James A. Liggett

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

Boundary integral equation solutions for solitary wave generation, propagation and run-up

Abstract The boundary integral equation method (BIEM) is developed as a tool for studying two-dimensional, nonlinear water wave problems, including the phenomena of wave generation, propagation and run-up. The wave motions are described by a potential flow theory. Nonlinear free-surface boundary conditions are incorporated in the numerical formulation. Examples are given for either a solitary wave or two successive solitary waves. Special treatment is developed to trace the run-up and run-down along a shoreline. The accuracy of the present scheme is verified by comparing numerical results with experimental data of maximum run-up.

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.

Governing Equations for Free Surface Flows

The best working definition of free surface flow is the following: Free surface flow occurs in a deformable solution region whereby the shape and size of the region is part of the solution. Free surface flow can be either steady or unsteady. In the unsteady mode the shape and size of the solution region is known at the initial time but it changes continually as the solution progresses. In the steady mode the boundaries of the solution region are not known and must be found by some technique. The steady problem — and to some extent the unsteady problem — forms a mathematical enigma: To find a solution, the differential equation must have well defined boundary conditions applied to the boundary of the solution region, but how can the conditions be applied if the location of the boundary is not known?

Flow in Three-Dimensional Fracture Networks Using a Discrete Approach

The flow in a three-dimensional network of discrete fractures is calculated by the boundary element method. The flow in any one fracture is two-dimensional but these fractures may be connected in a three-dimensional network. Alternatively, the same method of calculation (and the same computer program) can compute two-dimensional flow in fractures and the intervening media. The intersections of the fractures present special problems which require the application of “circulation equations” (or “path equations”) for their solutions. Often such circulation equations can be replaced by “generic equations” with acceptable accuracy.

Boundary Integral Equation Method for Free Surface Flow Analysis

As a numerical technique the boundary integral equation method has a number of outstanding advantages. These include: Problems are much easier to set up; it requires less data to define the grid; it is efficient, using less computer time and storage than finite differences and finite elements; approximations are confined to the boundaries giving interior solutions with at least as much accuracy; it has better accuracy than finite differences and finite elements for equal discretization; one can use intuitive grid spacing since derivatives are not approximated; velocities are obtained without inaccurate numerical differentiation; singularities are easily handled; infinite fields are easily handled; universal programs are easy to code; it has geometric flexibility; the grid size is easy to vary; and it can use a variety of approximations to conform to the demands of the problem and the desired degree of continuity. With that list of advantages, it should be a universal method that displaces all other methods. Indeed it would except for one disadvantage: The variety of problems it can solve — or at least the variety of problems it can solve while retaining all those advantages — is small.

Finite-Difference Methods for Shallow Water Flow Analysis

Although finite difference methods have a long and distinguished history of dealing with all kinds of fluid motion, including free surface flows, they have some definite limitations. True free surface flows — those where the solution domain is a part of the solution — are rarely treated by finite differences in modern times. Instead, a boundary integral equation method is used where it is applicable; otherwise, a finite element method is used. Finite differences may not be the best choice of method for multidimensional problems that are not true free surface problems, that is, shallow water theory where the free surface aspect is eliminated by integration in the vertical. The overwhelming use of finite difference methods is in one-dimensional, shallow water problems, which are not true free surface problems. Although methods of solution continue to be developed, the field matured 15 to 20 years ago. Most of the methods can now be found in books such as Chaudhry (1993), Abbott (1979), Abbott and Basco (1989), Fox (1989), Cunge, et al. (1980), and even the early book of Mahmood and Yeyjevich, eds., (1975).