# Health and Structural Integrity of Monitoring Systems: The Case Study of Pressurized Pipelines

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## Abstract

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## 1. Introduction

- internal pressure with induced vibrations,
- additional bending stress from the subsoil drop loaded with an internal pressure, and
- the pipeline wall thickness decreases caused by corrosion at the point of additional bending stress with an internal pressure, etc.

- which quantities should be measured continuously by sensors,
- what are their permissible limit values for a safe operation of the pipeline systems, and
- how to predict the corrosion process and its synergy with additional bending loading.

## 2. Methodology and Results

#### 2.1. Vibrations Induced in the Side Branches

- the gas flow rate is sufficiently high,
- there are necessary fluid and geometric conditions for the generation of excited pressure oscillations, and
- there was a resonant match between the excitation frequency and the natural frequency of the closed tap volume (existence of Helmholtz standing waves in the branch—the so-called “whistle effect”).

_{t}is the Strouhal number for the geometric and fluid ratios in the T-branch, and f

_{ne}is the oscillation frequency given as

- to determine cyclic properties of the critical volume of the material (often the weld joint) and
- the condition for assessing the criticality of the vibrations.

_{aeq}is an amplitude of equivalent strain in the critical cross-section, taking into account the mean value of the cycle (Goodman [16] or Morrow’s [17] method). Such a cycle is mainly induced due to stresses from the internal pressure and possible combination of normal (axial plus bending loading) and shear stresses (torsional loading). E is the Young modulus of the material.

- safety in terms of the pressure integrity of the pipe,
- fatigue damage accumulation state [19], and
- vibration permissibility.

#### 2.2. The Additional Bending in Operations of Pressurized Pipelines

#### 2.3. Weakening of Pipe Walls Due to Corrosion

- depth of existing corrosion defect found by pipeline inspection,
- kinetics of corrosion defect development,
- stress-strain state of the pipeline, and
- material properties of the pipeline.

_{0}is an integration constant calculated from at least one corrosion depth.

_{MBcor}is given by the equation:

**σ**is a true strength limit for given material of pipeline, and σ

_{UT}_{Cmax(t)}is the current value of the maximum stress calculated in the place of the corrosion defect using the diagram in Figure 11 for a measured value of the nominal stress in the pipe and an actual depth of the corrosion defect.

## 3. Conclusions

- induced vibrations due to fluid-geometry or the work of compressors,
- additional bending loading, and
- corrosion losses of the wall thickness.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Principle of self-excited oscillations in closed side branches. D is the diameter of the main pipe, and L (d) is a length (diameter) of a side branch.

**Figure 2.**Vibration of the pipe and branch: (

**a**) in-phase in the same direction (without the relative deflection) (

**b**) out p-hase in the same direction (inducing deflection of branch), and (

**c**) in a different direction (inducing deflection of the branch).

**Figure 3.**Frequency composition of signals measured by accelerometers and strain gauges on the vibrating pipe branch.

**Figure 4.**(

**a**) The arrangement of strain sensors along the perimeter of the pipeline, and (

**b**) the application of the strain sensors (gauges) on the real pipe.

**Figure 5.**Dependency σ

_{a}-2N

_{f}[15] for the base material and pipeline specimens made from the real pipeline with the weld joint.

**Figure 6.**Main screen of the monitoring system for the super-structure of the pipeline yard above the ground installed at the compressor station.

**Figure 7.**The progress of daily stress peaks in the cross-section of the pipe near the compressor obtained by a monitoring system with an extended thermal and device compensation concept.

**Figure 8.**Gas pipeline accident due to the additional bending of a pipeline system laid on a slope with insufficient amounts of compacted subsoil.

**Figure 10.**The schematic concept of the online monitoring of a pressurized pipeline system with corrosion defects.

**Figure 11.**The progress of the corrosion depth over time for different soil types and stress diagram for different depths of corrosion defects for nominal stress values obtained by direct measurements.

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**MDPI and ACS Style**

Chmelko, V.; Garan, M.; Šulko, M.; Gašparík, M. Health and Structural Integrity of Monitoring Systems: The Case Study of Pressurized Pipelines. *Appl. Sci.* **2020**, *10*, 6023.
https://doi.org/10.3390/app10176023

**AMA Style**

Chmelko V, Garan M, Šulko M, Gašparík M. Health and Structural Integrity of Monitoring Systems: The Case Study of Pressurized Pipelines. *Applied Sciences*. 2020; 10(17):6023.
https://doi.org/10.3390/app10176023

**Chicago/Turabian Style**

Chmelko, Vladimír, Martin Garan, Miroslav Šulko, and Marek Gašparík. 2020. "Health and Structural Integrity of Monitoring Systems: The Case Study of Pressurized Pipelines" *Applied Sciences* 10, no. 17: 6023.
https://doi.org/10.3390/app10176023