Head- and flow-based formulations for frequency domain analysis of fluid transients in arbitrary pipe networks

Applications of frequency-domain analysis in pipelines and pipe networks include resonance analysis, time-domain simulation, and fault detection. Current frequency-domain analysis methods are restricted to series pipelines, single-branching pipelines, and single-loop networks and are not suited to complex networks. This paper presents a number of formulations for the frequency-domain solution in pipe networks of arbitrary topology and size. The formulations focus on the topology of arbitrary networks and do not consider any complex network devices or boundary conditions other than head and flow boundaries. The frequency-domain equations are presented for node elements and pipe elements, which correspond to the continuity of flow at a node and the unsteady flow in a pipe, respectively. Additionally, a pipe-node-pipe and reservoir-pipe pair set of equations are derived. A matrix-based approach is used to display the solution to entire networks in a systematic and powerful way. Three different formulations are derived based on the unknown variables of interest that are to be solved: head-formulation, flow-formulation, and head-flow-formulation. These hold significant analogies to different steady-state network solutions. The frequency-domain models are tested against the method of characteristics (a commonly used time-domain model) with good result. The computational efficiency of each formulation is discussed with the most efficient formulation being the headformulation.John P. Vítkovský; Pedro J. Lee; Aaron C. Zecchin; Angus R. Simpson; and Martin F. Lambert

Discrete blockage detection in pipelines using the frequency response diagram: Numerical study

© 2008 American Society of Civil EngineersThis paper proposes the use of fluid transients as a noninvasive technique for locating blockages in transmission pipelines. By extracting the behavior of the system in the form of a frequency response diagram, discrete blockages within the pipeline were shown to induce an oscillatory pattern on the peaks of this response diagram. This pattern can be related to the location and size of the blockage. A simple analytical expression that can be used to detect, locate, and size discrete blockages is presented, and is shown able to cater for multiple blockages existing simultaneously within the system. The structure of the expression suggests that the proposed technique can be extended to situations where system parameters may not be known to a high accuracy and also to more complex network scenarios, although future studies may be required to verify these possibilities.Pedro J. Lee, John P. Vítkovský, Martin F. Lambert, Angus R. Simpson, and James A. Ligget

Leak location in pipelines using the impulse response function

Current transient-based leak detection methods for pipeline systems often rely on a good understanding of the system—including unsteady friction, pipe roughness, precise geometry and micro considerations such as minor offtakes—in the absence of leaks. Such knowledge constitutes a very high hurdle and, even if known, may be impossible to include in the mathematical equations governing system behavior. An alternative is to test the leak-free system to find precise behavior, obviously a problem if the system is not known to be free of leaks. The leak-free response can be used as a benchmark to compare with behavior of the leaking system. As an alternative, this paper uses the impulse response function (IRF) as a means of leak detection. The IRF provides a unique a relationship between an injected transient event and a measured pressure response from a pipeline. This relationship is based on the physical characteristics of the system and is useful in determining its integrity. Transient responses of completely different shapes can be directly compared using the IRF. The IRF refines all system reflections to sharp pulses, thus promoting greater accuracy in leak location, and allowing leak reflections to be detected without a leak-free benchmark, even when complex signals such as pseudo-random binary signals are injected into the system. Additionally, the IRF approach can be used to improve existing leak detection methods. In experimental tests at the University of Adelaide the IRF approach was able to detect and locate leaks accurately.Pedro J. Lee, John P. Vitkovsky, Martin F. Lambert, Angus R. Simpson and James Ligget

Frequency domain analysis for detecting pipeline leaks

The original publication can be found at http://scitation.aip.org/hyoThis paper introduces leak detection methods that involve the injection of a fluid transient into the pipeline, with the resultant transient trace analyzed in the frequency domain. Two methods of leak detection using the frequency response of the pipeline are proposed. The inverse resonance method involves matching the modeled frequency responses to those observed to determine the leak parameters. The peak-sequencing method determines the region in which the leak is located by comparing the relative sizes between peaks in the frequency response diagram. It was found that a unique pattern was induced on the peaks of the frequency response for each specific location of the leak within the pipeline. The leak location can be determined by matching the observed pattern to patterns generated numerically within a lookup table. The procedure for extracting the linear frequency response diagram, including the optimum measurement position, the effect of unsteady friction, and the way in which the technique can be extended into pipeline networks, are also discussed within the paper.Pedro J. Lee, John P. Vítkovský, Martin F. Lambert, Angus R. Simpson and James A. Ligget

Parameters affecting water-hammer wave attenuation, shape and timing. Part 2: Case studies

This two-part paper investigates parameters that may significantly affect water-hammer wave attenuation, shape and timing. Possible sources that may affect the waveform predicted by classical water-hammer theory include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Part 1 of this two-part paper presents the mathematical tools needed to model these sources. Part 2 of the paper presents a number of case studies showing how these modelled sources affect pressure traces in a simple reservoir-pipeline-valve system. Each case study compares the obtained results with the standard (classical) water-hammer model, from which conclusions are drawn concerning the transient behaviour of real systems.Anton Bergant, Arris S. Tijsseling, John P. Vítkovský, Dídia I. C. Covas, Angus R. Simpson and Martin F. Lamber

Systematic evaluation of one-dimensional unsteady friction models in simple pipelines

In this paper, basic unsteady flow types and transient event types are categorized, and then unsteady friction models are tested for each type of transient event. One important feature of any unsteady friction model is its ability to correctly model frictional dissipation in unsteady flow conditions under a wide a range of possible transient event types. This is of importance to the simulation of transients in pipe networks or pipelines with various devices in which a complex series of unsteady flow types are common. Two common one-dimensional unsteady friction models are considered, namely, the constant coefficient instantaneous acceleration-based model and the convolution-based model. The modified instantaneous acceleration-based model, although an improvement, is shown to fail for certain transient event types. Additionally, numerical errors arising from the approximate implementation of the instantaneous acceleration-based model are determined, suggesting some previous good fits with experimental data are due to numerical error rather than the unsteady friction model. The convolution-based model is successful for all transient event types. Both approaches are tested against experimental data from a laboratory pipeline.John P. Vítkovský, Anton Bergant, Angus R. Simpson and Martin F. Lamber

Single-event leak detection in pipeline using first three resonant responses

Hydraulic transients (water hammer waves) can be used to excite a pressurized pipeline, yielding the frequency response diagram (FRD) of the system. The FRD of a pipeline system is useful for condition assessment and fault detection, because it is closely related to the physical properties of the pipeline. Most previous FRD-based leak detection techniques use the sinusoidal leak-induced pattern recorded on the FRD, either shown on the resonant responses or the antiresonant responses. In contrast, the technique reported in the current paper only uses the responses at the first three resonant frequencies to determine the location and size of a leak. The bandwidth of the excitation only needs to be five times that of the fundamental frequency of the tested pipeline, which is much less than the requirement in conventional FRD-based techniques. Sensitivity analysis and numerical simulations are performed to assess the robustness and applicable range of the proposed leak location technique. The proposed leak location technique is verified by both numerical simulations and by using an experimental FRD obtained from a laboratory pipeline. © 2013 American Society of Civil Engineers.Jinzhe Gong, Martin F. Lambert, Angus R. Simpson, and Aaron C. Zecchi