**LEAK DETECTION IN PIPELINES THROUGH SPECTRAL ANALYSIS OF PRESSURE SIGNALS**

**A.L. Souza, S.L.Cruz and J.F.R. Pereira **DESQ/FEQ/UNICAMP, Caixa Postal 6066, 13083-970,

Campinas - São Paulo, Brasil,

E-mail: arlan@desq.feq.unicamp.br

*(Received: November 10, 1999 ; Accepted: April 06, 2000)*

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Abstract- The development and test of a technique for leak detection in pipelines is presented. The technique is based on the spectral analysis of pressure signals measured in pipeline sections where the formation of stationary waves is favoured, allowing leakage detection during the start/stop of pumps. Experimental tests were performed in a 1250 m long pipeline for various operational conditions of the pipeline (liquid flow rate and leakage configuration). Pressure transients were obtained by four transducers connected to a PC computer. The obtained results show that the spectral analysis of pressure transients, together with the knowledge of reflection points provide a simple and efficient way of identifying leaks during the start/stop of pumps in pipelines.

Keywords: leak detection, pressure wave propagation, spectral analysis.

**INTRODUCTION**

When a leak occurs in a pipeline a pressure wave will propagate through the pipeline, upstream and downstream relatively to the leak position. The detection and analysis of pressure transients generated by leak occurrence together with the measured pressure wave velocity, allow the detection and location of leaks in pipelines, as it is demonstrated by Silva et al. (1996).

Silva et al. (1996) detected and located leaks in a 1250 m long pipeline operating under steady-state conditions. The detection was based on the analysis of pressure transients through on-line computer techniques. The pressure transient profiles generated by leak occurrence presented a sudden drop in pressure, followed by a certain recovery, which depended on liquid flow rate and leak magnitude. Leaks as small as 5 % of the nominal liquid flow were readily detected and located with an error smaller than 5 metres.

In the cases where stronger transients occurs simultaneously with the transient generated by leak occurrence, as it happens in a sudden interruption of the pumping system, the direct analysis of the pressure signals can not be applied for leak detection. The pressure variation caused by the leak will be masqueraded by stronger variations caused by the flow interruption. Unfortunately, the cases in which strong transients are involved, are those with the greatest probability of rupture, since the pipeline is exposed to great mechanical efforts.

Jönsson and Larson (1992) studied the characteristics of pressure wave propagation in a 5040 m long drinking water pipeline, after pump stop both with and without leak occurrence. The pipeline system had a constant head reservoir at de upstream and a check valve at the downstream end. Leaks with a maximum magnitude of 7 % of the nominal liquid flow were simulated at a distance of 1450 m from the reservoir. Pressure measurements were carried out after pump stop to quantify the effect of the leak on pressure variations. By applying spectral analysis to the measured pressure time series, that is, by changing the time domain signal to frequency domain leak detection was possible through the identification of reflected wave from the leak. The existence of a total reflection point (the check valve) guaranteed the formation of stationary waves between the valve and the leak and, consequently, the appearance of the associated pipeline section frequency in the spectrum. In the absence of total reflection points, however, the reflected waves would have less intensity and the formation of strong stationary waves would be restricted to leaks located around the reflection points.

In this work a leak detection technique based on the spectral analysis of pressure signals has been developed and tested under conditions where pipeline rupture occurs during the start or stop of a centrifugal pump. The main purpose of the experiments was to reproduce situations that could lead to pipeline rupture as sudden stop of pumping system due to electric energy cut off, which generates alternating depressuring and pressuring in small intervals of time, or the start of a pump without adequate adjustment in the discharge valve, subjecting the pipeline to peaks of pressure. The detection of this type of faults, requires a quick analysis of the dynamic of a leak.

**LEAK DETECTION METHODOLOGY**

Ruptures in pipelines give rise to pressure waves that propagate throughout the hydraulic system. In addition, waves that propagate in the opposite direction due to the presence of reflection points such as valves, reservoirs, curves and bifurcation, are also generated (William-Louis and Tournier, 1996).

The superposition of these waves propagating in opposite directions between two reflection points gives rise to stationary waves which are characterised by variation of the amplitude of pressure oscillation from point to point along pipe length. There are points, nodes, in which the pressure does not change - zero amplitude. Between nodes, the pressure oscillates with the same frequency, but different amplitudes. The oscillation amplitude reaches a maximum in the middle point between nodes - the antinodes.

The oscillation frequency f_{1} is defined by the wave propagation velocity v and by the distance l between the reflection points. Other frequencies, multiples of f_{1}, can also appear in the stationary wave spectrum and are known as harmonics. The fundamental frequency f_{1} is the first harmonic, f_{2} = 2f_{1} the second harmonic and so on.

For pipeline sections having the ends closed, the fundamental frequency as well as its harmonics are given by (Kinsler, 1982):

(i = 1, 2, 3, ...) |
(1) |

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The ends of the pipeline sections constitute pressure nodes.

Open ends are also considered as reflection points. For cases where both ends are open, the oscillation frequencies are also given by the Eq. 1. When one end is open and the other closed, the frequencies are calculated through Eq. 2:

(i = 1, 2, 3, ...) |
(2) |

where, only the odd harmonics are present in the frequency spectrum.

The analysis presented above is extremely simplified and many factors that would contribute to deviations of the theoretical results were not taken into account as, for instance, the weakening of the pressure waves due to friction and roughness of pipeline walls. It is also true that hydraulic transients do not occur in an isolated way, but in a complex superposition of many of them. In this way, the direct analysis of pressure profiles to reveal its spectrum in a pipeline would not be adequate. In the following, the tools that allow the identification of frequencies of these complex signals spectrum will be presented.

Consider p(t) as the temporal function representing the pressure in a given point in the pipeline. Sampling the p(t) function, or the pressure signals, in time intervals equal to T, provides a sequence of values p[n] in a way that the k-th element is given by p[k] = p(kT). p[n] can be expressed as the sum of sinusoid sequences of different frequencies. The Discrete Fourier Transform (DFT) is one of the mathematical tools available to find out the sinusoid sequences that must be taken in order to obtain the original sequence p[n]. Through the DFT, the same information contained in p[n], which is in the time domain, can be expressed in the frequency domain by a new sequence P[n], the Discrete Fourier Transform of sequence p[n]. The inter-conversion between the two domains may be obtained by the following expressions (Oppenheim and Schafer, 1989):

(3) |

(4) |

where N is the total number of sampled points, and .

The Discrete Fourier Transform is implemented in digital computers through the algorithm called Fast Fourier Transform (FFT), allowing the calculation of the signals spectrum much more rapidly than the direct calculation through Eq. 3. For transitory signals, that is, with finite duration of time, the frequency spectrum is better expressed in terms of the Energy Spectral Density (ESD) (Arruda, 1999), which is defined as the square of the absolute values of the DFT coefficients, the result being m8ultiplied by the square of the total sampling time.

The strategy proposed in this work for the detection of leaks consists of monitoring the pressure signals spectrum through ESD, sampled in pipeline sections limited by nearly placed reflection points. The appearance of stationary waves in the test section indicates rupture in the pipeline.

**EXPERIMENTAL WORK**

^{o}short elbows. Water circulates in a closed loop from a constant head reservoir, being introduced in the pipeline through a 3 Hp centrifugal pump.

Pressure measurements were obtained trough four transducers located at 494 m, 744 m, 994 m and 1244 m from the entrance of the pipeline (see Table 1). In order to simulate leaks, side outlets fitted with solenoid valves were installed at 250 m and 750 m from the entrance. Each solenoid valve was coupled to a gate valve in order to control the leak flow rate. The pressure transducers and the solenoid valves were connected to a PC computer equipped with 12 bits A/D converter.

]]> Experiments were performed for liquid flow rates corresponding to Reynolds numbers of 6000, 12000 and 15000. The magnitude of simulated leaks corresponded to 10 and 50 % of the nominal liquid flow (under steady state). Pressure measurements were obtained through a data acquisition system during the start or the interruption of pumping. In the experiments with leak occurrence, the leak was provoked 5 s after pump start-up or shut-down. In each experiment, a total of 8000 points per channel were acquired.

Since the pipeline system was composed of a bundle of 17.66 m long tubes connected by 90^{o} short elbows, which resulted in five layers of tubes of 14 segments each, the formation of stationary waves were favoured. With that configuration, 70 reflection zones were available to be used as test sections. Only four of them were used, the ones which had installed pressure transducers.

**SIGNAL CONDITIONING**

In PVC pipelines, the pressure wave propagation velocity is approximately 500 m/s (Hunaidi and Chu, 1999). By applying Eq. 3 one obtains that the frequency in a 17.66 m long section were the pressure wave propagates at 500 m/s is 14 Hz.

In the test pipeline (Fig. 1) the signal coming from the transducers were directly sent to the AD converter. The sampling frequency f_{s} was 550 Hz. Anti-aliasing analogue filters were not used, as it was believed that the spectrum aliasing around f_{s}/2 (Nyquist frequency) would not interfere in the range of interest (below 50 Hz and about 14 Hz).

In its digital form, the pressure signal was treated in two distinct ways. It was transformed to frequency domain via FFT, being processed, beforehand, by a backward difference filter. In this filter, the n-th output value was given by y[n] = x[n]-x[n-1], where x[n] is the n-th value of the input sequence. In this way, the pressure signal became a transitory signal (time limited or square integrated), in a form adequate to the calculation of its energy spectral density. This procedure did not interfere with the spectral content of the signal. It is possible to demonstrate that the DFT of the input sequence x[n] of a backward difference filter is equal to the DFT of the output sequence y[n], diverging only in amplitude. Alternatively, the signal went through a band-pass digital filter with pass band between 10 and 20 Hz, allowing the frequency range of interest (14 Hz) to be isolated.

]]>**RESULTS AND ANALYSIS**

Figure 2 shows the pressure transient obtained after pump start-up, with and without leak and the same signal expressed in the frequency domain through its ESD. The pipeline was operated with Re number of 12000 and the pressure transient profile was determined through the transducer T1 (494 m from the entrance). In the experiments with leak occurrence, the leak magnitude was 10 % and situated at 750 m from the entrance of the pipeline. Pressure profiles shown in Fig. 2a and 2c were very similar so that it was not possible to easily identify leak occurrence at 8 s on Fig. 2c. On the other hand, Fig. 2b and 2d show clearly different ESD profiles obtained with and without leaking, especially in the region between 15 Hz and 20 Hz. Although the theoretical expected frequency was 14 Hz, the 10 % leak generated frequency oscillations of approximately 17 Hz.

Similar results were obtained after stop of the pump. As it is shown in Fig. 3 the pressure signals in time domain (Fig. 3a and 3c) were very similar, except for the higher noise level on Fig. 3c. The oscillations generated by the leak can be poorly identified at 6 s on Fig. 3c. Once again, the ESD profiles (Fig. 3b and 3d) clearly show leak occurrence with a frequency of about 12 Hz on Fig. 3d. The pipeline was operated with Re number of 12000 and the pressure transient profile was determined through the transducer T4 (1244 m from the entrance). In the experiments with leak occurrence, the leak magnitude was 10 % and its position at 750 m from the entrance of the pipeline.

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It is worth noticing the different scales obtained in the plots on Figs. 2 and 3, in the time domain as well as in the frequency domain. The measured pressure on Fig. 2 is significantly higher because transducer T1 is nearer to the pump than transducer T4.

A clearer way to identify the leak would be the restriction of the temporal signal spectrum around the frequency of interest, 14 Hz. Figure 4 shows again the four time signals presented in Figs. 2 and 3 after they were processed by a band-pass Butterworth digital filter of 3^{rd} order with a pass band going through 10 Hz and 20 Hz. Now, the oscillations generated by the leak, that were masqueraded by the signals in time domain on Figs. 2 and 3 are sharply identified.

Figure 5 shows the calculated standard deviation for groups of 500 points corresponding to intervals of approximately 0.9 s on the curves on Fig. 4. A maximum standard deviation value could be used as a condition for which an alarm could go off in the occurrence of leak.

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In the experiments in which the leak had a magnitude of 50 %, the differences between the pressure obtained with and without leak were more pronounced, since the generated waves had greater magnitude.

Experiments were also carried out where leak occurred simultaneously with the start or the stop of the pump. The practical relevance of the experiments of pump stop is small, since there would be no reason for pipeline rupture at the moment of shut-down. On the contrary, the start of the pumping system with a leak already present in the pipeline may happen mainly in long time inactive systems, which are commissioned without adequate inspection. Figure 6 shows the results of leak detection obtained during pump start and pump stop, under operational conditions corresponding to Re = 6000 for pump start (Fig. 6a) and to Re = 15000 for pump stop (Fig. 6b), when a 10 % leak occurred at 750 m from the entrance. Pressure signals were obtained through transducer T2 (744 m from the entrance). Once again, the oscillations generated by the leak can be readily identified.

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**CONCLUSIONS**

In this work a technique for leak detection in pipelines based on the spectral analysis of pressure signals has been developed and tested. Experimental tests were performed in a 1250 m long pipeline for various operational conditions of the pipeline (liquid flow rate and leakage configuration) during the start/stop of a pump. The obtained results show that the spectral analysis of pressure transients, together with the knowledge of reflection points provide a simple and efficient way of identifying leaks in pipelines.

**ACKNOWLEDGMENT**

** **Arlan Lucas de Souza is grateful to Tom Irvine (http://www.vibrationdata.com) for his comments and suggestions.

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**NOMENCLATURE**

DFT | Discrete Fourier Transform |

ESD | Energy Spectral Density mH_{2}O^{2 }s/Hz |

f | frequency Hz |

FFT | Fast Fourier Tranform |

l | distance between reflection points m |

N | number of samples |

p | pressure m H_{2}O |

P | pressure signal in frequency domain (ESD) mH_{2}O^{2 }s/Hz |

t | time s |

T | sample period s |

v | pressure wave velocity m/s |

**REFERENCES**

Arruda, J. R., "Comparando Laranjas com Bananas", Acústica e Vibrações, no. 23, 10-14, (1999). [ Links ]

Hunaidi, O. and Chu, W. T., "Acoustical Characteristics of Leak Signals in Plastic Water Distribution Pipes", Applied Acoustics, 58, 235-254, (1999). [ Links ]

Jonsson, L. and Larson, M., "Leak Detection through Hydraulic Transient Analysis", Pipeline Systems, Kluwer Academic Publishers, Dordrecht, Holanda, (1992). [ Links ]

Kinsler, L., Fundamentals of Acoustics, John Wiley & Sons, New York, (1982). [ Links ]

Oppenheim, A. V. and Schafer, R. W., Discrete-Time Signal Processing, Prentice-Hall Inc., New Jersey, (1989). [ Links ]

Silva, R. A., Buiatti, C. M., Cruz, S. L. and Pereira, J. A. F. R., "Pressure Wave Behaviour and Leak Detection in Pipelines", Computers and Chemical Engineering, 20, S491-S496, (1996). [ Links ]

William-Louis, M. J. P. and Tournier, C., "Calculation of Pressure Wave Propagation through a Pipeline Junction", Proc. Instn. Mech. Engrs., 210, pp. 239-244, (1996). [ Links ] ]]>