John P. Vítkovský

Experimental verification of the frequency response method for pipeline leak detection

This paper presents an experimental validation of the frequency response method for pipeline leak detection. The presence of a leak within the pipe imposes a periodic pattern on the resonant peaks of the frequency response diagram. This pattern can be used as an indicator of leaks without requiring the “no-leak” benchmark for comparison. In addition to the experimental verification of the technique, important issues, such as the procedure for frequency response extraction and methods for dealing with frequency-dependent friction are considered in this paper. In this study, transient signals are generated by a side-discharge solenoid valve. Non-linearity errors associated with large valve movements can be prevented by a change in the input parameter to the system. The optimum measuring and generating position for two different system boundary configurations—a symmetric and an antisymmetric system—are discussed in the paper and the analytical expression for the leak-induced pattern in these two cases is derived

Parameters affecting water-hammer wave attenuation, shape and timing—Part 1: Mathematical tools

This two-part paper investigates key parameters that may affect the pressurewaveform predicted by the classical theory ofwater-hammer. Shortcomings in the prediction of pressure wave attenuation, shape and timing originate from violation of assumptions made in the derivation of the classical waterhammer equations. Possible mechanisms that may significantly affect pressure waveforms include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction (FSI) effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Engineers should be able to identify and evaluate the influence of these mechanisms, because first these are usually not included in standard water-hammer software packages and second these are often “hidden” in practical systems. Part 1 of the two-part paper describes mathematical tools for modelling the aforementioned mechanisms. The method of characteristics transformation of the classical water-hammer equations is used herein as the basic solution tool. In separate additions: a convolution-based unsteady friction model is explicitly incorporated; discrete vapour and gas cavity models allow cavities to form at computational sections; coupled extended water-hammer and steel-hammer equations describe FSI; viscoelastic behaviour of the pipe-wall material is governed by a generalised Kelvin–Voigt model; and blockages and leakages are modelled as end or internal boundary conditions

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

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.

Field Tests for Leakage, Air Pocket, and Discrete Blockage Detection Using Inverse Transient Analysis in Water Distribution Pipes

Stephens, Mark Leslie; Lambert, Martin Francis; Simpson, Angus Ross; Vitkovsky, John; Nixon, John B. Field tests for leakage, air pocket, and discrete blockage detection using inverse transient analysis in water distribution pipes Critical transitions in water and environmental resources management [electronic resource] : proceedings of the World Water and Environmental Resources Congress : June 27-July 1, 2004, Salt Lake City, UT / sponsored by Environmental and Water Resources Institute (EWRI) of the American Society of Civil Engineers ; Gerald Sehlke, Donald F. Hayes, and David K. Stevens (eds.): pp. 1-10

Quantifying Linearization Error When Modeling Fluid Pipeline Transients Using the Frequency Response Method

The unsteady mass and momentum equations for pipe flow can be solved in the frequency domain and provides additional insight into the behavior of fluid transients. Additionally, this approach has significant computational advantages compared to the method of characteristics because it is not based on a rigid time-space grid. Despite its advantages, the frequency domain approach must be used with care as it uses linearized forms of the steady friction and orifice equations—which can deviate significantly from the true nonlinear solution. The conditions in which the frequency response method can be accurately used are currently unknown. This paper investigates and quantifies the error in the frequency-domain method, via comparison to a highly discretized time-domain model that uses the method of characteristics, and describes situations where the frequency response method can be used with accurate results. A reservoir-pipe-valve system was used in this study with transients generated by perturbation of the valve. The error consists of errors from two sources: the linear approximations of the steady friction and the steady orifice equations. The frequency response method was shown to produce identical results to the method of characteristics when these two sources of error are minimized. The error in the frequency-domain model was quantified as functions of the perturbation magnitude, frequency, and system parameters. The results indicate that errors are significant when the perturbation size is more than 25% of the steady-state condition and this error is frequency dependent with the largest errors occurring at the harmonic peaks of the system.

Leak Detection and Calibration of Water Distribution Systems using Transients and Genetic Algorithms

The use of genetic algorithm optimisation applied to solving engineering problems has gained popularity over the last 10 years. Applications to the design of water distribution systems based on genetic algorithm optimisation first appeared in the early 1990s. This paper starts out with a brief review of the past use of genetic algorithms applied to aspects of water distribution systems. Leak detection and calibration of pipe internal roughnesses in a network are important issues for water authorities around the world. Computer simulation of water distribution systems has become a routine task of water authorities and consultants. One of the big unknowns in developing these models is the condition of the pipes, especially if they are old. It is very difficult to obtain reliable estimates of the roughness height for each pipe in the system using steady state calibration techniques. Liggett and Chen at Cornell University in 1994 developed an innovative technique called the inverse transient technique. The technique is able to determine, from unsteady pressure traces at a number of nodes in the network, the locations and magnitudes of any leaks that are occurring and the friction factor for each pipe in the network. An alternative approach to solving the minimization problem is presented in this paper. Genetic algorithm optimisation is used. A population of solutions is generated with each string representing values of the decision variables that are to be found. These include the magnitudes of leaks at nodes in the network and friction factors for each pipe. A forward transient analysis is performed for each string in the population that represents different combinations of leak magnitudes and friction factors. The sum of the absolute deviations between the measured transient pressures and the pressures predicted by the numerical model are determined and are used to determine the fitness of the string. The smaller the sum of the deviations then the larger the fitness that is assigned to the string. The genetic algorithm operators that are used include tournament selection, crossover and mutation. A new crossover operator is introduced. The genetic algorithm optimisation technique that has been developed in the research is applied to an example network. The results are encouraging and compare favorably with the inverse transient technique.

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 head- formulation. DOI: 10.1061/(ASCE)HY.1943-7900.0000338.

Field Measurements of Unsteady Friction Effects in a Trunk Transmission Pipeline

The relative importance of unsteady friction effects in real pipelines remains a matter of debate. This paper presents the results of a set of field transient measurements on a 13.5 km long trunk transmission water pipeline located in regional South Australia. Modelling has been undertaken using efficient rough pipe turbulent weighting function methods to calculate the unsteady friction contribution. The relative importance of unsteady friction, for no-leak and leak cases, is assessed.

The effect of time–frequency discretization on the accuracy of the transmission line modelling of fluid transients

The operation of the transmission line models requires an input signal in the frequency domain describing the nature of the transient disturbance (for example, a valve closure) and an exact solution of the linearized mass and momentum equations for unsteady pipe flow. The use of the transmission line models does not require a strict adherence to a time–space discretization grid governed by the Courant condition, but it does require that the input signal be discretized in the frequency domain. This paper investigates the errors induced by the discretization of the input signal and provides guidelines for the appropriate selection of discretization size for the linear transmission line models. The accuracy of the model is quantified through comparison with a finely discretisated method of characteristics (MOC) model. The results show that the transmission line models are sensitive to the time–frequency discretization size and unlike the MOC, the appropriate size of the discretization changes depending on the transient event being modelled as well as the energy losses in the system.