Response Surface Methodology Approach to Optimize Parameters for Coagulation Process Using Polyaluminum Chloride (PAC)

Abstract

Coagulation is a process affected by multiple variables, nonlinear mapping and multiple perturbations. In order to realize the precise dosage of flocculants, polyaluminum chloride (PAC) was taken as the research object to explore the effects of temperature, water turbidity, pH and COD_Mn on the dosage of PAC and coagulation effect. A response surface methodology (RSM) experiment was carried out based on a single-factor experiment. The turbidity, pH and dosage of a single parameter, as well as the interaction term and secondary term, all have significant influence on coagulation effect. The optimal reaction conditions were calculated using Design-Expert software: pH, 7.48; turbidity, 14.59 NTU; dosage, 24.01 mg/L; and the error between the experimental value and the predicted value, 4.08%. Establishing a model with residual turbidity as a consideration index can help to calculate the optimal dosage of PAC, which is conducive to a reasonable and accurate control of the dosage of PAC in the coagulation process, so as to achieve the goal of low turbidity of effluent and low production cost.

1. Introduction

Coagulation is an important part of the removal of suspended matter and some dissolved matter in the conventional surface water treatment process. The basic principle is that by adding chemical agents, the suspended particles and colloids in the water can be destabilized and coagulate with each other to form a large particle floc that is easy to settle, which has the advantages of high efficiency, low cost and simple operation [1,2]. The final performance of the coagulation process depends largely on the coagulant used. Traditional coagulants (aluminum chloride, aluminum sulfate, alum) have some disadvantages, such as large dosage, slow coagulation rate, small and light alum flower, and a poor treatment effect on low-temperature and low-turbidity water. Polyaluminum chloride (PAC), as a commonly used inorganic polymer flocculant (IPF), is a polymer containing a hydroxyl group and has strong interfacial adsorption capacity. The coagulation effect of PAC is the result of multiple factors such as coulomb force, intermolecular van der Waals force, hydrophobic repulsion force and bonding force between the hydroxyl group and the surface, which greatly improves the coagulation efficiency. PAC is widely used in China, Japan, Russia and Western Europe because of its advantages of low dosage requirement, good settling performance and wide adaptability [3,4,5]. At present, the water quality of the water supply source in the water purification plant is unstable, which leads to the different mechanisms of compression in a double electric layer, electric neutralization, the adsorption bridge and net sweeping during the coagulation process. In this case, it is easy to run alum, the floc is difficult to settle, and the effluent turbidity is high, which affects the coagulation effect [6]. When the dosage of coagulant is too large, it is easy to cause the effluent aluminum concentration to exceed the sanitary standard of drinking water (0.2 mg/L), which is harmful to human health [7,8,9]. Therefore, it is necessary to calculate the optimal dosage of the coagulant according to the influencing factors to achieve accurate dosage. Recently, the organic pollution of the water source has become increasingly serious; some insoluble organic pollutants in the water can be accompanied by the existence of suspended matter, and some dissolved organic pollutants may also be attached to the suspended matter. The removal of turbidity is conducive to the removal of suspended matter, and it is also conducive to the elimination of bacteria and viruses. Therefore, turbidity is an important index to measure the coagulation process.

Many factors affect the coagulation effect. Trial and error have been conventionally practiced to optimize these factors. These studies were conducted using the “changing one factor at a time” method, i.e., a single factor is varied while all other factors are kept unchanged for a particular set of experiments. Zhang et al. studied the effects of PAC concentration and pH on the removal rates of COD and turbidity by using a single-factor test method [10]. Tomaszewska et al. studied the effects of pH on UV₂₅₄ and COD_Mn removal [11]. Likewise, other variables would be individually optimized through the single dimensional searches which are time-consuming and incapable of reaching the true optimum as interaction among variables is not taken into consideration. However, coagulation is a process affected by multiple variables, nonlinear mapping and multiple perturbations [12,13].

To solve this problem, the response surface methodology (RSM) is a tool that integrates the functions of experiment design, model establishment and analysis, evaluation and solution, etc. It overcomes the defect that a single-factor method and orthogonal experiment method cannot explain the interaction between various factors; moreover, RSM is widely used in food, the chemical industry and biology [14,15,16]. In the field of water treatment, applying RSM to optimize the coagulation process for the treatment of wastewater was reported in many studies [17,18]. However, in the drinking water treatment area, few studies reported the application of RSM to optimize the conditions of the coagulation process with respect to the highest removal of turbidity.

In this study, by exploring the influence of turbidity, pH, temperature and COD_Mn on turbidity removal, the main influencing factors were determined. On this basis, RSM was used to optimize the test, establish the model, find the best combination of each factor level, determine the best process parameters and guide the water plant to reasonably and accurately control the PAC dosage in the coagulation process so as to achieve the goal of low turbidity of effluent and low production cost.

2. Materials and Methods

2.1. Experimental Instruments and Materials

Main reagent: PAC [Al₂(OH)_nCl_6−n]_m (n < 6, m is the degree of polymerization) (Shengli Xinbang Petroleum Technology Co., Ltd., Dongying, China); the concentration of the liquid is 10%, and the liquid diluted for coagulation test is 1%. The detailed performance of PAC is shown in

Table 1. Properties of PAC.

Index	Unit	Number Range
Density (20 °C)	g/cm3	≥1.24
pH (1% water solution)		≥3.5–5.0
Al2O3	mg/L	≥10.0
Basicity	%	50.0–85.0

. All the reagents used in preparing each coagulant were of analytical grade, and deionized water was used to produce all solutions.

2.2. Test Methods

The beaker coagulation test was carried out on the automatic agitator ZKS-II-4L (Zhong Keshen Co., Ltd., Chengdu, China). A total volume of 500 mL of the water sample was added to each beaker (1 L) and its pH was adjusted to the required experimental values by adding HCl or NaOH solutions (1 mol/L) dropwise. The next step was the addition of the PAC dose with stirring for 1 min at a speed of 210 rpm. After that, the rate was reduced to 70 rpm and the second coagulation time was 9 min. After 20 min of settling, the turbidity was measured at about 2 cm below the liquid level. The speed and time set in this coagulation procedure refer to the literature research in

Table 2. Coagulation procedure.

Stage	Revolution Range (rpm)	Reaction Time (min)	Reference
The first coagulation stage (rapid mixing)	80–200	1–5	[19,20,21,22,23,24,25,26]
The second coagulation stage (slow mixing)	25–70	9–50
Sedimentation stage	0	20

.

2.3. Single-Factor Experiment Design

The first and most critical step in applying RSM to the coagulation process is to screen for independent factors that affect turbidity removal. The experiment explored the influence of temperature, pH, turbidity and COD_Mn on the turbidity of the effluent with an increase in PAC dosage. The water temperature (5 °C, 10 °C, 15 °C, 20 °C, 25 °C), pH (6.85, 7.48, 8.05, 8.43), turbidity (5.42 NTU, 15.13 NTU, 25.23 NTU, 40.18 NTU) and COD_Mn (4.23 mg/L, 5.12 mg/L, 6.07 mg/L, 7.11 mg/L) were controlled, respectively, and other conditions were set unchanged for testing to determine the optimal dosage of PAC. The optimal dosage in the experiment refers to the minimum dosage of coagulant corresponding to the lowest turbidity after coagulation under different conditions. Test method and equipment are shown in

Table 3. Test method and equipment.

Test Index	Test Method	Equipment Information
turbidity	Light scattering method	Turbidimeter model—Hach 2100N (Hach Company, Loveland, CO, USA)
pH	Glass electrode method	pH meter—PHS-2F (Shanghai Leici Co., Ltd. Shanghai, China)
CODMn	Spectrophotometric method	Digester—DRB200 (Hach Company, Loveland, CO, USA)

.

2.4. RSM Test Design

Design-Expert is a statistical software package that designs experiments and performs comparative tests and the optimization of process variables. It also contains the graphical tool that helps to determine the impact of each considered parameter on the yield of a process [27]. According to the results of the single-factor experiment, 3 factors were selected as the objects of investigation, and 3 levels were set for each factor, with residual turbidity as the response value. Seventeen experiment runs were generated using Box–Behnken design. Analysis of variance (ANOVA) was used for graphical analyses of the data to obtain the interaction between the process variables and the response [28]. The quadratic equation model for predicting the optimal conditions can be expressed according to Equation (1):

$$\mathrm{Y}={\mathsf{\alpha }}_0+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathsf{\alpha }}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathsf{\alpha }}_{\mathrm{i}\mathrm{i}}·{\mathrm{X}}_{\mathrm{i}}^2+{\sum }_{{\mathrm{i}}_{\mathrm{i}\le \mathrm{j}}}^{\mathrm{k}}{\sum }_{\mathrm{j}}^{\mathrm{k}}{\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}·{\mathrm{X}}_{\mathrm{i}}·{\mathrm{X}}_{\mathrm{j}}+\cdots \mathrm{e}$$

(1)

where Y is the response value (residual turbidity), X is the independent variable, X_i² is the square effects of variables, X_i·X_j is the variable interaction effects, α₀ is a constant coefficient, α_i is the linear coefficient, α_j is the quadratic coefficient, α_ii is the quadratic regression coefficient, α_ij is the interaction regression coefficient, k is the number of factors studied and optimized in the experiment and e is the random error. The coefficient parameters of the second-order models were estimated using a multiple linear regression analysis employing the Design-Expert software (version 8.0.6.1 Stat-Ease, Inc., Minneapolis, MN, USA). The Design-Expert software was also used to demonstrate the 3D surface and 2D contour plots of the response models.

3. Results and Discussion

3.1. Analysis of Single-Factor Experiment

3.1.1. Influence of Temperature on Dosage of PAC

With pH (8.34), turbidity (5.42 NTU) and COD_Mn (4.85 mg/L) unchanged, coagulation tests were carried out at controlled water temperatures of 5 °C, 10 °C, 15 °C, 20 °C and 25 °C. The changes in residual turbidity at different water temperatures are shown in Figure 1.

As shown in Figure 1a, with the increase in PAC dosage, the residual turbidity after coagulation showed a trend of first decreasing and then increasing. As shown in Figure 1b, with the temperature increasing from 5 °C to 25 °C, the optimal dosage of PAC decreased to 34 mg/L, 30 mg/L, 28 mg/L, 26 mg/L and 24 mg/L, respectively, and the residual turbidity decreased to 1.47 NTU, 1.03 NTU, 0.98 NTU, 0.85 NTU and 0.63 NTU, respectively. The results showed that the optimal PAC dosage and residual turbidity value after coagulation decreased with the increase in temperature. This is in agreement with the study [29]. The main reason for this phenomenon is that the hydrolysis of inorganic salt coagulants is endothermic reaction, and the hydrolysis of low temperature water coagulants is difficult. The high viscosity at low temperature weakens the Brownian motion strength of impurity particles in water and reduces the chance of collision, which is not conducive to the stability of colloidal agglomeration. At the same time, when the viscosity of water is high, the flow shear force increases, which affects the growth of flocculants. When the water temperature is low, the hydration film effect of colloidal particles is enhanced, which hinders the condensation of colloidal particles, and the water in the hydration film affects the adhesion strength between particles due to the increase in viscosity and weight [30]. So, when the temperature drops, more PAC is needed to accelerate the formation of dense, settleable flocs [31]. In the treatment of low-temperature and -turbidity water, air flotation, micro-flocculation contact filtration and other processes can be used to improve the water purification effect.

3.1.2. Influence of pH on Dosage of PAC

Under the condition of constant temperature (20 °C), turbidity (5.55 NTU) and COD_Mn (4.85 mg/L), the pH of water was controlled at 6.85, 7.48, 8.05 and 8.43 for the coagulation test. As shown in Figure 2, with the increase in pH, the optimal dosage of PAC was 20 mg/L, 20 mg/L, 22 mg/L and 24 mg/L, respectively, and the minimum residual turbidity was 0.53 NTU, 0.45 NTU, 0.67 NTU and 0.58 NTU, respectively. The results showed that PAC had relatively good coagulability under low alkalinity conditions. When the Zeta potential of flocs was close to the isoelectric point, the residual turbidity of the effluent was the lowest [32]. Canzares et al. [33] indicated that a pH below 8 will be more efficient than a coagulation treatment in which the pH is higher, as there can be more possibilities of interaction because of the opposite charge of the coagulant reagent and of the pollutants.

From an analysis of the reasons for this phenomenon, Al(OH)₃ was found to have obvious bipolarity, and increasing or decreasing the pH value can easily cause Al(OH)₃ to redissolve. H⁺ and OH⁻ in water participate in the hydrolysis reaction of PAC, so pH value affects the hydrolysis rate of PAC, the existence form and the properties of hydrolyzed products. Under the condition of low pH, Al³⁺ cannot be hydrolyzed to Al(OH)₃ in large quantities, and mainly exists in the form of Al³⁺, which cannot be adsorbed and bonded with granular colloid, and the coagulation effect is very poor. Under neutral conditions, it dissolves in water in the form of [Al(OH)₃⁻(H₂O)₃], can generate tiny colloids, adsorb and bond impurities in water and roll them, and the coagulation effect is good. Under alkaline conditions, it dissolves in water in the form of [Al(OH)₄(H₂O)₂]⁻ and [Al(OH)₂(H₂O)₈]⁴⁺, and this kind of low-charge polymer gel will make the coagulation effect worse [34].

3.1.3. Influence of Turbidity on Dosage of PAC

Under the conditions of constant water temperature (20 °C), pH (8.40) and COD_Mn (4.85 mg/L), the turbidity of water was controlled by 5.42 NTU, 15.13 NTU, 25.23 NTU and 40.18 NTU, respectively, and the coagulation test was carried out to observe the influence of turbidity on the dosage of PAC. As can be seen from Figure 3a, with the increase in PAC dosage, the residual turbidity after coagulation showed a trend of first decreasing and then increasing. As shown in Figure 3b, when the turbidity of water was 5 and 15 NTU, respectively, the optimal dosage of PAC remained unchanged, and the residual turbidity after coagulation decreased. When water turbidity increased from 15 NTU to 40 NTU, the optimal dosage of PAC increased and the residual turbidity decreased. Many other studies have also observed that as the turbidity of the treated water increases, so does the dosage of coagulant [35]. The residual turbidity after the coagulation test with optimal dosage was 0.85 NTU, 0.63 NTU, 0.49 NTU and 0.15 NTU, respectively, showing a decreasing trend. The results showed that the higher the turbidity of water, the lower the residual turbidity after coagulation with optimal dosage of PAC. When the water to be treated is low-turbidity water, the number of colloidal particles in the water is small and the distribution is too loose, that is, the collision chance between particles is small, which is not conducive to the formation of Al(OH)₃ colloids after PAC hydrolysis to capture solid impurity particles, and the flocs grow slowly, resulting in a poor flocculation effect [36].

3.1.4. Influence of COD_Mn on the Dosage of PAC

When the water temperature (20 °C), pH (8.35) and turbidity (5.45 NTU) remained unchanged, the COD_Mn of water was controlled to 4.23 mg/L, 5.12 mg/L, 6.07 mg/L and 7.11 mg/L for the coagulation test. As shown in Figure 4a, when COD_Mn increased from 4.23 mg/L to 7.11 mg/L, the optimal dosage was 26 mg/L. As shown in Figure 4b, when COD_Mn increased from 4.23 mg/L to 6.07 mg/L, the higher the concentration of COD_Mn in water, the lower the residual turbidity after coagulation under the condition of equal PAC dosage. When the concentration of COD_Mn increased to 7.11 mg/L, the coagulation effect decreased.

The above four groups of tests showed that there was no linear relationship between PAC dosage and residual turbidity. With the increase in PAC dosage, the residual turbidity after coagulation showed a trend of first decreasing and then increasing. Upon analyzing the reason for this phenomenon, the effect of PAC in the coagulation process is mainly affected by two factors: one is the electric neutralization, the other is the adsorption bridge. When the amount of PAC is small, PAC cannot destroy the mutual repulsion of the same charge on the surface of the colloid and the hydration film; it cannot destabilize the colloid, the multi-nuclear complex will decrease, and it is difficult to form a large floc, resulting in a poor turbidity-removal effect. Adding an appropriate amount of PAC can effectively hydrolyze positively charged ions and neutralize each other with negatively charged colloidal substances in water to form a macromolecular “colloidal-polymer-colloidal” floc wrapped in colloidal particles, which makes it easier for the floc to play its role of adsorption-bridging and net curling. When too much PAC is added, the colloidal particles adsorb too many negative ions to reach saturation, forming a protective film on the adsorption surface of colloidal particles, causing the colloidal charge to become the same charge, resulting in the “colloidal protection” phenomenon, which is not conducive to aggregation between colloids. Meanwhile, the hydrophilicity of the hydrophobic colloid formed in the early stage is gradually enhanced, making the formed floc particles not conducive to sedimentation. Eventually, the removal rate of turbidity decreases [37,38].

3.2. RSM Test Design Results and Analysis

Three factors, pH (A), turbidity (B) and dosage (C), were determined as the investigation variables of RSM design based on the above single-factor test results, and the residual turbidity was taken as the response value. The values of each independent variable were taken at three levels: low (−1), central (0) and high (1). The design factors, codes and levels are shown in

Table 4. Factors, codes and levels of the RSM test design.

Factor	Code	Level
		−1	0	1
pH	A	7.48	8.09	8.7
Turbidity (NTU)	B	5	12.5	20
Dosage (mg/L)	C	20	25	30

.

Input each influencing factor and level value into the system to generate a test plan table, as shown in

Table 5. Box–Behnken test design and results.

Test Number	Parameter 1—pH	Parameter 2—Turbidity (NTU)	Parameter 3—Dosage (mg/L)	Response Value—Residual Turbidity (NTU)
1	8.7	5	25	1.4
2	8.09	12.5	25	0.53
3	8.09	12.5	25	0.54
4	8.7	12.5	20	1.25
5	8.09	12.5	25	0.53
6	8.09	12.5	25	0.6
7	7.48	5	25	1.2
8	8.09	20	20	0.75
9	8.09	5	30	1.3
10	8.7	12.5	30	1.46
11	8.09	12.5	25	0.53
12	8.09	20	30	1.27
13	8.09	5	20	1.25
14	7.48	20	25	0.8
15	8.7	20	25	1.25
16	7.48	12.5	30	1.28
17	7.48	12.5	20	0.92

. Experiments are carried out according to the scheme, and the test results are filled in the corresponding table.

Design-Expert software was used to analyze the test results. First, we clicked the “Analysis” button to test the significance of linear function, second-order model and third-order model, and then compared the data of model significance, missing item and correlation. According to the comparison results, the second-order model was adopted. The quadratic polynomial Equation (2) between the influence parameter and the response value (residual turbidity value) was obtained, where Y represents residual turbidity, and parameters A, B and C represent pH, turbidity and PAC dosage, respectively:

Y = 0.55 + 0.15A − 0.14B + 0.14C + 0.063AB − 0.037AC + 0.12BC + 0.35A² + 0.27B² + 0.33C²

(2)

Under the central composite design, the reliability of the quadratic response surface regression model was analyzed [39], and the ANOVA results are shown in

Table 6. ANOVA statistical results.

	Sum of		Mean	F	p Value
Source	Squares	Df	Square	Value	Prob > F
Model	1.98	9	0.22	247.12	<0.0001 *	significant
A—pH	0.17	1	0.17	189.29	<0.0001 *
B—Turbidity	0.15	1	0.15	164.08	<0.0001 *
C—Dosage	0.16	1	0.16	182.82	<0.0001 *
AB	0.016	1	0.016	17.58	0.0041 *
AC	5.63 × 10−3	1	5.625 × 10−3	6.33	0.04 *
BC	0.055	1	0.0055	62.15	0.0001 *
A2	0.52	1	0.52	582.96	<0.0001 *
B2	0.3	1	0.30	334.65	<0.0001 *
C2	0.46	1	0.46	518.37	<0.0001 *
Residual	6.22 × 10−3	7	8.886 × 10−4
Lack of fit	2.50 × 10−3	3	8.333 × 10−4	0.9	0.5166	not significant
Pure error	3.72 × 10−3	4	9.300 × 10−4
Cor total	1.98	16

Note: * indicates significant difference.

. The F value of the regression model was 247.12, and the corresponding significance level value (Prob > F) was less than 0.0001, indicating that there was only 0.01% probability to respond to the interference parameters, and the confidence was 99.99%. The model is extremely significant and the model selection is reasonable. The p value of the missing fitting item indicates the degree of difference between the model and the actual experiment. The p value of the missing fitting item in this model was 0.5166 (>0.05), and the difference of the missing fitting item was not significant, indicating that the fitting effect was good [40]. The model determination coefficient R² was 0.9969, indicating a good correlation between the predicted value and the measured value [14,41]. Among all parameter terms (including constants) in the model, there were nine items that had significant influence on the objective function, namely linear terms A, B and C, interaction terms AB, BC and AC, and square terms AA, BB and CC.

The fitted model was evaluated using the diagnostic graph function in the Design-Expert software. Figure 5a presents the normal distribution diagram of the studied residuals. It showed that most of the residuals were linearly distributed, and a few residuals were deviated, indicating that the standard deviation of the fitted model followed a normal distribution. Therefore, the quadratic response regression model had a good fit. At the same time, it can be seen from Figure 5b that the measured results were basically consistent with the predicted values of the model, indicating that the established model had validity and reliability, and further confirming that the difference between the measured values and the predicted values of the model was random, that is, there was no systematic bias [42].

3.3. Response Surface Analysis

According to the regression equation fitted by the software, the level of one of the three parameters, pH (A), turbidity (B) and dosage (C), was set unchanged (the intermediate level value); the influence of the interaction between the other two parameters on turbidity removal was solved; and the 3D response surface and two-dimensional contour plot were drawn, respectively. In the response surface plot, if the slope of the response surface is relatively gentle, it indicates that this factor has little influence on turbidity removal. Conversely, if the slope of the 3D response surface is steep, it indicates that this factor has a greater influence on turbidity removal. In addition, the shape of the contour plot can reflect the strength of the interaction effect. When the contour plot is oval, the interaction between the two factors is more significant, while when the contour plot tends to be circular, the interaction between the factors is reduced.

There are two mechanisms for removing turbidity in a coagulation process: (a) the positively charged metal hydrolysate neutralizes the charge of negatively charged particles, causing unstable particles to aggregate; and (b) the “sweep flocculation” of colloidal particles is accompanied or followed by a flocculation composed of a metal hydroxide precipitate. The former requires a high concentration of colloids with a turbidity of 50–100 NTU, providing sufficient contact opportunities for the aggregation of unstable particles. The latter is the main mechanism for removing the low colloid concentration in water, and the raw water has a low turbidity (5–20 NTU). Therefore, the main mechanism of coagulation in this study may be “sweeping flocculation” [43]. As shown in Figure 6a, the PAC dosage of 25 mg/L was left unchanged, and the influence of different pH and turbidity on turbidity removal was determined. The contour map was elliptical, indicating that the interaction between pH and turbidity was obvious, which was consistent with the significance results of the ANOVA table. When the pH was 7.00~8.63, the residual turbidity after coagulation decreased first and then increased. When the pH was near 7.5, the residual turbidity after coagulation reached the lowest. As shown in Figure 6b, the turbidity was set at 12.5 mg/L, and the influence of different pH and PAC dosage on turbidity removal was oval, indicating that the interaction between pH and PAC dosage was obvious. Bouyakhsass et al. found that the interactions between coagulant dose and pH have a significant effect on turbidity reduction [44]. When the dosage was 18.84~28.84 mg/L and the pH was 7.2~8.4, the residual turbidity after coagulation was low. When the pH was 8.09, the influence of different turbidity levels and PAC dosage on turbidity removal was noted and is shown in Figure 6c. The contour chart was oval, indicating that turbidity and PAC dosage obviously interacted. When the dosage was 19.51~29.51 mg/L, the residual turbidity after coagulation showed a trend of decreasing first and then increasing. Ghafari et al. obtained in their study that in the pH range of 6.5 to 8.5, turbidity removal first increased and then decreased as PAC dosage increased from 1.0 g/L to 3.0 g/L [45]. Overdosing deteriorated the supernatant’s quality, indicating the “restabilization” of the colloidal particles; and therefore, the particles could not be coagulated well [46].

3.4. Model Validation by Experiments

On the basis of the above analysis of variance and response surface diagram, the Design-Expert software was used to optimize the conditions affecting the coagulation effect, and the optimal results were obtained. We selected “Optimization”, “Numerical” and “Criteria” successively, set each reaction condition and the optimal condition range, and then selected the “Solution” TAB. The optimum reaction conditions and parameters were obtained: pH value 7.48, turbidity 14.59 NTU, dosage 24.01 mg/L.

Three parallel coagulation tests were carried out under the above optimum conditions to verify the accuracy and repeatability of the RSM optimization results. The residual turbidity obtained from three parallel tests were 0.48 NTU, 0.53 NTU and 0.52 NTU, respectively, and the average value was 0.51 NTU (96.50%), while the theoretical predicted value was 0.49 NTU (96.64%). It can be seen that the relative error between the experimental value and the predicted value was 4.08% < 5%, which was consistent with the predicted model, indicating that the optimal test conditions obtained by the optimization of the quadratic response surface were reliable and accurate, and had certain guiding significance for the optimization of PAC dosage.

The main design strategies that are applied to PAC are single-variable experiments, central composite design (CCD) and the Box–Behnken design (BBD). The main influencing factors of coagulation selection are different. When compared with other reports, the results achieved in this study outweighed similar reported studies.

Table 7. Performance compassion of PAC used in the present study.

No.	Experimental Design	Factors	Optimization	Removal Efficiencies	Reference
1	Single-variable experiments	PAC concentration, pH	multi-response	91.38% COD, 92.41% turbidity	[10]
2	Single-variable experiments	Different PAC types, doses, contact times	multi-response	65–79% total pharmaceuticals, 73–83% total-pesticides,	[36]
3	Single-variable experiments	pH	multi-response	99% UV254, 81–89% CODMn	[11]
4	Central composite design	PAC dosage, pH	multi-response	43.1% COD, 94.0% turbidity, 90.7% color, 0.1% TSS	[45]
5	Box–Behnken design	KH2PO4, Glucose, pH	single-response	86.8% decolorization	[47]

shows a detailed comparison with the PAC used for coagulation.

In this study, the main factors affecting PAC dosing were selected, and the dosing model of PAC was obtained through coagulation experiment, which was based on the research results of the laboratory. However, the water quality of the water plant is complicated and diverse, so it is necessary to constantly revise the model according to the collected data, so as to improve the accuracy and applicability of the model and make it more in line with the actual production situation.

4. Conclusions

The physicochemical process that is known as coagulation–flocculation is common and necessary in water treatment. This work has demonstrated the application of RSM in seeking optimal conditions for this process. The influence of various factors on turbidity removal in the coagulation process was investigated. Turbidity, pH and dosage of single parameters, as well as interaction terms and secondary terms had significant effects on coagulation. According to the predicted results of the model, the optimal coagulation process parameters were as follows: pH value, 7.48; turbidity, 14.59 NTU; dosage, 24.01 mg/L. Under these conditions, the theoretical predicted value was 0.49 NTU. The results of the confirmation experiment agreed with predictions. This demonstrates that RSM can be successfully applied for modeling and optimizing the coagulation–flocculation process and it is the economical way of obtaining the maximum amount of information in a short period of time and with the least number of experiments and high accuracy.