**3. One-component Donnan dialysis in the feed compartment**

### **3.1 Counter-ion concentration effect**

The effect of counter-ion concentrations in the compartment receiver on the removal of nitrate and nitrite from the feed compartment separately was an important parameter of this investigation. One of the crucial factors influencing the elimination of nitrates and nitrites across the membrane is the counter-ion. Due to its high mobility, chloride appears to be the counter-ion that is employed the most.

**Figure 2.**

*The counter-ion concentration effect on nitrate removal for the three tested membranes.*

We investigated the effect of increasing the concentration of counter-ion Cl� in the receiver compartment from 0.01 to 0.5 mol./L on the removal of nitrates (100 mg/L) and nitrites (20 mg/L) separately from the feed compartment to the receiver compartment. We have tested three membranes (AFN, AMX, and ACS), with four-hours DD operations. **Figures 2** and **3** show the variation in nitrate and nitrite concentrations at the receiver solution's outlet.

## *Removal of Nitrate and Nitrite by Donnan Dialysis: Optimization According to Doehlert… DOI: http://dx.doi.org/10.5772/intechopen.112482*

For the three membranes, it was observed that increasing the concentration of Cl� from 0.01 to 0.5 mol/L resulted in a greater removal percentage for nitrate and nitrite. In the receiver compartment, the concentration of nitrate and nitrite was very low when Cl� was 0.01–0.05 mol/L. As the Cl�concentration increased from 0.1 to 0.5 mol/ L, nitrates and nitrites were greatly removed. To maintain electroneutrality, the crossion transfer between Cl� and nitrates and nitrites improves because the concentration gradient of the counter-ions increases. According to Donnan dialysis with three membranes, an increase in the counter-ion concentration in the receiver compartment is associated with a significant improvement in the removal of nitrates and nitrites in the feed compartment; this is reflected by an increase in the exchange kinetics. Ben Hamouda et al. [13] and Turki et al. [30] have also reported similar conclusions.

### **3.2 Nitrate and nitrite concentration effect in the feed compartment**

Depending on the geographic location, natural waters contained varying levels of nitrate and nitrite. Due to this, nitrate and nitrite concentrations were studied separately in the feed compartment. For this study, the initial concentration of nitrate was varied from 10 to 500 mg/L, and the initial concentration of nitrite was varied from 5 to 100 mg/L. The concentration of counter-ion Cl� was 0.1 mol/L in the receiver compartment. **Figures 4** and **5** show the variation of nitrate and nitrite concentrations at the receiver solution's outlet.

**Figure 4** shows the variation of nitrate concentration from 50 to 500 mg/L, the rate of removal significantly increased for all membranes. Nitrate removal improved when concentration going from 50 to 500 mg/L by 38 to 61% with AFN, 30 to 50% with AMX, and 34 to 50% with ACS. The highest nitrate exchange for chloride ion efficiencies was achieved with the AFN membrane when performing Donnan dialysis.

**Figure 4.** *Nitrate concentration effect in the feed compartment on nitrate removal for the three tested membranes.*

**Figure 5.** *Nitrite concentration effect in the feed compartment on nitrite removal for the three tested membranes.*

**Figure 5** shows the variation of nitrite concentration from 10 to 100 mg/L, the rate of removal significantly increased for all membranes. In the feed compartment when the nitrite concentration was the lowest (10 mg/L), the removal for AFN, AMX, and ACS was 17%, 15%, and 16% respectively. The removal was enhanced with an increase in nitrite concentration from 10 to 100 mg/L from 17 to 70% with AFN, 15 to 65% with AMX, and 16 to 66% with ACS. It appears that the AFN membrane removed nitrites most effectively.

We can conclude that the improvement in the removal of nitrate and nitrite was mostly caused by the rise in the initial concentration of nitrate and nitrite, regardless of all membranes AFN, AMX, and ACS. The increase in the concentration gradient of nitrate and nitrite, which increased the chloride ion flux from the receiver compartment to the feed compartment, can be attributed to this [11]. As a result, the cross-ion transfers between Cl� and nitrates and nitrites are improved.

## **4. Two components of Donnan dialysis in the feed compartment**

### **4.1 Choice of the membrane**

Three membranes, AFN, AMX, and ACS, were examined for the selection of anion-exchange membranes due to the intricacy of the correlation between their qualities given in catalogs and the real performances in Donnan dialysis process. With a counter-ion concentration of 0.5 mol/L, an initial nitrate concentration of 100 mg/L, and a nitrite concentration of 20 mg/L, Donnan dialysis was carried out. **Figure 6** illustrates the simultaneous testing of membranes (AFN, AMX, and ACS) for the removal of both nitrites and nitrates in the same compartment.

*Removal of Nitrate and Nitrite by Donnan Dialysis: Optimization According to Doehlert… DOI: http://dx.doi.org/10.5772/intechopen.112482*

**Figure 6.**

*Choice of the best membrane allowing the highest removal rate for both nitrate and nitrite.*

**Figure 6** shows the simultaneous elimination of nitrites and nitrates by three membranes (AFN, AMX, and ACS) in the same compartment. Because a higher proportion of nitrates and nitrites ions in the feed compartment increases the overall flow, which in turn causes a higher proportion of the counter-ions to be transported from the feed to the receiver, the presence of nitrite and nitrite in the same compartment improves their elimination.

In comparison to the AMX and ACS membranes, the AFN membrane has the superior performance. The AFN membrane is a macro-porous structure with a high concentration of inorganic groups and a low amount of a cross-linked agent. This membrane has a relatively high ion-exchange capacity and the highest water content [14].

### **4.2 Doehlert design**

The simultaneous removal of nitrate and nitrate was optimized using the membrane AFN and RSM via Doehlert design. The 15 tests of the Doehlert experimental design (**Table 3**) contained three replicates at the center field. Repeated measurements on the same center field can yield almost the same results for our solution, resulting in a significant lack of fit. Replication actually reduces the experimental data's variability, increasing its significance and level of confidence [31].

Using the experimental findings from **Table 3** and the second-order polynomial equations provided by Eqs. (4) and (5), the necessary data were fitted to the equation.

$$\begin{aligned} Y\_1 &= 87.2 - 1.36X\_1 + 8.70X\_2 + 12.35X\_3 - 2.50X\_2^2 - 10.40X\_3^2 + 1.33X\_1X\_2 \\ &+ 1.33X\_1X\_3 + 1.03X\_2X\_3 \end{aligned} \tag{4}$$

*Recent Advances on Nitrification and Denitrification*


**Table 3.**

*Experimental design and results of nitrate and nitrite removal.*

$$\begin{aligned} Y\_2 &= 96.3 + 9.11 \, X\_1 - 0.28 \, X\_2 + 5.94 \, X\_3 - 7.50 \, X\_1^2 - 2.50 \, X\_2^2 - 5.27 \, X\_3^2 \\ &+ 0.23 \, X\_1 \text{X}\_2 + 0.84 \, X\_1 \text{X}\_3 - 0.04 \, X\_2 \text{X}\_3 \end{aligned} \tag{5}$$

According to obtained results, the coefficients are presented and show that the counter-ion concentration had an important effect (b3 = 12.35) on the removal of nitrate. The second influenced factor was the nitrate concentration (b2 = 8.70). Except the concentration of nitrite had a less important effect on the removal of nitrate (b1 = 1.36). According to obtained results, the coefficients are presented and show that the nitrite concentration had an important effect (b1 = 9.11) on the removal of nitrite. The second influenced factor was the counter-ion concentration (b3 = 5.94). Nevertheless, the concentration of nitrate had a less important effect on the removal of nitrate (b2 = 0.28).

The multiple polynomial model coefficients (Eqs. (4) and (5)), which reflected the effects and interactions of the many components under investigation were identified. A check of the relative importance of various coefficients in the experimental region under investigation is possible thanks to the Pareto analysis (**Figure 7**). The following relation (Eq. (6)) allows to calculate this analysis:

$$P\_i = \left(\frac{b\_i^2}{\sum b\_i^2}\right)^2 \times 100\tag{6}$$

The concentration of chloride and nitrate both have a positive effect on the studied response, meaning that increasing their concentrations leads to improved nitrate removal. Their contributions to the studied response were only 30.5% for chloride

*Removal of Nitrate and Nitrite by Donnan Dialysis: Optimization According to Doehlert… DOI: http://dx.doi.org/10.5772/intechopen.112482*

### **Figure 7.** *Pareto analysis for nitrate (a) and nitrite (b) removal.*

concentration and 15.2% for nitrate concentration. Thus, the removal can be considerably influenced by two parameters: chloride concentration and nitrate concentration. However, the other interactions have a negligible effect; they represent only 1.0% of the studied response. The concentration of nitrites and the concentration of chloride are two factors that affect nitrate elimination. The concentration of nitrite has a positive effect, which translates to improved elimination via Donnan Dialysis as nitrite concentration rises. This improvement was attributed to the rise in the concentration gradient of nitrates, which enhanced the chloride ion flux from the receiver to the feed solution, hence the cross-ion transfer between Cl� and nitrate improves to maintain the electroneutrality.

Two factors positively impact the studied response, indicating that an increase in these factors leads to an improvement in nitrite removal. Their contributions to the studied response were only 33.24% for nitrite concentration and 14.13% for chloride concentration. The nitrate concentration has a negative effect, meaning that an increase in nitrate concentration leads to a decrease in nitrite removal. However, the interaction between nitrite and chloride has a negligible effect of 0.28%. Similarly, the other interactions also have a negligible effect, accounting for only 0.3% of the studied response.

The concentration of nitrites and the concentration of chloride are two factors that affect nitrite elimination. The concentration of nitrite has a positive effect, which translates to improved elimination via Donnan Dialysis as nitrite concentration rises.

This improvement was attributed to the rise in the concentration gradient of nitrates and nitrites, which enhanced the chloride ion flux from the receiver to the


### **Table 4.**

*Variance analysis of nitrate and nitrite removal.*

feed solution, hence the cross-ion transfer between Cl� and nitrite improves to maintain the electroneutrality.

Using the regression coefficient (R2 ) and the percentage of absolute errors of deviation (AED), the validity of the model was evaluated. According to Y1, the regression coefficient is 0.999, while according to Y2, it is 0.997. However, the percentage absolute error of deviation, AED (%) = 0.262%, was less than 10% for nitrate removal, and AED (%) = 0.311% for nitrite removal. These confirm the validation of the models suggesting that the model is suitable to describe the removal of nitrate and nitrite.

Analysis of variance (ANOVA) was carried out to support the models'suitability. The results are shown in **Table 4** in this regard. The F-ratio is the mean square error, and the p-value is the ratio of the mean square effect.

The P-value has been used to identify the effects that are statistically significant. The P-value is crucial since it is close to zero, which denotes the significance of the data. The Fischer value (F0.05, 1, 1.16) for 5% error, 1 degree of freedom, and 16 factorial testing is 4.77, according to the Fischer table. Due to the fact that every effect's value is higher than 4.77, it appears that they are all important. At a level of 5%, the experimental model's Fischer value is significantly greater than the crucial F value. The model is therefore regarded as statistically significant.

The software NemrodW®s desirability function produced the optimal conditions. The optimum values for each factor are therefore 82 mg/L for nitrite concentration, 406 mg/L for nitrate concentration, and 0.412 mol/L for counter-ion concentration. The maximal elimination of nitrates (95.5%) and nitrites (100%) was achieved under these conditions. In order to confirm the accuracy of the predictions, the experiment was replicated three times under optimal conditions. Since the coefficient of repeatability was less than 1%, it can be said that Donnan dialysis's simultaneous removal of nitrates and nitrites is repeatable. The experimental results'statistical analysis revealed that the analysis has a normal distribution.

## **5. Application on real water**

Simultaneous removal of nitrate and nitrite from real water was performed to ensure the feasibility and effectiveness of Donnan dialysis. We used water from the eastern side of the Tunisian Cape Bon, a region well-known for its intensive

*Removal of Nitrate and Nitrite by Donnan Dialysis: Optimization According to Doehlert… DOI: http://dx.doi.org/10.5772/intechopen.112482*


### **Table 5.**

*Composition of the groundwater from Menzel Bouzelfa.*

cultivation of vegetables and fruit, mainly citrus. The large quantities of chemical fertilizers have caused real problems with the quality of both surface and groundwater. **Table 5** shows the anion content of water taken from a well in the town of Menzel Bouzelfa. We notice the high contents of nitrates and nitrites which are respectively of the order of 100 and 10 mg/L.

We used the experimental parameters resulting from the optimization of this process for similar nitrate and nitrite contents, namely a chloride concentration of 0.4 mol/L and a removal time of 4 hours under agitation. We also tested the three membranes AFN, AMX, and ACS. The results obtained are given in **Figure 8**. It can be seen that the most efficient membrane is AFN and that the removal rates for this membrane are around 98% for nitrates and 85% for nitrites. These results are perfectly consistent with theoretical predictions and confirm that Donnan dialysis remains very efficient for the removal of these two anions.
