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DH. Abbas M, Yousefi Kebria D. Simulation of Heavy Metals Adsorption Using Recycled Bentonite Clay Waste in a Fixed Bed Depth Column. J Environ Health Sustain Dev 2023; 8 (3) :2078-2095
URL: http://jehsd.ssu.ac.ir/article-1-630-en.html
Department of Environmental Engineering, Civil Engineering Faculty, Babol Noshirvani University of Technology, Iran.
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Simulation of Heavy Metals Adsorption Using Recycled Bentonite Clay Waste in a Fixed Bed Depth Column

Mukhtar DH. Abbas 1, Daryoush Yousefi Kebria 2*

1 Department of Environmental Engineering, Civil Engineering Faculty, Babol Noshirvani University of Technology, Iran & Engineer in Directorate of Al-Qadissiyeah Environment – Ministry of Environment, Iraq.
2Department of Environmental Engineering, Civil Engineering Faculty, Babol Noshirvani University of Technology, Iran.

A R T I C L E  I N F O ABSTRACT
ORIGINAL ARTICLE Introduction: The study objective is to remove heavy metals from an aqueous solution using recycled bentonite clay waste (RBCW) as a low-cost and green adsorbent in a continuous system. The produced RBCW results from thermal remediating of the hazardous industrial bentonite clay waste that is a by-product of used engine oil recycling plants.
Materials and Methods: The doses of the RBCW adsorbent were (1.0, 1.5, and 2.0) g mixed with (30, 40, and 50) g of the crystalline sand to produce bed depth columns of (22, 30, and 38 cm), respectively. The influent concentrations of all adsorbates were (20, 50, and 100) ppm, and the flow rates of the continuous system were (0.5, 1.0, and 2.0) mL/min.
Results: The BET, XRF, and SEM tests and the experimental data approved that RBCW is active material for heavy metals adsorption. The adsorption capacity and breakthrough time of Pb, Cd, Cr, Zn, and Ni for dominant parameters (flow rate of 1.0 mL/min, adsorbent mass of 1.0 g, and influent concentration of heavy metals of 20 ppm) were 70.36, 36.05, 27.55, 21.67, and 18.63 mg/g, and 35, 19.73, 11.38, 6.25, and 8.13 hr, respectively.
Conclusion: The RBCW adsorbent has more than one advantage in industrial and environmental issues. The (R2) values for Thomas, Yoon-Nelson, and BDST models were higher than 0.9. Moreover, the breakthrough curves of experimental data were more fitted with the Yoon-Nelson model due to the high value of R2 and low values of Chi-square, absolute average deviation, and standard deviation.

Article History:
Received: 19 May 2023
Accepted: 10 July 2023

*Corresponding Author:
Daryoush Yousefi Kebria
Email:
Dy.kebria@nit.ac.ir
Tel:
+98 911 777 7123

Keywords:
Adsorption,
Sand,
Metals,
Heavy,
Water,
Permeability.
Citation: DH. Abbas M, Yousefi Kebria D. Simulation of Heavy Metals Adsorption Using Recycled Bentonite Clay Waste in a Fixed Bed Depth Column. J Environ Health Sustain Dev. 2023; 8(3): 2078-95.
Introduction
In recent decades, the rapid development in industrial and agricultural activities is prominent. However, the detrimental aspect of this development is the increase in pollutants in the environmental components due to using various chemical materials in the production process1. According to the nature of most industrial activities, there are input materials and output of the productions in addition to the by-products. Sometimes, the waste by-products have hazardous impacts on the environment like industrial bentonite waste resulting from used engine oil recycling plants, which was saturated with oil and impurities. They are often released into the environment without adequate remediation. The risks of bentonite waste are contamination of the surrounding soil and groundwater, and affecting living organisms due to aromatic and aliphatic hydrocarbon components that are toxic, mutagenic, and carcinogenic2. The wastewater which results from industrial and agricultural activities has a high number of heavy metals. Heavy metals are toxic pollutants, non-biodegradable, prevalent, and accumulating in living organisms3. According to the World Health Organization (WHO), the maximum permissible limits in drinking water of Pb, Zn, Cd, Cr, and Ni are 0.01, 3.00, 0.003, 0.05, and 0.07 mg/l, respectively4. Different techniques have been utilized for heavy metals treatment in wastewater as electrochemical reduction, membrane filtration, chemical precipitation, and ion exchange5. However, low efficiency, high operational cost, and other secondary problems are vital factors in not using these methods for heavy metals treatment6. In the adsorption process, the dissolved species are moved from the liquid phase into the particles of the adsorbent by diffusion and then are adsorbed onto the inner surface of particles by chemical reaction or physical attraction. The advantages of the adsorption technique are low cost, flexibility in the design and operation stages, the capability of removing all contaminants even with a low concentration, ease and safety of operation, using both batch and continuous systems, no sludge formation, and regeneration of the adsorbent7. The adsorption processes are physical and chemical due to the nature of their characteristics. The characteristics of the physical adsorption are reversible, having low enthalpy values of about 20 kJ/mol due to weakness in the forces of the Van der Waals attraction, wear attractive, and electrostatic. Conversely, the chemical sorption is irreversible, having a high enthalpy value of about 200 kJ/mol due to stronger electrostatic forces or chemical bonds8. There are prominent classes of adsorbents as a natural material, industrial waste, bio-sorbent, miscellaneous sorbent, and agricultural waste9. Adsorbent materials that are efficient in heavy metals removal include modified bentonite
clay10, 11, activated carbon12, 13, activated cashew nutshell14, and waste materials (waste rock, tailings, coal ash clinker, and slag)15.

Two well-known methods for pollutant removal from aqueous solution in the adsorption experiments are batch and continuous. The fixed bed depth is one class of continuous approaches, which is the most applicable method due to the ease in cyclic adsorption and desorption, treating a high volume of wastewater, and simplifying design and operation16. The fundamental parameters in the bed depth column system are flow rate, influent concentration, and bed depth of adsorbent, which are used in model building. The novelty in this work is recycling the oily industrial waste into a new, green, available, low-cost, environmentally-friendly adsorbent. The aim of this study was to investigate the maximum adsorption capacity of recycled bentonite clay waste (RBCW) to remove the heavy metals of Pb, Zn, Cd, Cr, and Ni from aqueous solution using bed depth column system with different parameters, and also analyze the experimental data and define the compatibility with the models of bed depth service time (BDST), Thomas, Yoon-Nelson, and Adam-Bohart.

Materials and Methods
Adsorbent and adsorbates
The origin of bentonite clay waste in this study is the used engine oil recycling plants drived sludge containing a high amount of engine oil. It was remediated thermally to diminish all residual oil and impurities and converted to reddish-white powder as a new adsorbent and it was called recovered bentonite clay waste (RBCW) in this study. More details of the preparation process are reported 17. The media of the bed depth column was produced by mixing of the RBCW (1.0, 1.5, and 2.0 g) with (30, 40, and 50 g) of quartz sand at ratios of (3, 3.75, and 4%) to produce bed depth (22, 30, 38 cm), respectively. The utilized sand was rinsed with distilled water to vacate extra salt and then sieved to a desired particle size range of 0.5 and 1 mm, with three support layers of different sizes of sand at the bottom to prevent the adsorbent from escaping. The heavy metals (adsorbates) were prepared by dissolving a required quantity of the specified salts including (ZnCl2), (PbCl2), (CdCl2.H2O), (NiCl2.6H2O), and (CrCl3. 6H2O) in distilled water to prepare stock solutions (1000 mg/L) of (Zn, Pb, Cd, Ni, and Cr) ions. Then, the stock solutions were diluted with distilled water to prepare the demanded influent concentrations (20, 50, and 100 ppm). The salts were of analytical grade and purchased from Pan REAC. Co., Spain and the concentration of samples was investigated via flame atomic absorption spectrophotometer (SHIMADZU, AA-7000, JAPAN).
Fixed-bed adsorption experiments
The executed laboratory set-up of a fixed bed column system was in a Pyrex glass column with a length of 44 cm and 1.06 cm of internal diameter and laden with different depths of mixed adsorbents (RBCW and sand mixtures). The solution was down-flowed by gravity using the principle of constant pressure with accurate valves where all RBCW particles were immersed in the aqueous solution to ensure the adsorption process. At the bottom of the column, three supporting layers of sand with different particle sizes (small than < 0.5, 0.5 to 1, and 1.5 to 2 mm) were arranged from top to down to eliminate adsorbent loss as shown in Figure 1. The fixed bed depth was designed to adsorb heavy metals (Pb, Zn, Cd, Ni, Cr) with three parameters of depth, flow rate, and influent concentration. Then, 30, 40, and 50 g of quartz sand were mixed with 1, 2, and 3 g of RBCW to yield a total depth bed of 22, 30, and 38 cm, to avoid the occurrence of clogging, and achieve appropriate permeability of mixed bed depth18 (Table 1). The dominant depth was 20 cm for all except the experiment of depths. The flow rates in the experiments were 0.5, 1, and 2 mL/min, and the flow rate of 1 mL/min was prevailing for all except the experiments' flow rates. The influent concentrations were 20, 50, and 100 ppm, and also 20 ppm was the dominant concentration in the other experiments. The operation was terminated when the removal efficiency became less than 5%. All experiments were accomplished at room temperature (25 ± 3ċ). It specified that the breakthrough and exhaustion time were (Ct/C0) equal to 5% and 95%, respectively19.
Table 1: Details of mixing process of RBCW with sand
No. Weight of RBCW
(g)
Weight of sand
(g)
% Ratio of (RBCW/sand) Total bed depth column
(cm)
Permeability
(cm/sec)
1 1.0 30 3.33 22 0.4134
2 1.5 40 3.75 30 0.2349
3 2.0 50 4.00 38 0.1292



Figure 1:
Schematic diagram of fixed bed depth column system

Study of fixed bed depth column
The breakthrough curve is a significant plot to identify the performance of the continuous system. The plotting was between (Ct/C0) and time. The most significant factors resulting from the breakthrough curve are breakthrough time (tb) and exhaustion time (te). The (tb) is the time compatible with concentration ratio (Ct/C0) ranging from 1 to 10 %, in some research studies, it was reported 1%  20, 5%  21, and 10% 11. The (te) is consistent with the time when (Ct/C0) is approached (0.85- 0.95) or becomes steady. In this study, the used time was consistent with Ct/C0 = 0.05 and 0.95 to be breakthrough time and exhaustion time, respectively. The total quantity of solutes interred in bed depth is m (mg), calculated by (Equation (1)).
m= C0*Q*te                                                   (1)

The total adsorbed quantity (q, mg) is calculated using (Equation (2))20.
q=QA1000=Q10000tC0-Ctdt                         (2)

Where q (mL/min) is the flow rate in the bed depth column, C0 (mg/L) is the influent concentration, Ct (mg/L) is the effluent concentration, and A (mg.min/L) expresses the region under the breakthrough curve from (C0) to (C𝑡) and from (t0) to any (t𝑡).
The breakthrough capacity (qb, mg/g) at the breakthrough point refers to the mass of molecules or ions adsorbed onto adsorbent material as written in (Equation (3)).
qb=Q1000*w0tbC0-Ctdt                               (3)

The exhaustion capacity (qe, mg/g) at the point of exhaustion refers to the mass of molecules or ions adsorbed onto adsorbent material according to (Equation (4)).
qe=Q1000*w0teC0-Ctdt                                           (4)

Where tb (min) refers to the entire time of treated effluent at the point of breakthrough, w is the adsorbent weight (g), and te (min) refers to the whole time of treated effluent at the exhaustion point.
The removal efficiency (R%) results from dividing the adsorbed quantity of ions qt (mg) by the total amount of solute m (mg) used in the bed depth (Equation (5)).
R%=qtm                                                                                                 (5)

The mass transfer zone (MTZ) (cm) is the active adsorbent region where the contaminants were adsorbed. It is dependent on the total bed depth Z (cm), the time of breakthrough and exhaustion point (Equation (6)). tz is the required time of moving MTZ (Equation (7))  20.
MTZ=Z1-tbte                                                                      (6)
tz=te-tb                                                                               (7)

Error analysis
To demonstrate the adequacy of the BDST, Adam-Bohart, Thomas, and Yoon–Nelson model, the average absolute deviation (AAD)22, standard deviation Δq23, and Chi-square (x2) tests 24of statistical analysis were applied. These tests are non-linear approaches used to compare the experimental data and calculated model values via the excel sheets.
AAD=100*qexp.-qmodel2/qexp.2NumberOfTests              (8)

q= qexp.-qmodel/qexp.2Number of Tests-1*100              (9)

X2= qexp.-qmodel2qmodel                                                      (10)


Ethical issues
The research was performed in accordance with the ethical guidelines of the Babol Noshirvani University of Technology.

Results
Characterization of the RBCW adsorbent
From the results of XRF, BET, and SEM tests, it was apparent that the characterizations of RBCW materials were promising as a new adsorbent to remove the heavy metals from aqueous solution, including ravines, excavations, and pores in the texture as shown in Figure 2. These are significant factors in increasing the adsorption process as soon as the particle size was arranged from 21.08 to 37.17 nm. Also, the BET test approved that the specific surface area, pore size, and pore volume are positive indicators for the adsorption and are equal to 67.17 m2/g, 8.54 nm, and 0.15 cm3/g, respectively. pHpzc of the RBCW adsorbent was 10.4, and this value is alkaline and assists in the sedimentation of the heavy metals and increases the removal efficiency. In the XRF test illustrating the chemical components of the RBCW adsorbent, the elements of AL, Mg, and Ca increased from the cationic exchange with existing heavy metals in the liquid phase and then contributed to the adsorption process18. It was approved that the RBCW adsorbent is eco-friendly as shown in Table 2.
Table 2: Chemical and physical characteristics of RBCW
Characteristics Value XRF analysis
Chemical composition      Weight %
Specific surface area m²/g 67.17 SiO2 77.342
External surface area (m²/g) 77.29 Al2O3 10.177
Total pore volume (cm3/g) 0.15 CaO 5.443
Pore size (nm) 8.54 Mg O 3.396
pHPZC 10.4 Fe2O3 1.112
Real density (g/cm3) 2.133 SO3 1.11
Bulk density (g/cm3) 0.768 K2O 0.913
CEC ( meq) 22.9 Na2O 0.201
Color Reddish-white TiO2 0.097



Figure 2: (a) Image of RBCW sample, (b) SEM test of RBCW

Effect of adsorbent weight in the bed
To identify the effect of the variation in the weight of the RBCW adsorbent on the adsorbing of the Pb, ZN, Cd, Ni, and Cr with flow rate and influent concentrations of 1 mL/min and 20 ppm, respectively, three employed quantities of the RBCW adsorbent 1, 1.5, and 2 g to produce equivalent bed depths of 22, 30, and 38 cm, respectively. According to Table 3, by increasing the bed depth from 22 to 38 cm, the removal capacity increased from 70.36 to 74.30, 36.05 to 72.20, 27.55 to 28.29, 26.42 to 31.00, and 18.63 to 20.99 mg/g for Pb, Cd, Cr, Zn, and Ni, respectively. The increase in the bed depth or adsorbent quantity induced high removal efficiency due to the availability of the active sites in the RBCW surface.
Table 4 shows that an increase in the bed depth increased the time of MTZ moving (tz), where the (tz) increased from 41.10 to 56.48 hr, 22.85 to 41.25 hr, 19.60 to 29.25 hr, 23.42 to 34.63 hr, and 14.23 to 33.70 hr for Pb, Cd, Cr, Zn, and Ni, respectively. Generally, MTZ increased by increasing the bed depth column. However, the increase was high for Ni, medium for Cd, Zn, and Cr, and low for Pb, and these variations in the ability of the RBCW for adsorbing ions were due to the difference in the electrochemical properties of the targeted heavy metals25. Both the breakthrough time and exhaustion time in Figure  3 increase with the increase in the adsorbent mass or bed depth column of the RBCW, which ultimately increases the service time of adsorption column due to available adsorption sites and additional contact time and supplying superior intra-particle phenomena 26. The axial dispersion and axial convection are the two influential features in the bed depth column system, and the effect on the removal efficiency, service time, and the (MTZ) is noticeable. These features are affected by the increase in the bed depth column to increase the axial convection and decrease the axial dispersion27.
Table 3: Effect of column bed depth on the adsorption capacity (mg/g) and removal efficiency (%)
H
(cm)
Pb Cd Cr Zn Ni
qexp.
(mg/g)
Removal efficiency (%) qexp.
(mg/g)
Removal efficiency (%) qexp.
(mg/g)
Removal efficiency (%) qexp.
(mg/g)
Removal efficiency (%) qexp.
(mg/g)
Removal efficiency (%)
22 70.36 0.77 36.05 0.71 27.55 0.74 21.67 0.61 18.63 69.42
30 72.49 0.81 39.68 0.75 27.84 0.76 23.03 0.68 19.35 69.44
38 73.49 0.83 42.24 0.78 28.29 0.77 26.22 0.71 20.99 69.45
R2 0.956 0.980 0.991 0.989 0.984 0.956 0.949 0.914 0.951 0.971


Table 4: Effect of column bed depth on the MTZ and the moving time
H
(cm)
Pb Cd Cr Zn Ni
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
22 41.10 11.88 22.85 11.81 19.60 13.92 23.42 17.37 14.23 14.00
30 48.22 12.89 31.90 14.51 24.32 16.02 25.82 18.38 22.43 19.32
38 56.48 14.45 41.25 17.46 29.25 18.12 34.63 21.27 33.70 24.66
R2 0.998 0.985 1.000 0.999 1.000 1.000 0.902 0.929 0.996 1.000


Figure 3: Effect of bed depth on the breakthrough time curve for Pb, Cd, Cr, Zn, and Ni

Effect of flow rate
Three examined levels in the flow rate experiments (0.5, 1, and 2 mL/min), and influent concentration, and the bed depth column were constant at 20 ppm and 22 cm. Flow rate is a significant parameter that affects the contact time between the heavy metals (adsorbate) and the RBCW adsorbent and then determines the adsorption behavior.
Based on Table 5, the removal efficiency and the adsorption capacity declined with the increase of flow rate from 0.5 to 2 mL/min, where the adsorption capacity decreased from 75.90 to 58.87, 40.40 to 32.54, 30.14 to 19.98, 29.19 to 23.15, and 19.54 to 16.43 mg/g for Pb, Cd, Cr, Zn, and Ni, respectively. Table 6 shows that increasing the flow rate increases the height of MTZ and reduces the time of moving (tz) due to decreasing the breakthrough and exhaustion times. Figure 4 reveals the effect of the flow rate on the breakthrough curves, and it was evident that increasing the flow rate reduces the times of breakthrough and exhaustion to shorten the service time.
The low flow rate means an increase in the contact time, and subsequently, the opportunity of heavy metals to diffuse into the pores and active sites of the RBCW was more for achieving the equilibrium state between adsorbates and adsorbents. At a high flow rate, the film diffusion is more controlled than intra-particle diffusion, minimizing the adhesion of heavy metals
on the RBCW adsorbent to reduce the removal efficiency
28.


Figure4: Effect of flow rate on the breakthrough time curve for Pb, Cd, Cr, Zn, and Ni

Table 5: Effect of flow rate on the adsorption capacity (mg/g) and the removal efficiency %
Q
(mL/min)
Pb Cd Cr Zn Ni
qexp.
(mg/g)
Removal efficiency % qexp.
(mg/g)
Removal efficiency % qexp.
(mg/g)
Removal efficiency % qexp.
(mg/g)
Removal efficiency % qexp.
(mg/g)
Removal efficiency %
0.5 77.94 0.83 40.40 0.72 30.14 0.80 24.65 0.68 19.54 0.72
1.0 70.36 0.77 36.05 0.71 27.55 0.74 21.67 0.61 18.63 0.69
2.0 58.87 0.67 27.80 0.66 19.72 0.54 17.36 0.54 16.43 0.67
R2 0.995 0.998 1.000 0.988 0.991 0.990 0.993 0.951 0.998 0.978

Table 6: Effect of flow rate on the MTZand the moving time
Q
(mL/min)
Pb Cd Cr Zn Ni
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
0.5 54.52 7.64 49.50 11.62 1577 9.26 26.28 15.52 27.25 13.20
1.0 41.10 11.88 22.85 11.81 1176 13.92 19.60 17.37 14.23 14.00
2.0 24.98 15.08 10.73 13.51 731 17.61 12.18 18.53 6.87 14.74
R2 0.981 0.928 0.848 0.941 0.975 0.936 0.903 0.901 0.883 0.955
Effect of influent concentration
The investigated influent concentrations of heavy metals (20, 50, and 100 ppm) with flow rate and bed depth column were constant at 1 mL/min and 22 cm. Table 7 shows that the increase of influent concentration from 20 to 100 ppm increased the adsorption capacity from 70.36 to 95.50 mg/g, 36.05 to 49.16 mg/g, 27.55 to 40.77 mg/g, 26.42 to 39.41 mg/g, and 18.63 to 29.77 mg/g and decreased the removal efficiency from 0.77 to 0.65 %, from 0.71 to 0.63 %, from 0.74 to 0.65 %, from 0.61 to 0.56 %, from 0.69 to 0.51 % for Pb, Cd, Cr, Zn, and Ni, respectively.
Table 8 reveals that rising influent concentration expands the MTZ and reduces the time of MTZ moving (tz). Figure 5 shows the role of influent heavy metals concentration on the breakthrough curves where it was evident that increasing the influent concentrations decreases the period times of breakthrough and exhaustion to shorten the operation service time of the column. High influent heavy metals concentration means high competition between the molecules that provide a more vital driving force26 and an increase in the intra-particle diffusion 19 that creates significant factors in increasing the transportation of heavy metals and achieving a rapid equilibrium state of the adsorption.

Table 7: Effect of influent concentration on the adsorption capacity (mg/g) and the removal efficiency%
C0
(mg/l)
Pb Cd Cr Zn Ni
qexp.
(mg/g)
Removal efficiency % qexp.
(mg/g)
Removal efficiency % qexp.
(mg/g)
Removal efficiency % qexp.
(mg/g)
Removal efficiency % qexp.
(mg/g)
Removal efficiency %
20 70.36 0.77 36.05 0.71 27.55 0.74 21.67 0.61 18.63 0.69
50 84.87 0.69 43.22 0.66 35.17 0.68 36.48 0.58 25.29 0.58
100 95.50 0.65 49.16 0.63 40.77 0.65 48.14 0.56 29.77 0.51
R2 0.947 0.912 0.961 0.932 0.947 0.911 0.956 0.934 0.936 0.944


Table 8: Effect of influent concentration on the MTZ and the moving time
C0
(mg/l)
Pb Cd Cr Zn Ni
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
tz
(hr)
MTZ
(cm)
20 41.10 11.88 22.85 11.81 19.60 13.92 23.42 17.37 14.23 14.00
50 23.70 12.73 15.75 15.91 13.28 16.97 18.73 18.85 11.27 17.17
100 15.78 14.08 11.30 19.20 10.22 21.41 13.40 20.62 9.53 21.37
R2 0.878 1.000 0.926 0.958 0.888 0.999 0.989 0.991 0.916 0.996



Figure 5: Effect of the influent concentration on the breakthrough time curve for Pb, Cd, Cr, Zn, and Ni

Discussion
The well-known parameters that affect the adsorption process on the fixed column are the mass of the adsorbent (depth), flow rate, and influent concentration of the adsorbate; therefore, most of the experiments on the fixed bed column were conducted on these parameters. The built breakthrough curves were from the experimental data between effluent and influent concentration ratios (Ct/C0) versus time. The most common theoretical models utilized for the adsorption process in the fixed column were Adam-Bohart, Thomas, Yoon–Nelson, and BDST. The effluent concentration, run time, and adsorption capacity can be anticipated from these models26.
Adams–Bohart model
Adams-Bohart model is a relationship between Ct/C0 and t in a continuous system using the surface reaction theory. It has been established for the first region of the breakthrough curve, so it is suitable for effluents at low concentrations (Ct < 0.15C0)19. This model is a simple and comprehensive method to conduct and evaluate the adsorption process in the continuous system. It deals with presence of one adsorbate in aqueous solution without the effect of ionic form and pH on system performance.
lnCtC0=KABC0t- KABqABZF                                         (11)

Where KAB (L/mg.min) is the kinetic constant, F (cm/min) is the velocity of the flow, Z (cm) is the bed depth of column, and qAB is the maximum adsorption capacity (mg/L).
Tables 9, 10, and 11 show the obtained results from the Adam-Bohart model for bed depth, flow rate, and influent concentration, respectively. Generally, it was apparent that an increase in the bed depth and influent concentration column increases the adsorption capacity qAB (mg/l) and decreases the rate constant (KAB). However, increasing the flow rate decreases the adsorption capacity and increases the rate constant (KAB). Table 13 shows the difference between the experimental adsorption capacity (qexp.) values and Adam-Bohart adsorption capacity qAB, where values of linear correlation factor (R2), AAD, ∆q, and Chi-square ranged from (0.460 to 0.936), (56.67 to 19.748), (5.68 to 1.136), and (3435.93 to 1041.6), respectively for all experiments of heavy metals. The table also reveals low values of (R2) and high value of other parameters of error analysis. The results indicated that Adams-Bohart model is less compatible with adsorption data for all heavy metals, since this model is applicable almost for the determined range of the adsorption (C0/Ct < 0.7) that the kinetic adsorption depending on the physical (or external) mass transfer18. The adsorption constant increases with the rise of flow rate and decreases with an increase in influent concentration and bed depth column to be similar to that in29.
Thomas model
Thomas has offered a model using the assumptions of pseudo second order kinetics and Langmuir kinetics for the breakthrough curves19, subsequently, some researchers used it to predict the breakthrough curve of heavy metal adsorption with different  adsorbent in experiments of fixed-bed column. The formula of linear Thomas model is shown below.
lnC0Ct- 1=KThqThmQ- KThC0t                (12)

Where KTh (mL/(mg min)) is the Thomas rate constant, qTh (mg/g) is the maximum adsorption capacity, C0 and Ct (mg/L) are the influent, and effluent concentration of adsorbates, respectively, m (g) is the quantity of absorbent in the column, Q (mL/min) is the flow rate, and t (min) is the filtration time. The plot of ln [(C0/Ct)–1] against (t) at a specified flow rate and mass of adsorbent should produce a straight line if the measurements follow the Thomas model. The kinetic parameters of KTh and q0 can be calculated from the slope and intercept30, and this model depends on the axial dispersion and internal mass transfer 31.Adsorption capacity qTh (mg/g) and rate constant KTh (ml/mg.min) that result from applying Thomas model for different bed depth, flow rate, and influent concentration are shown in Tables 9, 10, and 11, respectively. It was apparent that increasing the bed depth and influent concentration increases the adsorption capacity due to the availability of high adsorption sites and more competition between the ions of heavy metals. However, at the same time, the rate constant (KTh) decreased. Moreover, increasing the flow rate decreased the adsorption capacity due to reducing the contact time between the adsorbates and the adsorbent. However, the increase rate was constant, which was similar to the study by (Alamin. AH & Kaewsichan L)32. The experimental (qexp.) values were close to the values that result from Thomas model qTh, where the values of linear correlation factor (R2), AAD, ∆q, and Chi-square ranged from 0.995 to 0.998, 0.6935 to 1.2056, 0.0253 to 0.0910, and 0.0274 to 0.1899, respectively for all experiments of heavy metals as shown in Table 13.
Yoon–Nelson model
The Yoon–Nelson model is relatively simple and demands no detailed data about the properties of the adsorbate, the kind of adsorbent, and adsorption characteristics parameters. The assumption of the model is that the rate of decrease in the probability of adsorption for each molecule is proportional to the probability of adsorbate adsorption and the probability of adsorbate breakthrough on the adsorbent24.The linear Yoon–Nelson model can be expressed by the following equation.
lnCtC0-Ct=KYNt- τKYN                                          (13)

Where KYN (mL/(min.mg)) is the Yoon–Nelson rate constant, τ (min)is the time required for 50% adsorbate breakthrough, and C0 and Ct (mg/L) are the influent and effluent concentration of adsorbates, respectively (mg/L).
Parameters of Yoon-Nelson model shown in Table 9 approved that increasing the bed depth increased the values of τ and decreased KYN due to a more binding site. Tables 10 and 11 explain that increasing flow rate and influent concentration increased KYN and decreased 50% of breakthrough time τ due to rapid saturation33. There was a slight contrast between experimental τand model τYN, where the values of linear correlation factor (R2), AAD, ∆q, and Chi-square ranged from 0.998 to 1.0, 0.6248 to 2.6715, 0.0275 to 0.100, and 0.3795 to 13.1256, respectively for all experiments of heavy metals as shown in Table 13.

Table 9: Adams–Bohart, Thomas, and Yoon–Nelson model parameters of heavy metals at different bed depths
Bed
Depth
(cm)
Heavy metals qexp.
(mg/g)
qexp.
(mg/l)
Adams–Bohart model Thomas model Yoon–Nelson model
qAB
(mg/l)
KAB
(ml/mg.min)
R2 qTh
(mg/g)
KTh
(ml/mg.min)
R2 τ
(Min)
τexp
(Min)
KYN
(Min-1)
22 Pb 70.4 3427 4053 0.0756 0.982 70.3 0.0972 0.989 3516 3518 0.0019
30 72.5 3883 4376 0.0679 0.986 72.8 0.0808 0.995 5457 5437 0.0016
38 73.5 4144 4559 0.0627 0.989 74.1 0.0715 0.998 7407 7349 0.0014
22 Cd 36.1 1756 2080 0.2001 0.924 36.9 0.2486 0.985 1847 1803 0.0050
30 39.7 2126 2455 0.1196 0.969 39.7 0.1487 0.996 2977 2975 0.0030
38 42.2 2380 2712 0.0881 0.979 42.3 0.1068 0.991 4232 4224 0.0021
22 Cr 27.6 1342 1655 0.1538 0.983 27.7 0.2070 0.987 1384 1378 0.0041
30 27.8 1492 1747 0.1422 0.977 27.9 0.1795 0.996 2091 2088 0.0036
38 28.3 1596 3396 0.1112 0.980 28.4 0.1393 0.993 2843 2829 0.0028
22 Zn 21.7 1055 1489 0.1249 0.932 21.8 0.2028 0.998 1088 1083 0.0041
30 23.0 1234 1573 0.1267 0.959 23.2 0.1800 0.997 1738 1728 0.0036
38 26.2 1479 1762 0.1229 0.945 26.7 0.1553 0.995 2672 2622 0.0031
22 Ni 18.6 907 1158 0.2277 0.954 18.7 0.3251 0.997 934 932 0.0065
30 19.4 1037 1791 0.1396 0.969 19.4 0.1975 0.996 1452 1451 0.0040
38 21.0 1184 2552 0.1119 0.963 21.3 0.1521 0.994 2128 2099 0.0030
Table 10: Adams–Bohart, Thomas, and Yoon–Nelson model parameters of heavy metals at different flow rates
Flow
Rate
(cm)
Heavy metals qexp.
(mg/g)
qexp.
(mg/l)
Adams–Bohart model Thomas model Yoon–Nelson model
qAB
(mg/l)
KAB
(ml/mg.min)
R2 qTh
(mg/g)
KTh
(ml/mg.min)
R2 τ (Min) τexp
(Min)
KYN
(Min-1)
0.5 Pb 77.9 3796 4146 0.0685 0.991 78.4 0.0777 0.997 7835 7794 0.0016
1.0 70.4 3427 4053 0.0756 0.982 70.3 0.0972 0.989 3516 3518 0.0019
2.0 58.9 2867 3701 0.1312 0.946 59.3 0.1886 0.997 1482 1472 0.0038
0.5 Cd 40.4 1967 2368 0.0723 0.970 40.9 0.0938 0.997 4088 4040 0.0019
1.0 36.1 1756 2080 0.2001 0.924 36.9 0.2486 0.985 1847 1803 0.0050
2.0 27.8 1354 1779 0.3039 0.940 28.3 0.4431 0.995 706 695 0.0089
0.5 Cr 30.1 1468 1664 0.1258 0.988 30.3 0.1504 0.994 3033 3014 0.0030
1.0 27.6 1342 1655 0.1538 0.983 27.7 0.2070 0.987 1384 1378 0.0041
2.0 19.7 960 1462 0.2400 0.916 19.8 0.4383 0.997 494 493 0.0088
0.5 Zn 24.7 1201 1536 0.0795 0.956 24.7 0.1138 0.996 2471 2465 0.0023
1.0 21.7 1055 1489 0.1249 0.932 21.8 0.2028 0.998 1088 1083 0.0041
2.0 17.4 845 1360 0.2311 0.904 17.5 0.4452 0.991 437 434 0.0089
0.5 Ni 19.5 952 1192 0.1099 0.996 19.5 0.1538 0.989 1950 1954 0.0031
1.0 18.6 907 1158 0.2277 0.954 18.7 0.3251 0.997 934 932 0.0065
2.0 16.4 800 1095 0.4387 0.936 16.5 0.6887 0.996 413 411 0.0138


Table 11: Adams–Bohart, Thomas, and Yoon–Nelson model parameters of heavy metals at different concentrations
Concentration
(cm)
Metal
Ions
qexp.
(mg/g)
qexp.
(mg/l)
Adams–Bohart model Thomas model Yoon–Nelson model
qAB
(mg/l)
KAB
(ml/mg.min)
R2 qTh
(mg/g)
KTh
(ml/mg.min)
R2 τ (Min) τexp
(Min)
KYN
(Min-1)
20 Pb 70.4 3426 4053 0.0756 0.982 70.3 0.0972 0.990 3516 3518 0.0019
50 84.9 4133 5002 0.0727 0.935 86.4 0.0942 0.994 1728 1697 0.0047
100 95.5 4651 6108 0.0472 0.926 99.3 0.0662 0.980 993 955 0.0066
20 Cd 36.1 1756 2080 0.2001 0.924 36.9 0.2486 0.985 1847 1803 0.0050
50 43.2 2105 2803 0.0758 0.956 43.2 0.1147 0.995 864 864 0.0057
100 49.2 2394 3418 0.0485 0.955 48.9 0.0801 0.982 489 492 0.008
20 Cr 27.6 1342 1655 0.1538 0.983 27.7 0.2070 0.987 1384 1378 0.0041
50 35.2 1713 2290 0.0921 0.948 34.8 0.1429 0.988 696 703 0.0071
100 40.8 1985 2795 0.0660 0.912 41.4 0.1030 0.981 414 408 0.1030
20 Zn 21.7 1055 1489 0.1249 0.932 21.8 0.2028 0.998 1088 1083 0.0041
50 36.5 1776 2714 0.0590 0.924 36.8 0.1048 0.993 637 730 0.0052
100 48.1 2344 3771 0.0356 0.918 47.1 0.0711 0.986 471 481 0.0071
20 Ni 18.6 907 1158 0.2277 0.954 18.7 0.3251 0.997 934 932 0.0065
50 25.3 1232 1751 0.1075 0.920 25.8 0.1700 0.995 517 506 0.0085
100 29.8 1450 2560 0.0428 0.923 29.2 0.0926 0.994 292 298 0.0093
The BDST model
The BDST model was applied to estimate the design parameters such as bed depth and breakthrough time (tb) of fixed-bed column. This model was revised by Hudchins from the Bohart-Adams model, stating that molecules are directly adsorbed onto the adsorbent surface and the forces of intra-particle diffusion and external mass transfer are negligible24.
tb=N0C0U0Z- 1K0C0LnC0Ct-1                                     (14)

Where t (min) is the breakthrough time of bed column, Z (cm) is the bed depth of adsorbent, N0 (mg/L) is the column adsorption capacity, K0 [L/(mg.min)] is the rate constant, C0 (mg/L) is the influent concentration, Ct (mg/L) is the effluent concentration, and U0 (cm/min) is the linear flow velocity.
At three different experimental conditions, bed depths, flow rates, and influent adsorbent concentration were investigated to determine the model parameters (rate constant, K0 and adsorption capacity, N0). Figure 6 explains the relationship between the service time and bed depth of column for breakthrough time (tb) and exhaustion time (te) with R2 values ranging > 0.998, > 0.997, > 0.999, > 0.983, and > 0.999 for Pb, Cd, Cr, Zn, and Ni, respectively.
Table 12 shows the values of experimental adsorption capacity qexp, modeling adsorption capacity N0, the rate constant K0, and R2 that result from the BDST model. It approved that increasing bed depth and influent concentration increase the adsorption capacity N0 and decrease the rate constant K0. In contrast, an increase in flow rate decreased the adsorption capacity and increased the rate constant K0. These results of modeling are consistent with the study by (Kapur. M & Mondal. MK) 34. Table 12 shows that the BDST model was compatible to the experimental value where the values of linear correlation factor (R2), AAD, ∆q, and Chi-square ranged from 0.9947 to 0.998, 0.6353 to 2.6716, 0.0261 to 0.2280, and 0.8506 to 28.9217, respectively for all experiments of heavy metals.
Finally, the rank of the applied models was Yoon-Nelson > Thomas > BDST, where all values of R2 were more than 0.9, and the most suitable model for experimental data was the Yoon-Nelson model, since Table 13 displays that it has the highest R2 value and lowest values of deviation. The Adam-Bohart was the least suitable model because it was suitable only for the determined range of the C0/Ct and was equal to or less than < 0.7 in this study.

Figure6: The time of breakthrough point and exhaustion obtained from BDST model

Table 12: BDST model parameters of heavy metals at different bed depths, flow rates, and concentrations
Heavy
metals
Experimental conditions
Bed depth (cm) 22 30 38 22 22 22 22
Influentconcentration
(ppm)
20 20 20 20 20 50 100
Flow rate (ml/min) 1.0 1.0 1.0 0.5 2.0 1.0 1.0
BDST model parameters
Pb qexp. (mg/l) 3246 3883 4144 3796 2867 4133 4651
N0 (mg/l) 3425 3898 4177 3816 2887 4208 4836
K0 (ml/mg.min) 0.097 0.081 0.072 0.078 0.189 0.094 0.066
R2 0.990 0.995 0.998 0.997 0.997 0.994 0.980
Cd qexp. (mg/l) 1756 2125 2382 1967 1354 2105 2394
N0 (mg/l) 1799 2126 2386 1991 1376 2104 2383
K0 (ml/mg.min) 0.249 0.149 0.107 0.094 0.443 0.115 0.080
R2 0.985 0.996 0.990 0.997 0.995 0.995 0.982
Cr qexp. (mg/l) 1342 1492 1596 1468 960 1713 1985
N0 (mg/l) 1348 1494 1603 1477 962 1694 2018
K0 (ml/mg.min) 0.207 0.179 0.139 0.150 0.438 0.143 0.103
R2 0.987 0.996 0.993 0.997 0.997 0.988 0.992
Zn qexp. (mg/l) 1055 1234 1479 1201 846 1776 2344
N0 (mg/l) 1060 1242 1507 1203 851 1794 2293
K0 (ml/mg.min) 0.203 0.180 0.155 0.114 0.445 0.105 0.071
R2 0.998 0.997 0.995 0.996 0.991 0.993 0.986
Ni qexp. (mg/l) 907 1037 1184 952 800 1232 1450
N0 (mg/l) 909 1037 1200 950 804 1258 1423
K0 (ml/mg.min) 0.325 0.198 0.152 0.154 0.689 0.170 0.093
R2 0.997 0.996 0.994 0.989 0.996 0.995 0.994
Table 13: Results of error analysis for Adams–Bohart, Thomas, Yoon–Nelson, and BDST models
Parameters Adam-Bohart Thomas
Pb Cd Zn Cr Ni Pb Cd Zn Cr Ni
AAD 19.748 25.083 41.468 41.904 56.669 1.206 0.871 0.959 0.694 0.938
∆q 1.211 1.136 2.165 4.753 5.687 0.038 0.091 0.091 0.025 0.062
Chi-square 1218.81 1041.61 2097.28 2960.22 3435.93 0.19 0.035 0.036 0.016 0.027
R2 0.792 0.794 0.936 0.460 0.7684 0.997 0.998 0.999 0.998 0.995
Parameters Yoon-Nelson BDST
Pb Cd Zn Cr Ni Pb Cd Zn Cr Ni
AAD 1.175 0.868 2.672 0.625 0.935 2.672 1.035 1.039 0.635 0.895
∆q 0.036 0.100 0.0835 0.027 0.057 0.228 0.100 0.084 0.026 0.056
Chi-square 2.894 1.853 13.126 0.379 0.784 28.922 2.522 1.951 0.851 1.297
R2 1.000 0.999 0.999 1.000 0.999 0.985 0.998 0.998 0.998 0.995
Comparison of adsorption capacity
Remediating the industrial solid waste and recycling to adsorbent materials for the removal of heavy metals should possess several specifications, including effective for the adsorption of a broad number of heavy metals, low cost, easily
disposed of after adsorption or regeneration, and eco-friendly.

There is no study utilizing oily industrial solid waste as a green and new adsorbent, and the RBCW was more available, cost-effective, eco-friendly, and had high adsorption capacity compared to the determined conventional adsorbents in Table 14. It was approved that RBCW is sufficient as a novel adsorbent to remove the heavy metals via the fixed bed depth column system.
Table 14: Previous studies for comparison according to the adsorption capacity
Adsorbent Adsorbate Flow rate
(ml/min)
Bed depth
(cm)
Influent concentration
(ppm)
Diameter of column
(cm2)
Adsorbent mass
(g)
qm (mg/g) Reference
Modified beer lees Pb (II)
Zn (II)
1 ----- 30
15
----- 4 29.6
5.43
(26)
Calcined clay Pb (II)
Cd (II)
Cr (II)
5.6 4 100 1.5 ----- 28.6
21.4
14.2
(35)
PAMAM/CNT nanocomposite* Zn (II) 3 12 100 ----- ----- 462 (36)
Modified A. barbadensis Miller leaves Ni (II) 10 6 20 2 3 14.4 (37)
Waste tea factory Ni (II) 10 30 100 2 10.5 13.6 (38)
Dead calcareous skeletons Cd (II)
Pb (II)
10 1.1 100 4.4 20 20.5
44.1
(39)
RBCW Pb (II)
Cd (II)
Cr (II)
Zn (II)
Ni (II)
1 ----- 20 1.1 1 70.4
36.1
27.6
21.7
18.6
This study
*- Carbon Nanotubes (CNTs) coated Poly amidoaminedendrimer (PAMAM).
Conclusion
In this study, recycling of bentonite waste as a low-cost adsorbent for removing the heavy metals from an aqueous solution has advantages on the industrial and environmental issues. From the experimental results of RBCW characteristics and heavy metal adsorption in the bed depth column system, it can be concluded that
1- The RBCW can be utilized in the practical application of industrial wastewater treatment by batch and dynamic flow methods with a wide range of parameters, influent concentration, flow rate, and bed depth that have a role in the adsorption capacity.
2- Increasing bed depth increases adsorption capacity, removal efficiency, surface time, and MTZ. Increasing influent concentration increases adsorption capacity and MTZ and decreases removal efficiency and surface time. Increasing flow rate increases MTZ and decreases adsorption capacity, removal efficiency, and surface time.
3- The adsorption capacity of dominant parameters, flow rate, influent concentration, and depth bed (1 mL/min, 20 ppm, and 22 cm) for Pb, Cd, Cr, Zn, and Ni are 70.36, 36.05, 27.55, 21.67 and 18.63 mg/g, respectively.
4- The adsorption on the RBCW surface was more for Pb ion and less for Ni ion due to the electrochemical properties such as ionic radius, softness value, and hydration energy.
5-The coefficient of determination (R2) of breakthrough curves of Adams-Bohart was less than < 0.9, while for other models was more than > 0.9, and the Yoon-Nelson model was more compatible with experimental data due to higher R2 and low deviation. The rank of models was Yoon-Nelson > Thomas > BDST >Adams-Bohart.

Acknowledgement
The authors thank the laboratory members of the Directorate of Al-Qadissiyeah Environment – Ministry of Environment –Iraq for their valuable support.

Funding
No funding

Conflict of interest
The authors declare that they have no conflict of interest.

This is an Open-Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 4.0) license, which permits others to distribute, remix, adapt, and build upon this work for commercial use.

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Type of Study: Original articles | Subject: Environmental Health, Sciences, and Engineering
Received: 2023/05/19 | Accepted: 2023/07/10 | Published: 2023/09/30

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