Ion-Exchange Model for the Leaching Process of Ion-Adsorption-Type Rare-Earth Ores Considering the Influence of Anions

Abstract

Clay minerals have a specific adsorption capability for anions, which increases the amount of net negative charge on the surface, leading to the increased adsorption of rare-earth ions in clay minerals and some change from exchangeable to non-exchangeable. Further, anions show a shielding effect on rare-earth ions. The shielding capacity of anions in the leaching agents for rare-earth ions was measured in this study. The relationship between the solid-phase concentration of rare-earth ions shielded and the anion concentration was consistent with the Langmuir model. Based on the Kerr model describing the exchange of rare-earth ions by ammonium ions, an ion-exchange model considering the shielding influence of anions was proposed. The accuracy of the proposed model was higher than that of the Kerr model. When the leaching agent was ammonium sulfate, the calculation accuracy of XW and AY samples was increased by 1.15% and 5.75%, respectively. The improvement in accuracy positively correlated with the proportion of iron oxides, aluminium oxides, and Kaolin. The established ion-exchange model can provide accurate source and sink terms for the numerical simulation of the leaching process of ion-adsorption-type rare-earth ores.

1. Introduction

Ion-adsorption-type rare-earth ores (IATREOs) distributed in southern China are rich in medium and heavy rare earths [1]. Rare earth elements are essential for high-tech products and are known as industrial vitamins [1,2]. The characteristics of IATREOs are rare-earth ions adsorbed by clay minerals in the form of ions or hydrated ions [1,3,4]. Currently, the process of leaching IATREOs relies on in situ leaching technology, and the leaching agent is mainly ammonium sulfate. Determining the concentrations and amounts of leaching agents is based primarily on engineering experience. Due to the complex geological conditions in mines, the grade and permeability have significant spatial variability, and consequently, the required amount of leaching agent varies even in adjacent ore blocks. Therefore, it is difficult to determine accurate values of leaching agents only by engineering experience. If too much leaching agent is used, the cost increases, and at the same time, the leaching agent in the surrounding groundwater can exceed the environmental pollution standards; if the concentration and dosage of the leaching agent are insufficient, the leaching rate of rare earths will be low, resulting in a waste of resources [5]. Establishing a mathematical model corresponding to the physical and chemical process of the in situ leaching process and determining the liquid injection parameters is an effective solution to solve the difficulties of leaching IATREOs under complex geological conditions. From this perspective, studying the ion-exchange process between leaching agents and rare-earth ions is crucial to numerical simulation of the in situ leaching process.

There are broadly two types of theoretical research on the ion-exchange process between leaching agents and rare-earth ions. The first involves the kinetic analysis method considering ion-migration time. Tian et al. [6,7] found that the physical and chemical process of leaching IATREOs is similar to the aqueous–solid reaction process in the field of hydrometallurgy, and the internal diffusion controls the ion-exchange process when analysing the leaching process by the shrinking-core model. Subsequently, researchers began to use the shrinking-core model to analyse the kinetic process with different leaching agents such as magnesium sulfate, mixed ammonium salt, etc. [8,9,10,11,12]. However, unlike the aqueous–solid reaction process in the field of hydrometallurgy, as well as core non-shrinkage and reversibility characteristics of the leaching progress of IATREOs, the shrinking-core model can only describe the kinetic process in the early stage [13]. Therefore, Long et al. [14] established a kinetic model to describe the entire leaching process. The second type of theoretical research involves the use of mass action theory. Studies have shown that the exchange process between leaching agents and rare-earth ions is fast, and the exchange time is very short, irrespective of the migration time of ions on the surface of clay minerals [1]. Compared with the kinetic leaching method, the mass action theory has the advantages of requiring only a simple model, convenient calculations, and easy access to parameters. Chi et al. [15] proposed an equilibrium calculation formula for the co-leaching of rare earths and impurity ions based on the mass action theory, calculated the free energy, explained the reasons for the low exchange rate of rare earths, and also devised a method to improve the leaching rate of IATREOs. Long et al. [5] adopted the Kerr model, Vanselow model, and Gapon model to describe the exchange process of IATREOs, then recommended the Kerr model because of its low calculation errors, simplicity, and ease of analysis. Based on the mass action theory, Long et al. [16] proposed a two-parameter model with higher accuracy than the Kerr model to simulate the exchange process of IATREOs.

Existing research has not considered the influence of anions on the ion exchange process, but studies have shown that anions affect the exchange of cations through the following four mechanisms. (1) Anions are adsorbed onto the surface of the solid phase, changing the properties of the solid phase, increasing the negative charge on the surface, enhancing the electrostatic attraction of the solid phase, and transforming a portion of the ion-exchangeable cations into non-exchangeable cations [17,18,19,20]. The anions play a role in shielding some ion-exchangeable cations. (2) The specifically adsorbed anions form ion pairs with the cations, and the anion and cation are adsorbed together, which also shield a portion of rare-earth ions. (3) The anions pass through the diffusion layer into the surface of the solid phase, complex with high-valent cations, reduce the valence of the cation, weaken their electrostatic attraction with the surface of the solid phase, and make the cations easier to desorb [21,22]. (4) The anions in the aqueous phase interact with cations to reduce the ion activity and increase the difficulty of desorption of cations [23,24]. Therefore, anions have a significant effect on the desorption of cations. Wang et al. [25] and He et al. [10] verified the effects of anions through experiments but did not establish a mathematical model to quantify the influence.

In this study, we experimented on the shielding capacity of anions with different leaching agent concentrations to analyse the relationship between the level of shielding of rare-earth ions and anion concentrations and subsequently obtain the corresponding mathematical expressions. The Kerr model was used to describe the ion-exchange process of IATREOs. An ion-exchange model considering the shielding influence of anions was established by determining the mathematical relationship between the shielded rare-earth ions and the anion concentrations. The accuracy of the proposed model was also verified through experiments.

2. Materials and Methods

2.1. Ore Sample

The original ore was taken from IATREOs in Xunwu County (XW) and Anyuan County (AY), China. The original ore was placed in a ventilated environment to air dry until the mass water content was less than 2.0 wt%. Two kilograms of the original ore was sieved using a GZS-1-type high-frequency vibrating screen (aperture 0.25 mm, Nanjing Ningxi Soil Instrument Co., Ltd., Nanjing, China), and all of the original ore particles smaller than 0.25 mm were used as the test samples, which are referred to as the XW sample and AY sample. The rare-earth composition, main metal elements, and clay mineral composition of the test samples were analysed by the Center of Analysis and Testing of Jiangxi University of Science and Technology through inductively coupled plasma mass spectrometry (ICP-MS), X-ray fluorescence spectrometry analysis (XRF) and X-ray diffraction (XRD), respectively. The results of ICP-MS are shown in

Table 1. Rare-earth composition (wt%).

Type	La2O3	CeO2	Pr6O11	Nd2O3	Sm2O3
XW sample	31.57	1.02	2.41	26.32	5.29
AY sample	15.60	1.52	1.04	11.47	2.65
Type	Eu2O3	Gd2O3	Tb4O7	Dy2O3	Ho2O3
XW sample	0.43	4.16	0.26	2.57	0.44
AY sample	0.56	4.19	0.38	4.41	0.85
Type	Er2O3	Tm2O3	Yb2O3	Lu2O3	Y2O3
XW sample	1.12	0.14	0.77	0.09	23.43
AY sample	2.38	0.29	1.79	0.25	52.57

.

The relative molecular masses of rare-earth ions (RE³⁺) and rare-earth oxides (REO) were calculated from the distribution of the ore samples with a weighted-average method, as shown in Equations (1) and (2), respectively [26].

$$M_{\mathrm{RE}}={\displaystyle \sum _{i=1}^{15}\frac{n_i{M}_{\mathrm{RE},i}^2{\alpha }_i/M_{\mathrm{REO},i}}{{\displaystyle \sum _{i=1}^{15}{n}_i{M}_{\mathrm{RE},i}{\alpha }_i/M_{\mathrm{REO},i}}}}$$

(1)

$$M_{\mathrm{REO}}={\displaystyle \sum _{i=1}^{15}{\alpha }_i{M}_{\mathrm{REO},i}}$$

(2)

where M_RE and M_REO are the average relative molecular masses of RE³⁺ and REO, respectively. For the XW sample, M_RE and M_REO are 131.9 and 311.8 g/mol, respectively; for the AY sample, M_RE and M_REO are 117.7 and 283.4 g/mol, respectively. Further, i = 1, 2, 3, …, 15, which represent La, Ce, Pr, …, Y, respectively. n_i represents the number of rare-earth atoms in a certain REO. α_i represents the percentage of a certain REO in the total REO. The α_i values for the XW and AY samples are shown in Table 1. M_RE,i and M_REO,i are the relative molecular masses of RE³⁺ and REO, respectively. For example, for the XW sample, when i = 1, n₁ = 2 and α₁ = 31.57 wt%, M_RE,1 and M_REO,1 are 138.9 and 325.8 g/mol, respectively.

The average valence of RE³⁺ was calculated by the weighted average from Table 1, as shown in Equation (3). The average valence of RE³⁺ in the XW and AY samples was +3.05 and +3.03, respectively. For the convenience of calculation, the average valence of the RE³⁺ for the two ore samples analysed in this paper was taken as +3.

$$z_{\mathrm{RE}}={\displaystyle \sum _{i=1}^{15}\frac{n_i{z}_{\mathrm{RE},i}{\alpha }_i/M_{\mathrm{REO},i}}{{\displaystyle \sum _{i=1}^{15}{n}_i{\alpha }_i/M_{\mathrm{REO},i}}}}$$

(3)

where z_RE is the average valence of RE³⁺ and z_RE,i is the valence of the corresponding RE³⁺. For example, when i = 1, the RE³⁺ is a lanthanum ion, and z_RE,1 = 3.

2.2. Rare-Earth Grade Test

Forty grams of the ore sample was weighed and poured into a glass funnel with medium-speed filter paper (with a pore size of 30–50 μm, made by Fushun Civil Affairs Filter Paper Factory, Fushun, China). A 150 mL plastic bottle was placed at the bottom of the funnel. Then, 120 mL of ammonium chloride solution with a concentration of 32.4 g/L was added into the funnel at a time (analytical pure, made by Xilong Scientific Co., Ltd., Shantou, China). Two parallel tests were performed and recorded as group A and group B. The volume and concentration of the leachate collected were recorded as V_j and c_RE,j, respectively; Equation (4) was used to calculate the rare-earth grade of ore samples. The detailed test process can be found in the reference [17].

$$\epsilon =\frac{M_{\mathrm{REO}}{\displaystyle \sum _{j=1}^J{V}_j{c}_{\mathrm{RE},j}}}{2M_{\mathrm{RE}}{m}_{\mathrm{s}}}$$

(4)

where ε is the rare-earth grade in g/kg. j is the number of the collected solutions, j = 1, 2, …, J, where J is the total number of collected solutions. V_j and c_RE,j are the volume and the RE³⁺ concentration of the leaching solution, respectively, in L and g/L. m_s is the mass of the ore sample in kg.

2.3. Shielding Test for Sulfate Ions

Ammonium sulfate (analytical pure, made by Xilong Scientific Co., Ltd., Shantou, China)—in concentrations of 5.0, 10.0, 25.0, 40.0, and 60.0 g/L—was used to test the rare-earth grade of the AY sample. The test process was the same as for the rare-earth grade test in Section 2.2. Due to the adsorption of anions, some exchangeable rare-earth ions were shielded and became non-exchangeable. The solid-phase concentration of the shielded rare-earth ions was calculated by Equation (5).

$${\widehat{q}}_{\mathrm{RE}}=\frac{2M_{\mathrm{RE}}\left(\epsilon -{\epsilon }^{\prime }\right)}{M_{\mathrm{REO}}}$$

(5)

where ${\widehat{q}}_{\mathrm{RE}}$ is the solid-phase concentration of the shielded rare-earth ions in g/kg, and ε′ is the rare-earth grade obtained from the ammonium sulfate in this section, in g/kg.

2.4. Balanced Leaching Tests

A 2 cm rotor and 20 g of the XW ore sample were added to 14 centrifuge bottles. Then, 60 mL of ammonium sulfate solution at differing concentrations in the range 2.00–50.00 g/L was added to the respective centrifuge bottles. The speed and temperature of the 85-2A constant temperature magnetic agitators (made by Changzhou Yuexin Instrument Manufacturing Co., Ltd., Changzhou, China) were set to 400 r/min and 30 °C, respectively. A 1 L beaker with water was placed on the tray of the magnetic stirrer. After the water temperature in the beaker stabilized, the centrifuge bottle was placed in the beaker and stirred for 2 h. A TD5 centrifuge (with a centrifugal speed of 3000 r/min, made by Changsha Yingtai Instrument Co., Ltd., Changsha, China) was used to separate the solid and aqueous phases in the centrifuge bottle, and the EDTA volumetric method was used to analyse the concentration of RE³⁺ in the supernatant. Figure 1 shows the balanced leaching test process. Balanced leaching tests of ammonium chloride leaching of the XW sample, and ammonium sulfate and ammonium chloride leaching of the AY sample were performed in the same way as above.

3. Mathematical Model

3.1. Calculation Method for the Shielding Amount

The test results for rare-earth grades—with ammonium chloride as the leaching agent—are shown in Figure 2. When using Equation (4) to analyse the data shown in Figure 2, the rare-earth grades of the XW samples in groups A and B were 3.71 g/kg and 3.66 g/kg, respectively, and the rare-earth grades of the AY samples in groups A and B were 1.57 g/kg and 1.57 g/kg, respectively. Taking the average value of two parallel tests as the rare-earth grade, the rare-earth grades of the XW and AY samples were 3.68 g/kg and 1.57 g/kg, respectively.

The effects of different concentrations of ammonium sulfate solutions on the rare-earth grades of the AY ore samples are shown in Figure 3. It can be seen in the figure that as the concentration of ammonium sulfate increases, the rare-earth grade exhibits a decreasing trend, which eventually stabilizes. The data in Figure 3 for the rare-earth grade of the AY sample—tested using ammonium chloride—was analysed by Equation (5), and the result is plotted in Figure 4. With increases in the anion concentration, the solid-phase concentration of the shielded RE³⁺ first increases and subsequently stabilizes, and there is a maximum shielding solid-phase concentration. Concerning the Langmuir adsorption model, Equation (6) was used to describe the relationship between the solid-phase concentration of the shielded RE³⁺ and the added anion concentration. Fitting the shielding test data with Equation (6), α = 0.30 L/g and β = 2.43 × 10⁻² L/kg were obtained, and the fitted correlation coefficient reached 0.965. Equation (6) can quantify the shielding effect of anions on RE³⁺ well.

$${\widehat{q}}_{\mathrm{RE}}=\frac{\beta c_{\mathrm{an}}^0}{1+\alpha c_{\mathrm{an}}^0}$$

(6)

where α and β are model parameters (α in L/g, β in L/kg), and $c_{\mathrm{an}}^0$ is the concentration of anions in the added leaching agent.

3.2. Ion-Exchange Shielding Model

The stoichiometric reaction between ammonium ion (NH₄⁺) and RE³⁺ is shown in Equation (7) [15].

$${\left[{\mathrm{Al}}_2{\mathrm{Si}}_2{\mathrm{O}}_5{\left(\mathrm{OH}\right)}_4\right]}_m•n{\mathrm{RE}}_{\left(\mathrm{s}\right)}^{3+}+3n{\mathrm{NH}}_{4\left(\mathrm{aq}\right)}^{+}\rightleftharpoons {\left[{\mathrm{Al}}_2{\mathrm{Si}}_2{\mathrm{O}}_5{\left(\mathrm{OH}\right)}_4\right]}_m•{\left({\mathrm{NH}}_4^{+}\right)}_{3n\left(\mathrm{s}\right)}+n{\mathrm{RE}}_{\left(\mathrm{aq}\right)}^{3+}$$

(7)

Equation (7) is regarded as a reversible chemical reaction. The Kerr model can be used to quantify the relationship between the ion concentrations as follows:

$$K=\left(\frac{c_{\mathrm{RE}}}{q_{\mathrm{RE}}}\right){\left(\frac{q_{\mathrm{NH}}}{c_{\mathrm{NH}}}\right)}^3$$

(8)

where K is the ion-exchange selection coefficient, in L²/kg²; c is the ion concentration of the aqueous phase, in g/L; and q is the concentration of solid-phase exchangeable ions, in g/kg. The subscripts NH and RE represent NH₄⁺ and RE³⁺, respectively.

Before and after leaching of the ore samples, NH₄⁺ and RE³⁺ should follow the conservation law of mass. For RE³⁺, the total mass of solid-phase exchangeable RE³⁺, shielded RE³⁺, and aqueous-phase RE³⁺ after the leaching equilibrium is equal to the mass of solid-phase exchangeable RE³⁺ before leaching, as shown in Equation (9). Equations (10) and (11) display the mass conservation of NH₄⁺ and the equivalent relationship between c_RE and q_NH, respectively [17].

$$q_{\mathrm{RE}}^0{m}_{\mathrm{s}}=(q_{\mathrm{RE}}+{\widehat{q}}_{\mathrm{RE}})m_{\mathrm{s}}+c_{\mathrm{RE}}{V}_{\mathrm{L}}$$

(9)

$$c_{\mathrm{NH}}^0{V}_{\mathrm{L}}=c_{\mathrm{NH}}{V}_{\mathrm{L}}+q_{\mathrm{NH}}{m}_s$$

(10)

$$3\frac{c_{\mathrm{RE}}{V}_{\mathrm{L}}}{M_{\mathrm{RE}}}=\frac{q_{\mathrm{NH}}{m}_{\mathrm{s}}}{M_{\mathrm{NH}}}$$

(11)

where $q_{\mathrm{RE}}^0$ represents the concentration of solid-phase exchangeable RE³⁺ before leaching, and $q_{\mathrm{RE}}^0=2\epsilon M_{\mathrm{RE}}/M_{\mathrm{REO}}$. $c_{\mathrm{NH}}^0$ represents the concentration of aqueous-phase NH₄⁺ before leaching.

Rearranging Equations (9)–(11), q_RE, c_NH, and q_NH are all expressed by c_RE. Substituting Equations (6) and (9)–(11) into Equation (8), an ion-exchange model considering the shielding influence of anions in the leaching process of IATREOs is obtained (Equation (12)). Equation (12) is referred to as the shielding model.

$$K=\left(\frac{c_{\mathrm{RE}}}{q_{\mathrm{RE}}^0-\frac{\beta c_{\mathrm{an}}^0}{1+\alpha c_{\mathrm{an}}^0}-c_{\mathrm{RE}}\frac{V_{\mathrm{L}}}{m_{\mathrm{s}}}}\right){\left(\frac{3c_{\mathrm{RE}}{V}_{\mathrm{L}}{M}_{\mathrm{NH}}}{c_{\mathrm{NH}}^0{m}_{\mathrm{s}}{M}_{\mathrm{RE}}-3c_{\mathrm{RE}}{M}_{\mathrm{NH}}{m}_{\mathrm{s}}}\right)}^3$$

(12)

The parameters K, α, and β can be determined by using Equation (12) to fit the test data obtained in Section 2.2. The average relative error (Equation (13)) is the standard for quantifying the calculation error of the proposed model as follows.

$$\xi =\frac{1}{P}{\displaystyle \sum _{p=1}^P\frac{\left|{\tilde{c}}_{\mathrm{RE},p}-c_{\mathrm{RE},p}\right|}{{\tilde{c}}_{\mathrm{RE},p}}}$$

(13)

where ξ is the average relative error, P is the total number of test points, p is the test point number and ${\tilde{c}}_{\mathrm{RE}}$ is the test value of the aqueous-phase RE³⁺ concentration. After determining K, α, and β through test data, the calculated value of the aqueous-phase RE³⁺ concentration can be obtained by Equation (12).

4. Results and Discussion

4.1. Analysis of the Balanced Leaching Test Results

Figure 5 shows the balanced leaching test results. The c_RE increases with the increase in $c_{\mathrm{NH}}^0$. When $c_{\mathrm{NH}}^0$ reaches a value, c_RE stabilizes. For the same ore sample and $c_{\mathrm{NH}}^0$, the c_RE exhibits differences with different anions. For the XW sample, when the range of $c_{\mathrm{NH}}^0$ is 0.27–9.54 g/L, ammonium sulfate leaches more RE³⁺ than ammonium chloride, and the difference can be up to 31.81%. Because the high valence state of RE³⁺ causes an electrostatic effect, RE³⁺ easily coordinates with the anions in the solution and forms water-soluble chlorine and sulfate coordination ions. Analysing the coordination of Eu³⁺, when the concentrations of ammonium sulfate and ammonium chloride are 0.10 mol/L and 0.05 mol/L, respectively, Wang et al. [25,27] found that Eu³⁺ mainly exists in the form of EuSO₄⁺ (about 56%) and Eu(SO₄)₂⁻ (about 40%) when using SO₄²⁻, while the forms when using Cl⁻ were Eu³⁺ (about 76%) and EuCl²⁺ (about 21%). Compared with Cl⁻, RE³⁺ coordinates with SO₄²⁻ to form a lower ionic valence and has more coordination ability. The stronger the coordination ability, the higher the rare-earth leaching rate at the same cation concentration [28]. In cases with low NH₄⁺ concentration, the rare-earth leaching rate when using ammonium sulfate as the leaching agent is higher than with ammonium chloride.

When the range of $c_{\mathrm{NH}}^0$ is 10.91–13.62 g/L, ammonium chloride leaches more RE³⁺ than ammonium sulfate. After the leached RE³⁺ concentration stabilizes, the difference in $c_{\mathrm{RE}}$ between the two leaching agents is 3.12%. Because clay minerals have an adsorption effect on anions, SO₄²⁻ exhibits more obvious obligatory adsorption [29], which increases the net negative charge of clay minerals and the adsorption capacity for rare-earth ions. Further, some rare-earth ions change from exchangeable to non-exchangeable. However, clay minerals have very low specific adsorption of Cl⁻. Therefore, ammonium chloride leaches more RE³⁺ than ammonium sulfate after reaching the leaching equilibrium. The results for the AY sample are similar to those for the XW sample.

4.2. Model Validation

The proposed model and the Kerr model were used to analyse the experimental data shown in Figure 5 (check reference [5] for the calculation steps for the Kerr model), and the calculation results are listed in

Table 2. Model calculation results.

Type	Leaching Agent	Proposed Model				Kerr Model
		K/(L2/kg2)	α/(L/g)	β/(L/kg)	ξ/%	Kk/(L2/kg2)	ξ/%
XW sample	(NH4)2SO4	4.18 × 10−1	2.10 × 10−5	5.04 × 10−3	3.53	3.91 × 10−1	4.68
	NH4Cl	5.16 × 10−2	6.57 × 10−1	1.00 × 10−7	5.43	5.16 × 10−2	5.42
AY sample	(NH4)2SO4	3.03 × 10−2	1.25 × 10−1	2.75 × 10−2	2.08	1.95 × 10−2	7.83
	NH4Cl	5.17 × 10−3	9.86 × 10−6	2.58 × 10−3	4.83	4.81 × 10−3	5.57

Note: K_k is the ion-exchange selection coefficient for the Kerr model.

. When the leaching agent is ammonium chloride, the calculation accuracy of the shielding model is close to that of the Kerr model. Because the ore samples exhibit very low adsorption of Cl⁻ [30], the shielding effect of Cl⁻ on RE³⁺ is small, so the accuracy of the two methods is similar.

Compared with the Kerr model, the accuracies of the shielding model for the XW and AY samples are improved by 1.15% and 5.75%, respectively, when the leaching agent is ammonium sulfate. The main factors that affect the SO₄²⁻ adsorption of the ore sample are the content of iron and aluminium oxide, and the composition of the clay mineral in the ore sample. The higher the iron and aluminium oxide content in the ore sample, the greater the SO₄²⁻ adsorption; the adsorption capacity of clay minerals for SO₄²⁻ generally follows the order: Kaolinite > Illite > Montmorillonite [31].

Table 3. XRF test results.

Analyte	O	Na	Mg	Al	Si	K
XW sample	31.748	0.424	0.172	9.507	31.367	3.373
AY sample	30.390	0.063	0.342	12.658	26.134	3.716
Analyte	Ca	Ti	Mn	Fe	Cu	Zn
XW sample	0.076	0.180	0.026	0.988	0.004	0.008
AY sample	0.009	0.473	0.056	3.913	0.005	0.008

and Figure 6 show the XRF and XRD test results, respectively. The content of iron and aluminium oxides in the AY sample is higher than in the XW sample. According to Figure 6, the proportions of the peak area for the Illite and Kaolinite of the two ore samples are calculated and are listed in

Table 4. Ratio of the phase peak area to the total area.

Type	Illite	Kaolinite
XW sample	0.237	0.012
AY sample	0.177	0.135

. The content of Illite in the two ore samples is equivalent, but the Kaolinite in the AY sample is much greater than in the XW sample. In summary, the adsorptivity of the AY sample for sulfate ions is higher than that of the XW sample, and the analysis accuracy for the AY sample improves significantly with the shielding model.

The proposed model has higher accuracy than the Kerr model when analysing the ion-exchange process of IATREOs. The higher the iron and aluminium oxide content and the greater the proportion of Kaolinite, the better the accuracy of the calculation results.

4.3. Parametric Analysis

The ion-exchange selection coefficient K in the shielding model is a parameter that indicates the difficulty of ion exchange. The larger the value of K, the easier the ion exchange is, and at the same cation concentration of the leaching agent, more RE³⁺ can be leached. From Table 2, the K of ammonium sulfate is greater than that of ammonium chloride, indicating that ammonium sulfate can extract rare-earth ions more easily. In the chloride-ion system, rare-earth ions mainly exist as RE³⁺, while in the sulfate-ion system, rare-earth ions mainly exist as RESO₄⁺ [25,27]. The lower the valence, the easier the exchange [32]. Under the same NH₄⁺ concentration, ammonium sulfate can more easily leach rare-earth ions than ammonium chloride.

α is a parameter that indicates the difficulty of adsorption of anions by the ore sample. Before the adsorption equilibrium, the larger the α, the greater the adsorption capacity of anions at the same concentration and the faster the adsorption equilibrium is reached. The parameter β indicates the maximum adsorption capacity of anions. The greater the parameter β, the greater the amount of anion adsorption, resulting in a higher net negative charge on the surface of clay minerals. The more rare-earth ions that can be converted into a non-exchangeable state, the fewer the rare-earth ions that are leached. The parameter β mainly affects the maximum amount of leached rare-earth ions.

5. Conclusions

(1)

The amount of shielded rare-earth ions was quantified in Langmuir form with the anion concentration. Describing the ion-exchange process with the Kerr model, an ion-exchange model considering the shielding influence of anions on the leaching of rare-earth ions was established.

(2)

At low ammonium ion concentrations—with the same NH₄⁺ concentration—more rare-earth ions were leached when using ammonium sulfate as the leaching agent than when using ammonium chloride. While at high ammonium ion concentrations, compared with ammonium sulfate, using ammonium chloride as the leaching agent extracted more rare-earth ions.

(3)

When the leaching agent is ammonium sulfate, the accuracy of the shielding model—based on analysis of the experimental data of the XW and AY samples—was improved by 1.15% and 5.75%, respectively. The shielding model has a high calculation accuracy.