Extensive Study of Electrocoagulation-Based Adsorption Process of Real Groundwater Treatment: Isotherm Modeling, Adsorption Kinetics, and Thermodynamics

Abstract

In this study, several adsorption models were studied to predict the adsorption kinetics of turbidity on an electro-generated adsorbent throughout the electrocoagulation remediation of real groundwater. A new design for an electrocoagulation reactor consisting of a finned anode positioned concentrically in a tube-shaped cathode was fabricated, providing a significant active area compared to its immersed volume. This work completed a previous electrochemical study through a deep investigation of adsorption technology that proceeded throughout the electrocoagulation reactor under optimal operating conditions, namely a treatment period of 2–30 min, a 2.3-Ampere current, and a stirring speed of 50 rpm. The one-, two-, and three-parameter adsorption models investigated in this study possess significant regression coefficients: Henry (R² = 1.000), Langmuir (R² = 0.9991), Freundlich (R² = 0.9979), Temkin (R² = 0.9990), Kiselev (R² = 0.8029), Harkins–Jura (R² = 0.9943), Halsey (R² = 0.9979), Elovich (R² = 0.9997), Jovanovic (R² = 0.9998), Hill–de Boer (R² = 0.8346), Fowler–Guggenheim (R² = 0.8834), Dubinin–Radushkevich (R² = 0.9907), Sips (R² = 0.9834), Toth (R² = 0.9962), Jossens (R² = 0.9998), Redlich–Peterson (R² = 0.9991), Koble–Carrigan (R² = 0.9929), and Radke–Prausnitz (R² = 0.9965). The current behavior of the adsorption–electrocoagulation system follows pseudo-first-order kinetics (R² = 0.8824) and the Bangham and Burt mass transfer model (R² = 0.9735). The core findings proved that an adsorption-method-based electrochemical cell has significant outcomes, and all the adsorption models could be taken into consideration, along with other kinetic and thermodynamics investigations as well.

1. Introduction

The continuous development of industrial activities and population requirements put severe stress on sources of potable water [1,2,3]. As one of the primary sources of fresh water around the globe, groundwater varies in quantity depending on location [4,5,6]. Numerous sources of different contaminants caused by agricultural fertilizers and wastewater discharged from industrial activities into illegal dumping sites can pollute groundwater [7,8,9]. Total dissolved solids (TDS), turbidity, total suspended solids (TSS), total organic carbon (TOC), and heavy metals are some of these pollutants that are discharged and released into groundwater [10,11,12,13,14,15]. Therefore, polluted groundwater should be treated using efficient technologies to attain the requirements for acceptable fresh water [16,17]. Chemical, physical, and biological methods such as adsorption, precipitation, reverse osmosis, photocatalysis, ion exchange, electro-oxidation, the electro-Fenton process, electro-flotation, electrodialysis, and electrocoagulation are widely employed for that purpose [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28].

The electrocoagulation (EC) process is a non-conventional approach used to remove various contaminants, including organic and inorganic substances. It offers significant advantages over other treatment methods [2,26,27,28,29]. The EC method has a low electrolysis time, is easy to use and implement without the need for additional chemicals, is highly efficient, and is reasonably priced. The effective design and arrangement of electrodes in the EC cell, which affects this method’s effectiveness, determines whether EC can be used in systems that incorporate other technologies [19,30,31,32,33,34]. Redox reactions at electrodes are crucial to the EC process because they produce electro-coagulants in situ, which are less soluble and more available than chemical coagulants (Equations (1)–(5) for aluminum electrodes, for example), and iron and aluminum are the most frequently used metals for electrodes [26,35,36].

Al → Al⁺³ + 3e⁻

(1)

2H₂O → 4H⁺ + O₂ + 4e⁻

(2)

2H₂O + 2e⁻ → 2OH⁻ + H₂

(3)

3OH⁻ + Al³⁺ ⇔ Al(OH)₃

(4)

n [Al(OH)₃] → Al_n(OH)_3n

(5)

The goal of the EC reactor used in this investigation is to remove turbidity from brackish groundwater. The electrode arrangement in this reactor is novel; the electrodes are placed in a monopolar–parallel manner. The anode is positioned centrally within the tubular cathode electrode and has a finned shape.

This study aims to complete a previous study [35] through a deep investigation of the adsorption process, i.e., adsorption models and kinetics occurring in an electrocoagulation reactor under optimal conditions, namely a treatment period of 2–30 min, a current of 2.3 A, and a stirring speed of 50 rpm. In this investigation, real groundwater was drawn from a farm well in southern Iraq. To the best of our knowledge, there are no previous studies that have studied adsorption models and kinetics for the present configuration of electrodes via the electrocoagulation treatment of real groundwater.

2. Materials and Methods

2.1. Chemicals and Analytical Analysis

The actual groundwater was collected from a farm well in southern Iraq, and its primary characteristics are displayed in

Table 1. Properties of groundwater used in this study.

Parameters	TDS (mg/L)	TSS (mg/L)	Total Hardness (mg/L)	Turbidity (mg/L)	pH	Conductivity (µS/cm)
Values	1514	58	3053	49.34	8.1	2020

. The analytical measurement of its properties was performed based on standard procedures. The pH and conductivity values were measured with a pH meter (ATC company, Shijiazhuang, China) and a conductivity meter (CCP company, Shanghai, China), respectively. The turbidity of the samples was measured with a turbidity meter (Lovibond Inc., Dortmund, Germany). The brackish groundwater collected was treated with a batch electrocoagulation reactor, as depicted in Figure 1.

Using Equation (6), the percentage of turbidity removal efficiency (Y) was determined as follows:

$$Y\%=\frac{C_i-C_f}{C_i}\times 100$$

(6)

where the initial and final turbidity concentrations, expressed in mg/L, are C_i and C_f, respectively.

Furthermore, using 460 cm² of a defined active area, the theoretical consumption of electrodes (TCE) for the batch EC process was computed using the subsequent equation (Equation (7)) [26]:

$$TCE=\frac{ItM}{ZF}$$

(7)

where I is the applied current (Amperes), t is the electrolysis time (hours), Z is the number of electrons (three for Al), F is Faraday’s constant (96,485.34 Columbs/mol.), and M is the molecular weight of the electrode metal in grams per mol.

2.2. Adsorption Models

Adsorption models must be accurately understood and interpreted to improve adsorption mechanism paths overall and to successfully build any EC system. Linear regression analysis was widely employed to determine the most suitable adsorption models by evaluating the distribution of adsorbates, examining the adsorption system, and verifying the consistency of the theoretical assumptions underlying the adsorption isotherm model. Adsorption models, depicted in Figure 2 and categorized based on the number of their parameters [37,38,39,40,41,42,43,44,45,46,47], fall into various categories.

2.2.1. Henry Adsorption Model

In this foundational adsorption model, the amount of surface adsorbate is directly related to the partial pressure of the adsorptive gas. At relatively low concentrations, all adsorbate molecules remain separated from their nearest neighbors, as outlined in this model. The linear equation representing this model is presented as follows (Equation (8)):

$$q_e=K_{HE}{C}_e$$

(8)

where C_e and q_e are the amount of the adsorbate (mg/L) and the amount of the adsorption capacity (mg/g) at equilibrium status. Henry’s constant is designated as K_HE.

2.2.2. Langmuir Adsorption Model

Originally designed to explain gas–solid phase adsorption, Langmuir adsorption allows one to measure and compare the adsorptive capacity of various adsorbents. The Langmuir model, which maintains the matching rates of adsorption and desorption in balance, provides an explanation for the surface saturation. The process of adsorption is associated with the exposed part of the adsorbent surface, while the process of desorption is associated with the covered section of the adsorbent surface. This two-parameter model postulates that the adsorption sites exhibit uniform affinity for the contaminants. The linear representation of this model is depicted as follows (Equation (9)):

$$\frac{C_e}{q_e}=\frac{C_e}{q_{max}}+\frac{1}{K_e{q}_{max}}$$

(9)

The symbols K_e and q_max stand for adsorption energy in L/mg and the maximum capacity for adsorption (mg/g), respectively.

With the separation factor R_L, it would be possible to anticipate the affinity between the adsorbate and the adsorbent (Equation (10)):

$$R_L=\frac{1}{1+K_e{C}_o}$$

(10)

where the Langmuir model’s status—whether favorable (0 < R_L < 1) or unfavorable (R_L > 1)—is indicated by the factor’s value.

2.2.3. Freundlich Adsorption Model

The Freundlich model proves valuable for adsorption systems occurring on heterogeneous surfaces. This model provides an equation that captures both the surface heterogeneity and the exponential distribution of energies among all active sites. This two-parameter model describes the relationship, in an exponential manner, between the quantity adsorbed (q_e) and the oil content concentration (C_e) at equilibrium. The equilibrium state of adsorption on heterogeneous surfaces forms the foundation of this relationship. The linear expression of the model is illustrated by the following equation (Equation (11)):

$$\ln q_e=\ln K_F+\frac{1}{n}\ln C_e$$

(11)

In the Freundlich model, the constants representing adsorption intensity and relative adsorption capacity are designated by the symbols n and K_F, respectively.

The adsorption intensity (n) indicates the degree of nonlinearity between the concentration of the solution and the amount adsorbed, which has three values: n = 1, which indicates linear adsorption; n < 1, which implies chemical adsorption; and n > 1, which indicates physical adsorption. When the value of n is in the range of 1 to 10, the adsorption generally proceeds well.

2.2.4. Temkin Adsorption Model

The Temkin model accounts for the impact of indirect interactions between adsorbates on the adsorption process, proposing that the heat of adsorption for each molecule within the layer decreases proportionally with rising surface coverage. Application of the Temkin model is limited to an intermediate range of ion concentrations. The following provides the Temkin model’s linear form (Equation (12)):

$$q_e=\frac{RT}{b}\ln K_T+\frac{RT}{b}\ln C_e$$

(12)

where the heat of adsorption and the Temkin model constant are designated by b (J/mol) and K_T (L/mg). The absolute temperature (T) and the universal gas constant (R) are taken in kelvin and kJ mol⁻¹ K⁻¹, respectively.

2.2.5. Dubinin–Radushkevich Adsorption Model

This model is frequently employed as an empirical adsorption model to describe Gaussian energy distribution adsorption mechanisms on heterogeneous surfaces. It does not adhere to Henry's law at low pressures and exhibits unrealistic asymptotic behavior, rendering it suitable only for an intermediate range of adsorbate concentrations. A semiempirical equation models the pore-filling mechanism of adsorption. This equation, applicable to physical adsorption systems, assumes a multilayer structure involving van der Waals forces and provides a qualitative description of the adsorption of vapors and gases on microporous sorbents. According to this model, the adsorption process on heterogeneous surfaces depends on the porosity of electro-generated coagulants or a pore-filling mechanism. In cases of a multilayer nature, the D-R model can simulate the physical adsorption process influenced by van der Waals forces. Represented linearly by Equations (13)–(15), this model is categorized as temperature-dependent.

$$\ln q_e=\ln q_{max}+K_{DR} {\epsilon }^2$$

(13)

where

$$\epsilon =RT\ln \left(1+\frac{1}{C_e}\right)$$

(14)

$$E=\frac{1}{{\left(2K_{DR}\right)}^{1/2}}$$

(15)

in the sorption space, where E is the free energy required to transport a molecule to infinity and K_DR is the model’s constant.

2.2.6. Kiselev Adsorption Model

The Kiselev adsorption model has the following linearized expression (Equations (16) and (17)). It is applicable solely to surface coverage values (θ) greater than 0.68.

$$\frac{1}{C_e\left(1+\theta \right)}=\frac{K_K}{\theta }+K_K{K}_n$$

(16)

$$\theta =\frac{q_e}{q_{max}}$$

(17)

where K_n and K_K are the equilibrium constant of complex formation among the adsorbed molecules and the Kiselev equilibrium constant (L/mg), respectively.

2.2.7. Fowler–Guggenheim Adsorption Model

This model considers the lateral interactions among adsorbed molecules, where the heat of the adsorption process varies either positively or negatively depending on the loading. It is based on the linear relationship between adsorption heat and loading. When the interactions among adsorbed components are attractive, the heat increases as the interaction among adsorbed molecules intensifies with increasing loading (i.e., positive W). On the other hand, the heat of adsorption decreases with loading (that is, negative W) if the interaction between adsorbed molecules is repulsive. Nevertheless, since there is no longer any contact between the adsorbed molecules, this model collapses to the Langmuir model when W equals zero. Equation (18) provides this model’s linear form.

$$\ln \left[\frac{C_e\left(1-\theta \right)}{\theta }\right]=-\ln K_{FG}+\frac{2W\theta }{RT}$$

(18)

where K_FG is the F–G model parameter (L/mg) and W is the interaction energy among adsorbed molecules (kJ/mol).

2.2.8. Hill–Deboer Adsorption Model

This model considers both mobile adsorption and the lateral contact between the adsorption molecules, where the affinity varies depending on the type of force—either attractive or repulsive—between the adsorption molecules as determined by the parameter value of the model. As illustrated by Equation (19), this model can be linearly expressed:

$$\ln \left[\frac{C_e\left(1-\theta \right)}{\theta }\right]-\frac{\theta }{1-\theta }=-\ln K_1-\frac{K_2\theta }{RT}$$

(19)

where K₁ and K₂ represent the parameters of this model in L/mg and the energy constant of the adsorbed molecule interacting during the EC treatment of groundwater in kJ/mol, respectively.

2.2.9. Elovich Adsorption Model

The defining equation of this model is based on a kinetic concept suggesting an exponential increase in adsorption sites during the adsorption process, implying multilayer adsorption. Initially developed to elucidate the kinetics of gas chemisorption onto solids, this adsorption model can be linearly represented, as shown in Equation (20).

$$ln\frac{q_e}{C_e}=\ln \left(K_E q_{max}\right)-\frac{q_e}{q_{max}}$$

(20)

where the Elovich constant is represented by K_E (L/mg).

2.2.10. Jovanovic Adsorption Model

This model is founded on the assumptions of the Langmuir model and the possibility of mechanical interactions between the adsorbent and adsorbate. The linear expression of the Jovanovic model is presented in Equation (21):

$$\ln q_e=\ln q_{max}-K_J C_e$$

(21)

where K_J (L/g) is the Jovanovic parameter.

2.2.11. Harkins–Jura Adsorption Model

This adsorption model assumes that adsorbents with heterogeneous distributions of pores may exhibit multilayer adsorption on their surfaces. Equation (22) shows how this model is expressed:

$$\frac{1}{q_e^2}=\frac{B_H}{A_H}-\left(\frac{1}{A_H}\right) log{C}_e$$

(22)

where A_H and B_H are the model’s constants in g²/L and mg²/L, respectively.

2.2.12. Halsey Adsorption Model

Multilayer adsorption at a comparatively great distance from the surface is assessed using this approach. The following is a scenario of the adsorption model (Equation (23)):

$$ln q_e=\frac{1}{n_H}ln K_H-\frac{1}{n_H} ln C_e$$

(23)

where K_H (mg/L) and n_H are the Halsey model’s parameters.

2.2.13. Sips Adsorption Model

The Sips model is a combination of the Freundlich and Langmuir models. When applied to predict adsorption behavior on heterogeneous surfaces, it overcomes the limitation of high adsorbate concentrations often associated with the Freundlich model. As a result, this model reduces to the Freundlich model at low adsorbate concentrations and predicts the Langmuir model (monolayer adsorption) at high adsorbate concentrations. This model has concentration-, pH-, and temperature-dependent parameters. The model constants vary by nonlinear regression and linearization. This model’s linear form is given by Equation (24):

$$\frac{q_e}{q_{\max }}=\frac{K_S{C}_e^{ms}}{1+K_S{C}_e^{ms}}$$

(24)

where K_s (L/mg) and ms represent the equilibrium constant and the exponent of the Sips model, respectively.

2.2.14. Toth Adsorption Model

This model is another empirical modification to the Langmuir equation, aimed at reducing the disparity between experimental and equilibrium data predictions. This model fits best with the heterogeneous systems of adsorption that satisfy both the low and high-end limitations of the adsorbate amount. When n = 1, it simplifies to the Langmuir model equation; thus, the heterogeneity of the adsorption system is characterized by the parameter n, and the system is considered heterogeneous if it deviates significantly from unity. The adsorption model has been utilized to simulate many heterogeneous and multilayer adsorption systems. This model’s linear form is given by Equation (25):

$$\frac{q_e}{q_{\max }}=\frac{K_t{C}_e}{{\left[1+{\left(K_t{C}_e\right)}^n\right]}^{1/n}}$$

(25)

where K_t and n are the Toth model’s equilibrium parameters of surface affinity (mg/g) and surface heterogeneity (mg/g), respectively.

2.2.15. Jossens Adsorption Model

This model assumes a simple formula that represents the energy pattern of the adsorbent–adsorbate exchanges at the sites of adsorption. According to the Jossens model, the adsorbent’s surface is heterogeneous in terms of how it interacts with the adsorbate. This model’s linear expression is as follows (Equation (26)):

$$q_e=\frac{K_J{C}_e}{1+J{C}_e^n}$$

(26)

where K_J, J, and n are Jossens model constants.

2.2.16. Radke–Prausnitz Adsorption Model

At low adsorbate concentrations, the Radke–Prausnitz model is more desirable in most adsorption systems due to several significant features. This model lowers to a linear form at a low adsorbate amount and becomes the Langmuir isotherm at n = 0, while it turns into the Freundlich model at a high adsorbate concentration. Another essential characteristic of this model is its ability to give a satisfactory match over a wide range of adsorbate concentrations. The model is depicted by the following linear expression (Equation (27)):

$$q_e=\frac{ q_{max} A_{RP} C_e}{1+A_{RP} {C_e}^n}$$

(27)

where A_RP and n are the model constants.

2.2.17. Koble–Carrigan Adsorption Model

The Koble–Carrigan model combines the Freundlich and Langmuir models to represent equilibrium adsorption data. At high adsorbate concentrations, this model converges to the Freundlich model. It is valid only when the constant "n" is greater than or equal to one. However, despite having a high coefficient or low error value, the model fails to describe the experimental data when "n" is less than unity (1). Equation (28) below illustrates the linear form of this model.

$$q_e=\frac{ K_K {C_e}^n}{1+A_K {C_e}^n}$$

(28)

where K_K, A_K, and n are the model constants.

2.2.18. Redlich–Peterson Adsorption Model

This model is the integration of the Langmuir and Freundlich models. With the advantage of being close to the Henry zone at infinite dilution, the numerator originates from the Langmuir model. This empirical model consists of three parameters. By integrating elements from the Freundlich and Langmuir equations, the adsorption mechanism deviates from ideal monolayer adsorption to a mixture. Due to its flexibility, this model is applicable to both heterogeneous and homogeneous systems. Across a broad range of adsorbate concentrations, adsorption equilibrium is characterized by a combination of an exponential function in the denominator and a linear dependency on concentration in the numerator. The model is represented by the following linear expression (Equation (29)):

$$q_e=\frac{ K_{R-P} C_e}{1+A {C_e}^n}$$

(29)

where K_R-P is the model constant (L/g), A is the model parameter, and n is the model exponent that ranges between 0 and 1.

2.3. Thermodynamic Investigation

To estimate the behavior across the treatment system corresponding to these parameters, it is essential to investigate thermodynamic parameters such as the heat of adsorption (∆H), Gibbs free energy (∆G), and entropy (∆S). Enthalpy can be negative or positive, depending on whether the method of operation is exothermic or endothermic. The negative or positive value of Gibbs free energy indicates whether the adsorption process is spontaneous or not. Similarly, a negative or positive entropy value reflects the order or disorderliness at the liquid–solid interface in the adsorption–electrocoagulation system, respectively. Equations (30)–(32) explain the mathematical relations of thermodynamic parameters as follows:

$$K_C=\frac{q_e}{C_e}\hspace{1em}\hspace{1em}\hspace{1em}(K_c:\text{Equilibrium constant})$$

(30)

$$\Delta G^0=-R T\ln K_C$$

(31)

$$\ln K_C=\left(\frac{\Delta S^0}{R}\right)-\left(\frac{\Delta G^0}{RT}\right)$$

(32)

2.4. Kinetic Investigation

The widely studied kinetic models in this area include the pseudo-first-order and pseudo-second-order models [38]. The pseudo-first-order model describes the behavior of second-order pollutant consumption over time, but its mathematical relationship resembles that of a first-order reaction (Equation (33)). On the other hand, the pseudo-second-order model represents a higher than second-order disappearance of pollutants over time, but it tends to exhibit second-order kinetic behavior (Equation (34)).

$$\log (q_e-q_t)=\log q_e-\frac{K_{1}t}{2.303}$$

(33)

$$\frac{t}{q_t}=\frac{1}{K_2{q}_e^2}+\frac{t}{q_e}$$

(34)

2.5. Models of Mass Transfer via Adsorption

The adsorption mechanism is not a single phase, but rather a series of sequential events that include numerous critical steps. Thus, the process by which electro-generated adsorbents absorb contaminants from a solution can be divided into three phases: (1) the diffusion model of the boundary layer or external mass, (2) the diffusion model of the internal mass, and (3) the surface chemical reaction. Phases 1 and 2 take on the function of rate-limiting processes since phase 3 of the adsorption process is marked by quick response. Whether these rate-determining stages work alone or in concert, their contributions are essential to the reaction’s development.

2.5.1. Weber and Morris Model

This model is commonly used to illustrate the process of mass transfer from the outer surface of the adsorbent to its internal pores during adsorption. Its basis is Fick’s second law of mass transport. The intraparticle diffusion coefficient is derived from the linearized version of the Weber–Morris model equation (Equation (35))

$$q_t=K_{wmd} t^{0.5}+B_{th}$$

(35)

where K_wmd in mg/(g.min^0.5) is the specific coefficient of this model and B_th is the boundary layer thickness in mg/g.

In this model, intraparticle diffusion is the sole factor affecting the adsorption of contaminants onto electro-generated adsorbents when the plot of adsorption capacity versus the square root of time (t^0.5) is linear and passes through the origin. Otherwise, whether the visualization is nonlinear or linear, the mass transfer may be governed by two or more mechanisms as long as they do not pass through the origin. The three adsorption parts of this model show how a three-stage mechanism controlled the adsorption of pollutants onto adsorbents across the range of pollutant concentrations that were examined. During the early phase of adsorption, a linear relationship was observed for a certain period of time. This linear trend indicated that the diffusion of pollutants through the boundary layer at the surface of electro-generated adsorbents was the dominant mechanism at this stage. The second step, which was connected to the pollutant molecules’ pores diffusing onto adsorbents, demonstrated a gradual adsorption fit with all concentrations over a predetermined period. The intraparticle diffusion model is a rate-limiting phase at this point. At the end of the adsorption procedure, linear graphs were displayed for every concentration, indicating that the adsorption procedure had attained equilibrium and that all the adsorbents’ active sites had been completely saturated with pollutant molecules. If the plot of qt vs. t^0.5 does not pass via the origin, according to this interpretation, some of the intercept values indicate that intraparticle diffusion was not the only rate-controlling step.

2.5.2. Liquid-Film Diffusion Model

In this model, the surface of the adsorbent is covered in a liquid layer made up of molecules of adsorbate. This film of adsorbate is crucial to the adsorption process. Both film diffusion and pore diffusion mechanisms may have an impact on the mass transfer dynamics related to the adsorption of contaminants onto electro-generated adsorbents. Equation (36) denotes the mathematical form of this model as follows:

$$\ln (1-\frac{q_t}{q_e})=-K_{LF} t$$

(36)

where K_LF in min⁻¹ is the liquid-film parameter of this model.

2.5.3. Bangham and Burt Model

In certain adsorption systems, the rate-regulating step is solely controlled by pore diffusion. One way to determine whether pore diffusion controls the adsorption process is to apply this model. The model’s linearized expression is shown in Equation (37):

$$\log \log (\frac{C_i}{C_i-q_t\times TCE})=\log (\frac{K_b\times TCE}{2.203 V})+{\alpha }_b\times \log t$$

(37)

where V (L) is the solution work volume, TCE (g) is the weight of the electro-generated adsorbent, and K_b and ${\alpha }_b$ are the model’s constants.

3. Results and Discussion

3.1. Experimental Outcomes and Calculations

An experiment was conducted using the optimum operating variable values of 2.3 A and 50 rpm to conclude the examination of the innovative configuration of the EC reactor. Samples were collected at 2, 5, 10, 15, 20, 25, and 30 min.

3.2. Outcomes of Adsorption Models

The main findings of this study have detailed the behavior of the investigated adsorption models and their corresponding parameters, as illustrated in

Table 2. Core outcomes of adsorption models and their parameters.

Adsorption Model	Best-Fit Parameters	Determination Parameters
Henry adsorption model $q_e=K_{HE}{C}_e$	KHE = 1.282 L/g	R2 = 1.000 Adj-R2 = 1.000
Langmuir adsorption model $\frac{C_e}{q_e}=\frac{C_e}{q_{max}}+\frac{1}{K_e{q}_{max}}$	qmax = 28.986 mg/g Ke = 0.197 L/mg RL = 0.1 (favorable)	R2 = 0.9991 Adj-R2 = 0.9982
Freundlich adsorption model $ln{q}_e=ln{K}_F+\frac{1}{n}ln{C}_e$	KF = 157.779 mg/g n = 2.118 (it is a physical process)	R2 = 0.9979 Adj-R2 = 0.9958
Temkin adsorption model $q_e=\frac{RT}{b}ln{K}_T+\frac{RT}{b}ln{C}_e$	KT = 0.008 L/gm b = 129.758 kJ/mol	R2 = 0.9990 Adj-R2 = 0.9980
Kiselev adsorption model $\frac{1}{C_e\left(1+\theta \right)}=\frac{K_K}{\theta }+K_K{K}_n$	KK = 22.955 L/mg Kn = 1.136	R2 = 0.8029 Adj-R2 = 0.6058
Harkins–Jura adsorption model $\frac{1}{q_e^2}=\frac{B_H}{A_H}-\left(\frac{1}{A_H}\right) log{C}_e$	AH = 0.0084 g2/L BH = 0.738 mg/L	R2 = 0.9943 Adj-R2 = 0.9886
Halsey adsorption model $ln q_e=\frac{1}{n_H}ln K_H-\frac{1}{n_H} ln C_e$	KH = 45.126 g/L nH = 4.876	R2 = 0.9979 Adj-R2 = 0.9958
Elovich adsorption model $ln\frac{q_e}{C_e}=ln\left(K_E q_{max}\right)-\frac{q_e}{q_{max}}$	qmax = 13.755 mg/g KE = 0.009 L/mg	R2 = 0.9997 Adj-R2 = 0.9994
Jovanovic adsorption model $ln{q}_e=ln{q}_{max}-K_J C_e$	qmax = 68.910 mg/g KJ = 0.0299 L/g	R2 = 0.9998 Adj-R2 = 0.9996
Hill–Deboer adsorption model $ln\left[\frac{C_e\left(1-\theta \right)}{\theta }\right]-\frac{\theta }{1-\theta }=-ln{K}_1-\frac{K_2\theta }{RT}$	K1 = 2.26 × 10−15 L/mg (insignificant) K2 = 1049.3 kJ/mol	R2 = 0.8346 Adj-R2 = 0.6692
Fowler–Guggenheim adsorption model $ln\left[\frac{C_e\left(1-\theta \right)}{\theta }\right]=-ln{K}_{FG}+\frac{2W\theta }{RT}$	W = −35.337 kJ/mol KFG = 3.337 × 10−12 L/mg	R2 = 0.8834 Adj-R2 = 0.7668
Dubinin–Radushkevich adsorption model $ln{q}_e=ln{q}_{max}+K_{DR} {\epsilon }^2$	qmax = 3.559 mg/g KDR = 8.00 × 10−6 E = 0.25 kJ/mol	R2 = 0.9907 Adj-R2 = 0.9814
Sips adsorption model $\frac{q_e}{q_{max}}=\frac{K_s{C}_e^{ms}}{1+K_s{C}_e^{ms}}$	qmax = 43 mg/g KS = 0.03 (m3/kg)1/ms ms = 3.1	R2 = 0.9834 Adj-R2 = 0.9668
Toth adsorption model $q_e=\frac{q_{max}{K}_t{C}_e}{{\left[1+{\left(K_t{C}_e\right)}^n\right]}^{1/n}}$	qmax = 48.5 mg/g n = 1.1 (heterogeneous systems) KS = 0.35 mg/g	R2 = 0.9966 Adj-R2 = 0.9932
Jossens adsorption model $q_e=\frac{K_J{C}_e}{1+J{C}_e^n}$	KJ = 3.4 L/g J = 0.02 n = 1.04 (heterogeneous systems)	R2 = 0.9998 Adj-R2 = 0.9996
Redlich–Peterson adsorption model $q_e=\frac{ K_{R-P} C_e}{1+A {C_e}^n}$	KR-P = 4.15 L/g A = 0.051 n = 0.85 (heterogeneous systems)	R2 = 0.9991 Adj-R2 = 0.9982
Koble–Carrigan adsorption model $q_e=\frac{ K_K {C_e}^n}{1+A_K {C_e}^n}$	KK-C = 3.7 (L/g)−n AK-C = 0.05 n = 1.2 (heterogeneous systems)	R2 = 0.9929 Adj-R2 = 0.9858
Radke–Prausnitz adsorption model $q_e=\frac{ q_{max} A_{RP} C_e}{1+A_{RP} {C_e}^n}$	qmax = 50.3 mg/g ARP = 0.42 n = 1.01 (heterogeneous systems)	R2 = 0.9965 Adj-R2 = 0.9930

.

3.2.1. Henry Adsorption Model

In this model, the sole parameter predicted based on the mathematical form is Henry's constant, designated as K_HE, which equals 1.282 L/g. This value is associated with a highly significant determination coefficient (R²) and adjusted coefficient (adj-R²), indicating a substantial amount of variability.

3.2.2. Langmuir Adsorption Model

The main findings of this two-parameter model are based on the assumption that adsorption sites exhibit uniform affinity for pollutants, depending on the exposed and covered sections of the adsorbent surface. The maximum capacity of adsorption measured was 28.962 mg/g, the energy of adsorption (q_max) was 0.197 L/mg, and the separation factor (R_L) was 0.1, which is favorable and anticipated the affinity between the adsorbate and the adsorbent. The coefficients of determination R² and adj-R² of this model are 0.9991 and 0.9982, respectively, which suggest a better fit.

3.2.3. Freundlich Adsorption Model

As previously mentioned, the Freundlich model describes both the surface heterogeneity and the exponential distribution of energies among all active sites. Moreover, the results of this two-parameter model suggest that the adsorption process proceeded physically, as indicated by the estimated adsorption intensity (n) value of 2.118, reflecting the degree of nonlinearity between the solution's concentration and the adsorbed amount. Moreover, the relative adsorption capacity (K_F) obtained was 157.779 mg/g, with a higher validity of the predicted model due to the significant values of R² and adj-R², which were equal to 0.9979 and 0.9958, respectively.

3.2.4. Temkin Adsorption Model

Since the Temkin model concerns the impact of indirect interactions between molecules on the adsorption process, the heat of adsorption (b) measured was 129.758 kJ/mol, which may decrease linearly with increasing surface coverage. The predicted model has R² and adj-R² of 0.9990 and 0.9980, providing the Temkin model constant (K_T) of 0.008 L/mg.

3.2.5. Dubinin–Radushkevich Adsorption Model

Based on the previous prediction that physical adsorption proceeded throughout the electrocoagulation reactor, the adsorption process for the heterogeneous surfaces with a multilayer nature is dependent on the electro-generated coagulants’ porosity, or a pore-filling mechanism under the influence of van der Waals forces. The obtained values of the maximum adsorption capacity (q_max), the free energy (E) required to transport a molecule to infinity and the model’s constant (K_DR) were 3.559 mg/g, 0.25 kJ/mol, and 8.0 × 10⁻⁶, respectively. The coefficients of determination R² and adj-R² of this model are 0.9907 and 0.9814, respectively.

3.2.6. Kiselev Adsorption Model

The main outcomes showed that surface coverage values (θ) were greater than the reference value of 0.68, which indicates that the Kiselev model is applicable. The equilibrium constant for complex formation among the adsorbed molecules (K_n) was 1.136 L/mg, while the Kiselev equilibrium constant (K_K) was 22.955 L/mg. The corresponding determination coefficients (R² and adj-R²) were 0.8029 and 0.6058, respectively.

3.2.7. Fowler–Guggenheim Adsorption Model

The current model considers lateral interactions between adsorbed molecules. The loading-dependent heat of adsorption (W) was measured as −35.337 kJ/mol, indicating repulsive interactions among adsorbed components and a decrease in the heat of adsorption with loading. The F-G model parameters (K_FG), regression coefficient (R²), and adjusted regression coefficient (adj-R²) obtained were 3.337 × 10⁻¹² L/mg, 0.8834, and 0.7668, respectively.

3.2.8. Hill–Deboer Adsorption Model

This model accounts for the energy value of the adsorbed molecule interaction during the EC treatment of groundwater, which was −1049.3 kJ/mol. Since the value of the energy constant is negative, there is an attraction force between adsorbed species that decreases the affinity with loading. This finding aligns with the results obtained from the Fowler–Guggenheim adsorption model. The correlation coefficients of R² and adj-R² estimated are 0.8346 and 0.6692, respectively.

3.2.9. Elovich Adsorption Model

The Elovich model parameters q_max and K_E, along with the coefficients of correlation R² and adj-R², were estimated using Equation (20) to be 13.755 mg/g, 0.009 L/mg, 0.9997, and 0.9994, respectively. These results assume an exponential rise in the sites of adsorption with the adsorption process, suggesting multilayer adsorption.

3.2.10. Jovanovic Adsorption Model

The Jovanovic model predicts the potential for some mechanical interactions between the adsorbent and adsorbate. The agreement of adsorption outcomes with this model is highly significant, as the correlation coefficients R² and adj-R² are 0.9998 and 0.9996, respectively. According to this model, the maximum adsorption capacity predicted was 68.910 mg/g, with a model constant of 0.0299 L/g.

3.2.11. Harkins–Jura Adsorption Model

The H-J model parameters AH and BH, along with the coefficients of correlation R² and adj-R², were determined using Equation (20) to be 0.0084 g²/L, 0.738 mg/L, 0.9943, and 0.9886, respectively. According to highly significant regression coefficients, adsorbents with heterogeneous distributions of pores exhibit multilayer adsorption on their surfaces.

3.2.12. Halsey Adsorption Model

This model assesses multilayer adsorption at a comparatively great distance from the surface. The coefficients of correlation R² and adj-R², along with the model's constants (K_H, n_H), were determined to be 0.9979, 0.9958, 45.126 g/L, and 4.876, respectively.

3.2.13. Sips Adsorption Model

The core findings of the Sips model’s parameters of q_max, K_S, and ms could be used to predict adsorption action on heterogeneous surfaces. The obtained values of these parameters are 43.00 mg/g, 0.03 (m³/kg)^1/ms, and 3.1, respectively. The values of R² of 0.9834 and adj-R² of 0.9668 validate the predicted model. As mentioned earlier, the current model can be simplified to either the Freundlich model or the Langmuir model depending on the concentration of the adsorbate.

3.2.14. Toth Adsorption Model

Based on the obtained results represented by the value of n which equals 1.1, this model fits best with the heterogeneous systems of adsorption that satisfy both the low- and high-end limitations of the adsorbate amount. The values of the model’s parameters (q_max and K_t), as well as R² and adj-R² estimated, are 48.5 mg/g, 0.35 mg/g, 0.9966, and 0.9932, respectively.

3.2.15. Jossens Adsorption Model

The core results obtained for this model agree with those obtained using the Toth model, where the value of n equals 1.04, which explains how the adsorbent’s surface interacts with the adsorbate. The model parameters of K_J and J estimated were 3.4 L/g and 0.02, respectively, while the values of R² and adj-R² predicted are 0.9998 and 0.9996, respectively.

3.2.16. Radke–Prausnitz Adsorption Model

The core findings prove that this model fits best with the heterogeneous systems because the n-value is more than zero (n = 1.01) with a maximum adsorption capacity of 50.3 mg/g which gives a satisfactory match over a wide range of adsorbate concentrations. The model’s constant (A_RP) was predicted with a higher validity of R² of 0.9965 and adj-R² of 0.9930.

3.2.17. Koble–Carrigan Adsorption Model

Since the value of the n-indicator measured is more than one (n = 1.2), the current model is valid as mentioned; therefore, it is unable to describe the experimental data. The values of the model’s constants of K_K and A_K as well as the validity parameters (R² and adj-R²) obtained were 3.7 (L/g)-n, 0.05, 0.9929, and 9858, respectively.

3.2.18. Redlich–Peterson Adsorption Model

Given that the obtained n-indicator (n = 0.85) falls within an acceptable range, this model can be explored for use in an EC-based adsorption system to characterize adsorption equilibrium for both heterogeneous and homogeneous systems. The estimated values of the model constants (K_R-P and A) and the correlation coefficients (R² and adj-R²) are 4.15 L/g, 0.051, 0.9991, and 0.9982, respectively.

The results obtained indicate that the examination of one, two, and three parameters within the studied models yields high regression coefficients, suggesting that the parameters derived from these outcomes should be considered.

3.3. Thermodynamic Investigation Outcomes

To optimize the dosage conditions of the electro-generated adsorbent and preserve the initial turbidity concentration at 49.34 ppm, thermodynamic parameters were adjusted within the range of 303–317 K. The inclination and y-intercept of the graph of ln Kc against 1/T were used to obtain the enthalpy and entropy values (Figure 3). The obtained ΔH^o value (14.889 kJ/mol) suggests that the adsorption procedure is endothermic. As a result of the negative ΔG^o values (−2.022 to −3.064 kJ/mol), the adsorption is spontaneous. The adsorption of turbidity ions onto the electro-generated adsorbents appears to be more disordered near the liquid/solid interface, as indicated by the positive value of ΔS^o (24.238 J/mol K).

3.4. Kinetics Investigation Outcomes

Table 3. Core outcomes of adsorption kinetic models.

Adsorption Kinetic Model	Best-Fit Parameters
First-order model $log (q_e-q_t)=log q_e-\frac{K_{1}t}{2.303}$	k1 = 0.0919 (1/min) R2 = 0.8824
Second-order model $\frac{t}{q_t}=\frac{1}{K_2{q}_e^2}+\frac{t}{q_e}$	k2 = 0.0801 (g/mg.min) R2 = 0.8537

presents the main findings of the kinetic inquiry, demonstrating that the EC system adsorption is better explained by the first-order kinetic model than by the second-order kinetic model.

The correlation parameter of the first-order kinetic model exhibited superior performance compared to the pseudo-second-order model, as demonstrated in

Table 4. Core outcomes of mass transfer models.

Mass Transfer Model	Best-Fit Parameters
Weber and Morris model $q_t=K_{wmd} t^{0.5}+B_{th}$	Kwmd = 1.3387 (mg/(g.min0.5)) R2 = 0.9380
Liquid-film diffusion model $ln\left(1-\frac{q_t}{q_e}\right)=-K_{LF} t$	Klf = 0.1652 (1/min) R2 = 0.9556
Bangham and Burt model $log log \left(\frac{C_i}{C_i-q_t\times TCE}\right)=log \left(\frac{K_b\times TCE}{2.203 V}\right)+{\alpha }_b\times log t$	Klf = 0.5759 (L/mg) ${\alpha }_b=0.06$ R2 = 0.9735

. This agreement underscores the effectiveness of the pseudo-first-order model in describing the collected kinetic data, suggesting that pollutants are adsorbed by electro-generated adsorbents through a natural physical adsorption process.

3.5. Investigation Outcomes of Mass Transfer Models

The core outcomes of investigating the mass transfer models are listed in Table 4. For the Weber and Morris model, these results show that the first stage reached 4.47 min^0.5 with a linear trajectory, indicating the effect of the diffusion of the boundary layer as pollutants adhere to the adsorbents’ surfaces. The second section reached a value of 5 min^0.5, indicating the diffusion of pollutant molecules into the pores of the electro-generated adsorbents. The final stage continued until the end, confirming that the adsorption process had reached equilibrium with complete saturation of the adsorbent pores. With a significant regression indicator of 0.9556, the results of the liquid-film diffusion model demonstrate that film diffusion is not just a rate-limiting phase in the adsorption of pollutant molecules onto adsorbents. With a regression indicator of 0.9735, the Bangham and Burt model suggests that the primary controlling factor is the rate at which the pollutant molecules progress through the pores of the algae. Furthermore, either alone or in combination with both layer and pore diffusion mechanisms, boundary layer diffusion affects this diffusion process.

The current study demonstrated that the Bangham and Burt model provided a better fit compared to other models in explaining the mass transfer behavior of turbidity adsorption on the active sites of electro-generated adsorbents during the electro-coagulation treatment of real groundwater.

4. Conclusions

The current study involved a thorough investigation highlighting how the adsorption process progresses during the electrocoagulation treatment of real groundwater under the influence of significant operating conditions, namely treatment time, applied current, and stirring speed. One-, two-, and three-parameter adsorption models were investigated, and their parameters were obtained. The core findings proved that the Henry, Langmuir, Freundlich, Temkin, Kiselev, Harkins–Jura, Halsey, Elovich, Jovanovic, Hill–de Boer, Fowler–Guggenheim, Dubinin–Radushkevich, Sips, Toth, Jossens, Redlich–Peterson, Koble–Carrigan, and Radke–Prausnitz adsorption models should all be taken into consideration based on their highly significant regression coefficients obtained, which refer to the high validity of these adsorption models. Based on the thermodynamic study, the adsorption–electrocoagulation system is endothermic, spontaneous in nature, and more disordered near the solid/liquid interface. Furthermore, among the mass transfer models examined in this study, the Bangham and Burt model exhibited a better fit. The findings of the present study provide a comprehensive understanding of the performance of the new electrocoagulation reactor used for treating real groundwater through adsorption.