#### 3.2. Model Fitting and Statistical Analyses

Table 3 summarizes the experimental results of the 2 k full factorial design obtained for the removal of turbidity, humic, and fulvic acid-like species at the different coded levels. Similar results were observed for the duplicate of the central point at pH 7 and coagulant dose of 25 mg L

^{−1} with less than 2% error (runs 3 and 6), which corroborates that the pure error of coagulation experiments is negligible. The data for the experimental matrix were then modeled and statistically validated.

Analysis of variance (ANOVA) was utilized to determine the statistical significance of the factors and their corresponding goodness of fit.

Table 4 presents the values for the regression coefficients (RC), sum of squares (SS), standard error (SE), F-value (F), and p-value (

p). The p-value is the probability value that determines the significance of the effect of each factor in the model [

36]. Fisher’s test was used to determine the significance of the variables where the degree of significance was ranked based on the value of the F-ratio—the larger the value of F, the smaller the value of “Prob > F”. This translates to the greater significance of the corresponding model and the individual coefficient [

36]. The confidence level used to determine the statistical significance of the factors is 95%, which means that the p-value should be less than or equal to 0.05 for the effect to be statistically significant [

37]. Upon elimination of the insignificant terms, the final empirical models based on statistical analyses were defined.

The response surface equation defined for the use of FeCl

_{3} as coagulant for each response is defined by Equations (2)–(4):

Meanwhile, identical modelling approaches were employed to define the model equation for the coagulation treatment using PACl. Equations (5)–(7) describe the response surfaces for the removal of humic-like species, fulvic-like species, and turbidity.

It can be seen in

Table 5 that the values of adj- R

^{2} are greater than 0.98, which indicates that the variability of new data is expected to be about 98%. At 95% confidence level, the coefficients of determination (R

^{2}) for all responses obtained from coagulants FeCl

_{3} and PACl were more than 0.99. The value of R

^{2} is a measure of the proportion of total variability by the model, where values close to 1 and at least 0.80 mean that the model is a good fit [

38]. This implies that the generated model was sufficient in closely estimating the experimental HLS, FLS, and Turbidity removal efficiency [

39]. Previous studies suggested the use of adj-R

^{2}, a statistic that is adjusted for the size of the model, i.e., the number of factors, to evaluate the adequacy of the model in order to prevent the potential problem wherein the value of R

^{2} tends to increase as factors are added to the model [

36]. Adequate precision, included in

Table 5, pertains to the signal to noise ratio and typically has a value greater than 4, which implies that the signal is desirable. On the other hand, the coefficient of variation (CV) is the standard deviation calculated as a percentage of the mean, with values no greater than 10% [

36]. It was observed that all statistical results presented in

Table 5 demonstrate the good adequacy of the estimated model to fit all the responses. This was also further revealed by the predicted–observed plots in

Figure 2, which enables inferring the fair agreement of predicted responses to the experimental data for both coagulants, FeCl

_{3} and PACl.

#### 3.3. Effect of Initial pH, Coagulant Dosage, and Their Interaction

Figure 3 illustrates the percentage of contribution of each term defined by Equations (2)–(7) on the NOM removal performance using different coagulants (i.e., FeCl

_{3} or PACl). Note that the results refer to the effects of initial water pH (A) and coagulant dosage (B) on the coagulation process.

Figure 4 and

Figure 5 show the contour plots of the main factors, initial water pH and coagulant dosage, and interaction effects on the NOM removal percentage after using FeCl

_{3} and PACl coagulants, respectively. As shown in

Figure 3a, high percentage contributions of coagulant dosage were obtained for FLS and turbidity removals (93.36% and 87.90%, respectively) when FeCl

_{3} was used as the coagulant. This trend is attributed to the initial pH being set at near neutral levels, where charge neutralization occurs. This implies that, for all pH values considered, all runs were expected to yield high removal efficiencies. It was observed in

Figure 4 that the removal efficiency improved as the coagulant dosage was increased. This is attributed to the increase in the amount of FeCl

_{3} that hydrolyzed to positive ferric species and subsequently interacted with the negatively charged NOM fractions to form larger complexes [

2]. NOM fraction removal efficiency was reported to be constant at a coagulant dosage greater than 40 mg L

^{−1} [

25]. At a high coagulant dosage, FeCl

_{3} could not effectively remove NOM because only a portion of Fe could interact with NOM to form Fe–NOM complexes. Meanwhile, the excess of iron dosed will form negatively charged Fe(OH)

_{3} flocs and Fe(OH)

_{4}^{−} instead of desired Fe-NOM complex [

40].

On the other hand, when using PACl, the NOM removal was mainly due to the interaction of initial pH and coagulant dosage (AB) as deduced from

Figure 2b. Note that

Figure 5 also shows high interaction effects on the parameters considered when PACl coagulant was used. It is evident in the contour plots that pH affected the removal efficiencies. The highest removal percentages were recorded at 40 mg L

^{−1} coagulant dosage and an initial pH of 8, with values of 76% and 81% for fulvic acids and turbidity, respectively. It can be noted that the removal of fulvic at pH 6 and 8 are almost the same, which may be due to the solubility of fulvic acids in both alkali and acidic regions, while humic acids are only soluble in the alkali region [

41]. High PACl dosage is not effective in removing turbidity and NOM fractions because only a portion of Al reacts with NOM fraction to form an Al–NOM fraction complex. This is due to the formation of polymer bridges between particles that caused the destabilization of Al-NOM complex, resulting in the repulsion between particles at excessive dosage [

42].

Analysis of turbidity evolution shows interesting trends in the function of coagulant species employed and operational conditions of coagulation treatment, as can be seen in

Figure 6. The turbidity spiked up upon addition of FeCl

_{3} coagulant and 1 min rapid mixing, gradually reduced during the flocculation process of 30 min slow mixing, and dropped to near zero at the end of the 30 min sedimentation. Increase in turbidity can be explained by the formation of iron hydroxide flocs after coagulant addition, which removes suspended solids during its settlement [

43,

44]. Analysis of zeta potential changes during treatment shows a gradual change from initial negative values of −17.09 ± 1.03 to zero. These results that show a gradual increase in zeta potential towards zero can be attributed to charge neutralization.

Interestingly, a spike in zeta-potential at high doses of FeCl

_{3} of 40 mg L

^{−1} can be observed, which can be explained by the positive zeta potential of iron hydroxide flocs [

40]. The iron coagulation process is controlled by charge neutralization mechanism, which is said to occur at pH 6 and >7 where NOM is most negative [

28]. This trend demonstrates the dual role of pH not only on the coagula formation but also on the natural speciation of NOM in function of the pH. NOM is composed by a complex mixture of fulvic and humic acids of different molecular weights and different functional groups that are susceptible to be deprotonated (i.e., carboxylic groups) [

19,

45,

46]. The ratio of the different charged and non-charged species is determined by the respective pK

_{a} value of each organic acid. A higher density of negatively charged species will require higher doses to induce removal mechanisms ruled by charge destabilization and adsorption/complexation. The addition of positive coagulant disrupts the negatively charged NOM fractions and produces coagulant-NOM flocs [

19,

46], which also assists in the removal of solids from the suspension. The removal is therefore dependent not only on the formation of metal hydroxides as coagulants but also on the charge distribution of organic species in as a function of pH. Identical mechanisms are associated for PACl coagulant agent [

47,

48]. Generally, charge neutralization occurs at around neutral pH when aluminum salts are used. At neutral pH, the cationic hydrolysis products are only a small portion of the total soluble Al, while aluminate ions are the dominant form. Colloidal hydroxide particles are suggested to be effective charge-neutralizing species and may be positively charged up to pH 8, which explains the high removal up to pH 8 [

29]. At neutral pH, coagulants are said to be prone to further hydrolysis and polymerization into medium polymer species. A quick comparison between turbidity abatement can be conducted between the results described in

Figure 6a,b. Note that independent of experimental conditions, FeCl

_{3} outperforms PACl in turbidity reduction. However, PACl presents better performance on the abatement of NOM (i.e., humic and fulvic acid-like species), which highlights the use of PACl as an efficient approach to minimize the risk of disinfection by-products formation through NOM oxidation during disinfection steps. Therefore, these results encourage the use of PACl to remove NOM from raw waters.

#### 3.4. Optimization of Process Parameters

In order to improve the coagulation process, optimization of parameters was defined from the contour surfaces. The desirability function method was used to determine the most desirable condition in the responses [

28]. This method can combine multiple responses to generate a response called desirability function. Desirability function ranges from 0 to 1, with the desired value closest to 1 [

36].

The initial pH and coagulant dosage were set within a range, whereas the removal responses were set to maximum levels.

Figure 7 shows the desirability plot for all the responses, with an overall desirability of 1 at an initial pH of 8 and a coagulant dosage of 40 mg L

^{−1}. Optimized experiments allowed for attaining a maximum removal of 69.6% of humic acids, 73.9% of fulvic acids, and 84.0% of turbidity when using FeCl

_{3} as the coagulant. On the other hand, for PACl slightly higher removals of NOM, with percentage removals of 78.5% for humic acids, and 75.6% for fulvic acids, and lower turbidity reduction of 80.9% were attained. These results suggest superior performance of PACl as the coagulant to trap and precipitate NOM during coagulation treatment.