Evaluation of Desmodium Adscendens (Swartz) Extract as Corrosion Inhibitor on Carbon Steel in Hydrochloric Acid Using Response Surfacemethodology (Rsm)

Evaluation of Desmodium Adscendens (Swartz) Extract as Corrosion Inhibitor on Carbon Steel in Hydrochloric Acid Using Response Surfacemethodology (Rsm) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Evaluation of Desmodium Adscendens (Swartz) Extract as Corrosion Inhibitor on Carbon Steel in Hydrochloric Acid Using Response Surfacemethodology (Rsm) Awwal Abdullahi Adamu, Ogunkemi Risikat Agbeke Iyun, James Dama Habila This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6389170/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study focused on developing predictive models and optimizing the process variables for inhibiting corrosion of carbon steel in hydrochloric acid using Desmodium adscendens (Swartz). Gravimetric analysis was used to examine four corrosion inhibition factors such as inhibitor concentration, acid concentration, immersion time, and temperature as well as their correlations with corrosion rate (CR) and inhibition efficiency (IE) as response variables. Data from the analysis was used to determine optimal parameters for inhibiting corrosion and create mathematical models using Response Surface Methodology (RSM) with Design Expert software version 13 central composite design (CCD) tool. The models investigated the corrosion inhibition performance of Desmodium adscendens (Swartz) and were found to demonstrate high accuracy and reliability, with p-values below 0.0001. 3-D response surface plots showed that increasing the acid concentration, immersion time, and temperature led to an increase in CR with decrease in IE and vice versa, while inhibitor concentration had a similar impact only when inversely paired with the others. The study revealed that using 0.8 g/L of Desmodium adscendens (Swartz) in 2 M acidic conditions at a low temperature of 323 K had the greatest impact on corrosion IE, with a CR of 0.0007 g cm -2 min -1 and inhibitor efficiency of 82.02 % after 135 minutes of exposure. Numerical optimization showed that the best conditions for inhibition occurred at a concentration of 0.800 g/L, a temperature of 323 K, an exposure time of 135.001 minutes, and acid concentration of 2 M resulting in an inhibitor efficiency of 82.38 % and a CR of 0.001 g cm -2 min -1 . Physical sciences/Chemistry/Green chemistry Physical sciences/Chemistry/Electrochemistry/Corrosion Physical sciences/Chemistry/Theoretical chemistry/Computational chemistry Desmodium adscendens corrosion RSM weight loss carbon steel optimization CCD Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1.0 Introduction Progress in industrialization has brought society to an era in which industrial operations employ sophisticated machinery, structures, and infrastructure composed of metals and their alloys. Carbon steel is widely adopted in various industries, especially for transporting and storing oil products, due to its mechanical strength and effectiveness in different conditions 1 . In the oil and gas sector, it is used in wellbore casing pipes, storage tanks, and oil rigs. However, exposure to corrosive agents during processes like well acidizing leads to reduced operational lifespan due to corrosion 2 . Corrosion management in industrial settings is expensive, especially when metals interact with strong acids like hydrochloric and sulphuric acid. Studies revealed that industrialized nations spend about 3.4% of their GDP on corrosion issues annually, totaling around $ 2.5 trillion 3 . Carbon steel, due to its excellent properties and low cost, is commonly used in facilities; thus, safeguarding it from aggressive internal conditions is crucial. Corrosion inhibitors are utilized to effectively manage corrosion risks; however, synthetic inhibitors present safety, environmental, and financial challenges. This has led to increased research into alternative solutions to mitigate the detrimental effects of corrosion on metals and alloys 4 , 5 . Researchers are prioritizing environmentally friendly biodegradable materials, particularly in corrosion inhibition. Many synthetic organic inhibitors are avoided due to adverse effects on health and the environment 6 . Plant extracts are increasingly recognized as eco-friendly alternatives for preventing material corrosion, benefiting both human health and the environment 7 . Natural bioactive chemicals in plants including alkaloids, tannins, flavonoids, and others, vary in presence and influence corrosion inhibition efficacy. Key molecular features, like heteroatoms (sulfur, nitrogen, oxygen) and complex structures (alkyl chains, aromatic rings), play a crucial role in their effectiveness 8 . Numerous scientists have successfully used various plant extracts as eco-friendly corrosion inhibitors, showing varying inhibition levels to enhance metal surface protection based on concentration and composition. Notable sources cocoa leaf 9 , Euphorbia heterophylla 4 , Coriandrum Sativum 10 , coffee husk 11 , Luffa cylindrica leaf 5 , Thymus zygis (subsp.) gracilis (TZ) 12 , Gongronema latifolium 7 , Phoenix Dactylifera 13 , Pomelo peel extract 14 , Pulicaria undulate 15 , among others. Desmodium adscendens (SW) DC is a perennial herb in the Fabaceae family, known for its climbing vines that can reach up to 100 cm in height and its clusters of obliquely ovate-lanceolate leaves (0.5-1 cm long, 1.5-3 mm wide) adorned with pink flowers. The fruit is ovate, measuring 3.5–5.5 mm long and 2.5-3 mm wide, while its elliptical seeds measure 2.5-5 mm long and 1.5 mm wide 16 . This plant thrives in tropical areas such as West Africa and the Amazon, as well as various Asian regions 17 . Recognized for its medicinal properties, it remains unexplored in research regarding its effectiveness in preventing carbon steel corrosion in different HCl concentrations, presenting a unique opportunity for study. The Design of Experiment explores the effects of interactions among process variables (independent variables) by creating a model that connects them to the response variable(s). The conventional one factor at a time analytical approach, which does not consider the interactions among all factors, requires a greater number of experimental trials, leading to increased time and costs 18 . The experimental framework for performing investigations is established through CCD and utilized in carrying out the gravimetric experiments at the designated points. RSM was employed to develop the mathematical model illustrating the connection between various process factors and the response variable and evaluated for statistical significance using ANOVA to predict the optimal values of the process factors that produce the optimal outcome 19 . 2.0 EXPERIMENTALS 2.1 Preparation and Extraction of Desmodium adscendens The plant was thoroughly cleaned and rinsed with distilled water before being air-dried in the shade for two weeks. Once fully dried, the whole plant was ground into a powder and stored in a clean plastic bag for extraction. Cold maceration was employed for the extraction based on the method described by Okewale and Adebayo 20 . The powdered Desmodium adscendens sample (500 g) was introduced into 1000 cm 3 of 99.8% methanol in a macerator. Following four days of occasional stirring, the liquid was filtered through Whatmann filter paper. The concentrated extract was obtained by placing the filtrate in a rotary evaporator and heating it to approximately 65°C until the solvent evaporated. The concentrated Desmodium adscendens plant extract (DAPE) was then stored in an airtight container and used in the corrosion study. 2.2 Carbon Steel Preparation The carbon steel material was treated for the corrosion study following the method outlined by 7 . The metal was sectioned into coupons measuring 2.5 cm x 2 cm x 0.15 cm. Emery paper was utilized to polish the coupons, unveiling a glossy polished surface. The coupons were treated with acetone to remove any oil and organic impurities before being washed with distilled water, air-dried, and stored in a desiccator. Each coupon was precisely measured with an automated scale, and the initial weight was marked for convenient recognition throughout the experiment. 2.3 Experimental Design A CCD-RSM approach using Design Expert software was employed to create a matrix for gravimetric analysis to examine interactions among process factors, developing a model to correlate independent variables with associated responses. A template with four factors across five levels analyzed effects of acid concentration (A: 1.0 to 5.0 M), immersion time (B: 60 to 360 minutes), inhibitor concentration (C: 0.2 to 1.0 g/L), and temperature (D: 313 to 353 K) on inhibition efficiencies and CR. A total of thirty experimental runs were generated in the design matrix and the experiments were randomized to mitigate systematic errors, with factor levels arranged to include high/low axial points (+α, -α), high/low factorial points (+ 1, -1), and center points (0). 2.4 Corrosion Inhibition Study The corrosion inhibition study involved carbon steel coupons analyzed via gravimetric methods at various temperatures, immersion times, acid concentrations and DAPE concentrations. Metal coupons were submerged in 250 ml beakers containing 200 cm³ of varying HCl concentrations. The control experiments measured corrosion without DAPE in HCl, while inhibition experiments included DAPE and HCl at diverse concentrations in which weight loss was monitored across different temperatures, and immersion times. After immersion, coupons were rinsed, scrubbed, dried, and reweighed to calculate weight loss by subtracting final weight from initial weight. Experimental data was recorded, with weight loss (Δw) assessed using Eq. (1), followed by CR and IE determined through equations ( 2 ) and ( 3 ), and surface coverage (θ) calculated by Eq. (4) 5 ; WL \(\:\left(\varDelta\:w\right)=\:{W}_{i}-\:{W}_{f}\) (1) $$\:CR=\:\frac{\varDelta\:w}{At}$$ 2 $$\:IE=\:\frac{{CR}_{blank}\:-\:{CR}_{inhibitor}}{{CR}_{blank}}\:\times\:100$$ 3 $$\:\theta\:=\:\frac{IE}{100}$$ 4 where W i and W f are the initial and final weights of the coupon (g), A is the total surface area of the coupon (cm 2 ), and t is the immersion time (min), \(\:{CR}_{blank}\) and \(\:{CR}_{inhibitor}\) are the CRs without and with inhibitor. 2.5 Optimization Procedure Using RSM Experimental results from CCD facilitated the development of mathematical models for CR, and inhibition efficiencies through coded variables. A quadratic second-order polynomial model was proposed in Eq. (5) to fit response data, followed by model reduction to eliminate unimportant terms. Y = Χ 0 + Χ 1 . A + Χ 2 . B + Χ 3 . C + Χ 4 . D + Χ 11 . A 2 + Χ 22 . B 2 + Χ 33. C 2 + Χ 44 . D 2 + Χ 12 . AB + Χ 13 . AC + Χ 14 . AD + Χ 23 . BC + Χ 24 . BD + Χ 34 . CD (5) Y represents the expected outcome from the regression equation, where A, B, C, and D are independent variables—acid concentration, immersion time, inhibitor level, and temperature. Χ 0 is the regression model's intercept, while Χ 1 , Χ 2 Χ 3 , and Χ 4 are linear effect coefficients, and Χ 11 , Χ 22 , Χ 33 , and Χ 44 are quadratic effect coefficients. Interaction effect coefficients are represented by Χ 12 , Χ 13 , Χ 14 , Χ 23 , Χ 24 , and Χ 34 . ANOVA assessed the impact of these interactive effects on corrosion response data. The model's significance was evaluated using the p-value adjudged to be significant at p 0.1000. R 2 values close to one and low standard deviation indicate superior model predictability 21 while "Adeq Precision" measures the signal-to-noise ratio, with a value higher than 4 being preferred 22 . 3D response assessments were carried out to identify relationships between process variables and outcomes by evaluating their interactions and forecasting results at specific factor levels. Ultimately, process parameters were optimized focusing on CR, and IE models. The numerical optimization goals were aimed to minimize CR and maximize IE, adjusting the independent and dependent parameters within set limits. 3.0 RESULTS AND DISCUSSION 3.1 Corrosion Inhibition Study Table 1 presents corrosion inhibition results guided by CCD, detailing the distribution of independent variables across experimental trials. The findings revealed that higher acid concentrations resulted in increased CR thereby reducing IE compared to lower acid concentrations (e.g., run 10 vs. run 8; run 21 vs. run 18). A similar trend was noted when evaluating the effects of varying temperature (e.g., run 11 vs. run 20; run 9 vs. run 12) and immersion time (e.g., run 5 vs. run 19; run 3 vs. run 4). Conversely, experiments with higher inhibitor concentrations demonstrated reduced CR leading to enhanced IE compared to those with lower inhibitor concentrations (e.g. run 7 vs. run 23; run 29 vs. run 1). These observations imply that process parameters influence responses as follows: increased acid concentration, extended immersion time and elevated temperature accelerates CR and retards IE; whereas higher inhibitor concentrations reduce CR which further leads to improved IE. These observations are consistent with the findings of previous works 20 , 23 – 25 . Table 1 CCD Corrosion Inhibition Study Std Run Factor 1 A: Acid Conc. (M) Factor 2 B: Immersion Time (min) Factor 3 C: Inhibitor Conc. (g/L) Factor 4 D: Temperature (K) Weight loss (g) Corrosion Rate (gcm − 2 min − 1 ) Inhibition Efficiency (%) Surface coverage (θ) 1 29 2 135 0.4 323 0.032 0.0013 78.99 0.79 2 6 4 135 0.4 323 0.072 0.0038 73.29 0.73 3 11 2 285 0.4 323 0.086 0.0016 71.07 0.71 4 26 4 285 0.4 323 0.173 0.0061 66.61 0.67 5 1 2 135 0.8 323 0.017 0.0007 82.02 0.82 6 12 4 135 0.8 323 0.061 0.0024 78.01 0.78 7 24 2 285 0.8 323 0.070 0.0013 76.91 0.77 8 27 4 285 0.8 323 0.144 0.0027 73.13 0.73 9 21 2 135 0.4 343 0.122 0.0041 74.99 0.75 10 18 4 135 0.4 343 0.366 0.0103 62.41 0.62 11 20 2 285 0.4 343 0.273 0.0052 73.55 0.74 12 28 4 285 0.4 343 0.562 0.0124 55.84 0.56 13 19 2 135 0.8 343 0.077 0.0030 79.94 0.80 14 9 4 135 0.8 343 0.274 0.0072 67.97 0.68 15 5 2 285 0.8 343 0.219 0.0041 77.17 0.77 16 14 4 285 0.8 343 0.465 0.0086 60.50 0.61 17 10 1 210 0.6 333 0.078 0.0020 76.88 0.77 18 8 5 210 0.6 333 0.390 0.0098 55.83 0.56 19 3 3 60 0.6 333 0.049 0.0043 74.20 0.74 20 4 3 360 0.6 333 0.202 0.0030 71.42 0.71 21 7 3 210 0.2 333 0.167 0.0042 70.22 0.7 22 23 3 210 1 333 0.096 0.0024 78.91 0.79 23 25 3 210 0.6 313 0.053 0.0013 80.78 0.81 24 13 3 210 0.6 353 0.450 0.0113 72.16 0.72 25 22 3 210 0.6 333 0.137 0.0034 77.26 0.77 26 15 3 210 0.6 333 0.151 0.0038 73.51 0.74 27 30 3 210 0.6 333 0.142 0.0036 74.97 0.75 28 2 3 210 0.6 333 0.159 0.0040 72.24 0.72 29 17 3 210 0.6 333 0.126 0.0032 77.96 0.78 30 16 3 210 0.6 333 0.163 0.0041 71.63 0.72 3.2 Equations for Regression Models of the Dependent Variables The mathematical models derived for the dependent variables (CR, and IE) related to carbon steel corrosion inhibition in acidic media using DAPE, following the reduction of insignificant terms, are presented in equations (6) and (7) respectively. CR = 0.0592 + 0.0145A − 0.0028B − 0.0057C + 0.0170D − 0.0027AC + 0.0020AD + 0.0028A2 + 0.0027D2 + 0.0071A2B (6) IE = 74.38–4.96A − 0.6950B + 2.34C − 2.70D − 2.56AD − 2.12A² − 1.98A2B (7) The models for CR and IE were formulated by simplifying Equations (6) and (7) via manual reduction, omitting irrelevant terms to develop the ultimate empirical model reflecting actual factors. Every model has a maximum power of 2 for at least one variable, showing that the mathematical models are quadratic equations. Each model was discovered to include terms with positive or negative coefficients, indicating a synergistic or antagonistic influence on the overall model, as observed by Salam, et al. 22 . Within the CR response model, synergistic components such as A, D, AD, A2, D 2 , and A 2 B were identified, with D having the largest coefficient (0.0170). Additionally, antagonistic elements like B, C, and AC were noted, where C exhibited the lowest coefficient (-0.0057). This indicates that temperature and inhibitor concentration exerted the greatest synergistic and antagonistic influences on the CR, respectively. This noteworthy synergistic effect might indicate that an increase in temperature results in a rise in the overall energy of the system, causing some inhibitor molecules on the metal surface to be desorbed, thereby permitting the acid to access the active sites that facilitate the metal dissolution process. This finding is in accordance with the studies documented by Ogunleye, et al. 5 , Andoor, et al. 25 and Iroha and Ukpe 26 . The IE response model identified C as the most synergistic factor, exhibiting the highest coefficient (+ 2.34). The antagonistic terms comprised A, B, D, AD, A 2 , and A 2 B, where A exhibited the largest coefficient (-4.96). The results indicate that as CR decreased, IE was enhanced with the presence of the inhibitor at every concentration evaluated as more extract molecules are readily available to occupy active sites by adsorbing onto the carbon steel surface, enhancing protection coverage. This aligns with the findings of research carried out by Ajeigbe, et al. 18 , Yamin, et al. 24 , and Iroha and Ukpe 26 . 3.3 Analysis of Variance (ANOVA) and Statistical Significance of the Model The ANOVA results for carbon steel corrosion inhibition in acidic conditions using DAPE presented in Tables 2.1 and 2.2, indicate statistical significance at a 95% confidence level. High F-values for CR (134.15) and IE (33.43) were observed, with a mere 0.01% likelihood of occurrence due to random noise and all model equations showed p-values below 0.0001. In addition, significant model terms had p-values under 0.0500, with 100% of CR and 87.5% of IE model terms being significant. All models were evaluated for lack of fit, revealing that the CR model had an F-value of 1.19 and p-value of 0.4589, indicating a non-significant lack of fit against pure error with a 45.89% chance that the F-value could result from noise. Similar results for IE were observed, with F-values of 0.34 and p-values of 0.95. Alongside p-values, statistical tools like R 2 , adjusted-R 2 , predicted-R 2 , adequate precision, and standard deviation were used to evaluate model performance. The adjusted-R 2 for both CR and IE showed values of 0.9797 and 0.9693, respectively, demonstrating a strong correlation between the experimental and predicted data 27 . Predicted-R 2 values of 0.9264 and 0.9009 for CR and IE, respectively, emphasized the robust predictive ability of the models, supported by low standard deviations of 0.0031 and 1.83, demonstrating outstanding predictive accuracy. The signal-to-noise ratios for the models were also strong, with values surpassing the ideal threshold of 4 emphasizing their capacity to explore the design space 28 . Table 2.1 ANOVA Results for Corrosion Rate of Carbon Steel in HCl Source Sum of Squares Df Mean Square F-Value p-value Model 0.0137 9 0.0015 156.17 < 0.0001 significant A – Acid Conc. 0.0051 1 0.0051 519.52 < 0.0001 B – Immersion Time 0.0001 1 0.0001 6.49 0.0192 C – Inhibitor Conc. 0.0008 1 0.0008 79.92 < 0.0001 D - Temperature 0.0069 1 0.0069 711.18 < 0.0001 AC 0.0001 1 0.0001 12.04 0.0024 AD 0.0001 1 0.0001 6.84 0.0166 A 2 0.0002 1 0.0002 22.16 0.0001 D 2 0.0002 1 0.0002 21.29 0.0002 A 2 B 0.0003 1 0.0003 27.70 < 0.0001 Residual 0.0002 20 9.738E-06 Lack of Fit 0.0002 15 0.000 1.19 0.4589 not significant Pure Error 0.0000 5 8.531E-06 Cor Total 0.0139 29 Corrosion Rate Model Fit Statistics Std. Dev. 0.0031 R 2 0.9860 Mean 0.0636 Adjusted R 2 0.9797 C.V. (%) 4.91 Predicted R 2 0.9693 Adeq. Precision 46.0709 Table 2.2 ANOVA Results for Inhibition Efficiency of Carbon Steel in HCl Source Sum of Squares Df Mean Square F-Value p-value Model 1250.27 7 178.61 53.17 < 0.0001 significant A – Acid Conc. 589.75 1 589.75 175.55 < 0.0001 B – Immersion Time 3.86 1 3.86 1.15 0.2951 C – Inhibitor Conc. 131.98 1 131.98 39.29 < 0.0001 D - Temperature 175.50 1 175.50 52.24 < 0.0001 AD 104.96 1 104.96 31.24 < 0.0001 A 2 129.51 1 129.51 38.55 < 0.0001 A 2 B 20.96 1 20.96 6.24 0.0205 Residual 73.91 22 3.36 Lack of Fit 39.83 17 2.34 0.3438 0.9553 not significant Pure Error 34.07 5 6.81 Cor Total 1324.17 29 Inhibition Efficiency Model Fit Statistics Std. Dev. 1.83 R 2 0.9442 Mean 72.68 Adjusted R 2 0.9264 C.V. (%) 2.52 Predicted R 2 0.9009 Adeq. Precision 27.8913 3.4 Validation of Regression Models Diagnostic plots such as normality, predicted versus actual, residual versus predicted, and predicted versus run were employed to assess the model's adequacy and validity, ensuring its design aligns well with actual experimental results and illustrated in Figs. 1 – 4 . The normal probability plot of residuals serves as a crucial diagnostic tool to assess the model's characteristics. In Figs. 1 a and 1 b, straight lines in the normal probability versus externally studentized residual plots indicate that the residuals conform to the normality curve, confirming the data's normal distribution, thereby suggesting the model equations are the optimal fit for the CCD data 22 , 23 . Figures 2 a and 2 b presents a comparison of predicted and actual experimental data regarding CR and IE. The closer both data are to the diagonal line of the graphs indicates a strong relationship, evidencing that the design models are effective in predicting the mentioned parameters of carbon steel in inhibited conditions 23 , 29 . The variance scatter plot of residuals versus predicted values is depicted in Figs. 3 a and 3 b, demonstrating no significant increase in residuals with the predicted level and affirming the assumption of constant variance, with no noteworthy outliers detected 30 . Figures 4 a and 4 b illustrate residuals plotted against the order of experimental runs, revealing a random scatter of points within the confidence interval, without discernible patterns, further confirming the absence of outliers in all models 23 . 3.5 Response Surface Study on Influence of Process Parameter Interactions This study utilized graphical 3-D surface plots to examine the interactions between process factors (time, temperature, inhibitor concentration, acid concentration) and responses (CR and IE). The results are illustrated in Figs. 5 – 9 , highlighting the effects on corrosion inhibition of carbon steel in acidic media. 3.5.1 Acid concentration versus Immersion time Figures 5 a and 5 b shows the 3D plots of acid concentration and immersion time affecting CR and IE. Higher acid concentrations and longer immersion times resulted in increased CR but decreased IE. Excess hydrogen ions from higher acid concentrations enhanced cathodic corrosion, while longer immersion heightened interactions with the corrosive medium. Conversely, lower acid concentrations and shorter immersion times decreased CR, improving IE. 3.5.2 Acid concentration versus Inhibitor Concentration The study investigated the impacts of acid and inhibitor concentrations on CR and IE as shown in Figs. 6 a and 6 b. Higher acid concentrations increased CR while IE is reduced. Conversely, increased inhibitor concentration reduced CR by blocking active metal sites from acid interaction. Thus, the combination of high acid and low inhibitor concentrations led to maximum CR while higher inhibitor levels and lower acid concentrations enhanced IE. 3.5.3 Acid concentration versus Temperature Figures 7 a and 7 b analyzed the combined effects of acid concentration and temperature on CR and IE. Simultaneously raising both parameters significantly elevated CR with the lowest IE, likely due to increased kinetic energy detaching inhibitor molecules from the metal surface, enhancing interactions between hydrogen ions and metal active sites. 3.5.4 Immersion time versus Temperature Figure 8a and 8b presents a 3D response surface analysis of how immersion duration and temperature jointly influence CR and IE. Extended immersion enhances CR but retards IE. Temperature is shown to be the more dominant factor affecting these outcomes. Increasing both parameters elevates the CR while reducing IE, and the opposite occurs when both are decreased. Higher temperatures facilitate partial detachment of inhibitors from steel and increase reaction rates by enhancing particle kinetic energy. Longer immersion leads to more interaction but eventually reduces reactant concentration, thereby limiting effects. 3.5.5 Effects of Inhibitor concentration versus Temperature Figures 9 a and 9 b reveal the interaction between inhibitor concentration and temperature on CR, and IE. A reciprocal relationship was observed, requiring simultaneous opposing adjustments for optimal responses. Therefore, increasing inhibitor concentration while decreasing temperature reduces CR, enhancing IE, and vice versa. Temperature significantly affects this process in which higher levels can weaken the inhibitor effectiveness due to desorption of the protective layer and increased kinetic energy of hydrogen ions, while lower temperatures improve IE. 4.0 Numerical Optimization of Process Parameters Numerical optimization results for the optimal parameters affecting carbon steel corrosion in acidic conditions are presented in Figure 10. The optimal conditions for acid concentration (A), immersion duration (B), inhibitor concentration (C), and temperature (D) produced favorable outcomes in CR and IE. A total of 100 solutions were generated, with solution 1 achieving a desirability score of 0.988 demonstrating a minimum CR of 0.001 g cm -2 min -1 and a maximum IE of 82.38 %, establishing it as the optimal configuration. The ideal parameters included 2.000 M acid concentration, 135 minutes immersion, 0.800 g/L inhibitor concentration, and 323 K temperature. Conclusion The fundamental connection amidst the process variables of acid concentration, time, inhibitor concentration and temperature regarding the CR and IE of carbon steel corrosion inhibition in acidic media using DAPE was determined and articulated through the results of the CCD-RSM method. The CCD-gravimetric analysis indicated that run number 1 yielded the best outcome, displaying the smallest CR of 0.0007 gcm -2 min -1 and the highest IE of 82.02 % under operational parameters of 2 M, an immersion time of 135.001 mins, an inhibitor concentration of 0.800 g/L, and a temperature of 323 K The equations of the quadratic regression models developed for forecasting the experimental responses proved to be strong, dependable, and sufficient. 3D-response surface plots revealed that combined levels of acid concentration, immersion duration, and temperature increased the synergistic impact on the CR and IE, whereas the inhibitor concentration showed an opposing effect when combined with any of the other variables. Under the same operational conditions as the experimental, the numerical optimization produced a comparable set of process variables and responses to the experimental data, showing a modest enhancement in IE at 82.38 %. Declarations Ethics approval and consent to participate Not applicable. Consent for publication Not applicable. Availability of data and materials All data generated or analyzed during this study are included in this published article. Competing interests The authors declare that they have no competing interests. Funding The authors declare that no specific grants or external funding were received for this research from public, commercial, or not-for-profit funding agencies. This ensures transparency and acknowledges that the work was conducted without financial support from external sources. Authors' contributions A.A. conceptualized the study, designed the experimental methodology, and carried out the overall research process. He was also responsible for drafting the initial manuscript and interpreting the corrosion inhibition results. O.R.A. supervised the laboratory experiments, including the preparation of plant extracts, corrosion testing, and data collection. She also contributed significantly to the statistical analysis using Response Surface Methodology (RSM) and participated in revising the manuscript. J.D. provided expertise in corrosion science and materials characterization. He reviewed the data analysis, validated the experimental design, and critically revised the manuscript for important intellectual content. All authors read and approved the final manuscript. Acknowledgements Not applicable. References Parthipan, P. et al. Allium sativum (garlic extract) as a green corrosion inhibitor with biocidal properties for the control of MIC in carbon steel and stainless steel in oilfield environments. International Biodeterioration & Biodegradation 132 , 66-73, doi:10.1016/j.ibiod.2018.05.005 (2018). Attar, T. et al. Experimental and theoretical studies of polyvinylpyrrolidone-iodine on carbon steel corrosion in 1M hydrochloric solution. Revue Roumaine de Chimie 66 , 761-770, doi:10.33224/rrch.2021.66.8-9.10 (2021). Ashmawy, A. 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Corrosion inhibition of carbon steel in 2.0 M HCl solution using novel extract (Pulicaria undulate). Biointerface research in applied chemistry 12 , 6415-6427, doi:10.33263/BRIAC125.64156427 (2022). Seriki, S. A., A.O., O. & O.F., A. Analysis of Phytoconstituents of Desmodium Adscendens in Relation to its Therapeutic Properties. American Journal of Biomedical Science & Research 2 , doi:10.34297/ajbsr.2019.02.000598 (2019). Ayoola, G. A., Eze, S. O., Johnson, O. O. & Adeyemi, D. K. Phytochemical screening, antioxidant, antiulcer and toxicity studies on Desmodium adscendens (Sw) DC Fabaceae leaf and stem. Tropical Journal of Pharmaceutical Research 17 , doi:10.4314/tjpr.v17i7.11 (2018). Ajeigbe, S. O., Basar, N., Hassan, M. A. & Aziz, M. Optimization of corrosion inhibition of essential oils of Alpinia galanga on mild steel using response surface methodology. ARPN Journal of Engineering and Applied Sciences 12 , 2763-2771 (2017). Olawale, O., Idefoh, C., Ogunsemi, B. & Bello, J. Evaluation of groundnut leaves extract as corrosion inhibitor on mild steel in 1m sulphuric acid using response surface methodology (RSM). International Journal of Mechanical Engineering and Technology (IJMET) 9 , 829-841, doi:https://iaeme.com/MasterAdmin/Journal_uploads/IJMET/VOLUME_9_ISSUE_11/IJMET_09_11_084.pdf (2018a). Okewale, A. O. & Adebayo, A. T. Thermodynamic and Optimization Studies of Castor Leaf Extract as Corrosion Inhibitor on Stainless Steel (301). Nigerian Journal of Technological Development 17 , 229-238, doi:10.4314/njtd.v17i3.10 (2020). Kumari, M. & Gupta, S. K. Response surface methodological (RSM) approach for optimizing the removal of trihalomethanes (THMs) and its precursor's by surfactant modified magnetic nanoadsorbents (sMNP) - An endeavor to diminish probable cancer risk. Sci Rep 9 , 18339, doi:10.1038/s41598-019-54902-8 (2019). Salam, K., Agarry, S., Arinkoola, A. & Shoremekun, I. Optimization of Operating Conditions Affecting Microbiologically Influenced Corrosion of Mild Steel Exposed to Crude Oil Environments Using Response Surface Methodology. British Biotechnology Journal 7 , 68-78, doi:10.9734/bbj/2015/16810 (2015). Khormali, A. & Ahmadi, S. Experimental and modeling analysis on the performance of 2-mercaptobenzimidazole corrosion inhibitor in hydrochloric acid solution during acidizing in the petroleum industry. Journal of Petroleum Exploration and Production Technology 13 , 2217-2235, doi:10.1007/s13202-023-01675-6 (2023). Yamin, J., Ali, E. S. E. & Al-Amiery, A. Statistical analysis and optimization of the corrosion inhibition efficiency of a locally made corrosion inhibitor under different operating variables using RSM. International Journal of Corrosion and Scale Inhibition 9 , 502-518, doi:10.17675/2305-6894-2020-9-2-6 (2020). Andoor, P. A., Okeoma, K. B. & Mbamara, U. S. Adsorption and thermodynamic studies of the corrosion inhibition effect of Rosmarinus officinalis L. leaves on aluminium alloy in 0.25 M HCl and effect of an external magnetic field. International Journal of Physical Sciences 16 , 79-95, doi:10.5897/IJPS2021.4945 (2021). Iroha, N. B. & Ukpe, R. A. Investigation of the inhibition of the corrosion of carbon steel in solution of HCl by glimepiride. Communication in Physical Sciences 5 , 246-256 (2020). Bouiti, K. et al. Response surface methodology for optimizing corrosion inhibition: investigating the synergistic effect of Eriobotrya japonica extract and potassium iodide. Euro-Mediterranean Journal for Environmental Integration 9 , 1-13, doi:10.1007/s41207-023-00457-0 (2024). Sai, D., Nataraj, K. & Lakshmana, R. Response surface methodology-a statistical tool for the optimization of responses. Global Journal of Addiction & Rehabilitation Medicine 7 , 555705, doi:10.19080/GJARM.2023.07.555705 (2023). Edoziuno, F. O. et al. Optimization and development of predictive models for the corrosion inhibition of mild steel in sulphuric acid by methyl-5-benzoyl-2-benzimidazole carbamate (mebendazole). Cogent Engineering 7 , doi:10.1080/23311916.2020.1714100 (2020). Elganidi, I., Elarbe, B., Ridzuan, N. & Abdullah, N. Optimisation of reaction parameters for a novel polymeric additives as flow improvers of crude oil using response surface methodology. Journal of Petroleum Exploration and Production Technology 12 , 437–449, doi:10.1007/s13202-021-01349-1 (2022). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6389170","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":441217936,"identity":"c629b1c1-2d90-490a-847c-f0894c41deef","order_by":0,"name":"Awwal Abdullahi Adamu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYFCCBCjNznwASErIkKCFmQ3EkuAhRQuPAYgirIW/PfnpZp6aw4n9zTyfX92oseBhYD98dAM+LRJnnpnd5jl2OHHGYd5t1jnHgA7jSUu7gdeaGwlALWy3cxuAWoxz2IBaJHjM8GqRv5H+7TbPv9u58w/zPDPO+UeEFoMbOWa3edtu5244zMP8OLeNCC2GZ96U3Zzb979+42E2M+bcPgkeNkJ+kTuevu3Gm29pxnLHmx9/zvlWJ8fPfvgYfu8jATYJMEmschBg/kCK6lEwCkbBKBg5AADB9Ew4cVA1YwAAAABJRU5ErkJggg==","orcid":"","institution":"Ahmadu Bello University","correspondingAuthor":true,"prefix":"","firstName":"Awwal","middleName":"Abdullahi","lastName":"Adamu","suffix":""},{"id":441217937,"identity":"af638885-f0a2-475c-b518-b10cd7efe5bf","order_by":1,"name":"Ogunkemi Risikat Agbeke Iyun","email":"","orcid":"","institution":"Ahmadu Bello University","correspondingAuthor":false,"prefix":"","firstName":"Ogunkemi","middleName":"Risikat Agbeke","lastName":"Iyun","suffix":""},{"id":441217938,"identity":"4a43a261-1bcb-401c-ab9f-f84a7957b193","order_by":2,"name":"James Dama Habila","email":"","orcid":"","institution":"Ahmadu Bello University","correspondingAuthor":false,"prefix":"","firstName":"James","middleName":"Dama","lastName":"Habila","suffix":""}],"badges":[],"createdAt":"2025-04-07 01:38:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6389170/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6389170/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80365202,"identity":"8c95517d-f9fa-4bdd-86f3-ef4ff0a86104","added_by":"auto","created_at":"2025-04-11 05:09:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":68724,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDiagnostic Normal Probability Plot of Residuals for (a) Corrosion Rate (b) Inhibition Efficiency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/3451f672d30f697e06a1f4ac.png"},{"id":80364346,"identity":"2f7f5bc3-c59f-41e0-bba3-f7ca1122d0cd","added_by":"auto","created_at":"2025-04-11 04:53:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":58838,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDiagnostic Plot of Predicted versus Actual for (a) Corrosion Rate (b) Inhibition Efficiency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/48c3bd7fe331fe2ae274d6c8.png"},{"id":80364369,"identity":"8c7c33bf-8bf5-4fa0-996a-c8c252fcaee7","added_by":"auto","created_at":"2025-04-11 04:53:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":62613,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDiagnostic Plot of Residual versus Predicted for (a) Corrosion Rate (b) Inhibition Efficiency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/991328b9c28b728e86b1e8fc.png"},{"id":80364344,"identity":"bef4f052-7d9f-4210-a097-b0cb03036e32","added_by":"auto","created_at":"2025-04-11 04:53:43","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":72134,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDiagnostic Plot of Residual versus Run for (a) Corrosion Rate (b) Inhibition Efficiency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/a35443f686521656f6fb7ee6.png"},{"id":80364347,"identity":"9db6e16f-f89a-47c6-9421-70bb5624f738","added_by":"auto","created_at":"2025-04-11 04:53:44","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":252649,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e3D Response surface of the interactive effects of Acid Concentration versus Immersion Time on (a) Corrosion Rate (b) Inhibition Efficiency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/62894afe0f16a5ca13260545.png"},{"id":80364348,"identity":"bbee2a30-4542-4c02-aa3f-cf974de74280","added_by":"auto","created_at":"2025-04-11 04:53:44","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":249206,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e3D Response surface of the interactive effects of Acid Concentration versus Inhibitor Concentration on (a) Corrosion Rate (b) Inhibition Efficiency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/44fc1b4f5a14dc2091e46c5f.png"},{"id":80364350,"identity":"807c355c-1f37-4792-a454-280411c1684c","added_by":"auto","created_at":"2025-04-11 04:53:44","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":294920,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e3D Response surface of the interactive effects of Acid Concentration versus Temperature on (a) Corrosion Rate (b) Inhibition Efficiency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/7e7cf53d29e483562bccab1d.png"},{"id":80365200,"identity":"2bc894ce-3507-4c3d-9e67-69114f30b74a","added_by":"auto","created_at":"2025-04-11 05:09:44","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":288750,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e3D Response surface of the interactive effects of Immersion Time versus Temperature on (a) Corrosion Rate (b) Inhibition Efficiency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/91f0977869270a27da999194.png"},{"id":80364354,"identity":"ad98013f-a90f-4385-8135-6bd9e2f0e2c6","added_by":"auto","created_at":"2025-04-11 04:53:44","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":310490,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e3D Response surface of the interactive effects of Inhibitor Concentration versus Temperature on (a) Corrosion Rate (b) Inhibition Efficiency\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/f02d59235c63fa7a16713098.png"},{"id":80364357,"identity":"02c6d157-0200-4377-8def-d06864a8bd4f","added_by":"auto","created_at":"2025-04-11 04:53:44","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":53000,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eNumerical optimization result of process parameters for the corrosion Inhibition of carbon steel in acidic media\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/9df7c02c1caa8028904153e6.png"},{"id":81693286,"identity":"e22c528e-fee9-48d1-99d0-1eb8abf28a7a","added_by":"auto","created_at":"2025-04-30 11:47:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3684073,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6389170/v1/0974441e-e719-416c-8cbc-b4f0d4e0e544.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eEvaluation of Desmodium Adscendens (Swartz) Extract as Corrosion Inhibitor on Carbon Steel in Hydrochloric Acid Using Response Surfacemethodology (Rsm)\u003c/p\u003e","fulltext":[{"header":"1.0 Introduction","content":"\u003cp\u003eProgress in industrialization has brought society to an era in which industrial operations employ sophisticated machinery, structures, and infrastructure composed of metals and their alloys. Carbon steel is widely adopted in various industries, especially for transporting and storing oil products, due to its mechanical strength and effectiveness in different conditions \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. In the oil and gas sector, it is used in wellbore casing pipes, storage tanks, and oil rigs. However, exposure to corrosive agents during processes like well acidizing leads to reduced operational lifespan due to corrosion \u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eCorrosion management in industrial settings is expensive, especially when metals interact with strong acids like hydrochloric and sulphuric acid. Studies revealed that industrialized nations spend about 3.4% of their GDP on corrosion issues annually, totaling around \u003cspan\u003e$\u003c/span\u003e2.5 trillion \u003csup\u003e \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e \u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eCarbon steel, due to its excellent properties and low cost, is commonly used in facilities; thus, safeguarding it from aggressive internal conditions is crucial. Corrosion inhibitors are utilized to effectively manage corrosion risks; however, synthetic inhibitors present safety, environmental, and financial challenges. This has led to increased research into alternative solutions to mitigate the detrimental effects of corrosion on metals and alloys \u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eResearchers are prioritizing environmentally friendly biodegradable materials, particularly in corrosion inhibition. Many synthetic organic inhibitors are avoided due to adverse effects on health and the environment \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. Plant extracts are increasingly recognized as eco-friendly alternatives for preventing material corrosion, benefiting both human health and the environment \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Natural bioactive chemicals in plants including alkaloids, tannins, flavonoids, and others, vary in presence and influence corrosion inhibition efficacy. Key molecular features, like heteroatoms (sulfur, nitrogen, oxygen) and complex structures (alkyl chains, aromatic rings), play a crucial role in their effectiveness \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eNumerous scientists have successfully used various plant extracts as eco-friendly corrosion inhibitors, showing varying inhibition levels to enhance metal surface protection based on concentration and composition. Notable sources cocoa leaf \u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, \u003cem\u003eEuphorbia heterophylla\u003c/em\u003e \u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e, \u003cem\u003eCoriandrum Sativum\u003c/em\u003e \u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e, coffee husk \u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, \u003cem\u003eLuffa cylindrica\u003c/em\u003e leaf \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, \u003cem\u003eThymus zygis (subsp.) gracilis\u003c/em\u003e (TZ) \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e, \u003cem\u003eGongronema latifolium\u003c/em\u003e \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, \u003cem\u003ePhoenix Dactylifera\u003c/em\u003e \u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e, \u003cem\u003ePomelo\u003c/em\u003e peel extract \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e, \u003cem\u003ePulicaria undulate\u003c/em\u003e \u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e, among others.\u003c/p\u003e \u003cp\u003eDesmodium adscendens (SW) DC is a perennial herb in the Fabaceae family, known for its climbing vines that can reach up to 100 cm in height and its clusters of obliquely ovate-lanceolate leaves (0.5-1 cm long, 1.5-3 mm wide) adorned with pink flowers. The fruit is ovate, measuring 3.5\u0026ndash;5.5 mm long and 2.5-3 mm wide, while its elliptical seeds measure 2.5-5 mm long and 1.5 mm wide \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. This plant thrives in tropical areas such as West Africa and the Amazon, as well as various Asian regions \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. Recognized for its medicinal properties, it remains unexplored in research regarding its effectiveness in preventing carbon steel corrosion in different HCl concentrations, presenting a unique opportunity for study.\u003c/p\u003e \u003cp\u003eThe Design of Experiment explores the effects of interactions among process variables (independent variables) by creating a model that connects them to the response variable(s). The conventional one factor at a time analytical approach, which does not consider the interactions among all factors, requires a greater number of experimental trials, leading to increased time and costs \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. The experimental framework for performing investigations is established through CCD and utilized in carrying out the gravimetric experiments at the designated points. RSM was employed to develop the mathematical model illustrating the connection between various process factors and the response variable and evaluated for statistical significance using ANOVA to predict the optimal values of the process factors that produce the optimal outcome \u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"2.0 EXPERIMENTALS","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Preparation and Extraction of \u003cem\u003eDesmodium adscendens\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eThe plant was thoroughly cleaned and rinsed with distilled water before being air-dried in the shade for two weeks. Once fully dried, the whole plant was ground into a powder and stored in a clean plastic bag for extraction. Cold maceration was employed for the extraction based on the method described by Okewale and Adebayo \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. The powdered \u003cem\u003eDesmodium adscendens\u003c/em\u003e sample (500 g) was introduced into 1000 cm\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e of 99.8% methanol in a macerator. Following four days of occasional stirring, the liquid was filtered through Whatmann filter paper. The concentrated extract was obtained by placing the filtrate in a rotary evaporator and heating it to approximately 65\u0026deg;C until the solvent evaporated. The concentrated Desmodium adscendens plant extract (DAPE) was then stored in an airtight container and used in the corrosion study.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Carbon Steel Preparation\u003c/h2\u003e \u003cp\u003eThe carbon steel material was treated for the corrosion study following the method outlined by \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. The metal was sectioned into coupons measuring 2.5 cm x 2 cm x 0.15 cm. Emery paper was utilized to polish the coupons, unveiling a glossy polished surface. The coupons were treated with acetone to remove any oil and organic impurities before being washed with distilled water, air-dried, and stored in a desiccator. Each coupon was precisely measured with an automated scale, and the initial weight was marked for convenient recognition throughout the experiment.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Experimental Design\u003c/h2\u003e \u003cp\u003eA CCD-RSM approach using Design Expert software was employed to create a matrix for gravimetric analysis to examine interactions among process factors, developing a model to correlate independent variables with associated responses. A template with four factors across five levels analyzed effects of acid concentration (A: 1.0 to 5.0 M), immersion time (B: 60 to 360 minutes), inhibitor concentration (C: 0.2 to 1.0 g/L), and temperature (D: 313 to 353 K) on inhibition efficiencies and CR. A total of thirty experimental runs were generated in the design matrix and the experiments were randomized to mitigate systematic errors, with factor levels arranged to include high/low axial points (+α, -α), high/low factorial points (+\u0026thinsp;1, -1), and center points (0).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Corrosion Inhibition Study\u003c/h2\u003e \u003cp\u003eThe corrosion inhibition study involved carbon steel coupons analyzed via gravimetric methods at various temperatures, immersion times, acid concentrations and DAPE concentrations.\u003c/p\u003e \u003cp\u003eMetal coupons were submerged in 250 ml beakers containing 200 cm\u0026sup3; of varying HCl concentrations. The control experiments measured corrosion without DAPE in HCl, while inhibition experiments included DAPE and HCl at diverse concentrations in which weight loss was monitored across different temperatures, and immersion times. After immersion, coupons were rinsed, scrubbed, dried, and reweighed to calculate weight loss by subtracting final weight from initial weight. Experimental data was recorded, with weight loss (Δw) assessed using Eq.\u0026nbsp;(1), followed by CR and IE determined through equations (\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e2\u003c/span\u003e) and (\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e3\u003c/span\u003e), and surface coverage (θ) calculated by Eq.\u0026nbsp;(4) \u003csup\u003e5\u003c/sup\u003e;\u003c/p\u003e \u003cp\u003eWL \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(\\varDelta\\:w\\right)=\\:{W}_{i}-\\:{W}_{f}\\)\u003c/span\u003e\u003c/span\u003e (1)\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:CR=\\:\\frac{\\varDelta\\:w}{At}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:IE=\\:\\frac{{CR}_{blank}\\:-\\:{CR}_{inhibitor}}{{CR}_{blank}}\\:\\times\\:100$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\theta\\:=\\:\\frac{IE}{100}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eW\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eW\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e are the initial and final weights of the coupon (g), A is the total surface area of the coupon (cm\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e), and t is the immersion time (min), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{CR}_{blank}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{CR}_{inhibitor}\\)\u003c/span\u003e\u003c/span\u003e are the CRs without and with inhibitor.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Optimization Procedure Using RSM\u003c/h2\u003e \u003cp\u003eExperimental results from CCD facilitated the development of mathematical models for CR, and inhibition efficiencies through coded variables. A quadratic second-order polynomial model was proposed in Eq.\u0026nbsp;(5) to fit response data, followed by model reduction to eliminate unimportant terms.\u003c/p\u003e \u003cp\u003eY\u0026thinsp;\u003cem\u003e=\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u003cem\u003e+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eA\u0026thinsp;+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eB\u0026thinsp;+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eC\u0026thinsp;+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e4\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eD\u0026thinsp;+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e11\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eA\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;\u003cem\u003e+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e22\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eB\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;\u003cem\u003e+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e33.\u003c/em\u003e\u003c/sub\u003e\u003cem\u003eC\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;\u003cem\u003e+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e44\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eD\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u0026thinsp;\u003cem\u003e+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e12\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eAB\u0026thinsp;+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e13\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eAC\u0026thinsp;+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e14\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eAD\u0026thinsp;+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e23\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eBC\u0026thinsp;+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e24\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eBD\u0026thinsp;+\u0026thinsp;Χ\u003c/em\u003e\u003csub\u003e\u003cem\u003e34\u003c/em\u003e\u003c/sub\u003e.\u003cem\u003eCD\u003c/em\u003e (5)\u003c/p\u003e \u003cp\u003eY represents the expected outcome from the regression equation, where A, B, C, and D are independent variables\u0026mdash;acid concentration, immersion time, inhibitor level, and temperature. Χ\u003csub\u003e0\u003c/sub\u003e is the regression model's intercept, while Χ\u003csub\u003e1\u003c/sub\u003e, Χ\u003csub\u003e2\u003c/sub\u003e Χ\u003csub\u003e3\u003c/sub\u003e, and Χ\u003csub\u003e4\u003c/sub\u003e are linear effect coefficients, and Χ\u003csub\u003e11\u003c/sub\u003e, Χ\u003csub\u003e22\u003c/sub\u003e, Χ\u003csub\u003e\u003cem\u003e33\u003c/em\u003e\u003c/sub\u003e, and Χ\u003csub\u003e\u003cem\u003e44\u003c/em\u003e\u003c/sub\u003e are quadratic effect coefficients. Interaction effect coefficients are represented by Χ\u003csub\u003e\u003cem\u003e12\u003c/em\u003e\u003c/sub\u003e, Χ\u003csub\u003e\u003cem\u003e13\u003c/em\u003e\u003c/sub\u003e, Χ\u003csub\u003e\u003cem\u003e14\u003c/em\u003e\u003c/sub\u003e, Χ\u003csub\u003e\u003cem\u003e23\u003c/em\u003e\u003c/sub\u003e, Χ\u003csub\u003e\u003cem\u003e24\u003c/em\u003e\u003c/sub\u003e, and Χ\u003csub\u003e\u003cem\u003e34\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eANOVA assessed the impact of these interactive effects on corrosion response data. The model's significance was evaluated using the p-value adjudged to be significant at p\u0026thinsp;\u0026lt;\u0026thinsp;0.0500, with lack of fit considered not significant at p\u0026thinsp;\u0026gt;\u0026thinsp;0.1000. R\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e values close to one and low standard deviation indicate superior model predictability \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e while \"Adeq Precision\" measures the signal-to-noise ratio, with a value higher than 4 being preferred \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e3D response assessments were carried out to identify relationships between process variables and outcomes by evaluating their interactions and forecasting results at specific factor levels. Ultimately, process parameters were optimized focusing on CR, and IE models. The numerical optimization goals were aimed to minimize CR and maximize IE, adjusting the independent and dependent parameters within set limits.\u003c/p\u003e \u003c/div\u003e"},{"header":"3.0 RESULTS AND DISCUSSION","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Corrosion Inhibition Study\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents corrosion inhibition results guided by CCD, detailing the distribution of independent variables across experimental trials. The findings revealed that higher acid concentrations resulted in increased CR thereby reducing IE compared to lower acid concentrations (e.g., run 10 vs. run 8; run 21 vs. run 18). A similar trend was noted when evaluating the effects of varying temperature (e.g., run 11 vs. run 20; run 9 vs. run 12) and immersion time (e.g., run 5 vs. run 19; run 3 vs. run 4). Conversely, experiments with higher inhibitor concentrations demonstrated reduced CR leading to enhanced IE compared to those with lower inhibitor concentrations (e.g. run 7 vs. run 23; run 29 vs. run 1). These observations imply that process parameters influence responses as follows: increased acid concentration, extended immersion time and elevated temperature accelerates CR and retards IE; whereas higher inhibitor concentrations reduce CR which further leads to improved IE. These observations are consistent with the findings of previous works \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan additionalcitationids=\"CR24\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCCD Corrosion Inhibition Study\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStd\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRun\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFactor 1\u003c/p\u003e \u003cp\u003eA: Acid Conc. (M)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFactor 2\u003c/p\u003e \u003cp\u003eB: Immersion Time (min)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFactor 3\u003c/p\u003e \u003cp\u003eC: Inhibitor Conc. (g/L)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFactor 4\u003c/p\u003e \u003cp\u003eD: Temperature (K)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eWeight loss (g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eCorrosion Rate (gcm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003emin\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eInhibition Efficiency (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eSurface coverage (θ)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e323\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.032\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e78.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e323\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.072\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e73.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e323\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.086\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e71.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e323\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.173\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e66.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003e5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e135\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e323\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.017\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.0007\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e82.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e0.82\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e323\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e78.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e323\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.070\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e76.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e323\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e73.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.122\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e74.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.366\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0103\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e62.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.273\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0052\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e73.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.562\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e55.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e79.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.274\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0072\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e67.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e77.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.465\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0086\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e60.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.61\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.078\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e76.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.390\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0098\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e55.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.049\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0043\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e74.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.202\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e71.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e70.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e78.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e313\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e80.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e353\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0113\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e72.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0034\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e77.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.151\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e73.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.142\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e74.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0040\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e72.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.126\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0032\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e77.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.0041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e71.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Equations for Regression Models of the Dependent Variables\u003c/h2\u003e \u003cp\u003eThe mathematical models derived for the dependent variables (CR, and IE) related to carbon steel corrosion inhibition in acidic media using DAPE, following the reduction of insignificant terms, are presented in equations (6) and (7) respectively.\u003c/p\u003e \u003cp\u003eCR\u0026thinsp;=\u0026thinsp;0.0592\u0026thinsp;+\u0026thinsp;0.0145A \u0026minus;\u0026thinsp;0.0028B \u0026minus;\u0026thinsp;0.0057C\u0026thinsp;+\u0026thinsp;0.0170D \u0026minus;\u0026thinsp;0.0027AC\u0026thinsp;+\u0026thinsp;0.0020AD\u003c/p\u003e \u003cp\u003e+\u0026thinsp;0.0028A2\u0026thinsp;+\u0026thinsp;0.0027D2\u0026thinsp;+\u0026thinsp;0.0071A2B (6)\u003c/p\u003e \u003cp\u003eIE\u0026thinsp;=\u0026thinsp;74.38\u0026ndash;4.96A \u0026minus;\u0026thinsp;0.6950B\u0026thinsp;+\u0026thinsp;2.34C \u0026minus;\u0026thinsp;2.70D \u0026minus;\u0026thinsp;2.56AD \u0026minus;\u0026thinsp;2.12A\u0026sup2; \u0026minus;\u0026thinsp;1.98A2B (7)\u003c/p\u003e \u003cp\u003eThe models for CR and IE were formulated by simplifying Equations (6) and (7) via manual reduction, omitting irrelevant terms to develop the ultimate empirical model reflecting actual factors.\u003c/p\u003e \u003cp\u003eEvery model has a maximum power of 2 for at least one variable, showing that the mathematical models are quadratic equations.\u003c/p\u003e \u003cp\u003eEach model was discovered to include terms with positive or negative coefficients, indicating a synergistic or antagonistic influence on the overall model, as observed by Salam, et al. \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eWithin the CR response model, synergistic components such as A, D, AD, A2, D\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, and A\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003eB were identified, with D having the largest coefficient (0.0170). Additionally, antagonistic elements like B, C, and AC were noted, where C exhibited the lowest coefficient (-0.0057). This indicates that temperature and inhibitor concentration exerted the greatest synergistic and antagonistic influences on the CR, respectively. This noteworthy synergistic effect might indicate that an increase in temperature results in a rise in the overall energy of the system, causing some inhibitor molecules on the metal surface to be desorbed, thereby permitting the acid to access the active sites that facilitate the metal dissolution process. This finding is in accordance with the studies documented by Ogunleye, et al. \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, Andoor, et al. \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e and Iroha and Ukpe \u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe IE response model identified C as the most synergistic factor, exhibiting the highest coefficient (+\u0026thinsp;2.34). The antagonistic terms comprised A, B, D, AD, A\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, and A\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003eB, where A exhibited the largest coefficient (-4.96). The results indicate that as CR decreased, IE was enhanced with the presence of the inhibitor at every concentration evaluated as more extract molecules are readily available to occupy active sites by adsorbing onto the carbon steel surface, enhancing protection coverage. This aligns with the findings of research carried out by Ajeigbe, et al. \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e, Yamin, et al. \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e, and Iroha and Ukpe \u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Analysis of Variance (ANOVA) and Statistical Significance of the Model\u003c/h2\u003e \u003cp\u003eThe ANOVA results for carbon steel corrosion inhibition in acidic conditions using DAPE presented in Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2.1\u003c/span\u003e and 2.2, indicate statistical significance at a 95% confidence level. High F-values for CR (134.15) and IE (33.43) were observed, with a mere 0.01% likelihood of occurrence due to random noise and all model equations showed p-values below 0.0001. In addition, significant model terms had p-values under 0.0500, with 100% of CR and 87.5% of IE model terms being significant.\u003c/p\u003e \u003cp\u003eAll models were evaluated for lack of fit, revealing that the CR model had an F-value of 1.19 and p-value of 0.4589, indicating a non-significant lack of fit against pure error with a 45.89% chance that the F-value could result from noise. Similar results for IE were observed, with F-values of 0.34 and p-values of 0.95.\u003c/p\u003e \u003cp\u003eAlongside p-values, statistical tools like R\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, adjusted-R\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, predicted-R\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, adequate precision, and standard deviation were used to evaluate model performance. The adjusted-R\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e for both CR and IE showed values of 0.9797 and 0.9693, respectively, demonstrating a strong correlation between the experimental and predicted data \u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. Predicted-R\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e values of 0.9264 and 0.9009 for CR and IE, respectively, emphasized the robust predictive ability of the models, supported by low standard deviations of 0.0031 and 1.83, demonstrating outstanding predictive accuracy. The signal-to-noise ratios for the models were also strong, with values surpassing the ideal threshold of 4 emphasizing their capacity to explore the design space \u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2.1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eANOVA Results for Corrosion Rate of Carbon Steel in HCl\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSource\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eSum of Squares\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eDf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eMean Square\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eF-Value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e0.0137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e0.0015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e156.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003esignificant\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eA \u0026ndash; Acid Conc.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0051\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e0.0051\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e519.52\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e\u0026lt;\u0026thinsp;0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eB \u0026ndash; Immersion Time\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e6.49\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e0.0192\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eC \u0026ndash; Inhibitor Conc.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0008\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e0.0008\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e79.92\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e\u0026lt;\u0026thinsp;0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eD - Temperature\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0069\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e0.0069\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e711.18\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e\u0026lt;\u0026thinsp;0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eAC\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e12.04\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e0.0024\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eAD\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e6.84\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e0.0166\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eA\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0002\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e0.0002\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e22.16\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0002\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e0.0002\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e21.29\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e0.0002\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eA\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eB\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0003\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e0.0003\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e27.70\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e\u0026lt;\u0026thinsp;0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eResidual\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0002\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e20\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e9.738E-06\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eLack of Fit\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0002\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e15\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e0.000\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e1.19\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003e0.4589\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003enot significant\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ePure Error\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0000\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e5\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e\u003cem\u003e8.531E-06\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eCor Total\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.0139\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003e29\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eCorrosion Rate Model Fit Statistics\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eStd. Dev.\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003e\u003cem\u003e0.0031\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c8\" namest=\"c6\"\u003e \u003cp\u003e\u003cb\u003eR\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e0.9860\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMean\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003e\u003cem\u003e0.0636\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c8\" namest=\"c6\"\u003e \u003cp\u003e\u003cb\u003eAdjusted R\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e0.9797\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eC.V. (%)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003e\u003cem\u003e4.91\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c8\" namest=\"c6\"\u003e \u003cp\u003e\u003cb\u003ePredicted R\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e0.9693\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c8\" namest=\"c6\"\u003e \u003cp\u003e\u003cb\u003eAdeq.\u0026nbsp;Precision\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e46.0709\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2.2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eANOVA Results for Inhibition Efficiency of Carbon Steel in HCl\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSource\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eSum of Squares\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eDf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eMean Square\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eF-Value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e1250.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e178.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e53.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003esignificant\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eA \u0026ndash; Acid Conc.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e589.75\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003e589.75\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e175.55\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e\u0026lt;\u0026thinsp;0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eB \u0026ndash; Immersion Time\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e3.86\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003e3.86\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e1.15\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e0.2951\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eC \u0026ndash; Inhibitor Conc.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e131.98\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003e131.98\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e39.29\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e\u0026lt;\u0026thinsp;0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eD - Temperature\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e175.50\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003e175.50\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e52.24\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e\u0026lt;\u0026thinsp;0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eAD\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e104.96\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003e104.96\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e31.24\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eA\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e129.51\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003e129.51\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e38.55\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e\u0026lt;\u0026thinsp;0.0001\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eA\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e\u003cem\u003eB\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e20.96\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e1\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003e20.96\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e6.24\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e0.0205\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eResidual\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e73.91\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e22\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003e3.36\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eLack of Fit\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e39.83\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e17\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003e2.34\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e0.3438\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cem\u003e0.9553\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003enot significant\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ePure Error\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e34.07\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e5\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003e6.81\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eCor Total\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003e1324.17\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003e29\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"11\" nameend=\"c11\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eInhibition Efficiency Model Fit Statistics\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eStd. Dev.\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003e\u003cem\u003e1.83\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c9\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003eR\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e\u003cem\u003e0.9442\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eMean\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003e\u003cem\u003e72.68\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c9\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003eAdjusted R\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e\u003cem\u003e0.9264\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eC.V. (%)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e \u003cp\u003e\u003cem\u003e2.52\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c9\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003ePredicted R\u003c/b\u003e\u003csup\u003e\u003cb\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/b\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e\u003cem\u003e0.9009\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c6\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c9\" namest=\"c7\"\u003e \u003cp\u003e\u003cb\u003eAdeq.\u0026nbsp;Precision\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e\u003cem\u003e27.8913\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Validation of Regression Models\u003c/h2\u003e \u003cp\u003eDiagnostic plots such as normality, predicted versus actual, residual versus predicted, and predicted versus run were employed to assess the model's adequacy and validity, ensuring its design aligns well with actual experimental results and illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The normal probability plot of residuals serves as a crucial diagnostic tool to assess the model's characteristics. In Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea and \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, straight lines in the normal probability versus externally studentized residual plots indicate that the residuals conform to the normality curve, confirming the data's normal distribution, thereby suggesting the model equations are the optimal fit for the CCD data \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Figures\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb presents a comparison of predicted and actual experimental data regarding CR and IE. The closer both data are to the diagonal line of the graphs indicates a strong relationship, evidencing that the design models are effective in predicting the mentioned parameters of carbon steel in inhibited conditions \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. The variance scatter plot of residuals versus predicted values is depicted in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb, demonstrating no significant increase in residuals with the predicted level and affirming the assumption of constant variance, with no noteworthy outliers detected \u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. Figures\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb illustrate residuals plotted against the order of experimental runs, revealing a random scatter of points within the confidence interval, without discernible patterns, further confirming the absence of outliers in all models \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Response Surface Study on Influence of Process Parameter Interactions\u003c/h2\u003e \u003cp\u003eThis study utilized graphical 3-D surface plots to examine the interactions between process factors (time, temperature, inhibitor concentration, acid concentration) and responses (CR and IE). The results are illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e, highlighting the effects on corrosion inhibition of carbon steel in acidic media.\u003c/p\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e3.5.1 Acid concentration versus Immersion time\u003c/h2\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb shows the 3D plots of acid concentration and immersion time affecting CR and IE. Higher acid concentrations and longer immersion times resulted in increased CR but decreased IE. Excess hydrogen ions from higher acid concentrations enhanced cathodic corrosion, while longer immersion heightened interactions with the corrosive medium. Conversely, lower acid concentrations and shorter immersion times decreased CR, improving IE.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e3.5.2 Acid concentration versus Inhibitor Concentration\u003c/h2\u003e \u003cp\u003eThe study investigated the impacts of acid and inhibitor concentrations on CR and IE as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb. Higher acid concentrations increased CR while IE is reduced. Conversely, increased inhibitor concentration reduced CR by blocking active metal sites from acid interaction. Thus, the combination of high acid and low inhibitor concentrations led to maximum CR while higher inhibitor levels and lower acid concentrations enhanced IE.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e3.5.3 Acid concentration versus Temperature\u003c/h2\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea and \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb analyzed the combined effects of acid concentration and temperature on CR and IE. Simultaneously raising both parameters significantly elevated CR with the lowest IE, likely due to increased kinetic energy detaching inhibitor molecules from the metal surface, enhancing interactions between hydrogen ions and metal active sites.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e3.5.4 Immersion time versus Temperature\u003c/h2\u003e \u003cp\u003eFigure 8a and 8b presents a 3D response surface analysis of how immersion duration and temperature jointly influence CR and IE. Extended immersion enhances CR but retards IE. Temperature is shown to be the more dominant factor affecting these outcomes. Increasing both parameters elevates the CR while reducing IE, and the opposite occurs when both are decreased. Higher temperatures facilitate partial detachment of inhibitors from steel and increase reaction rates by enhancing particle kinetic energy. Longer immersion leads to more interaction but eventually reduces reactant concentration, thereby limiting effects.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e3.5.5 Effects of Inhibitor concentration versus Temperature\u003c/h2\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003ea and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003eb reveal the interaction between inhibitor concentration and temperature on CR, and IE. A reciprocal relationship was observed, requiring simultaneous opposing adjustments for optimal responses. Therefore, increasing inhibitor concentration while decreasing temperature reduces CR, enhancing IE, and vice versa. Temperature significantly affects this process in which higher levels can weaken the inhibitor effectiveness due to desorption of the protective layer and increased kinetic energy of hydrogen ions, while lower temperatures improve IE.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4.0 Numerical Optimization of Process Parameters","content":"\u003cp\u003eNumerical optimization results for the optimal parameters affecting carbon steel corrosion in acidic conditions are presented in Figure 10. The optimal conditions for acid concentration (A), immersion duration (B), inhibitor concentration (C), and temperature (D) produced favorable outcomes in CR and IE. A total of 100 solutions were generated, with solution 1 achieving a desirability score of 0.988 demonstrating a minimum CR of 0.001 g cm\u003csup\u003e-2\u003c/sup\u003e min\u003csup\u003e-1\u003c/sup\u003e and a maximum IE of 82.38 %, establishing it as the optimal configuration. The ideal parameters included 2.000 M acid concentration, 135 minutes immersion, 0.800 g/L inhibitor concentration, and 323 K temperature.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThe fundamental connection amidst the process variables of acid concentration, time, inhibitor concentration and temperature regarding the CR and IE of carbon steel corrosion inhibition in acidic media using DAPE was determined and articulated through the results of the CCD-RSM method.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe CCD-gravimetric analysis indicated that run number 1 yielded the best outcome, displaying the smallest CR of 0.0007 gcm\u003csup\u003e-2\u003c/sup\u003emin\u003csup\u003e-1\u003c/sup\u003e and the highest IE of 82.02 % under operational parameters of 2 M, an immersion time of 135.001 mins, an inhibitor concentration of 0.800 g/L, and a temperature of 323 K\u003c/p\u003e\n\u003cp\u003eThe equations of the quadratic regression models developed for forecasting the experimental responses proved to be strong, dependable, and sufficient. 3D-response surface plots revealed that combined levels of acid concentration, immersion duration, and temperature increased the synergistic impact on the CR and IE, whereas the inhibitor concentration showed an opposing effect when combined with any of the other variables.\u003c/p\u003e\n\u003cp\u003eUnder the same operational conditions as the experimental, the numerical optimization produced a comparable set of process variables and responses to the experimental data, showing a modest enhancement in IE at 82.38 %.\u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data generated or analyzed during this study are included in this published article.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that no specific grants or external funding were received for this research from public, commercial, or not-for-profit funding agencies. This ensures transparency and acknowledges that the work was conducted without financial support from external sources.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors' contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA.A. conceptualized the study, designed the experimental methodology, and carried out the overall research process. He was also responsible for drafting the initial manuscript and interpreting the corrosion inhibition results. O.R.A. supervised the laboratory experiments, including the preparation of plant extracts, corrosion testing, and data collection. She also contributed significantly to the statistical analysis using Response Surface Methodology (RSM) and participated in revising the manuscript. J.D. provided expertise in corrosion science and materials characterization. He reviewed the data analysis, validated the experimental design, and critically revised the manuscript for important intellectual content. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eParthipan, P.\u003cem\u003e et al.\u003c/em\u003e Allium sativum (garlic extract) as a green corrosion inhibitor with biocidal properties for the control of MIC in carbon steel and stainless steel in oilfield environments. \u003cem\u003eInternational Biodeterioration \u0026amp; Biodegradation\u003c/em\u003e \u003cstrong\u003e132\u003c/strong\u003e, 66-73, doi:10.1016/j.ibiod.2018.05.005 (2018).\u003c/li\u003e\n\u003cli\u003eAttar, T.\u003cem\u003e et al.\u003c/em\u003e Experimental and theoretical studies of polyvinylpyrrolidone-iodine on carbon steel corrosion in 1M hydrochloric solution. \u003cem\u003eRevue Roumaine de Chimie\u003c/em\u003e \u003cstrong\u003e66\u003c/strong\u003e, 761-770, doi:10.33224/rrch.2021.66.8-9.10 (2021).\u003c/li\u003e\n\u003cli\u003eAshmawy, A. 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Response surface methodological (RSM) approach for optimizing the removal of trihalomethanes (THMs) and its precursor\u0026apos;s by surfactant modified magnetic nanoadsorbents (sMNP) - An endeavor to diminish probable cancer risk. \u003cem\u003eSci Rep\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, 18339, doi:10.1038/s41598-019-54902-8 (2019).\u003c/li\u003e\n\u003cli\u003eSalam, K., Agarry, S., Arinkoola, A. \u0026amp; Shoremekun, I. Optimization of Operating Conditions Affecting Microbiologically Influenced Corrosion of Mild Steel Exposed to Crude Oil Environments Using Response Surface Methodology. \u003cem\u003eBritish Biotechnology Journal\u003c/em\u003e \u003cstrong\u003e7\u003c/strong\u003e, 68-78, doi:10.9734/bbj/2015/16810 (2015).\u003c/li\u003e\n\u003cli\u003eKhormali, A. \u0026amp; Ahmadi, S. Experimental and modeling analysis on the performance of 2-mercaptobenzimidazole corrosion inhibitor in hydrochloric acid solution during acidizing in the petroleum industry. \u003cem\u003eJournal of Petroleum Exploration and Production Technology\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 2217-2235, doi:10.1007/s13202-023-01675-6 (2023).\u003c/li\u003e\n\u003cli\u003eYamin, J., Ali, E. S. E. \u0026amp; Al-Amiery, A. Statistical analysis and optimization of the corrosion inhibition efficiency of a locally made corrosion inhibitor under different operating variables using RSM. \u003cem\u003eInternational Journal of Corrosion and Scale Inhibition\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, 502-518, doi:10.17675/2305-6894-2020-9-2-6 (2020).\u003c/li\u003e\n\u003cli\u003eAndoor, P. A., Okeoma, K. B. \u0026amp; Mbamara, U. S. 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Optimisation of reaction parameters for a novel polymeric additives as flow improvers of crude oil using response surface methodology. \u003cem\u003eJournal of Petroleum Exploration and Production Technology\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 437\u0026ndash;449, doi:10.1007/s13202-021-01349-1 (2022).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Desmodium adscendens, corrosion, RSM, weight loss, carbon steel, optimization, CCD","lastPublishedDoi":"10.21203/rs.3.rs-6389170/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6389170/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study focused on developing predictive models and optimizing the process variables for inhibiting corrosion of carbon steel in hydrochloric acid using \u003cem\u003eDesmodium adscendens\u003c/em\u003e (Swartz). Gravimetric analysis was used to examine four corrosion inhibition factors such as inhibitor concentration, acid concentration, immersion time, and temperature as well as their correlations with corrosion rate (CR) and inhibition efficiency (IE) as response variables. Data from the analysis was used to determine optimal parameters for inhibiting corrosion and create mathematical models using Response Surface Methodology (RSM) with Design Expert software version 13 central composite design (CCD) tool. The models investigated the corrosion inhibition performance of \u003cem\u003eDesmodium adscendens\u003c/em\u003e (Swartz) and were found to demonstrate high accuracy and reliability, with p-values below 0.0001. 3-D response surface plots showed that increasing the acid concentration, immersion time, and temperature led to an increase in CR with decrease in IE and vice versa, while inhibitor concentration had a similar impact only when inversely paired with the others. The study revealed that using 0.8 g/L of \u003cem\u003eDesmodium adscendens\u003c/em\u003e (Swartz) in 2 M acidic conditions at a low temperature of 323 K had the greatest impact on corrosion IE, with a CR of 0.0007 g cm\u003csup\u003e-2\u003c/sup\u003emin\u003csup\u003e-1 \u003c/sup\u003eand inhibitor efficiency of 82.02 % after 135 minutes of exposure. Numerical optimization showed that the best conditions for inhibition occurred at a concentration of 0.800 g/L, a temperature of 323 K, an exposure time of 135.001 minutes, and acid concentration of 2 M resulting in an inhibitor efficiency of 82.38 % and a CR of 0.001 g cm\u003csup\u003e-2\u003c/sup\u003emin\u003csup\u003e-1\u003c/sup\u003e.\u003c/p\u003e","manuscriptTitle":"Evaluation of Desmodium Adscendens (Swartz) Extract as Corrosion Inhibitor on Carbon Steel in Hydrochloric Acid Using Response Surfacemethodology (Rsm)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-11 04:53:30","doi":"10.21203/rs.3.rs-6389170/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"da2146e3-5a7c-40f2-8c66-9a70ab75ce99","owner":[],"postedDate":"April 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":47006230,"name":"Physical sciences/Chemistry/Green chemistry"},{"id":47006231,"name":"Physical sciences/Chemistry/Electrochemistry/Corrosion"},{"id":47006232,"name":"Physical sciences/Chemistry/Theoretical chemistry/Computational chemistry"}],"tags":[],"updatedAt":"2025-04-30T11:39:04+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-11 04:53:30","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6389170","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6389170","identity":"rs-6389170","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}