Determination of acoustic speed for improving leak detection and location in gas pipelines

Abstract

The commonly used cross-correlation technique for leak location requires that the acoustic speed is known and invariable. In practice, the gas leakage-induced acoustic waves propagate along multiple paths including in-pipe gas and pipe wall, and the acoustic waves in different transmission paths exhibit different acoustic speeds and different dispersive behaviors, which bring a great challenge for leak detection and location in the gas pipelines. In this study, based on the vibration theory of cylindrical elastic thin shell, the wavenumber formulae in different transmission paths are derived to predict the acoustic speeds and the acoustical coupling between the in-pipe gas and the pipe wall is analyzed to determine the dominant transmission path. In addition, the velocity dispersions in the dominant transmission path are suppressed by selection of a characteristic frequency band of the gas leakage-induced acoustic waves. The theoretical predictions are verified in the experiment and the results show that the theoretical acoustic speed is slightly larger than the measured acoustic speed. Thus, the theoretical acoustic speed formula is modified considering the effect of the structural loss factor and consequently the location error using the modified acoustic speed is reduced by two times compared to that using the theoretical acoustic speed.

Localization of CO2 leakage from transportation pipelines through low frequency acoustic emission detection

“…The speeds of the AE waves can usually be acquired by querying the technical manual of the pipeline [23]. However, due to the complex design and structure of the pipeline, the speed of AE wave can change along the pipeline even when the same material is used for the entire pipeline [24]. Therefore, the speed measurement should take into consideration the influence of both pipe materials including its inhomogeneity and the structure of the pipeline.…”

A Modified Leakage Localization Method Using Multilayer Perceptron Neural Networks in a Pressurized Gas Pipe

“…The energy of the AE signal reduces as the propagation distance increases due to geometric spreading, structural scattering, and energy absorption [14]. The weakening effect of the pipe on AE signals is similar with the low-pass filter [10], in that the cut-off frequency decreases as the propagation distance increases. When the AE signals propagate in one direction along the pipe wall, the energy attenuation of the AE signal can be described by an exponential decay [31]:…”

“…If Ψ g (ω) = 1, the Dirac delta function δ (τ + d) delayed by d will be broadened by S ss (ω), H 1 (ω) and H 2 (ω) [25]. In fact, S ss (ω) is often unknown as it depends on the leakage aperture, the gas pressure difference between inside and outside the pipe [10], etc. However, H 1 (ω) and H 2 (ω) can be obtained by the impulse response method [26], and can be calculated by using:…”

“…The prerequisite for the latter methods is that the wave speed is a known constant; however, the wave speed varies as a function of frequency due to the group speed dispersion nature of gas-leakage-induced guided waves [9]. To determine the speed of the AE signal, Li et al [10] derived the wavenumber formulae to predict the wave speeds, and thereby halved the location error compared to that using the theoretical wave speed. Davoodi and Mostafapour [11] derived the motion equation of the pipe for the simply supported boundary condition by the standard form of Donnell's nonlinear cylindrical shell theory.…”

“…Figure 11 shows the power spectral densities of the leakage-induced signals collected at the distances of 1 m and 2 m away from the simulated leak source. The center frequency of a leak-induced signal is proportional to the gas jet velocity and inversely proportional to the leakage aperture [10], and is also related to the resonant frequency of the sensor and the propagation distance between the leak and the sensor. As shown in Figure 11, the amplitude of the power spectral density decreases with increasing propagation distance.…”