Technoeconomic Assessment of Phosphoric Acid and Rare Earth Element Recovery from Phosphoric Acid Sludge

Abstract

Sustainability faces many challenges, including the availability of materials necessary for technological advancement. Rare earth elements (REEs), for example, are key materials for several manufacturing industries that can unlock renewable energy and sustainable development. In this study, a decanter centrifuge has been employed to successfully separated phosphoric acid and REE-containing particles from phosphoric acid sludge with concentrations ranging from 1000 to 2200 ppm REEs. Operating efficiently with up to 35 wt.% solids, the centrifuge was demonstrated to achieve approximately 95% phosphoric acid recovery and 90% REE recovery in a single pass, eliminating the need for additional processing steps. This breakthrough supports a proposed rare earth oxide (REO) recovery process integrating phosphoric acid (PA), elemental phosphorus (P4), and REO into two potential pathways: PA-REO and PA-P4-REO. These processes aim to reintroduce recovered phosphoric acid into the main product to significantly increase output and revenue. Post-separation, phosphorus-rich particles can be converted to P4, while REE-containing solids undergo further treatment including acid leaching, extraction/stripping, precipitation, and calcination to produce a marketable REO material. Technoeconomic analysis indicates promising profitability, with the PA-REO process showing a delta net present value (∆NPV) of USD 441.8 million over a 12-year period and expected return within a year of construction, while the PA-P4-REO process yields a ∆NPV of USD 178.7 million over a 12-year return period. Both pathways offer robust financial prospects and demonstrate the feasibility of commercial-scale REO recovery from phosphoric acid sludge, offering an economically feasible approach to produce REEs for future sustainable development challenges related to sustainability.

1. Introduction

Rare earth elements (REEs) are essential materials for the power, manufacturing, chemical, metallurgical, alloy, electronic appliance, glass, catalyst manufacturing, and other industries [1]. It has been recognized that sustainable development without REEs is not possible. The availability of natural resources for REEs is currently limited to China, Australia, Myanmar, the United States, and a few other countries. With 85% of the global supply, China is emerging as the major producer of REEs [2]. Recognizing the critical importance of REEs for manufacturing, renewable energy, and sustainability, the U.S. Department of Energy established the Critical Materials Institute to solve problems related to the reserves, supply, and recycling of REEs and other critical materials including lithium, aluminum, platinum, graphite, cobalt, copper, fluorine, iridium, magnesium, nickel, and silicon [3]. Securing REEs has become crucial to achieving sustainable development and maintaining national security. One possible resource for the recovery of REEs is the phosphate industry, which includes several streams of high REE concentrations and allows for the opportunity to recycle phosphoric acid (PA) for enhanced fertilizer production [4,5]. It is well known that the phosphate rock, specifically fluorapatite [Ca₁₀(PO₄)₆F₂], contains REEs at a concentration ranging from 100 to 1000 ppm [6]. In 2018, PA production and elemental phosphorus production reached 27 million tons [7]. During the mining/beneficiation process in Florida, for example, approximately 30% of the REEs in phosphate ore reports for waste clay, 10% to flotation tailings, and 60% to the phosphate rock products. In the PA manufacturing process (Figure 1), approximately 70% of the REEs in the phosphate rock reports to phosphogypsum (PG) and 30% to PA.

PA production generates a byproduct called phosphoric acid sludge or evaporation sludge, which contains PA and significant amounts of total REEs at a concentration ranging between 1500 and 3000 ppm. If an effective method could separate the solids from the sludge, recover PA (~54% P₂O₅ [8]), and then extract REEs from the recovered solids, the phosphate industry could become a major supplier of REEs. Traditional solid/liquid separation technologies, however, such as centrifugation, settling, and filtration, are ineffective due to the high viscosity, high density, and high solid content (e.g., 20–40%) of the sludge.

Recently, we employed a continuous-flow decanter centrifuge (CFDC) for the solid/liquid separation of PA and REE-containing solids from actual phosphoric acid sludge [5]. The CFDC offers the possibility of single-step separation without the necessity of pre- or post-processing steps. Continuous-flow separation of PA and REE-containing particles from phosphoric acid sludge was demonstrated using the CFDC in efforts to develop a profitable process for REE recovery in the PA industry. Using the decanter centrifuge, we were able to show the effective separation of solid particles from phosphoric acid sludge containing up to 33.5 wt.% solids without additional processing steps. This accomplishment led to the simultaneous recovery of liquid PA at approximately 93% efficiency and REE-containing solids at 90% efficiency after a single pass in a continuous flow.

Numerous research efforts have been conducted to recover REEs from various industrial byproducts and waste streams including e-waste, used catalysts, PG, geothermal brine water, acid mine drainage, coal ash, and phosphoric acid sludge. However, exploration of the economic feasibility of the proposed technologies for producing rare earth oxide as the final product is limited, as shown in

Table 1. Comparisons of REE recovery processes.

Method	Source (REE Amount, ppm)	Capacity	CAPEX (USD)	OPEX REO (USD/kg)	Value of REO (USD/kg)	Economic Viability	Critical Factor	Ref.
Supercritical extraction	Coal ash (270–1480)	-	-	690–2181	6–557	Low	Price of REE (i.e., Sc)	[9]
Leaching/ solvent extraction	Acid mine drainage precipitation (1103–1669)	1 mt REE/yr	2.6–3.4 million	3400–5900	-	Very low	Process improvement and market change	[10]
Nano-fluid extraction	Geothermal brine (0.25)	6800 gal brine/min	6.8 million	468	-	Low	REE conc./price, electromagnet price Need co-production of other valuable material	[11]
Our study (PA-REO)	Solid in PA sludge (1000–3000)	453,000 mt/yr	7.1 million	71	256	Promising	Co-production of PA
Our study (PA-P4-REO)	Solid in PA sludge (1000–3000)	453,000 mt/yr	7.6 million	551	256	Promising	Co-production of PA and elemental P

. The proposed technoeconomic analysis (TEA) shows that the operating cost of REE recovery (USD/kg) remains high compared to the value of REE particles. To achieve economic viability, process improvement and co-production of other valuable materials are required.

In this study, we conducted a long-term CFDC process to separate solid particles from phosphoric acid sludge. Based on the experimental results, we present a TEA evaluating the potential benefits of the CFDC process for PA and REE recovery from phosphoric acid sludge. The recovered PA can be returned to the main stream, increasing PA production, which will significantly increase the revenue, while solid particles containing REEs can be further processed to produce a commercial-grade rare earth oxide (REO) material. The remaining solids still require extensive treatment such as acid leaching, extraction/stripping, precipitation, and calcination to produce the REO product. Based on a rigorous literature review, we validate the feasible technologies for each process and propose two post-treatment scenarios for the final products: (1) PA and mixed REO and (2) PA, elemental phosphorus (P4), and REO. For the TEA, energy and mass balances are employed to estimate the capital and operating costs of the plant and the levelized value of the REO product. By exploring this innovative approach, we aim to contribute to the development of efficient and economically viable processes for the recovery of REO from PA sludge, thereby addressing the critical need of securing a supply of REO for current and future industrial demands in the U.S. and worldwide.

2. Materials and Method

2.1. Solid/Liquid Separation

Actual phosphoric acid sludge was provided by The Mosaic Company (Bartow, FL, USA). Considering the range of solid content in the sludge detected in PA operations [4,5], we adjusted the concentration of solids in the feed stream to between 25 and 35 wt.% for the experiments performed in this study. This was achieved by mixing estimated portions of the heavy and light sludge fractions. Solid/liquid separation experiments were carried out using a Lemitec MD 60 CFDC (Berlin, Germany) with a 60 mm internal bowl diameter. A continuous-flow process was set up to perform solid/liquid separation experiments using phosphoric acid sludge of varying solid contents. The feed suspension was constantly stirred using an impeller at 100 rotations per minute (rpm). CFDC operation was adjusted at varying rotational speeds, yielding 1000–1500 G acceleration to optimize operational stability and performance in terms of the recovery efficiency of the solids. A 1000 G acceleration achieved at a 5460 rpm rotational speed was selected as the baseline for the evaluation of other operating parameters, including the differential speed of the rotor and feed flow rate. The following relationships were used to quantify the recovery of the solids and liquid:

$$SolidsRecovery(\%)={\displaystyle \frac{Solidsindischargeoutlet}{Solidsamountinfeed\left(1\mathrm{k}\mathrm{g}base\right)}}\times 100$$

(1)

$$LiquidRecovery(\%)={\displaystyle \frac{Liquidinliquidoutlet}{Liquidamountinfeed\left(1\mathrm{k}\mathrm{g}base\right)}}\times 100$$

(2)

2.2. Technoeconomic Analysis

For the TEA analysis, we considered both the capital and operating costs to build a new facility against an “as-is” operation where the phosphoric sludge is used to produce a low-grade fertilizer. Currently, the phosphoric acid sludge is removed from the clarifiers; part of it is recycled in the previous clarifiers to increase the production of 54% PA and part of the sludge goes into fertilizer production processes that have ‘room’ to accommodate the sludge and still meet product specifications. An amount of 453,000 tons of PA sludge is considered the baseline of the mass and energy balances for the proposed processes. The mass and energy balances were used to estimate the size of the equipment and the operating costs associated with each unit operation (Supporting Information). The separated PA (54% P₂O₅) returns to the output stream (i.e., merchant-grade PA) to increase product recovery, while the separated solids require extensive treatment such as acid leaching, extraction/stripping, precipitation, and calcination to produce the REO product. Based on a literature review and the current prices of materials, reliable processes and parameters (e.g., 32 wt.% solids in the feed stream) were adopted. Feasible technologies were then validated for each process, and two final products were considered for analysis: (1) PA and REO (Figure 2a) and (2) PA, P4, and REO (Figure 2b).

The recovered PA and processed mixed REO solids (97.4% purity) are 316,000 metric tons/yr and 138 metric tons/yr, respectively, in the PA-REO process. In the PA-P4-REO process, due to the additional post-treatment of coke roasting, the production of mixed REO is further reduced to 49 tons/yr, and a new product (P4) is produced at 2360 tons/yr. All cost numbers were determined using prices from 2023. The equipment cost for the REE recovery plant based on phosphoric acid sludge was calculated based on the following assumptions: (1) Total equipment costs were calculated based on equipment sizing and cost data from Peters and Timmerhaus [12], with an inflation rate of 5% to convert to 2023 U.S. dollars. (2) Installation, piping, materials, buildings, and engineering were assumed to account for 15%, 15%, 15%, and 10% of total equipment costs, respectively. These assumptions are considered typical for similar activities in the phosphoric acid industry. (3) The total capital cost was then calculated and assumed to be spent within one year from the start of the project in 2023. Operating costs were calculated based on the materials’ cost, which was determined by multiplying the material requirement from the mass balance by the 2023 price (Supporting Information). For the key extraction agent (i.e., TODGA), a price of 6500 USD/kg was chosen for the current price. TODGA is still a new chemical agent which has not been produced in bulk. The price of TODGA is included in the sensitivity study. The cost of waste disposal has not been considered in this process because most of the waste consists of PG and aqueous acid dilution, which are byproducts of the phosphate process stream. The process is supposed to be built at the phosphate mining site, allowing the waste to be dumped into the gypsum stacks (landfill site). In addition to this cost estimation, the following yearly operating costs were also considered: (1) maintenance and repair costs, which account for 15% of the total equipment cost; (2) operating supply costs, estimated at 15% of the maintenance and repair costs; (3) additional charges including labor, overhead, taxes, and insurance, accounting for 2.45% of the operating costs.

Price of Phosphoric Acid: The recent history of phosphoric acid ‘market prices’ is shown in

Table 2. Recent average annual prices of P₂O₅ (obtained from various phosphate industry publications).

Price Point: (100% P2O5)	Average Price (USD/MT)								2016–2023 AVG	Spot Price
	2016	2017	2018	2019	2020	2021	2022	2023
Brazil Quarterly Spot/Contract CFR	756	665	781	746	683	1128	1773	1197	980	1034
India Quarterly Contract CFR	626	566	732	691	628	1073	1541	975	849	850
North Africa Quarterly Contract FOB	699	602	764	745	687	1114	1617	1073	906	887
NW Europe (non-food grade) Quarterly Spot/Contract CFR	N/A	N/A	N/A	N/A	N/A	1254	1712	1218	1427	1034
NW Europe Quarterly Spot/Contract CFR	826	705	855	852	791	1193	1729	1223	1024	1034

in terms of the average price of P₂O₅ per year. These prices are based on 100% P₂O₅, while the final product of the phosphoric acid industry is typically 54% P₂O₅. Based on the lowest 2023 average price of 100% P₂O₅ for India (i.e., 975 USD/MT), the value of 54% P₂O₅ would be 975 USD/100 units = 9.75 USD/unit of P₂O₅ × 54 units = 526.50 USD/ton of 54% P₂O₅ equivalent. Thus, for the purpose of the TEA of the process, the conservative price of 526.50 USD/ton or 0.53 USD/kg of 54% P₂O₅ was used.

Calculation of the delta net present value required the net present value (NPV) of the sludge sold as-is for low-grade fertilizer. A cost of 0.05 USD/kg, approximately 10% of the 54% phosphoric acid price, was assumed, with a revenue inflation rate of 5% over a period of 10 plus 2 years (i.e., 10-year operation and 2-year construction). The depreciation rate for the plant was assumed to be 10%, and the tax rate was set at 35%. Additional revenue was calculated based on the assumption that the recovered PA could be sold at USD 0.53 per kilogram, and the produced mixed REO (97% purity) could be sold at USD 255.6 per kilogram by using contemporary oxide prices. The price of yellow phosphorus (P4) is determined at USD 5380 per metric tonne (Supporting Information).

The annual delta net present value is then estimated by the following formula:

$$NPV={\displaystyle \frac{Revenue-Taxes-OPEX-Depreciation-CAPEX-{Revenue}_{sludge}}{{\left(1+i\right)}^{\left[y-cy\right]}}}$$

(3)

All costs are calculated for the considered year, y, and then calculated with inflation for the present value in the current year, cy. The delta net present value is then the summation of the NPV over the entire project life, i.e., 10 plus 2 years. Finally, the levelized cost is calculated by dividing the delta net present value by the total amount of sludge processed over the 10-year plant operation.

$$LC={\displaystyle \frac{\sum NPV}{m_{sludge}\mathrm{\ast }10yrs}}$$

(4)

3. Results and Discussion

3.1. Process Validation

Decanter Centrifuge: In a previous study, we demonstrated the effectiveness of the decanter centrifuge in separating phosphoric acid sludge containing up to 33.5 wt.% solids into a liquid-rich stream and a solid-rich stream. Concurrent recovery of REE-containing solids at ~90% efficiency and PA liquid at >95% efficiency in a continuous-flow operation was achieved after a single pass [5]. A field test at the Florida Industrial and Phosphate Research Institute, Lakeland Florida, was also performed to evaluate the operational feasibility and assess process performance (Figure 3). The experimental data showed effective continuous separation after a single pass through the CFDC.

Various process conditions were investigated to quantify the total power consumption and the solid/liquid separation efficiency and to determine the optimal range of the process variables (Figure 4). The solid removal rate versus operation time in Figure 4a suggests that as the concentration of solids increased from 26 wt.% to 35 wt.%, the removal rate of solids slightly decreased; however, the decanter removal efficiency remained stable over time. As shown in Figure 4b, the operational capacity of the screw engine and controller indicates a significant increase from 38% to 75% with increasing solid concentration, but the total power consumption did not change due to the operation running within limits. Figure 4c and d show that the flow rate of the sludge feed increased, while the acceleration was fixed at 1500 G. The solid removal efficiency decreased over the increasing range of feed flow rates, while the liquid recovery efficiency did not change. Increasing the flow rate contributed to an increase in operation capacity, but the total energy consumption did not change. The separated solid, as shown in Figure 4e, contains 1000 ppm REEs, while the separated liquid contains <60 ppm of REEs. The separated liquid consists of ~52% P₂O₅ with <5% solids (Figure 4f). The detailed experimental results are available in the Supporting Information, showing consistency with previously reported values [5]. In the material studies for the decanter centrifuge process [5], ICP-MS, SEM-EDS, and XRD showed that the solid particles are mainly PG along with other oxides such as CaCO₃, MgO, Al₂O₃, Fe₂O₃, and SiO₂, as well as trace minerals like mallardite, monazite, xenotime, ilmenite, and cassiterite. Characterization indicated that the crystallinity and composition of the solid particles separated by the decanter are not significantly different from those in the sludge. The decanter-separated wet solid particles still contain ~25% P₂O₅. Water rinsing of the particles is required to clean them, recover the P₂O₅, and enable acid leaching and solvent extraction. Note that an enrichment effect in REEs within the solid particles was observed after water rinsing [5]. The rinsing water contained up to ~20% P₂O₅ with 132 ppm of total REEs, while the REE concentration in the washed particles significantly increased to ~3000 ppm after drying.

The case considered here for the TEA, using the decanter centrifuge, is based on 93% liquid recovery and 90% solid recovery, resulting in a potential 92% recovery of rare earth elements from the phosphoric acid sludge. Based on these experimental data, when we consider a full-scale industrial plant, we can assume an increase in the PA product of 316,000 metric tons of 54% P₂O₅/yr that can be recovered through the CFDC process, and that the separated solid is further processed to recover REEs and/or elemental P.

Acid Washing (leaching REEs from solid particles with sulfuric acid): The solid stream separated from phosphoric acid sludge mostly contains insoluble hydrated calcium sulphate salt (i.e., phosphogypsum, PG). The recovery of REEs from PG has been well studied using mineral acid leaching. Conventional mineral acids such as H₂SO₄, HCl, and HNO₃ have been investigated to leach REEs out of PG under different conditions such as varying concentrations of acid, liquid/solid ratios, and combinations of acid type and leaching time [6]. The reported leaching efficiencies from PG with solely H₂SO₄ leaching were relatively average, ranging from 40% to 70%, and the process consumed large amounts of acid for high liquid (L)-to-solid (S) ratios, in the range of 1.3–8 [13,14,15,16]. Some studies reported that nitric acid (HNO₃) yields higher leaching efficiencies than sulfuric acid [17,18]. In our own work, where all leaching tests were conducted at 30% solids for 8 h, the recovery rate of REEs by HCl leaching was 89.7%. H₂SO₄ is still preferred, however, due to material costs (e.g., 64 USD/MT for sulfuric acid vs. 393 USD/MT for nitric acid on a Free on Board (FOB) Linden NJ basis at the end of the year 2023 [19]) and because H₂SO₄ is already available in phosphoric acid plants, while HNO₃ would need an additional acid circulation procedure. A recent study shows that the REE leaching efficiency can be increased up to 90% through process optimization using an acid concentration of ~3 mol/L, a liquid/solid ratio of 12 L/kg, and a temperature of 55 °C [20]. By adopting a clarifier for the continuous removal of undissolved solids being deposited by sedimentation, the supernatant can be transported to the solvent extraction process. Based on this process, REE recovery can be assumed at 85% with a six-stage circulation procedure. Thus, sulfuric acid and a clarifier system were assumed in this study to convert phosphate to sulfate salts of REEs, with a recovery rate of 85% of the REEs and 3% of the other solids.

Extraction and Stripping (REE extraction from the leaching solution): The hydrometallurgical separation of REEs from conventional sources, such as bastnaesite and monazite, has been accomplished using solvent extraction (SX) and ion exchange chromatography. SX offers several advantages for the separation of REEs from ore concentrates including flexibility in process design, good selectivity, and high REE concentrations in the solvent, which allow for more compact equipment. Solvent extraction is a mass transfer process between two immiscible phases, involving the selective transfer of the desired solute from an aqueous solution to an organic solvent phase. Multiple stages of extraction are typically required to achieve complete solute recovery, and a counter-current cascade is commonly used for efficient separation. Flowsheets of SX of REEs typically include saponification, extraction, scrubbing, and stripping processes. The affinity of the solvent extraction ligands increases with the increasing atomic weight of the REEs, facilitating fractionation and subsequent separation to yield individual REEs. In this study, the diglycolamide (DGA) ligand N, N, N, N’ Tetra-octyl-3-oxopentanediamide (TODGA) was selected as the key reagent for REE extraction. The extraction efficiency of 14 REEs from a sulfuric acid solution is reported to be between 91.0% and 99.8% [21]. TODGA exhibits higher selectivity for REEs and very low affinity for competing metals (e.g., Fe, Mg, and Al). This behavior is advantageous for extracting REEs from complex lean sources. TODGA has been found to have high solubility in paraffinic solvents, poor solubility in aqueous media, and a high distribution (D) value for trivalent actinides [22]. Trioctylamine (TOA) has also been used as an extractant in the form of pseudoprotic ionic liquid for the separation of REEs [23]. Based on the performance of TODGA and TOA, a formula comprising TODGA, TOA, Exxal^TM13, and ISOPAR L was proposed for effectively recovering dissolved REEs from a sulfuric acid medium. The formula allows for the complexation of REEs in the solution and their transfer from the aqueous phase to an aqueous-insoluble hydrophobic (non-polar) solution, where the extractant compound is dissolved [24]. The previously reported formula of a mixture of 0.2 M TODGA + 0.02 M TOA30% v/v Exxal^TM 13 in Isopar-L is assumed as the extraction solution in this study, while 0.01 M H₂SO₄ is assumed as the stripping solution. Extraction and stripping affinities reported in the literature are employed here to determine mass balances and REE recovery for the process flow diagram [24]. The extraction process consists of three stages with a leachant-to-acid volumetric ratio of 2, followed by stripping steps that have an acid-to-leachant volumetric ratio of 4.

Precipitation and REE Oxide Recovery: Oxalic acid is employed to selectively precipitate the REEs as oxalates, which are relatively insoluble. The precipitation reaction occurs by mixing a solution containing REEs with oxalic acid. By controlling the process parameters, such as increasing the oxalic acid concentration to 80 g/L and raising the solution pH from 0.5 to 2.5, significant improvements in the precipitation efficiency of REEs were achieved, reaching up to 95.0% and 98.9%, respectively [25].

The precipitation reaction of REEs with oxalic acid can be expressed by the following overall reaction [26]:

2REE³⁺ + 3C₂H₂O₄ + 10H₂O ⇄ REE₂(C₂O₄)₃∙10H₂O (s) + 6H⁺

(5)

Based on Equation (5), 1.5 mol oxalic acid is required to precipitate 1 mol REEs from solution. The resulting precipitate, known as rare earth oxalate, can be further processed to yield purified REE compounds or metals.

Filtration and Calcination: To filter the REE oxide products, a rotary vacuum drum filtration unit is assumed in this study. This equipment involves the use of a rotating drum, a vacuum system, and a filter medium to achieve efficient solid/liquid separation. Widely used in various industrial fields, this filtration technique enables the continuous filtering, clarification, cake washing, extraction, and dewatering of slurries and waste materials [27]. An oxalic acid precipitator with an acid-to-feed ratio of 1.2 and a vacuum drum filter with a wash water ratio of 4.0 were assumed to recover REEs as oxalic acid complexes with 96% purity and 95% recovery. Calcination was the final unit operation to convert REEs to the oxide form for calculation of the mixed REO production rate. The required air ratio for calcination was assumed to be 1.0. After washing the calcinated product, mixed REO of 97.4% purity is obtained.

Elemental Phosphorus Production from Sludge Solids: Elemental phosphorus is commercially produced through an electrothermal process commonly known as coke roasting. The primary source for this process is fluoroapatite, 3Ca₃(PO₄)₂·CaF₂, commonly known as ‘phosphate rock’. Impurities present in phosphate rock include calcium and magnesium carbonates, iron (lll) oxide, aluminum oxide, and silica. In the furnace, a mixture of phosphate rock, coke, and silica (sand) in a mass ratio typically of 16:30:100 is smelted, resulting in the formation of carbon monoxide and phosphorus. The phosphorus is released as an element at temperatures ranging from 1200 to 1500 °C. The reaction can be represented as follows:

2Ca₃(PO₄)₂ (s) + 6SiO₂ (s) + 10 C (s) → 6 CaSiO₃ (s) + P₄(g) + 10 CO(g)

(6)

Gaseous phosphorus and carbon monoxide, obtained from the top of the furnace, are then passed into a water spray at 343 K. Most of the phosphorus (melting point 317 K) condenses during this process and condensation is completed by using cold water. The carbon monoxide can be either oxidized or recycled as a fuel source that can be utilized in the preparation of nodules from phosphate rock or sold to local power producers. Molten calcium silicate slag and an alloy of iron and phosphorus, known as ferrophosphorus, are removed from the bottom of the furnace. Following the traditional approach, the P₂O₅ from the separated solids (CaSO₄·2H₂O) is recovered to yield elemental phosphorus. We demonstrated that approximately 60% of the total P₂O₅ in the solid is converted into elemental phosphorus through thermal coke roasting [Supporting Information]. The REEs are further concentrated into the byproduct solid, which can be further processed to produce REE oxides.

REE Leaching from the Roasted Byproduct: The leaching of REEs from the roasted byproduct is conducted at room temperature with a 30% solid concentration using either a 5M nitric acid solution or a 5M hydrochloric acid solution. Nitric acid is preferred as it does not react with the residual carbon in the roasted product. Through leaching, a REE recovery rate of 98% is achieved [Supporting Information]. Approximately one-fifth of the acid is consumed during leaching, while the remainder is recycled. Leching is accomplished in a single stage.

Liquid Waste after REE Recovery: Based on the mass balances of the proposed PA-REO processes, the composition of the waste liquid is investigated in

Table 3. The mass balance of the liquid waste presented in Figure 2a. The number in parentheses ( ) represents the process stream.

	PA Sludge [mt/yr (1)]	Liquid Waste [mt/yr (11)]	Aqueous Waste [mt/yr (13)]	Aqueous Waste [mt/yr (15)]
Total REE	291	48	13	-
CaSO4	79,000	-	-	-
CaO	21,200	18,300	-	-
AlPO4	9430	-	-	-
Al2(SO4)3		11,400	-	89
Al2(C2O4)3	-	-	2	-
FePO4	7990	-	-	-
Fe2(SO4)3	-	9150	-	275
Fe2(C2O4)3	-	-	7	-
Mg(H2PO4)2	5850	-	-	-
MgSO4	-	2780	-	-
Oxalic Acid	-	-	31	-
H2SO4	-	-	313	-
H3PO4	-	-	3260	-
Water	-	-	19,900	506
Total Mass	453,000	41,700	23,600	874

. Metal phosphate in the sludge was converted to metal sulfate after sulfuric acid leaching. The metal sulfate was removed from the process stream, ending up in the liquid waste. A significant amount of water 19,900 mt/yr is required for the vacuum drum filter process to purify the REO precipitate, resulting in 23,600 mt/yr of aqueous waste. After calcination, further water is required to rinse out the metal sulfate residue. The liquid waste may be dumped in the landfill. The waste mass balance for PA-P4-REO is available in the Supporting Information.

3.2. Technoeconomic Analysis Validation

The technoeconomic performance of the two REE extraction processes presented in Figure 2 is assessed for a representative feedstock of the PA sludge obtained from passive treatment beds by The Mosaic Company in Florida. The materials used, energy expended, and costs for a hypothetical processing plant designed to produce a solid REO are first presented. The revenue is then quantified using both scenarios for lifecycle economic metrics, such as the net present value and internal rate of return. Finally, the sensitivity of the net profit to cost components is evaluated, and recommendations for process modifications to make REE extraction economically viable are discussed.

Based on the annual production of PA sludge (453,000 metric tons/year) with a content of 32 wt.% solids, the recovered PA and processed REO solids are 316,000 metric tons/yr and 138 metric tons/yr, respectively, in scenario I, while due to the additional post-treatment of coke roasting in scenario II, the production of REO is further reduced to 49 tons/yr and a new profit from elemental P is produced at 2360 tons/year (Figure 2a). The capital costs of the process equipment for scenarios I and II, as shown in

Table 4. CAPEXs of the equipment for the two operational scenarios presented in Figure 2.

	PA-REO (USD)	PA-P4-REO (USD)
Centrifugal Decanter	756,594	756,594
Roster	-	882,480
Acid Washer	1,088,849	562,587
Clarifier	161,910	158,047
Extractor	1,670,663	1,638,071
Stripper	464,497	472,427
Precipitator	29,587	27,826
Drum Filter	373,052	352,104
Calciner	22,415	21,648
Total Module Cost	4,567,565	4,871,798
Installation	685,135	730,770
Piping/Materials	685,135	730,770
Buildings	685,135	730,770
Engineering	456,756	487,180
Total Capital Cost	7,079,725	7,551,286

, are estimated at USD 7.08 million and USD 7.55 million, respectively. The capital cost of a REE recovery facility processing 297,000 tons of amine sand tailing per year, with ~229 ppm of REEs, is reported to be USD 13.5 million [28]. Another study reported the capital cost of a facility producing 1 ton REEs/year from acid mine drainage precipitate to be USD 2.6–3.4 million [10]. A commercial SX process accounts for ~20% of the total equipment cost for both scenarios. The total capital cost for scenario II is slightly higher than that for scenario I because after producing P4 in the coke roasting process, the mass flow rate of the process stream (i.e., concentrated solids) is significantly reduced by acid washing. The extracting and stripping are the most expensive processing steps in terms of capital expenses. The decanter centrifuge appears to have a medium CAPEX.

Table 5. OPEX of operating units for both processes (details available in Supporting Information).

	PA-REO			PA-P4-REO
	Category	Stream	Operating Cost (USD/yr)	Category	Stream	Operating Cost (USD/yr)
Centrifuge Decanter	Electricity	1	43,843	Electricity	1	43,518
Water Washing	Process Water	2	92,715	Process Water	2	93,893
Roster	-	-	-	Coke/Air	3	8,405,691
Acid Wash	Sulfuric Acid/Electricity	3/4	2,846,754 /69,410	Nitric Acid/ Electricity	4/5	11,903,503 /36,435
Extraction	TODGA /Trioctylamine	5a	4,348,734 /113	TODGA/ Trioctylamine	6a	4,298,506 /112
	Exxal 13 /Isopropanol	5b	6049 /6600	Exxal 13 /Isopropanol	6b	5979 /6535
Precipitation	Oxalic Acid	6	441,637	Oxalic Acid	7	314,582
Drum Filter	Process Water and Electricity	7	2681	Process Water and Electricity	8	2310
Calcination	Air and Power	8	21,175	Air and Power	9	14,669
Total			7,879,711			25,125,734
Maintenance and Repairs	15% Capital		685,135			730,770
Operating Supplies	15% Maint. Rep.		102,770			109,615
Charges	15% Op. Suppl.		15,415			16,442
Labor	Operator Salary = USD 60k		309,240			302,884
Overhead			695,582			717,115
Taxes			91,351			97,436
Insurance			45,676			48,718
Total Operating Costs			9,824,880			27,148,714

shows that the operating costs of sludge processing via PA-REO and PA-P4-REO are determined at USD 9.82 million (equivalent to 21.7 USD/ton of sludge) and USD 27.15 million (equivalent to 59.9 USD/ton of sludge), respectively. The levelized cost of REO solids produced from the PA-REO and PA-P4-REO processes as shown in

Table 6. Levelized operating costs (per kg) of products PA, P4, and REO.

	PA-REO	PA-P4-REO
54% PA	0.9 USD/mt	0.9 USD/mt
P4	-	4104.8 USD/mt
Mixed REO (97.4%)	71.0 USD/kg	550.6 USD/kg

and is determined to be 71.0 USD/kg and 550.6 USD/kg, respectively. As a reference, the levelized cost of REEs from coal mining drainage (~0.9 ppm) is reported to range between 86,000 and 278,000 USD/kg [29]. Due to the production of P4, the production rate of REO from the PA-P4-REO process is reduced by ~64.5%, and nitric acid is used for the extraction instead of sulfuric acid.

Figure 5a shows that 71.0% of the revenue in the PA-REO process comes from phosphoric acid, while REO accounts for 29% of the revenue. In the PA-P4-REO process, the production of P4 could not increase the total revenue compared to that from PA-REO, because of the reduction in REO production and the relatively low revenue contribution associated with the high operating costs in scenario II (Figure 5b).

Based on the CAPEX, OPEX, and revenues, we determined the net present value, which is the sum of all future cash flows over the investment’s operation time (i.e., 10 years), discounted to the present value. The calculation of the delta net present value requires the net present value (NPV) of the sludge sold as-is for low-grade fertilizer. Figure 5c shows the delta net present value (ΔNPV; light green and blue bars), assuming a revenue inflation rate of 5% over an operational period of 10 plus 2 years, comparing the total value of the project (acid and REO recovery) against the current scenario (i.e., sale of sludge for low-grade fertilizer). The ΔNPV of the PA-REO process is estimated at USD 441.8 million, while the ΔNPV of the PA-P4-REO process is estimated at USD 178.7 million. Figure 6 shows both profiles of the NPV over 12 years. Capital costs and a loss of current profit (i.e., sale of sludge; no change) can be returned after construction of the sludge treatment facilities. Overall, the TEA concluded that both processes are profitable.

A sensitivity analysis was performed on both scenarios using the current pricing of PA, elemental P4, and REO for the delta NPV. The results of the sensitivity analysis are presented as a tornado plot in Figure 7. The tornado plot clearly shows that three project parameters, i.e., phosphoric acid, sludge, and REE prices, have a significant impact on the profitability of the PA-REO project. In contrast, in the PA-P4-REO project, the REE price has a marginal impact due to the significantly reduced production amount. The prices of coke and elemental phosphorous also have an impact on the profitability.

4. Conclusions

Rare earth elements (REEs) hold the key to sustainable development. Searching for new REE resources, we focused on processing streams of the phosphate industry in this study. Specifically, phosphoric acid sludge, a byproduct of phosphoric acid production, has been found as a source of relatively high REE concentrations. Using actual phosphoric acid sludge, we employed a decanter centrifuge to successfully demonstrate continuous separation of phosphoric acid and REE-containing particles from phosphoric acid sludge, achieving efficiencies of around 95% for phosphoric acid and 90% for REE recovery in a single pass. This breakthrough has led to the proposal of two profitable processes, PA-REO and PA-P4-REO, which aim to reintroduce recovered phosphoric acid into the mainstream product, while producing saleable elemental phosphorous and rare earth oxide materials. The ∆NPV of the PA-REO process is estimated at USD 441.8 million, with a projected investment return a year after process construction. Similarly, the PA-P4-REO process shows a ∆NPV at USD 178.7 million, with the same return period over the next 12 years. The TEA indicates that both processes offer promising financial returns despite the need for further processing to extract the REO product. This study has, therefore, led to a potential resource for REEs using an economically feasible process which could be employed to manufacture REEs to help achieve sustainable development.