Frequency Domain Analysis for Detecting Pipeline Leaks

This 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.     

Address-Oriented Impedance Matrix Method for Generic Calibration of Heterogeneous Pipe Network Systems

The generic evaluation of pipeline parameters is one of the most demanding technological tasks in the efficient management of a water distribution system. Information about current pipeline status is feasible by monitoring the pressure variation online. Conventional methods of transient computation and parameter calibration for a heterogeneous pipeline network suffer from cost issues both in time and storage as well as several other constraints associated with the numerical representation of a real-life system. As an alternative approach, an extension of the impulse response method, namely the address-oriented impedance matrix method (AOIMM), has been developed for a more robust calibration of a heterogeneous and multilooped pipe network system. The genetic algorithm was incorporated into the AOIMM for generic calibration of several parameters, such as the location and quantity of leakage, friction factor, and wave propagation speed. The potential of the proposed calibration algorithm over other conventional approaches was demonstrated when it was applied to a hypothetical heterogeneous pipe network system.     

Numerical Sensitivity Study of Unsteady Friction in Simple Systems with External Flows

This paper investigates the importance of unsteady friction effects when performing water hammer analyses for pipe systems with external fluxes due to demands, leaks, and other system elements. The transient energy equation for a system containing an orifice-type external flow is derived from the two-dimensional, axial momentum equation. A quasi-two-dimensional flow model is used to evaluate the relative energy contribution of total friction, unsteady friction, and the external flow, in a 1,500?m pipeline, with orifice flows ranging from steady-state flows of 2–70% of the mean pipe flow, and a Reynolds number of 600,000. It is found that for initial lateral flows larger than around 30% of the mean flow, unsteady friction effects can probably be neglected, whereas for external flows smaller than this, unsteady friction should generally be considered. Overall, the relative role of unsteady friction is found to diminish as the external flux increases, implying that unsteady friction is not critical for systems with large external flows. These results imply that unsteady friction may have a significant impact on the validity of transient leak detection techniques that have been derived assuming quasi-steady friction. To demonstrate this point, an existing transient leak detection method, originally derived under quasi-steady conditions, is tested with unsteady friction included.     

Standing Wave Difference Method for Leak Detection in Pipeline Systems

The current paper focuses on leakage detection in pipe systems by means of the standing wave difference method (SWDM) used for cable fault location in electrical engineering. This method is based on the generation of a steady-oscillatory flow in a pipe system, by the sinusoidal maneuver of a valve, and the analysis of the frequency response of the system for a certain range of oscillatory frequencies. The SWDM is applied to several configurations of pipe systems with different leak locations and sizes. A leak creates a resonance effect in the pressure signal with a secondary superimposed standing wave. The pressure measurement and the spectral analysis of the maximum pressure amplitude at the excitation site enable the identification of the leak frequencies and, consequently, the estimation of the leak approximate location. Practical difficulties of implementation of this technique in real life systems are discussed.     

Range of Validity of the Transient Damping Leakage Detection Method

In a recent paper, an elegant, efficient, and easy to apply transient-based leakage detection method was proposed. The method exploits the fact that friction and leakage damp the modes of transient waves in a different manner. The method involves six major assumptions. These are: (1) the periodic motion in time of each mode is linearly independent of all other modes; (2) the amplitude of the induced transient is small; (3) the magnitude of the leak is small in comparison with the flow rate; (4) the wall friction can be represented by the Darcy–Weisbach equation; (5) the transient is initiated by an instantaneous small amplitude disturbance; and (6) the pipe system is a simple reservoir–pipe–valve type system or reservoir–pipe–reservoir type system. These six assumptions are relaxed and the validity of the transient damping method is assessed. The analysis shows that the first four assumptions do not pose any serious restriction to the applicability of the damping rate method provided that the mathematical model, used to generate the transient head trace in the leak-free pipe, accurately represents the frictional damping in the system. On the other hand, Assumptions (5) and (6) restrict the applicability of the method to systems that do not involve internal boundary conditions, such as junctions and pumps, and to transients triggered by impulses whose duration is smaller than the wave travel time. Extension of this method to complex pipe systems requires that the linearized waterhammer equations are solved under more general initial and boundary conditions. In addition, more investigation in relation to the frequency content of the input signal and its importance in leakage detection is warranted. The general framework used to derive the damping rate method has led to an efficient and direct algorithm for identifying leaks and future research should seek ways to adapt this framework to more complex pipe systems.     

Unsteady Friction in Rough Pipes

An energy dissipation model is presented for the computation of unsteady friction losses adapted to smooth-to-rough transition and fully rough pipes. The eddy viscosity model used to compute the Reynolds stresses in turbulent flow is modified to include the effect of roughness, which is considered in the computation of the velocity profiles. The model is tested by comparing the computed transient pressures with measured data from a laboratory test facility and a prototype test. Details of the experimental setup, pressure-head measurements, and valve characteristics during transient flow conditions are presented. The quasi-steady approximation gives an inaccurate prediction of the pressure head history; however, significantly better results are obtained if the unsteady friction effects are included.     

Leak Detection in Pipelines using the Damping of Fluid Transients

Leaks in pipelines contribute to damping of transient events. That fact leads to a method of finding location and magnitude of leaks. Because the problem of transient flow in pipes is nearly linear, the solution of the governing equations can be expressed in terms of a Fourier series. All Fourier components are damped uniformly by steady pipe friction, but each component is damped differently in the presence of a leak. Thus, overall leak-induced damping can be divided into two parts. The magnitude of the damping indicates the size of a leak, whereas different damping ratios of the various Fourier components are used to find the location of a leak. This method does not require rigorous determination and modeling of boundary conditions and transient behavior in the pipeline. The technique is successful in detecting, locating, and quantifying a 0.1% size leak with respect to the cross-sectional area of a pipeline.     

Efficient Inverse Transient Analysis in Series Pipe Systems

Measurement of the changes in heads initiated by a valve closure are used to calibrate the friction factors in a hydraulic system consisting of a series-connected pipeline and a downstream valve joining two reservoirs. The calibration is performed by minimizing the inverse least-squares problem representing the difference between the measured and predicted transient response in the network. The hydraulic transient is modeled using the method of characteristics. Unlike previous approaches, the sensitivity information required for the minimization or error is obtained by direct differentiation of the method of characteristic equations and the valve equation with respect to the friction factors. The sensitivity of the calibration results to the amount of data included in the analysis, the initial friction factor estimates, and modeling and simulated measurement errors is discussed.     

Leak Detection in Pipes by Frequency Response Method

The frequency response method is used to determine the location and rate of leakage in open loop piping systems. A steady-oscillatory flow, produced by the periodic opening and closing of a valve, is analyzed in the frequency domain by using the transfer matrix method, and a frequency response diagram at the valve is developed. For a system with leaks, this diagram has additional resonant pressure amplitude peaks (herein referred to as the secondary pressure amplitude peaks) that are lower than the resonant pressure amplitude peaks (herein called primary amplitude peaks) for the system with no leaks. Several piping systems are successfully analyzed for all practical values of the friction factor to detect and locate individual leaks of up to 0.5% of the mean discharge. The method, requiring the measurement of pressure and discharge fluctuations at only one location, has the potential to detect leaks in real-life pipe systems conveying different types of fluids, such as water, petroleum, and so on.     

A novel method to detect the water leakage from tuyere nose cooling circuit in blast furnace

The water cooled tuyere noses, through which hot blast is blown into the furnace, are exposed to very high temperature region of raceway inside the furnace. As a result the chances of rupture of cooling pipes within the tuyere nose are significantly high. The rupture causes water dripping into the furnace and if it continues and unnoticed for a prolonged period it lowers down the local raceway temperature and thus adversely affects the product hot metal and slag quality. Moreover, with heavy water leakage, there is a danger of explosion; monitoring of the cooling water is therefore essential. Despite the availability of water flow metre at each tuyere it is difficult to identify the leaking tuyere at the early stage unless the rupture size grows bigger and so the leakage. In several cases the furnace is forced to shut down to manually inspect the leakage occurring without prior knowledge of the exact tuyere number. Identification of water leakage at an early stage is therefore necessary to prevent process disturbances due to chilling of the furnace and avoid the unscheduled downtime for tuyere replacement. This paper presents a method to identify the water leakage from tuyere nose cooling circuit in blast furnace and the adverse effect of water leakage on the performance of the blast furnace. A system called water leak detection system is developed for different blast furnaces in Tata Steel Jamshedpur to monitor the water leakage through tuyere nose and identify the exact leaking tuyere based on a dimensionless number called leak detection factor.     

Impulse Response Method for Pipeline Systems Equipped with Water Hammer Protection Devices

Surge protection devices, such as surge tanks and air chambers, have been modeled with the impulse response method for transient analysis of water distribution systems. The lumped inertia model and continuity equation are used to represent nonpipe hydraulic elements. Results of pressure or discharge variations obtained by using the impulse response method and the method of characteristics are in good agreement. The impulse response method provides total pressure and discharge along any pipeline segment by direct integration of the ratio of complex head or complex discharge to a complex downstream discharge, respectively. A modification is proposed so that transition between turbulent and laminar flows can be considered. The representation of hydraulic devices has been incorporated into the impedance matrix method, which was developed for heterogeneous and multilooped pipe network systems. The potential advantages of the proposed method over other conventional approaches were investigated by applying the proposed method to hypothetical pipe network systems.     

Local Balance Unsteady Friction Model

The paper proposes the evaluation of unsteady friction by a one-dimensional local balance model. The model is applied for the case of water hammer in a single pipeline for both the downstream end and upstream end valve, and for both rapid valve closure and opening. The model is based on local balance of the friction force. Comparisons with experimental results show that the model correctly predicts the extreme values of pressure head oscillation, as well as its shape for both rapid valve closure and opening, and then overcomes the limits of previous unsteady friction models based on instantaneous acceleration. As the comparisons with experimental results can be made easily only for pressure oscillations and can be affected by dissipation mechanisms other than friction, the performance of the model is examined also by comparison with the results of a two-dimensional low-Reynolds number k–ε model.     

Numerical Modeling for Hydraulic Resonance in Hydropower Systems Using Impulse Response

An effective numerical method to compute hydraulic resonance in pressurized piping of hydropower systems is presented. For this purpose, the impulse response method is used, i.e., a unit pressure impulse is introduced at the downstream waterway as an exciter. The method of characteristics is used to solve the governing equations for the hydraulic transient and to get the pressure response of the system in the time domain. The discrete Fourier transform is used to compute the frequency response of the system which gives the resonance frequencies in the hydropower plant system. To increase the accuracy of the results, unsteady friction is incorporated into the methodology. The influence of the unsteady friction, wave speed, and power on the pressure response diagram is investigated for the waterway of a multiunit hydropower plant which has been recently installed. Computed results agree very well with those obtained from the standard method of the characteristics.     

New Algorithm for Hydraulic Calculation in Irrigation Laterals

A new approach for solving lateral hydraulic problems in laminar or turbulent flow is presented. The outflow is treated as a discrete variable event by means of Taylor polynomials used to calculate flow rates along the lateral (minimal outflow included). The friction head losses are calculated using the Darcy-Weisbach equation with a nonconstant logarithmic friction factor f. This algorithm allows hydraulic computation for a set of connected laterals (with different pipeline diameter, slope, flow regime, or emitter spacing) if a residual outflow Qr is used. The new approach can be used to calculate flow variation on laterals and submains in trickle or sprinkler irrigation systems without an excessive calculation effort. Results are comparable to those obtained in the literature.     

数字化加热炉煤气和空气压力修正补偿算法及应用

数字化加热炉采用脉冲燃烧控制技术进行控制,与传统的采用比例燃烧控制技术的加热炉相比具有诸多优势。脉冲燃烧控制取消了传统比例控制所需要的流量调节阀和流量孔板等,通过控制煤气和空气主管道的压力来确保各区烧嘴在开启后就能在所设计的额定功率下正常工作。但是,当煤气热值和环境温度等发生变化时,必然会使煤气和空气系统的设计压力在实际生产过程中发生偏离,导致烧嘴功率偏离额定功率。针对此问题笔者提出了修正算法,可对上述因素所造成的压力偏差进行修正和补偿。运行实测结果证明了该算法的正确性和可靠性,同时也为同类加热炉的控制提供了成功的案例。     

Saturated-Unsaturated Flow through Leaky Dams

This research investigated seepage flow through leaky dams using the well known finite-element method. Different areas, locations, and hydraulic conductivities of leaks were examined. An area of leak, equal to 4.4% of the core area, increased the seepage flow through the dam to be about 9.5 times the seepage flow through tight (nonleaky) core. This happened for a dam having a downstream horizontal drainage filter. When the drainage filter did not exist, the increase of flow because of the same area of leak was about seven times the flow through a tight core. When the leak existed at the centerline of the core in the out-of-plane direction, its impact was slightly greater than when it existed at the edge of the core. Moreover, as the location of the leak moved up vertically, its impact was observed to be less. It was also observed that when the leak existed in curtain wall driven into underneath the dam, its impact was not significant compared with the case when it existed in the core.     

2 unusual cutaneous T-cell lymphomas with extracutaneous involvement

The effects of neonatal endotracheal tube (ETT) leakage on inspiratory compliance (Ci) and resistance (Ri) were examined using a lung model with constant compliance. An air leak was created at the end of an ETT. Flow was measured at, above and below the leak by a hot wire anemometer and a pneumotach. Tidal volume (VT) was derived from digitally integrated flow. Pressure was measured at the side port of the ETT adaptors above and below the leak. Percent of air leak (% leak) was defined as the difference between inspiratory volume above (VTa) and below (VTb) the leak divided by VTa and multiplied by 100. Ci and Ri were analyzed conventionally and by linear regression. Percent error of Ci was defined as the difference between inspiratory compliance above the leak (Cia) and below the leak (Cib) divided by Cia and multiplied by 100. The results showed that the inspiratory time (Ti) of the ventilatory setting is the most important factor for determining %leak. Percent error of Ci is in proportion to %leak. The change in inspiratory resistance is complicated, depending on the ventilatory setting, leak site resistance and the method of analysis. This study demonstrates the origin of the computational error in breaths with ETT leakage diagramatically and by use of mathematics. It suggests that air leakage may contribute to a high variability in compliance and resistance measurements.     

Valve Design for Extracting Response Functions from Hydraulic Systems Using Pseudorandom Binary Signals

The analysis of the dynamic response of a pressurized water pipeline system is important for the design and also the integrity monitoring of these systems. An efficient method for summarizing the behavior of a pipeline system is through the determination of their system response functions. These functions can be extracted by injecting a pressure signal with a wide bandwidth that persists over the length of a pipeline system. Unlike electrical and mechanical systems, generating such signals in pressurized water systems is difficult. Valves capable of generating a signal against the system back-pressure often lack the necessary maneuverability to ensure the signal is sharp (and hence with high-frequency content) and the generated transient is often large in amplitude, risking damage to the system. A method for generating a small amplitude transient signal with a wide band of frequencies is desirable. This paper presents the design for a side discharge valve for generating a pseudorandom binary sequence of pressure changes that are of a small magnitude in relation to the steady state head of the pipeline. The pseudorandom pressure sequence is used to provide an estimate of the system response function. The continuous form of the signal allows the amplitude of each individual pulse within the signal to be small while maintaining the same signal bandwidth. The valve has been tested experimentally and was found to provide a good match with the theoretical response of the pipeline. The method provides a practical alternative to frequency sweeping using sinusoidal signals or sharp valve closures for the extraction of the response functions. Once determined, the system response function can be utilized to detect system faults such as leaks and blockages.     

Wavelet-Galerkin Solution to the Water Hammer Equations

In this paper, a wavelet-Galerkin method is utilized to solve the hyperbolic partial differential equations describing transient flow in a simple pipeline. Two wavelets (Haar and Daubechies) are utilized as bases for the Galerkin scheme. The governing equations are solved for the expansion coefficients, which are then used to reconstruct the signal at the downstream end of the pipeline; the computed results are in an excellent agreement with those calculated by using the method of characteristics including laminar or linearized turbulent friction terms. Most importantly, the wavelet-Galerkin approach allows the transient flow equations to be solved directly for the expansion coefficients at a certain level of resolution. This can be used to form the wavelet multiresolution framework that can be utilized for further analysis, such as feature extraction and signal identification.     

填埋场防渗效果检测的重要性分析

在分析填埋场HDPE膜渗漏原因和介绍渗漏检测技术的基础上,对某垃圾填埋场进行了渗漏预测,得出渗漏量占渗滤液总量的3．67％．7LHDPE膜防渗层渗漏检测的重要性,并阐明了渗漏检测和维护修补减少的渗漏污染对应的价值将远大于检测和修补的投资。