A stochastic model for the speed of leak noise propagation in plastic water pipes

A good estimate of the speed of leak noise propagation is necessary to pinpoint the location of a leak using acoustic correlators. Models currently exist for this purpose, but they do not consider uncertainties in the pipe geometry and the properties of the pipe and soil. Using the fact that leak noise propagates as a predominantly fluid-borne wave, this paper develops a stochastic model of the speed of leak noise propagation in plastic water distribution pipes that can account for these uncertainties. The model provides confidence limits for the estimate of the wave speed related to the leak noise excitation. It is based on the mean and standard deviation of the pipe geometry as well as the pipe and soil material properties, which have strong influence on the speed in which the leak noise propagates in the pipe. Numerical examples, using parameters from water supply systems found in the field, in which the pipe is made from Medium-Density Polyethylene (MDPE) and Polyvinyl Chloride (PVC) are presented to validate the model. Monte Carlo simulations for both in-air and buried pipes are presented to check the 99.7% confidence interval. To verify that the predictions from the stochastic models give realistic results, they are compared with some measurements from different sites, in which nominal properties and tolerances for the pipe and soil properties are assumed

A Simplified Model of the Ground Surface Vibration Arising from a Leaking Pipe

Acoustic techniques remain the bedrock of pipeline leak detection, particularly for the water industry. The correlation technique, in which leak noise measurements are made at accessible locations on the pipe, either side of the leak, is used world-wide. Unfortunately, especially in the case of plastic pipes, access points are often not spaced closely enough for effective leak detection to take place. An alternative to sensing on the pipe is to measure directly on the ground surface, using discrete sensors such as geophones or accelerometers. However, to do this, the vibrational field on the ground, produced by the leak, needs to be fully understood. The present author, alongside colleagues, has developed an analytical model to show how axisymmetric elastic waves propagating within the pipe radiate to the ground surface. The model, only valid directly above the pipe, shows that, dependent on the soil properties, both a conical shear wave and a conical compressional wave may radiate into the soil, and thence propagate to the ground surface. Moreover, the axial dependence of the ground surface response mirrors the axial dependence of the waves propagating within the pipe. Here, a simplified analytical model of the conical pipe-radiated waves, which encapsulates the essential phase-related features of the more complex development described previously, is presented. This then allows a relatively simple extension to predict the off-axis ground surface as well as that directly above the pipe. Numerical simulations and experimental investigations are also carried out to demonstrate the potentialities of the proposed model to reveal the underlying physics through a simple way

Estimating the spectrum of leak noise in buried plastic water distribution pipes using acoustic or vibration measurements remote from the leak

An appropriate model of leak noise at source is necessary in analytical and numerical approaches to investigate the characteristics of leak noise measured remotely from the leak in buried water pipes. It is extremely difficult to measure leak noise at source in practice, so an inverse method is needed to predict this from measurements made either side of the leak at convenient access points. This paper presents such a method, and illustrates the approach using four data sets from three different test sites. The method requires that the noise propagates in the pipe according to a simple model of wave propagation within the frequency range over which leak noise is detected at the sensors. Using the measured data, the real and imaginary parts of the wavenumber are estimated, and these, together with an estimated position of the leak between the two sensors, the frequency response functions corresponding to the sections of the pipe either side of the leak position are estimated. If pressure measurements are made, then both the level and shape of the leak noise spectrum can be estimated, but if accelerometers are used then only an estimate of the shape of the spectrum is possible. From the measurements presented, it is found that it is not possible to state categorically that the leak noise spectra decays according to a particular frequency power law. There is some evidence that it decays with a frequency power law of , which agrees with previous laboratory based experiments, but this is not definitive in all cases

An investigation into the physical mechanisms of leak noise propagation in buried plastic water pipes: a wave dynamic stiffness approach

In buried plastic water pipes, the predominantly fluid-borne wave is of particular interest, as it plays a key role in the propagation of leak noise. Consequently, it has been studied by several researchers to determine the speed of wave propagation and its attenuation with distance. These features are encapsulated in the wavenumber. By examining the factors that govern the behaviour of this wavenumber, this paper presents an in-depth examination of the physical mechanisms of leak noise propagation. To achieve this, an alternative physics-based model for the wavenumber is developed, using the concept of the wave dynamic stiffnesses of the individual components within the pipe system, i.e., the water in the pipe, the pipe wall, and the surrounding medium. This facilitates a clear interpretation of the wave behaviour in terms of the physical properties of the system, especially the interface between the pipe and the surrounding medium, which can have a profound influence on the leakage of acoustic energy from the pipe wall into the external medium. Three systems with different types of surrounding medium are studied, and the factors that govern leak noise propagation in each case are identified. Experimental results on two distinct test sites from different parts of the world are provided to validate the approach using leak noise as an excitation mechanism

An investigation into the factors affecting the bandwidth of measured leak noise in buried plastic water pipes

Inspection and preservation of buried water pipelines is of importance in the modern world. The wastage of water due to leaks is a global problem and existing technologies/methods to detect leaks in buried pipelines still face challenges, such as how to predict the bandwidth of measured leak noise using acoustic correlators, and what are the main factors affecting this frequency range. The leak noise bandwidth is useful information for operators to know before carrying out tests in the field, and currently there is no practical way of predicting this frequency range. This paper presents an approach to predict the bandwidth and investigates the main factors affecting it such as the distance between the sensors, wave speed and attenuation of the fluid-dominated wave, which is the main carrier of leak noise. To achieve this, a water-pipe-soil-sensor model is represented in terms of filters, allowing an investigation into the corresponding physical/geometric characteristics that affect the bandwidth of the measured leak noise. It is shown that the dominant factors are the material and geometry of the pipe, the properties of the surrounding soil and the type of transducer used

Key Factors That Influence the Frequency Range of Measured Leak Noise in Buried Plastic Water Pipes: Theory and Experiment

The frequency range of the leak noise in buried water pipes, measured using acoustic correlators, depends significantly on the type of pipe and its location as well as the type of sensors used. Having a rough idea of this frequency range can be beneficial for operators prior to conducting tests; however, there is currently no method of predicting it except through practical experience, and no model-based approach yet exists. This issue is addressed in the present paper by using a concise and relatively simple analytical model of the water-pipe–soil system combined with the sensors’ frequency response. The influence of the various physical parameters of the system, such as the pipe and soil properties and the sensor type, on the cross-power spectral density (CPSD) of leak noise signals and, furthermore, the frequency range are investigated. The main factors that affect the bandwidth are the distance between the sensors, wave speed of the predominantly fluid-borne wave in the pipe and the attenuation of this wave. It is shown that the external medium has a profound effect on the propagation and, in turn, on the bandwidth. The approach to predicting this bandwidth is validated using experimental data from three different test sites

Key factors that influence the frequency range of measured leak noise in buried plastic water pipes: theory and experiment

The frequency range of the leak noise in buried water pipes, measured using acoustic correlators, depends significantly on the type of pipe and its location as well as the type of sensors used. Having a rough idea of this frequency range can be beneficial for operators prior to conducting tests; however, there is currently no method of predicting it except through practical experience, and no model-based approach yet exists. This issue is addressed in the present paper by using a concise and relatively simple analytical model of the water-pipe–soil system combined with the sensors’ frequency response. The influence of the various physical parameters of the system, such as the pipe and soil properties and the sensor type, on the cross-power spectral density (CPSD) of leak noise signals and, furthermore, the frequency range are investigated. The main factors that affect the bandwidth are the distance between the sensors, wave speed of the predominantly fluid-borne wave in the pipe and the attenuation of this wave. It is shown that the external medium has a profound effect on the propagation and, in turn, on the bandwidth. The approach to predicting this bandwidth is validated using experimental data from three different test sites