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Analysis of transient fluid pressure signals has been investigated as an alternative method of fault detection in pipeline systems and has shown promise in both laboratory and field trials. The advantage of the method is that it can potentially provide a fast and cost effective means of locating faults such as leaks, blockages and pipeline wall degradation within a pipeline while the system remains fully operational. The only requirement is that high speed pressure sensors are placed in contact with the fluid. Further development of the method requires detailed numerical models and enhanced understanding of transient flow within a pipeline where variations in pipeline condition and geometry occur. One such variation commonly encountered is the degradation or thinning of pipe walls, which can increase the susceptible of a pipeline to leak development. This paper aims to improve transient-based fault detection methods by investigating how changes in pipe wall thickness will affect the transient behaviour of a system; this is done through the analysis of laboratory experiments. The laboratory experiments are carried out on a stainless steel pipeline of constant outside diameter, into which a pipe section of variable wall thickness is inserted. In order to detect the location and severity of these changes in wall conditions within the laboratory system an inverse transient analysis procedure is employed which considers independent variations in wavespeed and diameter. Inverse transient analyses are carried out using a genetic algorithm optimisation routine to match the response from a one-dimensional method of characteristics transient model to the experimental time domain pressure responses. The accuracy of the detection technique is evaluated and benefits associated with various simplifying assumptions and simulation run times are investigated. It is found that for the case investigated, changes in the wavespeed and nominal diameter of the pipeline are both important to the accuracy of the inverse analysis procedure and can be used to differentiate the observed transient behaviour caused by changes in wall thickness from that caused by other known faults such as leaks. Further application of the method to real pipelines is discussed.

Pipeline deterioration is a significant problem for engineers aiming to avoid costly failures or plan rehabilitation of pipeline assets. Typical forms of deterioration in pipeline systems include: internal or external corrosion of pipe walls, loss of lining and development of tubercles. These processes can lead to failure of the system through leak development, blockage formation or pipeline bursts which can lead to costly unexpected shutdowns, fluid contamination or increased running costs. Identification of pipeline deterioration has historically been carried out through external visual inspections, meaning that the identification of internal damage was more difficult. The development of closed circuit television (CCTV) cameras has enabled visual inspection of pipe interiors, however its range is limited and assessments can only be made based on damage that can be visually identified. Other inspection techniques such as eddy current analysis, ground penetrating radar, magnetic flux leakage and pipeline inspection gauges (PIGs) have been developed for pipeline inspection. While these methods enable the gathering of good quality data, they can be very expensive to implement and are intrusive, requiring physical entry to a pipeline system, excavation or system shutdowns [

To overcome the limitations of these existing methods the concept of analysing unsteady pressure responses within pipeline systems has been of interest to many research groups and is commonly referred to as transient analysis. An unsteady pressure response in a pipeline system is affected by any structural or geometric variations within that system and, as pressure waves can travel many kilometres within a pipeline, analysis of unsteady pressure responses within a system can potentially provide continuous information about the condition of that pipeline. Many methods for fault detection through transient analysis have been proposed, for which summaries can be found in Colombo

Transient analysis was first investigated by Stephens

To improve upon the versatility of these detection methods it is necessary to reduce the number of simplifying assumptions. This paper describes an ITA method which can account for variations in the wavespeed, diameter and length of a deteriorated section independently, thus reducing the number of assumptions to be made.

This investigation uses the Method of Characteristics (MOC) to solving the governing mass and linear momentum conservation equations for one dimensional unsteady pipe flow [_{f} is the sum of steady and unsteady frictional head losses. The derivation of these two equations assumes that both the fluid and the pipe behave in a linear elastic fashion. The equations can be solved using the MOC through confining the solution to a grid in the time and space domains by applying the following relationship:

Solving _{P}_{P}_{A}_{B}_{A}_{B}

The MOC model described is coded in Fortran using a constant time step discretisation such that numerical dissipation and dispersion errors that arise with the use of interpolation methods are avoided. The constant time step discretisation method requires the space step to be altered between sections of pipe to account for a change in the wavespeed as specified by

This section examines the effect that changes in pipeline wall condition have on transient behaviour within a pipeline. Changes in pipe wall conditions can alter three key parameters. The first is a change in the nominal diameter (

Research presented in Tuck _{S}_{C}

The wavespeed for a pipeline can be calculated by the wavespeed formula [^{3}, _{1} is a dimensionless parameter which accounts for constraint conditions on the pipeline and is taken as 1. To account for the relative strength of the cement lining an equivalent steel thickness can be calculated by the method in Stephens _{S}_{C}

Using _{J}_{J}

Following the initial drop in pressure head a reflection is observed from the upstream end of the degraded section which restores the pressure head back towards the observed values for the intact pipeline. Further secondary reflections are then observed before the pressure restoring reflection is observed from the upstream reservoir. The pressure response also shows a phase change, where the period of oscillation is increased for the system with the degraded pipeline.

Laboratory experiments were carried out using the transient pipeline facility at the University of Canterbury to further investigate the effect that variations in pipe wall thickness have on unsteady fluid behaviour in pipelines. The experimental system consists of a 41.517 m long stainless steel pipeline with an external diameter of 76.2 mm and wall thickness of 1.5 mm. The pipeline is bounded by a pressure tank at the upstream end to represent a constant head reservoir and a discharge valve at the downstream end which can be rapidly closed to induce unsteady behaviour. The resulting pressure response is measured at the point of generation at a sampling rate of 10 kHz by high resolution Thermo Fisher Scientific, flush face, dynamic pressure transducers. The pressure transducers are accurate to within ±1% of the magnitude of the measured signal. This error is largely linear, thus will have little effect on the comparisons between numerical and experimental responses as the magnitude of the numerical response is based upon the Joukowsky head rise. Variations in pipe wall thickness were investigated through adding a section of pipe with a wall thickness of 3.65 mm and outside diameter equivalent to the existing pipeline. Thicker walled pipe was used for this experiment as sections with thinner walls than the existing pipeline were not commercially available and it was not feasible to replace the whole pipeline. The length of the thick walled section (_{2}) is 10.407 m and it is located at a distance (_{1}) of 16.550 m from the downstream valve. The wavespeed of the standard pipeline (_{1,3}) is experimentally determined as 1,180 m/s and the wave speed of the thick walled section (_{2}) is 1,315 m/s.

It has been shown in

For this inverse problem the variables that are said to define the faulty section are its wavespeed (_{2}), diameter (_{2}), distance from the downstream valve to the fault (_{1}) and length of the faulty section (_{2}). The variables are assigned the following bounds; 800 m/s < _{2} < 1,440 m/s, 0 m < _{2} < 0.0762 m, 0 m < _{1} < _{0} and 0 m < _{2} < _{0} which are determined by allowing a lenient range of feasible values. To ensure that all solutions fall within the known pipeline geometry the following condition must also be met: _{1} + _{2} ≤ _{0}. Through selection of these variables and bounds the following assumptions are made; at most there is a single section of faulty pipeline, and the relative roughness does not increase significantly over the faulty section.

To improve the potential accuracy of the inverse analysis problem it is first necessary to determine an appropriate closure profile for the valve such that the head perturbation for the numerical response is similar to that of the experimental data. This step enables significantly more accurate results to be taken from the analysis and theoretically overcomes the problem discussed in Gong

_{1} and 0.63% for values of _{2}.

In an attempt to reduce the size of solution domain, cases 6 and 7 involved runs where changes in either the diameter or the wavespeed were excluded from the inverse calibration. An approximation such as this could prove useful where multiple faulty pipe sections are considered and can reduce the number of variables in the solution domain. This approximation is valid where the relative effect of one variable is much less than the others. The relative effects of diameter and wavespeed can first be considered by looking at the magnitude of the initial reflection from a fault. Scale analysis of

This paper has demonstrated how transient behaviour in a pipeline is altered by the presence of a degraded section of pipe which can be a precursor to pipeline failures. It has been shown that the degraded section can produce a reduction in wavespeed and changes in nominal diameter. These variations will alter the transient response of a pipeline, enabling transient analysis to be used to detect and classify degraded sections of a pipe. An inverse transient analysis method of fault detection has been implemented and shown to successfully determine the properties and location of a damaged pipe section. It has been demonstrated that the method can independently resolve changes in wavespeed and diameter over a wide solution space. This enables the method to be applied where prior information about a pipeline condition is minimal which is advantageous for field application of transient based condition assessment methods. The presented method has been evaluated using laboratory data which exhibit strong periodic behaviour. It is found that this periodic behaviour enables improvements in fault detection and classification accuracy. Where this periodic nature is not so strongly present, such as in large water distribution networks, improvements in accuracy could be achieved through a greater number of measurement points instead of increasing the duration of signal as considered here. Improvements in accuracy are also potentially achieved through increasing the sampling frequency and decreasing the modelled time step of the system response. For the experimental arrangement investigated it is demonstrated that the solution domain can be simplified through fixing the diameter variable in the ITA and varying only the wavespeed, length and location, however this reduces the accuracy of the fault detection method.

This research has been funded by the NZ Royal Society Marsden Grant UOC M1153 and the Brian Mason Trust E6022.

The authors declare no conflict of interest.

Schematic of reservoir, pipe and valve system for (

Comparison between an intact MSCL pipeline and a pipeline which has lost lining over a length of _{T}*

Comparison between numerical and experimental pressure responses for a pipeline with a thick walled section.

Inverse transient analysis results.

_{2}(m/s) |
_{2}(m) |
_{1}(m) |
_{2}(m) |
||||||
---|---|---|---|---|---|---|---|---|---|

Case | 1315 | - | 0.0688 | - | 16.550 | - | 10.407 | - | |

1 | 1054 | 19.8% | 0.0623 | 9.4% | 19.422 | 17.4% | 7.945 | 23.7% | |

2 | 1336 | 1.6% | 0.0706 | 2.6% | 15.814 | 4.4% | 12.211 | 17.3% | |

3 | 1360 | 3.4% | 0.0717 | 4.2% | 15.826 | 4.4% | 12.568 | 20.8% | |

4 | 1339 | 1.8% | 0.0704 | 2.3% | 16.777 | 1.4% | 10.457 | 0.5% | |

5 | 1326 | 0.8% | 0.0683 | 0.7% | 16.426 | 0.7% | 10.442 | 0.3% | |

_{2}=_{0} |
6 | 1320 | 0.4% | 0.0732 | - | 17.543 | 6.0% | 10.215 | 1.8% |

_{2}=_{0} |
7 | 1180 | - | 0.0590 | 14.2% | 18.997 | 14.8% | 12.325 | 18.4% |