Simultaneous Electrochemical Removal of Selenium and Strontium from Aqueous Solution

Abstract

Featured Application

Electrochemical treatment of water and wastewater, primarily those contaminated with selenium and/or strontium.

Abstract

This study investigated the removal of selenium (Se) and strontium (Sr) from water using a three-stage electrochemical reactor with integrated pH control. A total of 102 experiments were performed following a Box–Behnken design that varied the electrode material, applied current, number of electrodes, operating time, and initial pH to evaluate their effects on the Se and Sr removal efficiencies. The complete removal of Se was achieved under multiple conditions, even without pH control, while effective Sr removal required a high current and initial pH adjustment. The top performance for both elements was achieved with a 25 A current, four Fe electrodes, 15 min of operational time per phase (cycle), and a middle range of pH values, which resulted in 97.92% and 99.96% removals of Sr and Se, respectively. This research highlighted the novel approach of using electrochemical pH control to achieve high removal efficiencies of Se and Sr from water in a short operating time, which surpassed the efficiencies reported in previous studies.

1. Introduction

Selenium (Se) and strontium (Sr) are naturally occurring elements that can contaminate water sources through both natural and anthropogenic processes [1,2]. Se enters aquatic systems via the weathering of selenium-rich rocks, volcanic activity, and soil leaching [3]. Anthropogenic sources include agricultural runoff from selenium-enriched fertilizers, effluents from coal-fired power plants, and mining operations [3]. Similarly, Sr contamination arises from natural rock dissolution and industrial activities, such as mining, metallurgy, petrochemical processes, electronics, pyrotechnics, nuclear testing, and inappropriate nuclear waste disposal [4,5,6]. Although Se and Sr are often studied independently due to their distinct geochemical behaviors, they can coexist in specific natural waters [2,7,8,9] and industrial effluents, like mining tailings, flue gas desulfurization wastewater, coal-fired power plant effluents, oil and gas extraction, metal finishing and electroplating wastewaters, and radioactive waste repositories (⁹⁰Sr and ⁷⁹Se) [3,10,11]. Both elements, while essential or benign in trace amounts, become hazardous at elevated concentrations, impacting ecosystems and human health [1,2,3,4].

Conventional methods for removing Se and Sr from water include chemical coagulation; adsorption and ion exchange; and membrane technologies, such as reverse osmosis and biological treatments [12,13,14]. While effective, these approaches are often hindered by disadvantages such as incomplete removal, sensitivity to competing ions, fouling, slow operation, large spatial requirements, high costs, complex maintenance, and substantial secondary waste production [4,15]. These limitations have spurred interest in alternative treatment methods.

Electrochemical methods, particularly electrocoagulation (EC) and electrochemical reduction, offer promising alternatives due to their efficiency, cost-effectiveness, and environmental compatibility [16,17]. EC uses an electric current to dissolve sacrificial electrodes that generate coagulants in situ, and these coagulants facilitate the precipitation of various contaminants from water [18,19,20,21]. This process is also effective for strontium removal, where it can precipitate strontium in forms that are easily separable from water [15]. Furthermore, EC was shown to effectively remove selenium, transforming it from its dissolved forms to less soluble ones [3]. EC offers additional advantages, including operational simplicity, chemical-free treatment, reduced secondary waste, and potential for automation [22]. However, its efficiency is influenced by factors such as electrode material, current density, and water chemistry [4,15]. Table 1 provides a review of studies that used EC to treat various wastewaters that contained Se and Sr. While high removal efficiencies are frequently reported, these studies were typically conducted on small volumes (lab-scale) and at low initial Se and Sr concentrations.

The pH of the water significantly impacts the chemical forms, solubility, and environmental behavior of selenium and strontium. Se exists in various forms depending on the pH: selenate (SeO₄²⁻), selenite (SeO₃²⁻), elemental selenium (Se⁰), and selenide (Se²⁻) [3,28,29]. Selenate remains soluble across a wide pH range, while selenite’s solubility decreases with lower pH, making it less mobile in acidic conditions [3]. Strontium behaves similarly to calcium, forming carbonates and sulfates. Its compounds are more soluble in acidic environments, leading to increased dissolution, whereas alkaline conditions promote precipitation as strontium carbonates, thereby limiting mobility [15,30]. Adjusting the pH is an effective strategy to control the mobility of these elements in aquatic systems and enhance their removal from water and wastewater.

To avoid the unnecessary addition of chemicals, the pH value of the treated water can be adjusted through electrochemical pH control [31,32,33]. The main principle of controlling the pH through water electrolysis involves the electrochemical decomposition of water (H₂O) into its constituent elements—hydrogen (H₂) and oxygen (O₂)—by passing an electric current through the water containing some electrolyte [31,33]. This process fundamentally relies on two half-reactions occurring at the two electrodes (cathode and anode) immersed in the water. At the cathode, water is reduced to hydrogen gas and hydroxide ions. At the anode, the production of hydroxide ions increases the pH of the solution, making it more basic. Water is oxidized to oxygen gas and hydrogen ions at the anode [32]. The release of hydrogen ions decreases the pH of the solution, making it more acidic. By adjusting the electrical current and the duration of electrolysis, the amount of hydrogen ions (H⁺) or hydroxide ions (OH⁻) generated can be controlled, thereby adjusting the pH of the solution effectively [31,33]. Ion-selective membranes, such as cation-exchange and anion-exchange membranes, are often employed in electrochemical systems. These membranes selectively allow for specific ions to pass, effectively managing the ion transport to maintain or alter the pH in designated areas of the system [33]. Furthermore, membranes help concentrate ions in specific areas, reducing the overall energy required for ion movement and reaction processes. They also separate the electrodes to prevent the mixing of gases (hydrogen and oxygen) produced at each electrode, maintaining effective pH adjustments [33]. This method of pH control is advantageous because it avoids the addition of chemical reagents, allowing for a cleaner and potentially automated process of adjusting the pH in various applications, ranging from industrial processes to environmental management [31].

The aim of this study was to investigate the simultaneous electrochemical removal of Se and Sr from wastewater using a novel three-stage, two-phase (two-cycle) electrochemical reactor. To the best of our knowledge, this study was the first to explore the synergistic effects of electrochemical pH control combined with electrocoagulation for wastewater purification, primarily for the removal of Se and Sr from water. This research introduced an innovative approach where pH control was executed in two separate reactors, each set to different pH values, and across two phases (cycles) with an interchange of pH settings between the reactors in the second phase. Such a synergistic interaction resulted in a significantly greater efficiency for the contaminant removal compared with previously published studies, where it achieved higher purification levels in a substantially shorter time frame. Moreover, this method avoided the potential generation of harmful byproducts that can occur with chemical pH control. This study evaluated the effect of various factors such as electrode material, current density, pH, and operation time on the removal efficiencies, with the aim to optimize the conditions for the maximum removal of Se and Sr.

2. Materials and Methods

2.1. Experimental Setup

Experiments were conducted in a three-stage, two-phase recirculating batch reactor shown in Figure 1. It consisted of a pH value control reactor, 2 electrocoagulation (EC) reactors, and 2 settling tanks.

The electrochemical pH control reactor, constructed from Plexiglass, was divided into 3 sections by 2 cation-exchanging membranes (Nafion 117, DuPont, Wilmington, DE, USA), 10 cm × 20 cm, placed in Plexiglass frames, as pictured in Figure 2. Graphite plate electrodes (U20) with a total active surface area of 168 were positioned on either side of the membranes and connected to the laboratory power supply (CSP-3000–120 from Mean Well, Taiwan, China) in an anode/cathode cathode/anode configuration.

Two rectangular EC reactors, 4 L each, were also made of Plexiglass (Figure 3). Each reactor was equipped with an overhead mixer set to 150 rpm and electrode stands that accommodated up to 8 electrodes with a 1 cm inter-electrode distance. The electrodes were connected to another 3000 W laboratory power supply (CSP-3000-120 from Mean Well, Taiwan, China) in monopolar parallel mode. High-purity perforated aluminum (1050-H24) or iron (ARMCO G2) plate electrodes, each with an active surface area of 86.73 cm², were used during the EC stage of the process. A two-channel function generator (JT-JDS6600 from Joy It, Neukirchen-Vluyn, Germany) was used to control both power supplies. System cooling was achieved using thermoelectric cooling blocks (Peltier modules) paired with passive aluminum heatsinks on all reactor sides. Additionally, 3 heat pipes were inserted directly into each reactor, including the pH control reactor. For better heat dissipation, a fan (12 V, 1.1 W) was mounted on each heatsink, heat pipe, and thermoelectric cooling block with an additional mounted passive heatsink.

Two cone-shaped settlers, each with a 4 L volume, were used for sedimentation after the EC treatment. Each settler featured two valves. The side valves were connected to the two plastic pumps (Jebao DCP-4000, Jebao, Zhongshan, China) and the bottom valves were used to discard the sludge.

The process efficiency was analyzed using synthetic wastewater (model solution) containing 10 mg/L of Se and Sr. For each experimental run, 7 L of this model solution was used (3.5 L for each EC reactor). Each experimental run utilized 7 L of the model solution (3.5 L per EC reactor). Initially, the solution entered the pH control reactor, where the pH adjustment occurred. Acidic conditions were established in the outer sections, while the middle section was alkaline. The solution from the acidic sections was directed to one EC reactor, and the solution from the alkaline section to the other. After the electrochemical treatment, the treated solution flowed into the settlers for sedimentation. The sludge was separated, and the supernatant was recycled back into the pH control reactor—but into the opposite section—to alternate the solution’s exposure to acidic and alkaline conditions in the second phase. This alternating approach enhanced the Se and Sr removal.

The model solution had an average initial pH of 7.04, 316 mg/L of total dissolved solids, 1.9 FNU turbidity, 651 µS/cm conductivity, and a temperature of 21.9 °C. The physicochemical properties, including pH, were measured using an HI9829 multimeter (Hanna Instruments, Smithfield, VA, USA).

A total of 102 experiments were conducted based on a statistically designed experimental matrix. The variables included the electrode material (Al or Fe), number of electrodes (4, 6, or 8 per EC reactor), treatment time (5, 15, or 25 min), and applied current (5, 15, or 25 A). Comparisons were made between experiments with and without the electrochemical pH adjustment. By applying a maximum voltage of 120 V to graphite electrodes for 5 or 15 min, two pH ranges were achieved: 5–6 and 8–9 for the shorter operating time, and 2.5–3.5 and 9.5–10.5 for the longer operating time. Additional confirmation tests were conducted in order to validate the obtained models.

The process efficiency was evaluated by monitoring the changes in the concentrations of Se and Sr at each stage of every experiment. The concentrations were measured using optical emission spectrometry with inductively coupled plasma on an Agilent 5900 instrument (Agilent, Santa Clara, CA, USA).

2.2. Design of Experiments

The experiments were conducted following the design of experiments (DoE) method combined with the response surface methodology (RSM). This approach was utilized to understand the functional relationships between process variables and their influence on the numerical response, in this case, the Se and Sr removal efficiency. The primary advantage of the statistical design of experiments lies in significantly reducing the number of experiments required, as it allows for the prediction of variable behavior across a broad range of conditions [34,35]. This enables obtaining a lot of data from a relatively limited dataset. Within the RSM framework, a Box–Behnken design (BBD) was adopted—a three-level optimization approach (low, medium, and high variable values) that helps refine experimental conditions and develop a polynomial regression model for predicting responses. This method proves particularly effective in scenarios with non-linear interactions between independent variables and dependent outcomes [36]. For example, the quadratic model, a second-order RSM formulation, can be expressed as

(1)$Y(x)={\beta }_0+\sum _{i=1}^n{\beta }_i{x}_i+\sum _{i=1}^n\sum _{j=1}^n{\beta }_{ij}{x}_i{x}_j+\epsilon$

where Y represents the result derived from input variables x_n, while β_i and β_ij denote the first- and second-order regression coefficients for individual and interactive variable effects, respectively, and ϵ accounts for errors in the observed response Y [36].

The goal of this study was to determine the most influential parameters and their optimal values for maximizing the efficiency of the Se and Sr removal from water. Five parameters (factors) were tested: electrode material, applied current, number of electrodes, operating time, and initial pH value of the solution. As shown in Table 2, the electric current, electrode surface, and treatment time were numeric factors tested at three levels, while the electrode material and pH value were categorical factors. The treatment times of 5, 15, or 25 min represented the EC treatment time in one phase. The total EC treatment times for both stages were 10, 30, and 50 min, respectively. The applied current was consistent across both EC reactors during the EC phase of the treatment. The active (anodic) surface of the electrodes was adjusted by varying the number of electrodes used, which means that the current density varied from 72 (5 A, 8 electrodes per EC reactor) to 720 (25 A, 4 electrodes per EC reactor) A m⁻². Two electrode materials were used: aluminum (Al) and iron (Fe).

The pH factor in this study had three settings: unchanged initial pH (pH control stage of the treatment was skipped), a middle range, and a maximum range. For the middle range, the pH was set between 5 and 6 for acidic conditions and 8 and 9 for alkaline conditions. For the maximum range, it was set between 2.5 and 3.5 for acidic conditions and 9.5 and 10.5 for alkaline conditions. These pH levels were achieved by applying 120 V to graphite electrodes in the electrochemical pH control reactor for either 5 min (middle range) or 15 min (maximum range), producing a current of 7 to 10 A. In the second phase of the treatment, adjusting the pH became more challenging due to the lower electroconductivity of the solution, which required either more time or a higher current to reach the desired pH ranges. Despite the same voltage being applied, the current did not exceed 5 A. Initially, the solution was neutral, but it typically became slightly acidic or alkaline after the first phase of treatment, depending on the reactor used. In the second phase, the solution initially set to alkaline needed to be switched to acidic and vice versa, which demanded more time and/or current. With constant voltage and time settings across this study, smaller changes in the pH were observed in the second phase compared with the first. By the end of the second phase, the pH values were generally 0.5 to 1.5 units higher in the acidic section or lower in the alkaline section than those achieved in the first phase.

The average cumulative removal efficiencies of Se (Y₁) and Sr (Y₂) at the end of the two-phase electrochemical treatment were used as the responses. The key process variables were identified using analysis of variance (ANOVA). The experimental design, which included 102 experimental runs, along with the measured and predicted responses, is presented in Appendix A, Table A1.

3. Results

The results from all 102 experiments, as detailed in Appendix A Table A1, indicate that Se reached a 100% removal efficiency in several experiments, while the highest removal efficiency for strontium peaked at approximately 98%. Table 3 provides an overview of selected experiments—those that achieved the lowest and highest efficiencies for each element. Notably, the lowest efficiencies for Sr removal were observed using Fe electrodes for a short duration and without any pH adjustment (specifically in runs 54, 3, and 62). Runs 80, 48, and 84 yielded the highest removal efficiencies, suggesting that higher applied currents and the maximum range of pH values favored Sr removal. These results also suggest that Se was generally easier to remove than Sr. The complete removal of Se was achieved in experiments without a pH adjustment, 25 min duration, and 15 or 25 A of applied current. Considering the performance for both elements, run 48 achieved the top performance with 97.92% and 99.96% removals of Sr and Se, respectively. This indicates that the optimal operational parameters included 25 A of applied current, four Fe electrodes, 15 min of operational time, and the middle range of pH values. Generally, increasing the current strength and extending the duration enhanced the removal efficiencies of both elements. The choice of electrode material and the pH level also significantly influenced the outcomes, with the maximum pH range favoring better removal rates for Sr.

3.1. DoE Results

A reduced quartic model was selected to describe the electrochemical removal of both Se and Sr with the results of the analysis of variance (ANOVA) detailed in Table A2 and Table A3 in Appendix A. A quartic model can include terms up to the fourth power of each variable, as well as interaction terms between variables raised to powers that sum up to four or less. This allows the model to capture more complex patterns and interactions in the data, which might be missed by lower-degree polynomial models. Quartic models are particularly useful when the relationship between variables is complex and non-linear, and when simpler models (like linear or quadratic models) are insufficient to capture the trends in the data accurately [37].

Low p-values, an insignificant lack of fit, and high adjusted R² values indicate that the obtained models are statistically significant. The adequacy of the models is further validated by the comparison of the predicted and observed response values, listed in Table A1 and shown in Figure 4. A significance level of 0.05 was selected in accordance with other studies [35,38]. This means that for a term to be deemed significant in our analysis, it must have a p-value below 0.05. Nevertheless, some factors and their interactions with p-values above 0.1 were retained in the model. This decision was made to preserve the hierarchical structure and stability of the model, as removing these terms could potentially lead to a significant lack of fit.

The equations for the obtained models, detailed in Appendix A, are specific to each combination of the categorical factors, namely, pH and electrode materials. Since these factors are categorical, distinct equations were derived to address the various conditions set by these parameters. Table A4 provides the coefficients for each term required to apply these equations using the actual factors.

3.2. Selenium Removal

Selenium removal proved to be relatively straightforward, with generally high efficiencies across all the experiments (56–100%). The lower efficiencies were typically associated with shorter operation times, lower current strengths, or the absence of pH adjustment. On the other hand, complete Se removal was achieved with higher current strengths and longer treatment times. In the obtained model, four out of the five tested factors proved to be significant, with p-values less than 0.0001. The only insignificant factor was the number of electrodes. Significant interaction terms also emerged in the model, particularly those that involved the applied current and treatment time, applied current and electrode material, and treatment time and electrode material, all with p-values less than 0.0001. These interactions highlight the complex dynamics between these variables in influencing the efficiency of selenium removal. Figure 5 includes the three-dimensional response surface plots for each electrode material, illustrating the effects of the applied current and treatment time when the number of electrodes and pH ranges were averaged over.

Both electrode materials demonstrated better efficiencies when subjected to higher currents and/or extended treatment times, irrespective of the pH conditions. A notable difference in the performance between the two materials was observed when the treatment time was short; under these conditions, the Fe electrodes were more effective at lower current strengths compared with the Al electrodes. However, as illustrated in Figure 6, with the longest treatment, both materials behaved similarly regardless of the applied current.

While the influence of pH was less pronounced in the removal of selenium compared with strontium, adjustments to the pH still had a noticeable impact, particularly at the maximum pH range. This was especially true for Al electrodes during shorter treatment times, where an increase in the pH range notably improved the performance. Figure 7 depicts that with longer operating times, the pH range had a minimal effect on the removal efficiency.

3.3. Strontium Removal

The results show that Sr was far more challenging to remove than Se. Similar to the trends observed in the Se removal, lower current strengths (below 15 A), shorter durations, and unfavorable pH levels adversely affected the Sr removal efficiency. However, the influence of these factors on the Sr removal was more pronounced, reflecting its more resistant nature to electrochemical treatment. The obtained model showed that all of the factors were significant with p-values less than 0.0001, with the exception of the electrode number, which had a p-value of 0.0466. This suggests that while the number of electrodes played a role, its impact was less critical compared with the other factors.

Furthermore, several interactions were particularly significant in the context of Sr removal, including the applied current and pH, treatment time and pH, and electrode material and pH. These interactions underscore the complex interplay between the electrochemical settings and the chemical environment.

As expected, longer treatment times and higher current led to higher Sr removal rates. However, the pH value of the solution had significantly more influence on the efficiency of the Sr removal compared with Se. This heightened sensitivity to pH changes could be particularly observed in interactions between the applied current and treatment time, as shown in Figure 8. When the highest values of the treatment time and current were used, high efficiencies were achieved by using both Fe and Al electrodes, regardless of the pH. However, by comparing Figure 9a,b, the effect of the pH value is evident when the treatment time and current were low. The maximum pH range, meaning the most alkaline environment, drastically improved the performance of the Fe electrode. This effect can also be observed in Figure 10, where it can be seen that both materials show similar performances in alkaline conditions, as opposed to neutral conditions, where Al performed better. It is important to note that this is only valid for short treatment times and/or low applied currents.

3.4. Operational Costs Estimation

The cost estimates, including the electricity and material used, for the top-performing experiment (25 A, four Fe electrodes, 15 min, and middle pH range) could be calculated using Equation (2) [27,38,39]:

(2)$Operational costs=a·C_{el}+b·C_{EC}+c·C_p+d·C_m$

where C_el represents the electricity used per cubic meter of treated water (kWh m⁻³), encompassing the energy use by the electrodes in the pH control reactor, both EC reactors, and the pumps. C_EC (kg m⁻³) denotes the amount of electrode material per cubic meter of treated water, and C_p (kg m⁻³) indicates the pump material wear per cubic meter in a service cycle (1 year). C_m refers to the membrane area used to process (change the pH value) the total volume of model solution over its lifespan (0.04 m² for 9.5 m³). The coefficients a, b, c, and d represent the costs associated with the electricity (0.16 EUR kWh⁻¹), the price of Fe electrodes (36 EUR kg⁻¹), maintenance materials for the pumps (estimated as 70 EUR kg⁻¹ per service cycle), and membrane costs per m² used in this research (177 EUR for 2 membranes 10 cm × 20 cm), respectively.

The lifespan of a Nafion 117 membrane depends on various factors, such as the operating conditions, chemical environment, mechanical stress, and maintenance practices. Under optimal conditions and with proper handling, a Nafion 117 membrane can last several years. However, in typical applications, they can last from 1000 to 10,000 h of operation, depending on the specific conditions. In 68 experiments in which the pH value was changed, a total of 952 L of model solution was processed. Ultimately, no notable effectiveness in the pH rate of change was observed, indicating the absence of significant membrane fouling. Therefore, it was assumed that the membranes used in this research can process at least a total of 10 times the amount of processed solution, that is, about 9.5 m³.

The power consumption of graphite electrodes and Fe electrodes for both phases, as well as the pumps, were measured with an EMOS P5822 power meter as 0.079, 0.426, and 0.003 kWh, per phase, respectively, resulting in a total electrical energy consumption of 145.14 kWh m⁻³.

The electrode material release (kg m⁻³) was calculated according to Faraday’s law [40,41], expressed in Equation (3):

(3)$C_{EC}={\displaystyle \frac{\left(I·t·M_w\right)}{\left(z·F·V\right)}},$

M_w represents the molar mass (55.9 g mol⁻¹ for Fe), z is the number of electrons transferred (2 or 3), F is the Faraday constant (96 487 C mol⁻¹), t is the treatment time (s), and V is the volume of treated water (m³). Thus, the released Fe electrode material was 1.34 kg m⁻³.

The released electrode material from the graphite electrodes was not included in the calculations because for carbon electrodes used in electrochemical processes, such as electrocoagulation or pH adjustment through water electrolysis, there typically is not any release of electrode material into the solution. Graphite electrodes are generally used because they are inert, meaning they do not easily participate in chemical reactions and do not dissolve into the solution under typical conditions. While the carbon material itself does not dissolve or release, surface reactions can occur where reactants or products may adhere to or interact with the surface of the carbon. This interaction is more about surface chemistry and does not involve the breakdown or release of the carbon material itself.

The average operating costs for the top-performing experiment were calculated as 90.23 EUR m⁻³. In addition, the use of photovoltaic systems can reduce costs, making the operating expenses considerably lower. By utilizing solar energy through a typical setup containing photovoltaic panels, an inverter, a battery storage system, and a rectifier, the electricity costs, which are typically one of the largest operational expenses in EC systems, can be significantly reduced.

4. Discussion

Experimental run 48 (25 A, 15 min, four Fe electrodes, middle pH range) exhibited the best performance for the simultaneous removal of Sr and Se. The changes in Se and Sr concentrations during the process, as well as the relative and cumulative efficiency of each stage, are graphically presented in Figure 11. For each stage, the relative efficiency was calculated using the final concentration from the previous stage as the initial concentration. On the other hand, the cumulative efficiency considered only the initial concentration at the start of the experiment. The Se and Sr removal proceeded through two streams. After the pH stage, two streams were created: alkaline and acidic. The alkaline stream went to the alkaline EC reactor and then to the corresponding settler. After the sludge settled, the solution above the sludge was directed to the acidic part of the pH reactor. Following the pH treatment in phase 2, it became acidic and moved to the acidic EC reactor, and finally to another settler. The second stream followed the opposite pathway. The average efficiencies took both streams into account. In the first stage, the treatment in the pH control reactor during the first phase slightly reduced Se and Sr concentrations, with average relative and cumulative efficiencies of 23.90% and 36.12%, respectively. The EC stage in the first phase resulted in the highest removal rates—95.96% of Se and 92.85% of Sr (average relative efficiency). After the sludge settling, on average, 96.93% of Se and 95.43% of Sr were cumulatively removed at the end of the first phase. The second phase resulted in averages of 98.72% and 54.55% relative removal efficiencies for Se and Sr, respectively. Considering the total average cumulative efficiency of 99.96% for Se and 97.92% for Sr, it can be concluded that most of the contaminants were removed during the first phase of the treatment.

In the pH stage of the second phase, an increase in the Sr concentration was observed, which resulted in negative efficiencies that are represented as 0 in Figure 11. This issue likely arose from incomplete sludge removal. If a small amount of sludge remained in the solution before it progressed to the second phase of treatment, Sr could leach back into the solution when the pH value changed. Additionally, it is possible that some Sr deposited on the electrodes during the first phase could be released back into the solution due to the pH change. In situations where the complete or near-complete removal of Se and Sr is not necessary, the first phase of the process alone might suffice. However, the second phase is crucial to ensure that the quality of the treated water meets stringent standards, such as those required for drinking water.

When the pH control stage was skipped, the process was much simpler; however, the efficiencies, especially for Sr removal, were also lower. For comparison, the Se and Sr concentrations and cumulative and relative efficiencies for the best-performing experimental run without a pH adjustment (15 A, four Al electrodes, 25 min) for the simultaneous removal of Se and Sr are shown in Figure 12. In terms of the relative efficiencies, 91.21% of Se and 79.49% of Sr were removed after the first EC treatment, and 90.12% of Se and 75.12% of Sr in the second EC treatment. Cumulatively, removal efficiencies of 99.13% for Se and 94.90% for Sr were achieved.

4.1. pH Control Stage

In the electrochemical pH reactor, water oxidation occurs at the anode (connected to the positive terminal of the power supply), producing protons H⁺ (H₃O⁺) and oxygen gas O₂. The generated H⁺ ions increase the acidity of the anode side (reactor compartment where the anodes are). At the cathode (electrode connected to the negative terminal of the power supply), water reduction occurs, consuming protons (H⁺) and producing hydroxide ions (OH⁻) and hydrogen gas (H₂). The produced OH⁻ ions make the cathode side alkaline, causing the pH to rise. The proton exchange membrane (PEM) allows only protons to pass through from the acidic anode side to the alkaline cathode side, preventing other ions like OH⁻ or larger cations from crossing. As protons leave the anode side, the acidity increases. Simultaneously, protons arrive at the cathode side, neutralizing some OH⁻, but the continual production of OH⁻ keeps the cathode side alkaline.

During the pH control stage of the treatment, samples of the treated solution were taken and compared with the initial values of Se and Sr concentrations. A slight reduction in Se concentration on the cathode side and an increase in the Sr concentration were observed. The observed distribution of Sr and Se arose from the pH gradient created by the selective transport of protons through the PEM and the electrochemical reactions at the electrodes; the solubility changed due to the pH value and selective ion transport. These factors combined to influence how the different ions segregated under the influence of an applied electric field. The PEM allowed only cations to cross, while the other ions were confined to their compartments, which influenced the local solubility equilibria.

Depending on its chemical state in water, Se is an anion. Anions are repelled from the cathode due to the negative charge and tend to accumulate at or move toward the anode. However, since the PEM may block their passage, their concentration might decrease on the alkaline (cathode) side primarily because they are not being replenished from the anode side. The high concentration of H⁺ on the anode side stabilizes H₂SeO₃ and HSeO₃⁻, reducing the mobility of Se species. On the cathode side, SeO₃²⁻ ions are more mobile in the alkaline environment and may even precipitate with Sr²⁺ to form strontium selenite (SrSeO₃), which is sparingly soluble in water. This precipitation, if it does occur, reduces the overall Se concentration in the cathode-side solution.

As a cation, Sr is attracted to the cathode. The accumulation of Sr on the cathode side could be due to both the migration of Sr ions toward the negatively charged cathode and the possible passage through the PEM if it is not completely selective against divalent cations. The higher pH on the cathode side can also increase the Sr solubility or differentially affect its speciation. If any carbonate ions are present, they may also react with Sr²⁺, forming SrCO₃ precipitates in some areas.

Various other ions, like Na⁺, Cl⁻, Ca²⁺, and CO₃²⁻, likely present in the solution, can also participate in similar migration and electrochemical reactions. These ions can compete with or facilitate the movement of Se and Sr ions, affecting their overall distribution in the cell.

In summary, the observed reduction in Se concentration on the cathode side and the increase in Sr concentration can be attributed to the electrochemical reactions at the electrodes, selective ion migration through the PEM, and the effects of the changing pH across the cell.

4.2. EC Stage

EC relies on the dissolution of electrodes to release metal ions that form hydroxides or oxyhydroxides, which adsorb onto and co-precipitate the contaminants. The metal cations Al³⁺ or Fe^2+/3+ released from the anode hydrolyze to form metal hydroxides Al(OH)₃ and Fe(OH)₃. Se is adsorbed onto the surfaces of metal hydroxide particles and/or precipitated as metal selenates. Sr can co-precipitate with carbonate or hydroxide ions under alkaline conditions or adsorb onto the hydroxides. The colloidal particles formed aggregate into flocs that settle, removing contaminants from the water. At a neutral pH, Al(OH)₃ and Fe(OH)₃ flocs are optimally formed, providing high adsorption capacity. Se species are efficiently removed by adsorption and co-precipitation. Sr removal is moderate due to lower precipitation of carbonates or hydroxides. At very low pH values, Al³⁺ and Fe³⁺ ions remain highly soluble, reducing the formation of flocs. Sr removal is poor, as the precipitation of Sr compounds is minimal in acidic conditions. In alkaline conditions, Al(OH)₃ and Fe(OH)₃ flocs may dissolve to form soluble Al(OH)₄⁻ and Fe(OH)₄⁻, reducing their adsorption capacity. However, Sr removal improves because of increased precipitation with carbonate or hydroxide. On the other hand, Se removal is lower due to competition between hydroxide ions and selenate for adsorption sites. It can be concluded that optimal pH for removal of Se is neutral-to-slightly acidic pH (~5–7) where hydroxide flocs are stable, and Se species are effectively adsorbed. Slightly alkaline pH (~8–9) is better for Sr removal, favoring precipitation of its compounds. The best-performing experiment (run 48) confirmed this, as the middle range of pH value was used. pH governs the solubility and formation of hydroxide flocs, directly influencing the adsorption and co-precipitation efficiency of Se and Sr during electrocoagulation. Fine-tuning the pH ensures optimal contaminant removal, balancing the behavior of aluminum or iron species in the system.

The applied current directly affects the rate of electrode reactions, which is the core driver of electrocoagulation. According to Faraday’s law, the mass of ions released from the electrode (Al³⁺ or Fe³⁺) is proportional to the applied current. A higher current means more ions are generated per unit time, increasing the rate of hydroxide precipitation, as well as the adsorption and co-precipitation of contaminants, like Se and Sr. In addition, an increased current induces more vigorous gas bubbling (H₂ evolution at the cathode and O₂ at the anode), enhancing the mixing and dispersion of ions present in the solution. Basically, the current controls the rate of reactions and determines the availability of metal ions and hydroxide for contaminant removal. An insufficient current can lead to smaller ion production, while an excessive current might cause energy inefficiency and overheating without proportional gains in the removal efficiency.

Adding more electrodes does not inherently improve the process unless other parameters, such as the current distribution and spacing, are also optimized. Increasing the number of electrodes increases the total surface area available for reactions. However, if the applied current is fixed, the current density (current per unit surface area) decreases, which can slow the reaction rates at each electrode.

The electrical field created by the electrodes drives ionic movement and reactions. Simply adding more electrodes without changing the current or configuration may not significantly enhance the process if the spacing and arrangement do not optimize the current pathway. Once sufficient Al³⁺ or Fe³⁺ ions are generated to remove the available Se and Sr ions, adding more electrodes does not increase the removal efficiency.

It can be concluded that the number of electrodes alone does not directly affect the reaction kinetics; it only influences the available surface area for reactions. If the applied current is constant, the system may already be operating at a level where additional electrode surfaces have a diminishing impact, as can be seen for Se in Figure 13b.

However, the number of electrodes can affect the current density, which is a key parameter in any EC process. For instance, in the case of Sr removal (as shown in Figure 13a), when a low applied current was used with eight electrodes, the achieved current density was not sufficient for effective removal. While higher densities typically increased the effectiveness, there was a threshold beyond which further increases in the current density yielded negligible gains. The required current densities could be achieved through various combinations of the applied current strength and electrode surface used. The combinations used in this study resulted in current densities of 72, 96, 144, 216, 288, 360, 432, 480, and 720 A m⁻². The highest current density of 720 A m⁻² was achieved by applying 25 A of electric current to four electrodes in each EC reactor, and it was used in the top-performing experiment when considering the removal of both Se and Sr. Specifically for Se, the current densities of 480 and 432 A m⁻² both resulted in complete Se removal under the same treatment conditions (25 min, no pH control, Fe electrodes). This indicates that the current density threshold for these operating conditions was reached at 432 A m⁻², and a further increase was not needed for the removal of Se. However, under the same conditions, the current densities below 480 Am⁻² were not sufficient for effective Sr removal. Interestingly, that threshold current density applied for 25 min in maximum pH range resulted in similar efficiencies when applied to both the Al (97.26%) and Fe (96.10%) electrodes, with 97.26% being the highest removal rate of Sr overall.

4.3. Electrodeposition

Although removal by floc adsorption and sedimentation is typically the primary pathway, another possible mechanism for Se and Sr removal from water is electrodeposition, where these elements deposit on the electrode surface during the EC process. Se species, such as selenate or selenite, can undergo reduction at the cathode, as described by Equations (4) and (5):

(4)$Se{O}_4^{2-}+4H_{2}O+6e^{-}\to Se\left(s\right)+8O{H}^{-}$

(5)$Se{O}_3^{2-}+4H_{2}O+4e^{-}\to Se\left(s\right)+6O{H}^{-}$

This process leads to the deposition of elemental Se on the cathode surface. Selenium reduction is more likely under neutral-to-alkaline conditions, where hydroxide ions are abundant. Sr does not undergo direct electrochemical reduction due to its chemical nature. However, localized increases in pH near the cathode (due to the generation of hydroxide ions) can lead to the precipitation of compounds such as SrCO₃ and Sr(OH)₂. These precipitates may adhere to the electrode surface, especially the cathode, where hydroxide ions are generated. Also, if a passive oxide or hydroxide layer forms, Se and Sr can physically adsorb onto the layer on the electrode surface. Furthermore, in the presence of other ions, like CO₃²⁻ and HCO₃⁻, scaling may occur on the electrode surface, with strontium contributing to hard deposits.

Neutral-to-alkaline pH increases the likelihood of Se reduction and Sr precipitation near the cathode. On the other hand, acidic pH reduces the chances of deposition since the hydroxide and carbonate species required for Sr precipitation are scarce. A high current density can enhance the reduction of Se species at the cathode but may also lead to excessive gas evolution (e.g., hydrogen), which reduces the adherence of deposits.

To investigate the relevance of this mechanism, the electrodes were mechanically cleaned after the experiment, and the formed layer was analyzed using semi-quantitative ICP-OES analysis. The results show that while some Se was present, Sr was present in significant quantities. The deposition of Se and Sr can reduce the efficiency of the electrocoagulation process by impeding the current flow and mass transfer. However, periodic physical or chemical cleaning can remove these deposits and restore electrode functionality.

4.4. Scale-Up

The scalability of EC reactors is influenced by a multitude of factors for which the maintenance of electrical, geometric, kinematic, and thermal similarity criteria are crucial [42,43,44].

The uniformity of the current distribution across the electrodes is vital for ensuring that the electrochemical reactions occur evenly throughout the reactor volume. If the current distribution is not maintained during the scale-up, it can lead to localized overheating, inefficient coagulation, and reduced overall treatment effectiveness. The design of the electrode configuration, including the spacing and arrangement of anodes and cathodes, plays a significant role in achieving a uniform current distribution [45,46]. Moreover, the electrochemical kinetics of the reactions occurring at the electrodes must also be taken into account. The rate of electrochemical reactions is influenced by factors such as the electrode surface area, the concentration of reactants, and the applied current density. Thus, maintaining similar current densities and electrode surface areas relative to the reactor volume is necessary. Failure to do so can result in changes in the reaction rates, leading to inefficiencies in contaminant removal [47].

Geometric similarity ensures that the physical dimensions and configurations of the reactor maintain proportional relationships that influence the overall performance and efficiency of the system. This concept is particularly important because deviations from geometric similarity can lead to significant changes in the flow dynamics, mass transfer, and reaction kinetics, which can adversely affect the treatment process [46,48]. The distance between the anodes and cathodes significantly affects the electric field strength and the mass transfer rates of ions in the EC process. If the spacing is not maintained proportionally during the scale-up, it can lead to variations in the current density and, consequently, the efficiency of the contaminant removal [49].

The Reynolds number, which characterizes the flow regime, should remain consistent across scales to ensure that the flow remains either laminar or turbulent as intended. This is particularly important for the mixing efficiency and mass transfer rates [50,51]. In general, the maintenance of geometric similarity helps to achieve similar Reynolds numbers [48,51]. Similarity in the Froude number ensures that the effects of gravity on the flow behavior are consistent across different reactor sizes, which is particularly important in systems where buoyancy-driven flows are significant, such as in EC flotation processes [52].

Maintaining thermal similarities ensures that the temperature distribution, heat transfer characteristics, and thermal dynamics remain consistent across different reactor sizes. One of the primary aspects of thermal similarity is the heat transfer coefficient, which describes how effectively heat is transferred between the fluid, electrodes, and reactor surfaces. The heat transfer coefficient can be influenced by factors such as the fluid velocity, temperature gradients, and physical properties of the fluid. If the heat transfer characteristics differ significantly between scales, it could lead to variations in temperature profiles, which may affect the solubility of electrolytes and the kinetics of the electrochemical reactions occurring within the reactor. Additionally, the thermal effects associated with electrical operations must be considered. The Joule heating effect, which occurs due to the passage of the current through the resistive electrolyte, can lead to temperature increases that affect the EC process. Ensuring that thermal management strategies are in place to handle the heat generated during operation is crucial for maintaining the desired electrical characteristics and preventing thermal degradation of the reactor components [53].

By ensuring that these parameters are consistent across different scales, engineers can predict the performance of the larger reactor based on the data obtained from smaller models.

Despite the promising results, the transition from laboratory-scale studies to full-scale applications of EC remains a challenge. Factors such as energy consumption, electrode wear, and the need for continuous monitoring and control systems can impact the feasibility of large-scale deployment [54,55,56]. Nevertheless, ongoing research continues to address these challenges, exploring the integration of renewable energy sources and automated control systems to enhance the efficiency and sustainability of EC processes [57].

Regarding the scalability of the EC reactor from this study, equivalent efficiency tests on a pilot-scale reactor with a capacity 5 to 10 times larger is necessary. This pilot reactor should be designed based on the previously measured parameters from the EC reactor used in this study, while carefully considering scale effects. Finally, measurements should also be performed on real industrial wastewater, and the obtained results would serve as a basis for developing guidelines for designing even-larger-capacity systems. It can be expected that increasing the reactor’s capacity, while maintaining the stated similarities, will eventually reach a point where certain operational parameters become impractical to achieve due to size and volume limitations. Examples of such limitations include excessively large electrode surfaces or extremely high current intensities. In such cases, reactor capacity expansion can be achieved through a modular design, meaning an increase in the number of devices operating in parallel.

5. Conclusions

This study suggests that the conditions required to achieve high removal efficiencies for Se were less stringent compared with those for Sr. Sr removal required more precise control of conditions such as pH, higher currents, or specific electrode materials to reach near-optimal removal rates. These findings highlight that Se could be removed more effectively and with less operational specificity in the EC process compared with Sr.

The key factors that influenced the efficacy of the EC process included the treatment duration, current density, and the initial pH of the solution, which were critical for forming metal hydroxides and enabling the coagulation and sedimentation of the contaminants. These findings align with prior research, confirming the importance of these variables.

The novelty of this study lay in the use of electrochemical pH control in the water purification process. This method was found to be feasible and improved the efficiency of the Se and Sr removal without generating byproducts associated with chemical pH control. Alternating the pH optimized the removal by providing ideal conditions for both contaminants: Se in acidic-to-neutral and Sr in alkaline environments. This two-phase process prevents re-dissolution, enhancing the overall efficiency compared with a constant pH. Furthermore, a single-system approach enables the simultaneous removal of both contaminants, eliminating the need for separate treatments and lowering the equipment, energy, and operational expenses. This research confirmed that electrocoagulation, particularly when paired with effective pH management, offers a potent and sustainable alternative to traditional water treatment methods for hazardous elements, balancing the operational efficiency with environmental sustainability.

Author Contributions

Conceptualization, I.H. and K.L.; Methodology, K.L.; Software, H.P.; Validation, H.P. and D.N.; Formal Analysis, I.H. and K.L.; Investigation, K.L.; Resources, I.H.; Data Curation, H.P.; Writing—Original Draft Preparation, I.H. and K.L.; Writing—Review and Editing, D.N. and H.P.; Visualization, D.N.; Supervision, I.H.; Project Administration, I.H.; Funding Acquisition, I.H. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All main processed data are contained within this article. The remaining raw datasets from the conducted tests are available upon request from the authors.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of this study; in the collection, analyses, or interpretation of the data; in the writing of this manuscript; or in the decision to publish the results.

Abbreviations

The following abbreviations are used in this manuscript:

EC	Electrocoagulation
SS	Stainless steel
Sono-EC	Sonoelectrocoagulation
PEM	Proton exchange membrane
RE	Removal efficiency

Footnotes

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Figures and Tables

Figure 1. A photo and a schematic overview of the electrochemical water treatment system.

Figure 2. pH value control reactor.

Figure 3. EC reactors (representative view).

Figure 4. (a) A comparison of predicted and observed removal efficiencies for Se removal. (b) A comparison of predicted and actual values of Sr removal efficiencies.

Figure 5. RSM plots showing interactions of factors A (applied current) and C (treatment time) for Se for (a) Al electrodes and (b) Fe electrodes.

Figure 6. Interaction of factors A (applied current) and D (electrode material) for Se when the treatment time was (a) 5 min and (b) 25 min. The red line represents Al electrodes, green line Fe electrodes.

Figure 7. pH–applied current interaction for Se removal in the case of Al electrodes when the treatment time was (a) 5 min and (b) 25 min. The red line represents experiments with no pH adjustment, along with green line middle and blue line maximum ranges of pH values.

Figure 8. RSM plots showing interactions of factors A (applied current) and C (treatment time) for Sr for (a) no pH control and (b) maximum pH range.

Figure 9. pH–electrode material interaction for Se removal in the case of Al electrodes when treatment time and applied current were set to (a) 5 and (b) 25. Red line represents experiments with no pH adjustment, along with green line middle and blue line maximum ranges of pH values.

Figure 10. Electrode material–applied current interaction for Sr removal when treatment time was 5 min for (a) no pH adjustment and (b) maximum pH range. The red line represents Al electrodes, green line Fe electrodes.

Figure 11. Changes in the Se and Sr concentrations in each stage of the process (bars), relative efficiency trends (lines), and cumulative efficiency trends (dashed lines) for run 48 (25 A, 4 Fe electrodes, 15 min, middle pH range).

Figure 12. Change in the Se and Sr concentrations in each phase of the process (bars), relative efficiency trends (lines), and cumulative efficiency trends (dashed lines) for run 51 (15 A, 4 Al electrodes, 25 min, no pH adjustment).

Figure 13. The effect of the electrode number on the removal efficiencies of (a) Sr and (b) Se depending on the applied current for treatment time of 25 min. Black line presents 4 electrodes, red 8 electrodes.

Table 1

Literature review of electrochemical processes for the removal of Se and Sr.

Process	Conditions	Removal Efficiency	Refs.
Hybrid EC membrane process	1.5 L, 4 Fe anodes, 4 SS cathodes, 48 A m−2, 20 min	98.7% of Se	[23]
EC	0.5 L, Fe/Al anodes, 0.2/0.3 A, 60 min	97/96% of Se0	[16]
EC	1 L, 2 Fe electrodes, 153 A m−2, pH 5, added NaCl, 6 h, initial concentration of 0.3 mg L−1	90% of Se	[24]
EC	3 L, 4 Al anodes, 4 Fe cathodes, 4 A m−2, 15 mM NaCl, 52 min, initial concentration of 0.1 mg L−1	>90% of Se	[3]
EC	0.2 L, 2 SS/Al electrodes, 80 A m−2, 50 min	93/77% of Sr	[15]
Simultaneous EC and adsorption process	1.5 L, 4 Al electrodes, 75 A m−2, 120 min	72% of Sr	[25]
EC	0.4 L, 2 Fe electrodes, 11.5 A, 30 min, initial concentration of 1.14 mg L−1	99.5% of Sr	[26]
EC	1 L, Mg anode, 8 A m−2, pH 7	97% of Sr	[4]
Sono-EC	5.5 L, 4 Fe and 4 Al electrodes, 12.5 A, 10 min, initial concentration of 3 mg L−1	93% of Se 34% of Sr	[27]

Table 2

Factors used and their characteristics.

Factor	Name	Units	Type	Subtype	Minimum	Mean	Maximum
A	I	A	Numeric	Continuous	5	15	25
B	Electrode number		Numeric	Continuous	4	6	8
C	t	min	Numeric	Continuous	5	15	25
D	Electrode material		Categoric	Nominal	Al		Fe
E	pH		Categoric	Nominal	No pH adjustment	Middle range	Maximum range

Table 3

Experimental runs with the lowest and highest Se and Sr removal efficiencies.

Run	Factor A	Factor B	Factor C	Factor D	Factor E	Response 1	Response 2
	I (A)	A (m2)	t (min)	Material	pH	%Sr	%Se
54	5	6	5	Fe	No pH adjustment	8.39	86.67
3	15	8	5	Fe	No pH adjustment	11.21	96.31
62	5	8	15	Fe	No pH adjustment	18.89	90.14
65	5	6	5	Al	No pH adjustment	22.86	56.24
24	5	6	5	Al	Middle range	57.30	64.33
30	5	6	5	Al	Maximum range	71.85	67.62
80	25	6	25	Fe	Maximum range	96.10	99.91
84	25	6	25	Al	Maximum range	97.96	98.03
48	25	4	15	Fe	Middle range	97.92	99.96
13	25	6	25	Fe	No pH adjustment	84.67	100
29	15	4	25	Fe	No pH adjustment	90.62	100

Appendix A

Table A1 contains the experimental matrix obtained using DesignExpert software and the corresponding responses (removal efficiencies for Se and Sr). Table A2 and Table A3 show the results of the ANOVA for the reduced quartic model.

Table A1

Experimental matrix with actual and predicted response values.

Run	Factor AI (A)	Factor BNum	Factor Ct (min)	Factor DMaterial	Factor EpH	Response 1%Se	PredictedResponse 1	Response 2%Sr	Predicted Response 2
1	15	8	5	Al	Maximum range	93.13	93.64	76.80	74.46
2	25	8	15	Al	Minimum range	98.06	99.03	86.33	86.05
3	15	8	5	Fe	No pH adjustment	96.31	96.29	11.21	15.62
4	25	6	5	Fe	Minimum range	99.44	96.93	82.63	82.51
5	15	6	15	Al	Maximum range	96.21	96.21	89.36	89.72
6	15	4	25	Al	Minimum range	98.89	99.46	94.08	91.54
7	25	4	15	Al	Minimum range	98.97	98.39	94.74	97.61
8	25	4	15	Fe	Maximum range	99.74	100.09	90.96	92.81
9	15	6	15	Fe	Minimum range	99.40	99.10	75.32	76.73
10	25	6	5	Al	Maximum range	95.96	97.48	81.86	83.40
11	5	8	15	Fe	Maximum range	97.99	98.07	88.59	87.29
12	25	8	15	Al	Maximum range	97.58	97.89	91.90	92.14
13	25	6	25	Fe	No pH adjustment	100.00	100.90	84.67	87.18
14	15	6	15	Al	Maximum range	95.72	96.21	85.95	89.72
15	5	8	15	Al	Minimum range	95.89	94.72	82.38	86.05
16	15	6	15	Fe	Minimum range	99.29	99.10	74.89	76.73
17	25	4	15	Fe	No pH adjustment	99.70	100.27	88.03	82.44
18	5	6	25	Fe	Maximum range	99.54	101.27	85.69	87.68
19	25	8	15	Fe	Minimum range	98.98	99.61	93.24	92.92
20	15	6	15	Al	Minimum range	97.99	96.92	91.29	83.48
21	15	6	15	Fe	Maximum range	98.04	98.35	86.50	86.81
22	15	4	5	Fe	No pH adjustment	98.50	99.32	26.25	18.76
23	15	6	15	Al	Maximum range	95.50	96.21	87.16	89.72
24	5	6	5	Al	Minimum range	64.33	64.66	57.30	55.82
25	5	6	25	Al	Minimum range	97.73	95.91	88.42	87.98
26	15	6	15	Fe	Minimum range	99.74	99.10	76.58	76.73
27	15	4	5	Fe	Minimum range	95.94	95.09	83.36	82.84
28	5	4	15	Al	Minimum range	89.47	91.39	69.98	76.80
29	15	4	25	Fe	No pH adjustment	100.00	99.57	90.62	93.22
30	5	6	5	Al	Maximum range	67.62	68.11	71.85	70.39
31	5	6	25	Al	Maximum range	95.05	95.28	84.86	88.22
32	15	6	15	Fe	No pH adjustment	98.65	93.44	62.89	46.72
33	15	6	15	Fe	Minimum range	99.21	99.10	72.58	76.73
34	15	6	15	Al	No pH adjustment	95.12	96.39	78.59	69.85
35	25	8	15	Fe	No pH adjustment	99.08	97.29	55.75	42.76
36	15	6	15	Al	Minimum range	97.11	96.92	86.24	83.48
37	15	8	25	Al	No pH adjustment	91.59	92.37	59.22	62.71
38	15	6	15	Fe	No pH adjustment	86.00	93.44	35.37	46.72
39	5	6	5	Fe	Minimum range	84.23	85.49	56.68	60.79
40	15	6	15	Fe	No pH adjustment	92.66	93.44	42.34	46.72
41	5	4	15	Fe	No pH adjustment	92.97	92.01	19.98	32.04
42	15	6	15	Al	Minimum range	97.29	96.92	87.33	83.48
43	5	8	15	Fe	Minimum range	98.77	97.05	78.07	77.80
44	15	6	15	Al	Maximum range	95.81	96.21	87.49	89.72
45	5	4	15	Fe	Minimum range	94.09	96.23	79.42	75.78
46	5	6	25	Fe	Minimum range	99.38	100.95	75.73	73.39
47	5	8	15	Al	No pH adjustment	85.77	87.20	50.73	40.75
48	25	4	15	Fe	Minimum range	99.96	100.29	97.92	94.24
49	5	6	25	Fe	No pH adjustment	98.64	96.76	70.62	57.29
50	25	6	5	Al	No pH adjustment	94.90	92.22	74.20	62.87
51	15	4	25	Al	No pH adjustment	99.13	95.40	94.90	85.74
52	5	6	5	Fe	Maximum range	89.39	89.31	75.22	74.78
53	25	6	25	Al	Minimum range	98.01	98.05	90.65	93.46
54	5	6	5	Fe	No pH adjustment	86.67	84.07	8.39	-1.15
55	25	6	5	Fe	No pH adjustment	97.90	99.70	28.67	38.58
56	5	4	15	Al	Maximum range	95.24	92.80	83.83	82.99
57	15	8	25	Al	Maximum range	95.78	96.66	88.78	90.12
58	15	6	15	Al	Minimum range	96.22	96.92	81.20	83.48
59	15	4	5	Fe	Maximum range	99.28	99.48	85.64	85.10
60	15	6	15	Fe	Maximum range	98.79	98.35	90.63	86.81
61	15	4	5	Al	Maximum range	91.15	88.64	78.85	76.15
62	5	8	15	Fe	No pH adjustment	90.14	90.54	18.89	23.55
63	15	8	25	Fe	Minimum range	100.00	98.99	92.58	90.86
64	5	4	15	Fe	Maximum range	97.78	97.85	85.70	85.10
65	5	6	5	Al	No pH adjustment	56.24	56.84	22.86	28.91
66	15	8	25	Al	Minimum range	96.52	97.71	94.97	96.20
67	15	8	5	Fe	Minimum range	92.26	94.36	80.63	77.36
68	25	6	5	Al	Minimum range	93.27	95.85	67.99	71.15
69	5	8	15	Al	Maximum range	97.11	95.42	88.42	85.19
70	15	6	15	Al	No pH adjustment	96.27	96.39	74.21	69.85
71	15	8	5	Al	No pH adjustment	79.49	79.99	42.07	48.49
72	15	8	5	Al	Minimum range	91.61	90.61	62.19	63.14
73	15	4	25	Al	Maximum range	95.99	99.13	89.37	86.29
74	25	6	5	Fe	Maximum range	99.65	98.93	87.06	88.37
75	15	6	15	Fe	No pH adjustment	95.01	93.44	40.46	46.72
76	25	8	15	Al	No pH adjustment	98.40	95.69	84.72	83.20
77	15	8	25	Fe	No pH adjustment	96.74	98.15	42.69	48.19
78	25	4	15	Al	No pH adjustment	96.14	96.34	65.22	71.86
79	15	8	25	Fe	Maximum range	99.82	99.25	94.26	96.21
80	25	6	25	Fe	Maximum range	99.91	99.38	96.10	91.41
81	15	6	15	Al	No pH adjustment	96.63	96.39	69.04	69.85
82	15	6	15	Fe	Minimum range	99.26	99.10	76.78	76.73
83	15	6	15	Fe	Maximum range	98.43	98.35	88.04	86.81
84	25	6	25	Al	Maximum range	99.85	95.59	97.96	91.37
85	25	4	15	Al	Maximum range	96.18	97.98	89.57	92.20
86	25	6	25	Fe	Minimum range	99.85	100.90	83.27	85.25
87	25	6	25	Al	No pH adjustment	96.90	99.69	88.08	93.11
88	15	4	25	Fe	Maximum range	99.62	98.99	87.05	90.32
89	5	4	15	Al	No pH adjustment	83.20	85.15	58.07	56.25
90	15	6	15	Fe	Maximum range	99.75	98.35	93.51	86.81
91	15	6	15	Al	Maximum range	95.81	96.21	87.49	89.72
92	15	6	15	Al	Minimum range	97.15	96.92	86.52	83.48
93	15	8	5	Fe	Maximum range	97.55	98.14	83.28	85.48
94	15	6	15	Fe	No pH adjustment	93.08	93.44	45.27	46.72
95	5	6	25	Al	No pH adjustment	93.21	93.36	64.46	69.01
96	15	6	15	Fe	Maximum range	97.14	98.35	81.51	86.81
97	15	4	25	Fe	Minimum range	99.74	98.12	82.41	84.69
98	15	4	5	Al	Minimum range	86.82	84.90	71.69	70.12
99	15	6	15	Al	No pH adjustment	97.42	96.39	69.84	69.85
100	15	6	15	Al	No pH adjustment	97.35	96.39	58.70	69.85
101	15	4	5	Al	No pH adjustment	73.97	75.56	26.86	29.63
102	25	8	15	Fe	Maximum range	98.91	98.81	95.75	96.90

Table A2

Results of ANOVA analysis for reduced quartic model describing electrochemical removal of strontium.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	42,617.30	39	1092.75	26.08	<0.0001	Significant
A—I	3871.74	1	3871.74	92.40	<0.0001
B—electrode number	172.75	1	172.75	4.12	0.0466
C—t	6957.60	1	6957.60	166.05	<0.0001
D—material	923.52	1	923.52	22.04	<0.0001
E—pH	20,297.40	2	10,148.70	242.21	<0.0001
AB	34.71	1	34.71	0.8284	0.3662
AC	145.78	1	145.78	3.48	0.0669
AD	54.18	1	54.18	1.29	0.2599
AE	1223.15	2	611.58	14.60	<0.0001
BC	101.86	1	101.86	2.43	0.1240
BD	113.32	1	113.32	2.70	0.1051
BE	530.08	2	265.04	6.33	0.0032
CD	12.56	1	12.56	0.2998	0.5860
CE	2562.42	2	1281.21	30.58	<0.0001
DE	1959.68	2	979.84	23.39	<0.0001
B2	20.31	1	20.31	0.4846	0.4889
C2	368.06	1	368.06	8.78	0.0043
ABD	55.20	1	55.20	1.32	0.2555
ABE	40.56	2	20.28	0.4840	0.6186
ADE	20.38	2	10.19	0.2432	0.7849
BCE	858.58	2	429.29	10.25	0.0001
BDE	377.52	2	188.76	4.50	0.0149
CDE	731.30	2	365.65	8.73	0.0005
B2D	178.22	1	178.22	4.25	0.0434
B2E	422.16	2	211.08	5.04	0.0094
C2D	166.39	1	166.39	3.97	0.0507
ABDE	406.06	2	203.03	4.85	0.0111
Residual	2597.81	62	41.90
Lack of fit	1786.66	38	47.02	1.39	0.1984	Not significant
Pure error	811.15	24	33.80
Cor total	45,215.11	101

Table A3

Results of ANOVA analysis for reduced quartic model describing electrochemical removal of selenium.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	5147.08	44	116.98	24.66	<0.0001	Significant
A—I	891.74	1	891.74	187.95	<0.0001
B—electrode number	0.5269	1	0.5269	0.1111	0.7402
C—t	1066.63	1	1066.63	224.82	<0.0001
D—material	501.39	1	501.39	105.68	<0.0001
E—pH	237.45	2	118.72	25.02	<0.0001
AB	6.61	1	6.61	1.39	0.2427
AC	616.67	1	616.67	129.98	<0.0001
AD	132.76	1	132.76	27.98	<0.0001
AE	76.15	2	38.07	8.02	0.0008
BC	12.91	1	12.91	2.72	0.1045
BD	14.69	1	14.69	3.10	0.0838
BE	6.54	2	3.27	0.6898	0.5058
CD	270.76	1	270.76	57.07	<0.0001
CE	55.31	2	27.65	5.83	0.0050
DE	10.65	2	5.32	1.12	0.3328
A2	76.78	1	76.78	16.18	0.0002
B2	18.10	1	18.10	3.81	0.0557
C2	228.22	1	228.22	48.10	<0.0001
ABD	0.5459	1	0.5459	0.1151	0.7357
ACD	115.56	1	115.56	24.36	<0.0001
BCD	30.82	1	30.82	6.50	0.0135
BDE	0.7698	2	0.3849	0.0811	0.9222
CDE	46.45	2	23.22	4.89	0.0109
A2D	27.95	1	27.95	5.89	0.0184
AB2	134.46	1	134.46	28.34	<0.0001
B2C	104.01	1	104.01	21.92	<0.0001
B2D	1.27	1	1.27	0.2686	0.6063
B2E	15.78	2	7.89	1.66	0.1986
C2D	220.05	1	220.05	46.38	<0.0001
C2E	11.28	2	5.64	1.19	0.3122
AB2D	55.88	1	55.88	11.78	0.0011
B2DE	59.45	2	29.73	6.27	0.0035
C2DE	72.63	2	36.31	7.65	0.0011
Residual	270.43	57	4.74
Lack of fit	176.12	33	5.34	1.36	0.2201	Not significant
Pure error	94.31	24	3.93
Cor total	5417.51	101

The obtained models could be described by the equations listed in Table A4 (the value of each term is multiplied by its according coefficient). The equations, expressed in terms of actual factors, allowed for predictions about the response based on the specific levels of each factor, where the levels were designated in their original units. However, this equation was not suitable for assessing the relative importance of each factor, as the coefficients were adjusted to fit the units of each factor, and the intercept did not lie at the center of the design space.

Table A4

Coefficients for model equations.

Selenium
	Al			Fe
Term	No pH Adjustment	Middle Range	Maximum Range	No pH Adjustment	Middle Range	Maximum Range
Intercept	102.59322	152.30846	167.46964	158.47179	128.98206	147.96128
I	−1.78133	−1.99085	−2.08221	0.174781	−0.034732	−0.126099
N	−28.45478	−40.88607	−43.61474	−26.02535	−18.24464	−21.90023
t	2.5182	1.48845	0.922576	−2.77511	−1.14904	−1.89877
I * N	1.61783	1.61783	1.61783	0.338102	0.338102	0.338102
I × t	−0.072632	−0.072632	−0.072632	−0.028747	−0.028747	−0.028747
N × t	0.789865	0.789865	0.789865	0.903191	0.903191	0.903191
I2	−0.027952	−0.027952	−0.027952	−0.006915	−0.006915	−0.006915
N2	2.54475	3.6074	3.81977	2.12081	1.52026	1.81221
t2	−0.080611	−0.055081	−0.043016	0.026132	−0.023444	−0.004316
I × N2	−0.137635	−0.137635	−0.137635	−0.029734	−0.029734	−0.029734
N2 × t	−0.0736	−0.0736	−0.0736	−0.0736	−0.0736	−0.0736
Strontium
	Al			Fe
Term	No pH adjustment	Middle range	Maximum range	No pH adjustment	Middle range	Maximum range
Intercept	−73.48373158	55.11664486	41.86531447	−87.71007808	134.9277131	103.0776063
I	−0.192039389	2.450689256	0.94349502	4.449440244	1.459543068	0.660441204
N	22.79774267	−8.014730563	4.418370306	12.26260226	−26.82815325	−11.75994274
t	7.182069021	2.77019658	2.513274865	6.562019783	0.254311182	0.729150493
I × N	0.3355	−0.2601186	−0.028288805	−0.389875	−0.041725209	0.023718531
I × t	−0.024646016	−0.024646016	−0.024646016	−0.024646016	−0.024646016	−0.024646016
N × t	−0.523615928	0.145629052	0.068968019	−0.523615928	0.145629052	0.068968019
N2	−1.707955788	0.78690759	−0.396730513	−0.381790695	2.113072684	0.92943458
t2	−0.063744891	−0.063744891	−0.063744891	−0.012487799	−0.012487799	−0.012487799

I—applied current, N—number of electrodes, t—treatment time.

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