As a vat dye indigo needs to be reduced to its water-soluble form before it can be used in dyeing. The reduction of indigo to leuco-indigo, represents an important type of industrial process which is operated worldwide on a considerable scale [15] .

The indigo (BEZEMA AG, Switzerland) reduction is industrially done, in the SITEX (Textile Industrial Company-Ksar Hellal, Tunisia), with Sodium dithionite (Fluka, Germany) as a conventional reducing agent. It is also known as sodium hydrosulphite, or Hydro (Na₂S₂O₄) and has been a major reducing agent [16] in the industrial reduction of vat dyes including indigo due to its chemical as well as economic advantages. It is used with all vat dyes at temperatures ranging up from 30˚C [17] .

Indigo is reduced by Sodium Hydroxide, and then the obtained form Leuco is filtered through a sieve of 23 µm to remove fibers. Afterwards, we transfer the filtrate to the electrochemical processing cell.

The electrochemical reactor was a 16.957 L acrylic column with a height of 60 cm and a diameter of 9.54 cm. It contained a set of one pair of electrodes made of aluminum. Dimensions of each electrode were 335 mm × 130 mm × 2 mm so, its total area (S) was 0.088960 m² and the distance between two electrodes in electrochemical cell was 7 mm in all experiments (Figure 1). The electrodes were connected to a DC power supply (Laboratory DC. Power supply Model M10-SP600 SL) with galvanostatic operational options for controlling the current density.

All the runs were performed at room temperature. In each run, 30 ml of the dye solution was filtered by Whatman® glass microfiber filters (7 µm). The filtrate obtained was collected for the analysis of water properties and the electrodes were well polished by sandpaper before each test. All experiments were repeated twice, and the experimental error was 3%.

During the runs, the solution in the reactor unit was stirred at 2 rpm by a magnetic stirrer. The experiments were carried out in a batch mode with a liquid sample of 13.71 L. Different current intensities were applied (0.5 to 1.5A).

The conductivity measurement was performed with a conductimeter (HANNA Instruments). The pH of the solutions was measured by a pH meter (370 pH Meter JENWAY) and adjusted by adding NaOH or H₂SO₄ (Merck, Germany) solutions. The batch experimental cell is shown in Figure 1. The conductivity of solutions was raised up and adjusted in different values by the addition of NaCl (1 g/L to 6 g/L).

The commercial dyes indigo used in this project were furnished by SITEX. Dye solutions were prepared by dissolving dyes in distilled water and reduced by sodium hydrosulfite under the conditions described above. In the present experimental study, aluminum has been used as elecrodes and the treatment time fixed at 25 min.

The Box-Behnken design (BBD), an experimental design for Response Surface Methodology (RSM) is a useful statistical tool for the optimization of different processes and widely used for experimental design. In this method, the leading objective is to optimize the response surface that is influenced by different parameters. RSM also identified the relationship between the controllable input parameters and the response variable [21] . It is usually applied following a screening study to explore the region of interest of the factors identified by the preceding study [22] .

The general behaviour of some phenomena in electrocoagulation can be simulated by a mathematical equation: this equation represents the regression model. Response surface methods are used to examine the relationship between one or more response variables and a set of quantitative experimental variables or factors [23] . The factors considered in this study are: initial concentration of dye (12.310, 21.155 and 31.540 mg/l), NaCl concentration (1, 3.5 and 6 g/l) and current intensity (0.5, 1, 1.5 Ampere) (Table 1), where, the experimental result or the response to treat is the Color Removal (%).

There are many types of equations that can give a good correlation between parameters, but the choice of which one should be used is dependent of the R² value of each model. The most appropriate regression model obtained for the response (CR(%)) is the following:

Equation I: a quadratic equation with interactions for CR(%) in Equation (7):

The results were analysed using the software Minitab 14 [24] [25] . Minitab, offers a collection of software, support materials and services that enables to manage and improve the quality of processes [26] [27] . Response Surface Methods are used to examine the relationship between one or more response variables and a set of quantitative experimental variables or factors.

The regression equation of the removed dye (CR(%)), it was found that the squared multiple correlation coefficient “R²” is equal, to 88.3%; so, we can probably assume that the models may be predictable, that can give a good correlation between parameters and responses.

We can concluded from the coefficients of the equations that current intensity and color concentration coefficients are the most important terms affecting the response value (RC(%)). To validate our experimental data, we used the statistical models: ANOVA.

A.R. Amani-Ghadim et al. (2013) studied the performance of aluminum anodes for removal of the C.I. Reactive Red 43 dye from aqueous solution. They modeled the decolorization by response surface methodology. The effects of four important operational parameters including current density, electrolysis time, pH and chloride concentration were evaluated by the response surface methodology. This study showed a high correlation coefficient (R² = 93.4) between experimental and predicted removal efficiencies. Furthermore the regression equation proved that the initial pH and the current density were the most important factors.

The analysis ANOVA of the regression equations stated above is performed in order to determine the good correlation between parameters and responses. The evaluation was based on the p-value obtained. Analysis of variance is similar to the regression in that it is used to investigate and model the relationship between a response variable and one or more independent variables [27] .

The P-value related to the F-value could be used to show whether the F-value is large enough or not. In other words, P-values lower than 0.01 (at the significance level of 95%) confirm that the regression model is statistically significant [28] . The model developed of regression for CR(%) given the P-values were much lower than 0.01. In this case, the related P-value is lower than 0.01, the regression will adequately be significant as the ANOVA results indicated. On the other hand, the sum of squares (SS) related to Residual Error is very less as compared to the total sum of squares. This confirms our hypothesis (Table 2).

Takes account of all considerations, we can assume, that a second order polynomial model with interaction allows properly explain the phenomenon studied for CR(%).

Based on the results Response Surface Regression and Analysis of Variance (ANOVA), as concluded, that current density and initial concentration of dye were the most important factors in electrocoagulation process for response (CR(%)).

Figure 2 shows that, when the decrease of current intensity with increase of color concentration was not suitable for the color removal. On the other hand, the effect of

the increase of current intensity until to 1.25 A with decrease of color concentration was suitable for color removal. But the response of CR(%) decease wen the current intensity as higher than 1.25 A and the dye concentration was less than 13.85 mg/l.

An interaction between factors occurs when the change in response from the low level to the high level of one factor is different from the change in response at the same two levels of a second factor. In other words, binary interactions between factors presented statistically significant effect, which signifies that the effect of one independent factor on the response depends upon the other factor. Interactions plots could be used to compare the relative strength of the effects across factors.

The analysis of the interactions between the experimental factors studied is shown in Figure 3. The interaction between different factors is obvious for the color removed (CR(%)).

A comparison for optimum conditions between predicted and experimental responses using Box-Behnken Design is given below:

The performance of all design and response variables are shown in Figure 4, where the best optimization is approached by an overall desirability of 0.75892 at optimum operating conditions of reaction time at 25 min, current density at 0.50 A, initial color concentration at 13 mg/l and NaCl concentration at 2.67 g/l. In these conditions, the Minitab Software gives respectively, a decolorization value for Indigo dye of 86.9783% and for Operating Cost OC = 0.0007378 US$/m³. When these conditions were applied experimentally, we obtained respectively CR(%) = 85.33% and OC = 0.000558 US$/m³.

Thus, when the experimental conditions proposed by Minitab were applied to our experimentation, the values of the responses obtained are almost equal to the values obtained by calculating. Hence our models are globally validated.

A.R. Amani-Ghadima et al. (2013) obtained, when using electrocoagulation process with aluminum anodes, a maximum removal efficiency equal to 98.90 of the C.I. Reactive Red 43 dye from aqueous solution. They achieved using the experimental optimum values of each studied factor, which was in a good conformity with the predicted values (99.99%).