**4. Conclusions**

The Fire Clay coal is an excellent source for REE extraction due to its elevated REE contents and high leaching recovery values. Reducing the particle size of the middings material prior to de-carbonization resulted in the liberation of the associated micro-dispersed mineral matter that contained significantly higher concentrations of REEs. Decreasing the P80 particle size from 38 μm to 5 μm nearly doubled the concentration of REEs in the tailings of the flotation steps, which was the material used a feed for the leaching tests. The major minerals present in the sample were quartz, kaolinite, illite, and muscovite. Exponentially increasing the particle surface area through grinding resulted in higher solid dissolution which elevates the consumption of hydrogen ions and the concentration of contaminant metal ions.

The type of inorganic acid does not a ffect leaching recovery significantly but has an impact on the initial leaching rate. The mixing condition is su fficient at rotational speed values above 500 rpm. Furthermore, solid concentration and acid concentration have a significant e ffect on leaching recovery of REEs. Scanning electron microscope (SEM) images showed no visible product layer or coating product on the particle surfaces. Therefore, the di ffusion process in this reaction may be contributed by the interfacial transfer of the products and the reagen<sup>t</sup> di ffusion through the porous structure of solid particles.

The kinetic data obtained from leaching over a range of temperatures suggested that the leaching process follows the di ffusion control shrinking core model. The activation energy determined from test data obtained over a range of temperatures using 1 M sulfuric acid was 36 kJ/mol for the first 20 min of reaction time and 27 kJ/mol for the leaching period between 20 and 120 min. The leaching of light REEs during the initial stage is much greater than the typical energy barrier of 20 kJ/mol, which indicates that a mixed control mechanism may occur as a result of several heterogenous materials leaching simultaneously. The energy required for later stage of leaching reduced significantly. The activation energy required for leaching the heavy REEs during the initial stage was significantly lower than that of the light REEs, which implies that the major rate controlling mechanism for heavy REE leaching is the di ffusion.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2075-163X/10/6/491/s1, Table S1: Solid loss and REs content in leaching solid residue and leachate solution.

**Author Contributions:** Conceptualization, X.Y. and R.Q.H.; methodology, X.Y. and R.Q.H.; software, X.Y.; validation, X.Y.; formal analysis, X.X.; investigation, X.Y. and R.Q.H.; resources, R.Q.H.; data curation, X.Y.; writing—original draft preparation, X.Y.; writing—review and editing, R.Q.H.; visualization, X.Y.; supervision, R.Q.H.; project administration, R.Q.H.; funding acquisition, R.Q.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the U.S. Department of Energy, Grant Number DE-FE0029900.

**Acknowledgments:** This material is based upon work supported by the Department of Energy under Award Number DE-FE0029900. Disclaimer: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

**Conflicts of Interest:** The authors declare no conflict of interest.
