Multiple response optimization of the coagulation process for upgrading the quality of effluent from municipal wastewater treatment plant

To meet the high quality standard of receiving water, the coagulation process using polyferric chloride (PFC) was used to further improve the water quality of effluent from wastewater treatment plants. Uniform design (UD) coupled with response surface methodology (RSM) was adopted to assess the effects of the main influence factors: coagulant dosage, pH and basicity, on the removal of total organic carbon (TOC), NH4+-N and PO43−-P. A desirability function approach was used to effectively optimize the coagulation process for the comprehensive removal of TOC, NH4+-N and PO43−-P to upgrade the effluent quality in practical application. The optimized operating conditions were: dosage 28 mg/L, pH 8.5 and basicity 0.001. The corresponding removal efficiencies for TOC, NH4+-N and PO43−-P were 77.2%, 94.6% and 20.8%, respectively. More importantly, the effluent quality could upgrade to surface water Class V of China through coagulation under optimal region. In addition, grey relational analysis (GRA) prioritized these three factors as: pH > basicity > dosage (for TOC), basicity > dosage > pH (for NH4+-N), pH > dosage > basicity (for PO43−-P), which would help identify the most important factor to control the treatment efficiency of various effluent quality indexes by PFC coagulation.


Results and Discussion
Optimization for TOC removal. TOC removal is an important indicator for the treatment efficiency of the coagulation process. As listed in Table 1, the different coagulation conditions had distinct difference in the residual TOC concentration of the effluent. The following equation was obtained by modeling the experimental results with the nonlinear regression method:  Table 1. UD experimental design and the response results for coagulation processes using PFC. Note: X 1 , X 2 , and X 3 represents to coagulant dosage, pH and basicity, respectively.
Statistical testing of the model was executed with the Fisher's statistical test for analysis of variance (ANOVA). The quadratic regression indicates that the model was significant, because the value of F-statistic (the ratio of mean square ascribed to regression to the mean square to the real error) of 14.644 was much greater than F 0.05,1,15 (4.543). The high value of coefficient of determination (R 2 = 0.87) and the low P-values (0.05) verified the sufficiency of the model. The plots of the predicted TOC residual concentration versus the measured ones are shown in Fig. 1a. Most points distributed near to the straight line, indicating that the regression model was able to predict these residual TOC concentrations. The optimized conditions to obtain the lowest TOC residue concentration were obtained by setting the partial differential of the response (Eq. 1) to zero as follows: coagulant dosage of 24 mg/L, pH of 7.5 and basicity of 0.30, where the minimum concentration of TOC was calculated to be 1.17 mg C/L, which was equivalent to 4.7 mg COD/L (according to the empirical value obtained through analyzing the relationship between TOC and COD in sewage treatment plants 26 ). The removal efficiency was 85.9%. The effects of coagulant dosage, pH and basicity on the TOC concentration as the response are shown in the 3-dimentional response surface graph (Fig. 2). The distinct peak in the response surfaces indicates that the optimal conditions were exactly in the experimental region. In other words, there were significant interactive effects on TOC removal between the three factors.
Optimization for PO 4 3− -P removal. PO 4 3− -P content is regarded as one of the important factors controlling water eutrophication 27 . It is essential to remove PO 4 3− -P from the effluent before it is discharged to receiving water. The effects of various coagulation operation parameters on the removal of PO 4 3− -P using PFC could be described by the following equation, which was obtained by modeling the results in coagulation experiments with the nonlinear regression method: The results of F = 18.175 > F 0.05,1,15 = 4.543 and R 2 = 0.90 for the PO 4 3− -P removal efficiency illustrated that the second-order polynomial model fitted the experimental results well. Figure 1b shows that the measured versus predicted plot values were distributed evenly near to the straight line. From Eq. 2, the optimized conditions for the minimum residual PO 4 3− -P concentration were calculated to be: coagulant dosage of 32 mg/L, pH of 7.0 and basicity of 0.25. Under these conditions the residual PO 4 3− -P concentration was calculated to be 0.01 mg/L, and the removal efficiency was 99.9%.
When the residual concentration of PO 4 3− -P was chosen as the response, the response surfaces of the quadratic model that one variable kept at the optimal value and the other two varied within the experimental ranges, respectively, are illustrated in Fig. 3. The distinct peak in the response surfaces indicates that the optimal conditions were exactly located inside the design boundary. The elliptical contour plots imply that there were significant interactive effects on PO 4 The quadratic regression indicates a high significance of the model, because the value of F-statistic of 6.30 was much greater than F 0.05,1,14 (4.60). The high value of the correlation coefficient (R 2 = 0.85) suggests a good agreement between the measured and predicted values of the residual NH 4 + -N concentration (Fig. 1c). Then, the optimal conditions for maximum NH 4 + -N removal were calculated to be: coagulant dosage of 27 mg/L, pH of 8.5 and basicity of 0.001. In this case, the minimum concentration of residual NH 4 + -N was calculated to be 1.52 mg/L and the removal efficiency was only 20.6%.
The response surfaces of the quadratic model with the concentration of residual NH 4 + -N as the response are shown in Fig. 4. The contour plots imply that there were significant interactive effects on NH 4 + -N removal between dosage and pH, dosage and basicity, as well as pH and basicity. This was evidenced by the obvious peak in the response surface, in which the optimal conditions were exactly located in the experimental range. 4 3− -P and NH 4 + -N by PFC. The residual organics in the effluent from the biological WWTPs include humic substances, proteins, microbial products and other inert matters, most of them are biopolymers and in the form of colloids 28,29 . The removal mechanisms of these organics through coagulation include a combination of charge neutralization, entrapment, adsorption and complexation with the iron based coagulant into insoluble particulate aggregates 4 . PFC was pre-hydrolyzed in the preparation process, and when it was dosed to the solution, it could slow down the rate of hydrolysis of PFC species through dilution. So PFC species might have sufficient time to react with the organic matters. More polymeric species with higher positive charge density were formed with the increase of basicity, which benefited TOC removal by adsorption and charge neutralization. Under these conditions, the coagulant PFC exhibited good charge neutralization, bridging and sweep-floc abilities, which contributed the high TOC removal efficiency. The coagulation of PO 4 3− -P with Fe(III) salts includes two major mechanisms: formation of Fe-hydroxo-phosphate complexes, Fe(OH) 3−x (PO 4 ) x , which either absorbs onto positively charged Fe(III) hydrolyzed species or precipitates with Fe(III) hydrolyzed products as the centers; and adsorption of PO 4 3− -P ions with polymeric species 9,30 . The pH plays an important role in the PFC coagulation process, and the PFC flocs formed at a neutral condition would give the largest floc size 7 . In addition, basicity is one of the important factors that affects the nature of Fe(III) species, thereby affecting coagulation performance. Therefore, under the optimized Scientific RepoRts | 6:26115 | DOI: 10.1038/srep26115   Because the coagulation process does not remove NH 4 + -N directly, the removal efficiency of NH 4 + -N was not very high. After PFC was dosed to the solution, the pre-hydrolyzed Fe species would enmesh and co-precipitate with the colloidal particles in wastewater, and then settle together. Partial of NH 4 + -N could bind to the surface of the negatively charged colloidal particles by electrostatic attraction 31 . As a result, partial NH 4 + -N could be removed from the wastewater together with the colloid particles.

Removal mechanisms for TOC, PO
Different removal mechanisms lead to the different optimal removal conditions, which are consistent with the above results. Furthermore, to confirm the validity of the statistical experimental strategies, additional confirmation experiments based on the optimized coagulation conditions above were conducted. The chosen conditions and results are listed in Table 2 -P or NH 4 + -N achieved under the different optimal conditions is a big concern in real wastewater treatment. Thus, it is necessary to consider the comprehensive removal of TOC, PO 4 3− -P, and NH 4 + -N in practical application. In this work, a desirability function approach 32,33 was used to optimize multiple responses in order to obtain a good quality of the effluent to match high water quality of receiving water. The completely desirable values of the response residual concentrations of TOC, PO 4 3− -P and NH 4 + -N were set at 1.19, 0.01 and 1.52 mg/L, respectively, which were the lowest residual concentrations of TOC, PO 4 3− -P, and NH 4 + -N obtained under the individual optimal conditions. And the completely undesirable values of those responses were above 10 (equivalent to 40 mg COD/L), 0.4 and 2.0 mg/L, respectively, which was based on surface water class V of China 3 . Then the values of desirability function D obtained by calculating the geometric mean of the three individual ideal functions at various experimental conditions are listed in Table 1, and was regressed using the following equation: The optimal conditions were calculated to be: dosage of 28 mg/L, pH 8.5, and basicity 0.001, respectively. The corresponding residual concentrations of TOC, PO 4 3− -P, NH 4 + -N concentration and D value were 1.41 mg/L, 0.03 mg/L, and 1.53 mg/L and 0.90, respectively. The overlay plot for the optimal region is presented in Fig. 5. The shaded portion gave the permissible values of the variables by defining the desired limits of the concentrations of TOC, PO 4 3− -P and NH 4 + -N as 10 mg/L, 0.4 mg/L and 2.0 mg/L, respectively, and the treated effluent satisfied surface water Class V standard of China.
A confirmation experiment under the compromised conditions was carried out in duplicates, and the concentrations of TOC, PO 4 3− -P, and NH 4 + -N in the obtained effluent were 2.49 (equivalent to 10.0 mg COD/L), 0.05, and 1.52 mg/L, respectively, and these results were in good agreement with the predicted ones, and the differences between predicted and experimental values were 0.90, 0.02, and 0.01 mg/L, respectively. As shown in Table 3, the effluent index, including the concentrations of TOC, PO 4 3− -P, and NH 4 + -N, dropped significantly after the treatment under the optimal conditions, especially for the PO 4 3− -P concentration (with a removal efficiency of 90.9%), which was reduced one order of magnitude compared to the value before the treatment, and the treated effluent could reach to surface water Class V standard of China.
Influential priority of the three factors. GRA method was used to evaluate the influential degrees of dosage, pH, and basicity on the removal of TOC, NH 4 + -N and PO 4 3− -P by coagulation using PFC. The grey relational grades γ of these factors for the treatment performance were calculated to be:  Results showed that the influential priorities on the removal of TOC, NH 4 + -N and PO 4 3− -P in the effluent after coagulation were quite different. The pH showed the most significant effect on TOC removal, followed by basicity. Dosage exhibited a less-significant effect. For NH 4 + -N, the influential priorities were in the order of: basicity > dosage > pH. In contrast, the influential priorities of these factors on PO 4 3− -P removal were in the order of: pH > dosage > basicity. The results in this work also demonstrated that pH was the most significant factor affecting the removal of organic matters and PO 4 3− -P from the WWTP effluent by coagulation using PFC. The pH determines the hydrolysis of PFC species and floc sizes, which in turn affect the coagulation mechanism. Because of the slow hydrolysis of PFC under acidic condition, the charge neutralization dominates the coagulation process of PFC. The hydrolysis tendency of PFC becomes much larger with pH increased, while bridging, absorption and sweep-floc play important roles in coagulation process of PFC. Furthermore, coagulants give bigger final floc sizes at neutral and alkaline conditions than acidic conditions which benefit the removal for PO 4 3− -P. This result agreed with previous studies, in which pH was also found to play an important role in the coagulation process using PFC 6,7 . In contrast, basicity, rather than pH and dosage that are usually considered in the coagulation process for wastewater 34 or drink water 35 treatment, was found to be the crucial factor influencing the removal of NH 4 + -N in this study. Basicity determines the species of pre-hydrolyzed products in preparation process of PFC. The hydrolyzed Fe species, such as amorphous ferric hydroxide precipitates, exhibit good enmesh and co-precipitate abilities with the colloidal particles, and in turn cause the reduction of NH 4 + -N bound to them.
Implications of this study. An integration of UD and RSM, with a rational statistical basis, is proved to be a valid approach for the optimization of the coagulation process for the treatment of the effluent from WWTP. The response variable was fitted by a second-order model when using the regression method to describe the relationship between the dependent output variable and the independent variables with the fewest multi-levels experimental trials. The value of F-statistic was much greater than F 0.05 indicated that the model was significant, and the high value of coefficient of determination (R 2 > 0.85), a sufficient large residual degree of freedom (17, much higher than 5) and the low P-values (0.05) verified the sufficiency of the model, these all illustrated the second-order model was suitable and effective in this study. Under the optimized conditions, the treated effluent could reach to surface water Class V standard of China. Due to serious water pollution in China, the WWTPs need to upgrade to meet the increasing strict discharge regulation, indicating that the sewage treatment plants face the problem of upgrading and reconstruction. The coagulation process is easy to implement without big changes in structures or technological process of sewage treatment plant. This integrated optimized approach for PFC coagulation also could further improve the effluent quality to meet the surface water Class V standard of China, which may significantly reduce the pollution of the receiving water body. However, the efficiency of the coagulation process is governed by the various factors, such as the type, dosage and basicity of the coagulant, pH in the solution, the characteristics of wastewater, e.g. anion, cation, the type and concentration of pollutants etc. Thus, the optimized parameters for coagulation obtained in this study may not be applicable for other sewage treatment plants, but it is suitable to upgrade the quality of the effluent from sewage treatment plants through coagulation by the multi-response optimization method.
Meanwhile, this study shows that this UD approach effectively optimizes the coagulation process by taking advantage of few data sets and factors with different levels, which is very attractive for the processes where data are obtained hardly or expensively. Thus, this optimization approach can be applicable for other complex or multivariate systems in the environmental field. UD focuses on the selected experimental points distributing uniformly within the factor space for all the three key factors with different levels influencing the efficiency of this process, i.e., dosage, pH and basicity in this study. Thus most response information is obtained through the fewest numbers of the experiments and multilevel factors. These characteristics are the advantages of UD compared with other experimental design approaches.
However, in addition to the treatment efficiency, the cost is also a big concern in practical application. GRA is adopted to assess the influential priorities of factors, which does a favor for selecting the most important factor, ultimately achieving a balance between the treatment efficiency and the cost. For example, GRA results show that basicity and pH have the most and least significant effect on the residual NH 4 + -N concentration, respectively.  Table 3. Effluent quality from a local wastewater treatment plant before and after coagulation treatment under optimal conditions (Dosage of 28 mg/L, pH of 8.5, basicity of 0.001).
Scientific RepoRts | 6:26115 | DOI: 10.1038/srep26115 However, the pH is usually uncontrollable in WWTPs before the coagulation process, while the basicity of commonly used coagulant PFC is determined with the experience without optimization during practical application. The results of UD and RSM reveal that NH 4 + -N removal could be improved through adjusting the basicity of PFC. Therefore, in the practical application, the sewage of high ammonium content could be treated without pH adjustment, which could reduce the operation cost to improve the effluent quality. All of these indicate that the results of UD, RSM and GRA are complementary. Through the multi-responses optimization of coagulation (a simple and efficient water treatment process), the water quality of the effluent from a WWTP could be upgraded to surface water class V of China.

Conclusions
In present work, a coagulation process with PFC was employed to treat the effluent from a WWTP to improve the effluent quality. A multiple responses optimized method RSM coupled with UD was used to successfully optimize the process, and the individual and interactive effects of the main influential factors were evaluated. An optimal condition of coagulant dosage 28 mg/L, pH 8.5 and basicity 0.001 was obtained when considering the removal of TOC, PO 4 3− -P and NH 4 + -N simultaneously. More importantly, the water quality of the treated effluent after PFC coagulation could reach surface water class V of China under the optimal region. This indicated that the PFC coagulation process after optimization could efficiently improve the quality of the effluent from WWTPs to meet more and more strict wastewater discharge policy. Experimental design with UD. U n (q m ) can be used to describe UD table, wherein, U, n, q and m represent the UD, the number of experimental trials, the number of levels and the maximum number of factors, respectively. In this study, coagulant dosage (X 1 ), pH (X 2 ), and basicity (X 3 ) were selected as three independent variables in the coagulation process. Twenty levels, ten levels and five levels were chosen for X 1 , X 2 , X 3 , respectively, to investigate the effect and interaction of the factors on coagulation. When considering the operability of all factors and ensuring the accuracy of the experiments, a mixed-level UD table with the different number of levels of each factor, U 20 (20*10*5) with discrepancy of 0.1664 in uniformity, was chosen to carry out the experiments. The range and levels of each factor are listed in Table 1.

Methods
The responses included the removal of TOC, NH 4 + -N and PO 4 3− -P, which represented the overall wastewater treatment efficiency. The response variable was fitted by a second-order model using the regression method to describe the relationship between the dependent output variable and the independent variables.  where X i refers to the independent input variable that influences output variable Y; b 0 , b i , b ii and b ij are the constant regression coefficients, the i th linear coefficient, the i th quadratic coefficient and ij th interactive coefficient of the equation, respectively. Uniform Design Software 3.0 (http://www.math.hkbu.edu.hk/Uniform Design/software) was used to evaluate the parameters of the response equations, and corresponding analysis on variations were assessed using MATLAB 7.0. Meanwhile, three-dimensional response surfaces or two-dimensional contour curves were illustrated to give the visual responses of TOC, NH 4 + -N and PO 4 3− -P. The confirmation experiments under individual and integrated optimal removal conditions were conducted to testify the accuracy of statistical experimental results.
Optimization for multiple responses. Desirability function approach is the most common method of optimizing multiple responses 32,33,36 . For each system response Y i , ideal function d i (Y i ) is assigned the value between the ranges of 0 to 1. Specifically, d i (Y i ) = 0 and 1 mean that Y i is a completely undesirable value and a completely desirable response, respectively. Then the general desirable function is obtained by calculating the geometric mean of all individual desirable function together: The specific calculation method for the individual desirable function value is as follows: where T i and L i represent the completely undesirable value and completely desirable value, respectively.

GRA.
It is essential to understand the most significant influential parameter for the coagulation process. To prioritize the various factors on the treatment efficiency, grey relational analysis (GRA) 37 was adopted to identify the interrelationships between multiple factors and variables. The grey relational grade γ is obtained by calculating the average values of all the grey relational coefficients with the methods mentioned in previous research 38,39 as follows: where z 0 and z j are the normalized data of the input factors and the output variables, respectively. γ (z 0 (k) and z j (k)) are the grey relational coefficient. The larger grey relational grade γ indicates the influential degree of the factor on the system is greater.