## Abstract

Response surface methodology (RSM) is used to optimize the electrocoagulation/electro-flotation process applied for the removal of turbidity from surface water in an internal loop airlift reactor. Two flat aluminium electrodes are used in monopolar arrangement for the production of coagulants. The central composite design is used as a second-order mathematical model. The model describes the change of the measured responses of turbidity removal efficiency and energy consumption according to the initial conductivity (*X*_{1}), applied voltage (*X*_{2}), treatment time (*X*_{3}) and inter-electrode distance (*X*_{4}). The evaluation of the model fit quality is done by analysis of variance (ANOVA). Fisher's F-test is used to provide information about the linear, interaction and quadratic effects of factors. Multicriteria methodology, mainly the desirability function (*D*), is used to determine optimal conditions. The results show that, for a maximal desirability function *D* = 0.79, optimal conditions estimated are *X*_{1} = 1,487 μS/cm, *X*_{2} = 5 V, *X*_{3} = 6.5 min, *X*_{4} = 14 mm. The corresponding turbidity removal rate and energy consumption are 84.15% and 0.215 kWh/m^{3} respectively. A confirmation study is then carried out at laboratory scale using the optimal conditions estimated. The results show a turbidity removal rate of 72.05% and an energy consumption of 0.210 kWh/m^{3}.

## INTRODUCTION

Surface waters are used for the production of drinking water. However, the presence of many undesirable agents such as silts, clays, and algae causes them to become turbid and makes them unsuitable for human consumption. These particles have a small size ranging from 0.1 to 0.01 μm (Moussa *et al.* 2016; Naje *et al.* 2016) and remain suspended in water. Therefore, agglomeration of particles into a larger floc is a necessary step for their removal by flotation or sedimentation. A chemical coagulation/flocculation (CC/F) process is often used for destabilization and agglomeration of suspended particles by the addition of salts (i.e. alum). This method has some drawbacks like handling large quantities of chemicals, proper assessment of requirements, feeding of chemicals and production of a large volume of sludge causing a disposal problem and loss of water (Paul 1996). The regulations for drinking water, as well as for wastewater discharge, and new environmental considerations have allowed electrochemical technologies to gain an important place worldwide during the past two decades (Chen 2004). These technologies are characterized by low sludge production, and do not require the addition of chemical reagents.

Electrocoagulation/electro-flotation (E_{C}/E_{F}) is an electrochemical technology which allows the generation of coagulants *in situ* by electrodissolution of a soluble anode. Metal ions (Al^{3+}, Fe^{2+} or Fe^{3+}) are generated at the anode while hydrogen gas bubbles are produced at the cathode. E_{C}/E_{F} has numerous advantages and some drawbacks as reported by many authors (Mouedhen *et al.* 2008; Zaroual *et al.* 2009; Khandegar & Saroha 2013). The electrode arrangement can be in a monopolar or bipolar mode (Kobya *et al.* 2011). Chemical reactions when aluminium is used as an electrode material are as follows.

- In the case of high anode potential, secondary reactions may occur (Hakizimana
*et al.*2017). This is the case of oxygen gas formation:

E_{C}/E_{F} efficiency is a function of three fundamental processes: electrochemical (electrolytic reactions at the surface of electrodes), coagulation (formation of coagulants in aqueous phase and adsorption of soluble or colloidal pollutants on coagulants), and flotation process (solid/liquid separation). The results of these processes and their interactions within the E_{C}/E_{F} reactor allow the removal of pollutants. However, their performance depends on some parameters such as pH, initial conductivity, treatment time, and applied voltage. To improve E_{C}/E_{F} efficiency, operating parameters have to be at their optimum values.

Most of the studies dealing with kinetics optimization make use of the traditional one-factor-at-a-time (OFAT) approach, examining the effect of one parameter on response, while holding all others constant. The result of this univariate analysis shows inadequate optimization towards response(s) (Sakkas *et al.* 2010). Indeed, the OFAT approach is time consuming, does not provide interaction effects and requires a large number of experiments (Zaroual *et al.* 2009). There is now increasing recognition that the OFAT approach is not efficient and ought to be replaced by soundly based chemometric methods such as response surface methodology (RSM) based on statistical design of experiments (DOEs). RSM is a multivariate analysis technic. It is based on the fit of a polynomial equation to the experimental data, which must describe the behaviour of a data set with the objective of making statistical previsions (Bezerra *et al.* 2008).

In this paper, a chemometric approach, especially RSM, is used to model and optimize turbidity removal efficiency (*T*_{R}) from surface water using the E_{C}/E_{F} process in an internal loop airlift reactor (ILAR) as a function of initial conductivity (*X*_{1}), applied voltage (*X*_{2}), treatment time (*X*_{3}), and inter-electrode distance (*X*_{4}).

## MATERIALS AND METHODS

### Preparation of the reconstituted solution

A reconstituted solution made by mixing clay particles and distilled water is used as a surface water. The clay particles are first ground and then sieved in order to remove particles exceeding 45 μm. Surface waters contain colloidal particles with a size ranging from 1 to 10^{−3} μm (Mickova 2015). In order to approach this characteristic, we study the sedimentation velocity of an isolated spherical particle in water (refer to Appendix A for the full survey results, available online).

*T*

_{i}) of 107 NTU, which is the approximate turbidity value for surface waters (Bejjany

*et al*. 2017), and pH = 7.3. The initial conductivity value is adjusted using sodium chloride (NaCl) as the electrolyte. An HI 99300 portable conductivity meter is used to measure the initial conductivity value. Turbidity is measured using a HACH series 2100 N brand turbidimeter. Tests are carried out in an ILAR with a volume capacity of 1 L. A sample of 850 mL from reconstituted solution is used for each test. Two flat aluminium electrodes are used in monopolar configuration and placed in a riser (refer to Appendix D) for the production of coagulants.

*T*

_{R}is given by: where

*T*

_{i}and

*T*

_{f}represent initial and final turbidity respectively.

### Statistical analysis

#### Mathematical model

^{k}), axial points (2

*k*) and central points (

*C*

_{0}). The central points are used to calculate experimental error (Sakkas

*et al.*2010). The experiment number is given by the following expression: where

*k*represents the number of factors.

Four factors are used in this study (*k* = 4). The experiment number can be divided into three groups as follows: 2^{k} = 2^{4} factorial experiments, 2*k* = 2*4 axial experiments and *C*_{0} = 7 central experiments (25–31, refer to Appendix C). Hence, 31 experiments are investigated in this study.

*Y*is the theoretical response function,

*X*

_{i},

*X*

_{j}represent the factors,

*β*

_{0}is the constant term, and

*β*

_{i},

*β*

_{ij},

*β*

_{ii}represent respectively main (linear), interaction and quadratic effects coefficients. Table 1 shows the codification of real values (refer to Appendix B for full method calculations).

Real factor () . | Units . | Symbols . | Factor coding . | ||||
---|---|---|---|---|---|---|---|

− 2 . | − 1 . | 0 . | 1 . | 2 . | |||

Conductivity | (μS/cm) | X_{1} | 250 | 725 | 1,200 | 1,675 | 2,150 |

Applied voltage | (V) | X_{2} | 2 | 4 | 6 | 8 | 10 |

Treatment time | (min) | X_{3} | 0.5 | 2.5 | 4.5 | 6.5 | 8.5 |

Inter-electrode distance | (mm) | X_{4} | 6 | 10 | 14 | 18 | 22 |

Real factor () . | Units . | Symbols . | Factor coding . | ||||
---|---|---|---|---|---|---|---|

− 2 . | − 1 . | 0 . | 1 . | 2 . | |||

Conductivity | (μS/cm) | X_{1} | 250 | 725 | 1,200 | 1,675 | 2,150 |

Applied voltage | (V) | X_{2} | 2 | 4 | 6 | 8 | 10 |

Treatment time | (min) | X_{3} | 0.5 | 2.5 | 4.5 | 6.5 | 8.5 |

Inter-electrode distance | (mm) | X_{4} | 6 | 10 | 14 | 18 | 22 |

#### Optimization approach

*et al.*2008; Sakkas

*et al.*2010). The scale of the individual desirability function ranges from

*d*= 0, for a completely undesirable response, to

*d*= 1 for a fully desired response, above which other improvements would have no importance (Bezerra

*et al.*2008). The overall desirability is calculated as follows: where

*n*represents the number of responses to optimize and

*d*

_{i}the individual desirability.

## RESULTS AND DISCUSSION

Preliminary experiments at the laboratory scale allowed factors to be highlighted which influence *T*_{R} from surface water by electrocoagulation/electro-flotation. The experimental domain is as follows: 250–2,150 μS/cm, 2–10 V, 0.5–8.5 min, 6–22 mm, for *X*_{1}, *X*_{2}, *X*_{3} and *X*_{4} respectively.

Figure 1 shows the prediction profiler for *T*_{R} and *W*_{C}. The prediction profiler is often used to show how the prediction model changes as the settings of individual factors change. According to Figure 1, *T*_{R} and *W*_{C} increase with *X*_{1}, *X*_{2} and *X*_{3}. On the other hand, when *X*_{4} increases, *T*_{R} and *W*_{C} decrease.

Mouedhen *et al.* (2008) reported that the amount of Al^{3+} released in the aqueous solution is a function of the NaCl concentration of the electrolyte (conductivity). Indeed, the increase in *X*_{1} leads to the breakdown of the anodic passive film. This allows the amount of Al^{3+} dissolved in the reactor to be increased, and therefore, suspended particles are quickly destabilized (Mouedhen *et al.* 2008). This result corresponds to those reported by Bejjany *et al*. (2017). In addition, the increase in *X*_{1} during E_{C}/E_{F} is known to increase the production of hydrogen gas bubbles. In ILAR, electrodes are placed in a riser. Thus, hydrogen gas bubbles produced at the cathode are located in the riser. The increase in the amount of hydrogen gas bubbles leads to the creation of a density difference between the *riser* and *downcomer* (*ρ*_{riser} < *ρ*_{downcomer}), which allows recirculation movement. This phenomenon properly disperses Al^{3+} dissolved in the reactor and allows mixing of the suspension. Therefore, the collision of particles is promoted, which leads to the agglomeration of destabilized particles and their removal by flotation.

Applied voltage is a key parameter in E_{C}/E_{F}, which controls the amount of Al^{3+} dissolved, as well as hydrogen gas bubble production within the reactor (Bande *et al.* 2008). When *X*_{2} increases, the amount of Al^{3+} dissolved, as well as the amount of hydrogen gas bubbles, increases in the reactor, which leads to the destabilization of suspended particles and their agglomeration.

*T*_{R} and *W*_{C} are strongly influenced by *X*_{3}. A longer *X*_{3} leads to improved *T*_{R} and to increased *W*_{C}.

During the E_{C}/E_{F} process, a very fine film of metal hydroxides would get formed on, the anode, generating an extra resistance (Ghosh *et al.* 2008). The inter-electrode distance is one of the parameters on which this resistance (IR) strongly depends. The IR refers to the resistance of the media during the flow of electrical current through the cell. When *X*_{4} increases, resistance to mass transfer becomes larger, therefore there is a smaller amount of Al^{3+} cations at the anode, leading to slower formation of coagulants in the middle (Ghosh *et al.* 2008). The rate of clay particle aggregation and adsorption of clays becomes lower, which explains the decrease in *T*_{R}. Nasrullah *et al.* (2012) and Khaled *et al.* (2015) report the same results.

*W*_{C} is defined as the electrical power consumed per unit volume. *W*_{C} is a function of *X*_{1}, *X*_{2}, *X*_{3} and *X*_{4} as shown in Figure 1. According to Figure 1, *W*_{C} increases with *X*_{1}, *X*_{2} and *X*_{3} as reported by Bejjany *et al*. (2017), Bazrafshan *et al.* (2014) and Zaroual *et al.* (2009), respectively. Inter-electrode distance has an opposite effect in comparison with other factors. Indeed, when *X*_{4} increases, *W*_{C} decreases.

Table 2 shows experimental and predicted data for two responses. Analysis of variance (ANOVA) is used to test the statistical significance of the ratio of mean square variation due to regression and mean square residual error. The *P*-value is used to estimate whether the F-ratio is large enough to indicate statistical significance. The model is statistically significant when the *P*-value is lower than 0.05 (Yi *et al.* 2010).

Standard Run . | T_{R} (%). | W_{C} (kWh/m^{3}). | ||
---|---|---|---|---|

Experimental values . | Predicted values . | Experimental values . | Predicted values . | |

1 | 0 | −4.229 | 0.0296 | 0.03216 |

2 | 0 | −18.15 | 0.0174 | 0.08764 |

3 | 50.99 | 46.29 | 0.081 | 0.05749 |

4 | 11.98 | 29.15 | 0.0466 | 0.02024 |

5 | 0.99 | 21.43 | 0.142 | 0.13959 |

6 | 0 | 5.549 | 0.0831 | 0.04634 |

7 | 87.62 | 76.84 | 0.3754 | 0.40204 |

8 | 66.13 | 57.75 | 0.207 | 0.21607 |

9 | 12.94 | 23.72 | 0.0604 | 0.03779 |

10 | 0 | 14.77 | 0.0359 | 0.01624 |

11 | 72.64 | 71.08 | 0.1664 | 0.21014 |

12 | 76.96 | 58.92 | 0.08 | 0.09587 |

13 | 75.88 | 62.71 | 0.3327 | 0.36604 |

14 | 44.7 | 51.8 | 0.1858 | 0.19577 |

15 | 94.42 | 114.97 | 0.8593 | 0.77552 |

16 | 92.62 | 100.85 | 0.5081 | 0.51253 |

17 | 0 | 4.736 | 0.0347 | 0.02169 |

18 | 86.92 | 75.78 | 0.3042 | 0.32377 |

19 | 1.92 | 7.09 | 0.0113 | 0.00139 |

20 | 86.25 | 74.68 | 0.509 | 0.52547 |

21 | 2.88 | −5.46 | 0.018 | −0.00261 |

22 | 92.16 | 94.11 | 0.3123 | 0.33947 |

23 | 72.4 | 66.93 | 0.2923 | 0.30204 |

24 | 39.8 | 38.88 | 0.0977 | 0.09452 |

25 | 73.84 | 68.277 | 0.1783 | 0.167986 |

26 | 65.67 | 68.277 | 0.1613 | 0.167986 |

27 | 71.05 | 68.277 | 0.1647 | 0.167986 |

28 | 69.32 | 68.277 | 0.1743 | 0.167986 |

29 | 67.78 | 68.277 | 0.1669 | 0.167986 |

30 | 57.88 | 68.277 | 0.1658 | 0.167986 |

31 | 72.4 | 68.277 | 0.1646 | 0.167986 |

Standard Run . | T_{R} (%). | W_{C} (kWh/m^{3}). | ||
---|---|---|---|---|

Experimental values . | Predicted values . | Experimental values . | Predicted values . | |

1 | 0 | −4.229 | 0.0296 | 0.03216 |

2 | 0 | −18.15 | 0.0174 | 0.08764 |

3 | 50.99 | 46.29 | 0.081 | 0.05749 |

4 | 11.98 | 29.15 | 0.0466 | 0.02024 |

5 | 0.99 | 21.43 | 0.142 | 0.13959 |

6 | 0 | 5.549 | 0.0831 | 0.04634 |

7 | 87.62 | 76.84 | 0.3754 | 0.40204 |

8 | 66.13 | 57.75 | 0.207 | 0.21607 |

9 | 12.94 | 23.72 | 0.0604 | 0.03779 |

10 | 0 | 14.77 | 0.0359 | 0.01624 |

11 | 72.64 | 71.08 | 0.1664 | 0.21014 |

12 | 76.96 | 58.92 | 0.08 | 0.09587 |

13 | 75.88 | 62.71 | 0.3327 | 0.36604 |

14 | 44.7 | 51.8 | 0.1858 | 0.19577 |

15 | 94.42 | 114.97 | 0.8593 | 0.77552 |

16 | 92.62 | 100.85 | 0.5081 | 0.51253 |

17 | 0 | 4.736 | 0.0347 | 0.02169 |

18 | 86.92 | 75.78 | 0.3042 | 0.32377 |

19 | 1.92 | 7.09 | 0.0113 | 0.00139 |

20 | 86.25 | 74.68 | 0.509 | 0.52547 |

21 | 2.88 | −5.46 | 0.018 | −0.00261 |

22 | 92.16 | 94.11 | 0.3123 | 0.33947 |

23 | 72.4 | 66.93 | 0.2923 | 0.30204 |

24 | 39.8 | 38.88 | 0.0977 | 0.09452 |

25 | 73.84 | 68.277 | 0.1783 | 0.167986 |

26 | 65.67 | 68.277 | 0.1613 | 0.167986 |

27 | 71.05 | 68.277 | 0.1647 | 0.167986 |

28 | 69.32 | 68.277 | 0.1743 | 0.167986 |

29 | 67.78 | 68.277 | 0.1669 | 0.167986 |

30 | 57.88 | 68.277 | 0.1658 | 0.167986 |

31 | 72.4 | 68.277 | 0.1646 | 0.167986 |

Figure 2 comes from linear regression between observed (experimental) and predicted values. It shows the fit of the predicted model to the experimental data. According to Figure 2, the *P*-values for the *T*_{R} and *W*_{C} regressions are lower than 0.05 (*P*-value < .0001). This result means that at least one of the terms in the regression equation has a significant correlation with the response variable. In conclusion, the form of model used in this study to explain the factors and response relationship is correct.

Furthermore, model precision is evaluated by a determination coefficient (*R*^{2}). The *R*^{2} values for *T*_{R} and *W*_{C} are 0.92 and 0.98, respectively. These results imply that 92% and 98% of the sample variation for *T*_{R} and *W*_{C}, respectively, are attributed to the four factors. Only about 8% and 2% of the total variation for *T*_{R} and *W*_{C}, respectively, cannot be explained by the model. This indicates that the accuracy and general ability of the polynomial model are good.

The ANOVA table also provides a term for residual error, which measures the amount of variation in the response data left unexplained by the model. The root-mean-square error (RMSE) is 13.554 and 0.037 for the *T*_{R} and *W*_{C} model, respectively.

Unlike one-factor-at-a-time methodology, RSM also provides information about the interaction and quadratic effects of factors. This analysis is done by Fisher's F-test. In general, the smaller the value of *P*-values (<0.05), the larger the magnitude of the F-ratio, and the more significant is the corresponding coefficient term. The estimated regression coefficients, F-ratio and *P*-values for all the linear, quadratic and interaction effects of the parameters are given in Tables 3 and 4 for *T*_{R} and *W*_{C}, respectively. In Table 3, it is observed that the linear effect of *X*_{1}, *X*_{2}, *X*_{3}, and *X*_{4}, and the quadratic effect of *X*_{1} (*X*_{1}^{2}), *X*_{2} (*X*_{2}^{2}) and *X*_{3} (*X*_{3}^{2}) are significant model terms. The corresponding *P*-value of all linear effects is <.0001, while the *P*-values of the quadratic effects are 0.0127, 0.0144 and 0.0287, respectively. All other model terms (all interaction effects and quadratic effect of *X*_{4}) can be said to be not significant (*P*-values > 0.05).

Terms . | Estimated coefficients . | Degree of freedom . | Sum of square . | F-ratio . | P-values
. |
---|---|---|---|---|---|

Constant | 68.277 | – | – | – | <.0001* |

X_{1} | 17.345 | 1 | 7,220.724 | 39.3033 | <.0001* |

X_{2} | 17.313 | 1 | 7,193.69 | 39.1562 | <.0001* |

X_{3} | 24.475 | 1 | 14,377.105 | 78.2564 | <.0001* |

X_{4} | −7.429 | 1 | 1,324.472 | 7.2093 | 0.0163* |

X_{1}*X_{2} | 3.957 | 1 | 250.51 | 1.3636 | 0.26 |

X_{1}*X_{3} | −1.413 | 1 | 31.951 | 0.1739 | 0.6822 |

X_{1}*X_{4} | 0.618 | 1 | 6.113 | 0.0333 | 0.8575 |

X_{2}*X_{3} | 1.849 | 1 | 54.723 | 0.2979 | 0.5928 |

X_{2}*X_{4} | 0.136 | 1 | 0.294 | 0.0016 | 0.9686 |

X_{3}*X_{4} | −1.429 | 1 | 32.69 | 0.1779 | 0.6788 |

X_{1}^{2} | −7.108 | 1 | 1,444.903 | 7.8648 | 0.0127* |

X_{2}^{2} | −6.952 | 1 | 1,382.08 | 7.5228 | 0.0144* |

X_{3}^{2} | −6.093 | 1 | 1,061.728 | 5.7791 | 0.0287* |

X_{4}^{2} | −3.948 | 1 | 445.792 | 2.4265 | 0.1389 |

Terms . | Estimated coefficients . | Degree of freedom . | Sum of square . | F-ratio . | P-values
. |
---|---|---|---|---|---|

Constant | 68.277 | – | – | – | <.0001* |

X_{1} | 17.345 | 1 | 7,220.724 | 39.3033 | <.0001* |

X_{2} | 17.313 | 1 | 7,193.69 | 39.1562 | <.0001* |

X_{3} | 24.475 | 1 | 14,377.105 | 78.2564 | <.0001* |

X_{4} | −7.429 | 1 | 1,324.472 | 7.2093 | 0.0163* |

X_{1}*X_{2} | 3.957 | 1 | 250.51 | 1.3636 | 0.26 |

X_{1}*X_{3} | −1.413 | 1 | 31.951 | 0.1739 | 0.6822 |

X_{1}*X_{4} | 0.618 | 1 | 6.113 | 0.0333 | 0.8575 |

X_{2}*X_{3} | 1.849 | 1 | 54.723 | 0.2979 | 0.5928 |

X_{2}*X_{4} | 0.136 | 1 | 0.294 | 0.0016 | 0.9686 |

X_{3}*X_{4} | −1.429 | 1 | 32.69 | 0.1779 | 0.6788 |

X_{1}^{2} | −7.108 | 1 | 1,444.903 | 7.8648 | 0.0127* |

X_{2}^{2} | −6.952 | 1 | 1,382.08 | 7.5228 | 0.0144* |

X_{3}^{2} | −6.093 | 1 | 1,061.728 | 5.7791 | 0.0287* |

X_{4}^{2} | −3.948 | 1 | 445.792 | 2.4265 | 0.1389 |

*Significant model term (*P*-values <0.05).

Terms . | Estimated coefficient . | Degree of freedom . | Sum of square . | F-ratio . | P-values
. |
---|---|---|---|---|---|

Constant | 0.1679 | – | – | – | <.0001* |

X_{1} | 0.0755 | 1 | 0.13688151 | 99.8671 | <.0001* |

X_{2} | 0.131 | 1 | 0.41199501 | 300.5864 | <.0001* |

X_{3} | 0.0855 | 1 | 0.17553151 | 128.0656 | <.0001* |

X_{4} | −0.052 | 1 | 0.06459475 | 47.1275 | <.0001* |

X_{1}*X_{2} | 0.0552 | 1 | 0.04876368 | 35.5774 | <.0001* |

X_{1}*X_{3} | 0.0367 | 1 | 0.02161635 | 15.771 | 0.0011* |

X_{1}*X_{4} | −0.0192 | 1 | 0.00593285 | 4.3285 | 0.0539 |

X_{2}*X_{3} | 0.059 | 1 | 0.05622827 | 41.0234 | <.0001* |

X_{2}*X_{4} | −0.037 | 1 | 0.02211913 | 16.1378 | 0.0010* |

X_{3}*X_{4} | −0.023 | 1 | 0.00859793 | 6.2729 | 0.0235* |

X_{1}^{2} | 0.0012 | 1 | 0.00004021 | 0.0293 | 0.8661 |

X_{2}^{2} | 0.0238 | 1 | 0.01628072 | 11.8782 | 0.0033* |

X_{3}^{2} | −0.00011 | 1 | 0.00000035 | 0.0003 | 0.9874 |

X_{4}^{2} | 0.0075 | 1 | 0.00164013 | 1.1966 | 0.2902 |

Terms . | Estimated coefficient . | Degree of freedom . | Sum of square . | F-ratio . | P-values
. |
---|---|---|---|---|---|

Constant | 0.1679 | – | – | – | <.0001* |

X_{1} | 0.0755 | 1 | 0.13688151 | 99.8671 | <.0001* |

X_{2} | 0.131 | 1 | 0.41199501 | 300.5864 | <.0001* |

X_{3} | 0.0855 | 1 | 0.17553151 | 128.0656 | <.0001* |

X_{4} | −0.052 | 1 | 0.06459475 | 47.1275 | <.0001* |

X_{1}*X_{2} | 0.0552 | 1 | 0.04876368 | 35.5774 | <.0001* |

X_{1}*X_{3} | 0.0367 | 1 | 0.02161635 | 15.771 | 0.0011* |

X_{1}*X_{4} | −0.0192 | 1 | 0.00593285 | 4.3285 | 0.0539 |

X_{2}*X_{3} | 0.059 | 1 | 0.05622827 | 41.0234 | <.0001* |

X_{2}*X_{4} | −0.037 | 1 | 0.02211913 | 16.1378 | 0.0010* |

X_{3}*X_{4} | −0.023 | 1 | 0.00859793 | 6.2729 | 0.0235* |

X_{1}^{2} | 0.0012 | 1 | 0.00004021 | 0.0293 | 0.8661 |

X_{2}^{2} | 0.0238 | 1 | 0.01628072 | 11.8782 | 0.0033* |

X_{3}^{2} | −0.00011 | 1 | 0.00000035 | 0.0003 | 0.9874 |

X_{4}^{2} | 0.0075 | 1 | 0.00164013 | 1.1966 | 0.2902 |

*Significant model term (*P*-values <0.05).

In addition, *X*_{3} is the most significant model term with an F-ratio equal to 78.2564. The corresponding estimated coefficient value is 24.475. Based on the F-ratio values, the ranking of the significant model terms for *T*_{R} is as follows: *X*_{3} > *X*_{1} > *X*_{2} > *X*_{1}^{2} > *X*_{2}^{2} > *X*_{4} > *X*_{3}^{2}.

In the same way, estimated regression coefficients, F-ratio and *P*-value results of *W*_{C} are indicated in Table 4. It shows that all linear effects of *X*_{1}, *X*_{2}, *X*_{3} and *X*_{4} are significant model terms (*P*-value < .0001). The two-level interaction effects of *X*_{1}**X*_{2}, *X*_{1}**X*_{3}, *X*_{2}**X*_{3}, *X*_{2}**X*_{4} and *X*_{3}**X*_{4} are significant model terms. Their corresponding *P*-values are <.0001, 0.0011, <.0001, 0.0010 and 0.0235, respectively. Only the quadratic effect of *X*_{2} (*X*_{2}^{2}) is a significant model term with a *P*-value = 0.0033. Thus, the two-level interaction effect of *X*_{1}**X*_{4} and the quadratic effects of *X*_{1} (*X*_{1}^{2}), *X*_{3} (*X*_{3}^{2}) and *X*_{4} (*X*_{4}^{2}) are not significant model terms. Based on F-ratio values, *X*_{2} is the most significant model term (F-ratio = 300.5864, estimated coefficient = 0.131). The ranking of significant model terms according to the F-ratio values for *W*_{C} is as follows: *X*_{2} > *X*_{3} > *X*_{1} > *X*_{4} > *X*_{2}**X*_{3} > *X*_{1}**X*_{2} > *X*_{2}**X*_{4} > *X*_{1}**X*_{3} > *X*_{2}^{2} > *X*_{3}**X*_{4}.

The regression model equations (second-order polynomial) relating *T*_{R} and *W*_{C} are developed and given in Equations (9) and (10), respectively. These equations only contain the significant model terms associated with their estimated coefficients. The regression model equations are written as follows.

Figures 3 and 4 show two-dimensional contour plots and three-dimensional response surface plots of *T*_{R} and *W*_{C}, respectively. These figures show interaction effects for two factors (the factors with most effect) when others are kept constant in their central values. These representations are often used to search optimal conditions of parameter process, especially when optimal values are located in the same region.

According to Figures 3 and 4, the optimum values of each response are located in different regions. For example, in Figure 3(a) (or Figure 4(a)), for a constant initial conductivity value (with *X*_{2} = 6 V and *X*_{4} = 14 mm), increase in treatment time leads to improvement in *T*_{R}. On the other hand, Figure 3(b) (or Figure 4(b)) shows that at a constant value of applied voltage, increase in treatment time leads to increase in *W*_{C} (with *X*_{1} = 1,200 μS/cm and *X*_{4} = 14 mm). Thus, changes in the level of a factor can improve one specific response and have a very negative effect on another one. Multicriteria methodology, especially the desirability function, is used to overcome this problem. Table 5 shows the scale of the individual desirability function for *T*_{R} and *W*_{C}. The scale of the individual desirability function ranges from *d* = 0.01, for a completely undesirable response (low *T*_{R} or high *W*_{C}) to *d* = 0.98, for a fully desired response (high *T*_{R} or low *W*_{C}). The overall desirability (*D*) close to 1 expressing the maximum of *T*_{R} and the minimum of the *W*_{C} is equal to 0.79. The optimum conditions relating to this value for each factor in coded values are 0.6046869 (*X*_{1} = 1,487 μS/cm), −0.5 (*X*_{2} = 5 V), 1 (*X*_{3} = 6.5 min) and 0 (*X*_{4} = 14 mm). The corresponding estimated values for *T*_{R} and *W*_{C} are 84.15% and 0.215 kWh/m^{3}, respectively. These values are used at the laboratory scale for the confirmation study as shown in Table 6.

. | T_{R}. | W_{C}. | ||
---|---|---|---|---|

T_{R} (%)
. | Desirability . | W_{C} (KWh/m^{3})
. | Desirability . | |

High value | 100 | 0.98 | 0.8 | 0.01 |

Mean value | 50 | 0.5 | 0.45 | 0.5 |

Low value | 0 | 0.01 | 0 | 0.98 |

. | T_{R}. | W_{C}. | ||
---|---|---|---|---|

T_{R} (%)
. | Desirability . | W_{C} (KWh/m^{3})
. | Desirability . | |

High value | 100 | 0.98 | 0.8 | 0.01 |

Mean value | 50 | 0.5 | 0.45 | 0.5 |

Low value | 0 | 0.01 | 0 | 0.98 |

Factors . | Units . | Estimated values . | Experimental values . |
---|---|---|---|

X_{1} | μS/cm | 1,487 | 1,500 |

X_{2} | V | 5 | 5 |

X_{3} | min | 6.5 | 6.5 |

X_{4} | mm | 14 | 14 |

T_{R} | % | 84.15 | 72.05 |

W_{C} | kWh/m^{3} | 0.215 | 0.210 |

Factors . | Units . | Estimated values . | Experimental values . |
---|---|---|---|

X_{1} | μS/cm | 1,487 | 1,500 |

X_{2} | V | 5 | 5 |

X_{3} | min | 6.5 | 6.5 |

X_{4} | mm | 14 | 14 |

T_{R} | % | 84.15 | 72.05 |

W_{C} | kWh/m^{3} | 0.215 | 0.210 |

Table 6 shows the results of the confirmation study. It shows that *T*_{R} and *W*_{C} under optimal conditions carried out at the laboratory scale are 72.05% and 0.210 kWh/m^{3}, respectively. The results found by Bejjany *et al*. (2017) for the same *T*_{R} value (72%) report a *W*_{C} of 0.357 kWh/m^{3} under *X*_{1} = 351 μS/cm, *X*_{2} = 12 V, *X*_{3} = 7.5 min and *X*_{4} = 18 mm conditions. In comparison with our results, we note that the RSM allowed us to obtain a *W*_{C} value of 41% less for the same *T*_{R} value.

## CONCLUSION

In the present study, RSM is used in conjunction with CCD to optimize the removal of turbidity from surface water by E_{C}/E_{F} in an ILAR. The validation of the model is carried out by an appropriate analysis of variance (ANOVA). The results revealed that the model prediction used to explain factors and response relationship is correct with *P*-values <.0001. Furthermore, the determination coefficients of *T*_{R} and *W*_{C} are 0.92 and 0.98, respectively. Fisher's test is used to check the significance of all model terms on two responses. Therefore, corresponding regression equations are developed. These equations are used to build 3D response surface and 2D contour plots. These graphical representations allow the optimal conditions of parameter process to be searched. Since optimal values are located in different regions, a desirability function is used to allow the determination of optimal conditions for each response simultaneously. For the overall desirability function of 0.79, the optimal conditions are 1,487 μS/cm, 5 V, 6.5 min and 14 mm, respectively for *X*_{1}, *X*_{2}, *X*_{3} and *X*_{4}. Under these conditions, the estimated *T*_{R} and *W*_{C} are 84.15% and 0.215 kWh/m^{3}, respectively. The confirmation study at the laboratory scale using optimal conditions shows 72.05% for *T*_{R} and 0.210 kWh/m^{3} for *W*_{C}.

## DISCLOSURE STATEMENT

The authors report no potential conflict of interest.

## SUPPLEMENTARY DATA

The Supplementary Data for this paper are available online at http://dx.doi.org/10.2166/ws.2019.129.