# Simulation Analysis of External Damage and Repair of the Gas Transmission Pipeline

Authors: Xinhui Wang; Heng Li; Bing Li; Jie Sheng; Jinqiang Zhao; Yanlong Ding; Duhui Lu
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

External damage and repair of a gas transmission pipeline were often encountered in industrial production. The damage of the gas transmission pipeline and the evaluation after repair could be solved by the finite element simulation method. Damage assessment and postrepair assessment were carried out for an external damage example of a gas transmission pipeline in an oil field based on finite element software ABAQUS. Ideally, the finite element simulation results were modified by using the theoretical calculation results of the gas transmission pipeline. Then, the simulation analysis of the defective gas transmission pipeline was carried out, and the corresponding maintenance suggestions were put forward. Finally, the B-type sleeve repair and carbon fiber composite repair were simulated and analyzed, respectively, and the bearing and stress of two kinds of repair were compared and analyzed. It was concluded that the repair effect of the carbon fiber composite was better than that of B-type sleeve. The research results could provide a new evaluation mechanism for pipeline defects and pipeline defects after repair and laid a foundation for quantitative risk assessment and repair of gas transmission pipelines.


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## Body

## 1. Introduction

With the rapid growth of the number of gas transmission pipelines, the risk of damage and destruction of gas transmission pipelines were also increasing. In recent years, pipeline leakage and explosion accidents had occurred all the time, which had brought great harm to safety production [1]. The main reason was that the main body of the pipeline was damaged. As long as there was internal and external corrosion thinning, defects left during manufacturing and installation, and third-party damage [2], especially the third-party damage, which had the greatest crisis on the pipeline [3], the analysis and evaluation of external damage of the pipeline were widely observed [4]. At present, the evaluation of pipeline external damage mainly focused on the strength check [5]. For a gas transmission pipeline of an oil field in northwest inland China (atmospheric pressure 0.89 atm), a simulation model was established via ABAQUS finite element analysis software for the external damage of the gas transmission pipeline found during regular inspection. The simulation analysis of pipeline defects was carried out in the instances. At the same time, the B-type sleeve repair and carbon fiber composite material repair models were established, and the simulation calculation and analysis were carried out, respectively [6]. The later stage laid the foundation for the establishment of the quantitative risk assessment method for gas transmission pipelines [7].


## 2. Mechanical Model

The materials and methods section should contain sufficient detail so that all procedures can be repeated. It may be divided into headed subsections if several methods are described.


### 2.1. Theoretical Model

Ideally, the strength calculation formula of the gas transmission pipeline is shown in the following equation:(1)δ=pD2σsφFt,where δ is wall thickness of gas transmission pipeline; p is design pressure of gas transmission pipeline; D is outer diameter of the pipe; σs is the minimum yield strength of pipeline material; ϕ is pipe weld coefficient, and equal to 1.0; F is strength design coefficient, the corresponding value shall be selected according to the specification for strength design coefficient of gas transmission pipeline; t is temperature coefficient, where it has a value of 0.1 as the temperature under 120°C [8]


### 2.2. Modeling in Defective State

The total strain of pit defects in the gas transmission pipeline mainly included circumferential strain and axial strain (Boiler Specification-ASME B 31.8: Strain Evaluation Method), and the strain in each direction can be divided into membrane strain and bending stress [9]. Therefore, the expression of total equivalent strain at the depression of the gas transmission pipeline could be calculated inthe following equation:(2)εeff=ε12+ε2+ε32−ε1⋅ε2+ε3,where εeff is the total equivalent strain at the depression; ε1 is the circumferential bending strain of the pipe; ε2 is the axial bending strain of the pipe; ε3 is the axial membrane strain [10].


## 2.1. Theoretical Model

Ideally, the strength calculation formula of the gas transmission pipeline is shown in the following equation:(1)δ=pD2σsφFt,where δ is wall thickness of gas transmission pipeline; p is design pressure of gas transmission pipeline; D is outer diameter of the pipe; σs is the minimum yield strength of pipeline material; ϕ is pipe weld coefficient, and equal to 1.0; F is strength design coefficient, the corresponding value shall be selected according to the specification for strength design coefficient of gas transmission pipeline; t is temperature coefficient, where it has a value of 0.1 as the temperature under 120°C [8]


## 2.2. Modeling in Defective State

The total strain of pit defects in the gas transmission pipeline mainly included circumferential strain and axial strain (Boiler Specification-ASME B 31.8: Strain Evaluation Method), and the strain in each direction can be divided into membrane strain and bending stress [9]. Therefore, the expression of total equivalent strain at the depression of the gas transmission pipeline could be calculated inthe following equation:(2)εeff=ε12+ε2+ε32−ε1⋅ε2+ε3,where εeff is the total equivalent strain at the depression; ε1 is the circumferential bending strain of the pipe; ε2 is the axial bending strain of the pipe; ε3 is the axial membrane strain [10].


## 3. Establishment of the Finite Element Model

### 3.1. Flawless Pipe Model

The finite element analysis model of flawless gas transmission pipelines was established by ABAQUS, as shown in Figure1. Among them, the outer diameter of the gas transmission pipeline was 325 mm, the wall thickness was 6 mm, the length was 100 mm, the design pressure was 6.40 MPa, the operating pressure was 4.50 MPa, the pipeline material was L360 steel, the minimum yield strength of the pipeline material was 360.00 MPa, the minimum tensile strength of the pipeline material was 460.00 MPa, the elastic modulus was 210.00 GPa, Poisson’s ratio was 0.3, and the density was 7.9 g/cm3. At the same time, the hexahedral element was used for grid division [11], and the number of grids were about 50000. The grid model of the flawless pipeline is shown in Figure 2.Figure 1
Modeling drawing of the flawless pipeline.Figure 2
Meshing model of the flawless pipeline.


### 3.2. Defective Pipe Modelling

During the regular inspection of a gas transmission pipeline in an oil field, external damages of the gas transmission pipeline were found. This was a kind of pit defect [12], usually caused by engineering machinery. The geometric parameters of the defect were obtained on the site. The axial length was 100 mm, the circumferential length was 20 mm, and the maximum depth was 20 mm. At the same time, there was loss weight at the bottom of the pit, resulting in the thinning of the wall thickness at the scratch. Here, the original wall thickness of the pipeline was 6.0 mm, the loss depth was 0.6 mm, and the actual wall thickness at the pipe pit was 5.4 mm, as shown in Figure 3.Figure 3
Actual damage diagram of the pipeline.According to the dimension and size of pipeline defects, finite element simulation modelling was established based on ABAQUS, as shown in Figure4. The eight node linear hexahedron element and mixed tetrahedron element were used for mesh generation, and the geometry segmentation and mesh refinement were carried out at the defect location to improve the accuracy of simulation calculation. From Figure 5, it appeared that the reduced integral was used for element control, two ends of the pipe were symmetrically constrained [13], and same loading was applied on the inner wall as the internal pressure of the pipe.Figure 4
Defective pipe geometry modelling.Figure 5
Defective pipe mesh modelling.


## 3.1. Flawless Pipe Model

The finite element analysis model of flawless gas transmission pipelines was established by ABAQUS, as shown in Figure1. Among them, the outer diameter of the gas transmission pipeline was 325 mm, the wall thickness was 6 mm, the length was 100 mm, the design pressure was 6.40 MPa, the operating pressure was 4.50 MPa, the pipeline material was L360 steel, the minimum yield strength of the pipeline material was 360.00 MPa, the minimum tensile strength of the pipeline material was 460.00 MPa, the elastic modulus was 210.00 GPa, Poisson’s ratio was 0.3, and the density was 7.9 g/cm3. At the same time, the hexahedral element was used for grid division [11], and the number of grids were about 50000. The grid model of the flawless pipeline is shown in Figure 2.Figure 1
Modeling drawing of the flawless pipeline.Figure 2
Meshing model of the flawless pipeline.


## 3.2. Defective Pipe Modelling

During the regular inspection of a gas transmission pipeline in an oil field, external damages of the gas transmission pipeline were found. This was a kind of pit defect [12], usually caused by engineering machinery. The geometric parameters of the defect were obtained on the site. The axial length was 100 mm, the circumferential length was 20 mm, and the maximum depth was 20 mm. At the same time, there was loss weight at the bottom of the pit, resulting in the thinning of the wall thickness at the scratch. Here, the original wall thickness of the pipeline was 6.0 mm, the loss depth was 0.6 mm, and the actual wall thickness at the pipe pit was 5.4 mm, as shown in Figure 3.Figure 3
Actual damage diagram of the pipeline.According to the dimension and size of pipeline defects, finite element simulation modelling was established based on ABAQUS, as shown in Figure4. The eight node linear hexahedron element and mixed tetrahedron element were used for mesh generation, and the geometry segmentation and mesh refinement were carried out at the defect location to improve the accuracy of simulation calculation. From Figure 5, it appeared that the reduced integral was used for element control, two ends of the pipe were symmetrically constrained [13], and same loading was applied on the inner wall as the internal pressure of the pipe.Figure 4
Defective pipe geometry modelling.Figure 5
Defective pipe mesh modelling.


## 4. Calculation and Analysis

### 4.1. Strength Calculation of the Flawless Pipeline

In order to verify the accuracy of the finite element model, the theoretical strength check results of the flawless gas transmission pipeline were used to correct the finite element calculation results [14]. It was assumed that the newly built gas transmission pipeline was in the most ideal state without any defects. The initial pressure in the gas transmission pipeline was set to 0.10 MPa, and then the conduct pressure test had been performed. When the internal pressure of the gas transmission pipeline increased to 12.87 MPa, the yield strength reached 355.00 MPa, which was close to the yield limit [15]. The stress diagram of the pipeline is shown in Figure 6.Figure 6
Stress nephogram of the flawless pipeline.According to the code for design of Gas Transmission Pipeline Engineering (GB 50251-2015), the strength design coefficientF was determined by the regional grade of the pipeline [16, 17]. Therefore, when F = 1 (in the ideal state), the design pressure of the gas transmission pipeline under the ideal state was 10.63 MPa through theoretical calculation. The finite element simulation displayed that the design pressure in the ideal state was 12.87 MPa. The finite element model was in an ideal state [18]. In order to be consistent with the actual working conditions, it was necessary to use the correction factor y for correction. Here, Y is taken as 0.82, the final design pressure value of the finite element model under the ideal working conditions was 10.55 MPa.It was confirmed onsite that laying area of the gas transmission pipeline classified was class II area [19]. Therefore, the theoretical design pressure value can be obtained by formula (1), which was very close to actual design pressure 6.40 MPa. At the same time, the design pressure obtained by calculating the pressure value of the simulation result through formula (1) was 6.33 MPa. The three results were very close, which verified the accuracy of the finite element model.


### 4.2. Simulation Calculation of the Defective Pipeline

The working pressure of the on-site gas transmission pipeline was set to be 4.50 MPa. It could be seen from above that the actual working pressure was needed to be converted into the pressure under the finite element model to ensure the accuracy of its calculation and analysis [20]. The calculated pressure under the finite model was 9.15 MPa. When the working internal pressure of 9.15 MPa was set for the pipeline, the stress nephogram is as shown in Figure 7. The stress of the pipeline had exceeded the yield strength and was close to the tensile strength as internal pressure reached 9.15 MPa, and stress concentration occurred at the tip of the pit.Figure 7
Stress nephogram of the defective pipeline under actual working conditions.The postprocessing technology was used to inspect the internal surface of the pipeline, and the pipeline defects were partially divided. It could be seen from Figure8 that the stress at the tip of the defect on the inner wall was the largest, and the stress value reached 450.60 MPa.Figure 8
Internal stress nephogram of the defective pipeline.Subsequently, the simulation test of internal pressure reduction was conducted on the model. When the internal pressure was reduced to 7.30 MPa, the stress at the defect of the pipeline still reached the yield strength. However, as the internal pressure of the pipeline began to decrease from 7.30 MPa, the maximum stress at the defect began to decrease. When the internal pressure was reduced to 0.10 MPa, the maximum stress at the defect was 11.30 MPa. The relationship between the internal pressure and the maximum stress of the defective pipeline was obtained from Figure9. Ideally, the maximum safety pressure was 7.30 MPa, which was converted into the actual maximum safety pressure of 3.59 MPa [20]. It was lower than the actual working pressure of the current gas transmission pipeline of 4.50 MPa. Therefore, it was recommended to repair the pipeline defects.Figure 9
Relationship between internal pressure and maximum stress of the defective pipeline.


## 4.1. Strength Calculation of the Flawless Pipeline

In order to verify the accuracy of the finite element model, the theoretical strength check results of the flawless gas transmission pipeline were used to correct the finite element calculation results [14]. It was assumed that the newly built gas transmission pipeline was in the most ideal state without any defects. The initial pressure in the gas transmission pipeline was set to 0.10 MPa, and then the conduct pressure test had been performed. When the internal pressure of the gas transmission pipeline increased to 12.87 MPa, the yield strength reached 355.00 MPa, which was close to the yield limit [15]. The stress diagram of the pipeline is shown in Figure 6.Figure 6
Stress nephogram of the flawless pipeline.According to the code for design of Gas Transmission Pipeline Engineering (GB 50251-2015), the strength design coefficientF was determined by the regional grade of the pipeline [16, 17]. Therefore, when F = 1 (in the ideal state), the design pressure of the gas transmission pipeline under the ideal state was 10.63 MPa through theoretical calculation. The finite element simulation displayed that the design pressure in the ideal state was 12.87 MPa. The finite element model was in an ideal state [18]. In order to be consistent with the actual working conditions, it was necessary to use the correction factor y for correction. Here, Y is taken as 0.82, the final design pressure value of the finite element model under the ideal working conditions was 10.55 MPa.It was confirmed onsite that laying area of the gas transmission pipeline classified was class II area [19]. Therefore, the theoretical design pressure value can be obtained by formula (1), which was very close to actual design pressure 6.40 MPa. At the same time, the design pressure obtained by calculating the pressure value of the simulation result through formula (1) was 6.33 MPa. The three results were very close, which verified the accuracy of the finite element model.


## 4.2. Simulation Calculation of the Defective Pipeline

The working pressure of the on-site gas transmission pipeline was set to be 4.50 MPa. It could be seen from above that the actual working pressure was needed to be converted into the pressure under the finite element model to ensure the accuracy of its calculation and analysis [20]. The calculated pressure under the finite model was 9.15 MPa. When the working internal pressure of 9.15 MPa was set for the pipeline, the stress nephogram is as shown in Figure 7. The stress of the pipeline had exceeded the yield strength and was close to the tensile strength as internal pressure reached 9.15 MPa, and stress concentration occurred at the tip of the pit.Figure 7
Stress nephogram of the defective pipeline under actual working conditions.The postprocessing technology was used to inspect the internal surface of the pipeline, and the pipeline defects were partially divided. It could be seen from Figure8 that the stress at the tip of the defect on the inner wall was the largest, and the stress value reached 450.60 MPa.Figure 8
Internal stress nephogram of the defective pipeline.Subsequently, the simulation test of internal pressure reduction was conducted on the model. When the internal pressure was reduced to 7.30 MPa, the stress at the defect of the pipeline still reached the yield strength. However, as the internal pressure of the pipeline began to decrease from 7.30 MPa, the maximum stress at the defect began to decrease. When the internal pressure was reduced to 0.10 MPa, the maximum stress at the defect was 11.30 MPa. The relationship between the internal pressure and the maximum stress of the defective pipeline was obtained from Figure9. Ideally, the maximum safety pressure was 7.30 MPa, which was converted into the actual maximum safety pressure of 3.59 MPa [20]. It was lower than the actual working pressure of the current gas transmission pipeline of 4.50 MPa. Therefore, it was recommended to repair the pipeline defects.Figure 9
Relationship between internal pressure and maximum stress of the defective pipeline.


## 5. Simulation of Pipeline Defect Repair

There were three ways to repair the defects: B-type sleeve reinforcement, composite material reinforcement, and pipe replacement [21, 22]. They had their own advantages and disadvantages.B-type sleeve repair technology was to fix two tubular steel plates at the location of pipeline defects by welding to strengthen the bearing capacity of the pipeline. Butt weld was often used for sleeve side seam [23], as shown in Figure 10.Figure 10
Schematic diagram ofB-type sleeve repair.Generally, the casing and pipe body were made of the same material, which could reduce stress concentration in the maintenance area. The calculation of sleeve wall thickness should be determined according to the maximum operating pressure of the pipeline. The detailed formula is shown in the following equation:(3)tn=pD12σsφ,where tn is the sleeve wall thickness specified in the pipeline design standard, D1 is the outer diameter or inner diameter of the pipe, σs is the yield strength of the sleeve material, ϕ is the weld coefficient, and for single-sided welded butt joints, ϕ = 0.9 (100% detection). According to the relevant dimensions of the defective pipeline, the wall thickness of the sleeve was determined to be 3.21 mm by equation (3), and the final value was 4.00 mm. According to the defect size and relevant standard requirements, the sleeve length was determined to be 200 mm.Composite repair technology was a kind of technology that used the cementation method to repair damaged structures [24], as shown in Figure 11.Figure 11
Schematic diagram of composite repair technology.In practical engineering applications, carbon fiber composites were often used to repair the external damage defects of pressure pipelines. The number of reinforcement layers and the thickness of the reinforcement layer were determined according to the size of defects and actual working conditions. The calculation relationship between the number of reinforcement layers and the thickness of the reinforcement layer is listed in the following equation:(4)trep=σbt−tsσsεcEC,which trep is the thickness of the reinforcement layer, t is the wall thickness of the pipe, ts is the residual wall thickness of the pipe, σb is the tensile strength of the pipe material, Ec is Young’s modulus of the carbon fiber composite, and εc is the maximum elongation of the carbon fiber composite. The parameters of carbon fiber composites are summarized in Table 1.(5)NH=Inttreptply+1,where NH is the number of reinforcing layers of the carbon fiber composite (rounded down plus 1), tply is the thickness of reinforced single layer of carbon fiber composite, Int [] is a rounding function, the thickness of carbon fiber composite was 3 layers, and the width of carbon fiber composite was 198 mm.Table 1
Parameters of carbon fiber composites.
Carbon fiber compositesParameterUnitCircumferential modulus of elasticity70.50GPaAxial modulus of elasticity36.40GPaCircumferential tensile strength938.00MPaAxial tensile strength558.00MPaCompressive strength of filling material103.00MPaAiming at the defects of the gas transmission pipeline in a certain area mentioned above, ABAQUS was used to simulate and analyze the two in-service pipeline repair methods of B-type sleeve reinforcement and carbon fiber composite reinforcement. The pressure used in the simulation was consistent with the actual working pressure, that is, the internal pressure converted into the finite element model was 9.15 MPa, and the stress nephogram of the repaired B-type sleeve is shown in Figure12.Figure 12
B-type sleeve repair stress diagram.It could be seen from Figure12 that the B-type sleeve repair method could maintain the internal pressure and could also bear the axial stress caused by the lateral loading, but it was easy to produce stress concentration at the edge of the casing. It could be seen from the cloud chart that after type B reinforcement, the overall pressure of the pipeline became stronger, and the stress value at the defect of the pipeline was 337.80 MPa. The stress value is lower than the yield strength of the pipeline, thus the repair of this pipeline is successful.It could be seen from Figure13 that when carbon fiber composite material was used for repair, the maximum stress value of the pipeline was 298.50 MPa, which was lower than the stress value of B-type sleeve reinforcement. This is because carbon fiber material has the characteristics of high strength and high modulus. The reinforcement layer formed could effectively reduce the stress and strain on the pipe surface and minimize the stress concentration at the pipe defects while bearing the load.Figure 13
Composite repair stress diagram.Pressurization tests were carried out on the repaired pipes withB-type sleeves and carbon fiber composite materials, respectively. When the internal pressure of the repaired pipes with B-type sleeves increased to 11.40 MPa, the maximum stress on the inner wall of the pipes was 360.00 MPa, which was converted into the internal pressure under actual working conditions of 5.61 MPa, greater than 4.50 MPa of the operating pressure, and the repaired pipes completely satisfied the request of strength requirements.When the internal pressure of the repaired carbon fiber composite pipeline increased to 13.80 MPa, the maximum stress on the inner wall of the pipeline was 360.00 MPa, which was equivalent to 6.88 MPa under the actual working condition, greater than 4.50 MPa of the operating pressure. The repaired pipeline fully met the strength requirements.Under actual working conditions, the comparison results of internal pressure borne by mechanically scratched defective pipes on the outer wall before and after repair are shown in Figure14. It could be found that with the gradual increasing of the internal pressure of the pipeline, the maximum stress value of the three pipelines increased. But the growth rate was different. The maximum stress value before repair (black line) increased the fastest and reached the maximum value of 360.00 MPa when the internal pressure was 7.30 MPa. The maximum stress value of the pipeline repaired with carbon fiber composites (blue line) increased the most slowly. When the internal pressure was 13.80 MPa, the maximum stress value slowly raised to 360.00 MPa. The pipeline repaired with the B-type sleeve (red line) was between them. When the internal pressure was 11.40 MPa, the maximum stress value reached the maximum. It could be drawn that the maximum stress at the stress concentration of the pipeline after repair was significantly lower than that before repair with the increase of the internal pressure of the pipeline. At the same time, the pipes repaired by both methods could meet the requirements of normal working conditions, but loading and stress concentration repaired by carbon fiber composites were better than those repaired by the B-type sleeve.Figure 14
Comparison of pressure bearing before and after the repair of the defective pipeline.


## 6. Conclusions

Through the comparison between the theoretical calculation results and the finite element simulation results of the flawless gas transmission pipeline, the finite element simulation results are modified, and then the modified combination is compared with the actual design results to verify the accuracy of the finite element model.According to the actual defect parameters of the pipeline, the finite element model of the flawless pipeline is established, the defects of the pipeline are quantitatively studied through simulation analysis, the bearing condition of the defect is analyzed, and the maintenance suggestions are given.The simulation repair model of the B-type sleeve and the simulation model of carbon fiber composite repair are established based on defects of the gas transmission pipeline. The bearing and stress of the two modes after repair are compared and analyzed. It is concluded that the repair effect of carbon fiber composites is better than that ofB-type sleeves as a whole.



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*Source: 3978649-2022-08-26.xml*