Introduction

Cooling towers are considered one of the most important pieces of equipment in the industry. It faces many problems like corrosion, scaling or scaling & clogging (especially biofilm formation) [1,2,3]. The scale is formed from water-soluble minerals deposited on heat transfer surfaces or in water pipes. Adding acid, lowering the pH of the water or adding a scale inhibitor can be done to reduce scale problems [2,4]. Two basic techniques are used to protect against corrosion in cooling towers: Using chemical corrosion inhibitors and increasing the pH of the water. Biocides, scale inhibitors should be added to prevent corrosion and Microbiological Influenced Corrosion, MIC, deposition [4,5,6]. Statistical analysis is fundamental for all branches of science and engineering, as well as in the field of corrosion [7,8]. Experiment design, DOE, is a statistical and mathematical method design for systematically performing experiments and analyzing data efficiently, in order to optimize accuracy and derive results [9,10]. The most popular DOE models are the Factorial and Taguchi methods. They make it possible to optimize the results and to study the main effects of the independent variables and their interactions with the dependent variable [11,12,13]. Monte Carlo simulation is a model used to predict the probabilities of different outcomes when random variables are involved. It is used to assess the impact of fluctuations on the dependent variable in the system [14].

This study aimed to investigate the optimal conditions to minimize the corrosion rate of low carbon steels in cooling towers under static conditions in the presence of commercial corrosion inhibitor ku-2050 and different immersion times at different values of pH then simulate the obtained models to evaluate random events on the rate of corrosion and its variation according to the change of working parameters.

Experimental

Mass loss is one of low cost, easy, and most widely recognized strategies to explore the corrosion rate. Many researchers have used immersion tests followed by a weight loss method to calculate the corrosion rate. Mass loss procedure is given in ASTM G31 standard and the general procedure to clean and prepare the material samples is given in ASTM G1 [15-18].

Corrosive Media

Twenty liters of each of makeup water and recirculating water (basin water) were sampled from CTS present in AL-Daura Refinery /Middle Refineries Company (MRC).

Additives

500 ml sample of Kurita 2050(ku-2050) commercial corrosion inhibitor was used in AL-Daura Refinery / MRC.

Metals

Strip low carbon steel coupons with the surface area of about 20 cm² for each coupon were applied. Table 1 demonstrates some properties of makeup and recirculating water samples.

Method

Coupon preparation

Each coupon was polished, ground using emery papers (220.320.400.600) then washed with tap water, distilled water, dried by clean tissue, rinsed with acetone for several seconds, dried and put in desiccator. Then the coupon was weighed to nearest 0.1 mg (w1) by using analytical balance to measure the weight loss.

Immersion test

After weighing, the prepared coupons were immersed in makeup water samples in the absence and presence of different concentrations of (ku-2050) (25, 50, 75,100, 300, 500, 700, 800, 900, 1000, 1500, 2000) ppm at different periods ranging from 1 day to 6 weeks at different pH values (7-8.5) under static conditions (velocity=0) and at room temperature. Figure 1 shows weight loss method.

Corrosion rate estimation

Corrosion rate calculations from weight loss data was performed according to Eq.1 in (mpy) units:

Where △w is difference between weights of coupon before and after immersion test, t is time (period of immersion), d is density of low carbon steel, 7.86, g/cm³ and A is surface area of coupon, cm².

Results and discussion

Experimental design & Analysis (DOE models)

First factorial Model

A two-levels two-factor 2² (with replication) factorial design was used to determine the effect of time (period of immersion) (weeks) and conc. of ku-2050 (ppm) on the CR in mpy unit of low carbon steel in makeup water. The low and high levels of the factors mentioned are shown in Table 2, where (-1,+1) are low and high levels for each factor.

Table 3 represents the design matrix for 2² (with replication) with CR values measured in mpy units for each experiment. Table 3 demonstrates the design matrix for 2² (with replication) with CR values of low carbon steel in makeup water.

By analyzing factorial design in Minitab software 2021, multivariable equation were obtained with correlation coefficient R²₌ 0.9603:

CR= 0.4708+ 0.2206 X₁+0.00195 X₂- 0.0012 X₁ X₂                                                                                                               (2)

The complete Analysis of Variance (ANOVA) for the corrosion of low carbon steel in makeup water for periods of immersion (2, 4) weeks using ku-2050 inhibitor (25, 100) ppm under static conditions is shown in Table 4.

DF denotes the degree of freedom, SS is the sum of squares, and MS signifies mean of squares.

From Table 4, p value for the (time and conc.) is <0.05 but for their interaction, it is > 0.05, meaning that the two variables are more significant than their interaction (more influence on CR than their interaction). Interaction plot between the means of CR values and conc. of ku-2050 at two levels of time are depicted in Figure 2.

From Figure 2, it is clear that the lines are less non parallel, which means that less effect can be noticed by the interaction between Ku-2050 conc. and time on the response CR.

The two residual plots that are explained in the right part of Figure 3 show a fairly random pattern. The random patterns in Eq. 2 provide a decent fit to the data. At the left of Figure 3, Normal Probability (NP) and Histogram (Hist.) plots can be observed, which are a more specialized types of plots that can be used to see how data fits the norm, or skews from the norm. NP and Hist. plot demonstrate that the data are normally distributed.

An optimization plot was drawn by a Minitab response optimizer tool as shown in Figure 4. It is illustrated that the lowest corrosion rate of 0.8671 mpy could be obtained at 100 ppm of ku-2050 inhibitor and 2 weeks immersion period.

Contour plots, sometimes called level plots, are a way to show a three-dimensional surface on a two-dimensional. They have two predictor variables XY on the y axis response variable z as contours. It is shown from the contour plot in Figure 5 that CR is < 0.9 mpy at 2 weeks and 100 ppm of ku-2050, while at 4 weeks and 25 ppm of ku-2050, CR is  >1.2 mpy.

Second factorial model

The low and high levels of the factors mentioned are shown in Table 5.

Table 6 represents the design matrix for 2²(with replication) with CR values that were measured in mpy units for each experiment.

An equation was obtained with correlation coefficient of R²=0.945 as follows:

CR=2.29521-0.109448 X₁-0.000972 X₂+0.000798 X₁ X₂                                                          (3)

From ANOVA results in Table 7, p value for conc. of ku-2050 is <0.05 but for pH and its interaction with conc. is > 0.05, meaning that the conc. of ku-2050 is more significant than pH and their interaction (conc. of ku-2050 effects on CR significantly). Figure 6 depicts the interaction plot for Eq. 3.

Taguchi models

In Taguchi design, a standard orthogonal array, L9, was designed by Minitab software 2021 including two factors (time & ku-2050 conc.) with 3 levels for each factor as shown in Tables 7and 8.

Table 9 demonstrates the responses (CR values in mpy units) for each mentioned experiment in Table 8.

The measurement of performance in Taguchi design is called signal to noise, S/N ratio. There are mainly three different types of S/N ratio that are applicable in the most situations: Larger is better (LTB), smaller is better (STB), and nominal is better (NTB). In this study, the quality to optimize is the corrosion rate. The used type of S/N ratio is smaller better (STB). Eq.(4) is used to calculate the ratio [12].

Regarding analyzing Taguchi design, Table 10 clarifies the effect of each of the studied factors on the CR₁ and CR₂. These outputs are shown in Figure 7. From Figure 7, it can be noted that the time has negative influence on the corrosion rate while, the conc. Of ku-2050 has a positive influence on it. Based on the recordings, time has the largest effect on the CR of low carbon steel in makeup water as shown in Figure 8.

Tables 11 and 12 show the ANOVA results for the S/N ratio and the mean respectively. It is also clear from those tables that the time has an effect larger than the conc. of ku-2050.

The ANOVA analysis is shown in Figure 9, which should be explained. In this figure, there are four sub-figures. For the NP plot, it is noticed that it follows a straight line. The Hist. plot represents the normal distribution of the results about mean of zero, and since the values of skewness and kurtosis are within the range (2-(-2)), this confirms normal univariate distribution. The residual versus fit plot shows that the residuals are randomly distributed about zero-line. The residual versus order plot also confirms a random pattern around zero-line.

By using the correlation analysis for Taguchi design in Minitab software 2021, the best multiple regressions that fit the responses (CR of low carbon steel immersed in makeup water) versus the effective parameters (time & Conc. of ku-2050) were obtained for the highestR² with p-value < 0.05, as shown in the following Equations:

CR₁=0.445+ 0.2872 X₁- 0.001663 X₂- 0.0223 X₁²       R²=0.948                                                    (5)

CR₂=0.808+ 0.1912 X₁- 0.00995 X₂+0.000093 X₂²-0.001103 X₁ X₂     R²=0.984                        (6)

It was recorded that the above statistical models can predict the CR of low carbon steel in makeup water with high level of trust depending on the correlation obtained coefficients (R²), and this indicates that the relation between CR and variables is strongly significant. The minimum corrosion rates for the above founded regressions Eq.5 and Eq.6 were obtained by using the minitab-2021 optimization tool. Table 13 shows the results at optimum levels from both experiments, application of designed equations, and % error between the both.

The contour plots for CR ₁ & CR₂ vs. time (weeks) and Conc.(ppm) are shown in Figures 10 and 11. It is illustrated from these figures that CR₁ was at the minimum levels when the conc. of ku-2050 increased from (46 to 78) ppm for approximately 2 weeks of immersion, while CR₂ was at the minimum levels when the conc. of ku-2050 increased from (32 to 100) ppm for (2 to 3) weeks of immersion.

Monte Carlo simulation results

Monte Carlo Simulation was executed using Risk Simulator Tools in Microsoft Excel, through which 1000 random values were generated for inputs (time, conc. of ku-2050 & pH) and applied in the mentioned above DOE models. Table 14 demonstrates the Monte Carlo results for the above DOE models. Figure 12 illustrates Forecast Normal distribution obtained by Monte Carlo Simulation.

From Table 14, it is noticed that the skewness and kurtosis have acceptable values which are included in the range of (2- (-2)) and this means the decent normal distribution for the four DOE models as shown in Figure 12.

Sensitivity analysis results

Based on Monte Carlo Simulation, it is easy to make a sensitivity analysis by the same simulator tools in Microsoft Excel. Figure 13 demonstrates the sensitivity analysis results.

In Figure 13, positive correlations are shown in green while negative correlations are shown in red. This means that there is a positive correlation between (time, pH) and corrosion rate, while there is a negative correlation between conc. of inhibitor and corrosion rate. Also, it is noticed from the same figure that the highest percentage variation in corrosion rate is caused by the variation in time and pH more than conc. of ku-2050.

Inhibitor efficiency

The efficiency of ku-2050 inhibitor was evaluated in the presence of different concentrations (25, 50, 100, 300, 500,700, 800, 900, 1000, 1500 & 2000) ppm, at constant conditions (room temperature, pH=7.3 & 1day period of immersion) on the corrosion rate of low carbon steel in makeup and recirculating water. Figures 14 and 15 demonstrate the efficiency of the ku-2050 inhibitor at the mentioned conditions.

From the above figures, it is illustrated that the highest eff.% is 69.7~ 70 % at 500 ppm of ku-2050 inhibitor in makeup water while in recirculating water the highest eff.% is 60.6 ~61% at 800 ppm of ku-2050 inhibitor. Above these concentrations, the eff.% demonstrated a direct decrease up to 2000 ppm of ku-2050 inhibitor.

Conclusion

It was found that Factorial and Taguchi designs prepare a useful methodology for the setup and optimization of CR of low carbon steel in makeup water with the minimum number of trials. The DOE models proved the strong relation between CR of low carbon steel and independent parameters (time, pH, conc. of ku-2050). Contour plot offers a useful method to know under which ranges we can work to have the desired CR in the situation of fixing one of the working parameters. Monte Carlo Simulation technique demonstrated the agreement of DOE models with random fluctuations in the input variables through the decent normal distribution for the results. Sensitivity analysis proved that the highest percentage of variation in CR is caused by the variation in time and pH more than the conc. of ku-2050 inhibitor. 

Acknowledgments

The researchers express gratitude Iraqi Petroleum Research and Development center for their financial and scientific support.

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How to cite this article: Zaydoon Khalaf Kuraimid, Dhuha Abdulsalam, Hayder Mudhafar, Qais Muthana, Waleed Ismael. Studying optimum conditions to reduce low carbon steel corrosion in cooling towers system of Al-Daura refinery. Eurasian Chemical Communications, 2021, 3(11), 786-799. Link: http://www.echemcom.com/article_138178.html

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Copyright © 2021 by SPC (Sami Publishing Company) + is an open access article distributed under the Creative Commons Attribution License(CC BY)  license  (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.