#
Burst Pressure Prediction of Subsea Supercritical CO_{2} Pipelines

^{1}

^{2}

^{3}

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## Abstract

**:**

_{2}pipeline is the best choice for large-scale and long-distance transportation inshore and offshore. However, corrosion of the pipe wall will occur as a result of the presence of free water and other impurities present during CO

_{2}capture. Defects caused by corrosion can reduce pipe strength and result in pipe failure. In this paper, the burst pressure of subsea supercritical CO

_{2}pipelines under high pressure is investigated. First, a mechanical model of corroded CO

_{2}pipelines is established. Then, using the unified strength theory (UST), a new burst pressure equation for subsea supercritical CO

_{2}pipelines is derived. Next, analysis of the material’s intermediate principal stress parameters is conducted. Lastly, the accuracy of the burst pressure equation of subsea supercritical CO

_{2}pipelines is proven to meet the engineering requirement by experimental data. The results indicate that the parameter b of UST plays a significant role in determining burst pressure of pipelines. The study can provide a theoretical basis and reference for the design of subsea supercritical CO

_{2}pipelines.

## 1. Introduction

_{2}is transported through pipelines from the capture point to a suitable geological location. To improve transportation efficiency, high-pressure supercritical CO

_{2}transportation is the best choice for inland and offshore transportation of large-scale and long-distance CO

_{2}. Due to the presence of free water or other corrosive substances that are present in the captured carbon dioxide, corrosion defects will be caused in the pipeline [2]. In addition, corrosion defects can thin the pipe wall and further reduce the pipe’s bearing capacity, which also affects the safe operation of the high-pressure pipes [3,4,5]. As an essential parameter for evaluating pipeline integrity and safety, the burst pressure of the pipeline is usually defined as the ultimate load when the pipeline fails plastically [6]. The accurate prediction of the burst pressure of corroded CO

_{2}pipes is necessary for reducing pipeline operation risks and ensuring its strength and safety [7].

_{2}transportation pipelines can learn from the research methods of high-pressure transportation pipelines. The main research methods are the limitation of state equations based on different criteria, the finite element method [9,10,11], and industry standards, such as ASME [12], DNV [13], CSA [14], PCORRC [15] and other evaluation criteria. In most of the abovementioned methods, the corrosion defects are simplified into geometric shapes containing length and depth to fit the experimental results. Some researchers use neural network to study the failure behavior of pipelines [16,17]; however, empirical models tend to overestimate or underestimate the burst pressure. Hence, some researchers have studied the failure modes of corroded pipelines from a theoretical point of view and proposed some burst pressure equations based on different criteria. Over the last few decades, based on the theory of elastoplastic mechanics, a number of analytical formulas or empirical formulas for the burst pressure of unflawed pipes have been proposed by researchers, and many prediction models for the failure pressure of corroded pipes have been developed. The choice of strength criterion is the key factor for accurately predicting burst pressure, and scholars are also interested in it. Klever et al. [18,19] adopted the Tresca and von Mises yield criteria, considered large strain and material strain hardening, and proposed an analysis model for failure pressure of unflawed pipelines and corrosion-defective pipelines, then verified the analysis by comparison with experimental data. Several studies have demonstrated that the predicted pipe burst pressure is closely correlated with the adopted yield criteria. Christoper et al. [20] conducted experiments to study the burst pressure of unflawed pipes, and found that no single strength criterion could predict the burst pressure of all different types of material. Zhu and Leis [21,22,23] found that the Tresca criterion is appropriate for predicting the burst pressure of high-strain strengthened pipes, whereas the von Mises criterion is suitable for predicting the failure pressure of low-strain strengthened pipes. On this basis, a new multiaxial yield criterion is proposed, namely, the Zhu-Leis criterion, and a theoretical calculation method for the failure pressure of the unflawed pipe was proposed. The theoretical solution has been combined with the results of the pipeline failure pressure experimental data and has a good agreement. Law and Bowie [24] used different criteria to determine the burst pressure of high yield ratio pipelines. It then compared its predictions with the experimental results and determined that every criterion had its own applicability and limitations. Unified strength theory (UST) was first proposed by Yu [25], commonly used in engineering, which takes into account the strength differential effect (SD) of materials and the impact of the intermediate principal stresses of different materials on materials properties. Some researchers have achieved some results when applying UST to the theoretical study of pipeline burst pressure prediction. Based on the von Mises, Tresca, Zhu-Leis criteria, and TS criterion, Wang [26] used the unified strength criterion to derive the failure pressure calculation formula for unflawed thin-walled pipelines. Lin and Deng et al. [27,28,29] proposed the through-walled yield collapse pressure equation of thick-walled pipelines based on UST and verified the accuracy of the equation through experimental data. Zhang [30] proposed a new yield criterion—a weighted unification to predict the burst pressure of a pipe elbow. Deng [31] established a mechanical model capable of calculating the internal pressure strength of metallurgically bonded composite pipes and provided a calculation method for the internal pressure strength. Considering the influence of the ratio of metal yield strength to tensile strength (Y/T) on the bursting pressure, Chen [32] proposed a multi-parameter failure criterion including (Y/T). Chen [33,34] first proposed the DCA model, a theoretical model using thick-walled worn casing, and obtained the stress analytical solution for thick-walled corroded pipes. The model is used to develop a series of burst pressure equations to predict the burst pressure of corroded pipes.

_{2}transportation pipelines with defects are rare. Due to high pressure design requirements, dense phase or supercritical carbon dioxide requires high wall thickness pipelines [35]; therefore, a novel burst pressure model of corroded dense or supercritical CO

_{2}pipelines was proposed based on the DCA model and the UST model. The accuracy of the equations for calculating burst pressure was confirmed with experimental data. An integrity assessment framework is provided by the new equation for the supercritical CO

_{2}transportation pipeline. The burst pressure equation is compared with the existing pipeline burst experimental data. The result shows that the error is within the acceptable range of practical engineering applications.

## 2. Unified Strength Theory

## 3. Mechanical Model of the Corroded Supercritical CO_{2} Pipeline

_{2}pipeline containing corrosion defects. In the model, the corrosion defects are assumed to be long-term corrosion defects, and the pipes with corrosion defects are solved as a plane problem.

_{0}is the initial circle center, and O

_{1}is the circle center after corrosion. The thickness of the unflawed pipeline wall is t. t

_{min}is the minimum wall thickness after corrosion. The depth of corrosion defects is d. The corrosion ratio of the pipeline is:

## 4. Equation for the Burst Pressure of the Corroded CO_{2} Pipeline

#### 4.1. Stress Analysis

_{2}pipeline is as follows:

_{2}pipelines can be expressed as:

_{2}pipeline can be expressed as:

_{2}pipeline can be simplified as:

_{2}pipeline can be expressed as:

- q is an intermediate variable and $q=1-2/\xi $;
- k is an intermediate variable and $k=2\epsilon /\xi $.

_{2}pipelines with corrosion defects can be further expressed as:

_{2}pipelines with corrosion defects:

#### 4.2. Determination of Burst Pressure Equation Based on UST

_{2}pipelines to predict the burst pressure as follows:

_{2}pipeline based on the UST. Equation (15) is a function of the geometric parameters of the pipeline (D and t), the geometric parameters of the corrosion defect (d), and the pipeline material characteristics (parameter b). It is not a single equation for predicting burst pressure of pipelines but a series equation under different strength criteria when parameter b takes different values. For the supercritical CO

_{2}pipeline without defects ($\epsilon =0$), the burst pressure equation can be simplified as:

#### 4.3. Equations of Burst Pressure under Different Yield Criteria

#### 4.3.1. The Burst Pressure Equation Based Tresca Criterion

_{2}pipelines with or without defects can be presented by solving Equations (15) and (16):

#### 4.3.2. The Burst Pressure Equation Based on the on Mises Criterion

#### 4.3.3. The Burst Pressure Equation Based on the Zhu-Leis Flow Theory

#### 4.3.4. The Burst Pressure Equation Based on the TS Criterion

## 5. Influence of Parameter b on Burst Pressure

_{2}pipeline transportation [43], was selected to investigate the effect of parameter b on the burst pressure. The material properties and geometric parameters are listed in Table 1 [44]. The burst pressure of corroded pipelines of API X65 at different values of parameter b and different corrosion rates were calculated by using Equation (15). The results have been shown in Figure 4 and Figure 5.

## 6. Validations and Discussions

#### 6.1. Comparisons with Experimental Data for Unflawed Pipeline

#### 6.2. Comparisons with Experimental Data for Corroded Pipelines

_{2}pipes with existing experimental data [46] is presented. The calculated results by Equation (15) and comparison results are listed in Appendix A. The corrosion rate of the experimental samples in the literature ranges from 0.02 to 0.83, and the ratio of diameter to wall thickness ranges from 16 to 88. Detailed geometric parameters and material properties of corroded pipelines are shown in Appendix A. According to the previous analysis of unflawed pipelines, when verifying the burst pressure equation of corroded pipes with, the value of parameter b, it is 0.5 [28].

## 7. Conclusions

_{2}transport pipeline has been proposed, and the effect of intermediate principal stress on the predicted burst pressure was considered. The bursting pressure increases with the increase of the b value, and it decreases with the increase of the diameter–thickness ratio. Through the discussion, it is evident that different yield criteria based on the unified strength theory have a significant impact on the accuracy of prediction burst pressure. Finally, the accuracy of the predicted burst pressure equations in this paper have been verified by comparison with the experimental data, and the results indicate that our equations are reasonably accurate, especially when the corrosion rate is below 0.5. The findings of this research can provide a theoretical basis for the transportation and storage of carbon dioxide; however, the material intermediate principle, stress parameter b, is not sufficiently understood. It is necessary to further study how to determine the value of b in specific applications.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Conflicts of Interest

## Nomenclature

${\sigma}_{1},{\sigma}_{2},{\sigma}_{3}$ | First principal stress, second principal stress, third principal stress |

${\sigma}_{\alpha},{\sigma}_{\beta},{\sigma}_{z}$ | Radial stress, hoop stress, axial stress |

${f}_{0},{f}_{1},{f}_{2}$ | Coefficients in Equations (15) and (16) |

${\omega}_{0},\cdot \cdot \cdot ,{\omega}_{5}$ | Coefficients in Equations (15) and (16) |

${\sigma}_{\mathrm{UST}}$ | UST equivalent stress |

${\tau}_{\mathrm{s}},{\tau}_{\alpha \beta}$ | Shear strength and shear stress |

$a$ | Yield-to-tensile strength ratio |

$t$ | Influence coefficient of intermediate principal stress on material failure |

Thickness of an ideal pipeline | |

${t}_{\mathrm{min}}$ | Minimum wall thickness after corrosion |

$d$ | Depth of corrosion defect |

$\epsilon $ | Corrosion ratio |

${p}_{i},{p}_{b}$ | Inner pressure, the burst pressure of the pipeline |

$\lambda $ | The ratio of thickness to diameter |

$\mu $ | Poisson’s ratio |

${\sigma}_{u},{\sigma}_{y}$ | Ultimate tensile strength, yield strength |

$\alpha ,\beta $ | Variables in bipolar coordinate system |

${P}_{\mathrm{exp}}$ | Experimental bursting pressure |

q, k | Intermediate variable |

${\sigma}_{t}$ | Tensile strength |

${P}_{\mathrm{i}}^{cal}$ | The calculated burst pressure using Equation (15) in Table 2 and Appendix A |

${P}_{\mathrm{i}}^{\mathrm{exp}}$ | The experimental data of burst pressure for the i-th sample |

N | The total number of experiments |

${P}_{Chen}$ | Burst pressure calculated by Chen’s model. |

## Appendix A

**Table A1.**Errors of predictions compared with the actual burst pressure and two other evaluation model. (Experimental data source [46]).

No. | D (mm) | t (mm) | σ_{y}(MPa) | σ_{u}(MPa) | d (mm) | P_{exp}(MPa) | P_{Equation}_{(15)}(MPa) | Errors (P _{Equation} _{(15)}) | Errors (P _{Chen}) | Errors (P _{RAM}) |
---|---|---|---|---|---|---|---|---|---|---|

1 | 342 | 13.5 | 840 | 980 | 0.24 | 80.6 | 82.19 | 1.97% | 6.45% | 0.74% |

2 | 342 | 13.5 | 840 | 980 | 0.64 | 80.2 | 79.97 | −0.29% | 3.87% | −5.99% |

3 | 342 | 13.5 | 840 | 980 | 2.54 | 74.5 | 69.22 | −7.09% | −4.03% | −22.01% |

4 | 342 | 13.5 | 840 | 980 | 3.64 | 66.1 | 62.85 | −4.92% | −2.27% | −23.90% |

5 | 252 | 15.7 | 930 | 1070 | 0.33 | 143 | 138.9 | −2.87% | 5.94% | −2.66% |

6 | 252 | 15.7 | 930 | 1070 | 1.43 | 136 | 130.57 | −3.99% | 4.04% | −13.60% |

7 | 252 | 15.7 | 930 | 1070 | 2.63 | 130 | 121.23 | −6.75% | 0.31% | −22.08% |

8 | 252 | 15.7 | 930 | 1070 | 4.53 | 110 | 105.91 | −3.72% | 2.36% | −26.45% |

9 | 1219 | 19.9 | 585 | 715 | 15.41 | 7.6 | 5.99 | −21.18% | −25.00% | −40.79% |

10 | 1219 | 19.9 | 585 | 715 | 4.12 | 21.4 | 20.52 | −4.11% | −7.01% | −16.82% |

11 | 1219 | 19.9 | 592 | 723 | 7.44 | 17.7 | 16.51 | −6.72% | −9.60% | −23.73% |

12 | 1219 | 19.9 | 592 | 723 | 1.77 | 23.3 | 23.71 | 1.76% | −0.86% | −6.87% |

13 | 1219 | 13.8 | 568 | 705 | 10.78 | 4.7 | 3.94 | −16.17% | −21.28% | −34.04% |

14 | 1219 | 13.8 | 568 | 705 | 2.3 | 15.3 | 14.74 | −3.66% | −7.84% | −13.73% |

15 | 1219 | 13.8 | 589 | 731 | 5.45 | 12 | 11.17 | −6.92% | −10.83% | −21.67% |

16 | 1219 | 13.8 | 589 | 731 | 1.54 | 16.1 | 16.27 | 1.06% | −3.11% | −8.07% |

17 | 1320 | 22.9 | 782 | 803 | 2.52 | 27 | 27.35 | 1.30% | 7.04% | −8.52% |

18 | 1320 | 22.9 | 782 | 803 | 2.27 | 27.7 | 27.67 | −0.11% | 5.78% | −9.03% |

19 | 1320 | 22.9 | 782 | 803 | 2.31 | 27.5 | 27.62 | 0.44% | 6.18% | −8.73% |

20 | 1320 | 22.9 | 782 | 803 | 6.73 | 21.3 | 21.89 | 2.77% | 7.98% | −14.08% |

21 | 1320 | 22.9 | 782 | 803 | 6.73 | 21.8 | 21.89 | 0.41% | 5.50% | −16.06% |

22 | 1320 | 22.9 | 782 | 803 | 6.57 | 22 | 22.1 | 0.45% | 5.45% | −15.91% |

23 | 1320 | 22.9 | 782 | 803 | 11.45 | 15.9 | 15.66 | −1.51% | 3.14% | −22.64% |

24 | 1320 | 22.9 | 782 | 803 | 11.45 | 15.7 | 15.66 | −0.25% | 4.46% | −21.66% |

25 | 1320 | 22.9 | 782 | 803 | 11.45 | 15.9 | 15.66 | −1.51% | 3.14% | −22.64% |

26 | 1320 | 22.9 | 782 | 803 | 18.55 | 6.2 | 6.04 | −2.58% | 1.61% | −29.03% |

27 | 1320 | 22.9 | 782 | 803 | 19.01 | 5.5 | 5.41 | −1.64% | 1.82% | −27.27% |

28 | 1320 | 22.9 | 782 | 803 | 18.55 | 6.4 | 6.04 | −5.63% | −1.56% | −31.25% |

29 | 1320 | 20.6 | 782 | 803 | 2.06 | 23.2 | 24.89 | 7.28% | 13.36% | −2.16% |

30 | 1320 | 20.6 | 782 | 803 | 5.89 | 18.9 | 19.91 | 5.34% | 10.58% | −11.11% |

31 | 1320 | 20.6 | 782 | 803 | 11.33 | 13.2 | 12.69 | −3.86% | 0.00% | −24.24% |

32 | 1320 | 20.6 | 782 | 803 | 16.48 | 5.1 | 5.7 | 11.76% | 15.69% | −15.69% |

33 | 1320 | 22.9 | 782 | 803 | 4.58 | 25 | 24.69 | −1.24% | 4.00% | −14.40% |

34 | 1320 | 22.9 | 782 | 803 | 4.58 | 25.7 | 24.69 | −3.93% | 1.17% | −16.73% |

35 | 1320 | 22.9 | 782 | 803 | 11.45 | 16 | 15.66 | −2.13% | 2.50% | −23.13% |

36 | 1320 | 22.9 | 782 | 803 | 11.45 | 16.2 | 15.66 | −3.33% | 1.23% | −24.07% |

37 | 1320 | 22.9 | 782 | 803 | 18.32 | 6.3 | 6.36 | 0.95% | 4.76% | −25.40% |

38 | 1320 | 22.9 | 782 | 803 | 18.32 | 6.3 | 6.36 | 0.95% | 4.76% | −25.40% |

39 | 1320 | 20.6 | 782 | 803 | 4.12 | 21.8 | 22.22 | 1.93% | 7.34% | −11.01% |

40 | 1320 | 20.6 | 782 | 803 | 10.3 | 14.3 | 14.07 | −1.61% | 2.80% | −21.68% |

41 | 1320 | 20.6 | 782 | 803 | 16.85 | 5.1 | 5.19 | 1.76% | 5.88% | −23.53% |

42 | 1320 | 22.9 | 782 | 803 | 2.29 | 28.6 | 27.65 | −3.32% | 2.10% | −12.24% |

43 | 1320 | 22.9 | 782 | 803 | 2.29 | 28.2 | 27.65 | −1.95% | 3.55% | −10.99% |

44 | 1320 | 22.9 | 782 | 803 | 6.87 | 22.5 | 21.71 | −3.51% | 1.33% | −19.56% |

45 | 1320 | 22.9 | 782 | 803 | 6.87 | 22.1 | 22.71 | 2.76% | 3.17% | −18.10% |

46 | 1320 | 22.9 | 782 | 803 | 11.45 | 15.1 | 15.66 | 3.71% | 8.61% | −18.54% |

47 | 1320 | 22.9 | 782 | 803 | 11.45 | 15.5 | 15.66 | 1.03% | 5.81% | −20.65% |

48 | 1320 | 22.9 | 782 | 803 | 18.32 | 5.6 | 6.36 | 13.57% | 17.86% | −16.07% |

49 | 1320 | 22.9 | 782 | 803 | 18.32 | 5.7 | 6.36 | 11.58% | 15.79% | −17.54% |

50 | 1320 | 20.6 | 782 | 803 | 2.27 | 24.6 | 24.62 | 0.08% | 5.69% | −9.35% |

51 | 1320 | 20.6 | 782 | 803 | 6.39 | 19.4 | 19.25 | −0.77% | 4.12% | −16.49% |

52 | 1320 | 20.6 | 782 | 803 | 10.3 | 14.2 | 14.07 | −0.92% | 3.52% | −21.13% |

53 | 1320 | 20.6 | 782 | 803 | 15.86 | 5.1 | 6.55 | 28.43% | 33.33% | −3.92% |

54 | 1320 | 22.9 | 782 | 803 | 11.45 | 18.1 | 15.66 | −13.48% | −9.39% | −32.04% |

55 | 1320 | 22.9 | 782 | 803 | 11.45 | 15.4 | 15.66 | 1.69% | 6.49% | −20.13% |

56 | 1320 | 22.9 | 782 | 803 | 11.45 | 17.9 | 15.66 | −12.51% | −8.38% | −31.28% |

57 | 1320 | 22.9 | 782 | 803 | 11.45 | 15 | 15.66 | 4.40% | 9.33% | −18.00% |

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**Figure 1.**Transportation system in CCS (Source: Provided by Global CCS Institute [8]).

**Figure 3.**Illustration of the bipolar coordinate system [33].

**Table 1.**The material properties and geometrical parameters of API 5L X65 (Date from literature [44].

Parameters | Value |
---|---|

Steel grade | X65 |

Yield strength (${\sigma}_{y}$/MPa) | 467 |

Ultimate tensile strength (${\sigma}_{u}$/MPa) | 576 |

Diameter (mm) | 762 |

Wall-thickness (mm) | 17.5 |

No. | D (mm) | t (mm) | ${\mathit{\sigma}}_{\mathit{y}}\text{}\left(\mathbf{MPa}\right)\text{}$ | ${\mathit{\sigma}}_{\mathit{u}}\text{}\left(\mathbf{MPa}\right)\text{}$ | ${\mathit{P}}_{\mathbf{exp}}\text{}\left(\mathbf{MPa}\right)\text{}$ | ${\mathit{P}}_{\mathit{E}\mathit{q}\mathit{u}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}(16)}\text{}\left(\mathbf{MPa}\right)\text{}$ | ${\mathit{P}}_{\mathit{E}\mathbf{quation}(16)}/{\mathit{P}}_{\mathbf{exp}}$ |
---|---|---|---|---|---|---|---|

1 | 912 | 19 | 457.8 | 546.0 | 23.11 | 24.90 | 1.08 |

2 | 912 | 19 | 426.7 | 578.0 | 23.17 | 26.36 | 1.14 |

3 | 912 | 19 | 517.1 | 559.0 | 24.85 | 25.49 | 1.03 |

4 | 912 | 19 | 508.8 | 604.0 | 25.80 | 27.55 | 1.07 |

5 | 893.7 | 22.5 | 526.0 | 608.0 | 27.93 | 33.40 | 1.20 |

6 | 609.6 | 15.9 | 501.2 | 581.0 | 30.20 | 33.05 | 1.09 |

7 | 762.4 | 20 | 531.5 | 608.0 | 30.63 | 34.78 | 1.14 |

8 | 609.6 | 15.9 | 511.5 | 600.0 | 31.72 | 34.13 | 1.08 |

9 | 609.6 | 15.9 | 440.5 | 585.0 | 31.76 | 33.27 | 1.05 |

10 | 762.4 | 20 | 555.0 | 580.0 | 31.95 | 33.18 | 1.04 |

11 | 544.05 | 13.5 | 623.9 | 624.0 | 33.84 | 33.80 | 1.00 |

12 | 507.93 | 14.3 | 508.8 | 571.0 | 34.50 | 35.00 | 1.01 |

13 | 609.6 | 15.9 | 534.3 | 653.0 | 34.79 | 37.14 | 1.07 |

14 | 397.6 | 13.5 | 364.0 | 523.0 | 36.50 | 38.50 | 1.05 |

15 | 591.2 | 18.9 | 563.0 | 589.0 | 37.68 | 40.88 | 1.08 |

16 | 591.2 | 18.9 | 607.0 | 630.0 | 40.79 | 43.73 | 1.07 |

17 | 591.8 | 18.2 | 636.0 | 645.0 | 41.76 | 43.11 | 1.03 |

18 | 390.8 | 12.8 | 807.0 | 869.0 | 59.60 | 61.76 | 1.04 |

19 | 247.1 | 9.86 | 641.1 | 916.9 | 61.08 | 78.96 | 1.29 |

20 | 179.4 | 8.94 | 468.8 | 737.7 | 77.70 | 78.73 | 1.01 |

21 | 252.4 | 13.5 | 606.7 | 703.2 | 81.56 | 80.32 | 0.98 |

22 | 162.2 | 9.8 | 602.0 | 776.0 | 86.60 | 99.57 | 1.15 |

23 | 180.3 | 10.4 | 613.6 | 723.8 | 92.17 | 88.86 | 0.96 |

24 | 67.3 | 3.91 | 689.4 | 834.2 | 113.34 | 103.12 | 0.91 |

25 | 179.1 | 10.3 | 848.0 | 916.9 | 118.51 | 112.24 | 0.95 |

26 | 90.35 | 6.5 | 696.3 | 751.4 | 119.27 | 113.74 | 0.95 |

27 | 179.6 | 12.01 | 779.0 | 896.2 | 136.09 | 126.61 | 0.93 |

28 | 179.5 | 13.3 | 834.2 | 903.1 | 152.29 | 140.54 | 0.92 |

29 | 198.9 | 14.7 | 903.1 | 992.7 | 171.66 | 154.11 | 0.90 |

30 | 198.2 | 14.6 | 903.1 | 992.7 | 173.80 | 153.64 | 0.88 |

31 | 180.6 | 14.9 | 903.1 | 992.7 | 178.55 | 170.82 | 0.96 |

32 | 89 | 14.4 | 606.7 | 730.8 | 294.65 | 229.47 | 0.78 |

Mean | 1.03 |

Comparison Results | P_{Equation}_{(15)} | P_{Chen} | P_{RAM} |
---|---|---|---|

ME | 4.57% | 6.7% | 18.1% |

SD | 0.055 | 0.062 | 0.084 |

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**MDPI and ACS Style**

Li, Y.; Wang, W.; Chen, Z.; Chu, W.; Wang, H.; Yang, H.; Wang, C.; Li, Y.
Burst Pressure Prediction of Subsea Supercritical CO_{2} Pipelines. *Materials* **2022**, *15*, 3465.
https://doi.org/10.3390/ma15103465

**AMA Style**

Li Y, Wang W, Chen Z, Chu W, Wang H, Yang H, Wang C, Li Y.
Burst Pressure Prediction of Subsea Supercritical CO_{2} Pipelines. *Materials*. 2022; 15(10):3465.
https://doi.org/10.3390/ma15103465

**Chicago/Turabian Style**

Li, Yan, Wen Wang, Zhanfeng Chen, Weipeng Chu, Huijie Wang, He Yang, Chuanyong Wang, and Yuxing Li.
2022. "Burst Pressure Prediction of Subsea Supercritical CO_{2} Pipelines" *Materials* 15, no. 10: 3465.
https://doi.org/10.3390/ma15103465