Data-Based Modeling, Multi-Objective Optimization, and Multi-Criterion Decision-Making to Maximize the Electro-Oxidation of Metoprolol over Boron-Doped Diamond Electrodes in a Flow-By Reactor

Abstract

Metoprolol is a cardioselective beta-blocker drug often used to treat hypertension, but it is considered as a hazardous organic persistent contaminant in wastewater. In this study, a 2.5 L solution of metoprolol (50 mg/L) underwent electro-oxidation in a flow-by reactor using boron-doped diamond electrodes in the batch recirculation mode. The study used multi-objective optimization and multi-criterion decision-making to determine the optimal operating parameters. The response surface methodology and a central composite rotatable design were used with three factors (pH₀: 5–8, I: 2.5–4 A, and Q: 0.8–1.7 L/min) to model the chemical oxygen demand’s (COD’s) removal efficiency and the total organic carbon’s (TOC’s) removal efficiency. The experimental responses were modeled by reduced third- and second-order polynomials with determination coefficients (R²) of 0.9816 and 0.9430. The optimal operating parameters were found to be pH₀ 5, an I value of 3.84 A, and a Q value of 0.8 L/min with an electrolysis time of 7.5 h, resulting in a maximum COD removal efficiency of 60.8% and a TOC removal efficiency of 90.1%. The specific energy consumption was calculated as 9.61 kWh/mg of TOC, with a total operating cost of 0.77 USD/L. In conclusion, this study showed that the electrochemical process is efficient and reliable for treating wastewater containing metoprolol.

1. Introduction

Because of the scarcity of water on Earth, caused by global warming, and increased contamination of water sources because of global industrialization in recent years, the United Nations’ member states have declared the decontamination and sanitation of wastewater as priority tasks through Agenda 2030, which is the basis for objective 6 (clean water and sanitation) of the sustainable development goals [1]. Regarding contamination by anthropogenic activities, the emerging contaminant (EC) molecules in oceans, rivers, lakes, and soils from sources such as farming, cattle raising, and highways can provoke human health and environmental harm [2]. ECs include dyes, personal care products, endocrine disruptors, and drugs (e.g., antibiotics and beta-blockers among others), which are usually discarded in water bodies [3,4,5]. These pollutants are persistent, transported over long-range distances, bioaccumulate, and are highly toxic because they produce allergic reactions, immune system damage, endocrine disruption, and liver and kidney damage; increase cancer risk; cause neuronal damage; possess mutagenicity; and impact children’s development [6]. Metoprolol (MET) is the beta-blocker most used worldwide as a treatment for hypertension, tachycardia, cardiac insufficiency, heart failure, and myocardial infarction [7]. Approximately 1.28 billion people are suffering from arterial hypertension [8] worldwide, and in Mexico, around 30 million Mexicans are affected by arterial hypertension [9]. Between 3 and 10% of the medication dosage is excreted without undergoing any transformation and is released through urine [10]. Also, MET has been detected in treated wastewater from conventional treatment plants in Asia, America, and Europe, at concentrations of 0.268, 0.212, and 5.762 µg/L, respectively [11,12]. Therefore, it is crucial to remove this medication because of its health risks for both humans and aquatic organisms.

Numerous technologies have been developed to eliminate ECs (e.g., metoprolol) from wastewater, including physical, chemical, and biological. However, physical treatments are unable to completely degrade ECs; chemical methods produce secondary pollutants and are costly, and biological methods struggle to treat high-concentration pollutants, require long treatment times, and are sensitive to the environment [13]. In this sense, electrolysis, an advanced oxidation process, has emerged as an efficient and green technology for removing ECs, such as MET. It offers high efficiency, environmental compatibility, flexibility for automation, easy maintenance, and the possibility of the mineralization of recalcitrant pollutants and does not need additional chemicals to conduct the process [6,14,15,16].

In the process of electrolysis, electrodes play a crucial role. Various types of electrodes (e.g., Pt, PbO₂, SnO₂, Ta₂O₅-IrO₂, and Nb₂O₅-IrO₂) have been developed, including carbon-based materials (e.g., graphite, graphene, carbon nanotubes, and boron-doped diamond (BDD) electrodes). BDD electrodes are especially preferred for electrolysis because of their chemical, electrochemical, and mechanical stabilities [17]. They are also known for their ability to produce a large amount of hydroxyl radicals (^●OH, with an oxidation potential of 2.8 V) [18,19,20] and other oxidized species, depending on the electrolyte medium used. For example, in Na₂SO₄ media, persulfate, peroxydisulfate, and sulfate radicals are formed [21,22,23,24,25,26].

The removal of MET has been studied primarily using ozonation [27,28], UV/H₂O₂ [29], photo-oxidation [30], Fenton [31], photo-Fenton [7], heterogeneous photocatalyst [32], and photo-Fenton-like [7] methods, with a batch reactor being the most used configuration. Only a few studies on electro-oxidation for MET removal were found [33,34,35,36], with a batch lab reactor also being the commonly used configuration in these studies. The flow-by reactor is the best reactor configuration for electro-oxidizing recalcitrant pollutants because of its high mass transport coefficients and homogeneous current distribution on the electrodes [37]. It is important to note that no studies have reported optimizing the removal of MET (see Table 1).

Regarding the optimization of the electro-oxidation process for ECs carried out in a flow-by reactor setup, the most common method for performing the optimization is the response-surface-methodology-driven DoE [38,39,40]. Also, the central composite rotatable design (CCRD) is widely utilized [41] because it offers sufficient data for testing the lack of the fit.

Table 1 summarizes the literature results related to the removal of MET using different treatment technologies. It can be observed that the related literature reveals the high removal efficiency of MET; however, it is worth pointing out that the treated volume used in many cases is very low, on the order of fractions of liters.

Table 1. Removal of MET using different non-optimized technologies.

Process Type	Reaction Conditions	Results		Ref.
		MET Removal (%)	TOC Removal (%)
UV	[MET]0 = 50 mg/L; H2O2 = Stoich.; pH0 5.6; λ = 254 nm; Vtreated = 0.1 L; Catalyst: Cu-TiO2; t = 100 min	92	25	[7]
Ozonation (O3)	[MET]0 = 200 µg/L; [O3] = 380 mg/L h; Vtreated = 0.8 L; pH0 11; t = 120 min	63.4	---	[27]
Adsorption and Photocatalysis	[MET]0 = 50 mg/L; pH0 9; λ = 250–400 nm; Vtreated = 0.025 L; 100 pm; Catalyst: TiO2; t = 300 min	100	63	[42]
Thermal plasma and UV/H2O2	[MET]0 = 5 µg/L; Plasma 150 W; 1 MHz; t = 120 min; Vtreated = 0.1 L; T = 35 °C	64.7	---	[29]
Fenton	[MET]0 = 148.5 mg/L; Vtreated = 0.1 L; T = 35 °C; pH0 3; [Fe3+]0 = 0.5 mM; t = 360 min	---	80	[43]

Table 1. Removal of MET using different non-optimized technologies.

Process Type	Reaction Conditions	Results		Ref.
		MET Removal (%)	TOC Removal (%)
UV	[MET]0 = 50 mg/L; H2O2 = Stoich.; pH0 5.6; λ = 254 nm; Vtreated = 0.1 L; Catalyst: Cu-TiO2; t = 100 min	92	25	[7]
Ozonation (O3)	[MET]0 = 200 µg/L; [O3] = 380 mg/L h; Vtreated = 0.8 L; pH0 11; t = 120 min	63.4	---	[27]
Adsorption and Photocatalysis	[MET]0 = 50 mg/L; pH0 9; λ = 250–400 nm; Vtreated = 0.025 L; 100 pm; Catalyst: TiO2; t = 300 min	100	63	[42]
Thermal plasma and UV/H2O2	[MET]0 = 5 µg/L; Plasma 150 W; 1 MHz; t = 120 min; Vtreated = 0.1 L; T = 35 °C	64.7	---	[29]
Fenton	[MET]0 = 148.5 mg/L; Vtreated = 0.1 L; T = 35 °C; pH0 3; [Fe3+]0 = 0.5 mM; t = 360 min	---	80	[43]

The focus of this study was to maximize the degradation of MET in terms of the COD and TOC removal efficiencies. This was achieved through electro-oxidation in a flow-by reactor using two Nb/BDD electrodes operating in the batch recirculation mode. The multi-objective optimization was carried out using RSM driven by CCRD, with three operating parameters, namely, the current intensity (I), initial pH (pH₀), and volumetric flow rate (Q). In addition to the optimization process, this study also involved model validation, determination of the total operating cost, kinetic rate models for the degradation of MET, COD removal, TOC removal, and phytotoxicity testing.

2. Materials and Methods

2.1. Reagents and Aqueous MET Solution

Sulfuric acid (H₂SO₄), sodium hydroxide (NaOH), and metoprolol tartrate salt (MET), with purities of 95, 97, and 99.9%, respectively, were purchased from the Sigma-Aldrich Company (Ciudad de México, Mexico). Additionally, sodium sulfate (Na₂SO₄), with a purity of 99%, was supplied by the Karal Group (Ciudad de México, Mexico, a Mexican Company).

Before each experiment, a synthetic aqueous solution containing 50 mg/L of MET in 2.5 L with 0.1 M Na₂SO₄ was freshly prepared. This MET solution was added to the reservoir tank of the electrochemical plant (as shown in Figure 1) and homogenized by recirculating for 15 min. Distillate water was used for preparing all the aqueous solutions containing 50 mg/L of MET.

Table 2. Aqueous solution characteristics and physicochemical properties.

Chemical Structure of MET	Aqueous Solution Characteristics
	CMET (mg/L)	pH	Conductivity (µS/cm)	TOC (mg/L)		COD (mg/L)
				Theo.	Exp.	Theo.	Exp.
	50	7	14,180	29.81	31.53 a	98.13	96.00 a
	Physicochemical properties
	Property				Value
	Molar weight (g/mol)				684.81
	Melting point (°C)				120 [44]
	Boling point (°C)				695.37 [44]
	Water solubility (mg/mL) at 25 °C				>1000 [44]
	pKa				9.7 [45]
	λ (nm)				223 [42]
	Chemical formula: (C15H25NO3)2●C4H6O6				CAS No.: 56392-17-7

^a The average value of all the trials; Theo.: theoretical value; Exp.: experimental value.

shows the physicochemical properties of the MET compound.

Scheme 1 depicts the flowchart diagram of the methodology employed in this research. Also, this scheme shows the stages followed to conduct the data-based modeling, multi-objective optimization, and multi-criterion decision-making to maximize the electro-oxidation of the metoprolol over boron-doped diamond electrodes in a flow-by reactor. Additionally, each step is thoroughly described in detail in the following subsections.

2.2. Voltametric Experiment

A micro-electrolysis test was performed using an Autolab potentiostat/galvanostat^® 30 controlled using the GPE software V.4.3. The test used a three-electrode cell (100 mL) with Ag/AgCl, a graphite bar, and a BDD electrode (with an electroactive area of 1 cm²) serving as reference, auxiliary, and working electrodes, respectively. Cyclic voltammetry was conducted in a voltage range from 0 to 2 V, at a scan rate of 100 mV/s, at atmospheric pressure, and at a temperature of 25 °C. Also, the aqueous solution containing 50 mg/L of MET was stirred for 1 min to attain a homogeneous mixture.

2.3. Electrochemical Plant

The electro-oxidation of metoprolol took place at an electrochemical plant (see Figure 1) consisting of an electrochemical flow-by reactor (FBR) with a width of 4.5 cm, a channel thickness of 0.5 cm, an electroactive length of 20 cm; two BDD electrodes (20 cm) that function as an anode and a cathode; a 3.5 L polycarbonate reservoir; a heat exchanger to maintain a constant room temperature; a magnetic pump operating at 300 rpm; a glass flowmeter for the liquid flow rate control; a power supply for electrode energization; and PVC pipelines, connectors, and valves. Additional information about the electrochemical FBR can be found in the authors’ previous work [46].

2.4. Experimental Design

A 2.5 L aqueous solution containing 50 mg/L of MET was added to the electrochemical plant reservoir (refer to Figure 1). The studied operating parameters included the initial pH (pH₀), current intensity (I), and volumetric flow rate (Q), as outlined in

Table 3. Levels and studied operating parameters.

K Design Parameters	Design Parameter Levels
	−α	−1	0	+1	+α
$x_A:$ Initial pH	3.98	5.00	6.50	8.00	9.02
$x_B:$ Current intensity (A)	1.99	2.50	3.25	4.00	4.51
$x_C:$ Volumetric flow rate (L/min)	0.49	0.80	1.25	1.70	2.00

.

In Table 3, the lower, central, highest, and axial (±α) levels of each operating parameter are encoded as −α, −1, 0, +1, and +α, following the Equation (1):

$$\begin{array}{l}\mathcal{l}={\displaystyle \frac{x_{\mathcal{l},i}-x_{\mathcal{l},0}}{\mathsf{\Delta }{x}_{\mathcal{l}}}}\\ \mathcal{l}=A,B,andC\\ i:-\alpha ,-1,0,+1,+\alpha \end{array}$$

(1)

A central composite rotatable design (CCRD) with three operating parameters was adopted as an experimental design comprising 2^K factorial trials, 2K axial trials, and K central trials, giving 17 trials (see Section 3) The experimental design, data-based modeling, ANOVA test, and optimization were conducted using Design Expert^® V.10 software (license number 9839-2917-5744-6919 from State-Ease, Inc., Minneapolis, MN, USA). Additionally, the Q range was chosen according to the authors’ previous work, where ibuprofen was electrochemically oxidized in the same FBR [40].

2.5. Chemical Analysis

Samples of the MET solution for each trial were taken directly from the reservoir of the electrochemical plant to determine the chemical oxygen demand (COD) and total organic carbon (TOC) of MET solutions before and after the electro-oxidation treatment. The COD determination was gauged using the standard method (5220B) given in [47]. The TOC determination was measured using a 6001 TOC analyzer (ShimadFzu, Kyoto, Japan). The pH was measured with an HI2210 Hanna potentiometer.

2.6. Calculations

The COD removal efficiency of the MET (η_COD) was computed based on the change in the COD (mg/L) quantity between the initial sample and the treated sample, according to Equation (2):

$${\eta }_{COD}={\displaystyle \frac{{\left[COD\right]}_0-{\left[COD\right]}_t}{{\left[COD\right]}_0}}\times 100$$

(2)

where ${\left[COD\right]}_0$ and ${\left[COD\right]}_t$ are the COD of the MET solution before and after the electro-oxidation treatment.

The TOC removal efficiency of the MET (η_TOC) was computed based on the change in the TOC (mg/L) quantity between the initial sample and the treated sample, according to Equation (3):

$${\eta }_{TOC}={\displaystyle \frac{{\left[TOC\right]}_0-{\left[TOC\right]}_t}{{\left[TOC\right]}_0}}\times 100$$

(3)

where ${\left[TOC\right]}_0$ and ${\left[TOC\right]}_t$ are the TOC of the MET solution before and after the electro-oxidation treatment.

The total electricity energy consumed (E (kWh)), including the energy consumed by the electrodes ($E_{electrodes}$), energy consumed by the recirculation pump ($E_{pump,flow}$), and energy consumed by the heat exchanger pump ($E_{pump,heatexchanger}$), was calculated using the set of Equations (4)–(7):

$$E_{electrode}={\displaystyle \frac{\mathsf{\Psi }\times I\times t}{1,000}}$$

(4)

$$E_{pump,flow}=P_n\times t$$

(5)

$$E_{pump,heatexchanger}=P_m\times t$$

(6)

$$E=E_{electrodes}+E_{pump,flow}+E_{pump,heatexchanger}$$

(7)

where E is the total electricity consumed (kWh), Ψ is the average cell potential (23.75 V), I is the applied current intensity (A), t is the total electro-oxidation time (7.5 h), P_n is the supplier catalog’s nominal power (0.198 kW) for the recirculating pump, and P_m is the supplied catalog’s nominal power (0.123 kW) for the heat exchanger pump.

The total operating cost was determined as a function of the electricity and electrolyte prices according to Equation (8):

cost = p_electricity E + p_electrolyte m_electrolyte

(8)

where p_electricity is the electricity price (0.058 USD/kWh, based on 1 USD/MXN = 18.36) for commercial use in Mexico, p_electrolyte is the price of the electrolyte (0.81 USD/kg), and m_electrolyte is the consumed electrolyte’s mass (0.36 kg).

2.7. Data-Based Modeling and Optimization Procedure

Experimental data responses (η_COD and η_TOC) were modeled using surrogate models, according to Equation (9), in terms of encoded variables:

$$\begin{array}{ll}{\eta }_j=& {\beta }_0+{\beta }_{1}A+{\beta }_{2}B+{\beta }_{3}C+{\beta }_{4}AB+{\beta }_{5}AC+{\beta }_{6}BC+{\beta }_7{A}^2+{\beta }_8{B}^2+{\beta }_9{C}^2+\cdots \\ & {\beta }_{10}ABC+{\beta }_{11}{A}^{2}B+{\beta }_{12}{A}^{2}C+{\beta }_{13}A{B}^2+{\beta }_{14}A{C}^2+{\beta }_{15}{B}^{2}C+{\beta }_{16}B{C}^2+\cdots \\ & {\beta }_{17}{A}^3+{\beta }_{18}{B}^3+{\beta }_{19}{C}^3\\ j=& CODandTOC\end{array}$$

(9)

where ${\eta }_j$ is the surrogate model for the responses of the COD and TOC removal efficiencies; the β-values are the coefficients of the third-order polynomial function (see Equation (9)); and A, B, and C are the encoded operating parameters according to Equation (1). The β-values were calculated using the stepwise regression method in the Design Expert^® V.10 software package.

It is essential to prioritize accuracy when building models. In this study, the accuracy of the adjusted surrogate models was evaluated using the determination coefficient (R²), mean absolute error (MAE), and root-mean-square error (RMSE). The performance indexes, R², MAE, and RMSE, are represented by Equations (10) [48], (11) [49], and (12) [50], respectively. Also, a high-quality model has a high R² value and low values of MAE and RMSE.

$$R^2={\displaystyle \frac{{\displaystyle \sum _q^n\left({\eta }_{Exp,q}-{\overline{\eta }}_{Exp,q}\right){\displaystyle \sum _q^n\left({\eta }_{Model,q}-{\overline{\eta }}_{Model,q}\right)}}}{\sqrt{{\displaystyle \sum _q^n{\left({\eta }_{Exp,q}-{\overline{\eta }}_{Exp,q}\right)}^2{\displaystyle \sum _q^n{\left({\eta }_{Model,q}-{\overline{\eta }}_{Model,q}\right)}^2}}}}}$$

(10)

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _q^n\left|{\eta }_{Exp,q}-{\eta }_{Model,q}\right|}$$

(11)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _q^n{\left({\eta }_{Exp,q}-{\eta }_{Model,q}\right)}^2}}$$

(12)

where n is the total of number of trials, ${\eta }_{Exp}$ is the experimental response, ${\eta }_{Model}$ is the modeled response, and ${\overline{\eta }}_{Exp}$ and ${\overline{\eta }}_{Model}$ are the average values of the experimental and modeled values, respectively.

The multi-objective optimization and multi-criterion decision-making for the determination of the optimal operating parameters were assessed using Design Expert^® V.10 software to attain the maximum COD and TOC removal efficiencies of the MET solution by applying a surrogate model of the responses (η_COD and η_TOC) represented by Equation (9). For this purpose, the Design Expert software package performs multi-objective optimization and multi-criterion decision-making using the steepest ascent method. It is necessary to input additional information into the software to achieve the multi-objective optimization in this study, as shown in

Table 4. Multi-objective optimization and multi-criterion decision-making of the electrochemical process.

Response	Objective	Limits		Unit	Importance
		Min.	Max.
pH0	Is in range	5	8	Dimensionless	+++
I	Is in range	2.5	4.0	A	+++
Q	Is in range	0.80	1.7	L/min	+++
ηCOD	Maximize	37.5	62.5	%	+++
ηTOC	Maximize	54.58	91.24	%	+++

. The two objectives for the selected responses (η_COD and η_TOC) need to be maximized. Also, the importances of each objective and the operating parameters (A, B, and C) were set as +++ (the default importance). Also, the desirability function was used to indicate the degree to which all the objectives were to be reached. Values close to 1 indicate that all the objectives were met [51].

2.8. Phytotoxicity Test

After determining the best operating conditions for the electro-oxidation of a MET aqueous solution, a phytotoxicity test was conducted before and after the electrochemical wastewater treatment containing MET, using mung bean seeds (Vigna radiata) because their fast-duration crop is suitable for various soil types [52]. For this purpose, 30 mung bean seeds were planted in four 250 mL glasses. Over ten days, each set of seeds was irrigated with 10 mL of distilled water, tap water, and MET aqueous solution before and after the electrochemical treatment. After ten days, the germination percentage and lengths of the shoot and root were measured. Also, the germination percentage was computed utilizing Equation (13) [53]:

$$GP(\%)={\displaystyle \frac{NSG}{NSS}}\times 100$$

(13)

where GP is the germination percentage, NSG is the number of seeds germinated, and NSS is the number of seeds sown.

2.9. HPLC and Mass Spectrometry

The MET electro-degradation progress was conducted using reverse-phase high-performance liquid chromatography (RP-HPLC) equipped with a photodiode detector (Agilent 6410) in the range 200–600 nm. The column used was a Hypersil GOLD, 5 μm, 150 × 4.6 mm, and the mobile phase was methanol (grade HPLC) and an aqueous solution of 0.1% formic acid. Isocratic separation was performed at 90/10 (v/v) at a flow rate of 0.5 mL/min. The sample was concentrated for a Sep-Pak^® C18 cartridge (water–acetonitrile), the injection volume was 15 μL, and a temperature of 30 °C was used. To identify the MET electro-degradation species, triple Quad LC/MS and an electrospray ionization (ESI) source were used. Mass spectrometry (MS) was carried out in the positive ion mode at a capillary voltage of 3000 V and a nitrogen gas flow rate of 10 L/min, and the gas temperature was 380 °C.

3. Results and Discussion

3.1. Voltammetry Study

The electrochemical behavior of the aqueous solution containing 50 mg/L of MET on the Nb/BBD anode was studied using cyclic voltammetry measurements. Figure 2 illustrates the cyclic voltammetry of the Na₂SO₄ (black line) and Na₂SO₄ + MET (blue line) with the Nb/BDD anode at a potential scan rate of 100 mV/s. This figure exhibits the typical hysteresis behavior of a non-reversible system when wastewater contains MET, with a well-delineated peak at around +1.3 V, indicating that MET is directly oxidized on the Nb/BDD anode’s surface. Also, when the potential is increasing, a smoothed current signal is seen after the peak at +1.3 V, indicating a signal of the oxidation byproducts from MET. Furthermore, these intermediates could be directly oxidized by the free heterogeneous radicals (^●OH) on the Nb/BDD anode’s surface [54,55] and other oxidants (e.g., sulfate radicals and persulfate ions) present in the aqueous medium because Na₂SO₄ was utilized as the electrolyte support [56,57,58], which could contribute to the fast degradation/mineralization of organic pollutants, such as MET, in synthetic wastewater. The formation of sulfate radicals $(S{O}_4^{-•})$ and the persulfate ions $(S_2{O}_4^{2-})$ formed on the Nb/BDD anode follow the reaction mechanisms given by Equations (14)–(17) [23,26,59,60]:

$$BDD+H_{2}O\to BDD{(}^{•}OH)+H^{+}+e^{-}$$

(14)

$$S{O}_4^{-}+BDD(H{O}^{•})\to S{O}_4^{-•}+H_{2}O$$

(15)

$$S{O}_4^{-•}+S{O}_4^{-•}\to S_2{O}_8^{2-}$$

(16)

$$2S{O}_4^{2-}\to S_2{O}_8^{2-}+2e^{-}$$

(17)

3.2. Data-Based Model Fitting

Table 5. Design matrix (CCRD) and experimental results of the electro-oxidation of MET.

Std.	Run	Design Space	Actual Parameters			Encoded Parameters			Responses
			pH0	I (A)	Q (L/min)	A	B	C	${\mathit{\eta }}_{\mathit{C}\mathit{O}\mathit{D}}$	${\mathit{\eta }}_{\mathit{T}\mathit{O}\mathit{C}}$
1	1	Factorial	5.00	2.50	0.80	−1	−1	−1	45.83 ± 0.67	65.41 ± 0.83
9	2	Axial	3.98	3.25	1.25	-α	0	0	62.50 ± 0.70	80.15 ± 0.57
10	3	Axial	9.02	3.25	1.25	+α	0	0	41.67 ± 0.57	83.46 ± 0.68
12	4	Axial	6.50	4.51	1.25	0	+α	0	56.33 ± 0.35	78.72 ± 0.55
3	5	Factorial	5.00	4.00	0.80	−1	+1	−1	58.33 ± 0.67	91.24 ± 0.64
16	6	Central	6.50	3.25	1.25	0	0	0	52.17 ± 0.76	70.91 ± 0.56
8	7	Factorial	8.00	4.00	1.70	+1	+1	+1	49.83 ± 0.64	81.87 ± 0.85
4	8	Factorial	8.00	4.00	0.80	+1	+1	−1	45.83 ± 0.72	84.99 ± 0.80
13	9	Axial	6.50	3.25	0.49	0	0	-α	38.58 ± 0.50	79.15 ± 0.75
5	10	Factorial	5.00	2.50	1.70	−1	−1	+1	37.50 ± 0.53	59.64 ± 0.74
7	11	Factoria	5.00	4.00	1.70	−1	+1	+1	50.00 ± 0.80	82.86 ± 0.25
11	12	Axial	6.50	1.99	1.25	0	-α	0	49.99 ± 0.50	54.58 ± 0.55
2	13	Factorial	8.00	2.50	0.80	+1	−1	−1	51.00 ± 0.62	67.29 ± 0.61
6	14	Factorial	8.00	2.50	1.70	+1	−1	+1	58.30 ± 0.95	77.02 ± 0.87
14	15	Axial	6.50	3.25	2.00	0	0	+α	58.33 ± 0.46	71.08 ± 0.35
17	16	Central	6.50	3.25	1.25	0	0	0	52.33 ± 0.59	76.77 ± 0.97
15	17	Central	6.50	3.25	1.25	0	0	0	50.67 ± 0.74	79.82 ± 0.53

records the 17 trials in the experimental design for the electro-oxidation of MET, as proposed in Section 2.4. The reported experimental values of the COD and TOC removal efficiencies of the MET are in the ranges 37.50–62.50% and 54.50–91.24%, respectively. Given the experimental responses of ${\eta }_{COD}$ and ${\eta }_{TOC}$, reduced cubic and quadratic polynomials were fitted for ${\eta }_{COD}$ and ${\eta }_{TOC}$, respectively.

Table 6. Beta values of the data-based models in encoded terms.

Response/ β-Values	Terms of Data-Based Polynomial Models
	Intercept	A	B	C	AB	AC	BC	A2	B2	C2	A2C	AB2
${\eta }_{COD}/{\beta }_i$	51.75	−6.19	1.61	5.87	−4.83	3.50	---	---	---	−1.50	−6.54	7.86
	R2 = 0.9816; Adj_R2 = 0.9632; Model_R2 = 0.7826; C.V. = 2.69%; Std. Dev. = 1.36; Adeq_Precision = 24.80
${\eta }_{TOC}/{\beta }_i$	75.71	1.29	8.22	−1.55	−3.31	2.59	−1.93	2.52	−2.84	0.15	---	---
	R2 = 0.9430; Adj_R2 = 0.8698; Model_R2 = 0.7036; C.V. = 4.56%; Std. Dev. = 3.45; Adeq_Precision = 14.36

shows the coefficients ($\beta$ values) of the data-based polynomials fitted.

The data-based models’ fit statistics, shown in Table 6, indicate that the fitted models are in excellent agreement with the experimental values because the determination coefficients (R²) for responses ${\eta }_{COD}$ and ${\eta }_{TOC}$ (0.9816 and 0.9430, respectively) are close to 1 [61], as confirmed by the parity graphics’ shape in Figure 3. Also, the Modeled_R² values (0.7826 and 0.7036) for ${\eta }_{COD}$ and ${\eta }_{TOC}$ are in reasonable agreement with the Adjusted_R² values (0.9632 and 0.8698) for ${\eta }_{COD}$ and ${\eta }_{TOC}$ because the differences are less than 0.2. Additionally, the adequate precision measures (24.28 and 14.36 for ${\eta }_{COD}$ and ${\eta }_{TOC}$, respectively) are greater than 4, indicating that the fitted data-based models can be used to navigate the design space [62]. In addition, the obtained values of the coefficient of variance (C.V., 2.69 and 4.556% for ${\eta }_{COD}$ and ${\eta }_{TOC}$, respectively) showed the great accuracy of the performed test because the C.V.s were under 10%, indicating that the adjusted data-based models (${\eta }_{COD}$ and ${\eta }_{TOC}$) have a high degree of reproducibility [63]. Furthermore, the performance indexes, MAE (0.79 and 1.80 for ${\eta }_{COD}$ and ${\eta }_{TOC}$, respectively) and RMSE (0.93 and 2.21 for ${\eta }_{COD}$ and ${\eta }_{TOC}$, respectively), for ${\eta }_{COD}$ and ${\eta }_{TOC}$ indicate that the reduced cubic and quadratic polynomial models are appropriate for modeling the responses (${\eta }_{COD}$ and ${\eta }_{TOC}$) because the values of MAE and RMSE are less than the standard deviations (1.36 and 3.45 for ${\eta }_{COD}$ and ${\eta }_{TOC}$, respectively), and the ratios of RSME/(Std. Desv.) are 0.68 and 0.64 for ${\eta }_{COD}$ and ${\eta }_{TOC}$, respectively, indicating satisfactory data-based model simulations for both responses (${\eta }_{COD}$ and ${\eta }_{TOC}$) because the RSME/(Std. Desv.) values are less than or equal to 0.70 [64].

The ${\beta }_0$ values (51.75 and 75.71 for ${\eta }_{COD}$ and ${\eta }_{TOC}$, respectively) represent the averages of all the runs for both responses (${\eta }_{COD}$ and ${\eta }_{TOC}$). An analysis of the variance inflation factors (VIFs) for the reduced cubic data-based model (${\eta }_{COD}$) reveals that the VIF values of the terms B, AB, AC, and C² are 1, indicating that these terms are orthogonal. Also, the VIF values of the terms A, C, A²C, and AB² are 2.42, suggesting that these terms are multicollinear because all the VIF values are greater than 1. A similar analysis of the VIF values for the quadratic data-based model (${\eta }_{TOC}$) reveals that the VIF values of the terms A, B, C, AB, AC, and BC are 1, suggesting that these terms are orthogonal. Additionally, the VIF values of the terms A², B², and C² are 1.16, indicating that these terms are multicollinear because all the VIF values are greater than 1. Moreover, a higher value than 1 indicates a hard correlation factor. As a general rule of thumb, VIF values lower than 10 are acceptable [65].

The parity graphic (see Figure 3a,b) and the normal percentage probability residual versus the studentized residual plot (see Figure 3c,d) demonstrate the model’s adequacy to predict both responses (${\eta }_{COD}$ and ${\eta }_{TOC}$). Figure 3a,b reveal high-quality correlations between the experimental values of both responses (${\eta }_{COD}$ and ${\eta }_{TOC}$) and both modeled responses (${\eta }_{COD}$ and ${\eta }_{TOC}$). Figure 3c,d show normal distributions because the plotted points align closely to a straight line at a 45-degree angle. This suggests that the experimental responses follow a normal distribution. Additionally, the outlier values fall within the ranges ±1.05 and ±0.99 for ${\eta }_{COD}$ and ${\eta }_{TOC}$, respectively, indicating that the data-based models used to fit the responses were reasonably accurate, with minimal data register errors and high degrees of reproducibility.

3.3. ANOVA Test

Table 7. ANOVA test results for the data-based models (${\eta }_{COD}$ and ${\eta }_{TOC}$).

Source	Sum of Squares	Degrees of Freedom	Mean Squared	F-Value	p-Value	Remark
$\mathit{COD}\mathit{removal}\mathit{efficiency}({\eta }_{COD}$)
Model	78.15	8	98.39	53.28	<0.0001	Significant
A	216.94	1	216.94	117.48	<0.0001
B	35.36	1	35.36	19.15	0.0024
C	195.03	1	195.03	105.62	<0.0001
AB	186.92	1	186.92	101.23	<0.0001
AC	97.93	1	97.93	53.03	<0.0001
C2	29.20	1	29.20	15.81	0.0041
A2C	141.64	1	141.64	76.71	<0.0001
AB2	204.67	1	204.67	110.84	<0.0001
Residual	14.77	8	1.85
Lack of fit	13.10	6	2.18	2.60	0.3034	Not significant
Pure error	1.68	2	0.8385
Cor total	801.92	16
$\mathit{TOC}\mathit{removal}\mathit{efficiency}({\eta }_{TOC}$)
Model	1379.37	9	153.26	12.88	0.0014	Significant
A	22.65	1	22.65	1.90	0.2102
B	921.77	1	921.77	77.44	<0.0001
C	32.64	1	32.64	2.74	0.1417
AB	87.78	1	87.78	7.37	0.0300
AC	53.87	1	53.87	4.53	0.0709
BC	29.88	1	29.88	2.51	0.1571
A2	71.76	1	71.76	6.02	0.0439
B2	90.73	1	90.73	7.62	0.0281
C2	0.2739	1	0.2739	0.030	0.8837
Residual	83.32	7	11.90
Lack of fit	42.31	5	8.46	0.4127	0.8162	Not significant
Pure error	41.01	2	20.51
Cor total	1462.69	16

displays the results of the ANOVA test for the data-based models fitted. The test results indicate that the adjusted model for the COD removal efficiency is statistically suitable for modeling the electro-oxidation of MET within the studied operational parameter range. The model’s F-value of 54.38 for ${\eta }_{COD}$ suggests that the adjusted polynomial data-based model is significant because the F-value is higher than the p-value (0.0001). Additionally, the lack of fit is not significant for the pure error, as the F-value of 2.6 is higher than the p-value (0.3034). Furthermore, the terms A, B, C, AB, AC, C², A²C, and AB² are significant because their p-values (0.0001, 0.0024, 0.0001, 0.0001, 0.0001, 0.0041, 0.0001, and 0.0001) are less than 0.05. Similarly, the model’s F-value of 1379.37 for ${\eta }_{TOC}$ suggests that the adjusted polynomial data-based model is significant because the F-value is higher than the p-value (0.0014). Moreover, the lack of fit is not significant for the pure error, as the F-value of 42.31 is higher than the p-value (0.8162). Moreover, the terms B, AB, A², and B² are significant because their p-values (0.0001, 0.0300, 0.0439, and 0.0281) are less than 0.05.

3.4. Influences of the Operational Parameters

From the previous analysis, the models are summarized in Table 6. The negative signs of the β-values of the terms A, AB, C², and A²C display negative effects on ${\eta }_{COD}$ compared to the positive signs of the β-values of the terms B, C, AC, and AB². Similarly, the negative signs of the β-values of the terms C, AB, BC, and B² exhibit negative effects on ${\eta }_{TOC}$ compared to the positive signs of the β-values of the terms A, B, AC, A², and C² [66].

The perturbation graphics (Figure 4a,b) reveal that all the operating parameters (A, B, and C; i.e., the initial pH, current intensity, and volumetric flow rate, respectively) are important because of their distinguished slopes. However, the importances of the operating parameters for the response of the ${\eta }_{COD}$ follow the order of the initial pH (A), current intensity (B), and volumetric flow rate (C) because of their slopes. Additionally, the importances of the operating parameters for the response of the ${\eta }_{TOC}$ follow the order of the initial pH (A), volumetric flow rate (C), and current intensity (B). Additionally, the Spearman rank values are shown in Figure 4c. Figure 4c reveals that the current intensity (B) is the most significant variable for ${\eta }_{TOC}$ because the Spearman rank value is 0.773. Meanwhile, the volumetric flow rate (C) is the most significant variable for ${\eta }_{COD}$ because the Spearman rank value is 0.20. Also, pH₀ exerts a negative effect on ${\eta }_{COD}$ because of its negative Spearman rank value (−0.211), and Q displays a similar effect on ${\eta }_{TOC}$ because of its negative Spearman rank value (−0.125).

The Pareto test was performed utilizing Equation (18) to assess the impacts of the terms on the responses (${\eta }_{COD}$ and ${\eta }_{TOC}$).

$$P_i=\left({\displaystyle \frac{{\beta }_i}{{\displaystyle \sum {\beta }_i}}}\right)\times 100$$

(18)

Figure 5 shows the Pareto graphic analysis. This figure suggests that the interaction terms A²C and AB² have large effects (17.26 and 20.74%) on ${\eta }_{COD}$, respectively. Meanwhile, A, C, and AB have moderate effects (16.33, 15.49, and 12.74%) on ${\eta }_{COD}$, respectively. Also, the rest of the terms (B, AC, and C²) have the least effects (4.25, 9.23, and 3.96%) on ${\eta }_{COD}$, respectively. Similarly, the term B has a higher effect (33.69%) on ${\eta }_{TOC}$. Also, the terms AB, AC, A², and B² have moderate effects (13.57, 10.61, 10.33, and 11.64%) on ${\eta }_{TOC}$, respectively. In addition, the rest of the terms (A, C, BC, and C²) have the least effects (5.29, 6.35, 9.9, and 0.61%) on ${\eta }_{TOC}$.

3.5. Optimization of the Electro-Oxidation of MET

A maximum COD removal efficiency (${\eta }_{COD}$) of 60.81% and a TOC removal efficiency (${\eta }_{TOC}$) of 90.07% were achieved at pH₀ 5.0, an I value of 3.84 A, and a Q value of 0.8 L/min within 7.5 h of the total operating time. The overall desirability was 0.9502 (see Figure 6g), indicating that both objective functions ($\max \left({\eta }_{COD}\left(A,B,C\right)\right)$ and $\max \left({\eta }_{TOC}\left(A,B,C\right)\right)$) were fully met because the desirability attained is classified as fully acceptable [67]. Additionally, both objective functions (responses ${\eta }_{COD}$ and ${\eta }_{TOC}$) were simultaneously optimized. These functions were fitted through data-based modeling using Equation (9).

The 3D surface plots (Figure 6a–f) show the interaction effects among the three operating parameters (A, B, and C) studied herein. All the 3D surface plots form saddle areas because the contour plots are hyperboles, indicating that all the interactions between the chosen operating parameters are significant. Figure 6a–f show increases in ${\eta }_{COD}$ and ${\eta }_{TOC}$ when pH₀ (A) increases because there is a large amount of hydroxyl radicals (^●OH) produced on the Nb/BDD electrode’s surface. Also, Figure 6a,b,d reveal increases in ${\eta }_{COD}$ and ${\eta }_{TOC}$ when the current intensity (B) increases, indicating a large amount of ^●OH produced on the Nb/BDD anode’s surface and that the main reactions are taking place on the BDD’s surface. Similarly, Figure 6d–f display increases in ${\eta }_{COD}$ and ${\eta }_{TOC}$ when the volumetric flow rate (C) increases because the high mass transport of the pollutant from the bulk to the Nb/BDD anode electrode is achieved. Meanwhile, Figure 6c shows an increase in ${\eta }_{COD}$ when the volumetric flow rate (C) decreases because of the low mass transport of the pollutant from the bulk to the Nb/BDD anode’s surface. In addition, Figure 6a,b demonstrate that the interaction between the A and B operating parameters exerts negative effects on both responses (${\eta }_{COD}$ and ${\eta }_{TOC}$) because the production of ^●OH at low A and B values is insufficient to remove the MET. Figure 6c,d reveal that the interaction between the A and C operating parameters produces positive effects on both responses (${\eta }_{COD}$ and ${\eta }_{TOC}$) because the amount of ^●OH is sufficient to remove the MET, and the contact time of the MET with the ^●OH is enough to react effectively when the electrochemical treatment operates at low A and C values. As well, Figure 6e,f show that the interaction between the B and C operating parameters has negative effects on ${\eta }_{COD}$ and ${\eta }_{TOC}$ because of the low amount of ^●OH produced and the low mass transport of the MET from the bulk to the Nb/BDD anode’s surface.

Figure 6h depicts the overlaid graphic, shaped according to the constraint criteria described in Table 4 and both objective functions (${\eta }_{COD}$ and ${\eta }_{TOC}$). The black lines in the overlaid graphic are assembled based on the constraint criteria; the area between the constraints is in blue, and the region that is not convened based on the constraints is in gray. Also, the feasible region is enclosed by pH₀ (2–11), and I = (2–5 A) at Q = 0.8 L/min within 7.5 h of the total operating time.

3.6. Data-Based Model Validation

Three complementary trials were conducted using the optimal operating parameters to validate the data-based models (${\eta }_{COD}$ and ${\eta }_{TOC}$). The modeled and experimental data for both responses (${\eta }_{COD}$ and ${\eta }_{TOC}$) are recorded in

Table 8. Modeled and experimental responses for the optimal operating parameters.

Operating Parameter	Response	Values (%)		Error (%)
		Modeled	Experimental
pH0 5.0 I = 3.84 A Q = 0.8 L/min	${\eta }_{COD}$	60.81	61.11 ± 1.60	0.49
	${\eta }_{TOC}$	90.07	83.12 ± 1.56	8.37

. The results in Table 8 indicate the high degree of effectiveness of the multi-objective optimization process employed in this study because the deviation between the modeled and experimental data is less than 10% for both responses (0.49 and 8.37% for ${\eta }_{COD}$ and ${\eta }_{TOC}$, respectively). Hence, the maximum experimental COD and TOC removal efficiencies were 61.11 and 83.12%, respectively, when the electrochemical plant operates at an initial pH of 5, a current intensity of 3.84 A, and a volumetric flow rate of 0.8 L/min within 7.5 h of the total operating time. Additionally, the high mineralization percentages of the MET achieved indicate the excellent performance of the Nb/BDD electrodes in the degradation of organic pollutants, such as MET [68].

3.7. The Total Operating Cost of the Electro-Oxidation of MET

The total operating cost of the electrochemical treatment of MET was calculated based on the electricity consumed and the spent mass of the electrolyte support (NaSO₄), using Equations (4)–(8). Hence, the total energy consumed was 3.09 kWh, with a total operating cost of 0.19 USD/L when the electrochemical plant operates under the optimal operating conditions (pH₀ 5.0, I = 3.84 A, and Q = 0.8 L/min) within 7.5 h of the electrochemical treatment. It is worth noting that this work includes the cost of the electricity consumed by the pump flow and heat exchanger and the costs of the used mass of the electrolyte support, unlike other studies in the literature.

3.8. Kinetic Models

The electro-oxidation of MET conducted in this work is mainly assumed to be driven by ^●OH on the Nb/BDD anode’s surface [69]. The pseudo first-, pseudo second-, and pseudo first-order kinetic models used to fit the MET, COD, and TOC abatements, respectively, were set to fit the experimental data according to Equations (20) and (21) for the MET, COD, and TOC abatements:

$${\displaystyle \frac{d\left[MET\right]}{dt}}=-\underset{k_{app,MET}}{\underbrace{k{[}^{•}OH]}}\left[MET\right]=-k_{app}\left[MET\right]$$

(19)

$${\displaystyle \frac{d\left[COD\right]}{dt}}=-{\underset{k_{app,COD}}{\underbrace{k{[}^{•}OH]}}}^2{\left[COD\right]}^2=-k_{app}{\left[COD\right]}^2$$

(20)

$${\displaystyle \frac{d\left[TOC\right]}{dt}}=-\underset{k_{app,TOC}}{\underbrace{k{[}^{•}OH]}}\left[TOC\right]=-k_{app}\left[TOC\right]$$

(21)

Figure 7a illustrates the MET’s depletion over time because of the treatment, reaching a 95.19% degradation efficiency of the MET after 5 h of the treatment (see Figure S1 in the Supplementary Materials). This behavior suggests that the electro-oxidation of MET forms other simple organic compounds (e.g., carboxylic acid and aromatic molecules) because ^●OH attacks the chemical structure of the MET. Additionally, Figure 7b–d show that pseudo first-, pseudo second-, and pseudo first-order kinetic models effectively describe the decays of the MET, COD, and TOC, with determination coefficients (R²) of 0.9999, 0.9977, and 0.9945, respectively. These high R² values indicate good model fits because the R² values are close to 1 [61], and the low RMSEs (0.16, 1.49, and 1.00 for MET, COD, and TOC decays, respectively) further support this conclusion (in line with

Table 9. Estimated kinetic coefficients, goodness-of-fit values, and determination coefficients.

Variable	Order (n)	kapp	R2	RMSE
[MET]	1	0.6072 1/h	0.9999	0.16
[COD]	2	0.0019 L/mg h	0.9973	1.49
[TOC]	1	0.2380 1/h	0.9945	1.00

). Also, Figure 7b–d suggest the constant production of HO^● on the Nb/BDD anode’s surface. Furthermore, the high correlation between the experimental and modeled MET depletions suggests a large amount of ^●OH generated on the Nb/BDD anode’s surface (see Figure S1), as stated in [70].

The kinetic constants of the pseudo first-, pseudo second-, and pseudo first-order fitted models for the MET, COD, and TOC abatements are summarized in Table 9. Also, the pseudo first-order models for the MET and TOC abatements agree with references [35,36,71]. Additionally, the kinetic constants for the decays of the COD and TOC (k_{app, COD} and k_{app, TOC}, respectively) can be considered as global because the electro-oxidation of the byproducts was not discriminated against for their calculations.

To understand whether the electro-oxidation of MET is controlled by the mass transport or current, the limit current intensity (I_lim) can be estimated using Equations (22)–(24) [72]:

$$Ln\left({\displaystyle \frac{{\left[TOC\right]}_t}{{\left[TOC\right]}_0}}\right)=-\underset{slope}{\underbrace{{\displaystyle \frac{A_A}{V_{treated}}}{k}_m}}t$$

(22)

$$I_{\lim }=N_e{A}_{A}F{k}_m{\left[MET\right]}_0$$

(23)

$$C_{34}{H}_{56}{N}_2{O}_{12}+56H_{2}O\to 34C{O}_2+2N{H}_4^{+}+160H^{+}+\underset{N_e}{\underbrace{162}}{e}^{-}$$

(24)

where A_A (0.0032 m²) is the anode’s surface area, N_e is the number of electrons, V_treated (0.0025 m³) is the treated volume, F (96,487 C/mol) is the Faraday constant, k_m (m/s) is the mass transfer coefficient, I_lim (mA) is the current intensity, t (s) is the time, [MET]₀ (0.073 mol/m³) is the initial concentration of the MET, and [TOC]_t and [TOC]₀ are the final and initial TOC concentrations (mg/L), respectively.

After performing the linear regression analysis of the TOC data and using Equation (22), the mass transfer coefficient was calculated at 5.16 × 10⁻⁵ m/s. This value is similar to those calculated for the electro-oxidations of ciprofloxacin [39] and 2-chlorophenol [73] using the same flow-by reactor. The electro-oxidation of MET is primarily controlled by the mass transfer because the applied current intensity (I_app = 3.84 A) is greater than the limiting current intensity (I_lim = 0.189 A), which is in line with what was reported in reference [68].

3.9. Byproduct Identification and Reaction Pathway

During the electro-oxidation of MET with two Nb/BDD electrodes under the optimal operating conditions (pH₀ 5, I = 3.84 A, and Q = 0.8 L/min within a 7.5 h reaction time), an LC/MS analysis was conducted to identify the byproducts. The LC/MS analysis revealed 11 intermediates (refer to

Table 10. Byproducts identified after the electro-oxidation treatment of MET.

Stage	Retention Time (min)	[M + H]+ m/z Experimental	Proposed Structure	Difference (%)
MET	34.59	268		0.05
I	2.56	206		0.02
II	4.78	226		0.04
III	5.68	240		0.03
IV	6.45	274		0.02
V	8.56	282		0.02
VI	9.35	284		0.03
VII	16.21	282		0.02
VIII	17.25	238		0.02
IX	19.54	254		0.02
X	20.47	226		0.02
XI	11.68	300		0.04
XII	14.26	284		0.05
XIII	18.08	256		0.02
XIV	5.26	134		0.03
XV	8.46	116		0.02
XVI	10.92	118		0.02
XVII	12.23	128		0.01
XVIII	18.43	140		0.01

). The electro-degradation of MET was observed to occur in three phases. In the first phase (indicated by the green line), the branched aromatic ring with an ether functional group in the MET was oxidized by ^●OH (see Figure 8 and Table 10). The second phase (marked by the orange line) involved the attack of the ^●OH on the aromatic ring, leading to the complete degradation of the compound, including the breakage of the aromatic ring and the degradation of the branch with the amine group (see Figure 8). These stages illustrate how MET is progressively broken down into simpler compounds through advanced oxidation processes. This observation aligns with reference [74]. It is important to note that because of the low abundance and complexity of the sample, there are additional unidentified intermediates, resulting in peak overlap and a lack of reference information.

The low susceptibility of the MET to degradation in the part containing the alcohol group is because of the stability of the C-O bonds, the absence of conjugated systems that facilitate electron delocalization, and the general resistance of secondary alcohols to oxidation [74,75,76]. The amino group, with a pH below 9.7, becomes protonated ($N{H}_3^{+}$), causing the lone pair of electrons on the nitrogen atom to bond with the additional proton, making the nitrogen less available to react with electrophilic species; this reduces the availability of the lone pair of electrons, decreasing the capacity of the ^●OH to participate in chemical reactions [77].

The proposed reaction pathway for the electro-degradation of MET consists of three main stages of transformation, as shown in Figure 9. In the first stage, metoprolol decomposes into several intermediate products: one with a molecular weight of 226 m/z, resulting from the loss of the isopropylamine group; another intermediate with a weight of 240 m/z, formed by the oxidation of the secondary alcohol group to a ketone; and a third product with a weight of 282 m/z, indicating the formation of an oxidized dimer. In the second stage, these intermediates undergo further decomposition: The 226 m/z compound transforms to another with a weight of 238 m/z, suggesting the oxidative cleavage of the branch with the ether group and the aliphatic chain of the aromatic ring of the metoprolol; the 254 m/z intermediate transforms to a 256 m/z compound through the additional oxidation of the aromatic ring and degradation of the aliphatic chain, and the 282 m/z product decomposes into a compound with a weight of 274 m/z, indicating the breakage of the aromatic ring. Finally, in the final stage, the products from the second stage decompose into even simpler compounds: one product with a weight of 140 m/z, another with a weight of 118 m/z, and a compound with a weight of 116 m/z, reflecting the complete breakage of the aliphatic bonds and oxidation of the functional groups.

3.10. Comparison of Results with Those in the Literature

The results obtained in this study were compared with those found in the literature (refer to

Table 11. Comparison of various electro-oxidations of MET.

Process	Reaction Conditions	Electrodes		Vtreated (L)	Main Results				Ref.
		Ca.	An.		COD Removal (%)	TOC Removal (%)	MET Removal (%)	Cost (USD/L)
EO	Flow-by reactor, AA = 32 cm2, [MET]0 = 50 mg/L, pH0 5.0, I = 3.84 A, [Na2SO4] = 0.1 M, Q = 0.8 L/min, T = 25 °C, and t = 7.5 h	BDD	BDD	2.5	60.81	90.07	95.19	0.19	This work
ENO	Batch cell, AA = 4 cm2, [MET]0 = 2 mg/L, 5 V, [NaCl] = 5000 mg/L, and t = 1.33 h	Pt	Graphite–PVC	0.1	---	---	>95.00	---	[33]
US/UV-ENO	Batch cell, AA = 78 cm2, Ultrasound at 200 W, UV at 250 nm, I = 2.34 A, [Na2SO4] = 0.035 M, [MET]0 = 100 mg/L, and t = 10 h	SS	BDD	1.0	---	100.00	100.00	---	[34]
SPEFNO	Flow reactor, four cells, AA = 100 cm2, pH0 3.0, I = 3 A, [Fe2+] = 0.5 mM, [Na2SO4] = 0.1 M, [TOC]0 = 10 mg/L, T = 35 °C, Q = 4.17 L/min, and t = 6 h	ADE	BDD	10.0	---	97.00	---	---	[35]
ENO	Batch cell, AA = 78 cm2, I = 1.2 A, [Na2SO4] = 5000 mg/L, [MET]0 = 10 mg/L, and t = 10 h	SS	BDD	0.6	---	100.00	100.00	---	[36]

Ca.: cathode; An.: anode; O: optimized; NO: not optimized; V_treated: volume treated; Ref.: reference; E: electro-oxidation; U-UV-E: ultrasonic/UV-assisted electro-oxidation; SS: stainless steel; SPEF: solar photo-electro Fenton; ADE: air-diffusion electrode.

). This work is the only one reporting the associated operating cost, using two Nb/BDD electrodes, and carrying out the optimized electro-oxidation of MET. Although previous studies have reported that MET was degraded and mineralized to 100% [34,36], it is essential to consider that the treated volume in those studies was less (0.6 L and 1.0 L, respectively) compared to the volume used in this work (2.5 L). Additionally, the active areas reported in the literature [34,36] are 2.44 and 3.13 times larger (78 and 100 cm², respectively) than the area used in this work (32 cm²). Reference [34] and this work are unique studies that used a flow-by reactor for the electro-degradation of MET. However, the literature typically reports that four cells were used to achieve the 100% degradation and mineralization of MET. Also, reference [35] achieves a TOC removal efficiency (97%) higher than that in this study for a treated volume four times higher (10 L) than the volume used in this study (2.5 L). Nevertheless, this study uses five times the initial MET concentration (50 mg/L) than the initial MET concentration (10 mg/L) reported in the literature [35]. Based on the results presented in this study, the electrochemical method employed for the wastewater treatment effectively removes MET.

3.11. Toxicity Test

To complement the information about the hazardousness of the aqueous solution of MET at the beginning of and after the electro-oxidation treatment, a phytotoxicity test was conducted using mung bean seeds (Vigna radiata) according to Section 2.8.

Table 12. Variables assessed in phytotoxicity test.

Variable	Controls			Wastewater Containing MET
	Tap Water	Distilled Water	Electrolyte	Initial	Final
Germination (%)	100	93.33	93.33	73.33	93.33
Average shoot length (cm)	20.7	24.0	5.7	5.6	6.8
Average root length (cm)	5.1	11.2	10.8	10.4	10.3

indicates that the germination percentage of Vigna radiata irrigated with the treated effluent (93.33%) equals those of Vigna radiata irrigated with the distilled water and electrolyte controls. However, the germination percentage of Vigna radiata drops to 73.33% for the solution containing 50 mg/L of MET, which is lower than the germination percentage of Vigna radiata (93.33%) irrigated with the treated effluent. Additionally, the germination percentage of Vigna radiata irrigated with tap water was 100%, with a shorter average root length (5.1 cm) compared to those of Vigna radiata irrigated with the distilled water, electrolyte support, and wastewater at the beginning and the end of the electro-oxidation process. Furthermore, the average shoot lengths of Vigna radiata (24.0 and 20.7 cm for irrigation with distilled water and tap water, respectively) are longer than those of Vigna radiata irrigated with the electrolyte support and wastewater, at the beginning and the end of the electro-oxidation process, when irrigated with distilled water and tap water. Finally, the germination percentages of Vigna radiata irrigated with the electrolyte solution and treated solution of the MET are equal (93.33%), and the average shoot length of Vigna radiata treated with the solution of the MET (6.8 cm) is longer than those of Vigna radiata treated with the solution of the MET and without treatment (5.6 cm), which demonstrates the removal and degradation of the MET from the wastewater through the application of the electrochemical process using BDD electrodes as the cathode and anode, as assessed in this work.

Figure 10 shows the growth of Vigna radiata when irrigated with different water types. It demonstrates that treated effluent (see Figure 10e) is less toxic than the solution without the electrochemical treatment (see Figure 10d).

4. Conclusions

The electro-oxidation of MET was successfully driven by ^●OH in a flow-by reactor equipped with two Nb/BDD electrodes and running in the batch recirculation mode.

The electrochemical treatment employed in this study effectively removed the MET (95.19%) from the wastewater when the flow-by electrochemical reactor operated under the optimal operating conditions (pH₀ 5, I = 3.84 A, and Q = 0.8 L/min within a 7.5 h reaction time).

The maximum COD and TOC removals were 60.8 and 90.1%, respectively, with an associated operating cost of 0.19 USD/L.

The polynomial equations adjusted to the experimental data (COD and TOC removal efficiencies) as functions of pH₀, I, and Q (A, B, and C, respectively) are as follows:

$$\left(\begin{array}{l}{\eta }_{COD}=51.75-6.19A+1.61B+5.87C-4.83AB+3.5AC-1.5C^2-6.54A^{2}C+7.86A{B}^2\\ {\eta }_{TOC}=75.71+1.29A+8.22B-1.55C-3.31AB+2.59AC-1.93BC+2.52A^2-2.84B^2+0.15C^2\end{array}\right)$$

The electro-oxidation of MET, COD removal, and TOC removal follow pseudo first-order, pseudo second-order, and pseudo first-order kinetic models, respectively, when the flow-by electrochemical reactor operates under the optimal operating conditions.

The LC/MS analysis of the byproducts from the electro-degradation of the MET molecule revealed 11 intermediates. It was also confirmed that the process occurs in three phases, which is consistent with previous reports.

The phytotoxicity test indicates that the proposed electrochemical wastewater led to a diminution in the phytotoxicity of the effluent produced because of an increase in the percentage germination of Vigna radiata.