Leakage as pressure-driven demand in design of water distribution networks

The loss of some amount of water through leaks is inevitable in a water distribution network (WDN). Usually, leakage losses are included as volume-based demands by increasing the nodal demands by a certain percentage in the design of WDNs. However, leaks are pressure dependent and increase with an increase in pressure in the pipeline. In this study, a methodology is proposed to include leakage as pressure-driven demands along with normal volume-based demands and both volume and pressure-based demands. Two cases for distribution of leakage in the network are considered during the design: (1) leakages that are distributed based on nodal demands, (2) those that are distributed based on the length of pipe. An iterative optimization methodology is proposed that considers the link diameters as continuous variables. It begins by assuming the nodal heads at all of the demand nodes are above the desired pressure heads. These assumed heads are successively corrected until the difference in cost in the two successive iterations is found to be negligible. The versatility of the methodology is shown by its application on various types of networks. The incorporation of pressure-driven leakage in the design process can be shown to generate optimal solutions that require incrementally larger diameters. However, when pressure-based demands are also considered with pressure-driven leakage, the increase in diameters is substantial.