Development of Predictive Mathematical Model using Scent Leaf, Cassava Leaf and Neem Leaf Extracts as Corrosion Inhibitors on Mild Steel in Seawater and Sodium Chloride Environments

Corresponding author: Nairobi Cletus Madawa Copyright © 2025 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0. Development of Predictive Mathematical Model using Scent Leaf, Cassava Leaf and Neem Leaf Extracts as Corrosion Inhibitors on Mild Steel in Seawater and Sodium Chloride Environments Nairobi Cletus Madawa 1, *, Emomotimi Amula 1 and Promise Mebine 2 1 Department of Mechanical Engineering, Niger Delta University, Wilberforce Island, Amassoma, Bayelsa State, Nigeria. 2 Director/Chief Executive, National Mathematical Center, Abuja, Nigeria. Global Journal of Engineering and Technology Advances, 2025, 24(03), 417-430 Publication history: Received on 25July 2025; revised on 14 September 2025; accepted on 17 September 2025 Article DOI: https://doi.org/10.30574/gjeta.2025.24.3.0269 Abstract Mathematical Model is a statistical tool used to evaluate the rate of corrosion on oil and gas pipeline and proffer corrosion inhibitor to mitigate corrosion on the material. Experimental values were utilized to achieve predictive values. The tool enables us to deduce values on the pipeline where experimental values are not available. Maple Software was the basic tool used to perform the analysis. Weight loss method was utilized to obtain the experimental values which were further applied to determine the predictive values by using Mean Square Error (MSE), Evaluation of Accuracy on Prediction, Multiple Absolute Errors (MAE), Multiple Regression Analysis (MRA) and Polynomial Equation. Green plant extracts like Scent Leaf (SL), Cassava Leaf (CL) and Neem Leaf (NL) extracts were served as corrosion inhibitors which were added to these corrosive environments, Seawater, SW and Sodium Chloride, NaCl. The Mild Steel C-1026 coupons were immersed in the various solutions for 100 days. The results obtained from the study on weight loss of Seawater and Sodium Chloride was 0.271 and 0.193. Then the Weight loss on MSE analysis show that Seawater had both experimental and predictive values as 0.48 and 0.048008474 with an error of 0.0008474, while Sodium Chloride had 0.32 and 0.32007343 with error of 0.0007343 respectively. The evaluation of accuracy on prediction, EAP of weight loss in Seawater had 0.48 and 0.48008474 with error of 0.0008474, and Sodium Chloride has 0.32 and 0.32007343 with error of 0.00007343. Deducing from the analysis, the errors obtained from the MSE and EAP were very minimal. Therefore, Mathematical model is ideal for the prediction of pipeline corrosion and maintenance. Keywords: Mathematical Model; Maple Software; Experimental Value; Predictive Value; Corrosion Inhibitor 1. Introduction In the construction of crude oil pipeline, Mild Steel is frequently used for its fabrication. This material is very much exposed to various types of corrosive media. The material is often laid underground whereby the nature of soil is identified as a major cause of corrosion on it (Uko et al, 2014; Uhlig. 1973; Ekot. 2012; Madawa et al, 2021). Corrosion is classified as a gradual depreciation of metal by diverse electrochemical reaction between the metal and its environment (Tuaweri et al, 2015; Madawa and Amula, 2024; Ambrish et al, 2012). When corrosion takes place on the crude oil pipeline in the underground, there is complexity in detecting the rate of corrosion at regular interval. In order to alleviate this intricacy, predictive mathematical model has been developed. It is designed to determine the weight loss or corrosion rate of the metal using experimental values. Also, the model is used to enable visualization (i.e., for interpolation and extrapolation) and to infer values where experimental values are not available. Furthermore, the model summarizes the relationship among the values of the experiment. Global Journal of Engineering and Technology Advances, 2025, 24(03), 417-430 418 As a matter of fact, corrosion poses a great threat to the oil and gas industry all over the world because of the enormous losses of the natural resources and finance associated with corrosion, and as such, protection against these menaces is increasing geometrically (Madawa and Amula, 2024; Oguzie. 2008). Consequently, inhibitors are applied in the process to mitigate corrosion. Inhibitor is said to be a substance when added to a system in small concentration reduces the corrosion rate of the metal (Tuaweri et al, 2015; Madawa and Amula, 2024; Ambrish et al, 2012). Initially, inorganic compounds were intensively utilized as corrosion inhibitors, such as chromate, arsenate, etc. These compounds have some adverse effects on human being and the environment most especially the toxicity and high cost (Madawa et al, 2021; Madawa and Amula, 2024; Ameena, 2015). Therefore, researchers have sought for alternative to mitigate corrosion by using green plants. Vast numbers of green plants have been studied by different researchers that proved to be very efficient. According to Madawa et al, and Oguzie (Madawa et al, 2021; Madawa and Amula, 2024, and Oguzie. 2008), researchers unanimously consented that most green plant extracts are green corrosion inhibitors because they are biodegradable, less toxic and do not contain heavy metals. Literature on corrosion and corrosion inhibitors using green plant extracts are accessible to Sanjay, et al., (Sanjay et al, 2015); Khadom et al, (2015); Hassan et al, (2020); Felintola et al, (2019); Tuaweri and Ogbonnaya, (2017); Tuaweri et al, (2015); Ndukwe. (2017); Suleiman et al, (2017); Anyanwu et al, (2014); Okafor et al, (2010); Thangavelu et al, (2011); Ejieh and Ejimofor (2012); Umoren and Udoh. (2011); Anyakwo (2007), etc. In this study, green plant extracts such as Scent Leaf (SL), Cassava Leaf (CL) and Neem Leaf (NL) extracts were investigated to alleviate corrosion on Mild Steel C-1026 oil and gas pipeline in Seawater (SW) and Sodium Chloride (NaCl). These corrosive media are used because they are predominately found in the soil where oil and gas pipelines are laid continuously. However, the monitoring, maintaining and determining corrosion rate of the pipeline in the ground at regular interval poses great intricacy. Technology has advanced a means of monitoring the corrosion rate on oil and gas pipeline with the application of predictive Mathematical Model. This approach enables the operators of the facilities to determine corrosion rate and predetermine the interval for maintenance to be carried out from the data obtained on areas where data were acquired and not acquired. The experimental data is the prime factor in predictive mathematical modeling. There are various approaches to the achievement of Mathematical Model, thus; Polynomial Equation, Multiple Regression Analysis (MRA), Mean Square Error (MSE) and Evaluation of Accuracy on Prediction of Corrosive media. 2. Materials and methods 2.1. Preparation of Mild Steel C-1026 Specimen The chemical composition of Mild Steel, MS C-1026 specimen of 1cm oil and gas pipeline comprises: 0.08% Mn, 0.17% Ti, 0.07% As, 0.07% Cu, and 98.88% Fe (Madawa et al, 2021, Madawa and Amula, 2024). This MS was cut with cutting machine into 2cm × 4cm sizes. The coupons were abraded with Carborandium paper to mirror finish and degreased with acetone to reduce the necessary impurities to the lowest level, and then utilized for the weight loss analysis and examination of the surfaces (Madawa et al, 2021; Madawa and Amula, 2024). 2.2. Preparation of Leaf Paste The green plants, Scent leaf, Cassava Leaf and Neem Leaf extracts weighing 31g were pound with mortar and pestle. 150ml of the plant extract solution was filtered and mixed with 250ml of Seawater and 3.5wt% of NaCl (Madawa et al, 2021; Madawa and Amula, 2024). 2.3. Weight Loss Method The Mild Steel C-1026 specimens were immersed in 400ml of the various plant extracts and corrosive media solutions for 100 days (2400 hours). However, the Corrosion Rate, CR and Inhibition Efficiency, (IE %) were calculated with the following formulae: 𝐶𝑜𝑟𝑟𝑜𝑠𝑖𝑜𝑛 𝑅𝑎𝑡𝑒,𝐶𝑅 =𝐾× 𝐿𝑜𝑠𝑠 𝑖𝑛 𝑤𝑒𝑖𝑔ℎ𝑡 (𝑔) 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 (𝐴)× 𝑃𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 𝑖𝑚𝑚𝑒𝑟𝑠𝑖𝑜𝑛 (𝐻𝑟) 𝑜𝑓 𝑠𝑝𝑒𝑐𝑖𝑚𝑒𝑛× 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 (ρ) 𝑜𝑓 𝑀𝑖𝑙𝑑 𝑆𝑡𝑒𝑒𝑙 𝐶𝑅 =𝐾(𝑊𝑙𝑜𝑠) 𝐴𝑇𝜌 = 𝐾(𝑊2−𝑊1) 𝐴𝑇𝜌 (1) Global Journal of Engineering and Technology Advances, 2025, 24(03), 417-430 419 Where, W1 - W2 = Weight loss in g, D (𝜌) = Density of Mild Steel (7.86g/cm3 for Mild Steel), A = Area in cm2, T = Exposure Time in hours (Madawa et al, 2021; Tuaweri et al, 2015; Madawa and Amula, 2024; Anyanwu et al, 2014). 𝐶𝑜𝑟𝑟𝑜𝑠𝑖𝑜𝑛 𝐼𝑛ℎ𝑖𝑏𝑖𝑡𝑖𝑜𝑛 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦,𝐼𝐸(%) =100[1−𝑊2 𝑊1 ]% (2) Where, W1 and W2 are weight loss in Mild Steel in the absence and presence of inhibitors (Madawa et al, 2021; Tuaweri et al, 2015; Madawa and Amula, 2024; Thangavelu et al, 2011). 2.4. Polynomial Equation This is an equation with multiple terms made of numbers and variables. It has root which values are 𝑥 and 𝑦, where 𝑦 = 0 (HSCALPE). Moreover, it is formed with variables, exponents and coefficients. Polynomial equation consist number of exponents, where the higher one is classified as the degree of the equation (BCMPE). 𝑎𝑥6+𝑏𝑥5+𝑐𝑥4+𝑑𝑥3+𝑒𝑥2+𝑓𝑥+ 𝑔 =0 (3) In this investigation, equation (4) was applied instead of the general equation (Ekot. 2012). The application of equation (Madawa et al, 2021) is because it contained 10 numbers. The variables, time and weight loss were derived from the exponents. Thus: 𝑎𝑡9+ 𝑏𝑡8+𝑐𝑡7+𝑑𝑡6+𝑒𝑡5+𝑓𝑡4+𝑔𝑡3+ℎ𝑡2+𝑖𝑡+ 𝑗=0 (4) 2.5. Multiple Regression Analysis (MRA) Regression analysis is a statistical tool for investigation between variables (Sykes. 1992). Laerd Statistics, (2013), stated that regression is an extension of simple linear regression. MRA is applied whenever there is an intention to predict variables of two or more values. 2.6. Mean Squared Error (MSE) MSE is the procedure to estimate an unobserved quantity which measures the average squares of the error. More precisely, it is the average squared difference between the estimated values and actual values. Furthermore, MSE tells us the closeness of a regression (fitted) line to the set (data) points (Ndukwe. 2017). The formula for Mean Square Error is shown as: 𝑀𝑆𝐸 =1 𝑛∑(𝛾−𝛾1)2 (5) 𝑛 𝑖=1 Where, n is time, y is experimental value, y1 is predicted value. 2.7. Mean Absolute Error (MAE) This analysis process tells the extent of variation between the predicted values and experimental values. That is, the difference between the forecast and observed values (Ndukwe. 2017). 2.8. Evaluation of Accuracy on Prediction of Corrosive Media Evaluation of Accuracy on Prediction is a statistics tool that states the ratio of error of the absolute value to the actual experimental value. Global Journal of Engineering and Technology Advances, 2025, 24(03), 417-430 420 3. Results 3.1. Corrosive Media - Weight Loss Analysis Table 1 Weight Loss of Mild Steel C-1026 in different Corrosive Media without corrosion inhibitor Weight loss/Medium Exposure Time SW NaCl 240 0.05 0.05 480 0.09 0.08 720 0.16 0.12 960 0.19 0.16 1200 0.29 0.12 1440 0.31 0.22 1680 0.34 0.26 1920 0.36 0.28 2160 0.44 0.32 2400 0.48 0.32 Average 0.271 0.193 Table 2 Weight Loss of Mild Steel C-1026 in SW and 3.5wt% of Baths with Scent Leaf, Cassava Leaf and Neem Leaf extracts Exposure Time SW NaCl Average 0.271 0.193 Addition of Leaf-paste of Scent Leaf 240 0.03 0.04 480 0.02 0.06 720 0.01 0.09 960 0.03 0.09 1200 0.05 0.12 1440 0.11 0.15 1680 0.06 0.17 1920 0.21 0.23 2160 0.19 0.25 2400 0.22 0.28 Average 0.093 0.148 Addition of Leaf-paste of Cassava Leaf 240 0.04 0.03 480 0.06 0.06 Global Journal of Engineering and Technology Advances, 2025, 24(03), 417-430 421 720 0.04 0.08 960 0.02 0.08 1200 0.01 0.08 1440 0.03 0.09 1680 0.06 0.10 1920 0.09 0.09 2160 0.12 0.1 2400 0.17 0.12 Average 0.064 0.083 Addition of Leaf-paste of Neem Leaf 240 0.02 0.02 480 0.03 0.06 720 0.01 0.06 960 0.01 0.09 1200 0.01 0.08 1440 0.01 0.09 1680 0 0.1 1920 0 0.11 2160 0.05 0.11 2400 0.08 0.14 Average 0.022 0.086 Table 3 Inhibition Efficiency of Corrosion Inhibitors on Mild Steel C-1026 in different Corrosive Media S/No Media Average Inhibition Efficiency, IE (%) 1 SW + SL 96.54 2 SW + CL 96.51 3 SW + NL 96.82 4 NaCl + SL 97.29 5 NaCl + CL 97.58 6 NaCl + NL 97.42 Global Journal of Engineering and Technology Advances, 2025, 24(03), 417-430 422 3.2. Mean Square Error (MSE) Table 4 Mean Square Error (MSE) of Seawater Time (χ) Weight Loss (𝛾) Predicted Value (𝛾/) Error (𝛾 − 𝛾/) Error Squared 1 0.05 0.05000000 0 0 2 0.09 0.09000000 0 0 3 0.16 0.16000007 0.00000007 7𝑒−08 4 0.19 0.19000014 0.00000014 1.4𝑒−07 5 0.29 0.29000264 0.00000264 2.64𝑒−06 6 0.31 0.31000224 0.00000224 2.24𝑒−06 7 0.34 0.34001654 0.00001654 1.654𝑒−05 8 0.36 0.36002894 0.00002894 2.894𝑒−05 9 0.44 0.44004434 0.00004434 4.434𝑒−05 10 0.48 0.48008474 0.00008474 8.474𝑒−05 3.3. Mean Square Error (MSE) Table 5 Mean Square Error (MSE) of Sodium Chloride Time (χ) Weight Loss (𝛾) Predicted Value (𝛾/) Error (𝛾 − 𝛾/) Error Squared 1 0.05 0.05000000 0 0 2 0.08 0.08000001 0.00000001 1−15 3 0.12 0.11999983 0.00000017 2.89−13 4 0.16 0.15999893 0.00000107 1.1449−11 5 0.12 0.11999923 0.00000077 5.929−12 6 0.22 0.22000583 0.00000583 3.39889−10 7 0.26 0.26001153 0.00001153 1.329409−9 8 0.28 0.27998613 0.00001387 1.923769−9 9 0.32 0.31994383 0.00005617 3.1550689−8 10 0.32 0.32007343 0.00007343 5.3919649−8 3.4. Evaluation of Accuracy on Prediction of Corrosive Media Corrosive Media and Corrosion Inhibitors Analysis Table 6 Evaluation of Accuracy on Prediction of weight loss on Mild Steel C-1026 in Corrosive Media Time Experimental Value Predicted Value Error SW 1 0.05 0.05000000 0 2 0.09 0.09000001 1𝑒−08 3 0.16 0.16000007 7𝑒−08 Global Journal of Engineering and Technology Advances, 2025, 24(03), 417-430 423 4 0.19 0.19000014 1.4𝑒−07 5 0.29 0.29000264 2.64𝑒−06 6 0.31 0.31000224 2.24𝑒−06 7 0.34 0.34001654 1.654𝑒−05 8 0.36 0.36002894 2.894𝑒−05 9 0.44 0.44004434 4.434𝑒−05 10 0.48 0.48008474 8.474𝑒−04 NaCl 1 0.05 0.05000000 0 2 0.08 0.08000001 1𝑒−08 3 0.12 0.11999983 1.7𝑒−07 4 0.16 0.15999893 1.07𝑒−06 5 0.12 0.11999923 7.7𝑒−07 6 0.22 0.22000583 5.83𝑒−06 7 0.26 0.26001153 1.15𝑒−05 8 0.28 0.27998613 1.387𝑒−05 9 0.32 0.31994383 5.617𝑒−05 10 0.32 0.32007343 7.343𝑒−05 3.5. Corrosion Inhibition Analysis Table 7 Evaluation of Accuracy on Prediction of weight loss on Mild Steel C-1026 in Corrosive Media with Corrosion Inhibition Time Experimental Value Predicted Value Error SW + SL 1 0.03 0.03 0 2 0.02 0.02 1𝑒−8 3 0.01 0.0099998 1.7𝑒−7 4 0.03 0.0299994 5.7𝑒−7 5 0.05 0.0499984 1.57𝑒−7 6 0.11 0.1099935 6.47𝑒−6 7 0.06 0.0600106 1.063𝑒−5 8 0.21 0.2099707 2.927𝑒−5 9 0.19 0.1899708 2.917𝑒−4 10 0.22 0.2197351 2.649𝑒−4 NaCl + SL 1 -0.47 -0.47 1𝑒−9 2 0.06 0.06 3.𝑒−9 Global Journal of Engineering and Technology Advances, 2025, 24(03), 417-430 424 3 0.09 0.09 7.𝑒−9 4 0.09 0.0900001 6.3𝑒−8 5 0.12 0.1199999 6.7𝑒−8 6 0.15 0.149999 9.97𝑒−7 7 0.17 0.1700002 1.73𝑒−7 8 0.23 0.2299978 2.157𝑒−6 9 0.25 0.2499896 1.039𝑒−5 10 0.28 0.2799955 4.517𝑒−6 Figure 1 Weight Loss of Seawater Figure 2 Weight Loss of Sodium Chloride Global Journal of Engineering and Technology Advances, 2025, 24(03), 417-430 425 Figure 3 Prediction on Mean Square Error (MSE) of Seawater Figure 4 Prediction on Mean Square Error (MSE) of Sodium Chloride Figure 5 Prediction on Evaluation of Accuracy on Seawater