# Finite Element Modelling and Retained Life Estimation of Corroded Pipelines in Consideration of Burst Pressures—A Fractural Mechanics Approach

## Abstract

**:**

_{b}) of internally, circumferentially corroded pipelines, with the corrosion defect depth (d), pipe wall thickness (t) and the pipe diameter (D). After modelling X46 and X52 grades of pipes, the P

_{b}estimated was compared with those determined experimentally and with industry standard models—ASME B31G (modified), RSTRENG, DNV F101, SHELL92 and FITNET FFS. The comparison specified a Root Mean Square Percentage Error (RMSPE) that ranged from 7.06% to 20.4% and a coefficient of determination (R

^{2}) that varied from 0.7932 to 0.9813. Multivariate regression was also used to compute a general linear relationship between the burst pressure (P

_{b}) and (d/t), (L/D) and (L/√Dt). The resulting FEM burst-pressure model, developed with multivariate regression, was later used to estimate the expected allowable operating pressure of a corroded X46 grade pipeline over the lifecycle duration, for low, mild, high and severe corrosion categories. It was observed that the burst pressure retention ratio (R

_{r}), which is an indicator of the reliability of the pipeline, decreased with the increase in (d) but did not show distinctive changes with the increase in (L). Considering the robustness of the FEM developed in this study, it can be concluded that it will be very vital for flowline design and pipeline integrity management.

## 1. Introduction

## 2. Finite Element Modelling (FEM) of Corroded Pipeline

## 3. Validation of the Finite Element Modelling Technique

_{t}, σ

_{t}, σ

_{u}, ɛ and n represent the true strain, true stress, tensile strength, total strain and strain hardening exponent, respectively. The elastic modulus (E) of the material was taken to be 207 GPa.

_{uts}and σ

_{YS}represent corrosion defect depth, corrosion defect length, external diameter of the pipeline, ultimate tensile strength and yield stress, respectively.

^{2}) of the FEM-predicted burst pressures and the experimental- and industry-model-estimated burst pressures of the pipes are shown in Table 3.

## 4. Burst Pressure Prediction for Circumferentially-Corroded Pipelines

_{b}) at the limit state is in the form shown in Equation (10) and uniformly affected the corroded section of the pipeline. The stress distribution on the corroded section of the pipe is shown in Figure 6.

_{b}’, then the burst pressure retention ratio (R

_{r}), which essentially gives an indication of the reliability of the pipe at a given corrosion defect, can be determined with the relationship in Equation (11).

## 5. Variability of the Retained Strength of the Corroded Pipelines

_{r}) of the pipes reduced with the increase in d/t, which is similar to the findings of other researchers [5,6,7,8,9]. This scenario was necessitated by the increasing corrosion defect depth, which generally results in increased stress concentration on pipelines [18,19,20]. For a given L/D and L/√Dt (Figure 9 and Figure 10), the retention ratios were fairly steady at each d/t as the L/D and L/√Dt values increased. Again, the increase in d/t saw the R

_{r}decrease for all the values of L/D and L/√Dt, which were also fairly uniform. It can be inferred from these results that pipelines have a lower risk of failure at lesser values of d/t, but increased risks are expected as the value of d/t increases. Again, the limited changes seen in Figure 8 and Figure 9 were indications of the limited influence the corrosion defect length has on the burst pressure of corroded pipelines.

_{ini}) for different corrosion categories are low corrosion (t

_{ini}= 1.56 years), mild corrosion (t

_{ini}= 0.58 years), high corrosion (t

_{ini}= 1.03 years) and severe corrosion (t

_{ini}= 1.89 years) [22]. In this case, the burst pressure at different lifecycle durations and various corrosion categories can be computed with Equations (12a,b). If the burst pressure of the pipeline computed with Equations (12a,b) represents the Maximum Allowable Operating Pressure (MAOP) at any given time in the lifecycle of the asset, and the maximum corrosion defect depth growth d

_{max}(t) can be computed with Equation (14) [23], then the MAOP for X46 grade of pipeline with 323.6 mm diameter will be patterned according to Figure 11.

## 6. Conclusions

^{2}) of the FEM-predicted burst pressures as compared to the experimental and industry-based models were experimental (R

^{2}= 0.8924), FITNET FFS (R

^{2}= 0.7932), SHELL 92 (R

^{2}= 0.9769), DNV F101 (R

^{2}= 0.9592), RSTRENG (R

^{2}= 0.9813) and ASME B31G (modified) (R

^{2}= 0.9812). A multivariate regression model was developed using 120 FEM-predicted burst pressures and other variables—d/t, L/D and L/√Dt—while the burst pressure retention ratio (R

_{r}) that indicated the reliability of the pipes was computed as the ratio of the burst pressure of the corroded pipe section to a non-corroded section.

## Conflicts of Interest

## References

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**Figure 2.**Finite Element Modelling (FEM) supporting and acting pressures on the modelled 1600 mm long X46 and X52 pipe.

**Figure 3.**Nonlinear FEM for X52 grade pipe of 273.05 mm diameter, 5.23 mm thick, d/t of 0.1 and L of 105 mm.

**Figure 4.**Summary of FEM estimated burst pressures for the pipes—samples 1 to 13 are for X46 (D: 321.56 mm to 324.1 mm), samples 14 to 16 are for X46 (D: 836.6 mm), samples 17 to 19 are for X52 (D: 273.05 mm) and samples 20 to 22 are for X52 (D: 611.35 mm to 612.54 mm).

**Figure 5.**Comparison of FEM analysis with experimental results for the 22 samples of X46 and X52 grade pipes.

**Figure 6.**Stress distribution around the corrosion defect section and the non-corroded sections of the X46 grade pipe with 273.05 mm diameter, 5.23 mm thick, d/t of 0.1 and L of 105 mm.

**Figure 7.**(

**a**) Comparison of the FEM estimation (P

_{b}) with the estimation from Equation (12a). (

**b**) Comparison of the FEM estimation (P

_{b}) with the estimation from Equation (12b).

**Figure 8.**Variation of the burst pressure retention ratio with d/t for 323.6 mm diameter and 8.51 mm thick pipe for various corrosion defect lengths mm.

**Figure 9.**Variation of the burst pressure retention ratio with L/√Dt for 534.4 mm diameter and 8.71 mm thick pipe for various d/t.

**Figure 10.**Variation of the burst pressure retention ratio with L/D for 863.6 mm diameter and 9.63 mm thick pipe for various d/t.

**Figure 11.**Predicted Maximum Allowable Operating Pressure (MAOP) for a 323.6 mm diameter and 8.51 mm thick pipeline with a 105 mm-long corrosion defect and an ultimate tensile strength of 469.27 MPa using Equation (12a).

Grade | D (mm) | t (mm) | d (mm) | L (mm) | σ_{u} (MPa) | σ_{Y} (MPa) | NOS |
---|---|---|---|---|---|---|---|

X46 | 321.56–324.01 | 8.33–8.74 | 0.00–3.30 | 0–144.78 | 469.27 | 356.38 | 13 |

X46 | 863.6 | 9.37–9.63 | 3.00–4.62 | 91.44–408.94 | 508.01 | 400.24 | 3 |

X52 | 273.05 | 5.23–5.28 | 0.00–1.85 | 0–408.94 | 502.25 | 388.7 | 3 |

X52 | 611.35–612.54 | 6.40–6.55 | 2.57–3.56 | 901.7–1371.6 | 533.82 | 402.52 | 3 |

_{u}: Ultimate tensile strength; σ

_{y}: Yield stress, NOS: number of samples.

**Table 2.**Summary of the Root Mean Square Percentage Error (RMSPE) of X46 and X52 grade pipes’ FEM-estimated burst pressures compared with the experimental and industry standard models (EISM) estimations.

EISM | Experimental | FITNET FFS | SHELL 92 | DNV F101 | RSTRENG | ASME-mod |
---|---|---|---|---|---|---|

RMSPE | 20.4% | 15.97% | 7.24% | 13.07% | 7.06% | 10.97% |

**Table 3.**Summary of the coefficient of determination (R

^{2}) of X46 and X52 grade pipe burst pressure as compared with the experimental and industry standard models (EISM).

EISM | Experimental | FITNET FFS | SHELL 92 | DNV F101 | RSTRENG | ASME B31G (mod) |
---|---|---|---|---|---|---|

R^{2} | 0.8924 | 0.7932 | 0.9769 | 0.9592 | 0.9813 | 0.9812 |

D (mm) | t (mm) | σ_{u} (MPa) | σ_{Y} (MPa) | d (mm) | L (mm) | NOS |
---|---|---|---|---|---|---|

323.6 | 8.51 | 469.27 | 356.38 | 0–6.81 | 105–735 | 40 |

534.4 | 8.71 | 491.65 | 373.21 | 0–6.97 | 136–955 | 40 |

863.6 | 9.63 | 508.01 | 400.24 | 0–7.70 | 182–1277 | 40 |

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**MDPI and ACS Style**

Ossai, C.I.
Finite Element Modelling and Retained Life Estimation of Corroded Pipelines in Consideration of Burst Pressures—A Fractural Mechanics Approach. *Infrastructures* **2017**, *2*, 15.
https://doi.org/10.3390/infrastructures2040015

**AMA Style**

Ossai CI.
Finite Element Modelling and Retained Life Estimation of Corroded Pipelines in Consideration of Burst Pressures—A Fractural Mechanics Approach. *Infrastructures*. 2017; 2(4):15.
https://doi.org/10.3390/infrastructures2040015

**Chicago/Turabian Style**

Ossai, Chinedu I.
2017. "Finite Element Modelling and Retained Life Estimation of Corroded Pipelines in Consideration of Burst Pressures—A Fractural Mechanics Approach" *Infrastructures* 2, no. 4: 15.
https://doi.org/10.3390/infrastructures2040015