A Hybrid Experimental and Theoretical Approach to Optimize Recovery of Rare Earth Elements from Acid Mine Drainage Precipitates by Oxalic Acid Precipitation

: The development of processing techniques for the extraction of rare earth elements and critical minerals (REE/CM) from acid mine drainage precipitates (AMDp) has attracted increased interest in recent years. Processes under development often utilize a standard hydrometallurgical approach that includes leaching and solvent extraction followed by oxalic acid precipitation and calcination to produce a ﬁnal rare earth oxide product. Impurities such as Ca, Al, Mn, Fe and Mg can be detrimental in the oxalate precipitation step and a survey of the literature showed limited data pertaining to the REE precipitation efﬁciency in solutions with high impurity concentrations. As such, a systematic laboratory-scale precipitation study was performed on a strip solution generated by the acid leaching and solvent extraction of an AMDp feedstock to identify the optimal processing conditions that maximize REE precipitation efﬁciency and product purity while minimizing the oxalic acid dosage. Given the unique chemical characteristics of AMDp, the feed solution utilized in this study contained a moderate concentration of REEs (440 mg/L) as well a signiﬁcant concentration (>7000 mg/L total) of non-REE contaminants such as Ca, Al, Mn, Fe and Mg. Initially, a theoretical basis for the required oxalic acid dose, optimal pH and predicted precipitation efﬁciency was established by solution equilibrium calculations. Following the solution chemistry calculations, bench-scale precipitation experiments were conducted and these test results indicate that a pH of 1.5 to 2, a reaction time of more than 2 h and an oxalic acid dosage of 30 to 40 g/L optimized the REEs recovery of at ~95% to nearly 100% for individual REE species. The test results validated the optimal pH predicted by the solution chemistry calculations (1.5 to 5); however, the predicted dosage needed for complete REE recovery (10 g/L) was signiﬁcantly lower than the experimentally-determined dosage of 30 to 40 g/L. The reason for this discrepancy was determined to be due to the large concentration of impurities and large number of potential metal complexes that cause inaccuracies in the solution equilibrium calculations. Based on these ﬁndings, a hybrid experimental and theoretical approach is proposed for future oxalic acid precipitation optimization studies.


Introduction
Rare earth elements (REEs) are considered critical raw materials by the USA Department of Energy, USA Department of the Interior and other federal agencies, particularly for their use in numerous green energy, defense and technology applications [1][2][3]. REEs are considered essential for modern society as key ingredients in magnets, batteries, phosphors and catalysts, which have implications for wind turbines, consumer electronics, electronic vehicles, petroleum refining and other application areas [1]. Over the last two decades, the global REEs market has been dominated by China for the mining, separation, refining Hassas et al. exploited the CO 2 mineralization process to precipitate RE-carbonates from acid mine drainage with 85% of REE recovery in the optimal conditions [25]. Despite these developments, the most common industrial precipitant for REE recovery from strongly acidic solutions is oxalic acid [25,26]. The oxalate ion has a strong affinity to REEs, which in turn prompts high selectivity and high recovery at low pH points. Unfortunately, oxalic acid can also be consumed by common contaminants, particularly Ca and Al, which can in turn prompt higher costs for unpurified solutions. As such, the influence of contaminant concentration on oxalic acid efficiency must be carefully considered [27].
To investigate the utility of oxalic acid precipitation in the recovery of REEs from AMDp, a systematic experimental study was conducted. Initially, solution equilibrium calculations were conducted to evaluate the underlying principles and reactions between oxalic acid and rare earth elements in aqueous solutions. Next, pilot-scale acid leaching and solvent extraction tests were performed to produce a loaded strip solution containing REEs as well as common non-RE contaminant metals. In the subsequent laboratory-scale experimental study, the effect of reaction time, endpoint pH, oxalic acid dose and base type on the REE recovery and selectivity was evaluated. Section 1 of this paper explains the background and motivation. Section 2 described the experimental methods and analytical techniques utilized in the oxalic acid precipitation study. Section 3 shows the solution equilibrium calculations and reconciles the findings with the experimental work and Section 4 provides the conclusion and recommendations for further study.

AMDp Sample Location, Acquisition
The acid mine drainage precipitate sample utilized in this study was collected from an abandoned coarse coal refuse disposal facility in Greenbrier County, West Virginia in the Central Appalachian Basin, USA. Various coal seams were extracted at this mine, including Pocahontas 3-6, Beckley, Firecreek, Sewell and Little Raleigh. The influent pH of the acid mine drainage is 2.94 and the on-site treatment facility uses NaOH for pH neutralization (pH ≈ 7). During sample recovery, the wet precipitate samples were recovered from the on-site sludge storage pond and placed in new high-density polyethylene (HDPE) buckets for transport and storage. Further details on the challenges and issues associated with AMDp sampling have been provided by [9,10,28].
For the AMDp feedstock, the average TREE concentration was determined to be 937.9 g/t with a 95% confidence interval of ±74.5 g/t. HREE and LREE concentrations were 475.9 and 462.0 g/t with 95% confidence intervals of ±39.8 and ±34.9 g/t, respectively. The AMDp samples display a pronounced convex-upward North American Shale Composite (NASC) normalized REEs pattern, which demonstrates the acid mine drainage was more enriched middle REEs (e.g., Sm-Dy) and HREEs than LREEs when compared to the NASC. The major mineralogical phases detected in the AMDp samples were Al-Fe-Mg hydroxides and silicate minerals such as quartz, calcium aluminum silicate and magnesium silicate. The REE geochemical speciation for the AMDp sample mainly contains phases in carbonate, iron and manganese oxide, organic matter and minor residue such as silicate minerals [28].

Sample Preparation
In order to systematically study the precipitation behavior of rare earth elements (REEs) in aqueous solution by oxalic acid, the AMDp sample was first processed by a standard hydrometallurgical flowsheet incorporating leaching, solvent extraction and stripping to produce an enriched strip solution suitable for REE recovery via oxalic acid precipitation. Figure 1 provides the schematic representation of the REEs processing circuits. The AMDp sample was leached by reagent grade nitric acid solution. After sufficient reaction time, the leachate was filtered to eliminate the residue solids to generate the highly pure pregnant leachate solution (PLS) without any solid particles, which was fed into the solvent extraction unit as the feed solution. The chemicals utilized for solvent extraction were diluent: Elixore 205, extractants: Di-(2-ethylhexyl) phosphoric acid (D2EHPA) and tributyl phosphate (TBP) with an Organic/Aqueous (O:A) ratio of 1:1. The loaded organic solution from the solvent extraction was then stripped by high concentration of nitric acid (6 mol/L). This stripping solution was utilized in the study for the precipitation optimization of rare earth elements (REEs) by oxalic acid. The rare earth elemental and major metal concentration in the stripping solution is provided in Table 1. highly pure pregnant leachate solution (PLS) without any solid particles, which was fed into the solvent extraction unit as the feed solution. The chemicals utilized for solvent extraction were diluent: Elixore 205, extractants: Di-(2-ethylhexyl) phosphoric acid (D2EHPA) and tributyl phosphate (TBP) with an Organic/Aqueous (O:A) ratio of 1:1. The loaded organic solution from the solvent extraction was then stripped by high concentration of nitric acid (6 mol/L). This stripping solution was utilized in the study for the precipitation optimization of rare earth elements (REEs) by oxalic acid. The rare earth elemental and major metal concentration in the stripping solution is provided in Table 1.  Major contaminant elements and their concentrations relative to that of the REEs included: Mn (1:1), Ca (10:1) and Al (6.5:1). Fe, Mg and Si were also present but in much lower concentrations (<10% of that of the REEs). The initial pH was measured to be <1.0.  Major contaminant elements and their concentrations relative to that of the REEs included: Mn (1:1), Ca (10:1) and Al (6.5:1). Fe, Mg and Si were also present but in much lower concentrations (<10% of that of the REEs). The initial pH was measured to be <1.0.

Oxalic Acid Precipitation Tests
For each precipitation test, 100 mL of stripping solution was first poured into a glass beaker. Dry oxalic acid powder was added to the stripping solution at designated concentrations and the pH was further adjusted to the desired value for the reaction.
After sufficient reaction time, the reactant was filtered for solid-liquid separation. The solid residue was further digested by the solid assaying method described below, while the leachate was then diluted and analyzed directly by ICP-MS to complete the mass balance. Figure 2 shows the schematic for the precipitation test procedure, while Table 2 shows the experimental design. All tests were conducted at room temperature and open atmospheric pressure. The parameters use in the experimental design are based on the solution equilibrium calculations published by Chi and Xu [29].

Oxalic Acid Precipitation Tests
For each precipitation test, 100 mL of stripping solution was first poured into a glass beaker. Dry oxalic acid powder was added to the stripping solution at designated concentrations and the pH was further adjusted to the desired value for the reaction. After sufficient reaction time, the reactant was filtered for solid-liquid separation. The solid residue was further digested by the solid assaying method described below, while the leachate was then diluted and analyzed directly by ICP-MS to complete the mass balance. Figure  2 shows the schematic for the precipitation test procedure, while Table 2 shows the experimental design. All tests were conducted at room temperature and open atmospheric pressure. The parameters use in the experimental design are based on the solution equilibrium calculations published by Chi and Xu [29].

Analytical Procedures
Solid samples were dried in an oven at 107 °C and digested using a microwave-assisted acidic (HNO3) and alkaline (NaOH) digestion. After drying, the solid specimens were first digested using concentrated NaOH in a microwave carousel as prescribed by the EPA3052 method. After adding a small amount of deionized water into the microwave carousel and cooling, another aliquot of concentrated HNO3 (TraceMetal TM Grade, Fisher Chemical) was added and digested using a modified EPA 3052 method [30] at a temperature of 200 °C. The fully digested REEs were then diluted in 2% HNO3 and metal content was determined by ICP-MS.
REE and major metals concentrations for liquid aliquots were diluted in 2% HNO3 and determined by inductively coupled plasma-mass spectrometry (ICP-MS). An Agilent

Analytical Procedures
Solid samples were dried in an oven at 107 • C and digested using a microwave-assisted acidic (HNO 3 ) and alkaline (NaOH) digestion. After drying, the solid specimens were first digested using concentrated NaOH in a microwave carousel as prescribed by the EPA3052 method. After adding a small amount of deionized water into the microwave carousel and cooling, another aliquot of concentrated HNO 3 (TraceMetal TM Grade, Fisher Chemical) was added and digested using a modified EPA 3052 method [30] at a temperature of 200 • C. The fully digested REEs were then diluted in 2% HNO 3 and metal content was determined by ICP-MS.
REE and major metals concentrations for liquid aliquots were diluted in 2% HNO 3 and determined by inductively coupled plasma-mass spectrometry (ICP-MS). An Agilent 7900 ICP-MS was used for quantitative determination of trace metals. All samples were analyzed in both ICP-MS standard operating mode and optimized with KED mode, which allows the user to supply a non-reactive gas (He) that physically interacts with the ionized sample.

Oxalate Speciation
In order to systematically study the precipitation behavior of oxalic acid and to predict the optimal oxalic dosage, solution equilibrium calculations were performed. The procedure utilized in this study followed that originally derived by Chi and Xu with key adaptations to accommodate the unique attributes of the AMDp-based feedstock [29]. In addition, the concentrations of REEs and other gangue metals was adjusted to reflect the actual values of the strip solution obtained from pilot-scale solvent extraction testing. These calculations show the species distribution of oxalic acid as a function of pH, as well as the oxalic acid consumption by REEs, excess consumption by REEs for complete precipitation and non-RE contaminants consumption.
The equilibrium equations used in this study are listed in Table 3. Equations (1) and (2) provide the equilibrium equations and corresponding reaction constants for speciation distribution of oxalic acid precipitants. Reaction constants of the rare earth elemental precipitation reactions were calculated using the Gibbs free energy of formation of the precipitates and the corresponding constituent components. Equations (4)- (6) give the fraction of each species to the total species, respectively, where ϕ 0 + ϕ 1 + ϕ 2 = 1. As described by Chi and Xu [29], the speciation of oxalate favors H 2 C 2 O 4 at pH values less than 1, HC 2 O 4 − at pH values between 1 and 4 and C 2 O 4 2− at pH values greater than 4. These balances collectively control the amount of oxalic acid needed to maintain a desired level of C 2 O 4 2− . The equilibrium equations considered in this study are at room temperature and consequently the experimental study was performed at room temperature. Table 3. The equilibrium equations, solubility constants and species distribution for oxalic acid precipitation.

Equation Equilibrium Equation Constants/Description
Total concentration of oxalic acid containing species The fraction of C 2 O 2− 4 to the total concentration The fraction of HC 2 O − 4 to the total concentration

Oxalic Acid Consumption
In addition to the oxalic consumption by REEs described by the reaction equations in Table 3, non-REE contaminants in the aqueous solution, such as Ca 2+ , also consume the oxalic acid, thus increasing the dosage needed to obtain a fixed REE precipitation efficiency. Total oxalic acid consumption can be calculated based on the stoichiometric consumption by REEs (H P ), excess consumption by REEs (H E ) to achieve complete precipitation and precipitation and complexation of other coexisting non-REE contaminants (H I ), which are calculated respectively by Equations (8)-(10) as shown in Table 4. Related equations and solubility product constants (Equations (15)- (24) are also listed in Table 4. After calculating the optimal dosage, the oxalic acid precipitation efficiency, which is a key metric in optimizing performance, can be calculated using Equation (14).
For the non-REE contaminants, initial calculations were performed considering only Ca 2+ as the primary contaminant, as per the procedure described by Chi and Xu [29]. However, this approach proved to be insufficient for the strip solutions evaluated in this study and as such, other metal ions, including Fe 3+ , Al 3+ , Mg 2+ and Mn 2+ , were later considered to improve the accuracy of the predictions. Table 4. Equations used to determine oxalic acid consumption for REE precipitation.

Equation Equilibrium Equation Notes
8 Stoichiometric consumption by REEs C RE -Total REEs concentration; RE 3+ -Remaining REEs concentration Excess consumption for complete precipitation by REEs Stoichiometric consumption; [M] represent the divalent and trivalent metal ions Excess consumption for the metal ion of [M] 12 Oxalic acid efficiency 15 Ca Al Mn

Effect of Reaction Time, pH and Oxalic Acid Dosage on Precipitation Efficiency
Laboratory-scale oxalic acid precipitation tests were conducted to identify influential factors and determine the optimal process conditions for recovery of REEs. Initial results from the solution equilibrium reaction modeling (see Section 3.2) showed that a pH of 1.5 to 2 and an oxalic acid dose of 10 g/L would be suitable for optimization studies. As such, values within these ranges were utilized for the initial parametric studies. Figure 3 shows the effect of reaction time on the recovery of REEs at a fixed pH of 1.5 and oxalic acid dosage of 15 g/L. These data show that recovery increases with increasing reaction time and levels off at approximately 120 to 150 min.
The relationship between REE precipitation and pH at a fixed oxalic acid dose and reaction time is shown in Figure 4. These data show a significant increase in REE recovery when pH is increased from 0.5 to 1.25 and more modest increases above 1.25. At pH 3 to 4, the REEs recovery tends to level off with no further improvements. These trends with respect to pH match very well with the solution equilibrium calculations, particularly those showing the speciation of oxalate as a function of pH (see Section 3.2). As indicated, the optimal pH of 1.25 to 2 tends to maximize both RE recovery and the purity of REE precipitates.
In Figure 5, REE recovery as a function of oxalic acid dosage is shown. These data indicate that the oxalic acid dosage required for complete REEs precipitation with recovery of nearly 100% is approximately 30 g/L. This value is much higher than the calculated  The relationship between REE precipitation and pH at a fixed oxalic acid dose reaction time is shown in Figure 4. These data show a significant increase in REE recov when pH is increased from 0.5 to 1.25 and more modest increases above 1.25. At pH 4, the REEs recovery tends to level off with no further improvements. These trends w respect to pH match very well with the solution equilibrium calculations, particul those showing the speciation of oxalate as a function of pH (see Section 3.2). As indica the optimal pH of 1.25 to 2 tends to maximize both RE recovery and the purity of precipitates.  The relationship between REE precipitation and pH at a fixed oxalic reaction time is shown in Figure 4. These data show a significant increase in when pH is increased from 0.5 to 1.25 and more modest increases above 1. 4, the REEs recovery tends to level off with no further improvements. Thes respect to pH match very well with the solution equilibrium calculations those showing the speciation of oxalate as a function of pH (see Section 3.2). the optimal pH of 1.25 to 2 tends to maximize both RE recovery and the precipitates. In Figure 5, REE recovery as a function of oxalic acid dosage is show indicate that the oxalic acid dosage required for complete REEs preci Elemental recovery for both rare earth elements (REEs) and contaminants (Al, Ca, Fe, Mn, Si) was also plotted to evaluate the effect of precipitation parameters including reaction time, pH and oxalic acid dosage on the precipitation efficiency. Figures 6-8 show the effect of reaction time, pH and oxalic acid dosage on elemental recovery of REEs and contaminants, respectively. The Mg concentration is much lower than the detection limit of ICP-MS, which also indicates that Mg is not precipitated at all by oxalic acid and is relatively easier to be separated from rare earth elements. Tables 5-7 list the elemental recovery for rare earth elements and contaminants respectively.

Effect of Reaction Time, pH and Oxalic Acid Dosage on REEs Recovery and Contaminants (Al, Ca, Fe, Mn, Si) Separation
Elemental recovery for both rare earth elements (REEs) and contaminants (Al, Ca, Fe, Mn, Si) was also plotted to evaluate the effect of precipitation parameters including reaction time, pH and oxalic acid dosage on the precipitation efficiency. Figures 6-8 show the effect of reaction time, pH and oxalic acid dosage on elemental recovery of REEs and contaminants, respectively. The Mg concentration is much lower than the detection limit of ICP-MS, which also indicates that Mg is not precipitated at all by oxalic acid and is relatively easier to be separated from rare earth elements. Tables 5-7 list the elemental recovery for rare earth elements and contaminants respectively.   As seen in Table 5 and Figure 6, the recovery of both rare earth elements and contaminants increase with increasing reaction time. With the exception of Y, the recoveries for As shown in Table 6 and Figure 7, pH strongly controls the separation the rare elements from contaminants. The results clearly indicate that recovery of contamin (Al, Ca, Fe, Mn, Si) is reduced while the pH is lower than 3. However, when pH is gr than 3, more contaminants are precipitated, thus reducing the final REE product pu As such, pH control is critical to separate the rare earth elements from contaminan addition, rare earth elemental recovery increases when pH is lower than 1.28 and ten level off. Therefore, to keep the elemental recovery as high as possible and the con nants as low as possible, a pH of around 1.5 to 2 is recommended for separation. result is supported by the oxalic acid speciation calculations.   As shown in Table 7 and Figure 8, an oxalic acid dosage of 10 g/L is the minimum dosage that is able to recover rare earth elements and higher dosages of 20 g/L or greater lead to significant increases in REE recovery. The data suggest that an optimal dose of 20 g/L maximizes REE recovery at 90% to 95% , hile minimizing the recovery of impurities. As seen in Table 5 and Figure 6, the recovery of both rare earth elements and contaminants increase with increasing reaction time. With the exception of Y, the recoveries for REEs generally followed a strong correlation with respect to atomic number, as lanthanum had the lowest recovery (55.72% at 150 min), while lutetium had the highest recovery (87.9%) at a fixed pH of 1.5 and a dosage of 15 g/L. The contaminants were precipitated with fractions of Al 1.58%, Ca 25.82%, Fe 3.39%, Mn 1.58%, Si 67.09%, respectively, at the maximum reaction time of 150 min. Most of the contaminants, with the exception of calcium are successfully separated at the pH of 1.5 and dosage of 15 g/L. Silica was also precipitated; however, the total amount of silica in the stripping solution is low and as such, silica was not found to be a major contaminant in this case.  As shown in Table 6 and Figure 7, pH strongly controls the separation the rare earth elements from contaminants. The results clearly indicate that recovery of contaminants (Al, Ca, Fe, Mn, Si) is reduced while the pH is lower than 3. However, when pH is greater than 3, more contaminants are precipitated, thus reducing the final REE product purity. As such, pH control is critical to separate the rare earth elements from contaminants. In addition, rare earth elemental recovery increases when pH is lower than 1.28 and tends to level off. Therefore, to keep the elemental recovery as high as possible and the contaminants as low as possible, a pH of around 1.5 to 2 is recommended for separation. This result is supported by the oxalic acid speciation calculations.
As shown in Table 7 and Figure 8, an oxalic acid dosage of 10 g/L is the minimum dosage that is able to recover rare earth elements and higher dosages of 20 g/L or greater lead to significant increases in REE recovery. The data suggest that an optimal dose of 20 g/L maximizes REE recovery at 90% to 95%, hile minimizing the recovery of impurities. Excess dosages above this amount lead to nearly 100% REEs recovery but higher levels of contamination., particularly Al and Ca.

Solution Equilibrium Calculations Modeling and Discussion
Using the Equations in Table 4, solution equilibrium calculations were performed to determine the stoichiometric dose of oxalic acid, the excess oxalic acid needed for complete precipitation and the oxalic acid consumption by contaminant metals. Initially, the stoichiometric dosage of oxalic acid for the precipitation of REEs was calculated based on Equation (8) in Table 4. The REE concentration listed in Table 1 was converted from ppm to mol/L with an initial TREE concentration of 0.0032 mol/L and a desired ending REE concentration of 1.00 × 10 −5 mol/L, representing near complete recovery of REEs from solution. Based on Equation (8) Non-REE metallic ions such as Ca 2+ , Al 3+ , Fe 3+ , Mg 2+ and Mn 2+ are contained to some degree in the REE leachates and strip solutions. Equations (10)- (12) in Table 4 were utilized to calculate the quantitative oxalic acid consumption by non-REE metals. Solubility product constants for the contaminant ions are also given in Equations (15)- (24). For example, the stoichiometric amount of oxalic acid for a [Ca 2+ ] concentration of 0.106 mol/L was determined in this calculation.
The additional dosage of oxalic acid for complexing non-REE species can be calculated based on Equation (12) in Table 4. For calcium ion precipitation, 0.10 mol/L was consumed, which included both the stoichiometric and excess dosage for calcium contaminant. Of this total, excess dosage consumed by non-REE contaminants was minimal and may be considered negligible in most cases. Further calculation details from the solution chemistry model are shown in Tables S1-S3.
In addition to calcium, aluminum ion in this stripping solution was also found to be a major non-REE contaminant with a concentration of 2,855 mg/L. Considering the aluminum species distribution in an Al 3+ -H 2 C 2 O 4 -H 2 O system not only contains various species of aluminum oxalates, but also several aluminum hydroxylates [31], it is not appropriate to determine the oxalic acid consumption directly based on the total [Al 3+ ] concentration. However, a phase of Al 3 (OH) 7 (C 2 O 4 )·3H 2 O has been proven to be a possible precipitate with relatively higher [Al 3+ ] concentration at pH < 6.8 [32]. Together, these findings suggest that the amount of oxalic acid consumed by [ ]. Given these complexities and the potential errors propagated by insufficient knowledge of the contaminant complexes, we propose a hybrid approach to dose optimization. Initially, one could consider [Ca 2+ ] only as the major non-REE contaminant, in a manner similar to that proposed by Chi and Xu [29]. This approach provides a reliable minimum bound for oxalic acid dose since [Ca 2+ ] is mostly consumed by oxalates rather than hydroxylates in aqueous solution. For the low pH range under consideration, the predicted oxalic acid dosage for [Ca 2+ ] consumption with concentration of 0.106 mol/L was determined to be 0.105 mol/L. Thus, the total oxalic acid dosage was calculated as 10.13 g/L. Using this value and the optimal pH points dictated by oxalate speciation, one could conduct initial laboratory tests starting at that lower bound and incrementing upward by 5 to 10 g/L until a desired REE recovery is achieved.
After the optimal oxalic acid dose is achieved, the model can be refined using a semi-empirical approach. If all the non-REE metals are to be considered for oxalic acid consumption, most of the  2+ ] are used, the estimated final oxalic acid dosage for full precipitation would be 29.80 g/L at a pH of 1.5-a value that closely coincides with the experimental findings. By tuning this model to the specific strip solutions of interest, one could reiterate the model calculations to determine the economic impact of changing the pH point or the removing a contaminant prior to oxalic acid precipitation. This semi-empirical approach provides a suitable method for process synthesis and optimization.
The recovery of REEs from a solvent extraction strip solution derived from AMDp was investigated through both solution equilibrium calculations and laboratory-scale oxalic acid precipitation tests. The experimental optimization results investigated the influence of pH, reaction time and oxalic acid dose on the separation of REEs from contaminants. At a reaction time of 120 min and a pH of 1.5 and REE recovery of 95% was achieved with an oxalic acid dose of 20 g/L and this recovery approached 100% as the dose was increased to 30 g/L. The increased dose also led to more gangue metal contamination, suggesting that dose control can optimize purity, recovery and cost.

Summary and Conclusions
The solution equilibrium calculations determined the oxalic acid speciation, oxalic acid consumption due to REEs and contaminant metals and the theoretical influence of pH on product purity. Using the method of Chi and Xu [29], initial results, which only considered calcium as the major contaminant, predicted an optimal oxalic acid dose of approximately 10 g/L-a value significantly less than the experimental optimum of 20 to 30 g/L. Further analysis showed that this discrepancy was primarily due to the presence of other contaminants, such as iron, aluminum, manganese and magnesium; however, interactions between metal ion complex formation and pH suggests that it is not appropriate to utilize the total metal concentration in the calculation of oxalic acid consumption, as this approach will lead to a gross overestimation. As a more pragmatic approach, we recommended a hybrid optimization technique whereby the calcium-only consumption value is used at a starting point for experimentation and the oxalic acid does is gradually increased until a suitable recovery is obtained. Empirical or fundamentallyderived correlations (i.e., fractions of gangue metals that complex with oxalate) can then be integrated into the solution equilibrium calculation model to develop a useful tool for process analysis and improvement.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/min12020236/s1, Table S1. Calculated species fraction with respective to the total acid concentration as a function of pH; Table S2. Input variables and other parameters used in solution chemistry calculations. Table S3. Calculated excess oxalic acid usage (H E ) for REE precipitation at a final REE concentration of 1.00 × 10 −5 .
Funding: This material is based upon work supported by the USA Department of Energy under Award Number DE-FE0026927. The authors would also like to acknowledge support from the Virginia Tech Open Access Subvention Fund, which covered the publication costs for this article.