**3.3 Modeling and statistical analysis**

Suitable statistical models were chosen to model the interactions between the different experimental variables and their effect on the efficiency of corrosion inhibition, based on the "Fit Regression Model" of MINITAB 17.0 (Pen, USA). The response was modeled with a response surface quadratic model and further analyzed by analysis of variance (ANOVA) to assess the significance of each variable on corrosion inhibition. An empirical model that could relate the response measured to the independent variables was obtained using multiple regression analysis. The response (*Y*), can be represented by the following quadratic model:

$$Y = \mathbf{a}\_o + \sum\_{i=1}^{n} \mathbf{a}\_i \mathbf{X}\_i + \sum\_{t=1}^{n} \mathbf{a}\_{ii} \mathbf{X}^2 \ {}\_i + \sum\_{t=1}^{n-1} \sum\_{j=t+1}^{n} \mathbf{a}\_{ij} X\_i \mathbf{X}\_j + \mathbf{e} \tag{6}$$

where *X*1, *X*2, *X*3, …, *X*n are the independent coded variables, α0 is the offset term, and *α*i*, α*ii*,* and *α*ij account for the linear, squared, and interaction effects, respectively, and ε is the random error. A model reduction may be expedient, if there are many redundant model terms [40].

The statistical model summary based on the Lack-of-Fit Test explained the fitness of quadratic models. Using ANOVA to assess the significance of each variable in the model, empirical quadratic models were obtained from Eq. 6. These models, Eqs. (7) and (8), for gasometric and thermometric methods, respectively, were used to predict the efficiencies of the corrosion inhibition at the various values of the independent variables.

$$\mathbf{Y} = \mathbf{376.0} + \mathbf{2.660} \,\mathbf{X}\_1 - \mathbf{1.0910} \,\mathbf{X}\_2 \tag{7}$$

$$\mathbf{Y} = \mathbf{376.4} + \mathbf{2.928} \,\mathbf{X}\_1 - \mathbf{1.1038} \,\mathbf{X}\_2 \tag{8}$$

**51**

a greater effect.

*Exploring Musa paradisiaca Peel Extract as a Green Corrosion Inhibitor for Mild Steel Using…*

**Source DF Adj SS Adj MS F-value P-value** Regression 2 3807.7 1903.87 236.50 0.000 Conc. of BPE (g/L) 1 2284.8 2284.78 283.81 0.000 Temperature (K) 1 1523.0 1522.97 189.18 0.000

Regression results often show the statistical correlation and importance between

Terms Coef SE coef T-value P-value VIF

Conc. of BPE (g/L) 2.928 0.174 16.85 0.000 1.00 Temperature (K) −1.1038 0.0803 −13.75 0.000 1.00

Constant 376.0 25.1 14.97 0.000

percentage of inhibition efficiency (%) variation that is explained by its relationship with concentration (g/L) and temperature (K), adjusted for the number of

tool for comparing the explanatory power of models with different numbers of predictors. P-value for each coefficient tests the null hypothesis that the coef-

Graphical representation allows easy interpretation of experimental results and the prediction of optimal conditions. From the contour plots, **Figures 4** and **5**, BPE was most efficient at temperatures below 307.5 K and concentrations above 8 g/L. The least inhibitory effect was observed at temperature of 318 K and at lower concentrations. This corroborated the experimental results where the highest corrosion inhibition was 72.03 and 71.56%, for gasometric and thermometric methods, respectively. This peak performance occurred when concentration was 10 mol/L and temperature 303 K. Other higher values determined for inhibition efficiency occurred in the neighborhood of 303 and 308 K, and 10 mol/L. Furthermore, the interactive effect of the concentration and temperature on the system's response (inhibition efficiency) was assessed by plotting three-dimensional curves of the response against the independent variables (**Figures 6** and **7**). The response distribution in this experiment with respect to the variation of the independent variables shows that temperature has

Similar corrosion inhibition efficiencies have been reported for biomass extracts [37, 41]. In some other studies, inhibition efficiencies in the range of

age of inhibition efficiency (%) variation that is explained by its relationship with concentration (g/L) and temperature (K). Therefore, the adjusted *R<sup>2</sup>*

) is the percent-

for this model

is a useful

is the

the predictor and response. The coefficient of determination (*R<sup>2</sup>*

*ANOVA for corrosion inhibition efficiency of BPE (thermometric method).*

Error 22 177.1 8.05

S R-sq R-sq (adj) R-sq (pred) 2.83731 95.56% 95.15% 94.36%

Total 24 3984.9

**Model summary**

**Coefficient**

**Table 6.**

predictors in the model. This adjustment is important because *R<sup>2</sup>*

ficient has no effect [40].

**3.4 Graphical representation of the model**

increases when a new independent variable is added. The adjusted *R<sup>2</sup>*

*DOI: http://dx.doi.org/10.5772/intechopen.82617*

The ANOVA of the quadratic regression model for the corrosion inhibition showed the significant level of the model at 90.72 and 95.56% for gasometric and thermometric methods, respectively (**Tables 5** and **6**). It indicates how well the model fits the experimental data, implying that the total variance in the response could be explained using this model. The closeness in the values of R-sq (adj) and R-sq (pred) in both methods also shows the significance of the model.


#### **Table 5.**

*ANOVA for corrosion inhibition efficiency of BPE (gasometric method).*


*Exploring Musa paradisiaca Peel Extract as a Green Corrosion Inhibitor for Mild Steel Using… DOI: http://dx.doi.org/10.5772/intechopen.82617*

#### **Table 6.**

*Corrosion Inhibitors*

quadratic model:

independent variables.

**Model summary**

**Coefficient**

*Y* = α*<sup>o</sup>* + ∑*i*=1

there are many redundant model terms [40].

further analyzed by analysis of variance (ANOVA) to assess the significance of each variable on corrosion inhibition. An empirical model that could relate the response measured to the independent variables was obtained using multiple regression analysis. The response (*Y*), can be represented by the following

*<sup>n</sup>* α*iXi* + ∑

*i*=1 *n* α*iiX*<sup>2</sup>

where *X*1, *X*2, *X*3, …, *X*n are the independent coded variables, α0 is the offset term, and *α*i*, α*ii*,* and *α*ij account for the linear, squared, and interaction effects, respectively, and ε is the random error. A model reduction may be expedient, if

The statistical model summary based on the Lack-of-Fit Test explained the fitness of quadratic models. Using ANOVA to assess the significance of each variable in the model, empirical quadratic models were obtained from Eq. 6. These models, Eqs. (7) and (8), for gasometric and thermometric methods, respectively, were used to predict the efficiencies of the corrosion inhibition at the various values of the

Y = 376.0 + 2.660 X1 − 1.0910X2. (7)

Y = 376.4 + 2.928 X1 − 1.1038X2. (8)

The ANOVA of the quadratic regression model for the corrosion inhibition showed the significant level of the model at 90.72 and 95.56% for gasometric and thermometric methods, respectively (**Tables 5** and **6**). It indicates how well the model fits the experimental data, implying that the total variance in the response could be explained using this model. The closeness in the values of R-sq (adj) and R-sq (pred) in both methods also shows the significance of the model.

**Source DF Adj SS Adj MS F-value P-value** Regression 2 3372.9 1686.45 107.59 0.000 Conc. of BPE (g/L) 1 1885.6 1885.59 120.30 0.000 Temperature (K) 1 1487.3 1487.31 94.89 0.000

Terms Coef SE coef T-value P-value VIF

Conc. of BPE (g/L) 2.660 0.243 10.97 0.000 1.00 Temperature (K) −1.091 0.112 −9.74 0.000 1.00

Constant 376.0 35.1 10.72 0.000

Error 22 344.8 15.67

S R-sq R-sq (adj) R-sq (pred)

Total 24 3717.7

3.95907 90.72% 89.88%

*ANOVA for corrosion inhibition efficiency of BPE (gasometric method).*

*<sup>i</sup>* + ∑ *i*=1 *n*−1 ∑ *j*=*i*+1 *n*

α*ijXiXj* + ε (6)

**50**

**Table 5.**

*ANOVA for corrosion inhibition efficiency of BPE (thermometric method).*

Regression results often show the statistical correlation and importance between the predictor and response. The coefficient of determination (*R<sup>2</sup>* ) is the percentage of inhibition efficiency (%) variation that is explained by its relationship with concentration (g/L) and temperature (K). Therefore, the adjusted *R<sup>2</sup>* is the percentage of inhibition efficiency (%) variation that is explained by its relationship with concentration (g/L) and temperature (K), adjusted for the number of predictors in the model. This adjustment is important because *R<sup>2</sup>* for this model increases when a new independent variable is added. The adjusted *R<sup>2</sup>* is a useful tool for comparing the explanatory power of models with different numbers of predictors. P-value for each coefficient tests the null hypothesis that the coefficient has no effect [40].

#### **3.4 Graphical representation of the model**

Graphical representation allows easy interpretation of experimental results and the prediction of optimal conditions. From the contour plots, **Figures 4** and **5**, BPE was most efficient at temperatures below 307.5 K and concentrations above 8 g/L. The least inhibitory effect was observed at temperature of 318 K and at lower concentrations. This corroborated the experimental results where the highest corrosion inhibition was 72.03 and 71.56%, for gasometric and thermometric methods, respectively. This peak performance occurred when concentration was 10 mol/L and temperature 303 K. Other higher values determined for inhibition efficiency occurred in the neighborhood of 303 and 308 K, and 10 mol/L. Furthermore, the interactive effect of the concentration and temperature on the system's response (inhibition efficiency) was assessed by plotting three-dimensional curves of the response against the independent variables (**Figures 6** and **7**). The response distribution in this experiment with respect to the variation of the independent variables shows that temperature has a greater effect.

Similar corrosion inhibition efficiencies have been reported for biomass extracts [37, 41]. In some other studies, inhibition efficiencies in the range of

#### **Figure 4.**

*Contour plot showing the effects of concentration and temperature on the efficiency of corrosion inhibition of BPE (Gasometric method).*

#### **Figure 5.**

*Contour plot showing the effects of concentration and temperature on the efficiency of corrosion inhibition of BPE (Thermometric method).*

80–90 have been reported for mild steel in HCl solution [42–45]. In a study carried out by Ong and Karim [46], where the extract of red onion was used to inhibit corrosion of mild steel in HCl solution, an inhibition efficiency of 90% was reported also at temperature of 303 K. Since a combination of factors such as temperature, concentration of inhibitors, and immersion time affects inhibition efficiency, it is pretty difficult to compare extracts of different biomass. However, reports have shown that temperature and concentration of inhibitors are the predominant factors [47].

**53**

**4. Conclusion**

**Figure 7.**

*method.*

**Figure 6.**

*method.*

*Exploring Musa paradisiaca Peel Extract as a Green Corrosion Inhibitor for Mild Steel Using…*

*Surface plot of inhibition efficiency (%) against concentration (g/L) and temperature (K) for gasometric* 

Statistical analysis using full factorial and the Regression Fit Model of MINITAB 17.0 was carried out to assess the effectiveness of *Musa paradisiaca* (banana) peel extract as a green corrosion inhibitor for mild steel in acidic medium. The effect of concentration of inhibitor and reaction temperature was investigated while the efficiency of corrosion inhibition was evaluated by gasometric and thermometric methods. The system's response (inhibition efficiency) showed a stochastic distribution with respect to the independent variables, with the highest corrosion inhibition efficiency being 72.03 and 71.56%, for gasometric and thermometric methods, respectively. This peak performance occurred when the concentration was 10 mol/L

*Surface plot of inhibition efficiency (%) against concentration (g/L) and temperature (K) for thermometric* 

*DOI: http://dx.doi.org/10.5772/intechopen.82617*

*Exploring Musa paradisiaca Peel Extract as a Green Corrosion Inhibitor for Mild Steel Using… DOI: http://dx.doi.org/10.5772/intechopen.82617*

#### **Figure 6.**

*Corrosion Inhibitors*

**Figure 4.**

*BPE (Gasometric method).*

*Contour plot showing the effects of concentration and temperature on the efficiency of corrosion inhibition of* 

*Contour plot showing the effects of concentration and temperature on the efficiency of corrosion inhibition of* 

80–90 have been reported for mild steel in HCl solution [42–45]. In a study carried out by Ong and Karim [46], where the extract of red onion was used to inhibit corrosion of mild steel in HCl solution, an inhibition efficiency of 90% was reported also at temperature of 303 K. Since a combination of factors such as temperature, concentration of inhibitors, and immersion time affects inhibition efficiency, it is pretty difficult to compare extracts of different biomass. However, reports have shown that temperature and concentration of inhibitors are the

**52**

**Figure 5.**

*BPE (Thermometric method).*

predominant factors [47].

*Surface plot of inhibition efficiency (%) against concentration (g/L) and temperature (K) for gasometric method.*

#### **Figure 7.**

*Surface plot of inhibition efficiency (%) against concentration (g/L) and temperature (K) for thermometric method.*

## **4. Conclusion**

Statistical analysis using full factorial and the Regression Fit Model of MINITAB 17.0 was carried out to assess the effectiveness of *Musa paradisiaca* (banana) peel extract as a green corrosion inhibitor for mild steel in acidic medium. The effect of concentration of inhibitor and reaction temperature was investigated while the efficiency of corrosion inhibition was evaluated by gasometric and thermometric methods. The system's response (inhibition efficiency) showed a stochastic distribution with respect to the independent variables, with the highest corrosion inhibition efficiency being 72.03 and 71.56%, for gasometric and thermometric methods, respectively. This peak performance occurred when the concentration was 10 mol/L

#### *Corrosion Inhibitors*

and temperature 303 K. Furthermore, the ANOVA of the quadratic regression model for the corrosion inhibition showed the significant level of the model at 90.72 and 95.56% for gasometric and thermometric methods, respectively. The response surface as well as the contour plots indicated the extract from the agro-waste was most efficient at temperature below 307.5 K and at concentrations between 8 and 10 g/L. The least inhibitory effect was observed at temperatures above 318 K and at concentrations below 6 mol/L. Banana peel extract is one of those plant extracts that have shown to be promising in green corrosion inhibition.
