SCIENCE CHINA Technological Sciences • RESEARCH PAPER •
March 2012 Vol.55 No.3: 743–752 doi: 10.1007/s11431-011-4707-3
Leak detection in pipelines by exclusively frequency domain method GUO XinLei*, YANG KaiLin & GUO YongXin State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China Received May 31, 2011; accepted November 24, 2011; published online January 20, 2012
A further development of exclusively inverse frequency domain method for leak detection in pipelines is presented and validated. The location and leakage can be determined by analyzing the difference of transient water head response between the simulated and measured data in frequency domain. The transient signals are generated by portion sharp closure of a valve from the small constant opening and it needs only a few meters of water. The discrete boundary conditions and observation data are both transformed in frequency domain by Laplace transform. Example in numerical simulation is studied for demonstration of this approach. The application of the method to an experimental pipeline confirms the analysis and illustrates successful detection of the single pipeline leak. The precalibration approach is presented to minimize the effect of data and model error and it splits the method into two parts. One uses data from a known state to fit the parameters of the model and the other uses data from the current state for the fitting of leak parameters using the now calibrated model. Some important practical parameters such as wave speed, friction in steady and unsteady state and the adaptability of the method are discussed. It was found that the nonlinearity errors associated with valve boundary condition could be prevented by consideration of the induced flow perturbation curve shape. pipelines, leak detection, transient flow, frequency, friction, algorithm Citation:
1
Guo X L, Yang K L, Guo Y X. Leak detection in pipelines by exclusively frequency domain method. Sci China Tech Sci, 2012, 55: 743752, doi: 10.1007/s11431-011-4707-3
Introduction
Leaks occur commonly in all piping systems especially the long distance water diversion projects. Safety production, economic loss, and environmental issues associated with pipeline leaks are a growing concern around the world. Since leaks are inevitable, development of leak detection methodologies is a non-trivial scientific and engineering issue for the water resources community and pipeline operation. A number of different techniques for pipeline leak detec-
*Corresponding author (email:
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2012
tion have been applied to the oil industries. Most of them combine continuous monitoring of the physical parameters with some form of mathematical modeling. Two main parameters are measured: pressure and flow. The traditional technique is the mass or volume balance method [1], here the inflow and outflow are both measured and computed, and there must be leaks if the two are different. As the flow meters are not usually accurate, the detection method developed only relies on the pressure. Brunone [2] proposed a technique for leakage detection based on the well-known properties of transient pressure waves. Misiunas et al. [3] used the method based on negative pressure wave, utilizing the pressure data measured at one location along the pipe, and the timing of the initial and reflected transient waves tech.scichina.com
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induced by the leaks determines the location of the leak. This method relies on the fact that the pressure wave generated by a leak is accompanied by a sudden drop in pressure. Zhang et al. [4] presented a method based on the character of intermittent chaos of the system to detect weak signals under strong noise, also the detecting method relies on negative pressure waves. As the leaks in pipeline may result in damping of transient event, and each leak-induced component is damped differently, Wang et al. [5] used the damping of fluid transient to estimate the leak location. Ghazali et al. [6] used the Hilbert transform and the Hilbert-Huang transform to analyze the instantaneous phase and frequency of the signal for detecting leaks and features. Ferrante and Brunone [7] proposed wavelet analysis to detect leaks, in their work, the leak location was estimated using the discontinuity occurrence in time which can be attributed to the leak reflected pressure wave. Liou [8] used the cross-correlation method to locate the leak position, and besides, Beck et al. [9] employed an analysis technique based on extension of cross-correlating the signal to identify specific pipeline features, they also used it to detect leaks in a network, both around bends and also when the leak was separated from the pressure transducer by junctions. Considering that the conventional leak detection approaches often had to work with explicit mathematical models, Feng and Zhang [10] proposed a leak fault detection method based on discrete incremental clustering (DIC) fuzzy neural network to resolve the problem, it combined advantages of DIC network with fuzzy clustering. Some literatures deal specifically with inverse transient analysis that was proposed by Liggett and Chen [11] and has been used successfully by many others [12, 13]. Inverse transient analysis takes pressure traces recorded in a real system and compares them with those generated by a numerical model of the same system experiencing the identical transient. Numerical aspects of this method that have been employed are algorithmic efficiency [14] and minimization algorithm [15] such as genetic algorithm (GA). However, it is based on the method of characteristics (MOC), thus the errors caused by discretization can lead to big error in the prediction of a leak location [16]. In addition, frequency response techniques have recently been developed for leak detection in pipelines. Mepsha et al. [17, 18] firstly used the frequency response method which is based on the principles of steady-oscillatory flow and the transfer matrix analysis to determine the location and rate of leakage in open loop piping systems, and the method has the potential to detect leaks in real-life pipe systems. Ferrante and Brunone [19] initially observed a similar pattern of decrease in pressure oscillations at the odd harmonics for a single leak in simple pipelines when they compared the experimental transfer function of a pipe with a leak to one without a leak. Covas et al. [20] utilized this leak-induced oscillatory pattern in the system response at the odd harmonics and proposed a method for leak detection based on
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the standing wave difference method, which is used for cable fault location in electrical engineering. In the frequency domain analysis area, Lee et al. [21, 22] proposed two numerical methods for leak detection in simple pipelines, i.e. the inverse resonance method and the peak-sequencing method. An inverse technique in the frequency domain analysis forms the former and the latter uses the relative size of resonance peaks at various odd harmonic frequencies. Besides, they presented a number of formulations for the frequency-domain solution in pipe networks of arbitrary topology and size [23]. It is one of the representative methods that can suit to complex networks. Each of these techniques above has its advantages and disadvantages, and no single method is totally reliable for the accurate detection of a leak in all cases. The frequency response method sometimes requires the periodic operation of a valve and it is not permitted in the practice. On the other hand, both leaks and the effect of unsteady friction in pipeline systems contribute to the damping and aberration of hydraulic transient [24], the applications require transient simulations over an extended or whole period of time [25], so first a relatively accurate simulation of a transient in pipeline is essential for the successful calibration of leakage [16]. A comprehensive review of unsteady friction of a hydraulic transient for the simulation was provided by Bergant et al. [26] and a systematic approach for the characterization of transient flow types and transient event types suggested the instantaneous acceleration-based (IAB) model when considering that unsteady friction can be used to adequately simulate transient flow for certain transient event types such as valve-closure test which is exactly needed in the studies. In this paper, the research focuses on leakage detection in water distribution systems by means of inverse transient method in the pure frequency domain. It consists of identification of the unknown parameters: leak position and size, using observed transient data transformed in frequency domain by Laplace transform. The parameter identification is translated into an optimization problem in which the system’s behaviors is simulated by the IAB model in frequency domain and the difference between the observed and calculated variables is minimized by the GA method. The transient IAB model is totally algebraic analyzed in frequency domain without dealing with differential equations and the transient flow is caused by the sharp closure of the valve from the small dimensionless valve opening which abstain the operation difficulty of other special maneuver. The detection technique is verified in numerical tests and the experimental data. Practical issues and the limits of the proposed methodology are also discussed.
2 Frequency domain analysis The piping system under investigation in the paper is shown in Figure 1 which consists of an upstream constant-head
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reflection time of transient; Tw
LQr is the water inertia gAH r
fL Qr Qr
ka Qr ; M . The above gA H r gDA2 H r linearized equations may be written by Laplace transform:
time constant;
Figure 1
d(h) d(q) M Tw (k 1) s q 0, dx dx
Layout of the single pipeline system.
s h
reservoir and a downstream oscillating valve discharging into the atmosphere. The leak orifice is regarded as the internal boundary condition, so the pipe is made up of pipe 1 and pipe 2 and the leak, xL* is the dimensionless position of leak, given by xL/L, and L is the total length of the pipeline.
(5)
Tw d(q) 0, Tl 2 dx
(6)
where the constant s is referred to as the Laplace variable, and the variable h (q) is the function of x* and s in frequency domain. The specific solutions to the oscillatory head and discharge of eqs. (5) and (6) are
q( x , s) C1er1 x C2 e r2 x ,
2.1
Unsteady flow in frequency domain
The simplified one-dimensional momentum and continuity equations describing unsteady pipe flow above (V
