On well-posedness of the leak localization problem in parallel pipe networks

Abstract

With the advent of integrated sensor technology (smart flow meters and pressure sensors), various new numerical algorithms for leak localization (a core element of water distribution system operation) have been developed. However, there is a lack of theory regarding the limitations of leak localization. In this work, we contribute to the development of such a theory by introducing an example water network structure with parallel pipes that is tractable for analytical treatment. We define the leak localization problem for this structure and show how many sensors and what conditions are needed for the well-posedness of the problem. We present a formula for the leak position as a function of measurements from these sensors. However, we also highlight the risk of finding false but plausible leak positions in the multiple pipes. We try to answer the questions of how and when the leaking pipe can be isolated. In particular, we show that nonlinearities in the pipes' head loss functions are essential for the well-posedness of the isolation problem. We propose procedures to get around the pitfall of multiple plausible leak positions.

Figures (7)

• Figure 1: Schematic view of a network of $n$ parallel pipes, where pipe $k$ is leaking.
• Figure 2: A water network with some parallel pipe structures. (EPANET epanet Example Network 2, available at https://github.com/OpenWaterAnalytics/epanet-example-networks.)
• Figure 3: Estimates of leak position $x$ for a network with three parallel pipes. The leak should not move as we vary the pressure, and we conclude that pipe 2 is the leaking pipe.
• Figure 4: External flows in Example \ref{['exmp:confusion_flow']} for nominal value $\Delta h=4.0$.
• Figure 5: Residuals and confusion flows in Example \ref{['exmp:confusion_flow']} for nominal value $\Delta h=4.0$.