Kinetic Analysis of Simultaneous Leaching of Lithium, Iron, and Phosphorus from LiFePO₄ Cathodes of Spent Batteries

Abstract

The high-value recovery of valuable components from spent LiFePO₄ (LFP) batteries is of considerable significance for both resource recycling and environmental conservation. This study systematically investigates the simultaneous sulfuric acid leaching of Li, Fe, and P from spent LFP cathode materials, integrating process optimization with kinetic analysis. The effects of acid concentration, temperature, and stirring speed on the leaching behavior of Li, Fe, and P were evaluated to elucidate the underlying kinetic mechanisms. The results demonstrated that under optimal conditions—namely, a sulfuric acid concentration of 2.0 mol/L, a leaching temperature of 60 °C, and a stirring speed of 300 r/min—the leaching rates of Li, Fe, and P all exceeded 99.5%. Kinetic analysis revealed a diffusion-controlled leaching mechanism well described by the Avrami model, with a selective dissolution sequence of Li > Fe > P. The leaching of Li, Fe, and P exhibited apparent activation energies of 9.56 kJ/mol, 14.83 kJ/mol, and 12.82 kJ/mol, respectively. These findings provide theoretical support for the leaching and resource recovery of Li, Fe, and P from spent LFP cathode materials.

1. Introduction

Global commitments to carbon neutrality and peak emissions are accelerating the rapid expansion of zero-carbon industries, notably new energy vehicles and energy storage [1,2]. LiFePO₄ (LFP) batteries now command a leading position in energy storage and electric vehicles, enabled by their long cycle stability, intrinsically safe chemistry, and favorable cost structure. Global production of LFP batteries is projected to increase from 3.94 million tons in 2025 to 10 million tons by 2030 [3]. Nevertheless, with a typical service life of 5–8 years, the escalating deployment scale is anticipated to generate a substantial and growing volume of spent batteries [4]. Improper handling of spent LFP batteries would not only result in the irreversible loss of strategic resources, including Li, Fe, and P, but the fluorinated compounds present in the electrolyte may also exert deleterious effects on human health and ecosystem integrity [5,6]. Consequently, the development of advanced technologies for the safe treatment and resource recovery of end-of-life power batteries is of critical importance for ecological conservation, climate change mitigation, and the security of critical raw material supply.

Currently, the valorization of spent LFP batteries is broadly categorized into direct regeneration [7] and hydrometallurgy routes [8]. Direct regeneration enables the repair of compositional and crystallographic defects in spent LFP cathode materials without disrupting the original lattice structure, thereby restoring its electrochemical performance [9,10]. Although this process is relatively straightforward and cost-effective, the consistency of the regenerated LFP cathode material often fails to meet the stringent standards required for new LFP battery applications [11]. In contrast, hydrometallurgy has emerged as the predominant industrial process for LFP cathode materials recycling, owing to its broad feedstock adaptability, flexibility in product diversification, and high efficiency in comprehensive resource recovery [12]. The hydrometallurgical recovery process typically employs an acidic solution as the reaction medium to transfer valuable elements—including Li, Fe, and P—from the cathode materials into the leachate in ionic form, followed by subsequent purification and refinement. Valuable element ions are subsequently recovered from the solution as metal salts or oxides through unit operations such as ion exchange, chemical precipitation, and solvent extraction [13,14]. Generally, the hydrometallurgical recovery process of LFP comprises four sequential stages: pretreatment, leaching of valuable elements, purification and refinement of the leachate, and product preparation [15]. Leaching is the most critical step that affects the recovery efficiency of valuable elements in LFP cathode materials.

During the leaching stage, it can be observed from previous studies that various types of acids, including inorganic acids and organic acids, are used as leaching agents. Mineral acids include H₂SO₄ [16], HCl [17], H₃PO₄ [18], and organic acids include oxalic acid [19], tartaric acid [20], malic acid [21], acetic acid [22], citric acid [23], and glycine [24]. Overall, sulfuric acid is widely employed in industrial practice and sustainable resource recovery due to its favorable attributes of low cost, minimal environmental impact, and strong leaching capability [25]. A tremendous amount of research has been directed toward the recycling of spent LFP batteries through acid leaching methodologies [26,27]. Vänskä et al. [28] investigated the oxidative leaching of spent LFP black powder in mild H₂SO₄ with Cu and Al impurities, finding that Li leaching remained consistently high (70–88 wt.%), whereas Fe leaching varied widely (5–76 wt.%) with acidity and Cu content. Song et al. [29] developed a streamlined acid leaching–hydrothermal synthesis route for direct LFP regeneration, achieving 96.67% Li and 93.25% Fe recovery under optimized conditions. Kinetic studies revealed a surface chemical reaction-controlled mechanism, with lower activation energy for Li⁺ than Fe²⁺, confirming the preferential leaching of lithium. Lou et al. [30] investigated sulfuric acid leaching of Al-bearing spent LFP cathode powder, achieving 91.53% LFP recovery with only 15.98% Al co-extraction under optimized low-temperature conditions. Kinetic studies revealed mixed surface reaction–diffusion control for LFP versus surface chemical reaction control for Al, confirming selective LFP leaching at reduced temperatures. Although there have been some studies on the sulfuric acid leaching process of spent LFP batteries, they all focused on the lithium and iron elements, while neglecting the phosphorus—the key element of lithium-ion new energy. Therefore, a comprehensive understanding of the leaching behavior and underlying kinetic mechanisms governing Li, Fe, and P dissolution is imperative for advancing the hydrometallurgical recycling of spent LFP batteries.

In this study, sulfuric acid was employed as the leaching agent to systematically investigate the effects of sulfuric acid concentration, reaction temperature, and stirring speed on the leaching behavior of Li, Fe, and P from spent LFP cathode materials. A thermodynamic model of the leaching process was established, and the kinetic mechanisms governing the dissolution of Li, Fe, and P were elucidated. The apparent activation energies and kinetic equations for Li, Fe, and P leaching were subsequently determined. These findings provide essential theoretical guidance for the hydrometallurgical recovery of Li, Fe, and P from spent LFP cathode materials.

2. Materials and Methods

2.1. Spent LFP Cathode Raw Materials

Spent LFP batteries were sourced from a lithium battery recycling enterprise situated in Jiangxi Province, China. To recover the cathode material powder, a multi-step pretreatment protocol was implemented, comprising deep discharge, manual disassembly, thermal pyrolysis, mechanical crushing, and sieving. Specifically, prior to recovery, spent batteries were submerged in an aqueous sodium sulfate bath (1.0 mol/L) for 48 h to fully deplete residual charge [2,6]. The batteries were then manually disassembled to recover the cathode plates, which were subsequently subjected to pyrolysis in a tube furnace at 400 °C under a nitrogen atmosphere for 2 h to decompose the organic binder [31]. Following thermal treatment, the cathode plates were pulverized using a crusher and sieved to obtain the spent LFP cathode material powder with a particle size of less than 0.15 mm.

2.2. Experimental Procedures

All leaching operations utilized a 2 L three-neck round-bottom flask kept in a constant-temperature water bath. A total of 1 L of sulfuric acid solution (1.0–3.0 mol/L) was introduced into the flask, and the mechanical stirring speed was set to 100–500 r/min. To minimize changes in solution volume during the kinetic study, the system was raised to the target reaction temperature (30–70 °C) prior to the addition of 10 g of spent LFP cathode material powder at a solid-to-liquid (S/L) ratio of 10 g/L, upon which the timer was initiated. Aliquots were withdrawn at predetermined time intervals (0.5, 2, 4, 8, 10, 15, 30, 45, 60, 90, 120 and 150 min) using a pipette. Following solid–liquid separation, the concentrations of Li, Fe, and P in the leachate were quantified at each time point, and the corresponding leaching rates were calculated using Equation (1):

$${\eta }_i={\displaystyle \frac{c_i\times V}{m\times {\omega }_i}}\times 100\%$$

(1)

where c_i and V denote the concentration of Li, Fe, or P in the leachate and the total volume of the leachate, respectively; m is the mass of the solid powder sample (g); and ω_i is the mass fraction of the element in the solid powder sample (%).

2.3. Sample Characterization

X-ray diffraction (XRD; Bruker D8 ADVANCE, Germany) was employed to determine the phase composition and crystallographic features of the solid samples. Thermal gravimetric analysis coupled with differential scanning calorimetry (TG/DSC; NETZSCH X70, Germany) was employed to investigate the thermal behavior of the spent LFP cathode material powder. Elemental concentrations in the leachate were quantified by inductively coupled plasma mass spectrometry (ICP-MS; Thermo Scientific ASX-560, USA). The microstructural features and chemical uniformity of the solid materials were assessed through scanning electron microscopy and energy-dispersive X-ray spectroscopy (SEM-EDS; JEOL JSM-6360LV).

3. Results and Discussion

3.1. Analysis of Spent LFP Cathode Material Powder

The XRD pattern of the spent LFP cathode material powder is presented in Figure 1a. The results indicate that the predominant crystalline phases identified are LiFePO₄ and C. The thermogravimetric experiment was conducted in the range of 30–800 °C to investigate the spent LFP cathode material thermochemical stability. Figure 1b shows a distinct heat absorption peak that emerged in the region beyond 400 °C, which might be attributed to the removal of the residual organic binder. The elemental composition of the spent LFP cathode material was analyzed by microwave-assisted digestion with aqua regia, followed by quantitative analysis of the major elements via ICP-MS. The chemical composition results are summarized in

Table 1. The chemical composition of spent LFP cathode material powder (%).

Elements	Li	Fe	P	Al	F	C
Wt (%)	4.33	34.71	20.07	1.24	0.33	4.62

, and the results show that the main elements in the powder are P (20.07%), Fe (34.71%), Li (4.33%), C (4.62%), and a small amount of Al (1.24%) and F (0.33%).

Figure 2 shows the SEM-EDS results of spent LFP cathode material powder. The SEM image demonstrates that the spent LFP cathode material powder is mainly composed of irregular particles of varying sizes. EDS mapping analysis results shown that the main element in the spent LFP cathode material powder is Fe, P, O with small amounts of C and F, and which aligns with the analytical findings presented in Table 1.

3.2. Influences of Various Factors on Li, P, and Fe Leaching Behavior

Using sulfuric acid solution as the leaching agent, under the conditions of S/L ratio 10 g/L, temperature 60 °C, and stirring speed 200 r/min, the effect of sulfuric acid concentration on the leaching behavior of Li, Fe, and P was investigated, and the results are presented in Figure 3. As the sulfuric acid concentration increased from 1.0 to 3.0 mol/L, the leaching rates of Li, Fe, and P exhibited a progressive increase with prolonged leaching time, accompanied by a corresponding increase in the slopes of the leaching rate curves (Figure 3a–c). This phenomenon can be attributed to the enhanced H⁺ concentration gradient at the surface of the spent LFP material particles, which accelerates the leaching kinetics and promotes the dissolution of Li, Fe, and P. At sulfuric acid concentrations ≥ 2.0 mol/L, the leaching reactions for all three elements attained dynamic equilibrium within 120 min, with corresponding leaching rates exceeding 99%. A comparative analysis of the leaching behavior reveals that Li exhibits the highest leachability among the three elements. Specifically, when the acid concentration was 1 mol/L and the reaction time was 2 min, the Li leaching rate exceeded 68% (Figure 3a), while the leaching rates of Fe and P were 59.5% (Figure 3b) and 53.4% (Figure 3c) respectively. This can be ascribed to the interstitial occupancy of Li⁺ within the olivine-type crystal structure of LFP, which renders it readily accessible for leaching by sulfuric acid [32].

The effect of temperature on the leaching behavior of Li, Fe, and P was investigated under the specified conditions (sulfuric acid concentration 2 mol/L, stirring speed 200 r/min, S/L ratio 10 g/L). Figure 4 displays that the reaction temperature significantly affected the leaching of Li, Fe, and P from the spent LFP cathode material powder, with their leaching rates increasing monotonically as the temperature rose. This trend can be attributed to the enhanced molecular collision frequency and accelerated reaction kinetics at elevated temperatures. At 15 min and 60 °C, the leaching rate of Li approached 95% (Figure 4a), whereas those of Fe and P were approximately 91% and 89% (Figure 4b and Figure 4c), respectively, indicating a leaching selectivity order of Li > Fe > P. After 120 min, dynamic equilibrium was attained for all three elements at temperatures ≥ 60 °C, with near-complete leaching observed under these conditions.

The effect of stirring speed on the leaching rates of Li, Fe, and P was systematically investigated under the conditions of sulfuric acid concentration 2 mol/L, leaching temperature 60 °C, and S/L ratio 10 g/L. As depicted in Figure 5, increasing the stirring speed from 100 to 500 r/min resulted in a marked enhancement in the leaching rates of Fe and Li. This trend indicates that elevating the stirring speed effectively facilitates mass transfer and thereby accelerates the leaching kinetics. Furthermore, the pronounced dependence of leaching rate on agitation intensity suggests that the dissolution of Li, Fe, and P is predominantly governed by diffusion-controlled mechanisms. Notably, at a stirring speed of 300 r/min, Li and Fe were almost completely leached within merely 10 min (Figure 5b,c), whereas the leaching of P required approximately 60 min to reach equilibrium (Figure 5c). In addition, Figure 6 presents the SEM characterization of the leaching residue at various time intervals under the reaction conditions of sulfuric acid concentration 2 mol/L, leaching temperature 60 °C, stirring speed 300 r/min, and S/L ratio 10 g/L. Initially, the leaching residue comprised predominantly fine particles (<10 μm). However, as leaching progressed, these fine particles gradually diminished while the proportion of coarser particles (>10 μm) increased concomitantly. Concurrently, the leaching residue morphology evolved from dense aggregates of fine spherical particles to loose, porous structures. This transformation can be attributed to the progressive dissolution of Li, Fe, and P from the spent LiFePO₄ cathode material, leaving behind a leaching residue composed primarily of residual organic binder.

3.3. Leaching Kinetics Analysis

Based on the SEM micrographs of the leaching residues obtained at various reaction times (Figure 6), the shrinking core model for liquid–solid reactions fails to adequately describe the leaching behavior of Li, Fe, and P from spent LFP cathode material. The leaching process can be regarded as the reverse of crystallization. Assuming that nucleation occurs randomly, the unreacted material remains homogeneous throughout the process, the growth rate is independent of the conversion extent, and the growth proceeds isotropically in all directions. The Avrami equation (Equation (2)) has been successfully employed to describe the multi-element leaching kinetics in several solid/liquid heterogeneous reactions [33]:

−ln(1 − x) = ktⁿ

(2)

where x is the volume fraction of Li, Fe, and P; k is the leaching rate constant; t is the leaching time (min); and n is the characteristic parameter of the leaching reaction. When the exponent n in Equation (2) is less than 0.5, the reaction process is diffusion-controlled [34].

Taking the logarithm of both sides of Equation (2) yields a linear relationship between ln[−ln(1 − x)] and ln t, where the slope corresponds to the reaction order n and the intercept corresponds to ln k. As shown in Figure 7, a satisfactory linear correlation is observed between ln[−ln(1 − x)] and ln t under various conditions, indicating that the Avrami equation is applicable for describing the leaching kinetics of LFP cathode material in sulfuric acid solution.

Table 2. Kinetic parameters of Li, Fe and P during the leaching process at different acid concentrations (C, mol/L), leaching temperatures (T, °C), and stirring speeds (S, r/min).

Conditions		Li			Fe			P
		n	ln k	R2	n	ln k	R2	n	ln k	R2
C	1.0	0.1529	0.3379	0.9966	0.2232	−0.2466	0.9993	0.1510	−0.3661	0.9996
	1.5	0.2066	0.4293	0.9951	0.3464	−0.1092	0.9988	0.2686	−0.1723	0.9989
	2.0	0.2387	0.5496	0.9957	0.3468	0.0505	0.9995	0.3017	0.1405	0.9990
	2.5	0.2503	0.6779	0.9993	0.5287	0.2451	0.9989	0.2562	0.3102	0.9996
	3.0	0.2706	0.7524	0.9957	0.5565	0.3438	0.9995	0.3074	0.3928	0.9983
T	30	0.2178	−0.3754	0.9986	0.2372	−0.5460	0.9989	0.1575	−0.4601	0.9980
	40	0.2916	−0.2555	0.9990	0.2618	−0.4067	0.9992	0.2278	−0.3089	0.9987
	50	0.3082	−0.1581	0.9994	0.3215	−0.2499	0.9995	0.2565	−0.1667	0.9993
	60	0.3165	−0.0683	0.9989	0.3843	−0.0376	0.9983	0.3012	0.0089	0.9990
	70	0.3563	0.0849	0.9982	0.4215	0.1291	0.9988	0.3751	0.1219	0.9970
S	100	0.1179	0.1551	0.9976	0.2227	0.0155	0.9996	0.1842	−0.1003	0.9989
	200	0.1454	0.4932	0.9987	0.2444	0.1862	0.9986	0.2169	0.0581	0.9997
	300	0.2502	0.6253	0.9995	0.2564	0.3289	0.9983	0.2590	0.1810	0.9991
	400	0.2624	0.7763	0.9990	0.2846	0.4709	0.9992	0.3418	0.3009	0.9985
	500	0.2933	0.9008	0.9988	0.3478	0.5468	0.9980	0.3912	0.3688	0.9982

presents the leaching kinetic parameters calculated using the Avrami equation under varying acid concentrations, temperatures, and stirring speeds. The average values of the characteristic parameter n for Li, Fe and P leaching were 0.25, 0.33 and 0.27, respectively, all of which are below 0.5, indicating that the leaching reactions of Li, Fe and P are governed by external diffusion.

To further identify the rate-limiting step of the leaching process, the natural logarithms of the leaching rate constants for Li, Fe and P at various reaction temperatures were substituted into the Arrhenius equation. Taking the logarithm of both sides yields Equation (3), from which a linear relationship between ln k and 1/T is obtained, with the slope corresponding to −E_a/R. Consequently, the activation energy (E_a) can be determined from the rate constants at different temperatures using Equation (3):

ln k = ln A − E_a/RT

(3)

where k is the reaction rate constant at temperature T; A is the pre-exponential factor; T is the absolute temperature (K); R is the gas constant, 8.3145 J/(mol·K); and E_a is the apparent activation energy (kJ/mol).

The plots of ln k versus 1/T are presented in Figure 8. The Arrhenius analysis yielded apparent activation energies of 9.56 kJ/mol, 14.83 kJ/mol, and 12.82 kJ/mol for Li, Fe, and P dissolution, respectively—magnitudes that are characteristic of an externally diffusion-limited process.

From the above analysis, it is evident that the rate constant k in the Avrami equation is related to sulfuric acid concentration, reaction temperature, and stirring speed; therefore, the rate constant k can be expressed by Equation (4):

k = A₀ × C^a × S^b × exp(−E/RT)

(4)

where C represents the concentration of sulfuric acid (mol/L), S represents the stirring speed (r/min), and a and b are the reaction orders of the reactants. Taking the logarithm of both sides of Equation (4) yields Equation (5):

ln k = ln A₀ + a ln C + b ln S −E/RT

(5)

The relationships between ln k and ln C for Li, Fe, and P at different sulfuric acid concentrations are shown in Figure 9a–c. The results indicate that a(Li), a(Fe), and a(P) are 0.39, 0.55, and 0.74, respectively. The relationships between ln k and ln S for Li, Fe, and P at different stirring speeds are shown in Figure 9d–e. The results indicate that b(Li), b(Fe), and b(P) are 0.45, 0.33, and 0.29, respectively. Substitute the obtained values of a and b into Equation (4) to obtain the rate constant equations for Li, Fe, and P:

k_Li = A₀ × C^0.39 × S^0.45 × exp(−1150/T)

(6)

k_Fe = A₀ × C^0.55 × S^0.33 × exp(−1783/T)

(7)

k_P = A₀ × C^0.74 × S^0.29 × exp(−1542/T)

(8)

The A₀ values for Li, Fe, and P obtained under varying temperature conditions were measured as follows: Li (2.13, 2.13, 2.10, 2.06, and 2.17; average: 2.12), Fe (1.80, 1.83, 1.91, 2.12, and 2.27; average: 1.99), and P (1.96, 2.02, 2.07, 2.22, and 2.25; average: 2.10). Consequently, the leaching kinetic equations for Li, Fe, and P from the spent LFP cathode materials are expressed as follows:

−ln(1 − x) = 2.12 × C^0.39 × S^0.45 × exp(−1150/T) t^0.25

(9)

−ln(1 − x) = 1.99 × C^0.55 × S^0.33 × exp(−1783/T) t^0.33

(10)

−ln(1 − x) = 2.10 × C^0.74 × S^0.29 × exp(−1542/T) t^0.27

(11)

The comparison of the theoretical and actual values of −ln(1 − x) calculated by this equation is shown in Figure 10a–c. The results indicate that the −ln(1 − x) values of the Li, Fe, and P leaching kinetic equations obtained through calculation are almost completely consistent with the actual values, suggesting that this equation can be used to describe the leaching kinetic behavior of Li, Fe, and P in the spent LFP cathode materials.

4. Conclusions

The present investigation validates a fast and efficacious sulfuric acid approach for the leaching of Li, Fe, and P from spent LFP cathode materials. The leaching behavior research results revealed that increasing the concentration of sulfuric acid, the reaction temperature and the stirring speed is beneficial for accelerating and enhancing the leaching effect of Li, Fe and P. Under the conditions of sulfuric acid concentration of 2 mol/L, leaching temperature of 60 °C, S/L ratio of 10 g/L, and stirring speed of 300 r/min, the leaching rates of Li, Fe, and P all exceeded 99.5%. By comparing the leaching rates, it was found that there is a selective dissolution sequence of Li > Fe > P. The leaching kinetics indicated that Li, Fe, and P leaching behavior is a typical external diffusion-controlled process with Li, Fe, and P apparent activation energies of 9.56 kJ/mol, 14.83 kJ/mol, and 12.82 kJ/mol, respectively.