Modeling of pressure-dependent background leakages in water distribution networks

In last decades, several mathematical models have been proposed to simulate background leakages in water distribution networks (WDNs). Some of these models already consider the dependence of leakages to pressure, but they still neglect the gradient of pressure along the pipes. In this article, new models to take into account of this gradient are presented. One of them computes reference background leakage outflows, using a recursive algorithm which discretizes the pipes into sub-pipes until the hydraulic grade line (HGL) along each pipe converges. The other new models consist in gradually refining a state of the art one. All models are then tested and compared on both a single leaky pipe and a WDN derived from a real leaky network. The results of this comparison show clearly the better estimations obtained from our new models when compared to the existing one. Finally, accurate leakage models are essential to estimate the level of leakages and, more generally, the good working order of WDNs. Thus, our new models will help in taking the best decisions for optimal functioning and rehabilitation of the WDNs. Moreover, our recursive discretization approach could be reused for other applications in WDNs, or derived to more general fields of applied mathematics and scientific computation.