3.2.6. Morphology

The morphology of the Fire Clay coal middling particles before and after sulfuric acid leaching was studied using SEM. As shown in Figure 12a, the feed material consisted of heterogeneous particles comprised of mostly quartz and clay, which agrees well with the XRD analysis shown in Figure 12b. After 2 h of leaching at 50 ◦C, the particles were found to have a porous structure on the surface with a micro pore structure as shown in Figure 12b. After 2 h of leaching at 75 ◦C, the porous structure on some of the particle surfaces appeared larger in size as shown in Figure 12c. The images show no visible layer on the surface instead of porous structure due to dissolution. Therefore, the diffusion process in this reaction may be the results of interfacial transfer of the products and the reagen<sup>t</sup> diffusion through the porous structure of solid particles.

**Figure 12.** SEM images of particles found in (**a**) leaching feed material; (**b**) solid residue after 2 h leaching at 50 ◦C; (**c**) solid residue after 2 h leaching at 75 ◦C (1 M H2SO4, 530 rpm, S/L = 10 g/L, D80 = 8.7 μm).

The leaching process involved several simultaneous reactions due to the mineral composition and the variety of REE associations. The REEs were found to exist in crystallized structures (mostly silicates and phosphate compounds), which usually require decomposition to be extracted under the current leaching conditions. A small portion of the REEs are present as RE ion substitution form in clays whereas most are associated with soluble RE containing minerals. Based on the results shown in Section 3.2.5, extraction of light REEs in this coal source was more sensitive to temperature thus the light REEs were more likely to be mineral associated, whereas the heavy REEs extraction was more independent to temperature thus more likely to be soluble metal oxides and adsorbed ions onto clay minerals.

#### *3.3. Kinetic Analysis*

The leaching process is classified as a fluid–particle heterogenous reaction in which a liquid reacts with a solid by contacting and transforms the solid into a product. A solid particle that reacts with a liquid and shrinks in size during the reaction can be described by a shrinking core model. The reaction is a five-step process, i.e., (1) di ffusion through the film layer, (2) di ffusion through the product layer, (3) chemical reaction on the surface, (4) product di ffusion through the product layer and (5) product di ffusion through the film layer to the solution. The slowest step is known as the rate determining process. The activation energy of a certain leaching step can be quantified by selecting the most accurate rate equation to represent the reactions [25].

A variety of rate equations have been developed and reported in literature that describe the leaching rate process [25,27,28]. Among the equations, the rate equation (Equation (2)) developed by Crank–Ginstling–Brounshtein, which describes the mass transfer across product layer, fits the experimental data well, i.e.,

$$k\_d t = \left[1 - \frac{2}{3}\alpha - (1 - \alpha)^{\frac{2}{3}}\right] \tag{2}$$

here α is the fraction that reacted; *kd* is the kinetic constant.

The Crank–Ginstling–Brounshtein equation was used to linearize the extraction fraction (α) among all the temperatures using the experimental data for the first 20 min of leaching and the following 20–120 min of the reaction as shown in Figure 13. The correlation coe fficient values (R2) and the corresponding slopes (k) of the plots are listed in Table 2. Rate constants were calculated and the Arrhenius plots of ln(k) versus 1/K are as shown in Figure 14 for the two leaching stages. The activation energy determined for the first 20 min was 36 kJ/mol and 27 kJ/mol for the following 20–120 min of leaching. The activation energy values for both leaching periods were close to the energy barrier that is typically used to identify a di ffusion controlled or chemical reaction controlled process, which is around 20 kJ/mol [26].

**Table 2.** Correlation coe fficients of di ffusion-controlled kinetics models at di fferent temperatures for total REEs.


Note: k denotes the slope of the regression line, and a denotes the intercept of the regression line.

**Figure 13.** Kinetic modeling of total REEs recovery during the (**a**) first 20 min, and (**b**) 20–120 min of leaching at various temperatures for the Fire Clay middlings (1 M H2SO4, 530 rpm, S/L = 10 g/L, D80 = 8.7 μm, retention time of 120 min).

**Figure 14.** Arrhenius plot for the total REEs leached from the Fire Clay coal middlings during the (**a**) first 20 min, and (**b**) 20–120 min of leaching (1 M H2SO4, 530 rpm, S/L = 10g/L, d80 = 8.7 micron).

Since the coal tailing material is a heterogenous material that contains a number of potential modes of occurrence of REEs, the leaching process is not a single reaction. The resulting requirement for activation energy is a combination of the various forms of REEs. In addition, the material contains both calcite and pyrite among other soluble minerals that create a complex solution environment where the localized pH elevation on the solid particle surface could cause a product layer to be formed. The interfacial transfer of product through the porous structure of the solid particles requires high activation energies as reported by Li et al. (2010 and 2013), which can be as high as 40 kJ/mol [23,29].

To support the hypothesis, the activation energies for light and heavy REE groups were calculated using the data provided in Tables 3 and 4, respectively. The activation energy values for leaching the light REEs over the first 20 min and the period between 20 and 120 min were 41.8 kJ/mol and 28.1 kJ/mol, respectively. On the other hand, the activation energy values for the leaching of heavy REEs for the first 20 min and the 20–120 min of reaction were 24.2 kJ/mol and 26.1 kJ/mol, respectively. These values indicate that the leaching of the light REEs during the initial stage is more of a chemical reaction followed by the formation of a product layer and a reduced activation energy. The activation

energy required for leaching the heavy REEs during the initial stage was significantly lower than that of the light REEs. This finding implies that the major rate controlling mechanism for heavy REEs leaching is di ffusion.


**Table 3.** Correlation coe fficients of di ffusion-controlled kinetics models at di fferent temperatures for light REEs.

Note: k denotes the slope of the regression line, and a denotes the intercept of the regression line.

**Table 4.** Correlation coe fficients of di ffusion-controlled kinetics models at di fferent temperatures for heavy REEs.


Note: k denotes the slope of the regression line, and a denotes the intercept of the regression line.

It was noted that the reaction kinetics was extremely fast within the first 1 min of the reaction. A possible explanation is that, due to the di fferent modes of occurrence of REEs in coal-based material, the easy-to-leach REEs was instantaneously released at the beginning of the leaching process, and the hard-to-leach fraction controlled the reaction rate. The mode of occurrence of REEs can be categorized into di fferent forms (i.e., ion exchange form, carbonate form, metal oxide form, acid soluble form, and insoluble form) with di fferent levels of activation energy needed for extraction [24]. Zhang and Honaker (2020) studied the REE mode of occurrence in coal using the sequential chemical extraction method and quantified the REEs associated with each mode [30]. The REEs associated with ion exchangeable form and carbonates are likely to be released instantaneously at the beginning of the extraction process under the leaching conditions of the current study.
