Treatment of Na₂SO₄-Containing Wastewater Generated During the Recycling of Spent Lithium-Ion Batteries: Comparative Study on the Operating Modes of Bipolar Membrane Electro-Dialysis

Abstract

The recycling of spent lithium-ion batteries generates Na₂SO₄-containing wastewater, resulting in environmental problems and resource losses. This study investigates a treatment method employing bipolar membrane electrodialysis (BMED) to recover H₂SO₄ and NaOH from such wastewater. The acid and base recovery efficiencies, energy consumption, operational stability, and economic feasibility of two BMED configurations, i.e., two- and three-compartment systems, were systematically compared. The current density, initial concentrations of the feed, and initial concentrations and volumes of the acid and base were optimized under constant current conditions. The three-compartment system exhibited higher acid purity and stability, whereas the other system exhibited lower energy consumption and membrane degradation. Under optimal conditions, both systems successfully recovered H₂SO₄ and NaOH from the Na₂SO₄-containing wastewater. A techno-economic analysis based on a lab-scale process revealed that the two-compartment system exhibited cost effectiveness while the three-compartment system showed long-term operational stability. These findings suggest that BMED is a viable and effective solution for the treatment of Na₂SO₄-containing wastewater generated from battery recycling processes.

1. Introduction

The current recycling processes for spent lithium-ion batteries (LIBs) involve using H₂SO₄ during leaching and solvent extraction stages to recover valuable metals, such as Li, Co, Ni, and Mn, and using NaOH during precipitation and solvent extraction stages [1,2,3]. Figure 1 illustrates a representative LIB recycling process, wherein approximately 0.81 tons of Na₂SO₄ is generated per ton of treated NCM622-derived black mass. Approximately 0.41 tons of Na₂SO₄ is generated during the Li recovery step, wherein Li is precipitated as Li₂CO₃ using Na₂CO₃ after the recovery of Co, Ni, and Mn. This results in a total Na₂SO₄-containing wastewater mass of approximately 1.22 tons [4,5]. This wastewater is also a major byproduct of cathode precursor synthesis, wherein co-precipitation reactions occur between sulfate-based metal salts and NaOH [6,7].

Currently, there are no regulations for the direct discharge of Na₂SO₄-containing wastewater. Na₂SO₄ is chemically stable and nontoxic, posing little immediate environmental threat. However, elevated concentrations of Na₂SO₄ in water systems can increase the water ionic strength, disturb aquatic ecosystems, and cause issues such as scaling and corrosion in industrial systems [7,8,9,10,11]. For treatment, evaporation and concentration processes, e.g., mechanical vapor recompression, are primarily used to convert wastewater into a solid form suitable for sale. However, these methods require high-temperature or vacuum conditions, which increases their capital and energy costs [12].

Recently, bipolar membrane (BPM) electrodialysis (BMED), which is an electro-separation technology, has gained attention as a regeneration method for NaOH and H₂SO₄ from Na₂SO₄-containing wastewater [13,14]. This process involves water dissociation within the BPM to generate H⁺ and OH⁻, which convert the salt into an acid and a base. There are two main BMED operating modes, i.e., two- and three-compartment systems [15,16].

Figure 2a shows the membrane structure of a two-compartment BMED system, consisting of a BPM and a cation exchange membrane (CEM). Under applied voltage, sodium ions (Na⁺) pass through the cation exchange membranes and react with OH⁻ to form NaOH [13,14,15,16,17]. S. Xue investigated the effects of operating mode and process parameters on the treatment of CH₃COONa using a two-compartment BMED system [18], and Y. Lee reported that NaOH (2.96 M) and H₂SO₄ (1.24 M) were recovered from Na₂SO₄-containing wastewater; however, the recovered acid solution contained Na₂SO₄ (0.58 M) as an impurity [19].

Figure 2b illustrates the structure of a three-compartment BMED system, which employs CEM, an anion exchange membrane (AEM) and BPM. In this configuration, Na⁺ and SO₄²⁻ migrate through the CEM and AEM, respectively, forming NaOH and H₂SO₄ [13,14,15,16,17]. J. Kroupa successfully recovered NaOH (4.00 wt%) and H₂SO₄ (4.44 wt%) with purities of 99% and 98%, respectively, using this system [20]. Wang et al. recovered 1.22 M H₂SO₄ from 15 wt% Na₂SO₄ treatment (energy consumption = 2.59 kWh/kg) [21].

The two-compartment BMED system exhibits a simpler structure with fewer membranes, leading to easy construction and operation. However, only an acid or a base can be recovered with high purity, and the ion-exchange membrane is exposed to acidic and basic environments, reducing its durability [21,22,23]. In contrast, the three-compartment BMED system allows high-purity recovery of acids and bases and minimizes back-diffusion and cross-contamination effects. However, it has a more complex structure and involves a greater number of membranes, increasing the maintenance costs [21,22,23].

This study compared the operational results of a two-compartment BMED system (using a CEM and BPM) and a three-compartment BMED system (using a CEM, AEM, and BPM). Experimental analyses under various operating conditions and different process parameters were conducted to evaluate the Na₂SO₄ desalination performance as well as acid and base recovery characteristics, focusing on the recovery rate of NaOH, concentrations of recovered NaOH and H₂SO₄, current efficiency (CE), and energy consumption. The optimal operating conditions were determined for each system and economic feasibility and operational stability were validated.

Previous studies did not conduct experiments that directly compared two-compartment and three-compartment BMED systems under identical operating conditions. In contrast, this study provides a direct comparison of these two configurations, specifically focusing on Na₂SO₄-containing wastewater from LIB recycling. It offers an integrated evaluation of recovery efficiency, energy consumption, membrane durability, and cost factors, aspects that have rarely been investigated simultaneously in the existing literature.

2. Materials and Methods

Herein, two types of BMED systems were designed for the recovery of NaOH and H₂SO₄ from Na₂SO₄ solutions and compared. As shown in Figure 3, the performance of the two- and three-compartment systems was evaluated under identical current conditions and similar solution compositions.

The experimental setup consisted of feed, base recovery, and acid recovery compartments as well as a membrane stack, circulation pumps, a power supply, conductivity and pH meters, and a control panel. Both systems employed Neosepta-series membranes (ASTOM Co., Ltd., Minato, Japan).

The membrane stack in the three-compartment system was composed of alternately arranged membranes: 11 BPMs, 10 CEMs, and 10 AEMs (effective membrane area = 0.055 m²). The structure of the two-compartment system was similar to that of the three-compartment system but without the AEMs.

The feed solution was a simulated solution of Na₂SO₄ (1.30 M) prepared to resemble the composition of Na₂SO₄-containing wastewater generated from the recycling of spent LIBs. Analytical-grade anhydrous Na₂SO₄ (Daejung Chem.) was dissolved in ultrapure water. In the base and acid recovery compartments, NaOH (0.1 M) and H₂SO₄ (0.1 M) solutions were used, respectively. The NaOH and H₂SO₄ solutions were prepared by diluting a NaOH solution (40 wt%) and a H₂SO₄ solution (95 wt%), respectively, with ultrapure water. A Na₂SO₄ solution (5 wt%) was used as the electrolyte to maintain conductivity between the membrane stack and electrodes.

Both systems were operated under galvanostatic (constant current) conditions. Depending on the experimental conditions, the initial concentrations (0.05–0.50 M) and volumes (750–1500 mL) of the acid and base, feed solution concentration (0.43–1.30 M), and current density (250–450 A/m²) were adjusted. In the two-compartment system, the experiment was terminated after 480 min, whereas the experiment in the three-compartment system was terminated when the cell voltage exceeded 3 V because the resistance increase due to the decreasing conductivity during operation may considerably affect membrane stability at voltages higher than this threshold.

Samples were collected at predetermined time intervals for determining the degree of desalination of the feed solution and confirm the generation of H₂SO₄ and NaOH. The concentrations of H₂SO₄ and NaOH in the collected samples were quantitatively analyzed via acid–base titration. Titration was performed using standard solutions (0.1 N) of NaOH and H₂SO₄ as well as methyl orange and phenolphthalein as indicators for the base and acid samples, respectively.

To precisely determine the Na⁺ and SO₄²⁻ concentrations in each compartment, inductively coupled plasma–atomic emission spectroscopy was employed. To assess water transport characteristics, changes in feed, base and acid solution volume before and after the reaction were measured based on scale markings on solution chambers.

Next, obtained experimental data were used to quantitatively evaluate the water migration rate ($W_{mg}$; %), recovery yield of the base and acid (%), energy consumption ($E_{weight}$; kWh/kg), C.E (%), and ion flux (J; mol/m²·h) using Equations (1)–(5).

$W_{mg}$ was calculated using Equation (1):

$$W_{mg}\left(\%\right)={\displaystyle \frac{V_f-V_i}{V_i}}$$

(1)

where $V_i$ is the initial volume of the solution and $V_f$ is the volume of the solution at the end of the experiment.

The recovery of the base and acid (%) was calculated using Equation (2):

$$Recovery\left(\%\right)={\displaystyle \frac{m_f}{m_i}}\times 100$$

(2)

where $m_f$ is the number of moles of Na⁺ or SO₄²⁻ in the base or acid recovery compartment and $m_i$ is the number of moles of Na⁺ or SO₄²⁻ initially present in the feed solution.

C.E was calculated using Equation (3):

$$C.E\left(\%\right)={\displaystyle \frac{m_{actual}}{m_{theortical}}}$$

(3)

where $m_{theortical}$ and $m_{actual}$ are the theoretical and actual amounts of the generated product, respectively.

$E_{weight}$ was calculated using Equation (4):

$$E_{weight}={\displaystyle \frac{I\times {\int }_0^{t}Vdt}{W}}$$

(4)

where V is the applied voltage (V), I is the applied current (A), t is the operation time (h), and W is the weight of initially loaded Na₂SO₄ (kg).

J was calculated using Equation (5):

$$J={\displaystyle \frac{m_f}{At}}$$

(5)

where $m_f$ is the number of moles of Na⁺ or SO₄²⁻ transferred to the base or acid recovery compartment, $A$ is the effective membrane area of the ion-exchange membrane (0.055 m²), and t is the operation time.

3. Results and Discussion

3.1. Comparison Between the Acid and Base Recovery Efficiencies of the Two- and Three-Compartment Systems

Experiments were conducted under identical operating conditions to compare the Na₂SO₄ desalination efficiencies as well as acid and base recovery efficiencies of the two- and three-compartment systems. The feed solution consisted of 1.5 L of Na₂SO₄ (1.30 M) and the acid and base recovery compartments were filled with 1.5 L of H₂SO₄ (0.1 M) and NaOH (0.1 M), respectively. The experiments were conducted at a current density of 360 A/m² and terminated after 480 min (Figure 4 and

Table 1. Effect of the operating mode on system performance.

Time (min)	Operating Mode	Na+ Flux (mol/m2h)	Recovery (%)		Recovered Concentration (M)		C.E (%)	Energy Consumption (kWh/kg) *
			NaOH	H2SO4	NaOH	H2SO4
30	2 compart.	14.19	9.97	9.55	0.35	0.13	99.99	-
	3 compart.	11.50	8.08	6.72	0.30	0.18	84.74	-
60	2 compart.	13.28	18.67	18.02	0.57	0.25	97.88	-
	3 compart.	10.99	15.44	13.15	0.48	0.26	80.96	-
120	2 compart.	11.35	31.91	31.96	0.89	0.45	83.67	-
	3 compart.	10.05	28.25	25.43	0.78	0.41	74.07	-
240	2 compart.	8.95	50.32	49.90	1.31	0.73	65.97	-
	3 compart.	8.96	50.34	45.95	1.25	0.64	66.00	-
360	2 compart.	7.02	59.22	57.15	1.49	0.88	51.76	-
	3 compart.	8.05	67.85	63.88	1.56	0.82	59.30	-
480	2 compart.	5.72	64.29	59.88	1.58	0.97	42.14	1.52
	3 compart.	6.74	75.18	77.35	1.67	0.96	49.69	1.43

* Energy consumption for the processing of 1 kg of Na₂SO₄.

).

As shown in Figure 4a, the Na⁺ flux in the two-compartment system was >2.5 mol/m²·h higher than that in the three-compartment system in the initial stage. However, the decrease in the Na⁺ flux was more pronounced in the two-compartment system as time progressed. After 240 min, the three-compartment system exhibited a higher Na⁺ flux. In both systems, the Na⁺ flux gradually decreased over time. This phenomenon was attributed to a reduction in the Na⁺ concentration in the feed compartment owing to ion transport to the base compartment. This resulted in concentration polarization [24,25] as well as the reverse diffusion of H⁺ and OH⁻, hindering ion migration [26].

Moreover, in the two-compartment system, the formation of H₂SO₄ within the feed compartment reduced the electrical resistance and consequently the operating voltage. This decreased the driving force for Na⁺ migration, which further accelerated the decrease in the Na⁺ flux. Similar changes were observed in the NaOH recovery rate Figure 4b. In the first 240 min, the two-compartment system exhibited a NaOH recovery rate that was 2–5% higher than that exhibited by the three-compartment system. However, after 240 min, the three-compartment system exhibited a recovery rate that was >8% higher than that of the two-compartment system.

Figure 4c shows the concentrations of recovered NaOH and H₂SO₄. The NaOH concentration exhibited fluctuations similar to those of the Na⁺ flux and NaOH recovery rate. Till 240 min, the two-compartment system exhibited a 0.06-M higher concentration (1.31 M) than the three-compartment system. However, after 360 min, the three-compartment system exhibited a NaOH concentration that was ~0.6 M higher than that of the two-compartment system.

The H₂SO₄ recovery rate showed fluctuations similar to those of the NaOH recovery rate, but the concentration of recovered H₂SO₄ was higher in the two-compartment system. This was attributed to the migration of Na⁺ and SO₄²⁻ in hydrated forms through the ion-exchange membranes, increasing the volume of the acid and base recovery compartments and decreasing the volume of the feed compartment [27]. This volume change reduced the concentrations of recovered NaOH and H₂SO₄ in the three-compartment system. In the two-compartment system, NaOH was also diluted but H₂SO₄ directly formed in the feed compartment became concentrated, resulting in a higher final concentration than that in the three-compartment system.

The purity of H₂SO₄ recovered from the three-compartment system exceeded 99%. Meanwhile, in the two-compartment system, recovered H₂SO₄ was mixed with residual Na₂SO₄, resulting in lower purity (58.2%).

The CE values of the two systems are shown in Figure 4d. In the two-compartment system, CE exceeded 80% within 30–120 min, which was >10% higher than that in the three-compartment system during the same period. However, after 240 min, CE exhibited a substantial decline, reaching 42.14% after 480 min. The three-compartment system also showed high CE (>70%) before 120 min. However, CE declined afterward, reaching 49.69% after 480 min. This decline was attributed to the reduction in the Na⁺ flux, which decreased the number of target ions contributing to the current.

Similar performances have been reported in previous studies. For example, León reported a decrease in CE from 79.20% to 52.70% over time during the recovery of NaOH from NaCl using BMED. The researcher attributed this to reverse ion diffusion and water transport [28].

The energy consumption values of the two systems after 480 min were also compared. The energy consumption of the two-compartment system was 1.52 kWh/kg, which was 0.09 kWh/kg higher than that of the three-compartment system. This difference was attributed to the lower recovery efficiency of the two-compartment system, which required additional energy for treating 1 kg of Na₂SO₄.

3.2. Effect of Process Parameters on the Recovery Characteristics of the Two Systems

The effects of process parameters, i.e., current density, feed solution concentration, and the concentrations and volumes of the acid and base, on the Na₂SO₄ desalination characteristics as well as NaOH and H₂SO₄ recovery characteristics of the two- and three-compartment systems were studied and compared.

The effect of current density on the desalination and recovery performances of the two systems were investigated via experiments conducted at current densities of 250–450 A/m² under identical conditions. The feed, acid recovery, and base recovery compartments were each filled with 1.5 L of Na₂SO₄ (1.30 M), 1.5 L of H₂SO₄ (0.1 M), and 1.5 L of NaOH (0.1 M), respectively. Each experiment was terminated after 240 min (Figure 5 and

Table 2. Effect of current density on the performance of the two- and three-compartment systems.

Current Density (A/m2)	Operating Mode	Na+ Flux (mol/m2h)	Recovery (%)		Recovered Concentration (M)		C.E (%)	Energy Consumption (kWh/kg) *
			NaOH	H2SO4	NaOH	H2SO4
250	2 compart.	6.64	37.35	37.21	1.02	0.54	69.94	0.87
	3 compart.	6.32	35.65	32.80	0.96	0.50	60.09	0.97
310	2 compart.	7.62	42.87	42.52	1.14	0.63	66.11	0.96
	3 compart.	7.78	43.72	40.02	1.14	0.57	60.69	1.03
360	2 compart.	9.00	50.57	49.66	1.31	0.73	66.30	1.00
	3 compart.	9.01	50.66	46.78	1.27	0.65	66.42	1.11
400	2 compart.	9.51	53.46	50.67	1.36	0.78	61.73	1.09
	3 compart.	10.27	57.72	51.18	1.40	0.70	61.91	1.11
450	2 compart.	10.61	59.63	51.64	1.50	0.81	62.54	1.13
	3 compart.	11.11	62.44	57.25	1.48	0.75	58.93	1.25

* Energy consumption for the processing of 1 kg of Na₂SO₄.

).

Figure 5a shows the Na⁺ flux. With increasing current density, the Na⁺ flux increased. At 250 A/m², the Na⁺ flux was 6.64 and 6.32 mol/m²·h for the two- and three-compartment systems, respectively. At 450 A/m², the flux increased to 10.61 and 11.11 mol/m²·h, respectively. Except at 250 A/m², the three-compartment system consistently exhibited higher Na⁺ flux. This was likely due to the structural advantage of the three-compartment system: the feed compartment was located between the acid and base compartments, enabling physical separation of ion flows and minimization of ion interference.

The NaOH recovery rate increased with increasing current density Figure 5b. While the recovery rate of the three-compartment system was approximately 1.5% lower than that of the two-compartment system at 250 A/m², it was 1–3% higher at current densities of >310 A/m².

As shown in Figure 5c, the CE of the two-compartment system decreased with increasing current density, whereas that of the three-compartment system increased up to 360 A/m² and then decreased. The decrease in the CE of the two-compartment system was likely due to heat accumulation because of its simpler structure and fewer compartments, which resulted in a higher temperature (2°C) compared to the three-compartment system. This may have caused side reactions, such as water dissociation, at the electrodes or within the BPM, reducing CE [29].

In the three-compartment system, CE decreased at current densities of >400 A/m², likely owing to ion depletion at the membrane surface due to over-limiting current. This led to concentration polarization, wherein ion transport no longer proportionally increased with current [25,30].

Figure 5d shows the energy consumption of both systems. In both systems, energy consumption increased with increasing current density, which was primarily due to an increase in the average voltage. Although the two-compartment system exhibited lower energy consumption than the three-compartment system, it may require additional thermal management equipment such as heat exchangers in large-scale applications since the process temperature needs to be reduced to ensure membrane stability.

The effect of the Na₂SO₄ concentration in the feed compartment on Na₂SO₄ desalination and acid or base recovery was investigated via experiments conducted at different initial Na₂SO₄ concentrations. For the three-compartment system, the optimal current density was found to be 360 A/m² because higher current densities substantially increased cell voltage, potentially affecting membrane stability, CE, and energy consumption. For the two-compartment system, the optimal current density was determined to be 450 A/m² based on the recovery performance and process duration.

The feed compartment was filled with 1.5 L of Na₂SO₄ solutions with concentrations of 0.43–1.30 M. All other conditions were identical to those set in the current density experiments. The three-compartment system was operated until the cell voltage reached 3 V, while the two-compartment system was operated for a fixed duration (480 min). The results are shown in Figure 6 and

Table 3. Effect of Na₂SO₄ concentration on the performance of the two- and three-compartment systems.

Conc. of Na2SO4 (M)	Operating Mode	Na+ Flux (mol/m2h)	Recovery (%)		Recovered Concentration (M)		C.E (%)	Energy Consumption (kWh/kg) *
			NaOH	H2SO4	NaOH	H2SO4
0.43	2 compart.	2.61	87.98	79.08	0.73	0.47	15.38	4.31
	3 compart.	10.80	79.62	76.51	0.73	0.40	69.58	1.23
0.65	2 compart.	3.67	82.61	72.52	1.00	0.64	21.66	3.03
	3 compart.	9.15	77.62	78.82	0.98	0.56	61.36	1.29
0.87	2 compart.	4.38	73.91	70.20	1.22	0.78	25.84	2.51
	3 compart.	8.65	80.82	73.64	1.27	0.66	59.69	1.29
1.09	2 compart.	5.39	72.73	68.60	1.46	0.96	31.78	2.05
	3 compart.	8.06	80.85	83.75	1.50	0.88	56.38	1.27
1.30	2 compart.	6.23	70.00	63.78	1.67	1.12	36.39	1.86
	3 compart.	7.07	75.18	77.35	1.67	0.96	49.69	1.43

* Energy consumption for the processing of 1 kg of Na₂SO₄.

. Figure 6a–d show the Na⁺ flux, NaOH recovery rate, concentrations of recovered NaOH and H₂SO₄, and energy consumption, respectively.

In the three-compartment system, moderately high Na⁺ fluxes were observed at low Na₂SO₄ concentrations, i.e., 10.80 and 9.15 mol/m²·h at 0.43 and 0.65 M, respectively. At high Na₂SO₄ concentrations (≥0.87 M), the Na⁺ flux decreased to 8.65–7.07 mol/m²·h. This reduction was attributed to the decrease in the average voltage due to the lower resistance of the feed solution at higher Na₂SO₄ concentrations, resulting in a low driving force for Na⁺ migration through ion-exchange membranes [31].

The NaOH recovery rate was >75% under all conditions. However, at concentrations of 0.43 and 0.65 M, the recovery rates were moderate because of short process times (120 and 199 min, respectively) despite high the Na⁺ flux values.

Low Na₂SO₄ concentrations yielded NaOH and H₂SO₄ concentrations of up to 1.0 and 0.6 M, respectively. In contrast, high Na₂SO₄ concentrations enabled the recovery of up to 1.67 M NaOH and 0.96 M H₂SO₄. The energy consumption under all conditions (except for a Na₂SO₄ concentration of 1.30 M) ranged from 1.23 to 1.27 kWh/kg.

In the two-compartment system, Na⁺ fluxes at low Na₂SO₄ concentrations were 2.61 and 3.67 mol/m²·h, which were 1–3 mol/m²·h lower than those at high Na₂SO₄ concentrations. In the three-compartment system, Na⁺ and SO₄²⁻ migrated through membranes, whereas in the two-compartment system, only Na⁺ migration occurred. Therefore, the effect of concentration polarization relaxation at high Na₂SO₄ concentrations played a more dominant role than the reduced driving force due to the low voltage, which increased ion flux [32].

A NaOH recovery rate of >82% was achieved at Na₂SO₄ concentrations of <0.65 M, whereas moderate recovery rates of 70–73% were observed at higher concentrations (≥0.87 M). However, similar to the three-compartment system, the concentrations of recovered NaOH and H₂SO₄ increased with increasing Na₂SO₄ concentration: up to 1.0 M NaOH and 0.65 M H₂SO₄ at low concentrations and up to 1.67 M NaOH and 1.12 M H₂SO₄ at high concentrations.

The CE value also increased from 15.38% to 36.39% with increasing Na₂SO₄ concentration, which was in good agreement with changes in the Na⁺ flux. Unlike that of the three-compartment system, the energy consumption of the two-compartment system decreased with increasing Na₂SO₄ concentration owing to the lower recovery rates at lower Na₂SO₄ concentrations, which increased the energy requirements for processing per kilogram of Na₂SO₄.

To increase the concentrations of recovered NaOH and H₂SO₄ and investigate their effects on NaOH and H₂SO₄ recoveries and Na₂SO₄ desalination, experiments were conducted by varying the initial concentrations of NaOH and H₂SO₄ in their respective recovery compartments. The current densities were set to 360 and 450 A/m² for the three- and two-compartment systems, respectively, based on the conditions set in the above-mentioned experimental investigations regarding the Na₂SO₄ concentration.

The feed compartment was filled with 1.5 L of a Na₂SO₄ solution (1.30 M), and the base and acid recovery compartments were each filled with 1.5 L of NaOH and H₂SO₄ solutions, respectively, with concentrations of 0.05–0.50 M. The experimental results are presented in Figure 7 and

Table 4. Effect of the initial concentrations of NaOH and H₂SO₄ on the performance of the two- and systems.

Initial Conc. of NaOH and H2SO4 (M)	Operating Mode	Na+ Flux (mol/m2h)	Recovery (%)		Recovered Concentration (M)		Water Migration (%)
			NaOH	H2SO4	NaOH	H2SO4	Base	Acid	Feed
0.05	2 compart.	5.90	66.39	63.42	1.59	1.02	20.30	-	−20.30
	3 compart.	7.50	79.41	77.78	1.72	0.91	23.34	16.69	−40.04
0.10	2 compart.	6.23	70.00	63.78	1.67	1.12	17.13	-	−17.13
	3 compart.	7.07	75.18	77.35	1.67	0.96	27.40	16.65	−44.05
0.30	2 compart.	6.24	70.14	63.32	1.83	1.08	16.16	-	−16.16
	3 compart.	6.95	76.37	78.39	2.03	1.14	13.20	16.25	−29.45
0.50	2 compart.	6.25	70.33	63.38	1.93	1.09	15.68	-	−15.68
	3 compart.	6.39	71.91	74.62	2.13	1.26	12.98	16.69	−29.67

.

Figure 7a shows the Na⁺ flux, revealing opposite performances of the two systems. In the three-compartment system, the Na⁺ flux decreased from 7.50 to 6.39 mol/m²·h with increasing initial concentrations of NaOH and H₂SO₄. In contrast, in the two-compartment system, the lowest flux (5.90 mol/m²·h) was observed at 0.05 M. The Na⁺ flux increased to 6.23 mol/m²·h at 0.10 M and maintained a similar level up to 0.50 M.

In the three-compartment system, high NaOH and H₂SO₄ concentrations in the acid and base compartments may have increased the concentration gradient relative to the feed compartment. This may have caused ion accumulation on the membrane surface, hindering ion transport. According to a study by Zhu [33], reverse diffusion of Na⁺ can occur with increasing NaOH concentration in the base compartment during operation, which was reported to reduce the NaOH recovery rate from 95.6% to 75.1%. These phenomena likely contributed to the observed decrease in the Na⁺ flux.

In contrast, in the two-compartment system, the electrical resistance decreased with increasing NaOH concentration. In addition, since H₂SO₄ was generated in the feed compartment, the concentration gradient relative to the base compartment became smaller than that in the case of the three-compartment system, enhancing Na⁺ transport.

Similar trend was observed for the NaOH recovery rate Figure 7b. In the three-compartment system, the NaOH recovery rate decreased from 79.41% at 0.05 M to 71.91% at 0.50 M. In the two-compartment system, the NaOH recovery rate increased from 66.39% at 0.05 M to 70.00% at 0.10 M and remained moderately stable up to 0.50 M.

Figure 7c shows the concentrations of recovered NaOH and H₂SO₄. Except for an initial NaOH concentration of 0.10 M, the concentration of recovered NaOH in the two-compartment system was ~0.20 M lower than that in the three-compartment system. The two-compartment system showed an approximately 0.15-M higher concentration of recovered H₂SO₄ at an initial H₂SO₄ concentration of ≤0.10 M. However, at concentrations of ≥0.30 M, the concentrations of recovered H₂SO₄ in the three-compartment system were >0.10 M higher than those in the two-compartment system.

These results were attributed to differences between the water migration and recovery rates of the two systems. At concentrations of <0.30 M, the three-compartment system exhibited 6–13% higher recovery rates than the two-compartment system. Moreover, at concentrations of ≥0.30 M, the rate of water migration into the base compartment was >3% lower in the three-compartment system than in the two-compartment system, which led to a high concentration of recovered NaOH in the former.

Figure 7d shows the energy consumption of the two systems. In the three-compartment system, the energy consumption substantially increased from 1.42 kWh/kg at 0.05 M to 1.84 kWh/kg at 0.50 M. In contrast, in the two-compartment system, the highest energy consumption was observed at 0.05 M (1.87 kWh/kg), which then gradually decreased to 1.81 kWh/kg at 0.50 M.

To increase the concentrations of recovered NaOH and H₂SO₄ and investigate their effects on Na₂SO₄ desalination and recovery performance, experiments were conducted using different initial volumes of NaOH and H₂SO₄ solutions loaded into the base and acid recovery compartments (Figure 8 and

Table 5. Effect of the initial volumes of NaOH and H₂SO₄ on the performance of the two- and three-compartment systems.

Initial Vol. of NaOH and H2SO4 (mL)	Operating Mode	Na+ Flux (mol/m2h)	Recovery (%)		Recovered Concentration (M)		Water Migration (%)
			NaOH	H2SO4	NaOH	H2SO4	Base	Acid	Feed
750	2 compart.	5.89	66.32	62.01	2.46	1.14	44.47	-	−22.23
	3 compart.	5.02	67.90	66.46	2.42	1.38	50.55	31.97	−41.04
1000	2 compart.	6.03	67.85	63.55	2.13	1.12	28.80	-	−19.20
	3 compart.	5.96	73.75	73.01	1.98	1.22	50.11	25.16	−50.48
1250	2 compart.	6.10	68.60	63.65	1.88	1.10	20.30	-	−16.92
	3 compart.	6.85	77.93	76.44	1.94	1.12	35.89	19.76	−44.52
1500	2 compart.	6.23	70.00	63.78	1.67	1.12	15.68	-	−15.68
	3 compart.	7.07	75.18	77.35	1.67	0.96	27.40	16.65	−44.05

). Similarly to aforementioned experiments, the current densities were set to 360 and 450 A/m² for the three- and two-compartment systems, respectively. The feed compartment was filled with 1.5 L of a Na₂SO₄ solution (1.30 M). The base and acid recovery compartments were each filled with NaOH (0.1 M) and H₂SO₄ (0.1 M) solutions, with volumes of 0.75–1.5 L. Figure 8a shows the Na⁺ flux. For both systems, the Na⁺ flux increased with increasing solution volume. For solution volumes of <1000 mL, the two-compartment system exhibited a Na⁺ flux that was 0.8–0.1 mol/m²·h higher than that exhibited by the three-compartment system. However, for volumes of ≥1250 mL, the three-compartment system exhibited an approximately 0.8 mol/m²·h higher Na⁺ flux.

This result was attributed to the fact that larger volumes result in a more gradual increase in the acid and base concentrations in the respective compartments. This allowed the system to maintain concentration gradient in the feed compartment, reducing back diffusion and enhancing ion transport [34].

The NaOH recovery rate exhibited a similar trend (Figure 8b). It increased with increasing solution volume in both systems. In the two- and three-compartment systems, the NaOH recovery rate increased from 66.32% to 70.00% and from 67.90% to 75.18%, respectively. The increase in the Na⁺ flux may have directly contributed to the increased recovery rate.

Figure 8c shows the concentrations of recovered NaOH and H₂SO₄. At low solution volumes, higher concentrations were observed. At a solution volume of 750 mL, the concentrations of recovered NaOH and H₂SO₄ in the three-compartment system were 2.42 and 1.38 M, respectively, whereas those in the two-compartment system were 2.46 and 1.14 M, respectively. At volumes of ≥1250 mL, the concentration of recovered NaOH in the three-compartment system was consistently 0.06 M higher than that in the two-compartment system. In contrast, at volumes of ≤1000 mL, the concentration of recovered NaOH in the two-compartment system was 0.04–0.15 M higher than that in the three-compartment system.

This difference at low volumes was attributed to the higher water migration rate (>6%) in the three-compartment system, which led to dilution in the base compartment. In the two-compartment system, H₂SO₄ was generated in the feed compartment. Owing to the lower recovery rates compared to those in the three-compartment system, lower final concentration of recovered H₂SO₄ was observed.

Figure 8d shows the energy consumption of the two systems. In the three-compartment system, the energy consumption decreased from 1.98 to 1.43 kWh/kg with increasing solution volume. This was attributed to the recovery rate increase observed at high solution volumes, which reduced the energy consumed per kilogram of Na₂SO₄ treated. Gao et al. reported a similar observation for a three-compartment BMED system, wherein increasing the initial volumes of H₂SO₄ and NaOH from 60 to 120 mL resulted in an increase in the energy consumption from 1.35 to 2.67 kWh/kg [35].

In contrast, the two-compartment system showed moderately stable energy consumption regardless of the solution volume (1.88–1.82 kWh/kg) under all tested conditions.

3.3. Techno-Economic Feasibility Analysis

The optimal operating conditions for each system were determined based on the results of the experiments discussed. Further, a techno-economic feasibility analysis was conducted.

The optimal conditions of the two-compartment system were a current density of 450 A/m², Na₂SO₄ (1.30 M) volume of 1.5 L in the feed compartment, and NaOH (0.1 M) volume of 0.75 L in the base compartment. The optimal conditions of the three-compartment system were a current density of 360 A/m², a Na₂SO₄ (1.30 M) volume of 1.5 L in the feed compartment, and NaOH (0.1 M) and H₂SO₄ (0.1 M) volumes of 0.75 L each in the base and acid recovery compartments, respectively.

The process flow diagrams for the two- and three-compartment systems under these conditions are shown in Figure 9 and Figure 10, respectively. The results of the optimal process and corresponding economic analysis are summarized in

Table 6. Comparison between the techno-economic factors of the two- and three-compartment systems.

Techno-Economic Factors	Two-Compartment System	Three-Compartment System
Membrane used	Cation exchange membrane and bipolar membrane	Cation exchange membrane, anion exchange membrane, and bipolar membrane
Bipolar membrane reaction	H2O → H+ + OH−
Recovery of Na2SO4 to NaOH	66.32%	67.90%
Recovery of Na2SO4 to H2SO4	62.01%	66.46%
Concentration of recovered NaOH	2.46 M	2.42 M
Concentration of recovered H2SO4	1.14 M (H2SO4 + Na2SO4 mixed solution)	1.38 M
NaOH purity	Comparably to commercial NaOH obtained from membrane plants
H2SO4 purity	63.3% (1.14 M H2SO4 + 0.66 M Na2SO4)	Comparable to commercial H2SO4 obtained from membrane plants
Operating temperature	27–30 °C	25–28 °C
Average voltage (V)	17.34	18.92
CE (%)	34.74	36.09
Process time (h)	9.00	9.87
Energy consumption (kWh/kg) #1	1.88	1.98
Process capacity (kg/year) #2,3	162.01	131.31
Total energy consumption (kWh/year)	305	260
Electricity charge (USD/kWh) #4	0.10	0.10
Total energy cost (USD/year)	30.5	26.0
Supplied Na2SO4 price (USD/year) #5	14.0	11.4
Produced NaOH price (USD/year) #6	27.88	21.08
Produced H2SO4 price (USD/year) #7	12.15	9.87
Total process cost (USD/year)	4.43	6.43

^#1 kg = weight of Na₂SO₄, ^#2 1 year = 260 days, ^#3 1 day = 18 h, ^#4 0.10 USD/kWh, ^#5 Na₂SO₄ = 0.09 USD/kg, ^#6 NaOH = 0.35 USD/L, ^#7 H₂SO₄ = 0.31 USD/L.

.

The economic analysis was based on the process time and energy consumption per plant. It was assumed that a plant operated for 260 days per year and 18 h a day. The electricity cost was calculated to be 0.10 USD/kWh.

Under these conditions, the two-compartment system was estimated to treat 162.01 kg of Na₂SO₄ per year, consuming 304.58 kWh of electricity, which corresponded to an annual energy cost of 30.46 USD. Assuming that recovered NaOH and H₂SO₄ were sold as industrial-grade products (40 wt% and 95 wt%, respectively) and applying retail price standards, the value of the recovered products was found to offset 40.03 USD annually. Thus, the process net annual cost was found to be 4.43 USD.

The three-compartment system was estimated to treat 131.31 kg of Na₂SO₄ per year, consuming 260.00 kWh of electricity (annual energy cost = 26.00 USD). Assuming the same market value for recovered NaOH and H₂SO₄ as for the two-compartment system, the recovered product value was found to offset 30.92 USD, resulting in a net annual cost of 6.43 USD.

Although the net process cost of the two-compartment system was 2.00 USD less than that of the three-compartment system, the total capital investment for the two-compartment system is expected to be higher. This is due to the greater temperature increase observed during operation, which may require additional cooling equipment such as heat exchangers.

Moreover, H₂SO₄ recovered from the two-compartment system was mixed with Na₂SO₄, requiring additional post-treatment, such as methanol-induced precipitation, to obtain pure H₂SO₄ [36].

In conclusion, while both systems incur some processing costs, the BMED method has potential as an effective technology for treating Na₂SO₄-containing wastewater. In particular, under stricter future environmental regulations regarding Na₂SO₄ discharge, BMED could serve as a suitable process for NaOH and H₂SO₄ recovery from waste streams.

3.4. Comparison of Operational Stability

To evaluate the operational stability of the two systems for future recovery applications of NaOH and H₂SO₄ from Na₂SO₄-containing wastewater, a comparative analysis was conducted focusing on temperature variations, potential membrane degradation, and voltage stability (

Table 7. Comparison between the operational stability of the two- and three-compartment systems.

Stability Factor	Two-Compartment System	Three-Compartment System
Membrane durability	The CEM is exposed to the acid and base, which adversely affect membrane durability	As the acid and base are separated, membrane durability is improved compared to the two-compartment system
Voltage stability	Owing to a reduced operating voltage, the system is more stable than the three-compartment system	The rapid increase in the voltage may affect membrane durability
Temperature stability	Higher than that of the three-compartment system	System stable at 25–28 °C
Operational stability	The two-compartment system exhibits superior voltage stability and electrical durability during long-term operation, whereas the three-compartment system offers better structural resistance to thermal and chemical stress

).

First, thermal stabilities of the two systems were compared. The two-compartment system had fewer solution chambers and used a lower total solution volume compared to the three-compartment system. This resulted in higher generated heat per unit solution volume in the two-compartment system under the same current conditions, leading to a faster increase in the internal cell temperature. Thus, there is a higher risk of heat accumulation in the two-compartment system during extended operation, potentially compromising the overall system stability. In contrast, the separate acid and base chambers and high solution volumes used in the three-compartment system allow more even heat dissipation, resulting in a slower temperature increase and a better overall thermal stability.

Second, the two systems exhibited distinct membrane degradation risks. In the three-compartment system, the acid and base were confined to separate chambers, exposing each ion-exchange membrane to a single chemical environment. This separation minimized chemical deterioration. In contrast, the CEM in the two-compartment system was located between the feed and base compartments, where it was repeatedly exposed to H₂SO₄ and NaOH. This continuous pH cycling accelerated degradation and compromised membrane integrity over time. Furthermore, the anion exchange layer was prone to degradation under strongly alkaline conditions via Hofmann β-elimination and nucleophilic substitution reactions by OH⁻ ions [37,38]. Similarly, the cation exchange layer is vulnerable to acidic environments and radical-induced chain scission [39]. These intrinsic stability limitations under harsh pH conditions contribute to reduced membrane lifespan [40].

Lastly, the two-compartment system exhibited higher voltage stability than the three-compartment system. In the former, as the operation process progressed, H₂SO₄ was generated in the feed compartment and NaOH in the base compartment, both of which reduced the electrical resistance. This helped maintain moderately stable cell voltages during long-term operation, minimizing the risk of overvoltage across the membranes. In contrast, in the three-compartment system, continuous Na₂SO₄ desalination from the feed compartment led to a reduction in the ion concentration, which increased the electrical resistance and caused a sharp voltage increase. This voltage increase can result in an overvoltage stress on the membranes, negatively impacting their stability and potentially leading to electrical damage and reduced membrane lifespan [40].

In summary, the two-compartment system shows better electrical and voltage stabilities during prolonged operation, whereas the three-compartment system offers better resistance to thermal and chemical degradations owing to its more robust structural separation between the acid and base compartments.

4. Conclusions

Herein, the effects of the operating modes and key process parameters of BMED systems were investigated for the treatment of Na₂SO₄-containing wastewater generated from the recycling of spent LIBs. Economic feasibility and operational stability were also evaluated, leading to the following conclusions:

• The two-compartment system initially showed higher Na⁺ flux and NaOH recovery rate. However, after 240 min, the three-compartment system demonstrated superior performance. The three-compartment system enabled the recovery of a high-purity acid and base and showed moderately stable long-term performance in terms of CE and energy consumption.
• With increasing current density, the Na⁺ flux, NaOH recovery rate, and energy consumption increased. In most cases, the three-compartment system outperformed the two-compartment system. The CE continuously decreased in the two-compartment system, while it increased up to 360 A/m² and then declined in the three-compartment system. This was attributed to different heat accumulation and concentration polarization effects in each system. Although the two-compartment system exhibited lower energy consumption, additional thermal control may be required for extended operations.
• With increasing Na₂SO₄ concentration, both systems exhibited higher concentrations of recovered NaOH and H₂SO₄ as well as improved CE. In the three-compartment system, the Na⁺ flux decreased owing to reduced voltage at high Na₂SO₄ concentrations, whereas in the two-compartment system, the flux increased owing to the weakening of the concentration polarization effect. The two-compartment system was less energy efficient at low concentrations, but it showed improved energy efficiency at high concentrations.
• With increasing initial concentrations of NaOH and H₂SO₄, the three-compartment system showed a decline in the Na⁺ flux and recovery rate as well as increased energy consumption. In contrast, the two-compartment system exhibited an improved flux and recovery rate beyond a certain concentration threshold, with a corresponding decrease in the energy consumption. These results were attributed to the differences between the concentration gradients, back-diffusion effects, and water transport rates of the two systems, highlighting that recovery characteristics depend on the concentration conditions.
• Increasing the initial volumes of NaOH and H₂SO₄ in the recovery compartments increased the Na⁺ flux and NaOH recovery rates in both systems. At volumes of ≥1250 mL, the three-compartment system demonstrated superior recovery performance. Low initial volumes increased the concentrations of the recovered species; however, differences in the water transport and recovery rates caused variations in the final concentrations. Energy consumption substantially decreased in the three-compartment system with the increasing volumes, suggesting that volume control is critical for process optimization.
• Both configurations successfully recovered NaOH and H₂SO₄ from the Na₂SO₄-containing wastewater, with estimated annual process costs of USD 4.43 and USD 6.43 for the two- and three-compartment systems, respectively. Despite the lower processing cost of the two-compartment system, its capital investment is expected to be higher because it may require thermal management and post-treatment. Under future stricter environmental regulations, BMED can be an effective strategy for the recovery of resources and treatment of Na₂SO₄-containing wastewater.
• The operational stability assessment confirmed the higher voltage stability and electrical reliability of the two-compartment system and its susceptibility to membrane degradation due to heat accumulation and repeated acid or base contact. In contrast, the three-compartment system exhibited better structural resistance to thermal and chemical stress but experienced voltage increases in long-term operations, which can compromise membrane integrity.