Water-Hammer Method (Transient)

As explained earlier in the introduction chapter, the water hammer phenomenon produces waves, which travel at the speed of sound inside the conduit [12, 13]. When measuring the pressure at one point, it will be noticed that the pressure will oscillate between a range of values until, after a certain time, it reaches the steady state. The pressure waves attenuate because of pipe characteristics. It has been found that by developing a robust numerical model of the studied system and accurate measurements, the system features could be defined as changes in the cross-sectional area, blockage, topography and other characteristics [22, 35-39]. One of these features which affects the pressure wave is the leakage [38, 40, 41].

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In the following section, the water-hammer phenomenon will be critically analysed and discussed in further detail. Different approaches will be demonstrated by describing several works in this field. Also, some research studies which used the water hammer phenomena as a method to detect singularities, including leakage, will be demonstrated.

Before demonstrating the contribution of leak detection by this method, it is necessary to refer to three tools that are fundamental to achieving an approach to find new leak detecting techniques which can represent the system robustly and can be used in combination to avoid some limitations of each one, and to apply the transient leak detection method. These three tools are: numerical modelling, data from experimental rigs and signal processing. The following sections present a definition of each tool, its implementations, limitations and significant features.

a) Numerical Modelling

The response of any physical system which is described by mathematical equations for defined boundary condition can be predicted. Such a mathematical models could include the following equations: conservation of mass, conservation of momentum, first or second thermodynamic laws and equation of state. As a result, some variables will be constant, and some will be a function of other variables like time or space thus providing differential equations. Consequently, the governing equations will be ordinary differential equations with one or more unknown variables. Kreyszic [42] summarises the modelling process in three steps: firstly, converting the physical system into mathematical formulae; then, solving those equations; and finally, evaluating the outcomes. While the second step is fundamentally a process which can be done on a computer (PC), the first and the final steps are completely dependent on human experience and expert knowledge.

More specifically, some issues have been raised by researchers about modelling hydraulic transients and these include the boundary conditions or other parameters. For instance, Kosstaz [43] used the steady state to adjust the friction

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losses. He also recommended that to detect leaks, the model should be tuned to adjust some parameters like pipe thickness. Another major issue in leak detection and fluid transient modelling is the acoustic speed. Some researchers have measured the actual speed from the studied system [44]. Conversely, Vardy [24] estimated it to find the difference in the cross-sectional area and the system friction factor. Furthermore, Liou [45] limited the uncertainties that are produced from pumps by refraining from modelling this. Stoianov [27] took the pressure values directly from a file, thereby making the numerical solution easier to handle. Liou & Tian [46], meanwhile, took the pump discharge pressure and other boundary conditions directly from the Supervisory Control and Data Acquisition System (SCADA). They mentioned an important weakness of the water-hammer technique, namely, that is, in the case of high friction or of high inlet Mach number: the outcomes will not be as accurate. This point is critical as it is could be applicable to the field system in this study.

b) Experimental Measurements

Generally, an experimental rig gives a well-controlled environment to test many approaches when the researcher is trying to pilot or test a method before applying it in the real field. The flexibility of the laboratory apparatus allows for a variety of modifications and it is not expensive compared with field trials. Also, in large networks like a research field system, the errors in numerical models can be significant [2]. So a scaled experimental rig will enhance the study’s results. However, some techniques can be followed to mimic the field system, such as using the dimensionless parameters. The similarity can be divided into three categories: geometry, kinetic and dynamic [15]. The geometry similarity can be controlled by the scale factor between the real system and the rig components. The kinetic similarity is the motion similarity, and the dynamic is the forces’ similarity. Some useful dimensionless figures can be used in the rig design. As an example, the dimensionless Reynolds Number (𝑅𝑒) ( 4-3) measures the ratio between the inertia and viscous forces and the Euler number (𝐸) ( 4-6) is a factor between the drop in pressure and the kinetic energy.

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c) Digital Signal Processing

Features such as leaks or blockages in a fluid system create a discontinuity that produces a reflected wave [47]. Digital signal processing gives a powerful tool for analysing the signals collected from the field by using appropriate processes to select the desirable parameters. Cross-correlation and Cepstrum Analysis are two example approaches to analyse the collected signals. The former measures similarity of two signals and it is commonly used to find the time lag between the signals [27, 39]; hence, it can identify any spikes on the measurements despite its accuracy limitations. Most studies were implemented to compare the two signals at the same point between two systems, for example with/without leak. The second approach, Cepstrum Analysis, involves the Fourier transform of the logarithm of the Fourier Transform [47, 48] and it is used in water-hammer phenomena to avoid the dispersion of the wave [47], which is an obstacle when applying this technique in the field. The power of these tools as techniques for analysing the collected signals is obvious [49].

On the other hand, signal noise or uncertainties represent a major factor that limits the signal processing technique [2]. The noise sources are the transducers, data acquisition system and the hydraulic conditions. This noise can be monitored for a reasonable time period to account for each value or variation in reading when collecting data. So, applying the signal processing in combination with good error analysis can greatly improve the accuracy of this leak detection technique. One such realistic method is wavelet transform (WT) [19, 50, 51]. This method employs time or frequency scale transforms for de-noising, compression and extraction of the signal. Both the rapid and gradual signal deviations can be monitored by WT when measuring the hydraulic variables.