Model for Predicting Corrosion in Steel Pipelines for Underground Gas Storage

Abstract

The response surface methodology (RSM) is utilized to construct a corrosion prediction model for steel pipelines for underground gas storage (UGS). Four key corrosion-influencing factors—the CO₂ partial pressure, Cl⁻ concentration, temperature, and flow rate—are identified by investigating the operating parameters of 14 UGS extracted pipelines (Nos. S1–S14) in China. Based on the operating parameters, 29 sets of high-temperature and high-pressure autoclave corrosion tests are designed and carried out. A quadratic regression equation model for corrosion rate prediction is fitted using the data from the corrosion test results. The p-values of the model’s four influencing factors are <0.01, indicating that the influencing factors are significant and reasonable. The F-value of the model is greater than the critical value, and the noise probability p-value is <0.01, indicating that the model has good fitness. The determination coefficient R² of the model is 0.9753, which is close to 1. Therefore, the observed value and the response value of the model are obviously correlated: i.e., the model has a high degree of truth. The model is used to predict the corrosion rate of 14 UGS pipelines: S3 and S14 are severely corroded, while the others are moderately corroded.

1. Introduction

The role of underground gas storage (UGS) as a natural gas peak regulation, supply, and strategic reserve has attracted increasing attention [1,2]. China’s UGS capacity is being greatly expanded [3]. By the end of 2025, the working gas capacity of China’s UGS is expected to exceed 30 billion cubic meters, and the daily peak regulation capacity will reach >300 million cubic meters. Therefore, the rapid construction and stable operation of UGS are very important.

UGS involves natural gas injection and extraction systems, with the characteristics of cyclic injection and extraction, large-scale injection and extraction, and large flow and high pressure [4,5]. As a result, the associated safety risks have always attracted attention. The injected gas source is generally commercial natural gas, and it is a dry gas with weak corrosion properties. During gas extraction, the medium generally presents two phases of gas and liquid. The produced water is generally high in salinity, and it may also contain acid gases such as H₂S and CO₂. The corrosion problem of the production system is particularly prominent [6]. Therefore, to appropriately select materials, optimize process parameters, and formulate anti-corrosion strategies for the gas production pipeline, the prediction of its corrosion rate is important.

Presently, the corrosion rate prediction methods include theoretical models, big data models, and regression equation models. Representative theoretical models include the NorsokM506 empirical model [7], the Nesic mechanism model [8], and the DeWaard95 semi-empirical and semi-mechanism model [9]. However, the theoretical models consider individual influencing factors and corrosion mechanisms. The correlation and interactive coupling between factors are not fully introduced. Therefore, theoretical models produce large errors in practical applications. On the other hand, big data models are typically “black box” models obtained with the help of neural networks, genetic algorithms, fuzzy algorithms, gray association algorithms, etc. [10,11,12,13]. The predicted corrosion rate is obtained by inputting the influencing factors and iterative training data. However, the accumulation of a large number of sample data points is necessary to obtain reliable prediction results. Further, regression equation models are theoretical models established by using statistics to find the correlation, and these are easy to use. For example, the linear regression method was commonly used in the past, but it considers only the influence of one factor on the target value [14].

Therefore, the response surface methodology (RSM) is introduced in this study. RSM is an internationally emerging experimental statistical methodology that analyzes the “response effect” by fitting the regression of the test results to the function relationship between the factors and the target value. RSM has been widely used, from the initial use of physical test results, to the present in the pharmaceutical, biological, mechanical, aerospace, petrochemical, and other fields of test optimization [15,16,17,18]. Chung [19] used the RSM to study the environment of the buried pipeline under the effect of a combination of pH, chlorine, and sulfate on the density of corrosion current. Mehdi [20] investigated the synergistic effect of temperature, solution velocity, and sulphuric acid concentration on the corrosion behavior of carbon steel using RSM. In this work, the factors influencing UGS extracted pipeline corrosion are taken as independent variables, and the corrosion rate is taken as the target value to build a polynomial regression equation model under the interaction of multiple factors. By performing corrosion tests at set localized points, the results are regressed and fitted to a global or regional scale as a function of each influencing factor and the target value.

2. Investigation Scheme Design of Experiment

This study is mainly based on the design method of a second-order test at three levels or above, and uses multiple quadratic equations to express some functional relationships between factors and the value of the response. The application of RSM in this study includes six steps, as shown in Figure 1 [21].

2.1. Corrosion Influencing Factors

This study investigates the corrosion environment in 14 UGSs in China (

Table 1. Statistical results for the operating parameters of UGS pipelines.

UGS Name	CO2 Partial Pressure (MPa)	Cl− Concentration (×103 mg/L)	Temperature (°C)	Operating Pressure (MPa)	Water/Gas Ratio (m3/104 m3)	Flow Rate (m/s)	Pipeline Material
S1	0.14	2.62	20	12	0.22	1.67	L360N (X52)
S2	0.32	1.70	25	20	0.10	2.22	L450Q (X65)
S3	0.17	3.50	38	12	0.001	3.70	L450Q (X65)
S4	0.13	1.29	51	12.8	0.18	3.47	L450Q (X52)
S5	0.08	0.20	25	7.7	0.04	3.16	L415M (X60)
S6	0.25	1.85	35	10	0.20	1.60	L360N (X52)
S7	0.21	0.29	60	11.5	0.78	1.93	L450Q (X65)
S8	0.12	0.78	40	10	0.48	3.20	16Mn (X52)
S9	0.07	0.07	30	6	0.11	2.96	16Mn (X52)
S10	0.07	0.10	25	6.5	0.41	2.73	16Mn (X52)
S11	0.14	1.00	25	20	0.06	2.22	L450Q (X65)
S12	0.09	0.46	51	10.5	0.016	3.04	L415M (X60)
S13	0.15	1.60	26	5	0.002	2.56	L360N (X52)
S14	0.38	9.30	40	23	0.15	1.36	L450Q (X65)

). The following conclusions can be drawn:

(1)

Each UGS extracted pipeline generally contains a certain amount of water with a water/gas ratio of 0.001–0.78 m³/(10⁴ m³). This water causes the steel electrochemical corrosion [22].

(2)

The produced gas generally contains CO₂ at a concentration of 0.07–0.38 MPa. The CO₂ gas dissolves in water to form H₂CO₃, and the resultant acidic environment in steel pipelines produces hydrogen depolarization corrosion, resulting in FeCO₃ corrosion products [23].

(3)

The produced water generally contains Cl⁻ at a concentration between 1000 and 93,000 mg/L. Cl⁻ has a ring-breaking effect on the passivation film and the formation of corrosion product film on the surface of the pipeline, thus increasing the corrosion rate [24].

(4)

The operating temperature of the pipeline is 20–60 °C. A higher operating temperature typically accelerates the chemical reaction rate, i.e., the corrosion rate [25].

(5)

The flow rate of the produced gas is 1.36–3.70 m/s, which controls the mass transfer process of the chemical reaction. When the flow rate is low, a stable electrochemical corrosion environment is formed, and corrosion continues to occur. When the flow rate is high, the corrosion product film is not easily enriched, and the fresh metal surface is constantly exposed, which generally promotes corrosion.

The key factors that need to be considered and that have a large impact on the final predicted effectiveness have to be selected. Four main corrosion-influencing factors are considered in this study: the CO₂ partial pressure, Cl⁻ concentration, temperature, and flow rate.

2.2. The Level Value of the Factors

The independent variables, i.e., the CO₂ partial pressure, Cl⁻ concentration, temperature, and flow rate, are expressed as $X_1,X_2,X_3,X_4$, respectively. Here, +1, 0, and −1 indicate the high, medium, and low levels of the independent variables. The level value of the independent variables is calculated according to Equation (1):

X_i = (x_i − x_i0)/Δx_i

(1)

Here, X_i is the level value of the independent variable, x_i is the true value of the independent variable, x_i0 is the true value of the independent variable at the center point of the test, and Δx_i is the change step of the independent variable.

By referring to the parameters in Table 1, the CO₂ partial pressure x₁ is selected as 0.050 MPa, 0.275 MPa, and 0.500 MPa; the Cl⁻ concentration x₂ is selected as 1000 mg/L, 50,500 mg/L, and 100,000 mg/L; the temperature x₃ is selected as 20 °C, 40 °C, and 60 °C; and the flow rate x₄ is selected as 1.0 m/s, 2.5 m/s, and 4.0 m/s. The final design of the test program with four factors and three levels is shown in

Table 2. Influencing factors and levels.

Factors	Levels
	−1	0	1
CO2 partial pressure (MPa)	0.050	0.275	0.500
Cl− concentration (mg/L)	1000	50,500	100,000
Temperature (°C)	20	40	60
Flow rate (m/s)	1	2.5	4

.

2.3. Design of Test Points

The number of tests should be minimized, and the test should be carried out according to the principle of randomization. In this study, a total of 29 test points with four factors and three levels are designed, as shown in

Table 3. Parameters of the corrosion test.

Test Serial Number	CO2 Partial Pressure (MPa)	Cl− Concentration (mg/L)	Temperature (°C)	Flow Rate (m/s)
1	0.050	1000	40	2.5
2	0.500	1000	40	2.5
3	0.050	100,000	40	2.5
4	0.500	100,000	40	2.5
5	0.275	50,500	20	1.0
6	0.275	50,500	60	1.0
7	0.275	50,500	20	4.0
8	0.275	50,500	60	4.0
9	0.050	50,500	40	1.0
10	0.500	50,500	40	1.0
11	0.050	50,500	40	4.0
12	0.500	50,500	40	4.0
13	0.275	1000	20	2.5
14	0.275	100,000	20	2.5
15	0.275	1000	60	2.5
16	0.275	100,000	60	2.5
17	0.050	50,500	20	2.5
18	0.500	50,500	20	2.5
19	0.050	50,500	60	2.5
20	0.500	50,500	60	2.5
21	0.275	1000	40	1.0
22	0.275	100,000	40	1.0
23	0.275	1000	40	4.0
24	0.275	100,000	40	4.0
25	0.275	50,500	40	2.5
26	0.275	50,500	40	2.5
27	0.275	50,500	40	2.5
28	0.275	50,500	40	2.5
29	0.275	50,500	40	2.5

. Test points 1–24 were analyzed as the causality test, and test points 25–29 were the zero point test. The main function of the zero test was to estimate the test error, and it was performed five times in total.

In order to improve the test accuracy, a high-temperature and high-pressure reactor and detection device (autoclave corrosion test system, Cortest Inc., United States; the maximum volume = 10 L, maximum test pressure = 70 MPa, and the maximum test temperature = 350 °C) was used to simulate the corrosion process. A high-purity N₂ and CO₂ gas mixture was used to simulate the pipeline gas-phase corrosion media, and NaCl was used in accordance with a certain proportion of the preparation’s simulated produced water to substitute the actual liquid media. Although the water-to-gas ratios listed in Table 1 are different, they are all liquid water that are in direct contact with the bottom of the pipeline. When the pipeline encounters a slope (from the low point to the high point), it is more likely to accumulate liquid in the low-lying section. Therefore, this work considers the full immersion corrosion test; that is, the specimens were completely immersed in the aqueous solution. This can better reflect the harsh environment under actual working conditions.

The pipelines are composed of carbon steel, as shown in Table 1. It is commonly researched that carbon steel materials have a relatively close corrosion rate. Therefore, L360N carbon steel test specimens were selected to use in the test, with dimensions of 50 mm × 10 mm × 3 mm (including Φ5 mm holes).

After the test, the corrosion rate of the specimen was calculated according to the weight loss, as follows:

V = ΔG × 8.76 × 10⁶/(γ·t·S)

(2)

Here, ΔG is the weightlessness of the specimen (unit: g), γ is the density of the material (γ = 7.8 g/cm³), t is the test time (t = 168 h), S is the surface area of the test piece (mm²), and V is the corrosion rate (mm/a).

2.4. Data Analysis Based on RSM

The RSM uses k independent variables, such as X₁, X₂, …, X_k, to represent the influencing factors, while the dependent variable y is used to represent the output indicators, as follows [19,26]:

y = f(X₁, X₂, …, X_k) + e

(3)

Here, f is the response surface function, and e is the error. The spatial surface indicated by the function is called the response surface.

In order to optimize the response variable y, the quadratic model is usually adopted to find an appropriate relation g(X) to approximate the association between the independent variable X_k and the response surface. The spatial surface represented by g(X) is the simulated response surface; that is, the response surface of the actual operation:

$$g(X)=a_0+{\displaystyle \sum _{i=1}^k{a}_i{X}_i}+{\displaystyle \sum _{i=1}^k{\displaystyle \sum _{j=1}^k{a}_{ij}{X}_i{X}_j}}+e$$

(4)

Here, a₀, a_i, and a_ij are the undetermined coefficients.

Let g(X) be related to X₁, X₂, …, X_k; then for a defined set of independent variables, X₁, X₂, …, X_k, g(X) should have its distribution. When the mathematical expectation of g(X) exists, i.e., it is a function of X₁, X₂, … X_k, which can also be called the regression of (X₁, X₂, …, X_k).

Let (X₁₁, X₁₂, …, X_1p, g₁), …, (X_k1, X_k2, …, X_kp, g_k) be a sample, where X_np is the pth level of the nth factor. The parameter is estimated by the maximum likelihood estimation method. The undetermined coefficient is taken as $\stackrel{\wedge }{a_0},\stackrel{\wedge }{a_1},\dots ,\stackrel{\wedge }{a_p}$. Let $a_0=\stackrel{\wedge }{a_0},a_1=\stackrel{\wedge }{a_1},\dots ,a_p=\stackrel{\wedge }{a_p}$, and Q can obtain the optimal value at that time. If $Q={\displaystyle \sum _{i=1}^k{(g_i-a_0-a_1{x}_{i1}-\dots a_p{X}_{ip})}^2}$ has the smallest value, then the derivative of Q with respect to a_i is Q′ = 0; therefore,

$$\left\{\begin{array}{l}{\displaystyle \frac{\partial Q}{\partial a_0}}=-2{\displaystyle \sum _{i=1}^k(g_i-a_0-a_1{x}_{i1}-\dots a_p{X}_{ip})}=0\\ \dots =\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\dots \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=0\\ {\displaystyle \frac{\partial Q}{\partial a_j}}=-2{\displaystyle \sum _{i=1}^k(g_i-a_0-a_1{x}_{i1}-\dots a_p{X}_{ip})}{X}_{ij}=0\end{array}\right.$$

(5)

After simplifying the above differential results, the normal equations are obtained as follows:

$$\left\{\begin{array}{l}{a}_{0}n+a_1{\displaystyle \sum _{i=1}^k{X}_{i1}}+a_2{\displaystyle \sum _{i=1}^k{X}_{i2}+\dots +}{a}_p{\displaystyle \sum _{i=1}^k{X}_{ip}}={\displaystyle \sum _{i=1}^k{g}_i}\\ a_0{\displaystyle \sum _{i=1}^k{X}_{i1}}+a_1{\displaystyle \sum _{i=1}^k{X_{i1}}^2+a_2{\displaystyle \sum _{i=1}^k{X}_{i1}{X}_{i2}+\dots +}}{a}_p{\displaystyle \sum _{i=1}^k{X}_{i1}{X}_{ip}}={\displaystyle \sum _{i=1}^k{X}_{i1}{g}_i}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\dots \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=\hspace{1em}\hspace{1em}\dots \\ a_0{\displaystyle \sum _{i=1}^k{X}_{ip}}+a_1{\displaystyle \sum _{i=1}^k{X}_{i1}{X}_{ip}+a_2{\displaystyle \sum _{i=1}^k{X}_{i2}{X}_{ip}+\dots +}}{a}_p{\displaystyle \sum _{i=1}^k{X_{ip}}^2}={\displaystyle \sum _{i=1}^k{X}_{ip}{g}_i}\end{array}\right.$$

(6)

i.e., X′XA = X′Y

(7)

Here,

$$X=\left[\begin{array}{l}{1\mathrm{X}}_{11}{\mathrm{X}}_{12}\dots {\mathrm{X}}_{1p}\\ {1\mathrm{X}}_{11}{\mathrm{X}}_{22}\dots {\mathrm{X}}_{2p}\\ \dots \hspace{1em}\hspace{1em} \dots \dots \\ {1\mathrm{X}}_{11}{\mathrm{X}}_{\mathrm{k}2}\dots {\mathrm{X}}_{kp}\end{array}\right],\mathrm{g}=\left[\begin{array}{l}{\mathrm{g}}_1\\ {\mathrm{g}}_2\\ \dots \\ {\mathrm{g}}_{\mathrm{p}}\end{array}\right],\mathrm{A}=\left[\begin{array}{l}{a}_1\\ a_2\\ \dots \\ a_{\mathrm{p}}\end{array}\right]$$

(8)

When both sides of X′XA = X′g are multiplied by the inverse matrix (X′X)⁻¹ of X′X:

$${\stackrel{\wedge }{A}=\left[\stackrel{\wedge }{a_1}\stackrel{\wedge }{a_2}\dots \stackrel{\wedge }{a_p}\right]}^{-1}=(X^{\prime }X{)}^{-1}{X}^{\prime }g$$

(9)

The above Equations (8) and (9) are the solution equations of the response surface and their solutions. The obtained test data are processed and analyzed by using Equations (3)–(9). The test of the prediction result of the regression equation model: The deviation of the predicted value from the actual value is analyzed, and the correlation coefficient test method is used to solve the determination coefficient R² of the regression equation model. The closer R² is to 1, the higher the prediction accuracy of the model.

3. Results and Discussion

3.1. Corrosion Prediction Model

The results of 29 tests are shown in Figure 2. Then, the test data are analyzed by regression fitting according to Equations (3)–(9). The fitting coefficients of the interaction between the primary and secondary terms are obtained, as shown in

Table 4. Fitting coefficients of the predicted model.

Name	Fitting Coefficient
Intercept	0.1344
X1	0.068
X2	0.0137
X3	0.0391
X4	0.0122
X1X2	0.01
X1X3	0.0223
X1X4	−0.0001
X2X3	0.0062
X2X4	−0.0034
X3X4	0.0024
X12	0.0311
X22	−0.0028
X32	−0.0159
X42	0.0148

. Finally, the quadratic regression prediction model for the corrosion rate is obtained:

Y = 0.1344 + 0.068 X₁ + 0.0137 X₂ + 0.0391 X₃ + 0.0122 X₄ + 0.01 X₁X₂ + 0.0223 X₁X₃ − 0.0001 X₁X₄ + 0.0062 X₂X₃ − 0.0034 X₂X₄ + 0.0024 X₃X₄ + 0.0311 X₁² − 0.0028 X₂² − 0.0159 X₃² + 0.0148 X₄²

(10)

Here, Y is the response value of the corrosion rate of the pipeline. X₁, X₂, X₃, and X₄ are the level values of the CO₂ partial pressure, Cl⁻ concentration, temperature, and flow rate, respectively.

3.2. Validity Evaluation of the Fitted Model

The predicted values of 29 groups of test data are calculated according to the regression equation model, i.e., Equation (10). A comparison of the calculated and the actual values shows that the relative error is between −28.22% and 13.65%, as shown in

Table 5. Relative error of the prediction model.

Test Serial Number	Actual Value (mm/a)	Predicted Value (mm/a)	Absolute Error (mm/a)	Relative Error %
1	0.0739	0.06603	−0.0079	−10.65
2	0.2098	0.16183	−0.0180	−9.99
3	0.0923	0.16023	−0.0336	−17.32
4	0.2680	0.33603	−0.0438	−11.52
5	0.0752	0.0878	−0.0112	−11.31
6	0.1590	0.1362	0.0042	3.18
7	0.0995	0.156	−0.0087	−5.28
8	0.1928	0.1892	0.0068	3.73
9	0.1151	0.0672	−0.0199	−22.85
10	0.2459	0.197	0.0050	2.60
11	0.1348	0.1218	−0.0033	−2.64
12	0.2652	0.2636	0.0216	8.93
13	0.0832	0.07823	−0.0184	−19.02
14	0.0969	0.20283	−0.0042	−2.01
15	0.1421	0.10943	−0.0416	−27.53
16	0.1805	0.25323	−0.0274	−9.75
17	0.0659	0.0895	0.0047	5.54
18	0.1427	0.1999	−0.0099	−4.72
19	0.0959	0.1049	0.0126	13.65
20	0.2620	0.2661	−0.0019	−0.71
21	0.1139	0.05873	−0.0185	−23.92
22	0.1386	0.19713	−0.0073	−3.56
23	0.1451	0.12353	−0.0375	−23.27
24	0.1562	0.25353	−0.0997	−28.22
25	0.1350	0.1716	0.0014	0.82
26	0.1338	0.1716	0.0004	0.23
27	0.1339	0.1716	−0.0016	−0.92
28	0.1351	0.1716	−0.0009	−0.52
29	0.1344	0.1716	0.0007	0.41

. In order to more intuitively analyze the accuracy of the prediction model, the curves of the predicted and actual values are drawn, as shown in Figure 3; both curves are distributed near the 45° line, and there is good coincidence.

In addition, an ANOVA of the model is carried out, as shown in

Table 6. The results of the variance analysis of the prediction model.

Source	Sum of Squares	Degrees of Freedom	Mean Square	F-Value	p-Value	Salience
Model	0.0913	14	0.0065	38.31	<0.0001	*
X1	0.0554	1	0.0554	325.8	<0.0001	*
X2	0.0023	1	0.0023	13.25	0.0027	*
X3	0.0183	1	0.0183	107.66	<0.0001	*
X4	0.0018	1	0.0018	10.42	0.0061	*
X1X2	0.0004	1	0.0004	2.33	0.1494
X1X3	0.002	1	0.002	11.71	0.0041	*
X1X4	4.00 × 10−8	1	4.00 × 10−8	0.0002	0.988
X2X3	0.0002	1	0.0002	0.8962	0.3599
X2X4	0	1	0	0.2717	0.6103
X3X4	0	1	0	0.1326	0.7212
X12	0.0063	1	0.0063	36.9	<0.0001	*
X22	0	1	0	0.2907	0.5982
X32	0.0016	1	0.0016	9.59	0.0079	*
X42	0.0014	1	0.0014	8.39	0.0117
Residual	0.0024	14	0.0002
Lack of fit	0.0024	10	0.0002	655.96	<0.0001	*
Pure error	1.45 × 10−6	4	3.63 × 10−7
Cor total	0.0937	28

Note: * in the table indicates significant.

. The p-values of the CO₂ partial pressure, Cl⁻ concentration, temperature, and flow rate are all <0.01, indicating that the influencing factors are accurate and reasonable. Moreover, the F-value of the prediction model is 39.51, which is greater than the critical value F_0.01(1, 14) = 8.86, and the p-value of the prediction model is <0.01. Therefore, the fitted regression model has good fitness. In addition, the determination coefficient R² of the model is 0.9753—close to 1—which, once again, indicates that the observed value of the model and the response value show an obvious correlation; that is, the model has a high degree of truth. Each factor has a good relationship with the response value.

3.3. Example Application of the Model

The corrosion prediction model is used to predict the corrosion rate of UGS extracted pipelines (Table 1). The degree of corrosion is divided according to the classification provisions in the standard NACE RP-0775 [27] “Preparation, Installation, Analysis, and Interpretation of Corrosion Coupons in Oilfield Operations”: <0.0254 mm/a is considered mild, 0.0254–0.125 mm/a is moderate, 0.125–0.254 mm/a is severe, and >0.254 mm/a is extremely severe. As shown in

Table 7. The results of the corrosion rate prediction and classification.

UGS Name	Corrosion Rate Predicted Value (mm/a)	Degree of Corrosion
S1	0.0600	Moderate
S2	0.0970	Moderate
S3	0.1230	Severe
S4	0.1187	Moderate
S5	0.0812	Moderate
S6	0.1058	Moderate
S7	0.1106	Moderate
S8	0.1049	Moderate
S9	0.0873	Moderate
S10	0.0750	Moderate
S11	0.0702	Moderate
S12	0.1032	Moderate
S13	0.0763	Moderate
S14	0.1890	Severe

, the S3 and S14 UGS extracted pipelines show severe corrosion, whereas the others exhibit moderate corrosion.

4. Conclusions

Based on the results, the following conclusions could be drawn:

(1)

The operating parameters of 14 domestic UGSs are investigated and analyzed, and four main corrosion factors are determined as follows: the CO₂ partial pressure, Cl⁻ concentration, temperature, and flow rate. The p-values of the independent variables in the prediction model are <0.01, which confirms that the four corrosion-influencing factors selected are significant and reasonable.

(2)

Based on 29 groups of high-temperature and high-pressure corrosion tests designed as per the RSM, a quadratic regression equation for the prediction of corrosion in the UGS extracted pipelines is finally established. The F-value of the model is greater than the critical value, the p-value of the model is <0.01, and the coefficient R² is 0.9491, indicating that the model has a high degree of truth.

(3)

The corrosion rate in 14 domestic UGS extracted pipelines is predicted by using this model. The corrosion degree of each pipeline is determined, and these results provide a scientific basis for the material selection, anti-corrosion strategy formulation, and process parameter optimization of gas pipelines.