#
The Dynamic Behaviour of a Binary Adsorbent in a Fixed Bed Column for the Removal of Pb^{2+} Ions from Contaminated Water Bodies

^{1}

^{2}

^{*}

## Abstract

**:**

_{Th}, decreased with increasing bed depth with the maximum amount of Pb adsorbed being 28.27 mg/g. With the Yoon–Nelson model, K

_{YN}decreased with an increase in τ as the bed height increased. In this study, a novel approach was adopted where the proposed methodology enabled the use of a bio-composite adsorbent in heavy metal removal. The findings of this research will aid in the design and optimisation of the pilot-scale operation of environmentally friendly treatment options for metal laden effluent.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Preparation of the Biosorbents

#### 2.2. Characterisation of the Biosorbents

#### 2.2.1. Fourier Transform Infrared (FTIR) Spectroscopy

^{−1}.

#### 2.2.2. Scanning Electron Microscopy (SEM)

#### 2.3. Batch Experiments

_{3})

_{2}in 1L deionised water. The stock solution was subsequently diluted to the required concentration using deionised water. All chemicals used in the experiments, 0.1 M NaOH and 0.1 M H

_{2}SO

_{4}(for pH adjustment) and 1N HNO

_{3}which was used to clean the glassware, were of analytical reagent grade and obtained from Sigma-Aldrich (St. Louis, MO, USA) chemical company.

_{2}SO

_{4}or 0.1 M NaOH. All experiments were conducted at room temperature. After each experiment, the glassware used was cleaned with deionised water followed by 1N HNO

_{3}. The supernatant solution was filtered using 0.45 µm syringe filters where a Varian Spectra AA 50B atomic absorption spectrophotometer (product of Spain) was used to determine the concentration of the samples. A calibration curve of Pb was plotted by measuring the absorbance at 283.3 nm for Pb at varying concentrations. Absorbance values with a standard deviation greater than 1% were discarded, and an average value was taken from the duplicate results.

_{o}(mg/L) is the initial metal ion concentration, C

_{t}(mg/L) is the metal ion concentration at time t, W(g) is the mass of the adsorbent used and V (L) is the volume of the solution.

#### 2.4. Fixed Bed Experiments

_{total}is the total flow time in min, and Q is the volumetric flowrate which circulates through the column in (mL/min).

_{total}, in mg, for a given feed concentration and flowrate which is determined by integrating the following Equation:

_{ad}= C

_{i}− C

_{e}is the adsorbed metal concentration in mg/L, t

_{total}is the total flow time in min, Q is the flowrate (mL/min) and A is the area under the breakthrough curve (cm

^{2}).

_{o}is the initial concentration in mg/L, Q is the flowrate in mL/min and t

_{total}is the total time in min.

_{u}is the breakthrough time in min, and t

_{t}is the total time in min. H

_{T}is the total length in cm.

_{adsorbed}to the total amount of adsorbate sent to the column m

_{total}as given by the following Equation:

_{adsorbed}is the total adsorbed quantity of adsorbate in g and m

_{total}is the total amount of adsorbate sent to the column in g.

_{b}is the capacity at breakthrough in mg/g and q

_{e}is the capacity at exhaustion in mg/g.

#### 2.5. Mathematical Modelling

#### 2.5.1. The Thomas Model

_{o}) which is represented by the linearised form as given below:

_{TH}is the Thomas rate constant (mL/mg.min), q

_{o}is the equilibrium adsorbate uptake (mg/g) and m is the adsorbate quantity (g). The k

_{TH}and q

_{o}values are calculated from slope and intercepts of linear plots of ln [(C

_{o}/C

_{t}) − 1] against t using values from the column experiments [35].

#### 2.5.2. The Yoon–Nelson Model

_{YN}is the rate constant (L/min) and τ is the time required for 50% of adsorbate breakthrough to occur. The values of K

_{YN}and τ are estimated from slope and intercepts of the linear graph between ln [C

_{t}/C

_{o}− C

_{t}] versus t at different operational conditions [35].

## 3. Results and Discussion

#### 3.1. Characterisation

#### 3.1.1. Fourier Transform Infrared (FTIR) Spectroscopy Analysis

^{−1}, 1736 cm

^{−1}, 1364 cm

^{−1}, 1217 cm

^{−1}, 1035 cm

^{−1}and 899 cm

^{−1}. A medium broadband peak was observed at 3345 cm

^{−1}due to hydroxyl groups, and the sharp peak at 1736 cm

^{−1}represents C=O carbonyl groups. The bands observed within the range of 1364 to 1035 cm

^{−1}were due to the C–O stretching vibration of cellulose, lignin and hemicellulose as supported by Gurgel et al. [27] and Putra et al. [37]. The minor peak at 899 cm

^{−1}was due to the glycosidic bond in cellulose. With eggshells (Figure 2b), the weak minor band at 1740 cm

^{−1}was characteristic of C=O stretching of carboxylic acid. The characteristic of C=O stretching at the above wavenumber was further discussed by Flores-Cano et al. [24,35]. The sharp absorption bands at 1405, 873 and 712 cm

^{−1}were characteristic of the mineral carbonate with the absorption band at 1405 cm

^{−1}characteristic of the C–O bond in the carbonate due to a stretching vibration. Moreover, the two sharp bands at 874 and 711 cm

^{−1}were due to the out-of-plane and in-plane deformation modes of carbonate, respectively.

^{−1}due to the hydroxyl groups present in bagasse were completely inhibited in the binary adsorbents. This revealed that when the adsorbents were combined, both adsorbents interacted with each other, altering the chemical structure and functional groups of the adsorbents. Bagasse is an acidic lignocellulosic material. When combined with an alkaline biomaterial such as eggshells, it is plausible that a reaction (i.e., a modification of the structure) occurs. The weak narrow bands observed at 1217cm

^{−1}due to the C–O stretching vibration of cellulose, lignin and hemicellulose were still visible but were less pronounced. Additionally, the sharp, narrow peaks observed in eggshells at 713, 874, 1411 and 1741 cm

^{−1}were still prominent in the binary adsorbents with the peaks being more pronounced with increasing eggshell content. This was indicative that the adsorbent combinations were rich in the mineral carbonate with the C=O stretching of carboxylic acid and the stretching vibration of the C–O bond together with the in-plane and out-of-plane deformation modes of carbonate, respectively.

#### 3.1.2. Scanning Electron Microscopy (SEM)

#### 3.2. Comparative Performance of the Adsorbents

#### 3.3. Breakthrough Curve Analysis

#### 3.4. Effect of Bed Height

#### 3.5. Bed Volumes (BV)

#### 3.6. Adsorption Exhaustion Rate (AER)

#### 3.7. Mass Transfer Zone (MTZ)

_{UNB}represents the length of bed unused in a column and is pivotal in column design since it represents the mass transfer zone (MTZ). When this value is small, it suggests that the breakthrough curve is close to an ideal step with negligible mass transfer resistance and no axial dispersion [43]. However, in reality, an ideal case is rarely achieved where the value of the mass transfer zone is zero. The closer the column is operated to the ideal case, the more efficient the MTZ [44]. It is common practice to stop a column’s operation once the breakthrough point is reached since this implies that the usefulness of a column has expired. However, it is necessary to continue operation until exhaustion to determine the length of the bed unused, H

_{LUB}, which is an important technical variable needed for the column scale-up which also affects the feasibility of the process [44].

_{LUB}/H

_{L}ratio of less than 1. The MTZ length (H

_{LUB}) for the adsorbent 1:3 and eggshells were relatively small in comparison to H

_{L}(Figure 5 and Table 2), highlighting that most of the bed had been used at breakpoint (H

_{L}> H

_{LUB}) which is indicative of an efficient process [45].

#### 3.8. Breakthrough Curve Modelling

#### 3.8.1. Application of the Thomas Model

_{Th}) and the maximum solid-phase concentration (q

_{o,th}) which were ascertained by linearising the data and calculating the parameters from this model. As the bed height of the adsorbents increased, the values of the kinetic constant, K

_{Th,}decreased for all adsorbents concerned. In other words, a shorter contact time was required for adsorbent–adsorbate interactions to occur since there was a greater quantity of adsorbent particles available to adsorb the solute. Upon comparison between the experimental data (q

_{o,exp}) and the maximum capacity from the model (q

_{o,th}), there was a very close agreement between both values, highlighting that this model was a good fit as seen from the coefficients of determination (R

^{2}), most of which were found to be >0.9, indicating the goodness of fit. Supporting this, the work of Malkoc et al. [41] showed a negligible difference between experimental and predicted values of the bed capacity suggesting that the Thomas model is valid.

#### 3.8.2. Application of the Yoon–Nelson Model

_{YN}and τ, for the model. As shown in Table 4, K

_{YN}decreased and τ increased as the bed height increased for all adsorbents concerned. As the mass of the adsorbents increased, there were more available adsorbent particles in the column to interact with, and hence a longer time was required to reach 50% breakthrough. In addition, by increasing the mass, a larger number of particles was available for adsorption to occur, requiring a shorter contact time for adsorbent–adsorbate interactions. Upon comparison between the experimental times (τ

_{,exp}) and the calculated times from the Yoon–Nelson model (τ

_{,th}), there was a relatively good agreement between both values, highlighting that this model was a good fit as seen from the correlation coefficients (R

^{2}). The work of Zhang et al. [48] supported these results with the correlation coefficients R

^{2}being fairly close to 1 and the theoretical model matching the experimental data well. For this study, the Yoon–Nelson model was adequate in the description of the adsorption of Pb removal since the fixed bed experiments investigated a single-solute system. However, it should be noted that when dealing with multi-component systems, this model is not advisable since it is developed for single-solute systems. On the contrary, when estimates are required on the breakthrough times without physical information given on the adsorbent, the ease of use of this model makes it an ideal choice since it has a simple form when compared to other models as detailed data concerning the character of adsorbate–adsorbent interactions and parameters of the fixed bed are not required [49]. RMSE and MAE were used to analyse the variation in error of the experimental data against the Yoon–Nelson model. The RMSE and MAE values obtained were very low, highlighting the good fit between the model and experimental data. The RMSE values calculated were <0.06 and the MAE values <0.03.

## 4. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Effect of bed depth on the breakthrough curves of bagasse (

**a**), adsorbent 3:1 (

**b**), adsorbent 1:1 (

**c**), adsorbent 1:3 (

**d**) and eggshells (

**e**) (F = 4 ml/min, Co = 100 mg/L, pH = 5.5).

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**Figure 3.**SEM images of (

**a**) sugarcane bagasse, (

**b**) adsorbent 1:3, (

**c**) adsorbent 1:1, (

**d**) adsorbent 3:1 and (

**e**) eggshells of 1 µm at a magnification of 50,000.

**Figure 5.**Effect of bed depth on the length of unused bed (MTZ). (

**a**) Bed depth of 4 cm, (

**b**) bed depth of 8 cm, (

**c**) bed depth of 12 cm.

Bagasse | Adsorbent 1:3 | Adsorbent 1:1 | Adsorbent 3:1 | Eggshells | |
---|---|---|---|---|---|

Bagasse | 100% | 75% | 50% | 25% | - |

Eggshells | - | 25% | 50% | 75% | 100% |

$\mathbf{A}\mathbf{d}\mathbf{s}\mathbf{o}\mathbf{r}\mathbf{b}\mathbf{e}\mathbf{n}\mathbf{t}$ | ${\mathbf{t}}_{\mathbf{b}}\left(\mathbf{m}\mathbf{i}\mathbf{n}\right)$ | ${\mathbf{t}}_{\mathbf{e}}\left(\mathbf{m}\mathbf{i}\mathbf{n}\right)$ | ${\mathbf{H}}_{\mathbf{T}}\left(\mathbf{c}\mathbf{m}\right)$ | ${\mathbf{H}}_{\mathbf{L}}\left(\mathbf{c}\mathbf{m}\right)$ | ${\mathbf{H}}_{\mathbf{L}\mathbf{U}\mathbf{B}}\left(\mathbf{c}\mathbf{m}\right)$ | $\mathbf{\%}\mathbf{R}$ | ${\mathbf{V}}_{\mathbf{b}}\left(\mathbf{m}\mathbf{L}\right)$ | $\mathsf{\eta}$ | $\frac{{\mathbf{H}}_{\mathbf{L}\mathbf{U}\mathbf{B}}\left(\mathbf{c}\mathbf{m}\right)}{{\mathbf{H}}_{\mathbf{L}}\left(\mathbf{c}\mathbf{m}\right)}$ | ${\mathbf{q}}_{\mathbf{e}}\left(\frac{\mathbf{m}\mathbf{g}}{\mathbf{g}}\right)$ | $\mathbf{B}\mathbf{V}$ | $\mathbf{A}\mathbf{E}\mathbf{R}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Bagasse | 90 | 201 | 4 | 1.79 | 2.21 | 48 | 240 | 45 | 0.55 | 21.05 | $22$ | 4.75 |

210 | 435 | 8 | 3.82 | 4.18 | 56 | 600 | 48 | 0.52 | 22.77 | 25 | 4.39 | |

540 | 830 | 12 | 7.81 | 4.19 | 66 | 1200 | 65 | 0.35 | 28.97 | 43 | 3.45 | |

Adsorbent 3:1 | 90 | 242 | 4 | 1.49 | 2.51 | 45 | 240 | 37 | 0.63 | 12.32 | 21 | 8.12 |

270 | 585 | 8 | 3.69 | 4.31 | 65 | 600 | 46 | 0.54 | 14.90 | 31 | 6.70 | |

540 | 915 | 12 | 7.08 | 4.92 | 66 | 1200 | 59 | 0.41 | 15.53 | 41 | 6.44 | |

Adsorbent 1:1 | 210 | 477 | 4 | 1.76 | 2.24 | 61 | 480 | 44 | 1.27 | 15.57 | 48 | 6.22 |

420 | 925 | 8 | 3.63 | 4.37 | 67 | 1020 | 45 | 1.20 | 15.80 | 48 | 6.42 | |

780 | 1408 | 12 | 6.65 | 5.35 | 71 | 2160 | 55 | 0.80 | 16.06 | 59 | 6.32 | |

Adsorbent 1:3 | 540 | 1188 | 4 | 1.82 | 2.18 | 73 | 1680 | 45 | 1.20 | 27.95 | 122 | 3.35 |

1860 | 2385 | 8 | 6.24 | 1.76 | 78 | 4560 | 78 | 0.28 | 29.85 | 210 | 3.34 | |

2700 | 3336 | 12 | 9.71 | 2.29 | 91 | 6960 | 81 | 0.24 | 29.98 | 212 | 3.58 | |

Eggshells | 540 | 1071 | 4 | 2.02 | 1.98 | 71 | 1680 | 50 | 0.98 | 21.11 | 121 | 4.65 |

1380 | 2105 | 8 | 5.24 | 2.76 | 78 | 3120 | 66 | 0.53 | 21.48 | 155 | 4.74 | |

2340 | 3303 | 12 | 8.5 | 3.5 | 90 | 5520 | 71 | 0.41 | 22.08 | 175 | 4.53 |

Adsorbent | Bed Height | ${\mathbf{K}}_{\mathbf{t}\mathbf{h}}\left(\frac{\mathbf{L}}{\mathbf{m}\mathbf{g}\xb7\mathbf{m}\mathbf{i}\mathbf{n}}\right)$ | ${\mathbf{q}}_{\mathbf{o},\mathbf{t}\mathbf{h}}\left(\frac{\mathbf{m}\mathbf{g}}{\mathbf{g}}\right)$ | ${\mathbf{q}}_{\mathbf{e}\mathbf{x}\mathbf{p}}\left(\frac{\mathbf{m}\mathbf{g}}{\mathbf{g}}\right)$ | R^{2} | RMSE | MAE |
---|---|---|---|---|---|---|---|

Bagasse | 4 cm | 5.29 × 10^{−4} | 20.48 | 21.05 | 0.962 | 0.034 | 0.009 |

8 cm | 2.67 × 10^{−4} | 20.57 | 22.77 | 0.856 | 0.068 | 0.020 | |

12 cm | 1.47 × 10^{−4} | 28.90 | 28.97 | 0.978 | 0.033 | 0.003 | |

Adsorbent 3:1 | 4 cm | 3.55 × 10^{−4} | 12.44 | 12.32 | 0.9087 | 0.029 | 0.004 |

8 cm | 1.85 × 10^{−4} | 14.65 | 14.91 | 0.9155 | 0.039 | 0.001 | |

12 cm | 1.35 × 10^{−4} | 16.03 | 15.54 | 0.9486 | 0.037 | 0.010 | |

Adsorbent 1:1 | 4 cm | 2.42 × 10^{−4} | 14.99 | 16.06 | 0.890 | 0.047 | 0.019 |

8 cm | 1.35 × 10^{−4} | 15.00 | 15.57 | 0.9108 | 0.028 | 0.005 | |

12 cm | 5.29 × 10^{−4} | 16.06 | 15.80 | 0.9881 | 0.030 | 0.007 | |

Adsorbent 1:3 | 4 cm | 1.10 × 10^{−4} | 27.79 | 28.05 | 0.9482 | 0.078 | 0.013 |

8 cm | 8.20 × 10^{−4} | 22.16 | 29.95 | 0.884 | 0.080 | 0.036 | |

12 cm | 6.0 × 10^{−5} | 28.23 | 34.26 | 0.9265 | 0.048 | 0.017 | |

Eggshells | 4 cm | 1.27 × 10^{−4} | 21.48 | 20.33 | 0.9676 | 0.065 | 0.010 |

8 cm | 6.7 × 10^{−5} | 21.11 | 20.69 | 0.9828 | 0.021 | 0.000 | |

12 cm | 4.5 × 10^{−5} | 22.08 | 21.51 | 0.9804 | 0.036 | 0.001 |

Adsorbent | Bed Height | ${\mathsf{\tau}}_{\mathbf{exp}}$ $\left(\mathbf{m}\mathbf{i}\mathbf{n}\right)$ | ${\mathsf{\tau}}_{\mathbf{th}}$ $\left(\mathbf{m}\mathbf{i}\mathbf{n}\right)$ | ${\mathbf{K}}_{\mathbf{Y}\mathbf{N}}\left(\mathbf{m}\mathbf{i}{\mathbf{n}}^{-1}\right)$ | R^{2} | RMSE | MAE |
---|---|---|---|---|---|---|---|

Bagasse | 4 cm | 202 | 196 | 1.36 × 10^{−2} | 0.962 | 0.034 | 0.009 |

8 cm | 284 | 366 | 2.73 × 10^{−2} | 0.769 | 0.058 | 0.002 | |

12 cm | 800 | 877 | 5.29 × 10^{−2} | 0.979 | 0.027 | 0.006 | |

Adsorbent 3:1 | 4 cm | 242 | 263 | 2.95 × 10^{−2} | 0.895 | 0.058 | 0.032 |

8 cm | 585 | 575 | 1.85 × 10^{−2} | 0.916 | 0.039 | 0.001 | |

12 cm | 915 | 944 | 1.35 × 10^{−2} | 0.949 | 0.037 | 0.010 | |

Adsorbent 1:1 | 4 cm | 413 | 445 | 1.92 × 10^{−2} | 0.890 | 0.047 | 0.019 |

8 cm | 925 | 890 | 1.29 × 10^{−2} | 0.913 | 0.027 | 0.005 | |

12 cm | 1408 | 1427 | 8.40 × 10^{−3} | 0.985 | 0.048 | 0.017 | |

Adsorbent 1:3 | 4 cm | 1188 | 1106 | 1.10 × 10^{−2} | 0.948 | 0.078 | 0.013 |

8 cm | 2385 | 2246 | 8.20 × 10^{−3} | 0.884 | 0.08 | 0.036 | |

12 cm | 877 | 3374 | 6.00 × 10^{−3} | 0.927 | 0.048 | 0.017 | |

Eggshells | 4 cm | 1071 | 1024 | 1.26 × 10^{−2} | 0.971 | 0.060 | 0.006 |

8 cm | 2106 | 2106 | 6.20 × 10^{−3} | 0.968 | 0.024 | 0.011 | |

12 cm | 3304 | 3262 | 4.20 × 10^{−3} | 0.945 | 0.039 | 0.008 |

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## Share and Cite

**MDPI and ACS Style**

Harripersadth, C.; Musonge, P.
The Dynamic Behaviour of a Binary Adsorbent in a Fixed Bed Column for the Removal of Pb^{2+} Ions from Contaminated Water Bodies. *Sustainability* **2022**, *14*, 7662.
https://doi.org/10.3390/su14137662

**AMA Style**

Harripersadth C, Musonge P.
The Dynamic Behaviour of a Binary Adsorbent in a Fixed Bed Column for the Removal of Pb^{2+} Ions from Contaminated Water Bodies. *Sustainability*. 2022; 14(13):7662.
https://doi.org/10.3390/su14137662

**Chicago/Turabian Style**

Harripersadth, Charlene, and Paul Musonge.
2022. "The Dynamic Behaviour of a Binary Adsorbent in a Fixed Bed Column for the Removal of Pb^{2+} Ions from Contaminated Water Bodies" *Sustainability* 14, no. 13: 7662.
https://doi.org/10.3390/su14137662