# Factorial Design Statistical Analysis and Optimization of the Adsorptive Removal of COD from Olive Mill Wastewater Using Sugarcane Bagasse as a Low-Cost Adsorbent

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## Abstract

**:**

^{5−1}fractional factorial design of experiments was used to obtain the optimum conditions for each parameter that influence the adsorption process. The influence of the concentration of sugarcane bagasse, solution pH, reaction time, temperature, and agitation speed on the percent of COD removal were considered. The design experiment describes a highly significant second-order quadratic model that provided a high removal rate of 55.07% by employing optimized factors, i.e., a temperature of 60 °C, an adsorbent dose of 10 g/L, a pH of 12, a contact time of 1 h, and a stirring speed of 80 rpm. The experimental data acquired at optimal conditions were confirmed using several isotherms and kinetic models to assess the solute interaction behavior and kind of adsorption. The results indicated that the experimental data were properly fitted with the pseudo-first-order kinetic model, whereas the Langmuir model was the best model for explaining the adsorption equilibrium.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. OMW Sample

_{2})/L, a conductivity of 15.3 ms/cm, a phenolic content of 15.29 g/L and a pH of 4.27. The supplied effluent was immediately kept refrigerated at −4 °C to prevent any alteration in its physicochemical characteristics.

#### 2.2. Sugarcane Bagasse Material

^{−1}with 2 cm

^{−1}resolution. Therefore, X-ray fluorescence analysis was employed to investigate the chemical composition of the adsorbent using the “Axion” spectrometer.

#### 2.3. Batch Adsorption Experiments

_{max}) was 620 nm for this measurement. The quantity adsorbed and the removal efficiency of COD were calculated by measuring the solution’s concentration before and after adsorption using the following equations:

_{e}is the amount of COD removed by the adsorbent (mg/g); C

_{o}and C

_{e}are, respectively, the concentrations of COD before and after the batch adsorption study (mg/L); m is the mass of sugarcane bagasse (g); and V is the volume of the solution (L).

^{2}), adjusted determination coefficient (adj-R

^{2}), reduced chi-square (red-χ

^{2}), and Bayesian information criterion (BIC). A model with a higher adj-R

^{2}value, lower red-χ

^{2}and BIC value indicates a better fitting than the others [25].

_{i,exp}is the experimental adsorbed capacity value; q

_{i,model}is the modeled value; q

_{i,exp–mean}is an average of q

_{i,exp}values used for modelling; N is the number of experimental points; P is the number of model parameters; and DOF is the degrees of freedom.

#### 2.4. Experimental Design

^{5−1}fractional factorial design were conducted randomly to study the influence of the experimental variables on the percentage of COD removal (% Rem). The studied factors which are focused on this research; sugarcane bagasse dose (X

_{1}), solution pH (X

_{2}), contact time (X

_{3}), stirring speed (X

_{4}) and temperature (X

_{5}). Table 1 shows the five experimental variables and their chosen levels. After performing batch experiments for the optimization process, the regression analysis was conducted to attain the study’s statistical parameters with 95% confidence intervals using the Minitab 18 statistical software. The variance of the regression equation (mathematical relation between dependent and independent variables) is the most important analysis by the ANOVA method to find the desired function of COD adsorption. RSM is used as a sequential process to show the relation between the studied independent factors and the response to determine the set of optimal experimental parameters.

## 3. Results and Discussion

#### 3.1. Analysis of Factorial Design

^{5−1}Fractional factorial design was adopted using Minitab 18 to optimize the influence of the investigated parameters; sugarcane bagasse dose (X

_{1}), solution pH (X

_{2}), contact time (X

_{3}), stirring speed (X

_{4}) and temperature (X

_{5}) on the elimination of COD from OMW. This design yields in 16 experiments with all possible combinations of X

_{1}, X

_{2}, X

_{3}, X

_{4}and X

_{5}. COD removal efficiency (Y) was measured for each of these experiments as shown in Table 2. The response obtained was correlated using the second-order polynomial model, expressed by Equation (7):

_{0}+ b

_{1}X

_{1}+ b

_{2}X

_{2}+ b

_{3}X

_{3}+ b

_{4}X

_{4}+ b

_{5}X

_{5}+ b

_{12}X

_{1}X

_{2}+ b

_{13}X

_{1}X

_{3}+ b

_{14}X

_{1}X

_{4}+ b

_{15}X

_{1}X

_{5}+ b

_{23}X

_{2}X + b

_{24}X

_{2}X

_{4}

+b

_{34}X

_{3}X

_{4}+ b

_{25}X

_{2}X

_{5}+ b

_{35}X

_{3}X

_{5}+ b

_{45}X

_{4}X

_{5}

_{0}is a constant, bi correspond to linear coefficient of Xi, and bij is the interaction coefficient.

_{1}+ 0.39X

_{2}− 0.562X

_{3}+ 0.05958X

_{4}+ 0.2182X

_{5}− 0.01712X

_{1}X

_{3}− 0.0529X

_{1}X

_{3}+ 0.102X

_{1}X

_{4}− 0.0528X

_{1}X

_{5}− 0.05223X

_{2}X

_{3}− 0.01976X

_{2}X

_{4}− 0.01153X

_{2}X

_{5}− 0.003092X

_{3}X

_{4}− 0.00436X

_{3}X

_{5}− 0.000623X

_{4}X

_{5}

_{2}and X

_{4}factors and the X

_{1}X

_{4}interaction imply their positive effect on the response, while the negative signs of the coefficients for X

_{1}, X

_{3,}and X

_{5}factors as well as the X

_{1}X

_{2}, X

_{1}X

_{3}, X

_{1}X

_{5}, X

_{2}X

_{3}, X

_{2}X

_{5}, X

_{3}X

_{4}, X

_{3}X

_{5}, and X

_{4}X

_{5}interactions represent the negative effect on the response. Based on the equation, the most influential factor for response was the sugarcane bagasse dose with a coefficient value of 2.183. The sign (-) means that each one-point decrease will have an effect of 2.183 on the COD removal efficiency value.

_{1}, X

_{2}, X

_{3}, X

_{4}and X

_{5}factors as well as the X

_{2}X

_{3}, X

_{1}X

_{4}, X

_{3}X

_{5}, X

_{1}X

_{2}, X

_{3}X

_{4}, X

_{4}X

_{5}and X

_{1}X

_{3}interactions are statistically significant. In this way, the COD adsorption by sugarcane bagasse could be expressed using the following equation (Equation (9)):

_{1}+ 1.494 X

_{2}+ 1.387 X

_{3}− 0.0451 X

_{4}+ 0.4404 X

_{5}− 0.01712 X

_{1}X

_{2}

− 0.00497 X

_{1}X

_{3}+ 0.001892 X

_{1}X

_{4}− 0.09223 X

_{2}X

_{3}− 0.001131 X

_{3}X

_{4}− 0.01268 X

_{3}X

_{5}− 0.000743 X

_{4}X

_{5}

#### 3.2. Response Surface Analysis

_{2}) and contact time (X

_{3}) is shown in Figure 4A. The graph demonstrated that better COD removal is achieved at acidic pH and long contact time. Further, the % removal decreased from 39 to 30% with increasing pH. This can be explained by the impact of pH on the ionic configuration of the functional groups presented in the sorbent. Previous pH drift tests indicated that the pH

_{pzc}(point of zero charge) of sugarcane bagasse is equal to 5.0, which expresses that the surface of the bagasse is positively charged at a pH below 5 and negatively charged at a pH above 5 [21,27]. As a consequence, the electrostatic interaction between the adsorbent surface and the organic matter could be enhanced, which resulted in high adsorption of COD [28]. The interaction effect between the adsorbent dose (X

_{1}) and agitation speed (X

_{4}) shown in Figure 4B reveals that there will be a good COD removal equal to 44% when the adsorbent dose is 10 g/L and also at the stirring speed of 80 rpm. Nevertheless, an adsorbent dose greater than 10 g/L and an agitation speed above 80 rpm result in a substantial decrease in % removal. This phenomenon is due to the aggregation and glomeration of the sorbent particles and the reduction in the total surface area of the adsorbent [29].

_{5}) and reaction time (X

_{3}) on the % removal. The % removal increases with an increase in temperature, whereas it decreases with increasing contact time. There are more active surface sites when the temperature increases because the adsorbent swells more as well. This result suggests that the COD adsorption is an endothermic process [30]. As shown in Figure 4D, the interaction between the pH (X

_{2}) and adsorbent dose (X

_{1}) has a negative effect on % removal. An increase in either of these two parameters reduces the COD removal efficiency. The possible reason for such observations is that the changes in pH could lead to changes in the properties of the surface of adsorbent [31], and the agglomeration of the adsorbate particles occurs with an increase in the adsorbent dose. In Figure 4E, the % removal decreased with increasing contact time (X

_{3}) and stirring speed (X

_{4}). The % removal was very rapid in the beginning stages of contact time, reaching about 38%. This result was related to the availability of more active sites on the adsorbent and the fact that the gradient of concentration between the adsorbate molecules in the solution and the adsorbate molecules on the adsorbent is high, which improves COD diffusion to the adsorbent surface [32,33]. After 60 min, the removal decreases over time due to adsorption site saturation, and the adsorbate molecules may bind poorly to the active receptors on the adsorbent [34,35].

_{1}) and contact time (X

_{3}) (Figure 4G). The % removal is initially higher and more rapid, reaching up to more than 38% within the first 60 min and 10 g/L, which could be attributed to the greater availability of adsorption sites to bind COD and a greater adsorbent active sites/COD ratio [37]. Subsequently, it decreased slightly with the prolonging of the contact time and the increase in adsorbent dose, which could be caused by an aggregation of the adsorbent and the reduction of the surface area available to COD [20].

#### 3.3. Optimization Process

#### 3.4. Characterization of Sugarcane Bagasse

_{2}), as high as 62.23%, and low amounts of alkaline oxide, Al

_{2}O

_{3}and P

_{2}O

_{5}.

^{−1}indicate the presence of the O-H functional group and C–H stretching, respectively [20,38]. The peak at 1632 cm

^{−1}is assigned to C=O vibrations in hemicellulose [39]. These groups are thought to play a very important role in the process of adsorption [40]. The bands that appeared at wave numbers between 1471 cm

^{−1}and 1366 cm

^{−1}are related to C=C–H indicating several bands in cellulose and xylose [41]. The bands appeared at 1241 cm

^{−1}and 1029 cm

^{−1}can be attributed to the CH=CH stretching of lignin [39] and C-O stretching in cellulose and hemicellulose [42], respectively. The bands appeared at 640 and 593 cm

^{−1}in the FTIR spectra are attributed to the vibration of O-H groups out of the plane deformation [43].

#### 3.5. Adsorption Isotherms

_{e}) at equilibrium was analyzed by the models of Langmuir and Freundlich. The investigated adsorption isotherms for the COD adsorption on sugarcane bagasse are presented in Figure 7. Table 5 shows the calculated parameters for each of the sorption isotherm models obtained from non-linear regression forms. The best fit of the experimental data was analyzed based on R

^{2}, adj-R

^{2}, red-χ

^{2}and BIC. The obtained results displayed that the COD adsorption fitted well with the Langmuir isotherm model with the highest adj-R

^{2}of 0.994 and the lowest red-χ

^{2}and BIC values of 78.33 and 25.95, respectively. This result indicates that the adsorption process occurs on a homogeneous surface, and all adsorption sites are identical and energetically equivalent [44]. The maximum adsorption capacity (q

_{max}) of COD onto sugarcane bagasse was determined to be 331.92 mg/g from the Langmuir model.

_{max}value obtained in the present study is higher than that of other materials from previous studies. The q

_{max}value found in this study reveals a very good adsorption capacity of the sugarcane bagasse, which falls as a promising adsorbent.

#### 3.6. Kinetic Studies

^{2}value obtained from the pseudo-first order kinetic equation was found to be higher than that of pseudo-second order. In addition, the calculated q

_{e}value (337.45 mg/g) for the pseudo-first-order model is closer to the experimental value (326.29 mg/g) compared to the q

_{e}value (405.9 mg/g) calculated for the pseudo-second-order model. The pseudo-first-order model also presented the highest adj-R

^{2}(0.967), lowest red-χ

^{2}(467.41) and BIC (43.01) values. This result advises that the experimental data demonstrated the best fit to the pseudo-first order model, and its applicability also indicates that a physical process might control the sorption process.

## 4. Conclusions

^{1−5}fractional design associated to response surface methodology was successfully applied to optimize the effects of the operating variables of COD removal from OMW using the prepared adsorbent. The optimal conditions were found to be pH 12, the adsorbent dose of 10 g/L, a stirring speed of 80 rpm, a contact time of 1 h, and a temperature of 60 °C with a percentage of removal of 55.07% and a desirability close to 1. The experimental data are well correlated by the Langmuir isotherm model with an R

^{2}of 0.996, and the maximum sorption capacity of 331.92 mg/g under optimal conditions. The kinetic data of the COD removal process were properly fitted with the pseudo-first-order model instead of pseudo-second-order model.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Validation indicator plots of the model for the experiments (

**a**) Normal probability plot, (

**b**) Versus fits (

**c**) Histogram and (

**d**) Versus order.

Factors | Variable | Unit | Levels | |
---|---|---|---|---|

Low (−) | High (+) | |||

X_{1} | Adsorbent dose | g/L | 10 | 60 |

X_{2} | pH | - | 2 | 12 |

X_{3} | Contact time | h | 1 | 24 |

X_{4} | Stirring speed | rpm | 80 | 300 |

X_{5} | Temperature | °C | 25 | 60 |

N° | X_{1} | X_{2} | X_{3} | X_{4} | X_{5} | Y (Experimental) | Y (Predicted) |
---|---|---|---|---|---|---|---|

1 | −1 | −1 | −1 | −1 | +1 | 36.39 | 37.46 |

2 | 1 | −1 | −1 | −1 | −1 | 41.26 | 43.47 |

3 | −1 | 1 | −1 | −1 | −1 | 54.27 | 51.69 |

4 | 1 | 1 | −1 | −1 | +1 | 44.69 | 43.75 |

5 | −1 | −1 | 1 | −1 | −1 | 35.24 | 35.54 |

6 | 1 | −1 | 1 | −1 | +1 | 42.40 | 43.24 |

7 | −1 | 1 | 1 | −1 | +1 | 35.53 | 30.66 |

8 | 1 | 1 | 1 | −1 | −1 | 41.23 | 40.85 |

9 | −1 | −1 | −1 | 1 | −1 | 40.71 | 40.53 |

10 | 1 | −1 | −1 | 1 | +1 | 42.12 | 43.90 |

11 | −1 | 1 | −1 | 1 | +1 | 33.73 | 32.73 |

12 | 1 | 1 | −1 | 1 | −1 | 39.82 | 39.12 |

13 | −1 | −1 | 1 | 1 | +1 | 33.23 | 29.86 |

14 | 1 | −1 | 1 | 1 | −1 | 31.12 | 34.75 |

15 | −1 | 1 | 1 | 1 | −1 | 39.25 | 38.14 |

16 | 1 | 1 | 1 | 1 | +1 | 42.12 | 41.79 |

Source | DF | Adj SS | Adj MS | F-Value | p-Value |
---|---|---|---|---|---|

Model | 16 | 3214.58 | 200.912 | 22.24 | 0.000 |

Linear | 5 | 881.04 | 176.207 | 19.51 | 0.000 |

X_{1} | 1 | 224.88 | 224.876 | 24.90 | 0.000 |

X_{2} | 1 | 192.57 | 192.567 | 21.32 | 0.000 |

X_{3} | 1 | 146.82 | 146.823 | 16.25 | 0.001 |

X_{4} | 1 | 260.52 | 260.525 | 28.84 | 0.000 |

X_{5} | 1 | 56.25 | 56.245 | 6.23 | 0.025 |

Interactions | 10 | 2327.91 | 232.791 | 25.77 | 0.000 |

X_{1} × X_{2} | 1 | 146.54 | 146.538 | 16.22 | 0.001 |

X_{1} × X_{3} | 1 | 65.35 | 65.350 | 7.23 | 0.017 |

X_{1} × X_{4} | 1 | 865.84 | 865.839 | 95.86 | 0.000 |

X_{1} × X_{5} | 1 | 5.31 | 5.314 | 0.59 | 0.455 |

X_{2} × X_{3} | 1 | 900.00 | 899.998 | 99.64 | 0.000 |

X_{2} × X_{4} | 1 | 0.34 | 0.343 | 0.04 | 0.848 |

X_{2} × X_{5} | 1 | 5.26 | 5.260 | 0.58 | 0.457 |

X_{3} × X_{4} | 1 | 65.50 | 65.502 | 7.25 | 0.017 |

X_{3} × X_{5} | 1 | 208.31 | 208.306 | 23.06 | 0.000 |

X_{4} × X_{5} | 1 | 65.46 | 65.464 | 7.25 | 0.017 |

Error | 15 | 135.49 | 9.033 | ||

Total sum of squares | 31 | 3350.07 | |||

S square | R^{2} | R (^{2}ajust) | R (^{2}prev) | ||

6.2538 | 99.98% | 87.54% | 62.23% |

Composition | Concentration (%) |
---|---|

SiO_{2} | 62.23 |

SO_{3} | 24.00 |

CaO | 11.50 |

MgO | 0.68 |

Na_{2}O | 0.60 |

K_{2}O | 0.51 |

Al_{2}O_{3} | 0.28 |

P_{2}O_{5} | 0.1 |

Fe_{2}O_{3} | 0.10 |

**Table 5.**Parameters and error function data for sorption isotherm models obtained from non-linear regression forms.

Models | Equation ^{a} | Parameters | Values |
---|---|---|---|

Langmuir | ${\mathrm{q}}_{\mathrm{e}}=\frac{{\mathrm{q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathrm{K}}_{\mathrm{L}}{\mathrm{C}}_{\mathrm{e}}}{(1+{\mathrm{K}}_{\mathrm{L}}{\mathrm{C}}_{\mathrm{e}})}$ | qm (mg/g) | 331.92 |

K_{L} | 0.019 | ||

R^{2} | 0.996 | ||

Adj-R^{2} | 0.994 | ||

Red-χ^{2} | 78.33 | ||

BIC | 25.59 | ||

Freundlich | ${\mathrm{q}}_{\mathrm{e}}={\mathrm{K}}_{\mathrm{F}}{\mathrm{C}}_{\mathrm{e}}^{1/\mathrm{n}}$ | 1/n | 0.31 |

K_{F} | 51.13 | ||

R^{2} | 0.991 | ||

Adj-R^{2} | 0.985 | ||

χ^{2} | 208.11 | ||

BIC | 31.45 |

^{a}q

_{e}(mg/g): mass of adsorbed molecule per unit mass of sugarcane bagasse, C

_{e}(mg/L): concentration of no-adsorbed molecules, q

_{m}and K

_{L}are constants of the Langmuir model, and K

_{F}and n are constants of Freundlich isotherm model.

Adsorbent Types | q_{max} (mg/g) | Ref. |
---|---|---|

Sugarcane bagasse | 331.92 | This study |

Date-pit activated carbon | 252.81 | [14] |

Activated carbon | 41.3 | [17] |

Raw bagasse | 77.95 | [15] |

Bamboo-based activated carbon | 24.39 | [45] |

Areca Nut Husk | 64.94 | [46] |

**Table 7.**Parameters and error functions data for kinetic models studied obtained from non-linear regression forms.

Model | Equation ^{b} | Parameters | Value |
---|---|---|---|

Pseudo-first-order | ${\mathrm{q}}_{\mathrm{t}}={\mathrm{q}}_{\mathrm{e}}\left(1-{\mathrm{e}}^{-{\mathrm{k}}_{1}\mathrm{t}}\right)$ | q_{e.exp} (mg/g) | 326.92 |

q_{ecal} (mg/g) | 337.45 | ||

k_{1} | 0.20 | ||

R_{1}^{2} | 0.978 | ||

Adj-R^{2} | 0.967 | ||

χ^{2} | 467.41 | ||

BIC | 43.01 | ||

Pseudo-second-order | ${\mathrm{q}}_{\mathrm{t}}=\frac{{\mathrm{K}}_{2}{\mathrm{q}}_{\mathrm{e}}^{2}\mathrm{t}}{(1+{\mathrm{K}}_{2}{\mathrm{q}}_{\mathrm{e}}\mathrm{t})}$ | q_{ecal} (mg/g) | 405.9 |

k^{2} | 0.0006 | ||

R_{2}^{2} | 0.976 | ||

Adj-R^{2} | 0.964 | ||

χ^{2} | 503.52 | ||

BIC | 43.52 |

^{b}q

_{e}and q

_{t}(mg/g) are the amounts of COD removed at equilibrium and at time t, respectively; k

_{1}and k

_{2}are the adsorption rate constants.

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## Share and Cite

**MDPI and ACS Style**

Elayadi, F.; Achak, M.; Boumya, W.; Elamraoui, S.; Barka, N.; Lamy, E.; Beniich, N.; El Adlouni, C.
Factorial Design Statistical Analysis and Optimization of the Adsorptive Removal of COD from Olive Mill Wastewater Using Sugarcane Bagasse as a Low-Cost Adsorbent. *Water* **2023**, *15*, 1630.
https://doi.org/10.3390/w15081630

**AMA Style**

Elayadi F, Achak M, Boumya W, Elamraoui S, Barka N, Lamy E, Beniich N, El Adlouni C.
Factorial Design Statistical Analysis and Optimization of the Adsorptive Removal of COD from Olive Mill Wastewater Using Sugarcane Bagasse as a Low-Cost Adsorbent. *Water*. 2023; 15(8):1630.
https://doi.org/10.3390/w15081630

**Chicago/Turabian Style**

Elayadi, Fatima, Mounia Achak, Wafaa Boumya, Sabah Elamraoui, Noureddine Barka, Edvina Lamy, Nadia Beniich, and Chakib El Adlouni.
2023. "Factorial Design Statistical Analysis and Optimization of the Adsorptive Removal of COD from Olive Mill Wastewater Using Sugarcane Bagasse as a Low-Cost Adsorbent" *Water* 15, no. 8: 1630.
https://doi.org/10.3390/w15081630