Estimation of leakages in water distribution systems with measurements at few nodes.

Leakages in urban water networks can be a very high percentage of the supplied water. The lost volume represents an economic damage not only for the cost of water pumping and treatment, but even because it makes necessary investments into systems capacity expansion or in searching for other water sources. In most cases of Water Distribution Systems (WDS) the most relevant percentage of lost water can be considered as the sum of small leakages distributed all over the network. In order to reduce this lost volume it may be advisable to plan medium-long term rehabilitation policies of the network combined with suitable management policies for controlling pressure heads in the system. Pressure regulation can be achieved by means of pressure reduction valves (PRV) remotely controlled, whose purpose is to decrease excessive pressures, ensuring the service conditions. The control of the PRVs is generally performed by mean of a hydraulic simulator of the network able to model as realistically as possible, both the geometry of the network and the nodal discharges. For a more realistic simulation of the WDS performance, the implementation of a fully pressure-dependent leakage specification is required. In the work, in order to treat water losses as pressure dependent quantities, the calibration of the WDS simulation model is performed concentrating leaks at the nodes and considering their flow as a function only of the local pressure. The estimation of the calibration coefficients is carried out solving an optimization problem with Genetic Algorithms (GA) coupled with the hydraulic model of the network. In order to obtain more realistic values for the nodal demand and water consumption discharges, it is advisable to base this calibration on the largest possible set of pressure and discharge measurements all over the network. Unfortunately measurements in WDS are usually carried out only at few nodes with high level of users aggregation. To overcome this problem the spatial interpolation of nodal pressures is performed with a geostatistical technique that feeds the calibration procedure with pressure heads at each node of the network.