Decolorization of cationic red X-GRL by wet air oxidation: Performance optimization and degradation mechanism

Chemosphere 68 (2007) 1135–1142 www.elsevier.com/locate/chemosphere

Decolorization of cationic red X-GRL by wet air oxidation: Performance optimization and degradation mechanism Lecheng Lei *, Qizhou Dai, Minghua Zhou, Xingwang Zhang Institute of Environmental Pollution Control Technologies, Xixi Campus, Zhejiang University, Hangzhou 310028, PR China Received 25 November 2006; received in revised form 19 January 2007; accepted 22 January 2007 Available online 28 March 2007

Abstract The decolorization of a strong colored azo dye solution of cationic red X-GRL was investigated by wet air oxidation under relatively mild conditions (60–180 C, P O2 ¼ 0–1:2 MPa). Mono-factor experiments were carried out to investigate the effect of the operation factors and the relatively important parameters were selected for optimization using response surface methodology to explore the interactions of these relatively important parameters. Model regeneration analysis and the check experiments showed that the data of the general linear model agreed with the experiment results well. With multistage Monte-Carlo optimization, the best region of these variables could be predicted to dye color removal. At typical operational conditions, the intermediates of dye degradation were detected and confirmed by GC/MS system. Considering the intermediates and the structure analysis with the help of Gaussian 03W (version 6.0) and the theory of dye color, a possible degradation mechanism for the wet air oxidation of cationic red X-GRL was discussed and the probable degradation pathway was deduced.  2007 Elsevier Ltd. All rights reserved. Keywords: Wet air oxidation; Response surface methodology; Cationic red X-GRL; Degradation mechanism

1. Introduction The large quantity of dye wastewater has become a serious environmental problem due to their characteristics of high color, high chemical oxygen demand and fluctuation pH. Some dyes, especially azo dyes are known to be biorefractory pollutants even with carefully selected microorganism and under favorable conditions. Therefore, these wastewaters must be treated before discharge, to meet not only the ever-increasing stringent legislations required but also the aesthetic standards. Wet air oxidation (WAO) can be applied to treat a wide range of industrial wastewaters successfully including petrochemical industry (Lin and Ho, 1997), printing and dyeing (Hu et al., 2001). However, the application of WAO under rigorous condition (high temperature and *

Corresponding author. Tel.: +86 571 88273090; fax: +86 571 88273693. E-mail address: [email protected] (L. Lei). 0045-6535/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.chemosphere.2007.01.075

oxygen pressure) is limited due to the high requirements of apparatus, which results in high running cost. So, it is necessary to study into this process under mild conditions. If relatively good performance for the treatment of the dye wastewater can be received, the application of this WAO process would be potentially spread in industry widely. Mono-factor experiment perhaps is the most common method to optimize performance, but lacking of predicting the best point to reduce operation cost. Response surface methodology (RSM), a method widely used in biochemical and statistics, can be effective for responses that are influenced by many factors and their interactions (Douglas, 1991). By using RSM and hybrid design brought forward by Roquemore (1976), the two factorials response surface of one another factor can be drawn up, showing the interaction of the operational factors, and thus the best optimized operation point can be predicted. However, to the best of our knowledge, though WAO has been intensively investigated for various wastewater treatments since the invention of this process by Zimmermann

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(1958), there is almost no report on operation parameters optimization by RSM, especially under moderate conditions. Thus, using the dye of cationic red X-GRL (Color Index110825; Signed number 12221-69-1 in Chemical Abstracts) as model pollutant, the objective of the present work is to investigate the effects of main operational parameters and to disclose the interactions of the relatively important operation parameters aiming dye color removal. Special attention was paid to dye decolorization under mild conditions (temperature 6180 C and oxygen pressure 61.2 MPa) to reduce operation cost. Further, the degradation mechanism was explored to achieve a better understanding of the reaction process (Mishra et al., 1995) in such a moderate condition with the help of mathematic and chemical softwares. 2. Experimental and methods 2.1. Experimental apparatus Fig. 1 is the schematic diagram of the WAO system, which has a gas supply (nitrogen and oxygen), a 2 l reactor, a reactor controller, a wastewater charging and sampling system, and a gas outlet system. The reactor is cylindrical, equipped with a water cooling coil and a magnetic stirring system in the center. The reactor controller dominates the operational conditions (e.g., temperature and stirring rate) by the temperature sensor, electric heating jacket and the magnetically stirrer system. The operation procedures are described as below. First, the reactor was pre-heated to 298 K. Then the wastewater (1.3 l) was fed into the reactor through sample inlet pipe. After that, nitrogen was supplied to purge the air inside the reactor for 5 min, after which the pressure was set at 0.5 MPa and cut off the nitrogen supply valve to isolate the system. The reactor was heated to the desired tempera-

ture, then pure oxygen was fed in through gas pipe and the reaction was considered to start. This point was defined as ‘zero time’ in all experiments. Liquid samples were taken through sampling pipe at designated time intervals. 2.2. Materials Cationic Red X-GRL is selected as the model pollutant because it is hardly biodegradable by the conventional biological process, but widely used in the textile, color solvent, ink, paint, varnish, paper, and plastic industries. The dye used in the experiments was purified from industrial cationic red X-GRL (Jin-jiang chemical dyestuff Co. Ltd., China) by extraction with methanol at 50 C until received the purity of 99.5%. The structure of the purified dye is shown in Scheme 1. The synthetic wastewater is prepared by the purified dye and an inert electrolyte sodium sulfate which is used to form the required conductance of 3.6 mS cm1. The oxygen and nitrogen used were high-purity gases. The amount of stoichiometric oxygen was calculated by the dye scheme and dye concentration of the solution, with the oxidization products thought to be CO2 and H2O. The amount of stoichiometric oxygen was 3.44 g when the dye solution is 2000 mg l1, and the relative pressure was 0.4 MPa at 298 K. For the convenience of comparison, the pressure of oxygen and nitrogen at different temperature was converted to that of 298 K in the paper. The gas pressure of the experiment operational condition was calculated by the ideal gas law before the experiment was carried out. Other chemicals used in this work are all analytic grade. 2.3. Analysis methods Dye removal was measured based on the absorbency of dye solution at 530 nm by UV–Vis Spectrophotometer (Techcomp 8500, China). The color removal was deter-

Fig. 1. Schematic diagram of the experimental apparatus. 1. Sample inlet and sampling; 2. cooling water inlet; 3. pressure gauge; 4. stirring system; 5. temperature sensor; 6. gas outlet; 7. electric heating jacket; 8. reactor controller; 9. oxygen; 10. nitrogen.

L. Lei et al. / Chemosphere 68 (2007) 1135–1142

1 2 3

11

1137

12

N

5 N

6

7

N

N

13

21

N

8

20

N

4

Cl-

14 9

10

15

19

16 17

18

Scheme 1. Structural formula of cationic red X-GRL.

mined by the ratio of the integrated absorbency of intermediates from wavelength 180 nm to 800 nm to that of the original one. Degradation intermediates were analyzed using a trace 2000 GC/MS system (Trace 2000, ThermoQuest, USA) with HP-5 capillary column (30 m · 0.32 mm, film thickness 0.25 lm). The base temperature of the right SSL method was set at 260 C, the oven temperature program of the oven method was initially at 50 C, rising at 15 C min1 to a final temperature of 250 C. The concentration NO 3 was detected by ion chromatograph (Techcomp 1000, China) with mobile phase of sodium carbonate (1.8 mM) and sodium bicarbonate (1.7 mM) at the flow rate 1.0 ml min1. 3. Results and discussion 3.1. Effect of operation parameters Dye removal depends on the operation parameters. The mono-factor experiment method was adopted to investigate the effect of individual operational parameters including temperature, pH, oxygen pressure, stirring speed and dye initial concentration. Fig. 2 shows the influence of these parameters on dye removal. As is shown in Fig. 2a, temperature has a significant influence to the dye removal. With the increase of temperature, promoted dye removal efficiency is observed. At 60 C, the dye removal is only 4% after 60 min, and at 120 C, it is 41%. With the temperature further rises to 160 C, the dye removal efficiency increases to 88%, and that of 180 C is 92%. The dye degradation at different temperatures is found to obey the apparent first-order reaction. The apparent reaction constants of these reactions are presented in Table 1. It indicates that an increase of temperature greatly increases the dye degradation rate. Further, the apparent reaction constants are found to be well agreed with the Arrhenius-like relationship, which showed the relationship between the activation, the universal gas constant, and temperature with the pre-exponential factor. The activation energy is presented in Table 1. The activation energy is lower than ordinary WAO system as compared with traditional WAO process (Mishra et al., 1995; Idil and John, 2002). For most WAO kinetic models under mild conditions, organic compounds are inclined to oxidize to the intermediates (such as methanoic acid, acetic acid and oxalic acid, etc.) instead of carbon dioxide and water. In our operational conditions, the low activation energy means that the dye is more likely to be

oxidized to varieties of intermediates, resulting in the easy decolorization of dye. So, this type of dyeing wastewater is suitable to be treated by WAO system, which means WAO would potentially be cost-effective in decolorization of this kind of wastewater in industry. Fig. 2b shows that the neutral condition has the least efficiency to dye removal and the removal efficiency increased at a higher pH in alkaline condition. Based on the dye color theory, the auxochrome of some kinds of dye may be affected with the absence of H+ and OH in acid or alkaline conditions (Hao et al., 2000). In our research, to the purified cationic red X-GRL, the color varies little at different pH. But in non-neutral solution, the stability of the dye molecular structure would be affected more than that of neutral condition during the oxidation at high temperature. In alkaline condition the chromophore of anion dye is more likely to be destructed resulting in a better dye removal. The effect of oxygen pressure on dye removal is shown in Fig. 2c. The oxygen pressure is part of the driving force for mass transfer, so the removal efficiency increases with the increasing oxygen amount. But the differences varies only a little after the oxygen reaching the stoichiometric amount. Increasing the oxygen amount could only result in higher total pressure but improves little to dye decolorization since the oxygen beyond the stoichiometric amount contributes little to the concentration of the dissolved oxygen, which leads to the destruction of dye molecules. The stirring system controls the mass transfer between the gas and liquid phase. Fig. 2d shows that the difference of dye removal is insignificant when the stirring speed reached 300 rpm, indicating that the mass transfer is not the controlling factor. The efficiency of pollutants removal by WAO was reported to be effected by the wastewater characteristics, especially the initial concentration. Some reported that the initial concentration of wastewater had little influence on the removal efficiency while others argued that higher initial concentration favored the wastewater treatment (Willms et al., 1987; Fu et al., 2005). Fig. 2e shows the effect of initial dye concentration on dye removal. Neither too dilute nor too high dye concentration was benefit to dye decolorization. The initial dye concentration for the best dye removal efficiency was between 1000 and 2000 mg l1. 3.2. Interaction of the operation factors Based on the results of mono-factor experiments, stirring speed beyond 300 rpm seemed to be an insignificant

1138

100

80

60

d

80 20

0 100

80

60

40

e

pH = 4 pH = 7 pH = 9 pH = 10

20

0

Concentration removal (%)

c

60

40

100 rpm 300 rpm 500 rpm 700 rpm

20

0

Concentration removal (%)

Concentration removal (%)

b

100

40

Concentration removal (%)

Concentration removal (%)

a

L. Lei et al. / Chemosphere 68 (2007) 1135–1142

100 0102030405060

80

100

80

60

40

-1

500 mg l -1 1000 mg l -1 2000 mg l

20

60

0 0

40

10

20

30

40

50

60

Time, min 1 stoichiometric oxygen 1.5 stoichiometric oxygen 2 stoichiometric oxygen

20

0 10

0

20

30

40

50

60

Time, min

Fig. 2. Effect of operational parameters on dye removal. (a) Temperature, (b) pH, (c) oxygen amount, (d) stirring speed, (e) initial dye concentration (experimental conditions: (a) P O2 ¼ 0:6 MPa, P N2 ¼ 0:5 MPa, pH 4.3, C = 2000 mg l1, stirring speed = 300 rpm. (b) T = 160 C, P O2 ¼ 0:6 MPa, P N2 ¼ 0:5 MPa, C = 2000 mg l1, stirring speed = 300 rpm. (c) T = 160 C, P N2 ¼ 0:5 MPa; pH 4.3, C = 2000 m l1, stirring speed = 300 rpm. (d) T = 160 C, P O2 ¼ 0:6 MPa, P N2 ¼ 0:5 MPa, pH 4.3, C = 2000 mg l1. (e) T = 160 C, P O2 ¼ 0:6 MPa, P N2 ¼ 0:5 MPa, pH 4.3, stirring speed = 300 rpm.). Table 1 Apparent rate constants and activation energy T (C)

WAO

Ea

3 1

k (10 120 160 180

0.30 0.79 1.56

s )

R

2

0.986 0.999 0.995

Ea (kJ mol1)

R2

39.9

0.987

factor on dye removal comparing with the temperature, pH, oxygen pressure and dye initial concentration. There-

fore, RSM was applied to study the interaction of the latter four important factors, using the design of 416B (Roquemore, 1976). The hybrid design and the real values of the codes in the hybrid design are listed in Tables 2 and 3, respectively. There are many types of intermediates produced during the dye removal and the color removal could response the dye degradation including the intermediates indirectly, so the color removal is used to replace the dye removal to express the degradation of the dye. The dye color removals at 60 min at different operational conditions

L. Lei et al. / Chemosphere 68 (2007) 1135–1142 Table 2 Matrix for hybrid design with the experiment Run no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Variables (Xi)

Color removal g (%)

(X1) T (C)

(X2) Pe/Pc

(X3) pH

(X4) C (mg l1)

Experiment results

Predicted results

0 0 1 1 1 1 1 1 1 1 1.5177 1.5177 0 0 0 0 0.50 1.20 1.35

0 0 1 1 1 1 1 1 1 1 0 0 1.5177 1.5177 0 0 1.20 0.50 1.00

0 0 1 1 1 1 1 1 1 1 0 0 0 0 1.5177 1.5177 0.20 0.40 1.20

1.7317 0.2692 0.6045 0.6045 0.6045 0.6045 0.6045 0.6045 0.6045 0.6045 1.0498 1.0498 1.0498 1.0498 1.0498 1.0498 0.20 0.30 0.52

19 22 3 50 4 62 6 61 7 77 85 1 23 7 23 16 28 82 97

19 22 3 50 4 63 6 61 8 77 85 1 23 7 23 16 31 80 99

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relative errors were within 10% which showed that the model was quite significant and the model agreed with the experiment results well within scope of the given operational conditions. With STATISTIC 6.0 and the matrix of the hybrid design, the interaction of the temperature, oxygen pressure, pH and dye initial concentration could be disclosed one another. The response surface illustrates that temperature is the dominating influence parameter, dye color removal rose at a higher temperature. Fig. 3a shows the interaction of pH and the oxygen pressure. The higher oxygen pressure is, the more dye color removal would be. The increasing rate would release after the zero level which means after the stoichiometric amount, the oxygen amount is not the control factors to dye degradation. At the same oxygen

Table 3 The actual values of variables versus the coded values Coded values

1.5177 1.0498 1 0.2692 0 0.6045 1 1.5177 1.7317

Variables T (C)

Pe/Pc

pH

C (mg l1)

60 – 80 – 120 – 160 180 –

0 – 0.34 – 1 – 1.66 2 –

2 – 3.4 – 6 – 8.6 10 –

– 500 – 1208 – 2000 – – 2931

were calculated and shown in Table 2. Pe is the experiment oxygen pressure while Pc is the calculated oxygen pressure. The pressure was converted to that of 298 K before comparison. With the software of STATISTIC 6.0 and the experiment results of Table 2 (Run Nos. 1–16), a general linear model of the dye color removal could be described by response surface regeneration. The model showed the relationship of these operational factors aiming dye decolorization. The predicted values by this model of relative operation conditions could also be predicted, as were also listed in Table 2. The regression analysis shows the sum of square value of this model is obvious larger than that of the model residual. Considering with the adjusted R2 value is 0.996, it shows that the model is significant. To estimate this model better, two check experiments (Run Nos. 17 and 18 in Table 2) were carried out to estimate the experiment error and to check the reproducibility of the model. The

Fig. 3. 3D Isoresponse contour plots for the response surface function. (a) pH  oxygen pressure; (b) concentration  oxygen pressure; (c) concentration  pH (variable those not shown in the figure at zero level).

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Table 4 Intermediates determined by GC/MS Code M1

Retention time (min) 5.46

m/z

Molecular formula

Name

106

C7H6O

Benzaldehyde

Structure O

N

M2

7.35

113

C4H7N3O

2,4-Dimethyl-2,4-dihydro-[1,2,4]triazol-3-one

O N N

O

M3

8.00

122

C7H6O2

Benzoic acid

OH

O

M4

10.00

148

C9H10NO

N-(a-Methylbenzyl)-formamide

N

H

CH 3

M5

12.50

197

C14H15N

N

Benzenamine, N-phenylmethylene

CH 3

M6

14.55

211

C14H13NO

Benzenamine, N-phenylmethylene, N-oxide

N

O

Experimental conditions: T = 160 C, P O2 ¼ 0:6 MPa, P N2 ¼ 0:5 MPa, pH 4.3, C = 2000 mg l1, stirring speed = 300 rpm.

pressure, the dye color removal continues to go up after neutral condition. This means that the best color removal is at the alkaline condition. Fig. 3b shows that dye color removal rises as the oxygen pressure arising, while the dye initial concentration has a best point aiming the dye color removal with the codes value at 0.50 or so. Of theses interactions, that of pH and dye initial concentration is the most obvious one, as is shown in Fig. 3c. The color removal goes down with the pH rising and in an alkaline condition, it goes up with the increasing pH, which means that there exists a minimum value. As for initial dye concentration to the color removal, the color removal continues to increase with the dye concentration rising until the code value gets 0.5 or so. These mean that there exist a best dye initial concentration and a minimum point of pH aiming to the dye color removal. With multistage Monte-Carlo Optimization, the best region of these variables can be found to the removal of dye color. One experiment was carried out at the optimized predicted operation condition (Table 2, Run 19), which showed the experiment result was quite close to that of the model predicted.

tion could be identified by GC–MS system. Table 4 lists the main intermediates including benzaldehyde, benzoic acid and benzenamine, N-phenylmethylene, etc. Also there are confirmed kinds of organic acid, except for the benzoic acid. 3.4. Degradation mechanism analysis Generally, organics degradation by WAO were recognized as a free-radical mechanism (Li et al., 1991), and hydroxyl radical is an extremely potent oxidizing agent with a short life which is able to oxidize organic compounds and generate other free radicals in the presence of organic compounds (RH). The following reaction may take place by the addition of molecular oxygen (Legrini et al., 1993; Mantzavinos et al., 1997; Suresh et al., 2006) RH þ O2 ! R þ HO2 H2 O þ O 2 ! H2 O 2 þ O

ð3Þ



OH þ RH ! R þ H2 O

ð4Þ

R þ O2 ! ROO

ð5Þ



In order to analyze the reaction pathways of cationic red X-GRL, the intermediates of cationic red X-GRL degrada-

ð2Þ

H2 O þ O2 ! HO2 þ OH 

3.3. Intermediates analysis with GC/MS

ð1Þ 

OH þ RH ! HORH 



HORH þ O2 ! ROH þ

ð6Þ HO2

ð7Þ

L. Lei et al. / Chemosphere 68 (2007) 1135–1142 Table 5 Characteristic of cationic red X-GRL ˚) Bond Bond lengths (A Bond

Bond angles ()

N(1)–C(2) C(2)–N(3) N(3)–N(4) N(4)–C(5) N(1)–C(5) C(5)–N(6) N(6)–N(7) N(7)–C(8)

113 108 107 109 104 107 107 118

1.462 1.260 1.469 1.300 1.462 1.456 1.362 1.404

C(2)–N(1)–C(5) N(1)–C(2)–N(3) C(2)–N(3)–N(4) N(3)–N(4)–C(5) N(4)–C(5)–N(1) C(5)–N(6)–N(7) N(6)–N(7)–C(8) C(13)–N(14)–C(15)

1141

N N N

N

N

N

OH

O2

CH3 N N

O

NO 3 N 2

N

N CH3

OH OH

O2

OH

These reactions generate organic radicals and other free radicals which in turn initiate chain reactions of dye oxidative degradation with the help of dissolved oxygen. Thus in the WAO system, the reaction intermediates, especially the organic radicals increased, accelerate the speed of the reaction. With Gaussian 03W (version 6.0), the bonds length and the bond angles of cationic red X-GRL can be calculated. Table 5 shows values of the length and angle of the main structure in cationic red X-GRL structure. As for traditional organic compounds, the five or six element ring is the most stable in chemical reaction, while the line structure, especially the azo bond is relatively easier to be attacked. As for the color formation theory, the color of dye is formed by the cooperation of the chromophore and the auxochrome mainly containing phenyl annulus (Zollinger, 2003). While to the cationic red X-GRL, the chromophore is the azo bond and when the cooperation of the azo bond and the auxochrome is broken, the dye absorbance detected at 530 nm would be removed which means the removal of dye. With the compounds of GC/MS detected and the stability compound theory, the probable degradation pathway of cationic red X-GRL can be deduced. In WAO system, at first, the azo bond (–N@N–) would first be attacked by heat energy and free radicals. The length of the bond of ˚ , 1.362 A ˚ C(5)–N(6), N(6)–N(7) and N(7)–C(8) is 1.456 A ˚ , respectively. Compared the length and angles and 1.404 A of these bonds in Table 5, the C(5)–N(6) is the first potential broken among the three as for the stability of the five element ring. After the azo bond was attacked, most of the nitrogen element went away from the liquor phase as nitrogen (Spadaro et al., 1994) and little came into the solution, which led to the destruction of the dye molecular. To prove it, NO 3 of the solution was detected and low concentration was confirmed by the ion chromatograph. Related to that a great deal of benzenamine N-phenylmethylene (M5) and M2 were detected by the GC/MS, these further proved that the attack of the azo bond was the initial step of dye degradation, which was also the first step of dye decolorization. After the C–N (–C–N@N–) was broken, the oxygen at high temperature continued to react with the intermediates with the help of free radicals, which led to the formation of M1, M3, M4, M6 and kinds of organic acids. With the continuous oxygen and the reaction time at

O2

OH

O2

O2 O N N

OH

H

O

O2

OH

OH

O2

O2

O

OH

OH

organic acids and other oxidation products

O2

OH

O2

O

Fig. 4. Major degradation pathways proposed for WAO of red cationic X-GRL.

higher temperature, these intermediates including kinds of organic acids could be oxidized to small molecule organic acids, part of these intermediate would convert to the final oxidation products, such as water and carbon dioxide during to the total organic carbon removal. The probable pathway can be described by Fig. 4. 4. Conclusions To low the cost of wet air oxidation treating such wastewater, mono-factor experiments under mild conditions were carried out to study the effect of the operation parameters to dye removal. It showed that temperature influenced dye removal obviously. The increasing of the oxygen accelerated the dye removal and the increasing removal rate slowed down after the oxygen amount got the stoichiometric amount. In an alkaline solution, the dye removal was more thorough than that of neutral and acid solution. Based on the results of mono-factor experiments, dye color removal was carefully studied to disclose the interaction of these relative important operation factors. With the help of the software of STATISTIC 6.0 and response surface methodology regeneration, the general linear model can be got, and the model regeneration analysis showed that the data predicted by the model agreed well with the experiment results. It was found that temperature played the key role, and the interactions of other three parameters were discussed detailed. With multistage Monte-Carlo Optimization, the best region of these variables can be predicted. Check experiments were carried out to get a better understanding of the model, which showed the experiment results were quite close to those of the model predicted.

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At typical operational condition, the intermediates of the dye degradation were detected and affirmed by the GC/MS system. Considering the intermediates, with the help of the theory of dye color and dye structure analysis by the software of Gaussian 03W, the bond of C(5)–N(6) ˚ and would be first potential be attacked. With is 1.456 A the analysis of the traditional WAO system, the degradation mechanism of wet air oxidation of cationic red X-GRL was discussed and the probable degradation pathway was deduced. Acknowledgements We would like to acknowledge financial support for this work provided by the National Natural Science Foundation of China (Grant No. 20306027), the Analysis and Detection Fund of Zhejiang Province (04173) and the Natural Science Foundation of Zhejiang Province (Grant No. Y504129). References Douglas, C.M., 1991. Design and Analysis of Experiments, third ed. John Wiley & Sons, Inc., USA. Fu, D.M., Chen, J.P., Liang, X.M., 2005. Wet air oxidation of nitrobenzene enhanced by phenol. Chemosphere 59, 905–908. Hao, O.J., Kim, H., Chiang, P.C., 2000. Decolorization of wastewater. Crit. Rev. Environ. Sci. Technol. 30, 449–505.

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