Next Article in Journal
Groundwater Depletion: Current Trends and Future Challenges to Mitigate the Phenomenon
Next Article in Special Issue
The Effect of Glycerol on Microbial Community in Industrial Wastewater Treatment Plant
Previous Article in Journal
Flood Simulation in the Complex River Basin Affected by Hydraulic Structures Using a Coupled Hydrological and Hydrodynamic Model
Previous Article in Special Issue
Environmental and Economic Evaluation of the Sequential Combination of Coagulation–Flocculation with Different Electro-Fenton-Based Configurations for the Treatment of Raw Textile Wastewater
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Comprehensive Cost–Benefit and Statistical Analysis of Isotherm and Kinetic Models for Heavy Metal Removal in Acidic Solutions Using Weakly Base Polymeric Chelating Resin as Adsorbent

1
Faculty of Public Health, Burapha University, Chonburi 20131, Thailand
2
Faculty of Engineering, Mahasarakham University, Khamriang, Mahasarakham 44150, Thailand
3
School of Energy and Environment, University of Phayao, Phayao 56000, Thailand
4
Faculty of Arts and Sciences, Chaiyaphum Rajabhat University, Chaiyaphum 36000, Thailand
5
MARE, Ctra. Torres-Reocín, B◦ La Barquera 13, 39311 Cartes, Spain
6
Faculty of Engineering, Ubon Ratchathani University, Ubonratchathani 34190, Thailand
7
Business School, Mahasarakham University, Khamriang, Mahasarakham 44150, Thailand
*
Author to whom correspondence should be addressed.
Submission received: 31 July 2024 / Revised: 15 August 2024 / Accepted: 23 August 2024 / Published: 25 August 2024

Abstract

:
This study investigates the removal of heavy metals, particularly copper and nickel, from acidic aqueous solutions using the weakly base polymeric chelating resin Dowex M-4195. The research conducts comprehensive cost–benefit and statistical analyses of various kinetic and isotherm adsorption models. The results show that the PSO and general order models provide high accuracy for the Cu2⁺ adsorption kinetics, while the Avrami fractional order model excels for Ni2⁺. In terms of the isotherm models, the Langmuir and Jovanovic models are highly accurate for both metals, with the Toth model being particularly effective for Ni2⁺ due to its ability to account for surface heterogeneity and multi-layer adsorption. This study also reveals that the kinetic adsorption process is more economically beneficial than the isotherm adsorption process, highlighting the importance of model selection for optimizing heavy metal removal. Incorporating circular economy principles, this research emphasizes the sustainability of using regenerable and reusable adsorbents like Dowex M-4195. The findings provide valuable insights for designing efficient adsorption systems, promoting environmental sustainability, and ensuring public health safety.

1. Introduction

Heavy metals such as copper (Cu) and nickel (Ni) are among the most persistent and toxic environmental contaminants, particularly in aquatic ecosystems [1,2]. These metals can accumulate in water bodies from a variety of sources, leading to significant ecological and human health risks. Human activities are the primary contributors to heavy metal pollution, encompassing industrial discharges, mining operations, agricultural practices, and urban runoff [3]. Industrial processes release substantial quantities of metals through effluents and emissions, while mining activities disturb the earth, exposing and releasing metals into surrounding water systems. Agricultural activities contribute to metal contamination through the use of fertilizers and pesticides, which contain trace amounts of these metals [4]. Urban runoff further exacerbates the issue by carrying metals from roads, buildings, and other infrastructure into water bodies [5]. In addition to human activities, natural processes such as volcanic eruptions, weathering of rocks, and soil leaching also contribute to the presence of heavy metals in the environment [6].
The presence of heavy metals in water poses severe risks to human health [7]. These metals are known to cause mutagenicity, endocrine disruption, carcinogenicity, genotoxicity, neurotoxicity, and skin and eye irritations [8]. Prolonged exposure to even low concentrations of heavy metals can lead to chronic health conditions and significant biological damage. As these metals do not degrade easily, they persist in the environment, accumulating in sediments and entering the food chain through aquatic organisms [9]. Fish, in particular, can bioaccumulate heavy metals, which then pose risks to humans when consumed [10].
To address the issue of heavy metal contamination in water, adsorption techniques using various adsorbents have been widely studied and employed [11,12]. Prominent among these are activated carbon, biochar, chitosan, zeolite, clay minerals, and resin [13,14,15]. Each of these materials exhibits unique properties that make it effective for this purpose. Activated carbon is widely recognized for its high surface area and porosity, which enable the adsorption of a broad spectrum of contaminants, including heavy metals. Biochar, a form of charcoal derived from biomass, offers a sustainable and cost-effective alternative, with its surface functionality and pore structure enhancing its metal-binding capabilities [16]. Chitosan, a biopolymer derived from chitin, possesses functional groups such as amino and hydroxyl groups that facilitate the chelation of metal ions. Zeolites, aluminosilicate minerals, are valued for their ion-exchange properties and high affinity for certain metals. Clay minerals, with their layered structures and large surface areas, also play a significant role in heavy metal adsorption through mechanisms such as ion exchange and surface complexation [17]. Resins, particularly ion-exchange resins, are synthetically engineered to selectively bind specific metal ions, offering high efficiency and regeneration potential [18]. In summary, the selection of an appropriate adsorbent for heavy metal removal depends on the specific application requirements, including the type of metal contaminants, the characteristics of the water matrix, and economic considerations. Each of these adsorbents offers distinct advantages that can be leveraged to optimize the removal process. One promising adsorbent is the weakly base polymeric chelating resin Dowex M-4195, which has demonstrated significant efficacy in removing heavy metals (Cu2+ and Ni2+) from aqueous solutions [19]. Dowex M-4195 is a macroporous resin with a bispicolamine functional group [20], which is capable of withstanding high temperatures and a wide pH range. Its structure allows for effective ion exchange, making it suitable for capturing and holding metal ions from contaminated water. In addition, Dowex M-4195 is an ion-exchange resin specifically designed for selective recovery of metals like copper and cobalt. It offers several advantages over its counterparts, such as higher selectivity and better performance in acidic conditions. Unlike Amberlite IR-120, Dowex M-4195 maintains its efficiency even in the presence of strong acids, making it a superior choice for applications involving harsh chemical environments [12]. Additionally, its higher affinity for specific metal ions compared to Chelex 100 allows for more efficient metal recovery processes [1].
Incorporating the principles of a circular economy is crucial for addressing heavy metal contamination sustainably. A circular economy aims to minimize waste and optimize resource use by closing product lifecycles through greater recycling and reuse [21]. In the context of heavy metal removal, the use of adsorbents like Dowex M-4195 resin aligns well with these principles. This resin can be regenerated and reused multiple times, reducing the need for constant production of new adsorbents and minimizing the environmental impact. Additionally, the metals captured by the resin can potentially be recovered and reused in industrial processes, thus closing the loop and contributing to resource efficiency [22]. The circular economy approach addresses environmental and health concerns while offering economic benefits. By recycling and reusing materials, industries can reduce the costs associated with raw material procurement and waste disposal. Furthermore, it promotes innovation in product design and process optimization, driving sustainable growth and creating new business opportunities. Implementing circular economy principles in water treatment and heavy metal removal processes enhances sustainability and resource efficiency, aligning with global efforts to transition toward a more sustainable and resilient economy [23,24].
Various research streams currently devote significant attention to the definitions and functions of various adsorbents, which are well known in the field and may not require a detailed explanation. To better align the introduction with the research, it would be more effective to briefly mention the adsorbents in relation to the current research and shift the focus toward the methodological approach, particularly the application of Akaike’s information criterion (AIC) in evaluating adsorption models. AIC is a valuable statistical tool that effectively balances the fit of a model with its complexity, making it particularly useful for comparing different adsorption models while avoiding overfitting [25]. However, some research explains why AIC was chosen over other model evaluation methods such as the Bayesian information criterion (BIC) or adjusted R-squared, highlighting AIC’s ability to optimize the trade-off between accuracy and model simplicity. Although the BIC similarly penalizes model complexity, it does so more stringently, which might not be ideal for the specific requirements of adsorption models [26]. Additionally, some research explores other methods like the BIC and cross-validation, and then clarifies why AIC is especially suitable for adsorption studies. The innovation of adsorption research lies in its application of AIC across a wider array of models and its integration with a cost–benefit analysis, offering a more thorough evaluation of models. This dual approach not only pinpoints the most statistically sound model but also considers practical applications, which is critical for enhancing the efficiency of adsorption processes in industrial settings.
Overall, this study significantly contributes to understanding the cost-effectiveness and efficiency of using polymeric chelating resins for heavy metal removal. By combining thorough statistical analysis with the principles of a circular economy, it offers a robust framework for improving water treatment processes, promoting environmental sustainability, and ensuring the health and safety of communities. The study’s methodology includes batch experiments to determine the adsorption capacity and kinetics of Dowex M-4195 for Cu2⁺ and Ni2⁺. These experiments involve varying the concentrations of heavy metals and analyzing the equilibrium adsorption using atomic absorption spectroscopy. Statistical analyses, including AIC and corrected AIC, are then applied to identify the best-fitting models. This study focuses on comprehensive cost–benefit and statistical analyses of isotherm and kinetic adsorption models for the removal of heavy metals, particularly Cu2⁺ and Ni2⁺, using Dowex M-4195 in acidic solutions. The primary objective is to evaluate and compare different adsorption models to identify the most effective ones based on Akaike’s information criterion and the corrected Akaike’s information criterion.

2. Materials and Methods

2.1. Polymeric Bispicolamine Chelating Resin Preparation

The raw precursor chelating resin Dowex-M4195 (Figure 1), featuring a bispicolamine functional group, was procured from Dow Chemical Company through Supelco. The Dowex-M4195 beads possess a macroporous structure with a size range between 3 × 106 and 8 × 106 angstroms. In its initial form, it is in an ionic state (Na+) and can withstand temperatures up to 60 °C within a pH range of 0–7. To convert the resin into its hydrogen (H+) form, a ratio of 1 g of chelating resin to 10 milliliters of 2 M acetic acid (AR grade, Ajax Finechem, 99.99%) was soaked together for over 24 h. This process has been detailed in prior studies [19]. Following this, the wet H+ Dowex-M4195 chelating resin was thoroughly rinsed with double-distilled water to remove excess acid until the pH approached neutrality. Subsequently, it was dried in an oven at 50 °C for a duration of 12 h. The resulting dried Dowex-M4195 resin in H+ form was carefully stored and allowed to cool to room temperature (approximately 25 °C) in a glass tube. This prepared resin was then used for further batch ion-exchange investigations (adsorption process).

2.2. Adsorption Studies

The adsorption studies via batch experiments for adsorption were operated at ambient temperature using a 250 mL closed paraffin Erlenmeyer flask. A 2000 mg L−1 stock solution of acidic synthetic copper (II) was arranged by dissolving 2.0 g of copper citrate (salts (Cu(NO3)2.3H2O)) and nickel (II) nitrate (salts (Ni(NO3)2)) in 1 L of 2 M HCl, with a pH of approximately 2. The calibration standards and test samples were analyzed using an atomic adsorption spectroscope (AA-7000, SHIMADZU).
For the kinetic experiments, an initial concentration of 150 mg L−1 was achieved by diluting the acidic synthetic copper (II) and nickel (II) stock solution. In each Erlenmeyer flask sample, 100 mL of 150 mg L−1 acidic synthetic copper (II) and nickel (II) solution was combined with 0.1 g of each chelating resin Dowex-M4195, and the mixture was stirred at 120 rpm in a water bath at 25 °C. Aliquots were withdrawn at intervals of 5, 10, 15, 30, 60, 120, 180, 240 and 270 min, and subsequently filtrated on Whatman filter 0.45 GF/C for analysis via atomic adsorption spectroscopy.
In terms of the equilibrium adsorption, the isotherms were conducted with 0.1 g of each chelating resin Dowex-M4195 in closed paraffin Erlenmeyer flask samples, exposing them to varying acidic synthetic copper (II) and nickel (II) concentrations ranging from 0 to 250 mg L−1. The samples were agitated in a shaking water bath at 120 rpm for 24 h to reach equilibrium. After filtration, the aliquot part was introduced into the atomic adsorption spectroscope for analysis of the removal of copper (II) and nickel (II).
The equilibrium adsorption and adsorption at time t capacity for each sample were calculated as follows:
q e = ( C 0   C e ) m V
q t = ( C 0 C e ) m V
where C0 (mg L−1) is the initial concentration of acidic synthetic copper (II) and nickel (II), Ce (mg L−1) is the concentration of acidic synthetic copper (II) and nickel (II) at equilibrium, V (L) is the volume of the solution used, and m (g) is the mass of chelating resin used.

2.3. Statical Analysis and Its Appropriate Selection

A prevailing trend in the literature underscores the common observation that augmenting the number of parameters within a model typically results in improved correlations. Nevertheless, this research has elected to employ Akaike’s information criterion (AIC) [27,28] for evaluating the effectiveness of the adsorption isotherm and kinetic models, following the guidelines proposed by Akaike in 1998. This approach was chosen despite the potential influence of the number of parameters, which we have deliberately decided to disregard. According to this methodology, the model with the lowest AIC value is considered the most appropriate. AIC provides a measure of the relative quality of statistical models for a given dataset. It is based on the concept of information entropy and offers a means to balance the complexity of the model against its goodness of fit. Specifically, AIC is calculated using the formula:
AIC = N × ln SSE N + 2 K
In our context, to conduct the AIC’s assessment effectively, it is crucial to determine the error sum of squares (SSE). The plea is a fundamental component in this process as it quantifies the deviation of the experimental data from the values predicted by the model. This is achieved by summing the squares of the differences between the observed (experimental) values and the corresponding predicted values, as mathematically represented by the equation:
SSE = q e q e , pre 2
Table 3 provides a detailed enumeration of the SSE values for the models under consideration. By integrating these SSE values into the AIC formula, we can objectively compare the relative performance of different adsorption isotherm and kinetic models, thereby identifying the model that best describes the observed data while accounting for the model complexity.
In this analysis, ‘K’ denotes the number of parameters in the model, and ‘N’ represents the number of data points in the dataset. A thorough examination of Table 3 reveals that all the kinetic and isotherm models’ methods consistently yields lower AIC values. This observation underscores the superior efficacy of the FL-PFO method in fitting the data under the given conditions. However, it is important to note that when the dataset comprises fewer than 40 data points, the standard AIC may not provide an accurate assessment due to the finite sample size. In such cases, it is recommended to utilize the corrected Akaike’s information criterion (AICcorrected), which adjusts for the small sample size and provides a more reliable evaluation of model performance. The AICcorrected is calculated using the following formula:
A I C c o r r e c t e d = AIC + 2 K ( K + 1 ) N - K - 1

2.4. Cost and Benefit Analysis

A cost and benefit analysis is a methodical approach employed by water or wastewater treatment plants to evaluate decision options in engineering process design [29,30,31,32]. A cost–benefit analysis was conducted to assess the removal of copper using chelating resin Dowex-M4195 as an adsorbent via the ion-exchanger method [33]. The standard Mishan cost and benefit analysis method [34] was employed for this evaluation, as show the following formula:
B C = t = 0 n B t t n C t > 1
The net social benefit (NSB) [35,36] values representative of the removal of heavy metals in acidic solutions signifies the augmented consumption value resulting from the research project on water and wastewater treatment. This assessment encompasses diverse costs and benefits of decision-making that would arise from the implementation. The NSB (the desired payment (dp) minus indemnified cost (ic)) was determined using the following formula:
N S B = d p - i c
The assessment of both heavy metal removal methods involved an examination of the intangible but significant indirect advantages for human health and the environment. The primary focus of the evaluation was on the responsibilities of water and wastewater treatment plants, and this was conveyed through the presentation of quantitative data delivered verbally.

3. Results and Discussion

3.1. Kinetic Adsorption

In this investigation, the examination of the adsorption kinetics pertaining to the removal of heavy metals of Cu2+ and Ni2+ solution onto polymeric chelating resin is of paramount importance for elucidating the underlying adsorption mechanisms and acquiring crucial design insights for practical applications. Various kinetic models, namely the pseudo-first-order (PFO), pseudo-second-order (PSO), general (rational) order, Elovich, diffusion chemisorption, and Avrami fractional order models, were employed in the analysis. To mitigate issues associated with data linearization, exclusively nonlinear regression methods were utilized throughout this study.
The determination of the most suitable kinetic model was conducted through a meticulous comparison of the individual and mean numerical values of three critical statistical measures: the adjusted coefficient of determination (R2adj), the reduced chi-square (Reduced χ2), and the error sum of squares (SSE). These metrics collectively offer a comprehensive assessment of the model’s performance and goodness of fit. Table 1 encapsulates the outcomes derived at three distinct temperatures for the six selected models, providing a comprehensive assessment of their efficacy in characterizing the adsorption kinetics of a heavy metal solution onto on weakly base polymeric chelating resin Dowex M-4195.
The analysis of various kinetic models for the adsorption of Cu2⁺ and Ni2⁺ onto weakly base polymeric chelating resin Dowex M-4195 provides significant insights into the adsorption mechanisms and the effectiveness of these models. The pseudo-first-order (PFO) model, with an adjusted R2 (R2_adj) of 0.9718 for Cu2⁺ and 0.9867 for Ni2⁺, shows reasonable accuracy in describing the adsorption kinetics. However, its relatively high reduced chi-square (reduced χ2) values of 4.1769 for Cu2⁺ and 1.6256 for Ni2⁺, along with its error sum of squares (SSE) values of 54.3001 and 21.1330, respectively, indicate that there are more accurate models available.
The pseudo-second-order (PSO) model performs exceptionally well, with R2_adj values of 0.9989 for Cu2⁺ and 0.9859 for Ni2⁺. This model’s low reduced χ2 values of 0.1577 for Cu2⁺ and 1.7245 for Ni2⁺, and SSE values of 2.0503 and 22.4187, respectively, suggest that it provides a very close fit to the experimental data, particularly for Cu2⁺. The high accuracy of the PSO model indicates that the adsorption process is likely governed by chemisorption, involving electron sharing or exchange between adsorbent and adsorbate.
The general (rational) order model also demonstrates high accuracy, with R2_adj values of 0.9989 for Cu2⁺ and 0.9902 for Ni2⁺. Its reduced χ2 values are 0.1606 for Cu2⁺ and 1.1994 for Ni2⁺, and its SSE values are 1.9267 and 14.3923, respectively. These results suggest that this model is also highly suitable for describing the adsorption kinetics, with a slight edge over the PSO model for Ni2⁺ due to its lower reduced χ2 and SSE values.
The Elovich model, characterized by high initial adsorption rates (αe) of 859.5738 mg g⁻1 min⁻1 for Cu2⁺ and 11.6502 mg g⁻1 min⁻1 for Ni2⁺, shows moderate performance with R2_adj values of 0.9700 for Cu2⁺ and 0.9409 for Ni2⁺. However, its high reduced χ2 values of 4.4300 for Cu2⁺ and 7.2262 for Ni2⁺, and SSE values of 57.5904 and 93.9404, respectively, indicate that it is less accurate than the other models considered.
The diffusion chemisorption model shows good performance, with R2_adj values of 0.9881 for Cu2⁺ and 0.9492 for Ni2⁺. Its reduced χ2 values are 1.7675 for Cu2⁺ and 6.2157 for Ni2⁺, and its SSE values are 22.9777 and 80.8049, respectively. While this model is better than the Elovich model, it still falls short compared to the PSO and general order models.
Finally, the Avrami fractional order model exhibits excellent performance for both Cu2⁺ and Ni2⁺, with R2_adj values of 0.9694 for Cu2⁺ and an impressive 0.9998 for Ni2⁺. The reduced χ2 values are 4.5250 for Cu2⁺ and 0.7914 for Ni2⁺, and the SSE values are 54.3001 and 9.4965, respectively. This model’s superior fit for Ni2⁺ suggests that it effectively captures the complexities of the adsorption process, potentially involving multiple adsorption mechanisms and site heterogeneity.
In conclusion, while the PSO and general order models are highly accurate for Cu2⁺ adsorption, the Avrami fractional order model is particularly effective for Ni2⁺, providing the best fit among the models analyzed. These findings highlight the importance of selecting appropriate kinetic models for accurately describing the adsorption processes of different heavy metals, which is crucial for optimizing the design and operation of adsorption systems in water treatment applications.
Figure 2 provides a visual representation of how the kinetic data align with the six kinetic models discussed, ultimately demonstrating the superior performance of the PSO and general order models. As a best practice, it is essential to conduct a thorough examination of predicted versus measured data, as well as residual plots (although not included here), to identify any discernible trends that may indicate the unsuitability of the chosen models. Such analyses contribute to the robustness of the conclusions drawn from the study.

3.2. Adsorption Isotherm

Sorption equilibrium is achieved when the interaction between the adsorbent and the adsorbate persists over an extended period, allowing a stable mass balance to be established between the concentration of the adsorbate in the bulk solution and the amount of adsorbate accumulated on the surface of the adsorbent. This equilibrium state indicates that the rates of adsorption and desorption are equal, leading to a steady-state condition where no further net adsorption occurs. Therefore, the mechanism of adsorption needs to be explored. Numerous empirical and semi-empirical isotherm models exist for predicting equilibrium conditions. In this research, an exploration of several models was conducted to quantify the adsorption characteristics of the system, as shown in Table 2, offering insights into their respective predictive capabilities.
In the pursuit of understanding the adsorption isotherm of solute uptake onto weakly base polymeric chelating resin Dowex M-4195, the process design hinges on the meticulous determination of the isotherm models. Traditionally, linear regression with the least squares method has been the go-to approach, despite its limitations. Linearizing nonlinear equations through this method not only alters the error structure but also contravenes the fundamental assumptions of linear regression. Hence, this research opted for nonlinear regression employing the sum of squared residuals as the error function. This enabled a more accurate assessment of various models to characterize the adsorption process isotherms and shed light on the underlying controlling mechanisms. Table 2 encapsulates the key parameters of six adsorption isotherm models that integrate essential statistical metrics obtained from nonlinear regression analyses. This detailed presentation facilitates a thorough comparative evaluation of the models, thereby guiding the selection of the most appropriate model for describing the adsorption phenomena under study.
The analysis of various isotherm models for the adsorption of Cu2⁺ and Ni2⁺ onto weakly base polymeric chelating resin Dowex M-4195 provides significant insights into the adsorption mechanisms and the effectiveness of these models.
The Freundlich isotherm model, characterized by its capacity to describe adsorption on heterogeneous surfaces, shows moderate accuracy with adjusted R2 (R2_adj) values of 0.8582 for Cu2⁺ and 0.9045 for Ni2⁺. However, the high reduced chi-square (reduced χ2) values of 46.5335 for Cu2⁺ and 17.1315 for Ni2⁺, along with high root mean square error (SSE) values of 418.8013 and 154.1836, respectively, indicate significant deviations from the experimental data, making it less suitable for precise modeling in this context.
The Langmuir isotherm model, which assumes monolayer adsorption on a homogeneous surface, performs exceptionally well. It has high R2_adj values of 0.9742 for Cu2⁺ and 0.9925 for Ni2⁺, indicating an excellent fit to the experimental data. The low reduced χ2 values of 8.4493 for Cu2⁺ and 1.3477 for Ni2⁺, along with relatively low SSE values of 76.0442 and 12.1293, further support the model’s accuracy. The Langmuir model’s maximum adsorption capacity (qm) values of 47.9184 mg g⁻1 for Cu2⁺ and 36.4825 mg g⁻1 for Ni2⁺ reflect its effectiveness in describing the adsorption process.
The Temkin isotherm model, which considers adsorbent–adsorbate interactions, shows good performance, with R2_adj values of 0.9375 for Cu2⁺ and 0.9648 for Ni2⁺. However, its reduced χ2 values of 20.5152 for Cu2⁺ and 6.3223 for Ni2⁺, and SSE values of 184.6371 and 56.9039, respectively, indicate that it is less accurate than the Langmuir model but still a viable option for modeling adsorption.
The Harkin–Jura isotherm model, which is often used for multi-layer adsorption on heterogeneous surfaces, shows the least accuracy among the models analyzed. It has low R2_adj values of 0.7823 for Cu2⁺ and 0.8332 for Ni2⁺, and extremely high reduced χ2 values of 71.4453 and 29.9164, and SSE values of 643.0076 and 269.2474, respectively. These results indicate significant deviations and a poor fit to the experimental data, making this model unsuitable for describing the adsorption processes of Cu2⁺ and Ni2⁺ on Dowex M-4195.
The Jovanovic isotherm model, which assumes a more realistic scenario of localized adsorption without interactions between adsorbed molecules, performs very well, with R2_adj values of 0.9775 for Cu2⁺ and 0.9929 for Ni2⁺. The low reduced χ2 values of 7.3995 for Cu2⁺ and 1.2638 for Ni2⁺, along with SSE values of 66.5658 and 11.3739, indicate a close fit to the experimental data, making it a strong contender alongside the Langmuir model.
The Toth isotherm model, which accounts for both heterogeneity and the possibility of multi-layer adsorption, shows excellent performance, with R2 values of 0.9802 for Cu2⁺ and 0.9953 for Ni2⁺. It has the lowest reduced χ2 values of 6.5108 for Cu2⁺ and 0.8381 for Ni2⁺, and SSE values of 52.0867 and 6.7047, respectively, suggesting that it provides the best fit among all the models analyzed. The Toth model’s maximum adsorption capacity (qm) values of 44.7519 mg g⁻1 for Cu2⁺ and 34.4145 mg g⁻1 for Ni2⁺ further validate its suitability.
In conclusion, while the Langmuir and Jovanovic models provide highly accurate descriptions of the adsorption processes for both Cu2⁺ and Ni2⁺, the Toth model stands out as the most effective, particularly for Ni2⁺, due to its ability to account for surface heterogeneity and multi-layer adsorption. The Freundlich and Harkin–Jura models are less accurate and less suitable for this system. These findings highlight the importance of selecting appropriate isotherm models to accurately describe adsorption mechanisms, which is crucial for optimizing the design and operation of adsorption systems in water treatment applications.
In Figure 3, a comprehensive display of the fits to various two-parameter and three-parameter adsorption isotherms is presented, meticulously produced to ensure optimal visual clarity. This curated selection allows for a detailed examination of the models’ performance in capturing the experimental data, providing insights into the suitability of each model for describing the adsorption process. By showcasing a range of models, from simpler two-parameter ones to more complex three-parameter ones, the figure offers a nuanced understanding of the underlying mechanisms governing adsorption behavior. This visual representation serves as a valuable tool for researchers and practitioners alike in assessing the appropriateness of different models for their specific applications, ultimately enhancing the understanding and optimization of adsorption processes.
It could be inferred that ion exchange was likely the primary mechanism for Cu2+ and Ni2+ adsorption, as illustrated in Figure 4a,b. This process can be represented by the following reaction: (RHn + Cu2+ ⇄ R-Cu2+ + nH+). This equation indicates that the resin (RH_n) interacts with the Cu2+ or Ni2+ ion in the solution, resulting in the formation of a resin–metal complex (R-Cu2+ or R-Ni2+) and the release of hydrogen ions (H+). However, the adsorption mechanism of Dowex M-4195 for the removal of Cu2⁺ and Ni2⁺ from water has been extensively detailed in a previous study [19].
This mechanism is supported by the observed adsorption behavior, where the replacement of hydrogen ions on the resin with copper ions from the solution plays a pivotal role. The efficiency of this ion-exchange process is critical for the effective removal of Cu2+ and Ni2+ from aqueous environments, highlighting the resin’s capability to selectively adsorb metal ions through this exchange mechanism.
In comparison, the proposed method using Dowex M-4195 represents a significant improvement in heavy metal removal, particularly in acidic environments. Traditional adsorbents like activated carbon and chitosan often underperform in low pH conditions due to the reduced efficiency and selectivity [1,48]. In contrast, Dowex M-4195 maintains high adsorption capacities for metals such as copper and nickel, even in challenging conditions, due to its bispicolamine functional group, which enhances its stability and selectivity [12].
Furthermore, Dowex M-4195 is advantageous because it can be regenerated and reused without significant efficiency loss, unlike activated carbon, which degrades with harsh regeneration processes [11]. Its alignment with circular economy principles supports sustainable resource management, making it a superior alternative for modern applications [5].

3.3. Statical Analysis and Its Appropriated Results

The analysis of Akaike’s information criterion (Table 3) for the kinetic adsorption and isotherm models of Cu2⁺ adsorption on Dowex M-4195 resin provides significant insights into the model performance. For the kinetic adsorption models, the PSO model emerges as the most suitable, with the lowest AIC (−25.85) and AICcorrected (−24.85), indicating its high accuracy and better fit compared to the other models. On the contrary, the Elovich model is the least suitable, having the highest AIC (24.18) and AICcorrected (25.18), suggesting poor performance in describing the adsorption kinetics of Cu2⁺.
In terms of the adsorption isotherm models, the Toth model stands out as the best fit, with the lowest AIC (23.11), although its AICcorrected (26.53) is slightly higher, indicating a slight correction for a small sample size. The Jovanovic model also shows competitive performance with a slightly higher AIC (23.81) but lower AICcorrected (25.31) than the Toth model, making it another viable option. Conversely, the Harkin–Jura model exhibits the highest AIC (48.75) and AICcorrected (50.25), making it the least accurate isotherm model for Cu2⁺ adsorption on the resin.
In conclusion, the PSO and Toth models are recommended for accurately predicting Cu2⁺ adsorption kinetics and isotherms, respectively, which confirms and consists of the results in Section 3.1 and Section 3.2. These models’ lower AIC values suggest a better fit and reliability, which are crucial for optimizing adsorption processes in various applications. Conversely, the Elovich and Harkin–Jura models are less suitable and may require refinement or replacement in future studies. This comparative analysis underscores the importance of selecting appropriate models to enhance the efficiency and accuracy of adsorption systems in environmental and industrial processes.
Figure 5 illustrates the corrected Akaike’s information criterion (AICcorrected) values for the Cu2+ adsorption isotherm and kinetic adsorption models, providing a rigorous evaluation of the model performance. For the adsorption models, the PSO kinetic and Toth isotherm models are identified as the most suitable models, as evidenced by the lowest AICcorrected values. This finding confirms the superior fit of the PSO and Toth models in describing the kinetic and isotherm adsorption behavior of Cu2+. This comprehensive analysis underscores the importance of selecting an appropriate model based on the corrected AIC values, ensuring the reliability and validity of the conclusions drawn from the adsorption study.
The analysis of Akaike’s information criterion, as shown in Table 4, for the kinetic adsorption and isotherm models of Ni2⁺ adsorption on Dowex M-4195 resin reveals that the Avrami fractional order model is the most suitable kinetic model, with the lowest AIC (−373.17) and AICcorrected (−370.99), indicating its superior accuracy and fit. Conversely, the Elovich model is the least suitable for describing the adsorption kinetics of Ni2⁺, as indicated by its highest AIC (31.52) and AICcorrected (32.52). Among the adsorption isotherm models, the Toth model demonstrates the best fit with the lowest AIC (0.55) and AICcorrected (3.97), while the Harkin–Jura model performs the worst, having the highest AIC (39.18) and AICcorrected (40.68). These findings underscore the importance of selecting the appropriate models for accurately predicting and optimizing Ni2⁺ adsorption processes. The Avrami fractional order and Toth models are recommended for their superior performance, while the Elovich and Harkin–Jura models may require refinement or replacement in future studies. This comparative analysis is crucial for enhancing the efficiency and reliability of adsorption systems in various environmental and industrial applications.
The comprehensive analysis provided in Figure 6 underscores the importance of using AICcorrected values in model selection, enhancing the reliability and validity of the adsorption study’s conclusions. This detailed visual representation serves as a valuable tool for researchers in evaluating and comparing the predictive capabilities of various adsorption isotherm and kinetic models.
Based on the provided bar chart comparing the average absolute relative deviation (AARD%) in Figure 7 for Cu2⁺ and Ni2⁺ adsorption using various kinetic models, we can draw several key conclusions. The pseudo-second-order (PSO) model shows the lowest AARD% for Cu2⁺ (0.77%), indicating it is highly accurate for modeling Cu2⁺ adsorption. However, for Ni2⁺, the PSO model has a higher AARD% (3.77%), indicating a lesser fit for Ni2⁺ adsorption. Similarly, the general order model also demonstrates low AARD% for Cu2⁺ (0.76%), making it another accurate model, whereas for Ni2⁺, it performs moderately, with an AARD% of 3.38%.
The Avrami fractional order model stands out for Ni2⁺, exhibiting an extremely low AARD% (essentially zero), making it the most accurate model for Ni2⁺ adsorption. Conversely, this model shows moderate performance for Cu2⁺ with an AARD% of 4.03%. The Elovich model, on the other hand, performs poorly for both ions, with the highest AARD% for Cu2⁺ (8.09%) and a high value for Ni2⁺ (4.14%). The diffusion chemisorption model indicates moderate accuracy for Cu2⁺ adsorption, with an AARD% of 2.58%, but poor performance for Ni2⁺ adsorption, with a high AARD% of 7.98%. Lastly, the pseudo-first-order (PFO) model shows similar moderate accuracy for both Cu2⁺ and Ni2⁺, with AARD% values of 4.03% and 3.98%, respectively.
Overall, the PSO and general order models are recommended for studies focused on Cu2⁺ adsorption, while the Avrami fractional order model is most suitable for Ni2⁺ adsorption that is related to the results of the error function, as illustrated in Section 3.1 and Section 3.2 and the AICcorrected results. Further research should be conducted to validate these findings with additional data and to investigate the reasons behind the high AARD% for the Elovich model, potentially exploring improvements or alternative models. These insights can guide the design of adsorption systems and the prediction of Cu2⁺ and Ni2⁺ behavior in various environmental and industrial processes.
The bar chart comparing the AARD% for Cu2⁺ and Ni2⁺ adsorption using various isotherm models, as shown in Figure 8, reveals that the Toth model is the most accurate for Cu2⁺ adsorption, with the lowest AARD% at 5.55%, while the Langmuir model is the best for Ni2⁺ adsorption, with an AARD% of 14.87%. Conversely, the Harkin–Jura model exhibits the highest AARD% for both Cu2⁺ (36.93%) and Ni2⁺ (54.1%), indicating it is the least accurate for both ions. Other models, such as the Freundlich, Temkin, and Jovanovic models, show varying degrees of accuracy, with moderate performance for both ions. Therefore, for the accurate prediction of Cu2⁺ and Ni2⁺ adsorption, the Toth and Langmuir models are recommended, respectively. Further research should aim to validate these findings with additional data and explore improvements for the less accurate models like the Harkin–Jura model. These insights are essential for designing effective adsorption systems and predicting the behavior of these ions in various environmental and industrial processes.

3.4. Social Cost–Benefit Analysis

Table 5 presents the cost–benefit analysis for the adsorption of Cu2⁺ and Ni2⁺ using weakly base polymeric chelating resin Dowex M-4195, which demonstrates a clear economic advantage in the kinetic adsorption process compared to the isotherm adsorption process. The study examined the quantities and costs of the chemicals used, including sodium hydroxide, sulfuric acid, and Dowex M-4195, with a total cost of THB 18.31 (USD 0.517) for both metals. The maximum adsorption capacities were 46.02 mg g⁻1 for Cu2⁺ and 36.03 mg g⁻1 for Ni2⁺ in the kinetic adsorption process, and 44.37 mg g⁻1 for Cu2⁺ and 32.86 mg g⁻1 for Ni2⁺ in the isotherm adsorption process. The benefit–cost (B/C) ratios suggest that the kinetic adsorption process is more costly to implement, with B/C ratios of 2.513 for Cu2⁺ and 1.967 for Ni2⁺, compared to the isotherm adsorption process, which has B/C ratios of 2.423 for Cu2⁺ and 1.795 for Ni2⁺. The net social benefit (NSB) for both processes is calculated to be THB 14.648.
In conclusion, the kinetic adsorption models, particularly the PSO and general order models, offer a superior fit and higher adsorption efficiency for the removal of Cu2⁺ and Ni2⁺. While the isotherm models, especially the Langmuir and Toth models, are slightly less efficient, they still provide significant economic benefits. These findings underscore the importance of selecting appropriate adsorption models to enhance both the efficiency and economic viability in heavy metal removal processes. By integrating these insights into a circular economy framework, the sustainability of the process can be further improved through the reuse and recycling of adsorbents and recovered metals, leading to more effective water treatment solutions and reduced environmental and health risks.

3.5. The Significance of the Research

The innovation and significance of this research introduce a groundbreaking approach to heavy metal removal from acidic solutions through the innovative use of the weakly base polymeric chelating resin Dowex M-4195. By integrating advanced adsorption models with comprehensive statistical analyses, this study offers a deeper understanding of the adsorption kinetics and isotherms specific to copper and nickel ions, setting a new standard for efficient and sustainable water treatment technologies.
The study’s significance lies in its potential to revolutionize heavy metal remediation practices, particularly in challenging acidic environments. Dowex M-4195’s superior performance provides a solid foundation for future research and practical applications, especially in industries dealing with metal contamination. The inclusion of circular economy principles further enhances the study’s impact, promoting sustainable resource management and environmental protection.
The evaluation of various adsorption isotherm and kinetic models using AIC reveals that the optimal model varies depending on the specific heavy metal ion and adsorbent, highlighting the complexity of adsorption processes. This suggests that a one-size-fits-all approach is inadequate for accurately modeling adsorption across different systems. Notably, this study identifies models like the Avrami fractional order model, which, despite being less common in experimental research, may offer superior fits for certain scenarios.
The practical significance of this evaluation process is its ability to identify the most accurate models for specific adsorption systems, thereby improving the precision of experimental designs and industrial applications in water treatment and pollutant removal. However, conducting exhaustive evaluations for each adsorbent–metal ion combination can be economically and labor-intensive. To address this, this study suggests developing guidelines based on effective models identified in comprehensive evaluations, streamlining the model selection process for future research.
While full-scale evaluations may not always be feasible, applying insights from comprehensive studies to similar systems can reduce the effort required and enhance the efficient use of adsorption models in both research and industry.

4. Conclusions

This study thoroughly investigates the removal of heavy metals, particularly Cu2⁺ and Ni2⁺, from acidic aqueous solutions using the weakly base polymeric chelating resin Dowex M-4195. The key findings reveal that the PSO and general order models are highly accurate in describing the adsorption kinetics of Cu2⁺, with the PSO model showing superior performance. For Ni2⁺ adsorption, the Avrami fractional order model provides the best fit among the kinetic models analyzed. In terms of the isotherm models, the Langmuir and Jovanovic models offer highly accurate descriptions for both Cu2⁺ and Ni2⁺, while the Toth model is most effective for Ni2⁺ due to its ability to account for surface heterogeneity and multi-layer adsorption. The Freundlich and Harkin–Jura models are less suitable for this system.
The cost–benefit analysis indicates that the kinetic adsorption process is more economically beneficial than the isotherm adsorption process, with benefit–cost (B/C) ratios of 2.513 for Cu2⁺ and 1.967 for Ni2⁺ in kinetic adsorption, compared to 2.423 for Cu2⁺ and 1.795 for Ni2⁺ in isotherm adsorption. The total cost of chemicals used for the adsorption process is THB 18.31 (USD 0.517). Integrating the principles of a circular economy enhances the sustainability of the adsorption process, as Dowex M-4195 can be regenerated and reused, and the metals captured by the resin can potentially be recovered and reused in industrial processes.
Selecting the appropriate kinetic and isotherm models is crucial for accurately predicting and optimizing the adsorption processes of heavy metals, which is essential for designing efficient and reliable adsorption systems in environmental and industrial applications. This study’s findings provide valuable insights into the adsorption mechanisms and effectiveness of Dowex M-4195, guiding future research and practical applications in water treatment and pollution control. By combining thorough statistical analysis with cost–benefit considerations and circular economy principles, this study offers a robust framework for improving water treatment processes, promoting environmental sustainability, and ensuring the health and safety of communities.

Author Contributions

Conceptualization, methodology, validation, formal analysis, investigation and writing, K.S.; conceptualization, methodology, validation, investigation, formal analysis, resources, writing and funding acquisition, writing—review and editing, writing—original draft, S.W.; resources and validation, T.K., S.I., N.S., S.H., W.D., P.N. and J.R.; funding acquisition, S.W. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by EN − MSU grant number 2566.

Data Availability Statement

Data are contained within the article.

Acknowledgments

This research project was financially supported by the Faculty of Engineering, Mahasarakham University, providing an opportunity to pursue this research work. The authors also would like to express their gratitude to the unit of excellence, School of Energy and Environment, University of Phayao (UOE 219/2567), for the laboratory, help and suggestions.

Conflicts of Interest

The authors declare that there are no conflicts of interest related to the publication of this manuscript. This research was conducted without any financial support from commercial or non-profit funding agencies, and therefore, no external funding influenced the results or conclusions of this work.

References

  1. Mitra, S.; Chakraborty, A.J.; Tareq, A.M.; Emran, T.B.; Nainu, F.; Khusro, A.; Idris, A.M.; Khandaker, M.U.; Osman, H.; Alhumaydhi, F.A.; et al. Impact of heavy metals on the environment and human health: Novel therapeutic insights to counter the toxicity. J. King Saud Univ.-Sci. 2022, 34, 101865. [Google Scholar] [CrossRef]
  2. Xiaomei, L.; Qitang, W.; Banks, M.K. Effect of simultaneous establishment of sedum alfredii and zea mays on heavy metal accumulation in plants. Int. J. Phytoremediat. 2005, 7, 43–53. [Google Scholar] [CrossRef] [PubMed]
  3. Das, S.; Sultana, K.W.; Ndhlala, A.R.; Mondal, M.; Chandra, I. Heavy metal pollution in the environment and its impact on health: Exploring green technology for remediation. Environ. Health Insights 2023, 17, 11786302231201259. [Google Scholar] [CrossRef] [PubMed]
  4. Rashid, A.; Schutte, B.J.; Ulery, A.; Deyholos, M.K.; Sanogo, S.; Lehnhoff, E.A.; Beck, L. Heavy metal contamination in agricultural soil: Environmental pollutants affecting crop health. Agronomy 2023, 13, 1521. [Google Scholar] [CrossRef]
  5. Müller, A.; Österlund, H.; Marsalek, J.; Viklander, M. The pollution conveyed by urban runoff: A review of sources. Sci. Total Environ. 2020, 709, 136125. [Google Scholar] [CrossRef]
  6. Briffa, J.; Sinagra, E.; Blundell, R. Heavy metal pollution in the environment and their toxicological effects on humans. Heliyon 2020, 6, e04691. [Google Scholar] [CrossRef]
  7. Karki, B.K.; Lamichhane, K.; Joshi, L.; Kc, R.; Sah, M.K.; Pathak, M.; Karki, K.R. Risk assessment of heavy metals in the major surface water system of Nepal with potential remediation technologies. Environ. Chall. 2024, 14, 100865. [Google Scholar] [CrossRef]
  8. Wu, Y.-S.; Osman, A.I.; Hosny, M.; Elgarahy, A.M.; Eltaweil, A.S.; Rooney, D.W.; Chen, Z.; Rahim, N.S.; Sekar, M.; Gopinath, S.C.B.; et al. The toxicity of mercury and its chemical compounds: Molecular mechanisms and environmental and human health implications: A comprehensive review. ACS Omega 2024, 9, 5100–5126. [Google Scholar] [CrossRef]
  9. Maddela, N.R.; García, L.C. Innovations in Biotechnology for a Sustainable Future; Springer: Berlin/Heidelberg, Germany, 2021. [Google Scholar]
  10. Noman, M.A.; Feng, W.; Zhu, G.; Hossain, M.B.; Chen, Y.; Zhang, H.; Sun, J. Bioaccumulation and potential human health risks of metals in commercially important fishes and shellfishes from Hangzhou Bay, China. Sci. Rep. 2022, 12, 4634. [Google Scholar] [CrossRef]
  11. Dong, Z.; Wang, Y.; Wen, D.; Peng, J.; Zhao, L.; Zhai, M. Recent progress in environmental applications of functional adsorbent prepared by radiation techniques: A review. J. Hazard. Mater. 2022, 424, 126887. [Google Scholar] [CrossRef]
  12. Wongphat, A.; Wongcharee, S.; Chaiduangsri, N.; Suwannahong, K.; Kreetachat, T.; Imman, S.; Suriyachai, N.; Hongthong, S.; Phadee, P.; Thanarat, P.; et al. Using excel solver’s parameter function in predicting and interpretation for kinetic adsorption model via batch sorption: Selection and statistical analysis for basic dye removal onto a novel magnetic nanosorbent. ChemEngineering 2024, 8, 58. [Google Scholar] [CrossRef]
  13. Biswas, S.; Fatema, J.; Debnath, T.; Rashid, T.U. Chitosan–clay composites for wastewater treatment: A state-of-the-art review. ACS ES&T Water 2021, 1, 1055–1085. [Google Scholar] [CrossRef]
  14. Arif, M.; Liu, G.; Yousaf, B.; Ahmed, R.; Irshad, S.; Ashraf, A.; Zia-ur-Rehman, M.; Rashid, M.S. Synthesis, characteristics and mechanistic insight into the clays and clay minerals-biochar surface interactions for contaminants removal—A review. J. Clean. Prod. 2021, 310, 127548. [Google Scholar] [CrossRef]
  15. Vishnu, D.; Dhandapani, B.; Kannappan Panchamoorthy, G.; Vo, D.-V.N.; Ramakrishnan, S.R. Comparison of surface-engineered superparamagnetic nanosorbents with low-cost adsorbents of cellulose, zeolites and biochar for the removal of organic and inorganic pollutants: A review. Environ. Chem. Lett. 2021, 19, 3181–3208. [Google Scholar] [CrossRef]
  16. Hongthong, S.; Sangsida, W.; Wongcharee, S.; Chanthakhot, A.; Aungthitipan, P.; Suwannahong, K.; Kreetachat, T.; Rioyo, J. Enhanced biochar production via co-pyrolysis of biomass residual with plastic waste after recycling process. Int. J. Chem. Eng. 2024, 2024, 1176275. [Google Scholar] [CrossRef]
  17. Worasith, N.; Goodman, B.A. Clay mineral products for improving environmental quality. Appl. Clay Sci. 2023, 242, 106980. [Google Scholar] [CrossRef]
  18. Zagorodni, A.A. Ion Exchange Materials: Properties and Applications; Elsevier: Amsterdam, The Netherlands, 2006. [Google Scholar]
  19. Suwannahong, K.; Sirilamduan, C.; Deepatana, A.; Kreetachat, T.; Wongcharee, S. Characterization and optimization of polymeric bispicolamine chelating resin: Performance evaluation via rsm using copper in acid liquors as a model substrate through ion exchange method. Molecules 2022, 27, 7210. [Google Scholar] [CrossRef] [PubMed]
  20. Megia-Fernandez, A.; Ortega-Muñoz, M.; Lopez-Jaramillo, J.; Hernandez-Mateo, F.; Santoyo-Gonzalez, F. Non-Magnetic and Magnetic Supported Copper(I) Chelating adsorbents as efficient heterogeneous catalysts and copper scavengers for click chemistry. Adv. Synth. Catal. 2010, 352, 3306–3320. [Google Scholar] [CrossRef]
  21. Tambovceva, T.T.; Melnyk, L.H.; Dehtyarova, I.B.; Nikolaev, S. Circular economy: Tendencies and development perspectives. Mech. Econ. Regul. 2021, 2, 33–42. [Google Scholar] [CrossRef]
  22. Hagelüken, C.; Goldmann, D. Recycling and circular economy—Towards a closed loop for metals in emerging clean technologies. Miner. Econ. 2022, 35, 539–562. [Google Scholar] [CrossRef]
  23. Obaideen, K.; Shehata, N.; Sayed, E.T.; Abdelkareem, M.A.; Mahmoud, M.S.; Olabi, A.G. The role of wastewater treatment in achieving sustainable development goals (SDGs) and sustainability guideline. Energy Nexus 2022, 7, 100112. [Google Scholar] [CrossRef]
  24. Suwannahong, K.; Wongcharee, S.; Rioyo, J.; Sirilamduan, C.; Kreetachart, T. Insight into molecular weight cut off characteristics and reduction of melanoidin using microporous and mesoporous adsorbent. Eng. Appl. Sci. Res. 2022, 49, 48–57. [Google Scholar] [CrossRef]
  25. Burnham, K.P.; Anderson, D.R. Multimodel inference: Understanding AIC and BIC in model selection. Sociol. Methods Res. 2004, 33, 261–304. [Google Scholar] [CrossRef]
  26. Schwarz, G. Estimating the dimension of a model. Ann. Stat. 1978, 6, 461–464. [Google Scholar] [CrossRef]
  27. Rajahmundry, G.K.; Garlapati, C.; Kumar, P.S.; Alwi, R.S.; Vo, D.-V.N. Statistical analysis of adsorption isotherm models and its appropriate selection. Chemosphere 2021, 276, 130176. [Google Scholar] [CrossRef]
  28. Sodeifian, G.; Garlapati, C.; Hazaveie, S.M.; Sodeifian, F. Solubility of 2,4,7-triamino-6-phenylpteridine (triamterene, diuretic drug) in supercritical carbon dioxide: Experimental data and modeling. J. Chem. Eng. Data 2020, 65, 4406–4416. [Google Scholar] [CrossRef]
  29. Aynur, D. Evaluation of chrome vi removal with biological adsorption in business organization liability: Social benefit-cost analysis. Acad. J. Sci. 2012, 1, 67–73. [Google Scholar]
  30. Galtry, J. Suckling and Silence in the USA: The Costs and Benefits of Breastfeeding. Fem. Econ. 1997, 3, 1–24. [Google Scholar] [CrossRef]
  31. Demir, A.; Arisoy, M. Biological and chemical removal of Cr(VI) from waste water: Cost and benefit analysis. J. Hazard. Mater. 2007, 147, 275–280. [Google Scholar] [CrossRef]
  32. Cui, X.; Li, H.; Yao, Z.; Shen, Y.; He, Z.; Yang, X.; Ng, H.Y.; Wang, C.-H. Removal of nitrate and phosphate by chitosan composited beads derived from crude oil refinery waste: Sorption and cost-benefit analysis. J. Clean. Prod. 2019, 207, 846–856. [Google Scholar] [CrossRef]
  33. Mishan, E.J.; Quah, E. Cost-Benefit Analysis; Taylor & Francis: Abingdon, UK, 2020. [Google Scholar]
  34. George William, K.; Serkan, E.; Atakan, Ö.; Özcan, H.K.; Serdar, A. Modelling of adsorption kinetic processes—Errors, theory and application. In Advanced Sorption Process Applications; Serpil, E., Ed.; IntechOpen: Rijeka, Croatia, 2018; Chapter 10. [Google Scholar]
  35. Florio, M. Applied Welfare Economics: Cost-Benefit Analysis of Projects and Policies; Taylor & Francis: Abingdon, UK, 2014. [Google Scholar]
  36. Campbell, H.F.; Brown, R.P.C. Cost-Benefit Analysis: Financial and Economic Appraisal Using Spreadsheets; Taylor & Francis: Abingdon, UK, 2015. [Google Scholar]
  37. Largergren, S. Zur theorie der sogenannten adsorption geloster stoffe. Kungliga svenska vetenskapsakademiens. Handlingar 1898, 24, 1–39. [Google Scholar]
  38. Ho, Y.S.; McKay, G. Sorption of dye from aqueous solution by peat. Chem. Eng. J. 1998, 70, 115–124. [Google Scholar] [CrossRef]
  39. Bergmann, C.P.; Machado, F.M. Carbon Nanomaterials as Adsorbents for Environmental and Biological Applications; Springer: Berlin/Heidelberg, Germany, 2015. [Google Scholar]
  40. Aharoni, C.; Tompkins, F.C. Kinetics of adsorption and desorption and the elovich equation. In Advances in Catalysis; Eley, D.D., Selwood, P.W., Weisz, P.B., Eds.; Academic Press: Cambridge, MA, USA, 1970; Volume 21, pp. 1–49. [Google Scholar] [CrossRef]
  41. Juang, R.-S.; Chen, M.-L. Application of the elovich equation to the kinetics of metal sorption with solvent-impregnated resins. Ind. Eng. Chem. Res. 1997, 36, 813–820. [Google Scholar] [CrossRef]
  42. Sutherland, C.; Venkobachar, C. A diffusion-chemisorption kinetic model for simulating biosorption using forest macro-fungus, fomes fasciatus. Int. Res. J. Plant Sci. 2010, 1, 107–117. [Google Scholar]
  43. Cardoso, N.F.; Lima, E.C.; Pinto, I.S.; Amavisca, C.V.; Royer, B.; Pinto, R.B.; Alencar, W.S.; Pereira, S.F. Application of cupuassu shell as biosorbent for the removal of textile dyes from aqueous solution. J. Environ. Manag. 2011, 92, 1237–1247. [Google Scholar] [CrossRef]
  44. Temkin, M.; Pyzhev, V. Kinetics of ammonia synthesis on promoted iron catalysts. Acta Physiochim. URSS 1940, 12, 217–222. [Google Scholar]
  45. Harkins, W.D.; Jura, G. The decrease of free surface energy as a basis for the development of equations for adsorption isotherms; and the existence of two condensed phases in films on solid. J. Chem. Phys. 1944, 12, 112. [Google Scholar] [CrossRef]
  46. Jovanović, D. Physical adsorption of gases: I: Isotherms for monolayer and multilayer adsorption. Kolloid-Z. Und Z. Für Polym. 1969, 235, 1203–1213. [Google Scholar] [CrossRef]
  47. Tóth, J. A uniform interpretation of gas/solid adsorption. J. Colloid Interface Sci. 1981, 79, 85–95. [Google Scholar] [CrossRef]
  48. Rashid, T.U.; Kabir, S.M.F.; Biswas, M.C.; Bhuiyan, M.A.R. Sustainable wastewater treatment via dye–surfactant interaction: A critical review. Ind. Eng. Chem. Res. 2020, 59, 9719–9745. [Google Scholar] [CrossRef]
Figure 1. Polymeric bispicolamine chelating resin: (a) chelating resin Dowex M-4195 H+ form, (b) Cu2+ loaded onto chelating resin Dowex M-4195, (c) Ni2+ loaded onto chelating resin Dowex M-4195 and (d) structure of bis-(picolyl)amine (BPA), Dowex-M4195.
Figure 1. Polymeric bispicolamine chelating resin: (a) chelating resin Dowex M-4195 H+ form, (b) Cu2+ loaded onto chelating resin Dowex M-4195, (c) Ni2+ loaded onto chelating resin Dowex M-4195 and (d) structure of bis-(picolyl)amine (BPA), Dowex-M4195.
Water 16 02384 g001
Figure 2. Kinetics plots of heavy metal onto weakly base polymeric chelating resin Dowex M-4195: (a) Cu2+ and (b) Ni2+.
Figure 2. Kinetics plots of heavy metal onto weakly base polymeric chelating resin Dowex M-4195: (a) Cu2+ and (b) Ni2+.
Water 16 02384 g002
Figure 3. Isotherm plots of heavy metal adsorption on weakly base polymeric chelating resin Dowex M-4195: (a) Cu2+ and (b) Ni2+.
Figure 3. Isotherm plots of heavy metal adsorption on weakly base polymeric chelating resin Dowex M-4195: (a) Cu2+ and (b) Ni2+.
Water 16 02384 g003
Figure 4. Possible adsorption mechanism for copper and nickel adsorption onto chelating resin Dowex M-4195: (a) Cu2+ and (b) Ni2+.
Figure 4. Possible adsorption mechanism for copper and nickel adsorption onto chelating resin Dowex M-4195: (a) Cu2+ and (b) Ni2+.
Water 16 02384 g004
Figure 5. AICcorrected Cu2+ for the adsorption isotherm and kinetic adsorption models.
Figure 5. AICcorrected Cu2+ for the adsorption isotherm and kinetic adsorption models.
Water 16 02384 g005
Figure 6. AICcorrected Ni2+ for adsorption isotherm and kinetic adsorption models.
Figure 6. AICcorrected Ni2+ for adsorption isotherm and kinetic adsorption models.
Water 16 02384 g006
Figure 7. Overall AARD% of kinetic adsorption models.
Figure 7. Overall AARD% of kinetic adsorption models.
Water 16 02384 g007
Figure 8. Overall AARD% of adsorption isotherm models.
Figure 8. Overall AARD% of adsorption isotherm models.
Water 16 02384 g008
Table 1. Kinetic modeling results of Cu2+ and Ni2+ adsorption on weakly base polymeric chelating resin Dowex M-4195.
Table 1. Kinetic modeling results of Cu2+ and Ni2+ adsorption on weakly base polymeric chelating resin Dowex M-4195.
ModelParameterCu2+Ni2+
PFO [37]
q t = q e 1 - e x p ( - k 1 t ) qe (mg g−1)44.563835.7999
k1 (min−1)0.14030.0557
R2adj0.97180.9867
Reduced χ24.17691.6256
SSE54.300121.1330
PSO [38]
q t = k 2 q e 2 t 1 + q e k 2 t qe (mg g−1)47.115939.3801
k2 (g mg−1 min−1)0.00530.0020
R2adj0.99890.9859
Reduced χ20.15771.7245
SSE2.050322.4187
General (rational) order [39]
q t = q e - q e t k r q e n 1 n 1 + 1 1 / ( n 1 ) qe (mg g−1)47.430436.6441
kr [h−1 (g mg−1)n−1]0.00390.0188
n2.08881.3477
R2adj0.99890.9902
Reduced χ20.16061.1994
SSE1.926714.3923
Elovich [40,41]
q t = 1 β e l n ( 1 + α e β e t ) αe (mg g−1 min−1)859.573811.6502
βe (g mg−1)0.22020.1528
R2adj0.97000.9409
Reduced χ24.43007.2262
SSE57.590493.9404
Diffusion chemisorption [42]
q t = q e k D C t 1 / 2 k D C t 1 / 2 + q e qe (mg g−1)53.220652.0400
kDC (mg g−1 min−0.5)29.58359.9001
R2adj0.98810.9492
Reduced χ21.76756.2157
SSE22.977780.8049
Avrami fractional order [43]
q t = q e 1 exp ( ( k a v t ) ) n a v qe (mg g−1)44.563435.9428
kav (min−1)0.11120.5432
nav1.26210.0986
R2adj0.96940.9998
Reduced χ24.52500.7914
SSE54.30019.4965
Note: qex = 36.03 mg g−1(Ni2+) and 46.02 mg g−1 (Cu2+).
Table 2. Isotherm modeling results of Cu2+ and Ni2+ adsorption on weakly base polymeric chelating resin Dowex M-4195.
Table 2. Isotherm modeling results of Cu2+ and Ni2+ adsorption on weakly base polymeric chelating resin Dowex M-4195.
Model ParameterCu2+Ni2+
Freundlich
q e = k f C e   1 / n f kf (mg g−1)(L g−1)n17.059310.8396
nf3.79653.5675
1/nf0.26340.2803
R2adj0.85820.9045
Reduced χ246.533517.1315
SSE418.8013154.1836
Langmuir
q e = q m k l C e 1 + k l C e
R l = 1 1 + k l C o
qm (mg g−1)47.918436.4825
kl (L MB−1 mg−1)0.45560.2233
Rl0.02150.0429
R2adj0.97420.9925
Reduced χ28.44931.3477
SSE76.044212.1293
Temkin [44]
q e = b t | ln k t C e | bt (J mol−1)0.78156.4899
kt (L mol−1)2.23723.3449
R2adj0.93750.9648
Reduced χ220.51526.3223
SSE184.637156.9039
Harkin–Jura [45]
q e = a H b H - l o g C e 1 / 2 aH110.403179.5571
bH2.89172.9862
R2adj0.78230.8332
Reduced χ271.445329.9164
SSE643.0076269.2474
Jovanovic [46]
q e = q m 1 - e x p ( k j C e ) qm (mg g−1)44.089633.1401
kj0.37870.1774
R2adj0.97750.9929
Reduced χ27.39951.2638
SSE66.565811.3739
Toth [47]
q e = q m k t h C e 1 + ( k t h C e ) n t h 1 / n t h qm (mg g−1)44.751934.4145
kth0.33790.1742
nth1.73651.42925
R20.98020.9953
Reduced χ26.51080.8381
SSE52.08676.7047
Note: qex = 32.86 mg g−1 (Ni2+) and 44.37 mg g−1 (Cu2+).
Table 3. Akaike’s information criterion for six kinetic adsorption and isotherm models of Cu2+ adsorption on weakly base polymeric chelating resin Dowex M-4195.
Table 3. Akaike’s information criterion for six kinetic adsorption and isotherm models of Cu2+ adsorption on weakly base polymeric chelating resin Dowex M-4195.
Models NKSSEAICAICcorrected
Kinetic adsorption models
PFO15254.3023.3024.30
PSO1522.05−25.85−24.85
General (rational) order1531.93−24.76−22.58
Elovich15257.5924.1825.18
Avrami fractional order15354.3025.3027.48
Diffusion chemisorption15222.9810.4011.40
Adsorption isotherm models
Freundlich112418.8044.0345.53
Langmuir11276.0425.2726.77
Temkin112184.6435.0336.53
Harkin–Jara112643.0148.7550.25
Jovanovic11266.6023.8125.31
Toth11352.0923.1126.53
Table 4. Akaike’s information criterion for six kinetic adsorption and isotherm models of Ni2+ adsorption on weakly base polymeric chelating resin Dowex M-4195.
Table 4. Akaike’s information criterion for six kinetic adsorption and isotherm models of Ni2+ adsorption on weakly base polymeric chelating resin Dowex M-4195.
Models NKSSEAICAICcorrected
Kinetic adsorption models
PFO15221.139.1410.14
PSO15222.4210.0211.03
General (rational) order15314.395.387.56
Elovich15293.9431.5232.52
Avrami fractional order1531.57761 × 10−10−373.17−370.99
Diffusion chemisorption15280.8129.2630.26
Adsorption isotherm models
Freundlich112154.1833.0434.54
Langmuir11212.1355.086.58
Temkin11256.9022.0823.58
Harkin–Jara112269.2539.1840.68
Jovanovic11211.374.365.86
Toth1136.700.553.97
Table 5. Quantities of chemicals used in studying isotherm and kinetic adsorption for measuring the removal and cost per unit in the chemical removal process of Cu2+ and Ni2+.
Table 5. Quantities of chemicals used in studying isotherm and kinetic adsorption for measuring the removal and cost per unit in the chemical removal process of Cu2+ and Ni2+.
Chemical Name UsedCu2+Ni2+
Amont of Chemical Used
(g or L)
Current Cost
(2024, THB or USD)
Amont of Chemical Used
(g or L)
Current Cost
(2024, THD or USD)
Sodium hydroxide (5 mol L−1, >97%, Panreac)Average 0.001THB 0.98, USD 0.027Average 0.001THB 0.98, USD 0.027
Acetic acid (99.99%, AR grade, Ajex Finechem)Average 0.002THB 0.73, USD 0.020Average 0.002THB 0.73, USD 0.020
Dowex M4195 (Sigma-Aldrich)Fixed 0.1THB 16.60, USD 0.47Fixed 0.1THB 16.60, USD 0.47
Total cost (THB)-18.31-18.31
Total cost (USD)-0.517-0.517
Model and cost analysisMaximum adsorption (Cu2+ and Ni2+ removal)
Kinetic adsorption46.02 mg g−1 (B, Benefit = 46.02)36.03 mg g−1 (B, Benefit = 36.03)
Adsorption isotherm44.37 mg g−1 (B, Benefit = 44.37)32.86 mg g−1 (B, Benefit = 32.86)
B/C Kinetic46.02/18.31 = 2.513 (Baht)36.03/18.31 = 1.967 (Baht)
B/C Isotherm 44.37/18.31 = 2.423 (Baht)32.86/18.31 = 1.795 (Baht)
N S B (net socail benefit) kinetic and isotherm18.31 − (18.31/5) = 14.648 (baht)
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Suwannahong, K.; Wongcharee, S.; Kreetachat, T.; Imman, S.; Suriyachai, N.; Hongthong, S.; Rioyo, J.; Dechapanya, W.; Noiwimol, P. Comprehensive Cost–Benefit and Statistical Analysis of Isotherm and Kinetic Models for Heavy Metal Removal in Acidic Solutions Using Weakly Base Polymeric Chelating Resin as Adsorbent. Water 2024, 16, 2384. https://doi.org/10.3390/w16172384

AMA Style

Suwannahong K, Wongcharee S, Kreetachat T, Imman S, Suriyachai N, Hongthong S, Rioyo J, Dechapanya W, Noiwimol P. Comprehensive Cost–Benefit and Statistical Analysis of Isotherm and Kinetic Models for Heavy Metal Removal in Acidic Solutions Using Weakly Base Polymeric Chelating Resin as Adsorbent. Water. 2024; 16(17):2384. https://doi.org/10.3390/w16172384

Chicago/Turabian Style

Suwannahong, Kowit, Surachai Wongcharee, Torpong Kreetachat, Saksit Imman, Nopparat Suriyachai, Sukanya Hongthong, Javier Rioyo, Wipada Dechapanya, and Pakpilai Noiwimol. 2024. "Comprehensive Cost–Benefit and Statistical Analysis of Isotherm and Kinetic Models for Heavy Metal Removal in Acidic Solutions Using Weakly Base Polymeric Chelating Resin as Adsorbent" Water 16, no. 17: 2384. https://doi.org/10.3390/w16172384

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop