Leak Detection in Liquid Pipelines Using Lower Harmonics of Pressure Oscillations

Abstract

A leak detection technique in liquid pipelines is presented in this paper. The governing equations of continuity and momentum are simplified and solved in the frequency domain using the transfer matrix method (TMM). A relationship between the relative leak location and the amplitude of the pressure oscillations is obtained, which depends on the piping system parameters and the amplitude and frequency of the flow oscillation. This relationship is utilized to construct leak detection curves (LDCs), the characteristics of which are discussed briefly. Unlike frequency response diagram (FRD) methods, in which a large number of harmonics is used to predict the leak location, the current approach requires a minimum effort because it uses only the first four harmonics of the flow oscillation. The effect of steady and unsteady friction is discussed. The comparison with the solution in the time domain by the method of characteristics (MOC) shows that the odd harmonic LDCs are slightly overestimated owing to the linearity assumption in the TMM solution. However, the even harmonic LDCs agree closely because the calculations are carried out in the downstream end of the pipeline at which the pressure head oscillations at the even harmonics are much smaller than those at the odd harmonics. The approach is also applied on experimental data from the literature where even harmonic LDCs are used to give four predictions of the actual leak location with estimation errors of 9.3%, 3%, 12.5%, and 0%, respectively. These errors, however, are acceptable in most practical applications.