Thermodynamic Model for the Design of a Process of Production of Copper Sulfate Pentahydrate from Copper Ores

Abstract

In Chile, one of the ways in which small-scale mining industries sustain themselves is through the sale of copper ores to the state company ENAMI, which monetizes this product depending on the copper’s mineral grade. To sell this mineral, small mining companies must transport the product to ENAMI, which means a high monetary cost, added to the fact that there are large amounts of waste minerals that cannot be sold because of their low grade. The present work aims that small miners can process these copper ores in situ to commercialize a more valuable product, such as copper salts. Considering the high solar radiation and the scarce superficial water resources found in the north side of the country, a possible process alternative is the leaching of the ores using acid seawater solutions followed by crystallization by solar evaporation. As a necessary tool for this process design, the present work has developed a model able to predict the copper sulfate pentahydrate crystallization from multicomponent solutions, preventing the co-precipitation of undesired compounds (such as iron salts, sodium chloride, and sodium sulphate among others) that contaminate the final product. The Pitzer thermodynamic model was successfully applied to predict the crystallization process of copper sulfate pentahydrate from synthetic leaching solutions. These results were validated through experimental tests.

1. Introduction

Chile is one of the main copper producers worldwide, where a large percentage of copper production is carried out by large international mining companies (such as Codelco, BHP Billiton; Antofagasta Minerals, and Anglo American, among others). However, there is a sector that also contributes with the production of copper in the country, which is represented by the small and medium-sized mining companies (Pymes), where a large percentage of them sell their minerals to the National Mining Company (ENAMI) which processes them and subsequently inserts them into the world market.

In 2015, the annual copper production in Chile was around 5.832.551 tons, where of this total, the contribution of small mining companies was around 1%.

On the other hand, it is important to mention that in Chile approximately 180 tons of waste ore are produced monthly, which has a copper grade that varies between 0.5 and 2%, which is also susceptible to being processed.¹

However, small-scale mining industries do not have suitable technology and economic resources to carry out a technical-economic study to process, in situ, its copper ores to commercialize a more valuable product, such as copper sulfate pentahydrate (CuSO₄·5H₂O), which is one of the most common commercial products of copper because of the wide range of commercial uses and applications.²

On the other hand, in Chile, mining activities are concentrated in the north of the country, which is one of the driest areas on the planet, with the highest solar radiation worldwide, scarce superficial water resources, and where there is an increasing demand for water by the different production activities as well as for human consumption;^3,4 therefore, the mining sector requires the identification of alternative sources of water. One alternative is seawater, which can be a substitute for the limited freshwater resources in the region.²

Considering the aforementioned background, and due to small mining companies having scarce monetary resources, it is necessary to perform a scientific and technological study to process impure solutions obtained from leaching, avoiding a purification stage such as solvent extraction (SX).

For this reason, this paper is a scientific complement that offers an alternative to this problem giving added value to these minerals and changing the business model by producing copper salts directly from the leaching solutions [pregnant leaching solution (PLS)] of waste minerals. These salts will be obtained from heap leaching, at a small scale, using resources such as seawater to prepare the leaching solution, and solar evaporation to crystallize copper sulfate pentahydrate, which would reduce investment costs. This alternative would allow the commercialization of waste minerals that actually cannot be sold to ENAMI, due to the restrictions of copper grade, combined with the high transport costs to the sales centers (all the ore must be transported, however, ENAMI pays only the copper ore, which represents approximately 2% of the total transported ore). The copper sulfate pentahydrate obtained as a new product has between 22 and 25% of copper, adding a higher value to the commercialized product by small miners.

Figure 1 shows the process scheme to obtain copper sulfate pentahydrate crystals from PLS, avoiding the SX stage normally used in this process.

Figure 1.

Scheme process to obtain copper sulfate pentahydrate crystals from PLS. PLS and ILS: pregnant leaching solution and intermediate leaching solution, respectively.

In order to design this process, a crystallization equilibrium model is necessary. The thermodynamic Pitzer model is a recognized tool for the determination of activity coefficients, vapor pressures, water activities, solubilities, and saturation index. To carry this out, it is necessary to know the different binary and ternary ion interaction parameters of the Pitzer model through a rigorous bibliographic compilation.

Several authors have studied the applicability of the ion interaction model of Pitzer to correlate the solubility data at different temperatures. Harvie and Weare⁵ used this model to predict mineral solubilities at 298.15 K in the Na–K–Ca–Mg–Cl–SO₄–H₂O system at high ionic strengths concluding that the model can be used to predict solubilities in complex systems. Pabalan and Pitzer⁶ determined the mineral solubilities in binary and ternary electrolyte mixtures of the Na–K–Mg–Cl–SO₄–OH–H₂O system at high temperatures. Møller⁷ presented a temperature dependence model for the Na–Ca–Cl–SO₄–H₂O system that calculates the solubilities from dilute to high concentrations from 298.15 to 523.15 K. Later, Greenberg and Møller⁸ extended the model by including potassium interactions and increasing the temperature range from 273.15 to 523.15 K.

Christov⁹ studied the system Na–Cu–Cl–SO₄–H₂O at 298.15 K using the Pitzer model, where the crystallization of the simple salts CuCl₂·2H₂O and CuSO₄·5H₂O was evaluated. Additionally, the simulation of the NaCl–CuCl₂ (aq), Na₂SO₄–CuSO₄ (aq), and CuCl₂–CuSO₄ (aq) systems was performed, demonstrating a good agreement between the experimental and calculated solubility isotherms. Later, Christov and Moller¹⁰ studied the H–Na–K–OH–Cl–HSO₄–SO₄–H₂O system at high solution concentrations from 273.15 to 523 K, where a comparison with the experimental data validated the model.

Wang et al.,¹¹ predicted the solubility of gypsum at 298.15 K in the systems CaSO₄–HMSO₄–H₂SO₄–H₂O (HM = Cu, Zn, Ni, Mn) up to saturated concentrations of heavy metal sulfates and to a H₂SO₄ concentration of 2 m by the Pitzer thermodynamic model, concluding that Pitzer model can be used to predict the solubility of gypsum in the quaternary system.

Justel et al.¹² represented the solid–liquid equilibrium of the copper sulfate–sulfuric acid–seawater system using the Pitzer and the Born model to quantify the copper sulfate and sulfuric acid effect, respectively. Besides, the precipitated amounts of copper sulfate as a function of the sulfuric acid concentration were predicted. Then, Justel et al.¹³ determined the solid–liquid equilibrium of the CuSO₄–H₂SO₄–seawater system from 293.15 to 333.15 K, by means the thermodynamic study of the Cu–Na–H–SO₄–Cl–HSO₄–H₂O system using the Pitzer model.

Garcés¹⁴ used the ionic interaction model of Pitzer to determine activity coefficients of the evaporitic Andean deposits known as Salar de Loyoques in northern Chile. Through this model, the activity coefficients were evaluated, and it was determined that the first mineral precipitated was calcite, while gypsum and magnesite are close to equilibrium. These results are based on the calculations of the saturation index (I.S.), where a value of zero means that the solution is in equilibrium with respect to that phase. Positive or negative values of the I.S. indicate a situation of supersaturation or subsaturation, respectively, whose magnitude is a direct function of the absolute value of this quantity.

As shown above, several authors have used these thermodynamic models to work with electrolyte solutions, demonstrating that the Pizer model is valid over a wide range of temperatures and concentrations.

Accordingly, this work develops a model useful to design crystallization processes using the Pitzer ion interaction model for the simulation and validating this information with experimental tests. The present methodology consists of calculating the supersaturation index using the activity coefficients from the Pitzer model and according to its values to discriminate (or determine) the salts that would potentially precipitate during a natural evaporation process, which occurs with the natural salt brines. The model was validated using synthetic solutions with a similar composition to those obtained from leaching of mineral using mixtures of water, seawater, and sulfuric acid.

2. Thermodynamic Framework

2.1. Pitzer Ion Interaction Model

The Pitzer ion interaction model has been reported by several authors,^5,7,15−17 which have stated that this approach can be used to calculate solubilities in complex systems and to predict the behavior of natural fluids.

This model begins with a virial expansion of the excess free energy: G^ex/RT,⁵ as shown in eq 1.

1

where n_w is the number of kilograms of solvent and m_ijk is the molality of species i, j, and k. f(I) is the Debye–Hückel term which is a function of the ionic strength. λ_ij and μ_ijk are the second and third virial coefficients, respectively, and represent the effects of short-range forces between ions.¹⁶

Equation 2 is used to calculate the osmotic coefficient (ϕ), and eqs 3 and 4 are used to model the activity coefficients of the cation (M) and anion (X), respectively, as follows

2

3

4

where the subscripts M, c, and c′ represent the cations and X, a, and a′ are the anions; z_M and z_X correspond to the ion charges, and m_c and m_a to the molalities (mol/kg solvent) of the cations and anions, respectively; I is the ionic strength; and b is 1.2 and remains constant for all solutes.

The indices c < c′ and a < a′ are the sum over all of the distinguishable pairs of dissimilar cations and anions, respectively. ψ_ijk are the ion-mixing interaction parameters, which are assumed to be independent of the concentration.

The function F is shown in eq 5.

5

where A_ϕ is the Debye–Hückel term given by eq 6.¹⁸

6

The coefficients B_MX are functions of the ionic strength and in the case of electrolytes 1–1 and 1–2, these are represented by the eqs 7–9.

7

8

9

For electrolytes 2–2 (as copper sulfate), an additional term is added as shown in eqs 10–12:

10

11

12

where the symbols β_MX⁽⁰⁾, β_MX, β_MX⁽²⁾, and C_MX are solute specific parameters and the parameters α₁, α₂, and b, are constants. For copper sulfate, α₁ = 1.4 and α₂ = 12; for copper chloride, α₁ = 2.0 and α₂ = 1.0; for an electrolyte with one or two univalent ions, α₁ = 2 and β⁽²⁾ is not required.¹⁹

The functions g and g′ are given by eqs 13 and 14, as follows

13

14

where x = αI^1/2.

C_MX is related to the parameter C_MX^ϕ, as shown in eq 15.

15

Some terms containing C_MX parameters have a concentration dependence given by the function Z from eq 16.

16

Also, the equations for the second virial coefficients, Φ_ij, are the following

17

18

19

where θ_MX represents a single parameter for each pair of cations or anions and E_θMX accounts for the electrostatic unsymmetrical mixing effects, which are dependent on the charge of the ions and ionic strength. E_θMX and are zero when the ions i and j have the same charge.⁵

The higher-order electrostatic terms E_θMX and are calculated by the eqs 20 and 21 reported by Pitzer.²⁰

20

21

where x_MX = 6z_Mz_XA_ϕI^1/2

The expression for J was given by Pitzer,²⁰ as follows

22

where the corresponding values of the parameters for the eq 22 are presented in Table 1.

Table 1. Parameters for Eq 22(20)^a.

parameters	C1	C2	C3	C4
eq 22	4.5810	0.7237	0.0120	0.5280

^aOn the other hand, J′ values are the derivative of J functions and were calculated from Pitzer.²⁰

2.2. Determination of Supersaturation Indices

In order to predict the salts that crystallize in the multicomponent system analyzed in the present work, the supersaturation index proposed by Krumgalz et al.²⁵ and Garcés¹⁴ has been used, where the degree of saturation of a brine with respect to a mineral of the formula M_vMX_vX·nH₂O is defined by the following equation²⁵

23

where the numerator of the equation is the product of the real ionic concentrations in a particular system and the denominator contains parameters, which are functions of temperature and pressure (K_sp, γ^±, a_H2Oⁿ). Activity coefficients are estimated by applying the Pitzer model (eqs 3 and 4). Regarding the supersaturation indices’ results, a value of zero means that the solution is in equilibrium with respect to that phase. Positive or negative values indicate a situation of supersaturation or nonsaturation, respectively, whose magnitude is a direct function of the absolute value of this quantity.¹⁴

2.3. Evaporation Crystallization Experiments

In order to validate the thermodynamic model, batch evaporation crystallization experiments were carried out at room temperature (20 ± 3 °C). All reagents employed in this work were of analytical grade, and the solutions were prepared using an analytical balance (Mettler Toledo Co. model AX204, with 0.07 mg precision).

Based on the composition of leaching solutions (PLSs) obtained in previous experiments by this research group (data not shown), synthetic leaching solutions were prepared and used in the subsequent crystallization experiments. The following reagents (Merck) were used to prepare these synthetic PLSs: CuSO₄·5H₂O, Na₂SO₄, FeCl₂·4H₂O, FeSO₄·7H₂O, H₂SO₄, and Fe₂(SO₄)₃·nH₂O (Merk pa).

Table 2 shows the composition of the synthetic PLS at two different conditions (PLS₁ and PLS₂) used for the crystallization experiments, where PLS₁ has a higher concentration of iron and a lower concentration of copper compared with the PLS₂, they are among the ranges of interest for copper mining. It will allow us to validate the model at two different experimental conditions.

Table 2. Composition (wt %) of Crystallization Solutions PLS₁ and PLS₂.

samples	Cu (%)	Fe (%)	Na (%)	Cl (%)	H2SO4 (%)
PLS1	2.98	3.23	0.77	0.89	5.24
PLS2	4.75	1.39	0.67	0.92	3.57

The crystallization using solar evaporation experiments were carried out in pyrex glass containers with a capacity of 4 L. The duration of the tests was approximately 15 days for PLS₁ and 22 days for PLS₂, reaching evaporation percentages of 46.02 and 62.55%, respectively (see Table 8). The obtained crystals were washed with distilled water at a ratio of 1 L H₂O/kg crystals. The composition of the crystallized solids was determined using atomic absorption spectroscopy (AAS). The AAS measurements were performed using a Varian atomic absorption spectrophotometer, model 220. For the photography of the crystals, a Zeiss microscope, model Axio Lab1, was used.

Table 8. Percentage of Evaporation, Composition, and Yield of Crystallization Experiments Performed^a.

		composition crystallized solids (%)
Sample	evaporation (%)	CuT	FeT	Cl	SO4	Na	copper yield (%)
crystals from PLS1	46.02	9.42	10.88	<0.001	35.91	0.0015	44.27
crystals from PLS2	62.55	24.00	0.28	<1	36.30	0.377	71.91

^aCuT and FeT, correspond to the total copper and iron percentage of the crystallized solids.

3. Results and Discussion

3.1. Ion-Interaction Parameters of the Pitzer Model

Interaction parameters were obtained by the bibliographic revision from previously published works. Several authors have determined the ion interaction parameters of the binary subsystems of this work (CuSO₄–H₂O, CuCl₂–H₂O, Cu(HSO₄)₂–H₂O, Na₂SO₄–H₂O, NaCl–H₂O, NaHSO₄–H₂O, HSO₄–H₂O, HCl–H₂O, H₂SO₄–H₂O, FeSO₄–H₂O, FeCl₂–H₂O, and Fe(HSO₄)₂–H₂O.

For Na₂SO₄, binary parameters were calculated using the model proposed by Møller,⁷ which is valid in the temperature range from 298.15 to 523.15 K. For NaCl, these values were determined using the model of Pabalan and Pitzer,⁶ which is valid from 273.15 to 573 K. For HCl, parameters were taken from Holmes et al.,²¹ where the equations are valid from 273 to 523 K. For NaHSO₄, HSO₄^–, and H₂SO₄ values, the model proposed by Christov and Moller¹⁰ was used.

Parameters values for CuSO₄ and CuCl₂ at 298.15 K were taken from Christov.⁹ In the case of Cu(HSO₄)₂, Pitzer parameters at 298.15 K were reported by Tanaka²² and Justel et al.¹³ Pitzer parameters for FeSO₄, FeCl₂, and Fe(HSO₄)₂ at 298.15 K were determined using the model of Marion et al.²³

Table 3 shows the reported parameter values used in this work for CuSO₄, CuCl₂, Cu(HSO₄)₂, Na2SO4, NaCl, NaHSO₄, HSO₄^–, HCl, H₂SO₄, FeSO₄, FeCl₂, and Fe(HSO₄)₂ at 298.15 K.

Table 3. Pitzer Binary Parameters (β_MX⁽⁰⁾, β_MX, β_MX⁽²⁾, and C_MX) for Na₂SO₄, NaCl, NaHSO₄, HSO₄^–, HCl, H₂SO₄ FeSO₄, FeCl₂, and Fe(HSO₄)₂ at 298.15 K^a.

298.15 K	βMX(0)	βMX(1)	βMX(2)	CMXϕ
CuSO4 (aq)a	0.2340	2.5270	–48.3300	0.0044
CuCl2 (aq)a	0.1766	0.5740	0.6340	–0.0109
Cu(HSO4)2b	0.3212	0.3627		0.0988
Na2SO4 (aq)c	0.0187	1.0993		0.0063
NaCl (aq)d	0.0754	0.2770		0.0014
NaHSO4 (aq)e	0.1057	0.0208		–0.0058
HSO4– (aq)e	0.0910	0.0000		0.0552
HCl (aq)f	0.1766	0.2929		0.0007
H2SO4 (aq)e	0.2104	0.4411		0.0000
FeSO4 (aq)g	0.2569	3.0879	–42.0000	0.0209
FeCl2 (aq)g	0.3359	1.5323		–0.0086
Fe(HSO4)2g	0.4337898	3.48		0.0000

^aSuperscripts: a,⁹ b,;¹³ c;⁷ d,;⁶ e,¹⁰; f,;²¹ g,.²³ Where b = 1.2; α₁ = 1.4, α₂ = 12.0 for CuSO₄; α₁ = 2.0, α₂ = 1 for CuCl₂; and α₁ = 2.0 for the other species.

For the Cu–Na–H–Fe–SO₄–Cl–HSO₄–H₂O system, ternary systems have also been studied, where the parameters ψ_ijk and θ_ij, which are necessary to determine the thermodynamic properties of electrolyte solutions,⁶ have been reported at different temperatures by several authors.

Some authors reported θ_ij parameters at 298.15 K: Values for θ_Cl,SO4, θ_Cu,Na, and θ_Cu,H were reported by Pabalan and Pitzer,⁶ Downes and Pitzer,¹⁹ and Wang et al.,¹¹ respectively. Additionally, a temperature dependence model of the θ_SO4,HSO4, θ_Na,H, and θ_Cl,HSO4 parameters was reported by Christov and Moller.¹⁰ All this information is summarized in Table 4.

Table 4. θ_ij Parameter Values at 298.15 K Used in the Present Work^a.

298.15 K
θCl,SO4a	0.0700
θCu,Nab	0.0770
θCu,Hc	–0.0230
θSO4,HSO4d	–0.1190
θNa,Hd	0.0345
θCl,HSO4d	0.0000
θNa,Fee	0.0800
θH,Fee	0.0000

^aValues at 298.15 K were taken from: a;⁶ b;¹⁹ c;¹¹ d,¹⁰ and e.²³

Values of θ_Na,Fe and θ_H,Fe at 298.15 K were taken from Marion et al.²³ θ_Cu,Fe was determined as zero, due to the data not being found in the literature.

Values of ψ_ijk at 298.15 K have been reported by several authors as follows: Values for ψ_Cu,Cl,SO4, ψ_Cu,Na,SO4, and ψ_Cu,Na,Cl were determined at 298.15 K by Christov,⁹ ψ_Cu,H,SO4 has been reported by Wang et al.,¹¹ and the values for ψ_Cu,H,HSO4 and ψ_Cu,SO4,HSO4 were determined by Baes et al.²⁴

In addition, some authors reported equations for the ψ_ijk determination as a function of the temperature. Here, the temperature dependence of ψ_Na,Cl,SO4 was determined using the model of Møller,⁷ which is valid from 273.15 to 423.15 K. In the case of ψ_H,Cl,SO4, ψ_Na,H,SO4, ψ_Na,H,Cl, ψ_Na,H,HSO4, ψ_Na,SO4,HSO4, ψ_Na,Cl,HSO4, ψ_H,SO4,HSO4, and ψ_H,Cl,HSO4 the model of Christov and Moller was used.¹⁰ The ψ_ijk parameters at 298.15 K used in the present work are summarized in the Table 5.

Table 5. ψ_ijk Parameters Values at 298.15 K Used in the Present Work^a.

298.15 K
ψCu,Cl,SO4a	0.0100	ψNa,Cl,SO4e	–0.009	ψNa,Fe,SO4f	–0.0099
ψCu,Na,SO4a	0.0530	ψNa,H,SO4e	0.0131	ψNa,Fe,Clf	–0.0140
ψCu,Na,Cla	–0.0036	ψNa,H,Cle	–0.0025	ψH,Fe,SO4f	0.0000
ψCu,H,SO4b	0.0000	ψNa,H,HSO4e	–0.0146	ψH,Fe,Clf	0.0120
ψCu,H,HSO4c	–0.0250	ψNa,SO4,HSO4e	0.0052	ψH,Fe,HSO4f	0.0112
ψCu,SO4,HSO4c	–0.0440	ψNa,Cl,HSO4e	0.0000	ψFe,SO4,Clf	–0.0183
ψCu,H,Cld	0.0036	ψH,SO4,HSO4e	0.0000	ψFe,SO4,HSO4f	0.0000
ψCu,Na,HSO4d	0.0957	ψH,Cl,HSO4e	0.0000
ψCu,Cl,HSO4d	–0.0990	ψH,Cl,SO4e	0.0000

^aValues were taken from: a;⁹ b;¹¹ c;²⁴ d;¹³ e;¹⁰ f.²³

Parameters values of ψ_Cu,H,Cl, ψ_Cu,Na,HSO4, and ψ_Cu,Cl,HSO4 at 298.15 K were obtained from the work of Justel et al.¹³ Values of ψ_Cu,Fe,SO4, ψ_Cu,Fe,Cl, ψ_Cu,Fe,HSO4, ψ_Na,Fe,HSO4, and ψ_Fe,Cl,HSO4 were considered as zero because they were not found in the literature.

3.2. Determination of Solubility Products, Activity Coefficients, and Supersaturation Indices at 298.15 K

The solubility product (K_sp) is a value that can be obtained from the solubility, activity coefficient, and water activity of crystallized salts in H₂O. The solubility products of the solid phases K_sp at 298.15 K were determined by the following expression²⁶

24

From eq 24, saturation molality in a ternary system is obtained by

25

Table 6 shows the solubility product, activity coefficient, and water activity values of crystallized salts at 298.15 K.

Table 6. Values of Activity Coefficients, Water Activities, and Solubility Products at Different Concentrations.

298.15 K	m (mol kg–1 H2O)	γ±	aw	Ksp
CuSO4·5H2O	1.3900	0.0368	0.9753	0.0023
CuCl2·2H2O	5.5200	0.6250	0.7856	25.3406
NaCl	6.1537	0.9562	0.7523	34.6257
Na2SO4	3.1692	0.1818	0.9192	0.0824
FeCl2·4H2O	5.0866	4.3209	0.6531	1931.7758
FeSO4·7H2O	1.9442	0.0480	0.9525	0.0062

At 298.15 K, there is a mean deviation of 0.0001 between the solubility product of copper sulfate obtained in the present work and the one reported by Christov⁹ for aqueous copper sulfate solutions. In the case of FeSO₄, there is a mean deviation of 0.0003 between the solubility product obtained in this work and the one obtained by Christov.²⁷

Table 7 shows the values of activity coefficients and supersaturation indices obtained in both cases (PLS₁ and PLS₂):

Table 7. Activity Coefficients and Supersaturation indices of Crystallization Solutions at 298.15 K.

	PLS1		PLS2
298.15 K	γ±	Ω	γ±	Ω
CuSO4·5H2O	0.0484	1.0275	0.0447	1.1678
CuCl2·2H2O	0.4615	0.0001	0.3764	0.0001
NaCl	0.7936	0.0016	0.7044	0.0011
Na2SO4	0.2113	0.0268	0.2096	0.0164
FeCl2·4H2O	0.9002	0.0000	0.6109	0.0000
FeSO4·7H2O	0.1317	4.4684	0.0923	0.8506

From supersaturation indices results, it is possible to conclude that in PLS₁, where the concentration of iron is higher than the concentration of copper, the crystallization of both copper sulfate and ferrous sulfate occurs. However, when the copper concentration is increased, and iron concentration decreased (PLS₂), the precipitation of copper sulfate pentahydrate occurs and the precipitation of ferrous sulfate is not observed.

Figure 2 shows the supersaturation indices of copper sulfate pentahydrate and ferrous sulfate heptahydrate at 298.15 K, as a function of the Cu/Fe molal ratio, which varies from 0 to 2.6 approximately.

Figure 2.

Supersaturation indices of CuSO₄·5H₂O (●) and FeSO₄·7H₂O (■) as a function of the Cu/Fe molal ratios at 298.15 K.

From Figure 2, it is observed that from a Cu/Fe molal ratio higher than around 2.05, according to the thermodynamic model, only the precipitation of copper sulfate occurs, which is the product of commercial interest; however, under this ratio, the precipitation of both copper sulfate and ferrous sulfate occurs. These results allow us to know the Cu/Fe ratio necessary to obtain only the precipitation of copper sulfate pentahydrate, and hence, facilitate the process design.

3.3. Validation of the Model through Evaporation Crystallization Experiments

The validation of the thermodynamic model through evaporation crystallization experiments at two different conditions was performed. Table 8 shows the evaporation percentages of the solution, composition of crystals obtained, and yield (%) of crystallization experiments of the two initial solutions (PLS₁ and PLS₂).

These variations in the evaporation percentages are due to the fact that in the case of PLS₁, the crystals that first appeared were, with the naked eye, contaminated (blue-yellowish color), due to this, the evaporation stopped before than in PLS₂ because these did not correspond to high purity copper sulfate crystals that is the objective of this work. The opposite occurred in PLS₂, where the crystals, at a glance, corresponded to copper sulphate pentahydrate; therefore, the evaporation percentage was higher to obtain a greater amount of crystals.

As can be seen in Table 8, there is a significant difference in the compositions of the crystals obtained from the two initial PLS solutions, where, the percentage of CuT of the crystals obtained from PLS₁ (9.42%) is lower than those obtained in PLS₂ (24.00%); on the other hand, the Fe percentage of the crystals obtained from PLS₁ (10.88%) is higher than in PLS₂ (0.28%). Concluding that crystals from PLS₂ corresponds, mostly, to copper sulfate pentahydrate; on the other hand, a high concentration of Fe of crystals obtained from PLS₁ can be attributed to the presence of ferrous sulfate in the crystals.

These results agree with those from Figure 3, which shows the shape of the crystals obtained from PLS₁ and PLS₂, where it is possible to observe that for the crystals obtained from PLS₁ (Figure 3a) the crystalline structure is more elongated in comparison with crystals obtained from PLS₂ (Figure 3b) that have a rhomboid structure; it is similar to that of the copper sulfate pentahydrate crystals found in the literature.²⁸ According to the results of Table 8, the change in the shape of the crystals obtained in PLS₁ could be attributed to the higher presence of Fe in the crystal structure.

Figure 3.

(a) Image of crystals obtained from PLS₁ and (b) image of crystals obtained from PLS₂.

As predicted by the thermodynamic model, if the solution remains with a Cu/Fe ratio greater than 2.05, only copper sulfate crystallizes in PLS₂. In addition, according to the results from Table 8, the small amount of total ferrous and sodium in the crystallized solids could be attributed to the solution embedded and occluded in the crystals. On the other hand, in the case of PLS₁, ferrous sulfate, and copper sulfate precipitate, the results are also consistent with the results from Table 8. Addittionally, the copper yield obtained in the crystals, with respect to the initial copper, was 71.91% for PLS₂ and 44.27% for PLS₁. This is because of the longer evaporation time for PLS₂ because it does not precipitate ferrous sulfate.

Because of this, from the experimental results, it is possible to conclude that the Pitzer thermodynamic model can be successfully used as an applied tool to predict the potential crystallization of salts from a multicomponent system as the PLS from the mining industry, where only the composition of the initial solution is required.

The copper sulfate pentahydrate obtained as a new product has around 22–25% of copper, adding a higher value to the commercialized product by small miners. As a conclusion, if the process proposed in the present work is used, the product to be sold by the small miners would increase its law tenfold, and the mass to transport would decrease by more than 20 times.

4. Conclusions

The ion interaction model of Pitzer can be successfully used as an applied tool to predict the potential crystallization of salts from a multicomponent system as the PLS from the mining industry, where only the composition of the initial solution is required.

For a Cu/Fe ratio higher than approximately 2.05, it was observed that only copper sulfate pentahydrate crystallizes, which is a product of commercial interest; on the other hand, under this ratio, the precipitation of both copper sulfate and ferrous sulfate is observed.

Crystals obtained from PLS₁ have a more elongated shape in comparison with crystals obtained from PLS₂, which have a rhomboid structure similar to that of copper sulfate pentahydrate crystals found in the literature. The change in the shape of the crystals obtained in PLS₁ could be attributed to the higher presence of Fe in the crystal structure.

The present work corresponds to a contribution because it facilitates the design of the copper sulfate crystallization process to be carried out by small miners and realizes that the Pitzer’s thermodynamic model can be applied to optimize processes at the pilot and industrial scales.

The authors declare no competing financial interest.