# Predicting the External Corrosion Rate of X60 Pipeline Steel: A Mathematical Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}, and the inner product was composed mainly of FeCO

_{3}), while those formed after five years had only a single denser layer that was composed of FeOOH, 𝛾-Fe

_{2}O

_{3}, FeCO

_{3}, and a small amount of Fe

_{3}O

_{4}.

## 2. Materials and Methods

#### 2.1. Experimental Design

- The solution corrosivity factor, related to solution temperature, solution pH, and salt composition;
- The treatment factor, related to the absence or presence of various levels of CP;
- The pipe steel condition factor, related to the coated (different coating scenarios) or non-coated (i.e., bare steel) condition.

_{2}SO

_{4}solution in the test and is a categorical variable. The CP and coating are the two other categorical variables since they are not continuous numeric but discrete factors. A total of 42 experiments were generated using a quadratic model, which are listed in Table 3. The testing period was set to four-weeks (28 days). The CRs were collected by conducting the experiments in a random order of run numbers. A mathematical model was established, and is discussed below, to describe the relationship of CR with all of the factors that were studied. Six more tests (X1-X6 in Table 3), including applying an under-protection CP potential of −0.4 V vs. Ag/AgCl as well as a temperature that was periodically on and off (to model stoppage in the pipe flow), were conducted to consider more possible field conditions and to support model validation.

#### 2.2. Expriemental Procedure

#### 2.2.1. Weight Loss Tests and Electrochemical Tests for Bare Steel

^{2}) were simultaneously immersed and tested for four weeks to obtain an average CR (Figure 1a). One exception was for run #35, in which the CR was so high that four-week testing led to complete dissolution of the sample. Therefore, a four-day test was applied to obtain its CR. For samples with CP, a power supply was used to provide a constant negative current to the samples. During the tests, CP was checked/adjusted daily or every other day to ensure it was ±50 mV around its set values ($-$0.4 V, $-$0.8 V, or $-$1.6 V vs. Ag/AgCl reference electrode (+0.199 V vs. NHE)). This is because the changes in steel surface composition/morphology and/or the electrolyte resistance during the tests can alter the applied potential to the sample. A graphite rod was used as an anode.

^{2}surface area that were mounted in epoxy (Figure 1b). EIS was performed periodically by applying an AC ± 10 mV peak-to-peak signal in the frequency range of 100 kHz to 100 mHz. A three-electrode setup was used, i.e., the bare steel as the working electrode, a graphite rod as the counter electrode, and a double junction Ag/AgCl reference electrode. A constant potential was applied during the EIS tests. For samples without CP protection, this constant potential was the open circuit potential. For samples with CP, the constant potential was the applied CP potential. All electrochemical experiments were carried out using a potentiostat (VersaSTAT 3, Princeton Applied Research). It should be noted that samples tested at CP potentials were disconnected from the power supply during the EIS tests, but the potentiostat then served as the power source.

_{2}SO

_{4}, with its pH initially adjusted by either 0.03~0.3 M HClO

_{4}or 0.1~1 M NaOH solution. pH 2, 7, and 12 were studied to cover a wide spectrum of pH conditions that pipeline steel might encounter in the field. For example, in some areas, such as in the Rocky Mountains in British Columbia, pipelines are sited near acid-generating rocks (e.g., pyrite or other sulfides), where the pH can be as low as 2; pH 7 is the most representative of pipeline soil; in other areas, such as salt lakes in north-west China, highly saline soil is deemed as a risk to the pipeline integrity [25]. For bare samples as well as coated samples with a holiday, CP application results in proton consumption through hydrogen evolution in acidic electrolytes while hydroxyl ions are continually produced through water electrolysis in neutral and alkaline electrolytes. Both reactions lead to an increase of pH. For some of the bare steel samples tested, solution acidification was observed during the immersion tests, leading to a decrease of pH. In order to maintain the initial pH, it was adjusted either manually or by a pH controller. In this way, the electrolyte pH was adjusted around its initial value ($+$0.7/$-$0.4 to pH 2; $+$0.7/$-$2 to pH 7 and $+$0.5/$-$2 to pH 12).

#### 2.2.2. Electrochemical Tests for Coated Steel

## 3. Results

#### 3.1. Statistical Model Based on the CR Data

^{−8}to 10

^{2}mm/y), a power transformation of CR was applied. By using a modified quadratic model, a general mathematical equation was fitted to the data and is presented in Equation (7). As listed in Table 4, the value of coefficients $a$, $b$, and $c$ in the equation depends on the coating condition, salt type, and CP levels, respectively. Applying this equation, CR can be estimated for any pH from 2 to 12.

#### 3.2. ANOVA Analysis

^{2}, and adjusted R

^{2}are 0.7933 and 0.7078, respectively, which are high compared to those reported from quadratic regression equations developed for modelling the atmospheric corrosion of carbon steels [14]. The model explains 79.33% of the dependent variables. In addition, the adequate precision, which means the signal to noise ratio is 11.414 (>4 is desirable), indicates an adequate signal. In this case, only E-coating is considered as a significant model term. This result is not surprising as E-coating is expected to be the most critical and determinant factor. The two endpoints of the broad CR range presented in Table 3, i.e., 1.81 × 10

^{−8}and 30.87 mm/y, correspond to a sample with an intact coating versus bare steel. When statistically evaluating other factors along with the E-coating factor, the calculated p-values of factors other than the E-coating do not meet the 0.05 rule of thumb. On the other hand, from the p-values, the relative significance of individual factors as well as their interactions can be indicated. From Table 5, other than the E-coating, the A-Temp, with a p-value of 0.08, is the most influencing factor, followed by the D-CP (p-value of 0.15). There are two principles for choosing these model items: (1) all five individual factors were included in the model, as they all play roles in CR determination; (2) model items in the quadratic model were reduced to ensure that the generated model is significant and the lack of fit is not significant, and there is a good correlation between the CR predicted by the model and obtained by the experiments. The final model interaction terms include:

- AC—interaction between temperature and salt composition
- BD—interaction between pH and CP
- B
^{2}—a quadratic term of pH, which models/predicts the curvature on a response surface.

## 4. Discussion

#### 4.1. Model Explanation with Experimental Data and Results

^{2}) were identified as the influencing quadratic terms. This can be well-explained via an analysis of the experimental data. As revealed in the following discussion, the AC interaction affects the solution conductivity, the BD interaction determines the cathodic reaction process and influences the overall CR, and B

^{2}reflects the higher CRs observed at the two endpoints of the pH range studied, i.e., pH 12 and pH 2, when compared to that tested at pH 7. In order to provide an intuitive overview of CR obtained at various conditions, CR data presented in Table 3 are plotted as CR maps for bare (Figure 4) and coated (Figure 5) X60 samples, respectively.

- At pH 7, that which is most representative of “normal” pipeline soil, it is interesting to observe that the CR data fell into the three regions based on the level of CP. All three samples (F, G, and F’) without CP protection appeared in region I (CR > 1 mm/y); two samples (H and I) having a CP of $-0.8\text{}\mathrm{V}$, were located in region II (1 mm/y > CR > 0.1 mm/y); and the other two samples (J and K) were in region III with a negligible CR due to a CP of $-1.6\mathrm{V}.$ It is reiterated here that these CRs are based on mass loss.
- At pH 2, the highest CR (30.87 mm/y) is found in sample A, which was tested without CP, and at a temperature of 40 °C. At the same temperature of 40 °C (sample B), with a high CP of $-1.6\mathrm{V}$, there is still an unacceptably high CR of 3.69 mm/y. Comparing to sample B: (1) sample C, which has a higher testing temperature of 65 °C, a higher solution conductivity, but a lower CP level of $-0.8\mathrm{V}$, shows a much lower CR of 0.09 mm/y; and (2); sample D, which has the same CP of $-1.6\mathrm{V}$ but has a lower temperature of 10 °C, also shows an acceptable CR of 0.02 mm/y. One indication from the result is that the presence of both a high CP of $-1.6\mathrm{V}$ and a temperature higher than 10 °C in acidic solutions led to the high CR observed in sample B. A high CP of $-1.6\mathrm{V}$, i.e., an overprotection, results in a large amount of hydrogen produced from the acidic solution and from the cathodic reaction ($2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}={\mathrm{H}}_{2}$). CP that is more negative than $-1.1\mathrm{V}$ vs. Cu/CuSO
_{4}($-1.0\text{}\mathrm{V}\mathrm{vs}.\text{}\mathrm{Ag}/\mathrm{AgCl})$ can cause problems including hydrogen-induced cracking (HIC), hydrogen embrittlement (HE), and stress corrosion cracking (SCC) [31]. Though it is normally acknowledged that hydrogen-related attack does not cause significant material loss—rather, it makes the material more susceptible to mechanical failure [32]—there seems to be a correlation between the large amount of hydrogen produced at a high temperature and the observed high CR based on the tested results. The reasons for this are not yet clear and need more detailed research. - At pH 12, without CP protection, sample M has a CR of 0.124 mm/y at a low temperature of 10 °C. However, the highest CR of 2.86 mm/y was measured for sample L, which had a CP of $-0.8\mathrm{V}$ and a high temperature of 65 °C. The test solution also had the lowest electrolyte resistance/highest electrolyte conductivity. When the testing temperature was 10 °C, at the same CP level of $-0.8\text{}\mathrm{V}$, the CR of sample N was reduced (0.004 mm/y). An increase of the CP level to $-1.6\mathrm{V}$ also appeared to be very effective at depressing the CR to a negligible value, as seen for sample O, for which the testing temperature was 40 °C. The comparison among sample L, N, and O implies that in a hot alkaline environment, a moderate CP level of $-0.8\mathrm{V}$ is not sufficient to protect steel from corrosion. Furthermore, if considering coated samples with a holiday (exposed steel substrate area), it is well-known that an application of CP causes an alkaline environment at the coating/substrate interface, leading to a loss of adhesion at the interface and causing cathodic disbondment. The high pH environment is supposed to protect the exposed substrate from corrosion. However, based on the present result on bare steel samples, if the coated sample is tested at a high temperature of 65 °C with a CP of $-0.8\text{}\mathrm{V}$, both the exposed holiday area and the substrate underneath the disbonded coating may still experience corrosion. This is exactly what was found in holiday samples, as discussed in Figure 5.

- Coatings with a holiday: due to the exposed metal surface, which is similar to the bare steel samples, holiday samples show relatively high CRs. The top three samples shown in Figure 5 are those tested at a high temperature of 65 °C and at pH 2, pH 7, and pH 12. The one tested at pH 2 showing the highest CR is accompanied with a high CP of $-1.6\mathrm{V}$, followed by that tested at pH 12 with a CP of $-0.8\mathrm{V}$, and then the one tested at pH 7 with no CP. It can be found that these three conditions are predicted to result in the highest CR at each pH condition for bare metal samples. In other words, the CR results for holiday samples are consistent with that observed for bare steel samples, which further supports the proposal of two quadratic items in the mathematical model, i.e., temperature–salt type and pH–CP interactions.
- Coatings with a dent: most of the studied samples with a dent (yellow circles) are in the region where 5 × 10
^{−5}< CR < 1 × 10^{−3}mm/y, having comparable CRs to the holiday samples, indicating a similar corrosion resistance of the coating with these two kinds of defect. No particular trend in CR can be found in the dented samples with respect to temperature, pH, or CP. On the other hand, if looking at the volume of water ($\varnothing $) being absorbed in the coating (the data in the parentheses), it is found that, in general, when $\varnothing $ is higher than 65%, the CR is above 1 × 10^{−5}mm/y; when $\varnothing $ is below 65%, the CR is less than 1 × 10^{−5}mm/y. It is also interesting to observe that dented samples immersed in solutions with pH 7 show a relatively low water uptake (61% on average), while higher water absorption was observed in samples tested at pH 12 (186% on average) and pH 2 (146% on average). Compared to neutral solutions, a highly alkaline environment was reported to promote the absorption of moisture in FBE coatings, and with the presence of defects, the penetration of aggressive ions can be facilitated, contributing to increased CR [33]. The present work supports this statement and further shows that an acidic environment also can accelerate the process of water absorption in FBE coatings with the presence of defects. - Intact coatings: due to a good protection from the coating, the CRs for all the intact coating samples (green circles) are extremely low and less than 1 × 10
^{−5}mm/y. $\varnothing $ for these samples are all below 65%. Among all the factors, the temperature seems to be the most critical, which is consistent with the ANOVA analysis. Negligible CRs on the order of 10^{−8}were found for the four samples tested at 10 °C. Increasing the temperature accelerates the CR by one to two orders of magnitude.

#### 4.2. Model Application/Prediction

- The effect of coating

- The effect of CP

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A schematic of (

**a**) 1.5 cm

^{2}bare electrodes for weight loss tests; (

**b**) a 1 cm

^{2}bare electrode for electrochemical tests (EIS); and (

**c**) a coated X60 panel sample for corrosion immersion and electrochemical tests.

**Figure 2.**(

**a**) Normal probability plot of the studentized residuals to check for normality of residuals (the approximately linear plot allows to assume that the error/residual terms are normally distributed, and the estimates/predicted values are unbiased or on average correct); and (

**b**) Studentized residuals versus predicted values to check for constant variation (a random distribution should be expected and so the model predicts values higher and lower than the actual with equal probability).

**Figure 3.**Predicted CR using the established mathematical model vs. actual measured CR (designed points: runs 1–42; extra test points: runs X1–X6 in Table 3).

**Figure 4.**CR map of bare X60, small electrode samples, under different test conditions using the weight loss data (the data in the bracket is the electrolyte resistance estimated from EIS tests).

**Figure 5.**CR map of coated X60 steel under different test conditions (the data in brackets is the volume of water absorbed by the coating after the 28-day test).

**Figure 6.**CR as a function of both applied CP level and coating scenarios: (

**a**) pH = 2; (

**b**) pH = 7; and (

**c**) pH = 12. The temperature is 40 °C and the salt composition effect was averaged for that of sodium chloride and sodium sulfate (A is the temperature, B is the pH, C is the salt composition, D is the CP level and shows as abscissa X1, and E is the coating scenario and shows as abscissa X2).

**Figure 7.**CR predicted by the model for the coated samples with different scenarios: (

**a**) coating with a holiday, (

**b**) coating with a dent, and (

**c**) intact coating. The CP is fixed at $-0.8\text{}V$, and the salt is sodium chloride.

Pipe Steel | Coating Type | CP Application | Electrolyte | CR or Corrosion Current Density | Ref. |
---|---|---|---|---|---|

X52 | a 30-μm thick layer of coal tar applied in the lab | $-$0.8 V vs. Ag/AgCl | Soil (RT, pH 8.2) | Corrosion current density (EIS ^{1} estimation): ~0 µA/cm^{2} (~0 mm/y) | [3] |

X52 | Same as above but with a holiday | $-$0.8 V vs. Ag/AgCl | Soil (RT, pH 8.2) | Corrosion current density (EIS estimation): 10^{−5} to 10^{−4} µA/cm^{2} (~7.6 × 10^{−8} to 7.6 × 10^{−7} mm/y) | [3] |

X52 | No coating | No CP | Synthetic soil solution ^{2}(RT, pH = 7.7, 1825 Ω∙cm ^{2}) | CR (LPR ^{3} test) = 0.023 mm/y | [4] |

X60 | No coating | No CP | Sand–clay soil (RT, pH 3; 499.5 Ω∙cm^{2}) | CR (five hours after removed oxides, polarization test) = 0.56 mm/y Possible pitting occurs | [5] |

X65 | No coating | No CP | Sand–clay soil (RT, pH 3; 183 Ω∙cm^{2}) | CR (five hours after removed oxides, polarization test) = 1.29 mm/y Possible pitting occurs | [5] |

X70 | No coating | No CP | Sand–clay soil (RT, pH 3; 213 Ω∙cm^{2}) | CR (five hours after removed oxides, polarization test) = 1.08 mm/y Possible pitting occurs | [5] |

X70 | No coating | No CP | Sand–clay soil added with water (RT, pH 4.8~5.6) | CR (seven-day polarization test) = 0.085 mm/y | [8] |

No coating | $-$0.9 V vs. Ag/AgCl | Sand–clay soil added with water (RT, pH 4.8~5.6) | CR (seven-day polarization test) = 0.025 mm/y | [8] | |

X80 | No coating | No CP | Acidic red soil (buried underground, pH ~4.7) | CR (38-week electric resistance test) = 0.0902 mm/y CR (five-year electric resistance test) = 0.0226 mm/y | [10] |

^{1}EIS: electrochemical impedance spectroscopy;

^{2}Synthetic soil solution: NaHCO

_{3}(0.483 g/L); KCl (0.122 g/L); CaCl

_{2}∙2H

_{2}O (0.181 g/L); MgSO

_{4}∙7H

_{2}O (0.131 g/L);

^{3}LPR: Linear polarization resistance.

Independent Variables | Description | Type | |
---|---|---|---|

Solution corrosivity | Solution temperature | 10, 40, 65 °C | Numerical |

Solution pH | 2, 7, 12 | Numerical | |

Salt composition | NaCl or Na_{2}SO_{4} | Categorical | |

CP | Without or with (−0.8 V and −1.6 V vs. Ag/AgCl) | Categorical | |

Coating | Without or with (intact, dented, or with a holiday) | Categorical |

Factor A | Factor B | Factor C | Factor D | Factor E | Response | |
---|---|---|---|---|---|---|

Run | Solution Temperature (°C) | Solution pH | Salt Composition | CP (V vs. Ag/AgCl) | Coating Condition | CR (mm/year) |

1 | 10 | 12 | SO4 | Y-0.8 | N | $3.57\times {10}^{-3}$ |

2 | 40 | 12 | SO4 | N | Y | $5.85\times {10}^{-6}$ |

3 | 65 | 7 | Cl | Y-0.8 | Y-D | $7.02\times {10}^{-5}$ |

4 | 10 | 2 | Cl | Y-1.6 | N | $1.81\times {10}^{-2}$ |

5 | 40 | 7 | SO4 | N | N | $1.58\times {10}^{0}$ |

6 | 10 | 12 | Cl | Y-1.6 | Y-H | $5.11\times {10}^{-4}$ |

7 | 10 | 2 | SO4 | Y-1.6 | Y-H | $3.83\times {10}^{-4}$ |

8 | 10 | 12 | Cl | Y-0.8 | Y-D | $9.76\times {10}^{-5}$ |

9 | 40 | 7 | Cl | Y-0.8 | N | $1.20\times {10}^{-1}$ |

10 | 65 | 2 | SO4 | N | Y-D | $1.73\times {10}^{-4}$ |

11 | 65 | 12 | Cl | Y-0.8 | Y | $8.64\times {10}^{-6}$ |

12 | 10 | 2 | SO4 | N | Y-H | $6.91\times {10}^{-4}$ |

13 | 40 | 12 | SO4 | N | Y-H | $5.17\times {10}^{-4}$ |

14 | 65 | 2 | SO4 | Y-1.6 | Y | $1.09\times {10}^{-6}$ |

15 | 65 | 2 | SO4 | Y-0.8 | N | $8.53\times {10}^{-2}$ |

16 | 40 | 12 | SO4 | Y-1.6 | N | $1.00\times {10}^{-4}$ |

17 | 10 | 7 | SO4 | Y-1.6 | N | $3.69\times {10}^{-3}$ |

18 | 40 | 2 | Cl | N | Y | $6.60\times {10}^{-7}$ |

19 | 65 | 12 | SO4 | Y-0.8 | N | $2.86\times {10}^{0}$ |

20 | 65 | 12 | Cl | Y-0.8 | Y-H | $1.62\times {10}^{-3}$ |

21 | 40 | 7 | SO4 | N | N | $4.25\times {10}^{0}$ |

22 | 65 | 7 | SO4 | Y-0.8 | Y-H | $9.12\times {10}^{-4}$ |

23 | 10 | 12 | SO4 | Y-1.6 | Y-D | $2.93\times {10}^{-4}$ |

24 | 10 | 2 | Cl | Y-0.8 | Y-H | $1.86\times {10}^{-4}$ |

25 | 40 | 2 | Cl | Y-1.6 | Y-D | $3.19\times {10}^{-4}$ |

26 | 10 | 2 | Cl | Y-0.8 | Y-D | $2.22\times {10}^{-4}$ |

27 | 65 | 12 | Cl | Y-1.6 | Y-D | $7.60\times {10}^{-4}$ |

28 | 10 | 12 | Cl | N | N | $1.24\times {10}^{-1}$ |

29 | 10 | 12 | Cl | Y-1.6 | Y | $8.01\times {10}^{-8}$ |

30 | 40 | 2 | SO4 | Y-1.6 | N | $3.69\times {10}^{0}$ |

31 | 10 | 7 | Cl | Y-0.8 | N | $4.96\times {10}^{-1}$ |

32 | 65 | 2 | Cl | Y-1.6 | Y-H | $2.18\times {10}^{-3}$ |

33 | 10 | 7 | Cl | N | Y-D | $1.52\times {10}^{-4}$ |

34 | 10 | 2 | Cl | N | Y | $3.78\times {10}^{-8}$ |

35 | 40 | 2 | Cl | N | N | $3.09\times {10}^{1}$ |

36 | 10 | 2 | SO4 | Y-0.8 | N | $1.00\times {10}^{-4}$ |

37 | 65 | 7 | Cl | Y-1.6 | N | $7.33\times {10}^{-4}$ |

38 | 40 | 7 | SO4 | Y-0.8 | Y-D | $1.76\times {10}^{-4}$ |

39 | 65 | 7 | SO4 | Y-1.6 | Y-D | $4.78\times {10}^{-6}$ |

40 | 65 | 7 | Cl | N | Y-H | $1.50\times {10}^{-3}$ |

41 | 10 | 7 | Cl | N | Y-D | $7.79\times {10}^{-6}$ |

42 | 10 | 7 | SO4 | Y-0.8 | Y | $1.81\times {10}^{-8}$ |

X1 | 10 | 7 | SO4 | $-$0.4 V | Y | $1.78\times {10}^{-8}$ |

X2 | 10 | 7 | SO4 | $-$1.6 V | Y | $4.23\times {10}^{-8}$ |

X3 | 65 | 7 | Cl | N | N | $3.51\times {10}^{0}$ |

X4 | 65 | 7 | Cl | $-$0.4 V | YD | $8.08\times {10}^{-6}$ |

X5 | 65 (on and off) | 7 | SO4 | $-$1.6 V | YD | $3.58\times {10}^{-4}$ |

X6 | 65 (on and off) | 7 | Cl | $-$1.6 V | YD | $5.09\times {10}^{-5}$ |

Coating Conditions | $\mathit{a}$ | Salt Composition | $\mathit{b}$ | CP Level | $\mathit{c}$ |
---|---|---|---|---|---|

Bare steel | 0.97 ± 0.014 | NaCl | 0.00020 | no CP | −0.0047 |

Holiday sample | 0.93 ± 0.014 | $-$0.8 V | −0.0028 | ||

Dented sample | 0.91 ± 0.014 | Na_{2}SO_{4} | 0.00043 | $-$1.6 V | −0.0065 |

Intact sample | 0.86 ± 0.014 |

Source | Sum of Squares | Degree of Freedom | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 0.0709 | 12 | 0.0059 | 9.27 | <0.0001 | significant |

A-Temp | 0.0020 | 1 | 0.0020 | 3.18 | 0.0849 | |

B-pH | $2.059\times {10}^{-8}$ | 1 | $2.059\times {10}^{-8}$ | 0.0000 | 0.9955 | |

C-Salt comp | 0.0003 | 1 | 0.0003 | 0.4486 | 0.5083 | |

D-CP | 0.0026 | 2 | 0.0013 | 2.03 | 0.1491 | |

E-Coating | 0.0650 | 3 | 0.0217 | 33.99 | <0.0001 | significant |

AC | 0.0003 | 1 | 0.0003 | 0.4283 | 0.5180 | |

BD | 0.0016 | 2 | 0.0008 | 1.23 | 0.3059 | |

B^{2} | 0.0006 | 1 | 0.0006 | 0.9415 | 0.3399 | |

Residual | 0.0185 | 29 | 0.0006 | |||

Lack of Fit | 0.0181 | 27 | 0.0007 | 3.27 | 0.2611 | not significant |

Pure Error | 0.0004 | 2 | 0.0002 | |||

Cor Total | 0.0894 | 41 |

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## Share and Cite

**MDPI and ACS Style**

Xu, M.; Liang, H.; Liu, Y.; Asselin, E. Predicting the External Corrosion Rate of X60 Pipeline Steel: A Mathematical Model. *Metals* **2021**, *11*, 583.
https://doi.org/10.3390/met11040583

**AMA Style**

Xu M, Liang H, Liu Y, Asselin E. Predicting the External Corrosion Rate of X60 Pipeline Steel: A Mathematical Model. *Metals*. 2021; 11(4):583.
https://doi.org/10.3390/met11040583

**Chicago/Turabian Style**

Xu, Min, Hongxing Liang, Yu Liu, and Edouard Asselin. 2021. "Predicting the External Corrosion Rate of X60 Pipeline Steel: A Mathematical Model" *Metals* 11, no. 4: 583.
https://doi.org/10.3390/met11040583