Effect of Incorporation of Sulfation in Columnar Modeling of Oxidized Copper Minerals on Predictions of Leaching Kinetics

Abstract

Mathematical modeling of columnar leaching is a useful tool for predicting and evaluating the kinetics of copper extraction. One commonly used model for this process is the shrinking core model (SCM). In this study, the aim was to develop a model for column leaching of oxidized copper ore based on the SCM, which incorporates the ore sulfation stage before leaching. In sulfation and leaching laboratory-scale tests, we studied the effect of acid dosage (at 22.8, 34.2, and 45.6 kg/t), humidity (at 90%, 100%, and 110% of the saturation humidity of the mineral), ore granulometry (−3/4″ and −3/8″), and rest time (at 24, 48, 72, and 96 h) on sulfation. We found that the highest sulfation reached 49.7% for both granulometries in studies. In the column tests, the effects of acid dosage (at 34.2, 45.6 kg/t), ore granulometry (−3/4″, −3/8″), and rest time (at 24, 48 h) were studied. When the SCM was applied to these tests, we obtained fit qualities within 63.4% and 74.9%. By incorporating the sulfation factor into the SCM predictions, we observed an average increase in adjustment between 24% and 28%. This method is effective for minerals and operating conditions different from the ones studied.

1. Introduction

Chile produced 5.7 million metric tons of copper in 2021, making it the top global producer. Peru and China were the second and third largest producers, respectively, with 2.3 and 1.9 million tons [1]. This production is reached in two ways: (i) concentration by flotation for copper sulfide ores and (ii) hydrometallurgic leaching, solvent extraction, and electrowinning for oxidized copper ores [2,3]. Chile also leads the production of copper through hydrometallurgy, reaching 1.4 million metric tons in 2022 [4]. For oxidized copper ores, the most widely used method for processing consists of reducing the size of the ore, agglomeration and curing, heap leaching, solvent extraction, and electrowinning. Heap leaching is a widely used hydrometallurgical process within the mining industry. Due to its economic and environmental advantages, it has been considered a common treatment route for extracting low-grade ores. Given its significance, various investigations have been conducted to enhance its performance and predict the process outcomes. One approach has been to develop mathematical models that simulate heap leaching and can effectively demonstrate the effect of input variables on leaching performance. These models have revealed that choosing the appropriate input parameters can significantly impact leaching performance, highlighting the importance of careful consideration when optimizing the process [5,6]. In addition to the study of variables involved in the leaching phenomenon, efficiently optimizing costs is critical to leaching ores, mainly when dealing with low-grade ores. These pose various complexities that need to be appropriately addressed, and any deviations could result in significant implications. In this way, it is essential to balance the effects of the variables on metal recovery (and other process indicators) and the costs associated with the recovery of the metal [7]. Heap leach pad irrigation involves various sub-processes such as advection, inter-particle diffusion, intra-particle diffusion, and chemical reactions [8,9]. Ore beds have heterogeneous hydrodynamic conditions, and dual porosity models have been developed to describe the flow. However, most leach models simplify the ore bed as a single phase governed by either advection or diffusion [10,11,12].

On the other hand, before leaching copper oxide and secondary sulfide ores, acid curing and agglomeration techniques are commonly employed to enhance copper extraction. Agglomeration is the process of binding fine particles to coarser ones, which ultimately increases the permeability of an ore heap. On the other hand, acid curing inhibits the dissolution of certain silicates and accelerates the copper extraction process [13,14,15]. Curing causes the sulfation of solid particles of copper ore with concentrated sulfuric acid, which promotes favorable conditions for leaching [16,17]. In curing, sulfation in leaching is an important process because preparing ores by sulfating the copper causes copper dissolution in a shorter time, increasing the extraction speed and decreasing the leaching cycle times. Today, this stage is always present in the leaching processes of oxidized copper minerals due to its proven effects, mainly in the early days of leaching kinetics.

Concerning pilot tests in columns, heap leach test work involve loading the ore into columns and irrigating it with a leach solution. Daily drainage solution measurements calculate metal extraction over time. Columns of the same height as commercial heaps in the lab are used to represent a small segment [18]. This type of study is essential for scaling up from the laboratory to industrial applications. Column leaching tests are necessary to obtain relevant parameters and the effect of variables in a relevant environment [19]. Gómez studied the oxidized copper recovery kinetics in column tests on a sample without sulfation and another with sulfuric acid. On day 1 of leaching, copper recovery reached 3.40% for the mineral sample without sulfation vs. 25.72% for the sulfated mineral sample. On day 3 of leaching, it was 19.75% vs. 41.46%, and on day 5, it was 33.32% vs. 48.95% [20]. The mathematical modeling of columnar leaching is a helpful tool for predicting and evaluating the kinetics of copper extraction. There are two main models that describe this process: the Progressive Conversion Model and the Shrinking Core Model. However, the sulfation factor is not incorporated in any of them. The first model considers a porous spherical solid particle. It also considers that the mineralogical species present in the sample react with the acid continuously and progressively throughout the particle [21]. The other model, the shrinking core model, better explains the behavior of mineral leaching processes that present relatively homogeneous mineralization and is widely used [22,23].

The shrinking core model (SCM) considers that the reaction begins at the particle’s outer surface. The reaction zone moves into the solid, leaving behind fully reacted material and an inert solid. Therefore, an unreacted material core shrinks during the reaction [24,25], as seen in Figure 1.

The general dissolution reaction of metal (II) oxides is given by Reaction (R1) and for metal sulfides according to Reaction (R2) [26,27]:

$${MeO}_s+2HX\to {MeX}_2+H_{2}O$$

(R1)

$$\mathrm{MeS}+2{\mathrm{Fe}}^{3+}\to {\mathrm{Me}}^{2+}+{\mathrm{S}}^0+2{\mathrm{Fe}}^{2+}$$

(R2)

2. Materials and Methods

2.1. Ore Sample

Oxidized copper ore from a heap leaching operation located in Copiapó, Chile, was used in this study. The ore was crushed and screened to obtain two particle sizes samples, one under −3/4″ and another at −3/8″. P₈₀ values obtained were 7632 µm and 6563 µm. The chemical composition of the ore was determined by atomic spectrometry (SpectrAA 220, Varian, Palo Alto, CA, USA). Results of chemical composition are shown in

Table 1. Chemical composition of the ore.

Sample	Cutot (%)	Cusol (%)	Acid Consumption (kg/ton)
Mineral −3/4″	0.76	0.66	114
Mineral −3/8″	0.77	0.67	112

.

The main mineralogical species composition of the ore samples is given by chrysocolla, malachite, azurite, atacamite, brochantite, chalcocite, chalcopyrite, and bornite. These were determined by X-ray diffraction.

2.2. Reagents

Sulfuric acid, technical grade (H₂SO₄, 97%), and drinking water were used in all tests performed.

2.2.1. Pretreatment Test

Experiment techniques were used to evaluate the effect of the acid dosage, rest time, humidity, and P₈₀ on copper recovery. Some preliminary tests were performed to define ore saturation humidity and percentage acid dosage range.

Table 2. Pretreatment test evaluation conditions.

Variable	Level
Acid dosage	20, 30, 40% (1)
Humidity	110, 100, 90% (2)
P80	−3/4″, −3/8″
Resting time	24, 48, 72, 96 h

⁽¹⁾ Percentage of acid consumption by chemical analysis. ⁽²⁾ Percentage of ore saturation humidity: 59.1 kg/t for −3/4″ and 62.1 kg/t for −3/8″.

shows the conditions evaluated on pretreatment tests.

The pretreatment tests involved 2 kg of ore. On a plastic sheet, the ore sample was homogenized. Then, concentrated sulfuric acid and water were added at different levels. A second round of homogenization was developed, so the mineral was left in repose for the time defined. The pretreated ore was washed with 2 L water at 60 °C at the end of time repose. Solution and copper tail concentrations were determined using the atomic absorption spectrometry technique. Copper extraction was calculated based on the dissolved copper concentration in the solution and tails. Eight conditions from all of the tests were evaluated in column tests at different heights (two acid dosages, one humidity, two value P₈₀, and two repose times).

2.2.2. Leaching Column Test

In columns of a height of 2 m and internal diameter of 0.17 m, 8-column leaching tests were performed for 30 days. A factorial experimental design technique was applied. The levels of these variables are shown in

Table 3. Leaching column test conditions.

Column	P80 (µm)	Acid Dosage (kg/t)	Humidity (%)	Rest Time (h)
1	7862	34.2	5.91	24
2	6902	34.2	6.21	24
3	7862	34.2	5.91	48
4	6902	34.2	6.21	48
5	7862	45.6	5.91	24
6	6902	45.6	6.21	24
7	7862	45.6	5.91	48
8	6902	45.6	6.21	48

.

The extraction of copper was monitored by periodically measuring the volume of effluent solution from the column and analyzing the concentrations of copper in this solution by EAA. Once the leaching time ended, tails were chemically analyzed as well.

2.2.3. Modeling Leaching Column

The shrinking core model, as shown in Equation (1), was used on the leach kinetics data, so the rate constant was determined by linear regression.

$$1-\frac{2}{3}\propto -{\left(1-\propto \right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=kt$$

(1)

where α is the recovery of the chemical species, $k$ is the rate constant, and $t$ is the leaching time.

Table 4. Leaching column test conditions.

Column	P80 (µm)	Acid Dosage (kg/t)	Rest Time (h)	Rate Constant, k (1/s)
1	7862	34.2	24	0.004790
2	6902	34.2	24	0.005224
3	786	34.2	48	0.004757
4	6902	34.2	48	0.005057
5	7862	45.6	24	0.004529
6	6902	45.6	24	0.004823
7	7862	45.6	48	0.004763
8	6902	45.6	48	0.004577

shows the rate of the value constant obtained.

2.2.4. Sulfation Factor in Modeling Leaching Column

When the mineral is sulfated in a pretreatment stage, previous to the leaching stage, a sulfated mineral layer is formed on the mineral particle surface, often like a copper sulfate layer, as can be seen in Figure 2. This layer is quickly dissolved by an acid irrigation solution at the beginning of the leaching stage.

The sulfation factor (FS) was incorporated into the predictions of leaching kinetics in the final leaching column model (LCM), as shown in Equations (2)–(4).

$$\mathrm{If} n = 1 \mathrm{or} 2, \mathrm{then}: r_{LCM adjusted} \left(n\right)=\left[R_{LCM (n)}-R_{LCM (n-1)}\right]\ast \left[1+\mathrm{FS}\right]\ast \left[1+\frac{\mathrm{FS}}{2}\right]$$

(2)

$$\mathrm{If} n>2, \mathrm{then}:\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{r}_{LCM adjusted} \left(n\right)=\frac{\left\{\frac{R_{LCM \left(n\right)}-R_{LCM \left(n-1\right)}}{1+\mathrm{FS}}\right\}}{\left[1+\frac{\mathrm{FS}}{2}\right]}$$

(3)

$$R_{LCM adjusted } \left(n\right)=\sum _{i=0}^{n-1}{r}_{MNR ajusted (n-i)}$$

(4)

where $n$ is the point on the leaching kinetics curve at time t, $r_{MLC adjusted}(n)$ is the partial copper recovery predicted by LCM adjusted within FS at point n on the curve, $R_{LCM(n)}$ is the accumulated copper recovery predicted by the LCM model at point n on the leaching curve,$R_{LCM(n-1)}$ is the accumulated copper recovery predicted by the LCM model at point n − 1 on the leaching curve, $FS$ is the sulfation factor, and $R_{LCM ajusted} \left(n\right)$ is the accumulated copper recovery predicted by LCM adjusted within FS at point n on the leaching kinetics curve.

2.2.5. Validation Modeling Leaching Column

Equations (1)–(4) were applied to the bibliographic and historical database of column leaching tests to validate the incorporation of the sulfation factor in the column leaching modeling. Then, the increase in R² value between the shrinking core model (SCM) (Equation (1)) and leaching column model (LCM) (Equations (2)–(4)) was calculated. Note that this database considers minerals different from the one studied.

3. Results and Discussion

3.1. Pretreatment Test

Figure 3 shows the copper sulfation obtained on the pretreatment test. As can be seen, the best result was 49.7% for both granulometry and 45.6 kg/t acid. However, the rest time and humidity were 72 h and 100% for mineral −3/4″ and 24 h and 110% for mineral −3/8″. It should be noted that a smaller granulometry of the mineral allows a greater contact area of the valuable mineral species with acid. However, a higher presence of water due to higher humidity provides a better transport of sulfuric acid to the mineral studied. This would translate into faster copper dissolution kinetics, which would explain the reduction in the rest time observed in this case.

From these results, eight conditions were selected to be evaluated in tests in columns at different heights.

Table 5. Sulfation factor for leaching column test.

Column	P80 (µm)	Acid Dosage (kg/t)	Rest Time (h)	Sulfation Factor, FS
1	7862	34.2	24	0.443
2	6902	34.2	24	0.481
3	7862	34.2	48	0.459
4	6902	34.2	48	0.479
5	7862	45.6	24	0.423
6	6902	45.6	24	0.458
7	7862	45.6	48	0.401
8	6902	45.6	48	0.462

shows the sulfation factor obtained with these conditions.

3.2. Column Leaching

Figure 4 and Figure 5 show the copper recovery rate after 30 days of leaching on minerals −3/4″ and −3/8″, respectively, vs. the predicted values from the SCM model (Equation (1)) and LCM model with the sulfation factor (Equations (2)–(4)) for the same operating conditions. The biggest differences between experiment values and values from the SCM model were observed at the first leaching time for all columns. The determination coefficient (R²) was applied to evaluate the prediction performance of this model. The R² value was lowest in the SCM model for mineral −3/4″ in column 3 with 34.2 kg/t acid dosage and 48 h repose (R² = 66.0%), and the top one in column 5 with 45.6 kg/t acid dosage and 24 h repose (R² = 74.4%), as can be seen in Figure 4b,c. Once the LCM model with the sulfation factor was applied, the lowest R² value was obtained in column 7 with 45.6 kg/t acid dosage and 48 h repose. On the other hand, column 1 at 34.2 kg/t acid dosage and 24 h repose obtained the highest R² value, as shown in Figure 4a,d (R² = 90.8 and 97.9%).

The extraction percentage was characterized by copper recovery. This parameter is defined by the following equation:

$$\mathrm{Copper} \mathrm{Recovery} (\%)=\frac{{\mathrm{M}}_1}{{\mathrm{M}}_0}\times 100$$

(5)

where Copper Recovery (%) is the recovery percentage of copper, and M₀ and M₁ are the mass of copper passing to the solution and mass of copper in the ore sample, respectively.

Moreover, for mineral −3/8″, the lowest R² value in the SCM model was obtained in column 2 with 34.2 kg/t acid dosage and 24 h repose (R² = 65.8%) and the highest was in column 8 with 45.6 kg/t acid dosage and 48 h repose (R² = 75.8%), as shown in Figure 5a,d. The lowest and highest R² values in the LCM model with the sulfation factor were obtained in the same columns (90.6 and 95.0%).

In both cases, the LCM model with the sulfation factor increased the R² value between 14.2 and 31.2%. Therefore, a 23% average increase was obtained. This improvement can be attributed to the LCM model with FS involving the highest copper dissolution rate at the beginning of the leaching because of the ore sulfation’s previous stage (sulfated mineral layer on mineral surface particles), followed by a rate constant. Otherwise, the SMC considers the copper dissolution rate to be constant in time. That would explain the difference in copper recovery at the first point in the copper recovery curve.

3.3. Validation Modeling Leaching Column

Table 6. Operation conditions database for leaching column tests.

Mineral	P80 (µm)	Acid Dosage (kg/t)	Water (kg/t)	Rest Time (h)	Rate Constant, k (1/s)	Sulfation Factor, FS
A	15,153	35	33.6	24	0.003149	0.316
	10,576	35	54.2	24	0.002302	0.419
	2135	35	92.2	24	0.002486	0.366
B	9410	20	74.2	24	0.001935	0.309
	10,750	60	74.2	24	0.001590	0.294
	10,950	30	74.2	24	0.001779	0.367
	9480	22	74.2	24	0.001824	0.329
	8760	22	74.2	24	0.002123	0.329

shows the operation conditions from the historical database of column leaching tests. Figure 6 shows the increase in R² value between the shrinking core model (SCM, Equation (1)) and leaching column model (LCM, Equations (2)–(4)) where the sulfation factor was included.

The LCM model with the sulfation factor increased the R² value from the shrinking core model (SCM) between 7.9 and 48.5% (average 28%). These minimum and maximum increment values were observed where the R² value from SCM reached 88.1% and 43.4%, respectively. Therefore, the increase is lowest when the R² value from SCM is the highest.

4. Conclusions

Incorporating the sulfation factor FS in the SCM model predictions makes it possible to significantly increase the determination coefficient (R²) between the experimental data and the data modeled by the SCM for the kinetics of copper leaching, improving the predictions of the SCM model by an average of 24 to 28%. It was possible to validate this model through a database for different minerals.