causes. Unleached chrysocolla is also identified ( Figure 8, particle 2). The minerals identified in the residue are associated with black copper oxides, according to the classifications of [6,13,34]. Figure 9 shows the EDS information associated with the particles.

Black Copper Leaching Using FeSO 4
The residue obtained from O 3 with higher insoluble copper content was leached using FeSO 4 at three distinct solution potentials: 450, 500, and 600 mV (SHE). The highest copper dissolution of 90% was obtained at 450 mV after 8 h of leaching. The test with 500 mV yielded 77% copper extraction, while the test at 600 mV yielded 65%. The reducing conditions used in these tests (FeSO 4 ) demonstrate the possibility of leaching insoluble copper minerals. This is important considering the age of some deposits and the accumulation of residues, products of oxidizing acid leaching containing insoluble copper. Figure 10 shows the results of the copper dissolution under reducing conditions. According to [11], the authors obtained similar results with reducing conditions (up to 432 mV (SHE)) that favored dissolving copper from black copper oxides. The maximum acid consumption obtained in the tests was 40 kg/t in the test at 450 mV, followed by 30 kg/t in the test at 500 mV, and finally 25 kg/t in the test at 600 mV ( Figure 11). According to [11], an industrial mineral with a copper grade between 0.13 and 0.25% can consume between 10 and 14 kg/t, as obtained in column leaching tests using FeSO 4.
Metals 2020, 10, x FOR PEER REVIEW 7 of 12 the tests was 40 kg/t in the test at 450 mV, followed by 30 kg/t in the test at 500 mV, and finally 25 kg/t in the test at 600 mV ( Figure 11). According to [11], an industrial mineral with a copper grade between 0.13 and 0.25% can consume between 10 and 14 kg/t, as obtained in column leaching tests using FeSO4.   Metals 2020, 10, x FOR PEER REVIEW 7 of 12 the tests was 40 kg/t in the test at 450 mV, followed by 30 kg/t in the test at 500 mV, and finally 25 kg/t in the test at 600 mV ( Figure 11). According to [11], an industrial mineral with a copper grade between 0.13 and 0.25% can consume between 10 and 14 kg/t, as obtained in column leaching tests using FeSO4.   Metals 2020, 10, x FOR PEER REVIEW 7 of 12 the tests was 40 kg/t in the test at 450 mV, followed by 30 kg/t in the test at 500 mV, and finally 25 kg/t in the test at 600 mV ( Figure 11). According to [11], an industrial mineral with a copper grade between 0.13 and 0.25% can consume between 10 and 14 kg/t, as obtained in column leaching tests using FeSO4.      Figure 12 shows the summary of the solution associated with Cu, Mn, and Fe in the tests applying different solution potentials. The Cu dissolution (almost 90%) was highest at 450 mV. It is evident that breaking the manganese matrix associated with black oxides favors copper dissolution. The leaching proceeded on active sites present on the surface of MnO2 particles and controlled by Fe 2+ ion diffusion [22]. Similar results, favored by the minimal presence of FeSO4 and small amounts of sulfuric acid, have been reported by [25]. According to the characterization of the residue, the dissolution of chrysocolla-type species in copper is also favored. Iron dissolution rates varied little (between 10 and 12%) with variation in potentials. According to [35], copper limonite dissolution is limited in acid media.
Mineral residue retreatment can contribute to new sources of copper in mining operations like Spence, Lomas Bayas, Mina Sur, Centinela, and Chuquicamata that involve black copper oxides [6,30,36]. The search and development of new treatment alternatives for refractory copper, concentrate, or tailings is necessary for the utilization of the free capacity that hydro-metallurgical plants will have in the year 2030, according to [1].   Figure 12 shows the summary of the solution associated with Cu, Mn, and Fe in the tests applying different solution potentials. The Cu dissolution (almost 90%) was highest at 450 mV. It is evident that breaking the manganese matrix associated with black oxides favors copper dissolution. The leaching proceeded on active sites present on the surface of MnO 2 particles and controlled by Fe 2+ ion diffusion [22]. Similar results, favored by the minimal presence of FeSO4 and small amounts of sulfuric acid, have been reported by [25]. According to the characterization of the residue, the dissolution of chrysocolla-type species in copper is also favored. Iron dissolution rates varied little (between 10 and 12%) with variation in potentials. According to [35], copper limonite dissolution is limited in acid media.
Mineral residue retreatment can contribute to new sources of copper in mining operations like Spence, Lomas Bayas, Mina Sur, Centinela, and Chuquicamata that involve black copper oxides [6,30,36]. The search and development of new treatment alternatives for refractory copper, concentrate, or tailings is necessary for the utilization of the free capacity that hydro-metallurgical plants will have in the year 2030, according to [1].
Metals 2020, 10, x FOR PEER REVIEW 8 of 12 Figure 10. Copper extraction under reducing conditions using FeSO4 (40 g/L). Solution potential controlled at 450 mV (); 500 mV (▲) and 600 mV (•), at 25 °C and using 50 g/L H2SO4.  Figure 12 shows the summary of the solution associated with Cu, Mn, and Fe in the tests applying different solution potentials. The Cu dissolution (almost 90%) was highest at 450 mV. It is evident that breaking the manganese matrix associated with black oxides favors copper dissolution. The leaching proceeded on active sites present on the surface of MnO2 particles and controlled by Fe 2+ ion diffusion [22]. Similar results, favored by the minimal presence of FeSO4 and small amounts of sulfuric acid, have been reported by [25]. According to the characterization of the residue, the dissolution of chrysocolla-type species in copper is also favored. Iron dissolution rates varied little (between 10 and 12%) with variation in potentials. According to [35], copper limonite dissolution is limited in acid media.
Mineral residue retreatment can contribute to new sources of copper in mining operations like Spence, Lomas Bayas, Mina Sur, Centinela, and Chuquicamata that involve black copper oxides [6,30,36]. The search and development of new treatment alternatives for refractory copper, concentrate, or tailings is necessary for the utilization of the free capacity that hydro-metallurgical plants will have in the year 2030, according to [1].

Modeling of Copper Extraction with Nonlinear Regression
For the modeling of copper dissolution, the support of statistical software was necessary, since the experimental curves show strongly nonlinear behavior. In this work, the Minitab 18 computational tool (Minitab LLC, State College, PA, USA) was used. After extensive model testing, the following (Equation (1)) was chosen, due to its better fit: with coefficients theta0, theta1, theta2, beta1, and beta2, and where solution potential is measured in mV (SHE), and time in hours. The Gauss-Newton algorithm was applied to the model for calculating its parameters or coefficients. Table 3 shows estimate, standard error, and confidence interval of each coefficient of the model. The resulting equation is exposed in Equation (2).
With a confidence level of 95%, therefore, there is a 95% that the confidence interval contains the value of the parameter for the population. The parameter is statistically significant if the range excludes the value of the null hypothesis (that the term containing the parameter has no effect). For reference, in the case of linear regression, the null hypothesis value for each parameter is 0, so there is no effect. Table 4 exhibits a summary of statistical parameters of the model fit. Since the average of the measured values is 61.60%, the relative error is 2.55%, a low value; therefore, the mathematical model fits well with the experimental data, as seen in Figure 13. From the plot of residuals vs. fits, it is verified that the residuals are randomly distributed and have a limited variance. The points are located randomly on both sides of 0, but a point that is far from the others is observed on the left, which means that it is an influential point. The plot of residuals vs. order shows that the residuals are independent of each other. The residuals show no trends or patterns when displayed in chronological order. From the normal probability plot of the residuals, it is verified that the residuals are normally distributed. The normal probability plot of the residuals follows approximately a straight line. This is also manifested in the histogram of residuals ( Figure 13).

Conclusions
The dissolution of insoluble copper like copper pitch, copper limonites, and chrysocolla can result in 90% copper extraction under reducing dissolution conditions (450 mV), while the copper extraction is only 65% under oxidizing leaching conditions (600 mV).
Gross acid consumption increased from 25 to 40 kg/t with a decrease in potential from 600 to 450 mV, as a consequence of copper dissolution associated with the disruption of the Cu-Mn-Si matrix.
Reducing acid leaching using FeSO4 is an alternative for retreating solid residues containing black copper minerals (copper pitch and limonite) for the treatment and continuity of operation for hydrometallurgical plants.
With an error of 2.55%, Table 4 shows that the experimental results are in good agreement with the modeled equation (Equation (2)). Therefore, the mathematical model fits well with the experimental data.

Conclusions
The dissolution of insoluble copper like copper pitch, copper limonites, and chrysocolla can result in 90% copper extraction under reducing dissolution conditions (450 mV), while the copper extraction is only 65% under oxidizing leaching conditions (600 mV).
Gross acid consumption increased from 25 to 40 kg/t with a decrease in potential from 600 to 450 mV, as a consequence of copper dissolution associated with the disruption of the Cu-Mn-Si matrix.
Reducing acid leaching using FeSO4 is an alternative for retreating solid residues containing black copper minerals (copper pitch and limonite) for the treatment and continuity of operation for hydrometallurgical plants.
With an error of 2.55%, Table 4 shows that the experimental results are in good agreement with the modeled equation (Equation (2)). Therefore, the mathematical model fits well with the experimental data.

Conclusions
The dissolution of insoluble copper like copper pitch, copper limonites, and chrysocolla can result in 90% copper extraction under reducing dissolution conditions (450 mV), while the copper extraction is only 65% under oxidizing leaching conditions (600 mV).
Gross acid consumption increased from 25 to 40 kg/t with a decrease in potential from 600 to 450 mV, as a consequence of copper dissolution associated with the disruption of the Cu-Mn-Si matrix.
Reducing acid leaching using FeSO 4 is an alternative for retreating solid residues containing black copper minerals (copper pitch and limonite) for the treatment and continuity of operation for hydrometallurgical plants.
With an error of 2.55%, Table 4 shows that the experimental results are in good agreement with the modeled equation (Equation (2)). Therefore, the mathematical model fits well with the experimental data.