Modelling Arsenic-Removal Efficiency from Water Through Adsorption Using Modified Saxaul Ash as Adsorbent

Abstract

To overcome the consequences of arsenic contaminations, several methods are being proposed. However, practical implementation of those studied methods is rare, mainly due to uncertainties in perception regarding the treatment efficiency of a particular method under different operating conditions. A parametric mathematical model is proposed for the estimation of arsenic-trapping efficiency using saxaul ash sand as adsorbent for the treatment of arsenic-contaminated water under different input conditions. The developed model is based on three independent factors: adsorbent dose concentration, solution pH and initial arsenic concentration in the solution. These factors were selected based on a rigorous experimental study using saxaul ash as adsorbent, which was conducted earlier. Individual relationships between each of those contributing factors and arsenic-removal efficiencies were established based on experimental results. Each relationship was expressed with a best-fit equation and converted to a contributed factor. It is found that the derived best-fit relationships of removal efficiencies follow polynomial patterns with pH and logarithmic patterns with initial concentration and dose concentration. Finally, all the contributed factors were amalgamated into a single equation representing arsenic-removal efficiency for any pH, initial arsenic concentration, and dose concentration. Model-predicted results are compared with the original measured data from the earlier experiments. It is found that the developed best-fit equations for pH, initial arsenic concentration and dose concentration can replicate measured values with coefficient of determination values of 0.88, 0.96 and 0.99, respectively. A comparison of final equation predictions reveals that the predictions are quite accurate, except for a few estimations yielding general statistical errors such as RMSE = 8.07, MAE = 4.73 and RAE = 0.10. Discrepancies in a few predicted values can be attributed to the non-adherence of original measured values to the adopted best-fit trend, especially for the case of pH. Such a developed model can be used for the estimation of arsenic-trapping efficiency with any desirable mix of independent variables selected in this study.

1. Introduction

Arsenic, which is abundant in groundwater, is one of the twelve most toxic elements in the earth [1,2]. Arsenic in the water easily converts to inorganic forms such as pentavalent arsenate, As (V), and trivalent arsenite, As (III), in the presence of oxygen. Consequently, most common inorganic forms of arsenic in natural water are As (III) and As (V) [3]. Arsenic can be accumulated in groundwater in both natural and anthropogenic processes. Biological activities, volcanic eruptions, and weathering effects can be considered as the natural sources of arsenic in groundwater. Arsenic from oil refineries, ceramic industries, agricultural chemicals, and wastes from mineral industries are the anthropogenic sources in groundwater [4]. Excessive water requirements for an increased population also have the potential for extreme arsenic concentration in water [5,6,7].

The destructive impacts of arsenic contamination in water were already investigated by numerous studies around the world. Therefore, the arsenic concentration above a certain limit in water poses significant health risks. Excessive concentration of arsenic in water has detrimental effects not only on humans but also on animals and plants [8]. Due to the toxic nature of arsenic, it is considered as a serious community health problem [9]. Skin cancer, neurological, cardiovascular, and respiratory illnesses in humans are linked to the consumption of arsenic-contaminated water. Growth inhibition, yellowing of leaves, and a reduction in yields are common impacts of arsenic on plants. In animals, haematological crises, diarrhea, vomiting, gastric issues and blindness are common from arsenic. Poisoning from arsenic has been identified in numerous areas around the world, located in countries like America, Argentina, Bangladesh, Malaysia, Taiwan, and Iran [10,11]. Some areas of Iran (from which the studied adsorbent was sourced) such as Sistan and Baluchestan, Khorasan, East Azerbaijan and Tuyserkan are also affected by arsenic [11]. Due to the extreme health hazard of arsenic, the US Environmental Protection Agency and World Health Organization recommended arsenic in groundwater to be below 10 mg/L [12,13]. It is well-established that the removal of arsenic from usual domestic water is prevalent for the survival of humans, animals, and the ecosystem. Consequently, different methods of arsenic removal have been adopted from the ancient period [1].

Boiling, solar radiation, filtration through cloths, and water storage in copper vessels are the common ancient techniques for arsenic removal. However, they are ineffective for the trapping of dissolved arsenic from contaminated water [14]. For example, Thomas et al. [14] noted that slow sand filtration is capable of reducing arsenic by only 47%. The subsurface arsenic removal, which is one of the in situ groundwater treatment methods, was capable of reducing arsenic to 25 μg/L [15]. Furthermore, Adams [16] recognized that unsustainable technology-driven endeavours for arsenic removal failed to contribute to safe drinking water in South Asia. Therefore, technological advancements for arsenic removal became a common interest to scientists. As a result, several techniques such as ion exchange [17,18], reverse osmosis [19], membrane filtration [20], coagulation [21], electrodeionization [22], coal combustion [23] and precipitation [24] were proposed to investigate the trapping of arsenic from contaminated water. Gahrouei et al. [25] reported a comprehensive review of different methods used for the removal of heavy metals as well as arsenic from an aqueous solution. Large residue-generation including iron products, inefficiencies and cost-effectiveness hinder the rigorous adoption of the above-mentioned methods [26]. Adsorption [27,28] is another efficient practice to clean water from arsenic. Adsorption has been used for the removal of different pollutants for many years [29]. However, recently, with the emergence of nanomaterials and nanoparticles as well as nanocomposite materials, removal of arsenic by using multilayer adsorption has also been investigated in several studies [30,31,32]. Also, recently, with the focus on environmental sustainability and recycling, several used/waste materials are being tested as effective adsorbents [33]. Nevertheless, the trapping efficiency of an adsorbent depends extremely on different physiochemical properties of water and adsorbent, including pH, dosage, contact time, and amount of pollutants present [34]. Differences among the basic physicochemical processes of the available arsenic-removal techniques further complicate their worldwide adoption [35]. The socioeconomic aspect of a region is another important factor that needs to be addressed for the acceptance of arsenic-removal techniques in water treatment [35].

Field estimation of arsenic in water is the most challenging due to the requirements of advanced tools, experienced personnel, and high cost [36]. At present, most of the investigated techniques for arsenic removal require high initial investment and operational costs, produce high residue, and suffer from waste disposal problems [37,38]. Researchers strive to find simple, cheap and locally achievable techniques for the large-scale trapping of arsenic from water. Moreover, a successful technique for particular experimental conditions may not be practical in all the areas, as specific regions and contaminant samples may require different experimental conditions. It is costly to perform similar tests for varying different experimental conditions, especially in a large-scale setup. In such scenario, modelling techniques are widely useful to predict potential arsenic-removal efficiency for varying input parameters. Recent studies on arsenic also emphasised the urge for the application of improved mathematical modelling techniques [39]. However, only a few studies have been dedicated to the adoption of mathematical models for the prediction of arsenic-trapping efficiency from arsenic-contaminated water [40,41,42,43]. Roy et al. [9] investigated statistical approaches to determine the characteristics of arsenic and found that artificial neural network modelling techniques can be adopted for the prediction of arsenic. However, their models were developed based on only 22 experimental data sets. A simulation model for the transport of arsenic within a vertical column was proposed by Gupta and Sankararamakrishnan [42]. Rodríguez-Romero et al. [40] also examined the effectiveness of artificial neural network for predicting arsenic-removal efficiency. Statistical physics theory has been adopted by Sellaoui et al. [43] for developing novel adsorption equations for arsenic removal.

Each of the models was developed based on some assumptions for specific experimental conditions. The rigorous adoption of a specific modelling technique that represents the true nature of arsenic in water is yet to be investigated. Moreover, most of the stakeholders prefer to use a simple model for a specific process of arsenic removal. This paper presents the development of a simple mathematical model for the estimation of arsenic-trapping efficiency from contaminated water using saxaul ash as adsorbent. The saxaul plant (Figure 1) is one of the most available plants in the arid regions (especially in the eastern side of the Caspian Sea) due to its capability to withstand harsh environments. It was demonstrated by Rahdar et al. [11] that the saxaul ash has the potential to trap arsenic from water; data from the experiments using the same sand are used to develop the model in the current study. The development of the proposed model for predicting arsenic-trapping efficiency was accomplished through the integration of individual effects of three contributing factors (pH, initial arsenic concentration in the water and adsorbent dose). The factors were selected based on an earlier experimental study [11]. The objective of the current study was to develop a simple mathematical model for real-life (where different input variables may need to be altered for different practical conditions) estimation of arsenic-removal efficiency from water by saxaul ash under any combination of contributing factors selected.

The developed model's accuracy was assessed adopting experimental data from the published literature [11]. The developed model has the potential to replicate the true nature of arsenic removal from water. It is to be noted that the proposed model is only valid for arsenic removal with the same adsorbent (saxaul ash).

2. Methodology

The methodology is based on integrating individual controlling factors into one final factor and multiplying it with the maximum achievable removal efficiency (MRE). In reality, arsenic-removal efficiency depends on several independent variables. In some studies, including the one from which the current study data were sourced, the effects of contact time and temperature were also investigated. However, being a preliminary attempt of such a mathematical model, the effects of contact time and temperature were not incorporated, considering the fact that effects of both the variables are reaching optimum levels, which are easily achievable. In the current study, those independent variables and subsequent contributing factors were derived from detailed experimental data presented in Rahdar et al. [11].

In the original experimental study, the adsorbent, Saxaul trees, were collected from Zabol City, Iran. First, the tree branches were washed to remove possible contaminants and were cut to the size equal to approximately 1 cm². The cut pieces were rinsed with deionized water and then placed into an oven at 105 °C for 12 h. In order to modify the adsorbent, the tree was immersed in sodium hydroxide solution with 30% volume concentration for 24 h. Next, the absorbent was placed in the oven to dry again at a temperature of 105 °C for 12 h, and then, it was converted to ash in an electric furnace at a temperature of 650 °C for 3 h. The subsequent paragraphs detail the procedure adopted for the development of intended mathematical formulations.

The proposed model was developed applying experimental results of arsenic removal using saxaul ash involving different contributing factors. Employing similar techniques used by Imteaz et al. [44,45] for predicting removal efficiencies of different pollutants (BOD, COD, TSS, TDS and Methylene Blue), it is customary that the trapping efficiency of arsenic can be described by the Equation (1), which provides arsenic-removal efficiency after reaching equilibrium:

$$RE=f\left(p\right) \ast f\left(IC\right) \ast f\left(D\right) \ast MRE$$

(1)

where, “RE” is the trapping of arsenic in “%”, f(p) is the function-accounting effect of pH on arsenic trapping efficiency, f(IC) is the function-accounting influence of the initial arsenic concentration on arsenic trapping efficiency, and f(D) is the function-accounting influence of the dose concentration on arsenic-removal efficiency. “MRE” is the maximum achievable trapping efficiency for arsenic.

All the above-mentioned functions, i.e., f(p), f(IC) and f(D), can be derived from the patterns of individual relationships between the selected parameters (pH, initial arsenic concentration and adsorbent dose) and the achieved arsenic-removal efficiency as presented in the detailed study of Rahdar et al. [11]. This study explores the relationships between each of those parameters with the corresponding arsenic-removal efficiencies obtained from experimental measurements using best-fit technique. Thorough observations of the experimental results suggest following generic representations of f(p), f(IC) and f(D). Developments and the final forms of the relationships are demonstrated in the Section 3.

$$f(p)={\displaystyle \frac{({RE}_{pH})}{{RE}_{opt}^{pH}}}$$

(2)

$$f(IC)={\displaystyle \frac{({RE}_{IC})}{{RE}_{opt}^{IC}}}$$

(3)

$$f(D)={\displaystyle \frac{\left({RE}_D\right)}{{RE}_{opt}^D}}$$

(4)

where, $R{E}_{opt}^{pH}$, $R{E}_{opt}^{IC}$ and $R{E}_{opt}^D$ are the optimum removal efficiencies from the experimental results of Rahdar et al. [11] under varying pH, initial arsenic concentration and dose concentration, respectively. RE_pH, ${RE}_{IC}$ and ${RE}_D$ are actual measured arsenic-removal efficiencies under varying pH, initial arsenic concentration and dose concentration, respectively.

RE_pH, ${RE}_{IC}$ and ${RE}_D$ can be expressed as per the following expressions obtained from the study of Rahdar et al. [11].

$${RE}_{pH}=a_{pH} \ast {pH}^2+{b_{pH} \ast pH+c}_{pH}$$

(5)

$${RE}_{IC}=a_{IC}\ast ln\left(IC\right)+c_{IC}$$

(6)

$${{RE}_D=a}_D\ast ln\left(D\right)+c_D$$

(7)

where, $a_{pH}$, $b_{pH}$ and $c_{pH}$ are the coefficients and constant of the best-fit line for removal efficiencies with varying pH values. $a_{IC}$ and $c_{IC}$ are the coefficient and constant of the best-fit line for removal efficiencies with varying initial concentration. $a_D$ and $c_D$ are the coefficient and constant of the best-fit line for removal efficiencies with varying dose concentration. ‘IC’ is the initial concentration, and ‘D’ is the dose concentration in “g/L”.

Arsenic-trapping efficiencies for various values of selected independent variables (pH, initial arsenic concentration and dose concentration) were calculated using Equation (1). In the equation, the maximum removal efficiency (MRE) was assumed to be 100%, although the actual value was unknown. The Section 3 presents sequential derivations of f(p), f(IC) and f(D) based on the measured experimental values by Rahdar et al. [10]. Although original experiments were conducted for various temperatures and contact times, for the development of a generalized equation, a constant contact time of 60 min and temperature of 298 K were considered, as optimum removal efficiencies were already achieved under these conditions (i.e., contact time and temperature). $R{E}_{opt}^{pH}$, $R{E}_{opt}^{IC}$ and $R{E}_{opt}^D$ values were calculated by trial with the aim of achieving highest correlations through the derived equation.

Finally, the accuracy of calculated results through the developed equation was assessed through comparing the results with the original experimental data reported by Rahdar et al. [11]. The Section 3 outlines final derivation of the model equation and assessments of model accuracy.

Accuracy of the derived equation was assessed with the basic statistical error measures such as Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Relative Absolute Error (RAE), as defined by Dastkhoon et al. [46]. The RMSE of any predicted values compared to the observed values is defined as follows:

$$RMSE=\sqrt{{\displaystyle \frac{{\sum _{i=1}^n(X_{obs, i}-X_{model, i})}^2}{n}}}$$

(8)

where, X_obs is measured values, and X_model is modelled values at time i. ‘n’ is the number data. The Mean Absolute Error (MAE) is defined as the sum of the absolute value of the differences between all the measured values and modelled values, divided by the total number of estimations as mentioned below:

$$MAE={\displaystyle \frac{\sum _{i=1}^n(X_{obs, i}-X_{model, i})}{n}}$$

(9)

The Relative Absolute Error (RAE) is expressed as a ratio of cumulative errors to cumulative actual measured values and defined as follows:

$$RAE={\displaystyle \frac{{\left[{\sum _{i=1}^n(X_{obs, i}-X_{model, i})}^2\right]}^{1/2}}{{\left[{\sum _{i=1}^n(X_{obs, i})}^2\right]}^{1/2}}}$$

(10)

3. Results and Discussions

3.1. Derivation of Factors

In the original experiments on assessing effects of pH, the pH values were varied from 3 to 13, while initial arsenic concentration was 100 μg/L and adsorbent dose was 1 g/L. Figure 2 shows the derived best-fit relationship of pH with arsenic-removal efficiency. The derived best-fit equation, as shown below, has a coefficient of determination value of “0.88”:

RE_pH = −1.0937 × pH² + 18.6 × pH + 2.7937

(11)

where, RE_pH is the arsenic-trapping efficiency for varying pH values.

In experiments assessing the effects of initial arsenic concentration, the initial arsenic concentrations were varied from 10 to 250 μg/L, with constant adsorbent dosage of 1.5 g/L and a constant pH of 7. Figure 3 shows the derived best-fit relationship of initial arsenic concentration with the arsenic-removal efficiency. The derived best-fit equation as shown below has a coefficient of determination value of “0.964”:

RE_IC = 12.767 × ln(IC) + 21.344

(12)

where, RE_IC is the arsenic-trapping efficiency for varying initial concentrations of arsenic.

In experiments assessing the effects of adsorbent dose concentration, the dose concentrations were varied from 0.1 to 3.0 g/L, with constant initial arsenic concentration of 100 μg/L and a constant pH of 7. Figure 4 shows the derived best-fit relationship of dose concentration with the arsenic-removal efficiency. The derived best-fit equation as shown below has a coefficient of determination value of “0.99”:

RE_D = 8.8269 × ln(D) + 86.939

(13)

where, RE_D is the arsenic-trapping efficiency for varying dose concentrations.

For the available sixteen measurements from the experimental results of Rahdar et al. [10], the values of RE_pH, RE_IC and RE_D were calculated using Equations (2)–(4) for different combinations of values of pH, IC and D. Eventually, the values of f(p), f(IC) and f(D) were calculated by dividing RE_pH, RE_IC and RE_D values by $R{E}_{opt}^{pH}$, $R{E}_{opt}^{IC}$ and $R{E}_{opt}^D$ values, respectively. For the current study through trial, the RE_pH, RE_IC and RE_D were found to be 90, 89 and 95, respectively. Finally, substituting the values of f(p), f(IC) and f(D) into Equation (1), the final equation for arsenic trapping efficiency is derived.

3.2. Assessment of Developed Factors

It is difficult to verify the developed factors, as no one else completed a similar study with arsenic, except for pH. The relationship of arsenic-removal efficiencies with pH has been investigated by Imteaz et al. [47], who have established a generalized relationship considering several experimental results on arsenic-removal efficiencies with different adsorbents. For comparison, the earlier established generalized relationship was compared with the currently derived factor for pH. Figure 5 shows the comparison of f(pH) values through an earlier developed generalized equation and the current developed equation. From the figure, it is clear that the earlier developed equation's produced values are quite close to the current developed equation, except in the ranges of extreme acidic/alkaline pH.

3.3. Final Model's Accuracy

The developed models’ accuracy could not be verified with the results from others, as no one else has completed a similar study, especially with the studied adsorbent. However, the model-produced results were compared with the original experimental results.

Table 1. Input variables, measured and estimated removal efficiencies.

Dose (g/L)	Initial Conc. (μg/L)	pH	Estimated Removal Efficiency (%)	Measured Removal Efficiency (%)
0.5	100	7	79.9	80.5
1.0	100	7	86.0	86.0
1.5	100	7	89.5	90.5
2.0	100	7	92.0	93.5
2.5	100	7	94.0	94.5
3.0	100	7	96.0	96.0
1.0	10	7	54.4	50.5
1.0	50	7	76.5	70.5
1.0	100	7	86.0	85.0
1.0	250	7	98.5	90.5
1.0	100	3	69.9	50.5
1.0	100	5	82.1	63.0
1.0	100	7	86.0	86.0
1.0	100	9	81.5	81.5
1.0	100	11	68.7	69.5
1.0	100	13	47.6	61.0

presents the model-estimated values of arsenic-removal efficiency for various combinations of independent variables pH, IC and D. The corresponding measured values from the original experiments are also presented in the table. Figure 6 presents the comparison between model-estimated values with the experimentally observed values. An ideal line (dashed line) representing a 100% accurate model is also drawn in Figure 6. The closer the points to the ideal line, the better the developed model estimates. From the figure, it is clear that out of sixteen measurements, four measurements slightly differ with the model-calculated values. However, overall model estimations are quite accurate, especially for the higher values. Model-predicted values have a correlation coefficient of 0.86 with the measured values. Deviations of a few estimations from the measured values caused a slightly lower correlation coefficient. The model's estimates were further evaluated with the common error statistics, such as Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Relative Absolute Error (RAE). It is calculated that the model-calculated values have an RMSE value of “8.07”, MAE value of “4.73” and RAE value of “0.10”.

The moderate variations of the model-calculated values from the original observed values for a few measurements are customary, as while deriving the factors, not all the measurements closely matched with the proposed best-fit equations, especially for pH and initial concentration. Those slight variations of experimental values with the adopted best-fit curves ultimately cause variations of the model-calculated results with the observed values. For the experiments with pH variations, the measurement at pH = 7 significantly deviated from the best-fit line. For the experiments with the variations of dose concentration and initial arsenic concentration, the pH value was kept at 7.0 (which is the point having the highest deviation). All the highest deviations of modelled values are attributed to the values associated with pH = 7.0.

4. Conclusions

In order to provide an efficient decision-making process for the stakeholders, this paper presented the development of a parametric simple mathematical model for the estimation of arsenic-trapping efficiency using saxaul ash as adsorbent. Based on prior rigorous experimental measurements, three influential sovereign parameters were selected on which the arsenic removal efficiency will vary with the use of saxaul ash. The selected variables are pH, initial arsenic concentration and the dose concentration. From the earlier experimental results, the individual relationship of each selected independent parameter with the arsenic-removal efficiency was derived using the best-fit equation technique. From each developed relationship, a factor contributing to final arsenic-removal efficiency was deduced and, finally, an integrated complete mathematical formulation for the estimation of arsenic-trapping efficiency based on the above-mentioned variables was proposed. The accuracy of the predicted results from the final developed equation was assessed through comparing the calculated values with the original values obtained through experiments. It was proven that the equation can closely predict the original experimental measurements, except for a few cases. During the process of deriving contributing factors, few measurements were not closely matching with the adopted trendline equations, and this is the cause of slight discrepancies between the equation-predicted results and experimental measurements for a few points. The fundamental discrepancy of each best-fit equation with the corresponding measured values might be attributed to the quality control issue of the experimental measurements. As such, a further validation of the assessment of the influence of the selected variables on the arsenic-trapping efficiencies is recommended. Nonetheless, the overall model performance is quite good through achieving lower statistical error values such as RMSE = 8.07, MAE = 4.73 and RAE = 0.10. It is to be noted that in the developed equation, through trial, the Maximum Removal Efficiency (MRE) was found to be 100%, which is reasonable. Consideration of different MRE values would alter the accuracy of the developed equation.

It is to be noted that the lack of measured data points might be a concern for overconfidence in the model's accuracy. However, data points covered the effective ranges of arsenic removals, and overfitting is not likely to be an issue for the current modelling task. Nonetheless, it is recommended that further measurements to be conducted covering wider ranges of the input variables with the same material. Also, the model was developed based on a constant contact time of 60 min and temperature of 298 K. The efficiency will be lowered for a shorter contact time and lower temperature. From the original experimental measurements, in a complex robust equation following the same technique, it is possible to incorporate the factors of contact time and temperature in the model equation.

The developed model can be used by the stakeholders for deciding appropriate contributing factor values to achieve a target arsenic-removal efficiency. It is worth noting that the assessment of the developed model has been performed for arsenic removal using saxaul ash, which is the most common native plant within the deserts of Iran. For the similar purpose, the efficiency of native plants or locally available materials in other regions of the world may render different outcomes and, as such, should be assessed separately before concluding a generic final remark on the global acceptance of such a developed equation. In other words, the developed equation(s) will not be universally acceptable for other adsorbents or other pollutants. However, a similar technique can be applied to develop such a mathematical model for any other adsorption processes.