Experimental Observation and Analysis of Inverse Transients for Pipeline Leak Detection

TLDR: In this paper, the effects of data and model error on ITA results have been explored, including strategies to minimize their effects using model error compensation techniques and ITA implementation approaches.

Abstract: Fluid transients result in a substantial amount of data as pressure waves propagate throughout pipes. A new generation of leak detection and pipe roughness calibration techniques has arisen to exploit those data. Using the interactions of transient waves with leaks, the detection, location, and quantification of leakage using a combination of transient analysis and inverse mathematics is possible using inverse transient analysis (ITA). This paper presents further development of ITA and experimental observations for leak detection in a laboratory pipeline. The effects of data and model error on ITA results have been explored including strategies to minimize their effects using model error compensation techniques and ITA implementation approaches. The shape of the transient is important for successful application of ITA. A rapid input transient (which may be of small magnitude) contains maximum system response information, thus improving the uniqueness and quality of the ITA solution. The effect of using he...

Figures

Figure 6. Independent and measured boundary condition use investigation: (a) simulation with leak at node 5, (b) simulation with no leak, and (c) head sensitivity to leak at solution.

Figure 1. Experimental pipeline apparatus.

Figure 10. Model error investigation: Comparison of pressure response and residuals for ITA estimation.

Figure 2. Transient event sharpness investigation: Experimental and ITA pressure responses.

Figure 5. Transient event sharpness investigation: Error transmission multiplier for leak located along pipeline.

Table 1. Experimental inverse transient analysis test details

Full text

ACCEPTED VERSION
Vitkovsky, John; Lambert, Martin Francis; Simpson, Angus Ross; Liggett, James A.
Experimental observation and analysis of inverse transients for pipeline leak detection Journal of
Water Resources Planning and Management, 2007; 133 (6):519-530
© ASCE 2007
http://hdl.handle.net/2440/41996
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21 March 2014

1
EXPERIMENTAL OBSERVATION AND ANALYSIS OF
INVERSE TRANSIENTS FOR PIPELINE LEAK DETECTION
John P. Vítkovský
1
, Martin F. Lambert
2
, Angus R. Simpson
3
, M. A.S.C.E.,
and James A. Liggett
4
1 Graduate Hydrologist, Water Assessment Group, Department of Natural Resources and
Water, Queensland, Indooroopilly QLD 4068, Australia. Email:
john.vitkovsky@nrm.qld.gov.au
2 Associate Professor, School of Civil and Environmental Engineering, University of
Adelaide, Adelaide SA 5005, Australia. (Corresponding author). Tel: +61 8 8303 5414;
Fax: +61 8 8303 4359; Email: mlambert@civeng.adelaide.edu.au
3 Professor, School of Civil and Environmental Engineering, University of Adelaide,
Adelaide SA 5005, Australia. Email: asimpson@civeng.adelaide.edu.au
4 Professor Emeritus, School of Civil and Environmental Engineering, Cornell University,
Ithaca, NY 14853-3501, USA. Email: jal8@cornell.edu

2
ABSTRACT
Fluid transients result in a substantial amount of data as pressure waves propagate throughout
pipes. A new generation of leak detection and pipe roughness calibration techniques has
arisen to exploit those data. Using the interactions of transient waves with leaks, the
detection, location and quantification of leakage using a combination of transient analysis and
inverse mathematics is possible using inverse transient analysis (ITA). This paper presents
further development of ITA and experimental observations for leak detection in a laboratory
pipeline. The effects of data and model error on ITA results have been explored including
strategies to minimize their effects using model error compensation techniques and ITA
implementation approaches. The shape of the transient is important for successful application
of ITA. A rapid input transient (which may be of small magnitude) contains maximum
system response information, thus improving the uniqueness and quality of the ITA solution.
The effect of using head measurements as boundary conditions for ITA has been shown to
significantly reduce sensitivity, making both detection and quantification problematic. Model
parsimony is used to limit the number of unknown leak candidates in ITA, thus reducing the
minimization problem complexity. Experimental observations in a laboratory pipeline
confirm the analysis and illustrate successful detection and quantification of both single and
multiple leaks.
CE DATABASE KEYWORDS
Pipes; Transients; Unsteady Flow; Error Analysis, Leaks, Inverse Analysis

3
INTRODUCTION
Throughout the world, pipelines efficiently transport fluids. When a leak occurs in such a
pipeline, there is an associated loss of product and increased pumping and treatments costs
arising from the additional fluid needed to fill the loss. For fluids such as oil and gas,
detrimental environmental impacts are potential consequences of any loss. Under certain
transient conditions leaks may allow passage of contaminants into the pipeline causing
concerns about purity and, in some cases, health. For these reasons, increasing both the
accuracy and efficiency of detection and location of leaks is essential.
Wang et al. (2001) presented a review of many alternative leak detection techniques;
however, the focus of this paper is on inverse transient analysis (ITA) for leak detection in
pipelines. This paper examines ITA in greater detail including the general analysis of inverse
problems, types of error and their effect (in particular model error), and strategies to deal with
some error types. Additionally, the importance of transient shape for successful ITA
application, use of measured boundary conditions for simulation, and a model parsimony
approach are investigated. Finally, experimental observations in a laboratory pipeline
illustrate successful single and multiple leak detection.
INVERSE TRANSIENT ANALYSIS
Liggett and Chen (1994) proposed calibration and leak detection in pipe networks using fluid
transients. Their methodology used pressure head measurements made during a transient
event. Using inverse mathematics the pipe parameters—leak areas, friction coefficients, wave
speeds—were adjusted to match observed pressures in the numerical model. The solution

4
parameter set was determined by minimizing an objective function that represents the match
between the numerically modeled heads and measured heads. The objective function is
derived from maximum likelihood estimators (Press et al. 1992) giving rise to the least-
squares criterion,
()
∑
=
−=
M
i
i
m
i
HHE
1
2
(1)
where E = objective function, H
i
m
= measured head, H
i
= numerically modeled head and M =
total number of measurements. The most important assumption is that the model is a good
representation of the system behavior. The residuals of the fit should also be normally
distributed, of zero mean, of stationary variance, and not correlated. Violation of any of these
assumptions will result in ITA fits that are not of maximum likelihood.
Numerical aspects of ITA that have been studied are algorithmic efficiency (Nash and Karney
1999, Vítkovský 2001, and Vítkovský et al. 2002), minimization algorithms (Vítkovský et al.
2000, Kapelan et al. 2003), optimal sampling designs (Vítkovský et al. 2003), and prior
information use (Kapelan et al. 2001). Tang et al. (2000), Vítkovský et al. (2001), Covas and
Ramos (2001), Covas et al. (2003) performed experimental validations of ITA for leak
detection in pipelines. Experimental validations of ITA in pipe networks have been
undertaken by Covas and Ramos (2001) and Wang (2002). Field testing of ITA for leak
detection has been performed in a trunk main by Stephens et al. (2002), Stephens et al.
(2004), Covas et al. (2004) and Stephens et al. (2005).
APPLICATION OF INVERSE ANALYSIS
For any inverse calculation the basic properties of the particular inverse problem should be
considered. A set of questions should be asked of any inverse analysis result. The inverse

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Experimental observation and analysis of inverse transients for pipeline leak detection" ?

In this paper, the authors examined the effect of model error on the performance of inverse transient analysis ( ITA ) for leak detection in pipelines. 

Q2. What is the effect of using head measurements as boundary conditions for ITA?

The effect of using head measurements as boundary conditions for ITA has been shown to significantly reduce sensitivity, making both detection and quantification problematic. 

Q3. What is the first task used to fit the parameters of the transient model?

The first task uses data from a known state (e.g., a leak-free state, or a historical state) to fit the parameters of the transient model. 

Q4. What is the common method to limit the number of significant parameters required to adequately model a?

A method to limit the number of significant parameters required to adequately model a process (and not over-fit the data) is to use information criteria. 

Q5. What is the final question that is approached by an analysis of the confidence of each parameter?

A final question, which is approached by an analysis of the confidence of each solution parameter, is the plausibility of the inverse solution. 

Q6. What is the correlation coefficient between a pair of leak parameters?

The correlation coefficient, ρ, between a pair of leak parameters isbab,a b,a σσσ =ρ (3)where σa,b = covariance of the errors in parameters a and b, and σa ,σb = standard deviations of the error in parameters a and b. 

Q7. What is the behavior of friction in the experimental pipeline?

The behavior of friction in the experimental pipeline is unsteady dominant (Bergant et al. 2001); thus, modeling the unsteady friction effects is crucial. 

Q8. What are the main reasons for leak detection in pipelines?

Under certain transient conditions leaks may allow passage of contaminants into the pipeline causing concerns about purity and, in some cases, health.