A Transient-Based Analysis of a Leak in a Junction of a Series Pipe System: Mathematical Development and Numerical Modeling

In this paper, a numerical model is proposed to simulate the effect of a leak occurring at a pipe junction. The developed model, based on the method of characteristics, considers both hydraulic singularities, the leak and the junction, as superposed boundary conditions located in the same section. Obtained results representing the temporal evolution of pressure signals have allowed for locating the leak through the separation of its effect from that of the junction. For testing purposes, the transient was created by a sudden closure of a downstream valve in a reservoir-two series pipe-valve system. The novel proposed approach has proven its usefulness on locating and sizing the leak through detailed test cases. In sizing the leak, better accuracy is obtained when using the maximum pressure head reached by the incident wave before encountering the leaky junction instead of that of the transmitted wave through the leak. On the other hand, for the localization of the leak, rather than looking for an equivalent characteristic period of the two-pipe system, it was shown that the characteristic period of the pipe connected to the reservoir, once incorporated into the localization formula, leads to precise results with minimal uncertainty. For the piping system, two cases of configuration, viz. expansion and shrinkage (narrowing), were tested. In general, using the proposed approach, the maximum uncertainty values for the sizing and localization of a leak in the junction are 0.1513% and 1.09%, respectively. Additionally, the friction effect on the localization and sizing of the leak at the junction was investigated to conclude that the friction does not significantly affect the precision of the numerically obtained results for the sizing and localization of the leak at the junction.