Mild steel composition of C = 0.22; Si = 0.30; Mn = 0.65; Cu = 0.030; P = 0.045 and Fe balance. Mild steel sheet thickness of 3.0 mm was cut into coupons of 20 × 20 mm to carry out several tests. The mild steel surfaces were mechanically abraded with 400 grade of emery papers before it was used for the immersion tests. Before the immersion corrosion tests, the specimens were cleaned in acetone and purified water.

Crude oil used was brought from an oil field in Rivers state, Nigeria. The pH of the crude oil environment was adjusted using 0.1 mol / L HCl and 0.1 mol/ L NaCl solutions. Before the immersion experiments, the pH of the crude oil solution was measured by pH meter.

Immersion test experiments were performed using Minitab 17 statistical software to vary the process input variables into different levels to observe their effect on the corrosion rate. The result obtained from the experimental design matrix was evaluated using Box Behnken Design to derive mathematical model by applying RSM quadratic model and the same data obtained from Box Behnken Design was employed to train ANN utilizing normal multilayer feed-forward neural network.

In this study, mild steel coupons were immersed in crude oil at 27 °C, and the effect of pH,concentration of the binary inhibitor, and the time of the corrosion rate were investigated. Immersion tests were performed with three replicates of each experimental run designed as presented in Table 1. The weight of steel coupons before and after the tests was estimated using an electronic balance (Adventurer Ohaus SNR: 8728406387) to observe weight change. Corrosion rates were calculated based on the loss in the weight of the mild steel by Eq. (1) in accordance with the ASTM G31 standard [18, 19].

(1)

Where W_L = weight loss (g), A = area of the mild steel specimen (cm²), t = time (year(y)), and ρ = density (g/ cm³).

The experimental design was based on three factors and three levels as illustrated in Table 1. The table presents actual and coded variables, and 15 experimental runs were defined by Box Behnken design (BBD). The quality of the model fitness was determined by a test of significance and analysis of variance (ANOVA). The equation for the second-order polynomial was obtained from the interactional relationship of variables. The quadratic response model was fitted as given in Eq. (2).

(2)

Where Y is the response predicted value (corrosion rate), where d₀ represents offset term, d₁, d₂, and d₃ represent the linear coefficients, d₁₁, d₂₂, and d₃₃ are quadratic terms while d₁₂, d₁₃, and d₂₃ are cross products. The experiments were conducted in triplicates and the average value was used. The experimental data of BBD design matrix and their experimental responses are tabulated in Table 2. Minitab 17 statistical software was utilized for designing experimental sets and analysis of data using response surface methodology-Box Behnken design.

In this training procedure, a multilayer normal feed-forward network was applied to process information from the input layer through the hidden layer to the output layer. The output of the designated layer was obtained from the output layer [17]. The multilayer normal feed-forward network was used to determine the inhibitive property of the binary mixture of sesame and castor oil on the corrosion rate of mild steel in a crude oil environment. This statistical approach uses superintend learning known as backpropagation throughout the training period of the model. Training of the learning works as a result of the changes observed in the connection weights, as established by the errors calculated from the observed values, proceeding from the output and advancing to the input. Feedforward propagation was applied by the ANN, in this case, each layer progresses to the next layer without regress (Fig. 1). ANN input values are classified into categorical values as pH, the concentration of binary inhibitor and time, while the corrosion rate is the ANN output.

ANN performance was assessed by the error and accurate values of the model. The root mean square error (RMSE) and the coefficient of determination (R²) were estimated by Eqs. (3 and 4) respectively [20].

(3)

(4)

Where n represents the number of observations, x_i, represents the experimental corrosion rate (mm/ yr), and y_i represents the corrosion rate estimated by the model. These criteria were applied to determine the performance of ANN in modelling of the corrosion rate of mild steel in crude oil environments using sesame and castor oil as a binary inhibitor due to the quantitative variables presented by the output and input data, since these criteria are frequently used in evaluating the model's performance. The weights and bias for the output and hidden layer used in this study are illustrated in Table 3.

The results of the corrosion rate of identical mild steel coupons in different concentrations of binary inhibitor, time and pH of the crude oil solution are reported in Table 2. Table 2 reveals that the highest corrosion rate of mild steel (00.98 mm/yr) was observed at a low pH of 5, and binary inhibitor concentration of 23 mg/L over a period of 21 days. This can be as a result of the length of time which was 21 days; the layer provided by the inhibitor would have degraded at a fast rate. While the lowest corrosion rate of 0.04 mm/yr was observed at the maximum concentration of binary inhibitor used in this study which was 30 mg/L and a shorter length of time of 13 days, occurring at the same pH when the maximum corrosion rate was reported. This illustrates that the higher concentration of binary inhibitor and the lower reaction time at a low pH of 5 favor the reduction of the corrosion rate on mild steel in crude oil solutions.

According to experimental results, equation 5 shows an empirical relationship between the response (i.e. experimental corrosion rate) and independent variables (Concentration of binary inhibitor, Time and pH). In the equation, the pH is not represented by the quadratic model, this further validates the less effect of the pH in crude oil solutions.

(5)

Where X represents the concentration of binary inhibitor, and Y represents time.

The predicted values of the response (experimental corrosion rate) have been calculated by the quadratic model from Eq. (5) and are presented in Table 2. Table 2 shows a clear agreement between the RSM predicted values, ANN predicted and the experimental values; this thereby demonstrates the reliability of both the models in predicting the corrosion rate of mild steel in crude oil solutions. The ANOVA results were summarized for the quadratic model indicating the adequacy and significance of the model given in Table 4. The large F – value and low P-value of the model imply that the model is significant [15, 17, 21]. The determination coefficient (R²) and the adjusted coefficient of determination (R²) were 72. 95% and 65.57% respectively, thereby indicating a reasonable fitness of the model to the experimental data. R² of 72.95% implies that 72.95% of the variations experienced could adequately be illustrated by the fitted model in Eq. (5). The optimum corrosion rate of 0.04 mm/yr observed was at pH 5, at 30 mg/L concentration of the binary inhibitor over a period of 13 days. This validates the efficiency of the binary inhibitor in reducing the corroding potential of mild steel in crude oil solutions.

Fig. (1). Multilayer normal feed-forward network architecture applied in this study.

The effect of the binary inhibitor concentration and time on the experimental corrosion rate is displayed in Fig. (2) From the figure, it can be observed that at constant pH, the corrosion rate increased as time increased. For instance, with a constant binary inhibitor of 23 mg/L, at a pH of 5, the corrosion rate increased from 0.13 to 0.98 mm/yr when the time of exposure increased from 3 to 17 days. Also, increasing the concentration of the binary mixture at constant pH and time also affected the corrosion rate i.e. corrosion rate of mild steel reduces from 0.85 to 0.09 mm/yr, when the concentration of the binary mixture increased from 19 to 26 at a constant pH and time period of 17 days. This shows the effect of a binary mixture; the binary composition of sesame and castor oil forms a passive layer over the surface of the mild steel inhibiting the corrosion rate. The more the concentration of the binary mixture, the greater the thickness of the passive layer formed over the surface of the mild steel. Also, since the higher reaction time was also responsible for the rapid degradation of the mild steel surface, therefore, it can be said that a higher concentration of the binary inhibitor requires a longer period of time for the passive layer to be completely degraded. Consequently, in order to prevent the rapid degradation of mild steel in the crude oil environment, greater attention is required when considering the amount of the inhibitor to be used and the length of time the equipment is meant to serve.

Fig. (3) illustrates the effects of pH and the concentration of the binary inhibitor on mild steel at a constant time. The figure shows a decrease in the corrosion rate when the concentration of binary inhibitor increased. For instance, the corrosion rate of mild steel decreased from 0.58 to 0.04 mm/yr when the concentration of the binary inhibitor doubled at a constant pH of 5. Also at a constant pH of 4, the corrosion rate greatly reduced from 0.81 to 0.08 when the concentration of the binary inhibitor increased from 19 to 26 mm/yr. This implies that at an acidic concentration of the crude oil, the presence of a higher concentration of binary inhibitor was required to reduce the corrosion rate of mild steel, thus increasing its shelf life. This was in concordance with what was required at the near neutral pH of 6, whereby the corrosion rate reduced from 0.58 to 0.05 mm/yr when the concentration of the binary mixture increased from 19 to 26 mg/L. This also confirms that a broader passive layer of the inhibitor is formed over the surface of the mild steel at a higher concentration of brine, thus inhibiting the effect of crude oil as a corrosive agent on the mild steel.

Fig. (2). Surface and contour plots showing the effect of Concentration of binary inhibitor and time on the Corrosion rate at constant pH.

Fig. (3). Effect of pH and Concentration of the binary inhibitor on the mild steel in crude oil solutions at constant time.

Fig. (4). Effect of Time and pH on the corrosion rate of mild steel in crude oil environments at a constant concentration of the binary inhibitor.

Fig. (5). Importance levels of each parameter on the corrosion rate of mild steel in crude oil.

Fig. (6). Comparing experimental and predicted corrosion rates by RSM model (left) and ANN model (right).

The effect of crude oil pH and mild steel exposure time on crude oil environments was considered at a constant concentration of binary inhibitor in Fig. (4). Fig. (4) illustrates that at a constant concentration of the binary mixture and time, the corrosion rate decreased from 0.37 to 0.24 mm/yr when the pH increased from 3 to 7. Increasing the pH further to 8, the corrosion rate increased to 0.32 mm/yr. This shows that the pH has a very minimal effect on the corrosion rate; this was further explained in Fig. (5), which demonstrates a low significance level of 6.88% when compared to significance level of time (60.64%) and concentration of binary inhibitor (32.48%). At a constant pH of 5, the corrosion rate increased from 0.13 to 0.98 mm/L when the time increased from 3 to 21 days. This illustrates that at a longer reaction time, the passive layer formed by the binary inhibitor depletes. Moreover, the continuous exposure of mild steel surface to the corrosive environment gradually eliminates the presence of any corrosive layer formed on the mild steel by the binary inhibitor. This implies that in order to prevent future problems, the binary inhibitor should be reapplied into the corrosive environments.

The determination coefficient (R²) by ANN was observed to be 99.95%; this was far greater than what was observed by the RSM model. This implies that a greater variation of 99.95% can be explained by the ANN model while a lesser variation of 72.95% can be explained by the RSM model. Also, the root mean square error (RMSE) observed by the ANN model was 0.0099 while the RMSE observed by the RSM model was 0.1871. Since a lesser RMSE shows the greater efficiency of a model in predicting the corrosion rate of mild steel occurring in crude oil solutions. Therefore, based on the R² and RMSE values observed in this study with varying concentrations of the binary inhibitor, time and pH, ANN demonstrated a better efficiency than the RSM model in predicting the corrosion rate of mild steel in crude oil.

Furthermore, both the models (RSM and ANN) used in this study are compared in Fig. (6). Fig. (6) depicts the experi-mental and predicted plots for each model. From the figure, it is obvious that the trained ANN model is more effective in predicting the corrosion rate of mild steel in crude oil solutions. The better predictive capacity of the ANN model is as a result of its potential to adequately approximate the system non-linearity, in contrast to the RSM model which is limited to second-degree polynomial [15, 22]. Although, when the ANN technique is applied, it must be observed that its predictions are limited to the range of process factors considered in the training process [23].

The optimum condition of variables established by both models included pH 5, 30 mg/L of the concentration of binary inhibitor and 13 days of time. This essentially resulted in the lowest corrosion rate of mild steel at 0.04 mm/yr. Thus, this validates the efficiency of the binary inhibitor on mild steel in crude oil solutions.