Burst Pressure Prediction of Subsea Supercritical CO2 Pipelines
Abstract
:1. Introduction
2. Unified Strength Theory
3. Mechanical Model of the Corroded Supercritical CO2 Pipeline
4. Equation for the Burst Pressure of the Corroded CO2 Pipeline
4.1. Stress Analysis
- q is an intermediate variable and ;
- k is an intermediate variable and .
4.2. Determination of Burst Pressure Equation Based on UST
4.3. Equations of Burst Pressure under Different Yield Criteria
4.3.1. The Burst Pressure Equation Based Tresca Criterion
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
6. Validations and Discussions
6.1. Comparisons with Experimental Data for Unflawed Pipeline
6.2. Comparisons with Experimental Data for Corroded Pipelines
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Conflicts of Interest
Nomenclature
First principal stress, second principal stress, third principal stress | |
Radial stress, hoop stress, axial stress | |
Coefficients in Equations (15) and (16) | |
Coefficients in Equations (15) and (16) | |
UST equivalent stress | |
Shear strength and shear stress | |
Yield-to-tensile strength ratio | |
Influence coefficient of intermediate principal stress on material failure | |
Thickness of an ideal pipeline | |
Minimum wall thickness after corrosion | |
Depth of corrosion defect | |
Corrosion ratio | |
Inner pressure, the burst pressure of the pipeline | |
The ratio of thickness to diameter | |
Poisson’s ratio | |
Ultimate tensile strength, yield strength | |
Variables in bipolar coordinate system | |
Experimental bursting pressure | |
q, k | Intermediate variable |
Tensile strength | |
The calculated burst pressure using Equation (15) in Table 2 and Appendix A | |
The experimental data of burst pressure for the i-th sample | |
N | The total number of experiments |
Burst pressure calculated by Chen’s model. |
Appendix A
No. | D (mm) | t (mm) | σy (MPa) | σu (MPa) | d (mm) | Pexp (MPa) | PEquation(15) (MPa) | Errors (PEquation (15)) | Errors (PChen) | Errors (PRAM) |
---|---|---|---|---|---|---|---|---|---|---|
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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Parameters | Value |
---|---|
Steel grade | X65 |
Yield strength (/MPa) | 467 |
Ultimate tensile strength (/MPa) | 576 |
Diameter (mm) | 762 |
Wall-thickness (mm) | 17.5 |
No. | D (mm) | t (mm) | |||||
---|---|---|---|---|---|---|---|
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 | PEquation(15) | PChen | PRAM |
---|---|---|---|
ME | 4.57% | 6.7% | 18.1% |
SD | 0.055 | 0.062 | 0.084 |
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Li, Y.; Wang, W.; Chen, Z.; Chu, W.; Wang, H.; Yang, H.; Wang, C.; Li, Y. Burst Pressure Prediction of Subsea Supercritical CO2 Pipelines. Materials 2022, 15, 3465. https://doi.org/10.3390/ma15103465
Li Y, Wang W, Chen Z, Chu W, Wang H, Yang H, Wang C, Li Y. Burst Pressure Prediction of Subsea Supercritical CO2 Pipelines. Materials. 2022; 15(10):3465. https://doi.org/10.3390/ma15103465
Chicago/Turabian StyleLi, Yan, Wen Wang, Zhanfeng Chen, Weipeng Chu, Huijie Wang, He Yang, Chuanyong Wang, and Yuxing Li. 2022. "Burst Pressure Prediction of Subsea Supercritical CO2 Pipelines" Materials 15, no. 10: 3465. https://doi.org/10.3390/ma15103465