Article pubs.acs.org/IECR
Photoelectrocatalytic Oxidation of Textile Dye Effluent: Modeling Using Response Surface Methodology C. Ahmed Basha,*,† R. Saravanathamizhan,‡ P. Manokaran,† T. Kannadasan,§ and Chang Woo Lee*,∥ †
Department of Chemical Department of Chemical § Department of Chemical ∥ Department of Chemical 446-701, South Korea ‡
Engineering, Engineering, Engineering, Engineering,
Adhiyamaan College of Engineering, Hosur 635109, India National Institute of Technology, Tiruchirappalli 620 015, India Coimbatore Institute of Technology, Coimbatore 641014, India College of Engineering, Kyung Hee University, 1 Seochun, Gihung, Yongin, Gyeonggi
ABSTRACT: The present article reports the treatment of procion blue dye effluent using a thin-film photoelectrocatalytic novel reactor. Response surface methodology (RSM) was applied to design the experiments, and the optimum operating parameters were determined for chemical oxygen demand (COD) removal and energy consumption. Operating parameters such as initial effluent concentration, applied charge, and lamp wattage were selected. The COD removal and energy required for treatment were optimized using RSM, and a regression equation was developed for COD removal and energy consumption for a photoelectrocatalytic process. The present study concludes that the power consumption for the process can be optimized using RSM and that RSM is a good tool for studying combined variables and interaction effects on the response of a process.
1. INTRODUCTION Industrial wastewater is becoming increasingly complex because of the increasing diversity of industrial products. Textile industries are producing large amounts of wastewater primarily in the dyeing and finishing operations. Textile wastewaters are characterized by intense color, high chemical oxygen demand (COD), high biological oxygen demand (BOD), and fluctuating pH. The treatment of dye wastewater includes biological treatment, catalytic oxidation, filtration, sorption processes and combination treatments (such as ozonation and H2O2/O3 treatment). Dye wastes represent one of the most problematic groups of pollutants in the textile industries because they can be easily identified by the human eye and are not easily biodegradable. Efforts are being made to minimize the toxicity of industrial effluents using new technologies for the efficient treatment of effluents. Therefore, it is necessary to find an effective method for wastewater treatment that is capable of removing color and toxic organic compounds from textile effluents.1−7 It is worth pointing out that electrochemical oxidation is an effective method for degrading organic pollutants under high external electric field when organic contaminants are high. In recent years, an alternative to the conventional method has been provided by advanced oxidation processes (AOPs) (such as ultrasound, Fenton process, nanoscale iron oxidation), based on the generation of reactive species such as hydroxyl radicals that oxidize a broad range of organic pollutants quickly and nonselectively. Among AOPs, the heterogeneous photocatalytic process seems to be an attractive method that has been successfully employed for the degradation of various families of organic pollutants, including dyes.8−12 Peller et al.13 studied sonochemical effects along with photocatalysis for the treatment of organic compounds such as 2, 4-dichlorophenoxyacetic acid present in wastewater. They reported that sonochemical treatment is effective at the © 2012 American Chemical Society
beginning and simultaneously photochemical treatment is very effective for degradation of the organic compounds. The removal of reactive dye using H2O2-assisted photolysis requires UV irradiation and H2O2 addition. In addition, some specific conditions are needed for high dye removal efficiencies. Similar techniques have been studied for the degradation of dyes by ultrasound-enhanced heterogeneous Fenton-like processes.14−22 Sharpless et al.23 studied use of Hg lamps for the direct and H2O2-assisted UV photooxidation of N-nitrosodimethylamine (NDMA) in simulated wastewater. They observed that H2O2 enhances NDMA removal for short optical path lengths but that light-sourcing by H2O2 might decrease the removal rates. The development of wastewater treatment systems has not yet been successfully achieved because of a high degree of recombination of generated electrons and holes, despite numerous approved patents related to heterogeneous photocatalytic processes. Recent studies have repeatedly confirmed that external electric fields could greatly enhance photocatalytic efficiency, which is well-known as an electric field enhancement effect.24−41 Photoelectrocatalysis is considered to be a better approach, because the problem of a high degree of charge recombination present in heterogeneous photocatalysis can be solved successfully by applying an anodic bias. However, in most electrochemically assisted photocatalytic experiments, the applied anodic bias potentials were lower than the oxidation potential of organic pollutant, so that no direct electrochemical oxidation interfered with the photocatalysis. Received: Revised: Accepted: Published: 2846
October 20, 2011 December 30, 2011 January 1, 2012 January 2, 2012 dx.doi.org/10.1021/ie2023977 | Ind. Eng.Chem. Res. 2012, 51, 2846−2854
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Pelegrini et al.42 studied a photoassisted electrolysis process for the degradation of the organic pollutants. They used a thermally prepared anode of 70% TiO2/30% RuO2 (by weight) and a 125 W mercury lamp. They observed a phenol concentration decay of 85% and a 70% reduction in total organic carbon (TOC) in 90 min. Neelavannan et al.43 studied procion blue dye effluent treated by photooxidation and photocatalytic oxidation (using TiO2 suspensions) through a combined electrochemical oxidation process. Comparative studies showed that the photooxidation efficiency of the dye was high when photolysis was carried out in the presence of 40 mg L−1 TiO2. Actually, it is worth pointing out that the photooxidation and photocatalytic oxidation were carried out without anodic bias. Subsequently, the degradation of procion blue dye effluent by photocatalytic oxidation using TiO2 suspensions and by electrochemical oxidation was reported.31 The development of immobilized thin films is becoming a standard technique of TiO2-based photocatalysis for organic oxidation. Photocatalytic oxidation processes are highly effective clean technologies for the degradation and mineralization of a wide variety of priority pollutants in water and wastewater. The present research focused on the treatment of textile dye wastewater using a photoelectrocatalytic process in a batch reactor (falling-film cell) with electrolyte recirculation. The reduction of the COD of the dye effluent was examined in this reactor. Further, the application of heterogeneous photocatalysis for the oxidation of organics on an industrial scale has been impeded by a lack of mathematical models that can be readily applied to reactor design and scale-up. As a result, photocatalytic reactors in research and development were designed, the results were analyzed, and the operating parameters were optimized using response surface methodology.
expanded titanium mesh and firing it at 723 K in a preheated furnace. The process was repeated until a coating thickness of 5−6 μm of RuO2/TiO2 was achieved. 2.2. Response Surface Methodology (RSM) by Box− Behnken Experimental Design. In general, the response of an experiment depends on the experimental conditions. This means that the experimental results can be described as a function of the experimental variables by the following polynomial equation k
y = β0 +
k
k−1 k
∑ βixi +
∑ βiixi 2 +
∑ ∑ βijxixj + ε
i=1
i=1
i=1 j=2
(1)
where y is the response variable; xi and xj are coded independent variables; β0, βi, βii (i = 1, 2, ..., k), and βij (i = 1, 2, ..., k; j = 1, 2, ..., k) are regression coefficients for intercepts and linear, quadratic, and interaction terms, respectively; and ε is the statistical error. The combined effects of operating parameters on process efficiency cannot be estimated by conventional experimentation, in which experiments are carried out by varying a particular parameter, whose influence is studied while all other parameters are kept constant. Experimental design is an effective and efficient optimization strategy to overcome this drawback, and it has gained extensive applications in chemical engineering.44 The effects of combined variables can be critically examined, and optimization can be achieved with the help of response surface methodology (RSM). Further details on RSM can be found in Saravanathamizhan et al.45 In the present study, RSM was used to determine the relation between the percentage COD removal and energy consumption with operating parameters such as initial effluent concentration, applied charge, and lamp wattage. The uncoded variables were converted to coded variables using the following equation
2. MATERIALS AND METHODS All chemicals used in the present study were analytically pure and were used without further purification. Distilled water was used for the preparation of synthetic effluents and for the dilution purposes. 2.1. Electrode Preparation. An anode coated with RuO2/ TiO2 was prepared by applying a thin layer of a solution containing RuCl3 dissolved in isopropanol on a pretreated
x=
X − (X max + X min)/2 (X max − X min)/2
(2)
where X is a natural variable and x is the corresponding coded variable. A class of three-level complete factorial design for the estimation of the parameters in a second-order model was developed by Box and Behnken. Table 1 shows the
Table 1. Box−Behnken Experimental Design Table for Photoelectrocatalytic Oxidation coded units of factors
uncoded units of factors
run
IEC
Q
W
X1 (mg L−1)
X2 (A h L−1)
X3 (W h L−1)
COD removal (%)
EC [kWh (kg of COD)−1]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
−1 +1 −1 +1 −1 +1 −1 +1 0 0 0 0 0 0 0
−1 −1 +1 +1 0 0 0 0 −1 +1 −1 +1 0 0 0
0 0 0 0 −1 −1 +1 +1 −1 −1 +1 +1 0 0 0
500 2000 500 2000 500 2000 500 2000 1250 1250 1250 1250 1250 1250 1250
9 9 18 18 13.5 13.5 13.5 13.5 9 18 9 18 13.5 13.5 13.5
48 48 48 48 36 36 60 60 36 36 60 60 48 48 48
76.53 57.87 93.65 78.00 93.98 52.76 76.09 76.9 78.72 80.84 61.99 99.90 96.57 96.57 96.63
86.63 28.64 167.86 50.38 115.39 51.38 148.83 36.81 32.47 76.59 44.33 63.90 45.91 45.91 45.88
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galvanostatic conditions using a dc-regulated power source of 0−5 A and 0−10 V. A synthetic dye effluent of procion blue dye was prepared at 500, 1250, and 2000 mg L−1 concentrations (initial effluent concentration, IEC). One liter of effluent having a supporting electrolyte concentration (sodium chloride) of 3 g L−1 was fixed for each experiment. For photocatalytic oxidation, the UV lamp was switched on, and the effluent was continuously stirred with a magnetic stirrer for complete mixing. Samples were collected at regular time intervals for the estimation of COD removal. The experiments were carried out under batch recirculation conditions for 6 h with a flow rate of 20 mL min−1. For analysis, 1 mL samples were periodically withdrawn from the reservoir and subjected to COD estimation. To determine the extent of degradation of the effluent, chemical oxygen demand (COD) was measured. As the name implies, COD is the oxygen requirement of a sample for oxidation of organic and inorganic matter. COD is generally considered as the oxygen equivalent of the amount of organic matter oxidizable by potassium dichromate. To measure COD, the organic matter of the sample was oxidized with a known excess of potassium dichromate in a 50% sulfuric acid solution. The excess dichromate was titrated with a standard solution of ferrous ammonium sulfate solution. The CODs of all samples were determined by the dichromate closed reflux method using a Merck Themoreactor TR 620. According to the experimental design in Table 1, for each applied charge (Q = 9, 13.5, and 18 A h L−1), experiments were conducted at corresponding currents of 1.5, 2.25, and 3 A, respectively. Three different UV lamp wattages (6, 8, and 10 W) were used, and the corresponding applied powers (W) were 36, 48, and 60 W h L−1, calculated by multiplying by reaction time. The effluent was recirculated after oxidation. The COD and energy consumption (EC) of the sample were also computed. The setup included a thin film for photooxidation phenomena and electrochemical reactions. In this reactor, the known concentration of effluent was allowed to flow as a thin film along the walls of the reactor. When the effluent had been passed through the reactor, photoelectrocatalytic oxidation occurred on overflowing effluent on the surface of the anode as the UV lamp was provided inside the reactor for UV irradiation to initiate the reaction on the anode surface and the effluent in the annular space was subjected to electrochemical oxidation. The immobilized thin film on the reactor effectively decolorized the entire effluent film adjacent to it in a short interval to time.
experimental runs for a three-level three-factor Box−Behnken experimental design with three central points. The design was implemented using Minitab 14 (Minitab Inc., State College, PA). 2.3. Experimental Section. The experimental setup of the present work is shown in Figure 1. The setup consisted of an
Figure 1. Schematic diagram of experimental setup for photoelectrooxidation: (a) 1, Effluent holdup; 2, peristaltic pump; 3, effluent overflow arrangement; 4, catalytic anode; 5, stainless steel cathode; 6, stirring element; 7, lamp holder; 8, regulated power supply; 9, magnetic stirrer; 10, UV lamp. (b) Thin-film−carrier assemblage immersed in a solution containing dye. (c) UV light source to provide uniform irradiation of the surface of the catalyst. (d) Cartesian coordinates, defined in the thin-film catalyst, for the description of the contaminant and UV profiles.
electrochemical reactor, a UV lamp, a reservoir, a pump, a magnetic stirrer, and a power supply unit. The photoelectrocatalytic reactor consisted of a cathode made of a stainless steel cylinder of 5-cm diameter and 20-cm length the bottom of which was closed by a poly(vinyl chloride) (PVC) disk with rubber gaskets. At the top of the cathode, there was a provision for holding the UV lamp. The anode was cylindrical in shape, 4 cm in diameter and 15 cm in length, and was made of RuO2/Ti. The UV lamp was placed in the middle of the reactor. The holder was used to hold the UV lamp and maintain an electrical connection. A reservoir at the bottom of the reactor held the effluent, which was circulated through a pump to the top. A magnetic stirrer was used to maintain uniform mixing of the solution. An immersion-type 6-, 8-, or 10-W UV lamp of 2.5-cm diameter and 27-cm height (emitting UV light, λ = 365 nm) was placed inside the reactor and served as the light source. The UV lamp was turned on 30 min before the start of the photocatalytic reaction. Electrooxidation was carried out under
3. THEORETICAL DEVELOPMENT In the photoelectrocatalytic process with UV radiation occurring on the anode surface, the RuOx−TiOx thin film is activated and extra (RuOx−TiOx)(•OH) species are formed. This is the reason for the higher degradation rate of organic pollutants in the photoelectrocatalytic process (RuOx −TiOx ) + hν → (RuOx −TiOx ) + (h+ + e−)
(3)
(RuOx −TiOx ) + h+ + H2O → (RuOx −TiOx )(•OH) + H+ + e−
(4)
The development of photocatalytic wastewater treatment systems has not yet been successfully achieved because of the high degree of recombination of photogenerated electrons and holes as given in eq 4. Photoelectrocatalysis is considered to be a better approach, because the problem of a high degree charge 2848
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where τ is the residence time [(Vef − VR)/v] of organic contaminants in the effluent reservoir. A linear plot of ln(C/C0) versus t gives the slope, from which the value of kh, the pseudo-first-order heterogeneous rate constant, can be computed. The term for energy consumption (EC) is the quantity of energy consumed in the process per kilogram of COD digested and can be obtained using the equation
recombination presented in heterogeneous photocatalysis is suppressed by applying an anodic bias. A thin layer of RuOx− TiOx catalyst is immobilized on an inert carrier, as shown in Figure 1a. The thin-film−carrier assemblage is immersed in a solution containing organic contaminants, as shown in Figure 1b. A UV light source is positioned on the right side to provide uniform irradiation on the surface of the catalyst (shown in Figure 1c). The UV light attenuates as it penetrates into the catalyst layer. It is assumed that UV attenuation by the bulk liquid is negligible, as compared with the RuOx−TiOx thin film. Organic molecules in the bulk liquid migrate to the surface of the catalyst and diffuse into the catalyst layer. The diffusing molecules are oxidized by photoelectrocatalytic radicals generated by UV light penetrating the catalyst. As a result of these sequences of events, a concentration profile for organic molecules and an intensity profile for UV radiation are established. Cartesian coordinates are defined in the thin-film catalyst to allow the description of contaminant and UV profiles (see Figure 1d). The concentration variation of the organic contaminants in the reactor due to photoelectrocatalytic oxidation can be written as
AΔx
∂C ∂C = − vΔx − AΔxkhaC ∂t ∂x
EC =
dC = v(C − C′) dt
The objective of electro-assisted photocatalytic is not only to increase overall efficiency of organic pollutant removal but also to enhance decoloration initially by chlorination so that the photooxidation process can dominate in the remaining part of the process. The current efficiency of the electrolysis was calculated using the expression FVefΔ(COD) × 100/8It, and the values obtained were more than 100. This result is attributable to photochemical and electrochemical reactions taking place in the same reactor. In this reactor, the effluent was allowed to undergo degradation by photocatalytic oxidation as well as electrochemical oxidation following heterogeneous pseudofirst-order kinetics. The effluent degradation occurred because of photochemical and electrochemical reactions simultaneously, and rate constant kh was obtained from eq 8. Keeping W = 36 W h L−1, Q was varied from 9 to 18 A h L−1; the computed values of kh changed from 2.3 × 10−3 to 2.9 × 10−3 cm s−1 at IEC = 500 mg L−1 and from 2.5 × 10−3 to 3.2 × 10−3 cm s−1 at IEC = 2000 mg L−1. Similarly, when Q was kept at 9 A h L−1 and W was varied from 36 to 60 W h L−1, kh again changed from 2.3 × 10−3 to 2.9 × 10−3 cm s−1 at IEC = 500 mg L−1 and from 2.5 × 10−3 to 2.7 × 10−3 cm s−1 at IEC = 2000 mg L−1. The variations in the rate constant values were very marginal. To study the combined effects on COD removal, response surface methodology was applied. 4.1. Response Surface Methodology. Response surface methodology (RSM) is a statistical modeling technique employed for multiple regression analysis using quantitative data obtained from properly designed experiments to solve multivariable equations simultaneously. Response surfaces can be visualized as three-dimensional plots that display the response as a function of two factors while keeping the third factor constant. 4.1.1. Regression Equation. Table 1 shows the experimental runs for a three-level three-factor Box−Behnken experimental design with three central points. The design was implemented using Minitab 14, and the analysis was focused on the influence of independent variables, namely, Initial effluent concentration (X1), applied charge (X2), and lamp power (X3), on the percentage COD removal and energy consumption (EC). The mathematical relationships of the percentage COD removal and energy consumption with the operating variables can be given
(5)
(6)
(7)
where Vef is the volume of the effluent taken in the reservoir tank. The mass balance equation (eq 7) can be solved after substitution of the expression for C′ from eq 6, given the initial concentration of organic contaminants, C = C0 at t = 0 in the reservoir. Then, the following resultant equation gives the variation of of organic contaminants in the reservoir
C = exp C0
{ − τt [1 − exp( − k aτ )]} h
R
(9)
4. RESULTS AND DISCUSSION
where C′ is the concentration of organic contaminants leaving the reactor, a is the specific surface area of the catalytic anode (Ae/VR), kh is the heterogeneous rate constant, and τR is the residence time of organic contaminants (VR/v) in the reactor. The reservoir (effluent tank) is always a perfectly back-mixed system. Hence, the mass balance equation for the effluent reservoir is
− (Vef − VR )
ΔCOD × Vef /106
The actual wattage utilized for the photooxidation is 10% of the rated power. The power consumption was calculated according to the design Table 1.
where A is the cross-sectional flow area of the reactor, v is the volumetric flow rate, and C is the concentration of COD. The left-hand side of eq 5 represents the rate of change of COD in a differential volume (AΔx) in the reactor. The first term on the right-hand side of eq 5 is the net rate of change of COD due to the bulk flow in the differential volume, and v is the volumetric flow rate through the reactor. The last term on the right-hand side represents the rate of degradation of organic contaminants in the solution due to the photoelectrocatalytic reaction. Because there is no accumulation of organic contaminants in the liquid phase of the reactor, it can be assumed that the reactor is at steady state (∂C/∂t = 0). The resulting ordinary differential equation formed from eq 5, upon integration between proper boundary conditions, yields
⎛ k A ⎞ C′ = exp( − kha τR ) = exp⎜ − h e ⎟ ⎝ C v ⎠
(VQ + Wh)/103
(8) 2849
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concentration and applied charge on the percentage COD removal are given in both surface and contour plots in Figure 2. The surface and contour plots for COD removal show the interactive effects of initial effluent concentration and applied charge at a constant lamp power. It can be observed from Figure 2a,b that the percentage COD removal increased with increasing applied charge and decreased with increasing initial effluent concentration. This might be because the rate of generation of hypochlorite ion increased with applied charge, which eventually increased the pollutant degradation. The ratio of OCl− to effluent concentration decreased with increasing initial effluent concentration, which resulted in a decrease in the rate of COD removal. The combined effects of initial effluent concentration and lamp power on COD removal are shown as both surface and contour plots in Figure 3. It is observed from Figure 3a,b that
in uncoded form as
COD removal(%) = 16.2764 − 0.0148X1 + 3.6799X2 + 2.3285X3 − 0.3616X2 2 − 0.0618X32 + 0.0002X1X2 + 0.0012X1X3 + 0.1657X2X3
(10)
EC (kWh/kg of COD) = 40.3485 − 0.0934X1 + 13.1339X2 − 0.9935X3 + 0.0001X12 + 0.091X2 2 + 0.0457X32 − 0.0044X1X2 − 0.0013X1X3 − 0.1136X2X3
(11)
The predictions for COD removal and energy consumption using the above equations were compared with experimental observations. It was found that COD removal had an R2 value of 0.998, and the energy consumption predited values had a correlation coefficient of R2 = 0.991. It can be ascertained from the R2 values that the model equation predictions satisfactorily matched the experimenal values. 4.1.2. Surface and Contour Plots. RSM was applied to photoelectrocatalytic oxidation of procion blue dye effluent, and the results are presented in both surface and contour plots in Figures 2−5. The combined effects of initial effluent
Figure 3. Combined effects of initial effluent concentration (IEC) and lamp wattage (W) on the percentage removal of COD for an applied charge of 13.5 A h L−1: (a) response surface, (b) contour plot.
the COD removal increased with increasing lamp power and decreased with increasing initial effluent concentration. This might be because the light intensity was greater at higher lamp power. The combined effects of initial effluent concentration and applied charge on energy consumption are depicted as both surface and contour plots in Figure 4. It can be observed from Figure 4a,b that the energy consumption increased with increasing applied charge and decreased with increasing initial effluent concentration. The combined effects of initial effluent concentration and lamp power on energy consumption are shown as both surface and contour plots in Figure 5. It is observed from Figure 5a,b that the energy consumption
Figure 2. Combined effects of initial effluent concentration (IEC) and applied charge (Q) on the percentage COD removal for a lamp wattage of 48 W h L−1: (a) response surface, (b) contour plot. 2850
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Figure 4. Combined effects of initial effluent concentration (IEC) and applied charge (Q) on the energy consumption for a lamp wattage of 48 W h L−1: (a) response surface, (b) contour plot.
Figure 5. Combined effects of initial effluent concentration (IEC) and lamp wattage (W) on the energy consumption for an applied charge of 13.5 A h L−1: (a) response surface, (b) contour plot.
increased with increasing lamp power and decreased with increasing initial effluent concentration. This is because the applied charge and lamp power increased the quantity of energy utilized for the process, which resulted in greater energy consumption. 4.1.3. Main Effect Plots. The main effect plots for COD removal and energy consumption are shown in Figure 6. It can be observed from Figure 6a that the COD removal increased with increasing applied charge and lamp power but decreased with increasing initial effluent concentration. A further increase in lamp power will decrease the COD removal. The main effect plots for energy consumptions are shown in Figure 6b. It can be observed from the figure that the energy consumption decreased with increasing initial effluent concentration and increased with increasing applied charge. However, lamp power did not affect the energy consumption much. 4.1.4. Response Optimization for COD Removal and Energy Consumption. The optimization of COD removal and energy consumption is shown in Figure 7. For 80.20% COD removal and 22.94 kW h (kg of COD)−1 energy consumptions, the initial concentration and lamp power should be kept at their middle levels, and applied charge should be kept at a low level. 4.1.5. Significance of the Variables. The significance of the regression coefficients was analyzed using the p test and t test. p values are used to check the effects of interactions among variables. A larger-magnitude t value and a smallermagnitude p value are significant in the corresponding coefficient terms. The coefficients of COD removal and the
correspoding t and p values are reported in Table 2. It can be noticed from Table 2 that the coefficients for the linear effects of initial effluent concentration, applied charge, and lamp power are significant (p < 0.05). The coefficients in the quadratic term for initial effluent concentration, applied charge, and lamp power are also significant (p < 0.05). Finally, the coefficients in the interaction terms for initial effluent concentration−lamp power and applied charge−lamp power are significant compared to initial effluent concentration− applied charge. The coefficients of energy consumption and the correspoding t and p values are reported in Table 3. It can be noticed from Table 3 that the coefficients for the linear effect of initial effluent concentation is significant (p < 0.05) compared to applied charge and lamp power. In contrast, the coefficient of the quadratic term for initial effluent concentration (p < 0.05) is insignificant compared to those for applied charge and lamp power. Finally, the coefficients in the interaction terms for initial effluent concentration−applied charge and initial effluent concentration−lamp power are much more significant than that for applied charge−lamp power. 4.1.6. Analysis of Variance (ANOVA). Analysis of variance was used to determine the significant effects of process variables on percentage COD and energy consumption and is presented in Tables 4 and 5. It can be noticed from the tables that, for COD removal and energy consumption, the F-statistic values for the regressions are higher. The large F values indicate that most of the deviation in the response can be explained by the regression model equation. The associated P values were used 2851
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Figure 6. Main effects plots: (a) mean COD removal, (b) mean energy consumption.
Table 3. Estimated Regression Coefficients and Corresponding t and p Values for Energy Consumption
standard error
t
p
constant X1 X2 X3 X1 X1 X2X2 X3X3 X1 X2 X1 X3 X2 X3
16.2764 −0.0148 3.6799 2.3285 0 −0.3616 −0.0618 0.0002 0.0012 0.1657
15.0607 0.005 1.0425 0.4626 0 0.0316 0.0044 0.0002 0.0001 0.0114
1.081 −2.953 3.53 5.033 −19.938 −11.448 −13.919 1.225 17.099 14.557
0.329 0.032 0.017 0.004 0 0 0 0.275 0 0
standard error
t
p
constant X1 X2 X3 X1X1 X2X2 X3X3 X1X2 X1X3 X2X3
40.3485 −0.0934 13.1339 −0.9935 0.0001 0.091 0.0457 −0.0044 −0.0013 −0.1136
85.1389 0.0284 5.8933 2.6152 0 0.1786 0.0251 0.001 0.0004 0.0643
0.474 −3.293 2.229 −0.38 9.854 0.51 1.818 −4.281 −3.455 −1.767
0.656 0.022 0.076 0.72 0 0.632 0.129 0.008 0.018 0.138
source
Table 2. Estimated Regression Coefficients and Corresponding t and p Values for Percentage COD Removal coefficient
coefficient
Table 4. ANOVA Results for Percentage COD Removal
Figure 7. Optimization plot for COD removal and energy consumption.
model
model
regression linear square interaction residual error lack of fit pure error total
degrees of freedom
sum of squares
mean square
F statistic
P
9 3 3 3 5
3175.92 1453.81 958.1 764 7.55
352.88 24.198 319.367 254.668 1.511
233.61 16.02 211.43 168.59
0 0.005 0 0
3 2 14
7.55 0 3183.47
2.517 0.001
1843.25
0.001
Table 5. ANOVA Results for Energy Consumption source regression linear square interaction residual error lack of fit pure error total
to estimate whether the F statistics were large enough to indicate statistical significance. Lower P values (
