The aim of this study is to evaluate central composite design (CCD) and the Taguchi technique in the adsorption process. Contact time, initial concentration, and pH were selected as the variables, and the removal efficiency of Pb was chosen for the designated response. In addition, face-centered CCD and the L9 orthogonal array were used for the experimental design. The result indicated that, at optimum conditions, the removal efficiency of Pb was 80%. However, the value of R2 was greater than 0.95 for both the CCD and Taguchi techniques, which revealed that both techniques were suitable and in conformity with each other. Moreover, the results of analysis of variance and Prob > F < 0.05 showed the appropriate fit of the designated model with the experimental results. The probability of classifying the contributing variables by giving a percentage of the response quantity (Pb removal) made the Taguchi model an appropriate method for examining the effectiveness of different factors. pH was evaluated as the best input factor as it contributed 66.2% of Pb removal. The Taguchi technique was additionally confirmed by three-dimensional contour plots of CCD. Consequently, the Taguchi method with nine experimental runs and easy interaction plots is an appropriate substitute for CCD for several chemical engineering functions.

INTRODUCTION

Many studies have been carried out on the adsorption of heavy metals. Heavy metals are elements with atomic weights between 63.5 and 200.6 and specific gravity greater than 5.0. For decades, the excessive release of heavy metals into both surface and ground water resources has raised serious concerns among researchers around the world (Fu & Wang 2011). Unlike organic pollutants, heavy metals are not biodegradable and tend to accumulate in living organisms. Also, many heavy metal ions are known to be toxic or carcinogenic (Iye & Iye 2015). Over the years, various methods such as adsorption, precipitation, ion exchange and reduction have been proposed for heavy metal elimination (Gupta et al. 2016). One of the most known and widely applied methods is the adsorption process. Almost all research into adsorption processes has been carried out in batch systems without considering the number of required tests, expense, and time-saving along with a decrease in the consumption of reagents and material. To overcome each of the above problems and achieve the best probable response, the optimization process is the key solution (Andiappan et al. 2015; Steinbach et al. 2013). In fact, optimization denotes the development of process efficiency by applying some factors in various groupings. Two approaches, including univariate and multivariate aspects, are usually considered the best methods for optimization. The univariate approach (OFAT) includes the variability of one factor at a time, whereas the multivariate approach (MA) includes the investigation of more than one factor at a time (Gnanadesikan 2011). According to the following points, i.e. studying the relationship between the factors and nonlinear association with responses, smaller numbers of tests needed for process optimization, and high value of the data, MA has considerable advantages over OFAT.

Generally, it can be said that a significant mathematical and statistical tool is a design of experiment (DOE) for resolving multifactor and complex engineering problems accompanied by some advantages such as decreasing the number of tests, time, physical effort, and cost (Azari et al. 2015). Central composite design (CCD) is established as the most extensively used optimization method for the adsorption process because of the benefits of optimizing several factor problems with the best number of test runs according to DOE (Wu et al. 2012). On the other hand, in the adsorption process, the Taguchi method is also widely used. The Taguchi technique is a robust statistical tool which allows the free assessment of the responses with the least number of experiments (Lauro et al. 2016; Zarandi et al. 2016). In the experimental design and S/N ratio, orthogonal arrays are applied instead of the responses themselves to specify the optimum situations of control parameters; therefore, the variations affected by uncontrollable parameters are neglected (Dalton et al. 2013). The existing research into adsorption process optimization has been mostly focused on CCD. However, theres are a few studies related to the Taguchi method in the literature, but which model is suitable for the adsorption process has not yet been investigated. Consequently, this study was designed to compare two experimental design methods and the adsorption process with three factors, i.e. contact time, pH, and metal concentration. For the comparison, repeatedly used CCD and the Taguchi experimental design method were selected with a particular focus on matching the detailed statistical analysis and optimizing the experimental outcomes. In this study, Pb(II) as a representative of the heavy metals and Chitosan as the adsorbent were chosen. Pb(II), mainly because of its properties such as solubility and constancy, bioaccumulation, and long-term residence times at low concentrations is known to be one of the most hazardous elements, to which researchers have paid more attention (Abbas et al. 2016). Chitosan (CS) adsorbents are extensively utilized for removing heavy metal contaminants from the aqueous environment. Chitosan is a biopolymer of D-glucosamine created from the chitin deacetylation process utilizing strong alkali. Many previous studies have been carried out on the use of CS for heavy metals removal (Boamah et al. 2015). However, it should be noted that CS is not suitable as a bio-sorbent to remove high concentrations of pollution. In the literature, there are many reports that CS has a low solubility. Recently, there has been a growing interest in the chemical modification of Chitosan in order to improve its solubility and widen its applications in various conditions i.e. high concentrations.

MATERIALS AND METHODS

Reagents and analysis

All chemicals were of analytical grade. Lead nitrate (Pb(NO3)2) was purchased from the Merck Company (Darmstadt, Germany). Chitosan (CS) was obtained from Sigma Aldrich (St Louis, MO, USA). pH was adjusted to 0.1 mol L−1 HCl or NaOH and measured by means of a pH meter (HQ40d, Hach, Loveland, CO, USA).

Preparing adsorbate and analytical measurements

Stock solutions of the selected heavy metal were prepared by dissolving the determined amount of (Pb(NO3)2) in distilled water. The working solutions were prepared by diluting the stock solution. Heavy metal concentrations in both initial and withdrawn samples were measured by flame atomic absorption spectrophotometry (Analyst 200, Perkin Elmer).

Adsorption studies

In this study, adsorption of synthetic Pb was considered as a case study for comparing two optimization techniques, i.e. CCD and the Taguchi technique. More details about both models and the optimization process are provided in the Supplementary file (Technical details 1 and 2), available with the online version of this paper. Adsorption tests were carried out in batch mode at laboratory scale, with an Erlenmeyer flask (250 mL) set with a magnetic stirrer. For each test, 100 ml of Pb solution was placed in the flask and pH was adjusted to 3, 5 and 7 using HCl and NaOH solutions. The preferred amounts of CS (0.2 g L−1) were added to the sample over various contact times (10–60 min) at 200 rpm. Subsequently, the residual concentration of metal ions per filtered solution was found. The following equation was used to calculate the quantity of adsorbed metal ions:
formula
1
formula
2
where q (mg/g) is adsorbed metal ion; C0 and Ce (mg/L) are the initial concentration of Pb and concentration of Pb in the solution at equilibrium; v (L) is the solution volume; and m (g) is the amount of CS. All the experiments were performed at room temperature and atmospheric pressure.

For the kinetic study of Pb adsorption by CS, five initial Pb concentrations (10, 20, 30, 40 and 50 mg L−1) were used in optimized conditions (pH = 5 and 0. 2 g L−1 of CS) at room temperature during 0 to 60 min contact time.

RESULT AND DISCUSSION

Central composite design

All the experiments for the adsorption process were designed according to response surface methodology using CCD. According to the literature review, the most important parameters, which affect the efficiency of the adsorption process, are pH, initial concentrations of Pb, and contact time (Arcibar-Orozco et al. 2015). Therefore, these parameters were chosen as the control variables to be optimized using CCD, as given in Table 1.

Table 1

Experimental range and levels of process variables

Level (coded value)
VariablesSymbolsUnits− 10+ 1
pH X1 – 
Contact time X2 min 10 35 60 
Initial concentration X3 mg/L 10 30 50 
Level (coded value)
VariablesSymbolsUnits− 10+ 1
pH X1 – 
Contact time X2 min 10 35 60 
Initial concentration X3 mg/L 10 30 50 

Altogether, 20 runs with eight factorials, six axial and six center points were suggested by Design Expert software to optimize the responses, i.e. Pb removal efficiency. Based on the proposed model, the following quadratic equation was developed to predict the dependent variables (responses) in terms of independent variables and their interactions:
formula
3
where Y is the response variable (Pb removal efficiency), X1, X2 and X3 are the variables (see Table 1), b0 is constant, b1, b2, and b3 are coefficients for linear effects, b11, b22, and b33 are quadratic coefficients, and b12, b13, and b23 are interaction coefficients, respectively.

Model fitting and analysis of variance

Different concentrations of Pb were prepared and the adsorption process was performed under different conditions, according to the experimental runs, as suggested by the CCD model. Based on the experimental results, the following empirical second-order polynomial equations were developed, which show the interactions between the proposed independent variables to obtain Pb removal efficiencies:
formula
4

The aim of this empirical model was to adequately depict the interaction of genes determining the operation efficiency in the investigated concentration ranges. Experimental and predicted values for Pb removal efficiencies are provided in Table 2.

Table 2

Experimental design matrix, experimental runs, and predicted values for Pb removal efficiency

 Coded variables
Experimental removal %Predicted removal %
RunX1X2X3Pb(II)Pb(II)
0.000 −1.000 1.000 22.00 21.27 
−1.000 1.000 0.000 44.31 45.36 
0.000 0.000 0.000 51.14 50.09 
1.000 −1.000 0.000 73.41 74.14 
1.000 0.000 1.000 36.89 36.67 
1.000 1.000 0.000 75.41 73.41 
0.000 0.000 0.000 38.59 40.59 
0.000 0.000 0.000 51.75 51.97 
−1.000 0.000 1.000 43.4 44.35 
10 0.000 0.000 0.000 76.93 78.21 
11 0.000 1.000 −1.000 41.93 40.66 
12 0.000 1.000 1.000 65.33 64.39 
13 0.000 0.000 0.000 79.77 78.65 
14 0.000 0.000 0.000 76.77 78.65 
15 0.000 0.000 0.000 79.77 78.65 
16 0.000 0.000 0.000 79.77 78.65 
17 0.000 −1.000 −1.000 76.77 78.65 
18 −1.000 0.000 −1.000 79.77 78.65 
19 −1.000 −1.000 0.000 79.77 78.65 
20 1.000 0.000 −1.000 76.77 78.65 
 Coded variables
Experimental removal %Predicted removal %
RunX1X2X3Pb(II)Pb(II)
0.000 −1.000 1.000 22.00 21.27 
−1.000 1.000 0.000 44.31 45.36 
0.000 0.000 0.000 51.14 50.09 
1.000 −1.000 0.000 73.41 74.14 
1.000 0.000 1.000 36.89 36.67 
1.000 1.000 0.000 75.41 73.41 
0.000 0.000 0.000 38.59 40.59 
0.000 0.000 0.000 51.75 51.97 
−1.000 0.000 1.000 43.4 44.35 
10 0.000 0.000 0.000 76.93 78.21 
11 0.000 1.000 −1.000 41.93 40.66 
12 0.000 1.000 1.000 65.33 64.39 
13 0.000 0.000 0.000 79.77 78.65 
14 0.000 0.000 0.000 76.77 78.65 
15 0.000 0.000 0.000 79.77 78.65 
16 0.000 0.000 0.000 79.77 78.65 
17 0.000 −1.000 −1.000 76.77 78.65 
18 −1.000 0.000 −1.000 79.77 78.65 
19 −1.000 −1.000 0.000 79.77 78.65 
20 1.000 0.000 −1.000 76.77 78.65 

The relationship between observed values (actual) and the predicted values (Figure 1(a)) demonstrates a good correlation between data obtained by experiments and the values predicted by the model for Pb removal. Furthermore, it is clear from Figure 1(b) and 1(c), that the residuals were distributed randomly around ±3.00, indicating that the residual scattering of the regression equation follows normal and independent patterns. This reveals a high correlation and good agreement between the experiment and predicted values of the response for the selected contaminant.
Figure 1

Predicted and actual values for Pb removal efficiency versus initial concentration.

Figure 1

Predicted and actual values for Pb removal efficiency versus initial concentration.

A mathematical equation developed after fitting the function to the data might give misleading results and could not adequately describe the domain of the model (Gelman et al. 2014). Thus, analysis of variance (ANOVA) is an integral part of data analysis and is the more reliable way to evaluate the quality of the fitted model. Table 3 shows the ANOVA for Pb removal efficiency.

Table 3

ANOVA results for CCD

Metal ionsSourceSum of squaresDegrees of freedomMean squaresF-valueProb > F
Lead 930.10 930.10 148.29 <0.0001 
1,658.35 1,658.35 264.40 <0.0001 
253.51 253.51 40.42 <0.0001 
AB 0.017 156 13.57 0.0338 
AC 312.58 312.58 49.84 <0.0001 
BC 25.68 25.68 4.09 0.0706 
A^2 1,798.56 1,798.56 286.76 <0.0001 
B^2 562.72 562.72 89.72 <0.0001 
C^2 518.48 518.48 82.66 <0.0001 
Model 7,083.12 787.01 125.4 <0.0001 
Residual 62.72 10 6.27   
Lack of Fit 45.85 15.28 6.34  
Pure Error 16.87 2.41   
Cor Total 7,145.84 19    
Metal ionsSourceSum of squaresDegrees of freedomMean squaresF-valueProb > F
Lead 930.10 930.10 148.29 <0.0001 
1,658.35 1,658.35 264.40 <0.0001 
253.51 253.51 40.42 <0.0001 
AB 0.017 156 13.57 0.0338 
AC 312.58 312.58 49.84 <0.0001 
BC 25.68 25.68 4.09 0.0706 
A^2 1,798.56 1,798.56 286.76 <0.0001 
B^2 562.72 562.72 89.72 <0.0001 
C^2 518.48 518.48 82.66 <0.0001 
Model 7,083.12 787.01 125.4 <0.0001 
Residual 62.72 10 6.27   
Lack of Fit 45.85 15.28 6.34  
Pure Error 16.87 2.41   
Cor Total 7,145.84 19    

R2 = 0.9912.

Adjusted R2 = 0.9833.

Predicted R2 = 0.9743.

Adequate precision = 32.151.

Values of Prob > F less than 0.05 imply that the model terms were significant, while values of greater than 0.1 were insignificant for the regression model. In the current study, F values of 32.41 for Pb removal denoted the model as significant. The goodness of fit of the model was also checked by the R2 value. In this case, the values of this regression coefficient were 0.9912, which implied that this model was statistically significant and in reasonable agreement with the adjusted R2. Moreover, ‘Adeq precision’ is used to determine the signal to noise (S/N) ratio to determine the validity of the model and a ratio greater than 4 is recommended. In our case, S/N values of 25.9 for Pb removal indicated an adequate signal. They also showed that this model could be used to navigate the sCSe designs. The analysis of normal possibility plots is another checkpoint for confirming the experimental data, which indicates whether the residuals follow a normal distribution; in such a case the points will follow a straight line, as in the current study (Figure 2).
Figure 2

Normal probability plot of the studentized residuals for the Pb adsorption process.

Figure 2

Normal probability plot of the studentized residuals for the Pb adsorption process.

Considering the above ANOVA outcomes, it has been demonstrated that this model explained the adsorption process and can be employed to navigate the sCSe design in terms of Pb removal efficiencies.

Response surface plotting and optimization of operating parameters

Graphical interpretation of interactions using three-dimensional (3D) plots of the regression model is highly recommended, and is used to assess the interactive effects between the process variables and treatment efficiencies of the Fenton process (Wu et al. 2014). The surface response plots of Pb removal efficiencies of the adsorption process regarding the interaction between Pb concentration and other selected independent variables are presented in Figure 3.
Figure 3

3-D plot shows the effect of pH, contact time, and initial concentration on the percentage removal of the Pb.

Figure 3

3-D plot shows the effect of pH, contact time, and initial concentration on the percentage removal of the Pb.

Effect of solution pH

The pH of the solution plays an important role in the adsorption process by affecting metal speciation, functional groups on the CS surface, and competition generation between hydrogen ions and metal ions. Therefore, the effect of solution pH (3, 5, and 7) on the adsorption of metal ions for the initial concentrations of 10 mgL−1 was examined and the results are shown in Figure 3 (other parameters such as dose of CS and temperature were kept constant at 0.2 g L−1 and 25 °C). It was found that the metal uptake increased while increasing the pH from 3.0 to 5.0 and decreased at pH values >5. As shown, the removal efficiency was 33.34% for Pb at pH 3 and this value increased to 66.77% with pH increase to 5. It means that the uptake of metal ions is extremely dependent on the solution pH. At pH 3 (low pH), excessive protonation of nitrogen electrons (–CH = N–) decreased the electrostatic binding of ions to the corresponding –NH2 group; as a result, the number of binding sites available for the sorption of heavy metal ions was reduced, as described in Equation (5).
formula
5a
formula
5b
Also, at lower pH, a lot of competition occurred for the adsorption of a high concentration of hydrogen ions and/or metal ions for the active binding sites (Zhao et al. 2013).

With increasing pH to 5, –NH2 groups were deprotonated and Equation (5a) proceeded to the left and formed negatively charged sites (–CH = N–); thus, the adsorption of metals was increased using Equation 5(b). Moreover, a decrease in competition between hydrogen ions and positive metal ions could help increase removal efficiency. It can be seen that maximum uptake was observed at pH 5 in all ions studied. However, with increasing pH values of more than 5.0, metal speciation turned into an important factor in the adsorption process. At pH values >5.0, the solubility of Pb(II) ions was reduced and precipitation to Pb(OH)2 occurred because of the high concentrations of –OH ions in the aqueous solution (Zhu & Li 2015). Therefore, the experiments were performed with the pH value of 5. Albarelli (Albarelli et al. 2012) observed the maximum adsorption of copper (II) ions on the surface of glass beads coated with Chitosan at pH 5. Similar results have been also reported by other researchers for the adsorption of Pb ions on other types of adsorbents (Monier et al. 2012; Tirtom et al. 2012).

Effect of contact time and adsorption kinetics

The rate of metal adsorption is one of the important characteristics that defines the efficiency of sorption; thus, the effect of contact time on the adsorption of lead was investigated in the range of 0–60 min at room temperature using 0.2 g L−1 of CS for various metal ions and the results are shown in Figure 3. It was observed that the removal of Pb ions sharply increased during the first 35 min and no appreciable increase was observed beyond this time, which could prove the saturation of the active sites in glass beads (Auta & Hameed 2014). For the CS, the results demonstrated that around 80% of the metal ions were removed in the first 35 min. Hence, further experiments were carried out by fixing the contact time at 35 min for Pb2+ sorption on CS. In addition, to examine the mechanism of adsorption processes, the adsorption data were analyzed by fitting the experimental data to the linear form of the pseudo first-order rate equation (Equation (6)), the pseudo second-order rate equation (Equation (7)), and resistance to intraparticle diffusion kinetics (Equation (8)) (figures are not shown).
formula
6
formula
7
formula
8
where k1 is the pseudo first-order rate constant (min−1) of adsorption, k2 is the pseudo second-order constant (g mg−1 min−1), t is contact time (min), qe is the equilibrium adsorption capacity of the adsorbent (mg g−1), qt is the amount of pollutant adsorbed at t (mg g−1), and kint is the intraparticle diffusion constant (mg g−1 min−0.5). The kinetic models’ parameters and correlation coefficient, R2, for the selected models are shown in Table 4. As can be observed, sorption kinetics were well fitted to the pseudo second-order model. These results were also in agreement with the study of selective adsorption of heavy metal ions from the aqueous solution using magnetic EDTA-modified Chitosan/SiO2/Fe3O4 nanoparticles (Ren et al. 2013).
Table 4

Adsorption parameters of the pseudo first-order and pseudo second-order kinetics for the adsorption of Pb onto CS

  Pseudo first order
Pseudo second order
MetalsConcentration (mg L−1)k1 (min−1)qe1 (mg g−1)R2k2 (mg g−1 min−0.5)qe2 (mg g−1)R2
Pb2+ 10 0.107 52.3 0.989 0.0095 58.9 0.995 
20 0.095 92.2 0.983 0.0082 104.4 0.993 
30 0.054 115 0.967 0.0034 141.2 0.940 
40 0.038 130.6 0.958 0.0022 168.9 0.928 
50 0.045 137.3 0.978 0.0021 173.5 0.955 
  Pseudo first order
Pseudo second order
MetalsConcentration (mg L−1)k1 (min−1)qe1 (mg g−1)R2k2 (mg g−1 min−0.5)qe2 (mg g−1)R2
Pb2+ 10 0.107 52.3 0.989 0.0095 58.9 0.995 
20 0.095 92.2 0.983 0.0082 104.4 0.993 
30 0.054 115 0.967 0.0034 141.2 0.940 
40 0.038 130.6 0.958 0.0022 168.9 0.928 
50 0.045 137.3 0.978 0.0021 173.5 0.955 

Effect of initial metal concentration

The effect of initial concentration of Pb on adsorption was investigated by varying the initial metal concentrations (in the range of 10 to 50 mg L−1) at optimum pH values and 35 min of equilibrium time. For Pb, an increase in the initial concentration decreased the removal efficiency as well as increasing the amount of the adsorbed metal ion. At low concentrations, the ratio of available surface to the concentration of initial metal ions was larger, so the removal was independent of the initial concentrations. However, in the case of higher concentrations, this ratio was low; the percentage removal then depended upon the initial concentration. This behavior is well known as the ‘loading effect’, which describes the extent to which the total number of sorption sites is occupied by the sorbent. Some researchers have observed that the adsorption efficiency of heavy metal cations on adsorbents is significantly reduced when the initial concentration is increased, which is consistent with our results (Li et al. 2012). Moreover, as seen in Table 4, the value of k depended on the concentration of initial ions (C0) and the adsorption rate decreased as the concentration of initial ions increased. A decreasing kinetic rate constant can be explained by the fact that, at higher concentrations, the amount of the ions’ repulsion force is increased, which causes the metal ions to become competitors for occupying free adsorption sites. An optimization study of the experimental results was performed by keeping all the responses within the desired ranges using response surface methodology. In the present studies, Pb concentration was targeted to the maximum and other variables were kept in the range. Based on the suggested values given in Table 5, the experiment was conducted to validate the optimized results.

Table 5

Optimized operating parameters in CCD

Pb concentration (mg/L)Time (min)pHPb removal (%)Desirability
Maximum In range In range 79.1 0.927 
Pb concentration (mg/L)Time (min)pHPb removal (%)Desirability
Maximum In range In range 79.1 0.927 

According to the results obtained, approximately 79.1% of Pb removal was achieved, which could indicate good agreement of the experimental and predicted results under optimized conditions. This result implies that CCD is a suitable tool for optimizing the adsorption of Pb with improved efficiency and reduced consumption of chemicals.

Taguchi method

To assess the optimum situations for the adsorption process, the Taguchi method was used. Likewise, compared with the results received from the CCD, Design-Expert 8.0 software was used for designing orthogonal experiments. pH, metal concentration, and contact time were selected as control parameters for the optimization of conditions via Taguchi orthogonal arrays experimental design. Each parameter was at three different levels (Table 1) and the L9 orthogonal array was designed to optimize the conditions with the minimum number of experiments.

The number of the required tests decreased to nine, which is significantly less than CCD. This result indicated that only nine tests are needed for the adsorption process without considering the combination of factors, which is tested in the full factorial design of 33 = 27 runs. In the second phase, the experiments were conducted and response values were achieved. According to the analysis of the results, the Taguchi method pursued completely different stages in contrast to CCD. Due to previous studies, response values were changed to the S/N ratio that was applied to analyze the results (Asiltürk & Neşeli 2012; Astakhov 2012). The extreme Pb removal percentages are favorable for the adsorption process, which is why the ‘larger the better’ S/N ratio formula was utilized to measure the S/N value for each response. The results of the experiments and S/N ratios for each run are represented in Table 6.

Table 6

Factors and levels of orthogonal array

 Coded variables
Experimental removal %S/N ratio
RunX1X2X3Pb(II)Pb(II)
26.21 39.90 
41.53 39.82 
53.95 39.04 
71.01 38.45 
43.26 39.92 
77.64 39.45 
42.58 39.98 
49.10 39.54 
44.17 39.99 
 Coded variables
Experimental removal %S/N ratio
RunX1X2X3Pb(II)Pb(II)
26.21 39.90 
41.53 39.82 
53.95 39.04 
71.01 38.45 
43.26 39.92 
77.64 39.45 
42.58 39.98 
49.10 39.54 
44.17 39.99 

Compared with CCD, ranking the operating factors considering the contribution to response values can be done by the Taguchi technique. This technique can also be recommended for the screening of input factors in the initial steps of the studied process. In the current survey, three factors were selected and Table 7 shows that, for both forms of responses, pH was the most significant factor.

Table 7

Response table for signal to noise (S/N) ratio

LevelX1X2X3
39.45 34.00 39.95 
39.74 34.28 39.76 
39.61 35.84 39.16 
Delta 0.93 0.56 0.23 
Rank 
LevelX1X2X3
39.45 34.00 39.95 
39.74 34.28 39.76 
39.61 35.84 39.16 
Delta 0.93 0.56 0.23 
Rank 

Statistical analysis

ANOVA and models of regression are used as estimate criteria for the statistical analysis in the CCD. However, the Taguchi technique employs signal to noise ratio (S/N) as a key approach intended for the analysis. ANOVA can be used for the estimation of experimental contribution with the main purpose of determining the contribution of each factor to the variance result. This issue is related to the analysis of regression, which is applied to study and model the relationship between one or more responses and independent variables (Cohen et al. 2013). ANOVA results for Pb removal efficiency are presented in Table 8.

Table 8

ANOVA results

Metal ionsFactorsSum of squareDegrees of freedomMean squaresF-ratioProb > FPercent contribution
Pb X1 2,995.3 2,145.3 6.07 0.036 66.2 
X2 211 182 0.83 0.482 21.6 
X3 167 143.56 0.25 0.789 12.2 
Metal ionsFactorsSum of squareDegrees of freedomMean squaresF-ratioProb > FPercent contribution
Pb X1 2,995.3 2,145.3 6.07 0.036 66.2 
X2 211 182 0.83 0.482 21.6 
X3 167 143.56 0.25 0.789 12.2 

According to the table, it is clear that pH exhibited the maximum contribution of 66.2% of the Pb removal efficiency. Thus, with a confidence level of 95%, it was confirmed that the Taguchi method with the minimum number of experiments could be used as an alternative to CCD for the adsorption process. In order to confirm it, the optimized values for the responses were computed to be counter checked with those of CCD.

Confirming the test and optimizing operating parameters by the Taguchi method

The proof test is significant for proving the experimental results in the Taguchi method. However, this technique has limitations for many response procedures such as the adsorption process; considering the CCD difference, it proposes a unique sets of optimized factors for unique responses. In the present case, the removal efficiency of Pb was chosen as the response from measuring the optimized set of the contributing variables. The best situation in the adsorption process is indicated in Figure 4.
Figure 4

Mean S/N ratio for Pb removal.

Figure 4

Mean S/N ratio for Pb removal.

The maximum S/N ratio consequent to the removal of Pb recommended the best level for each parameter. It is obvious from the figure that pH indicated the maximum S/N ratio for the removal efficiency of Pb. Therefore, it proved the highest contribution of pH to the removal efficiency of Pb. The consequence of operating factors on the removal efficiency of Pb regarding the S/N ratio is presented in Figure 4. The peak S/N ratios related to Pb removal were favorable and recommended the significant levels for each parameter.

In the recent instance, Pb concentration (L1), contact time (L3), and pH (L2), were the optimized situations for the removal efficiency of Pb. Optimized principles regarding these stages are specified in Table 9.

Table 9

Optimized values for Pb removal by the Taguchi model

Pb concentration (mg/L)Time (min)pHActual Pb removal (%)Predicted Pb removal (%)
L1 L3 L2 81.2 79.06 
Pb concentration (mg/L)Time (min)pHActual Pb removal (%)Predicted Pb removal (%)
L1 L3 L2 81.2 79.06 

Unlike grouping with other factors, assessment of the in-service parameters using the mentioned plots with the Pb concentration of 10 mg L−1 indicates the maximum Pb removal efficiency. The intervention design was formed in Design-Expert 8.0, as shown in Figure 5. According to the figures, it can be stated that pH at L1 indicated the highest efficiency for all the arrangements of in-use parameters. Nearby, the concentration of Pb at L1 and a time of 60 min indicated the Pb removal efficiency of 80%.
Figure 5

Interaction of parameters for Pb removal.

Figure 5

Interaction of parameters for Pb removal.

Evaluation of the results of the interactive plots for both statistical methods indicated that the Taguchi technique with an easy graphical appearance could well clarify the interface of operating factors. The achieved results were in very good conformity with each other. Accordingly, the Taguchi method can be utilized as an alternative to CCD for evaluating the results. The response of the expected values for these optimized principles can be calculated using Equation (6) and considering the important parameters of this equation. Therefore, the parameters including pH, metal concentration, and contact time have to be optimized to take advantage of the removal efficiency of Pb. The expected S/N ratios for the optimized situations were calculated and the acquired values for removing Pb were 37.96. The expected and actually achieved values, according to the confirmatory analysis, are also represented in Tables 6 and 9. The expected values achieved via the Taguchi method were close to those achieved by CCD. The results obtained under good conditions (Taguchi method) were close to the expected values in addition to those acquired in CCD. The results indicated that the Taguchi method is a suitable and economical approach for optimizing operating factors for the adsorption process and can be used as a substitute to CCD.

CONCLUSION

This research was designed to compare two optimization methods of CCD and Taguchi orthogonal array for the adsorption process using three factors: pH, metal concentration and contact time. Overall, the following points can be obtained from this study.

  • (i) The Taguchi method presented nine experiments for the adsorption process analysis, whereas CCD recommended 20 experiments.

  • (ii) In the best situation, a Pb removal efficiency of 80% was obtained for the adsorption process by both CCD and the Taguchi technique.

  • (iii) The S/N ratio and ANOVA in the Taguchi technique indicated pH as the most important parameter, contributing 66.2% of the Pb removal efficiency.

  • (iv) The study of the parameters by 3D plots using CCD revealed pH as the most important parameter. However, quantitative intervention with CCD was not probable.

Therefore, it can be concluded that the Taguchi technique is a robust statistical tool for experimental design and procedure optimization. Optimization of operating parameters and data analysis were promising for minimizing the number of tests, and the obtained diagrams and reduced computational calculations were very easy to read and understand. The optimized values obtained by both methods were in good conformity with each other, which demonstrated the Taguchi technique's potential to be applied in chemical engineering functions. Consequently, it can be utilized as a substitute for CCD in the adsorption process.

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Supplementary data