2.1. Case-Study Network
A portion of the municipal WDN of the town of San Giovanni la Punta (Italy) was selected as case-study to evaluate benefits of some rehabilitation and active pressure control strategies.
The WDN (see
Figure 1) consists of about 39 km of pipes and supplies about 6100 users (about 2400 households). Two main DMAs were identified in a conjunct work carried out with the water company that manages the water distribution in the network. The two districts supply the northwest area (namely district DMA1, pipes reported in red in
Figure 1) and the southeast area (namely district DMA2, pipes reported in blue in
Figure 1) of the town.
The whole system is supplied by the reservoir “Alto”, which is located in the northern part of the town at 422 m a.s.l. (maximum capacity approximately equal to 100 m
3). The reservoir is supplied by well pumps operated through use of an inverter-based system that adjusts the inlet to maintain a constant water level of 2 m in the reservoir during a period of 24 h. A cast iron conduit conveys flow from the reservoir to the main branches and loops of the WDN including a 2 km long steel pipeline with the function of north–south main distribution line (reported in orange in
Figure 1). Most of the pipes larger than DN200 in the WDN are made of steel and cast iron, and date back to the 1980s and 2000s, respectively. Conversely, the small conduits are almost entirely in HDPE and were installed in the early 2000s. Various surveys carried out during the last decade by the water company have revealed the occurrence of leakages in several branches of the WDN. In this regard, a point of weakness of the network concerns the described north–south main distribution line. Indeed, this line is affected by high leakage levels that are the cause of pressure problems (and inadequate water supply) for several households belonging to DMA1.
2.2. Monitoring Campaign
A campaign of monitoring was carried out during the research work to explore the behavior of the network in terms of water consumption and pressure in the two districts.
The Specific objective of the experimental monitoring was to identify critical issues in the current operation of the WDN (e.g., identify areas of leakage, hydraulic malfunctioning, etc.). A further objective was to set up a dataset of measurements to be used for the calibration of the simulation model adopted for the analysis of the WDN.
The experimental campaign was carried out separately for the two districts (in the months of October 2018 for DMA2 and April 2019 for DMA1). Installation of pressure sensors and devices required preliminary works aiming at isolation of network sectors and assessment of the condition and settings of existing valves in the network. A flow meter (at the inlet of the district) and five pressure sensors were installed in nodes of each DMA (see
Figure 1) for two consecutive weeks. During such periods, flows and pressures were monitored at intervals of 1 and 10 min, respectively. The flow meters used allowed flows to be measured with an accuracy of 0.5%, while pressure sensors provided pressure measurements with 0.1% accuracy. All the data were stored locally and downloaded at the end of the monitoring period for the successive analyses. Recorded measurements enabled determining the daily pattern of the pressure in the two districts, thus, identifying areas at low or high pressure (thus, more or less prone to leakage) in the network during the 24 h. Furthermore, the analysis of the data allowed determining the daily pattern of flows supplied to the two DMAs, thus enabling a measure of the total sum of household consumption and of water leakages in the two districts.
Moreover, the comparison of the data of flow with quarterly data of grouped billed consumption (provided by the water company for each household of the WDN) allowed to unbundle leakage contribution by the total measured flow.
2.3. Model of the Network
A hydraulic model of the network was set up to assess benefits determined by implementation of scenarios of rehabilitation and active pressure control in order to reduce leakage levels in the WDN.
The extended period simulation (EPS) of the WDN was performed, i.e., the simulation was run assuming successive conditions of steady state for 24 h of the day.
Simulations were carried out under the MATLAB environment through the EPANET-MATLAB Toolkit [
22]. The toolkit allows exploiting the tools of EPANET software, developed by the EPA (U.S. Environmental Protection Agency) for the simulation of water distribution networks [
23]. The adopted skeletonization of the network was taken from the GIS owned by the water utility, which includes not only the primary level of loops but also the secondary one (i.e., the level of pipe branches before the building/household level). Overall, the network was skeletonized using 921 links and 869 nodes. The adopted skeletonization allowed considering a level-wise description of the network (primary and secondary branches and loops) appropriate for the correct allocation of nodal demands consistently with both acquired measurements and available billing data.
Preliminarily, pipe roughness was estimated based on the available information from surveys concerning pipe material and level of pipe corrosion. Notably, the inspection of pipes in different manholes of the network revealed a (high) level of corrosion of the north–south distribution pipeline typical of pipes in operation for several years. Differently, the plastic pipes and those in cast-iron showed better conditions, consistent with their lesser age. The inspection was carried out in about twenty manholes distributed in a rather uniform way in the two DMAs, thus providing an idea of the global conditions of the whole WDN. Roughness values for the three types of pipe materials were properly selected from the literature [
24] based on the observed conditions from the field survey.
On this background, values of Hazen–Williams roughness coefficients were set equal to 140, 95, and 75 for pipes in HDPE, cast iron, and old steel, respectively.
Network leakage was evaluated using a pressure-driven approach [
25], based on the following equation:
where
(L/s) is the leak at the
k-node and
(m) is the corresponding pressure;
nj,k is the total number of
j-pipes converging to node
k;
(m) is the length of pipe
j converging to node
k; and α and
β are leakage coefficients to be calibrated.
The analysis of the scientific literature shows efforts to characterize the behavior of leakage in WDNs in terms of values of the leakage exponent α. The value 1.18 has been proposed based on field data [
26]. Values ranging between 0.5 and 2.5 have been found depending on pipe material, on the background soil hydraulic characteristics, and on the prominent type of leak [
27,
28,
29,
30]. Instead, β has been shown to depend on the level of leakage and on the description of the WDN. Very often, given their large variability, the values of these two coefficients have been chosen in the literature based on the use of specific calibration procedures [
31].
A pressure control module was developed in MATLAB. The module was coupled to the hydraulic model to allow the simulation of potential benefits deriving from adoption of active control of pressure in the WDN based on remote RTC [
12]. The control module allows implementing architectures of RTC systems and to use various types of PCVs (e.g., screw-based valves; plunger valves, etc.) for pressure control in the WDN. A control strategy (i.e., the sequence of control actions to drive the pressure to the setpoint) derived from the literature [
17] was implemented in the module, which assumes that pressure at each of the two DMAs is controlled on the basis of the pressure value in one node (critical node) of the district. Specifically, in the pressure control module, it is assumed that pressure measurements acquired at the critical node are remotely transmitted in real time to the controller that operates the adjustment of the PCV. The control algorithm implemented in the pressure control module provides (at each control time step) the valve shutter displacement
(-) based on the deviation
(m) at time
t between the current pressure value and the related setpoint value at the critical node:
where
and
are valve opening degrees at time
t and
, respectively; Δ
tc is the control time step, and
K (m
−1) is the controller gain.
Equation (2) shows that is proportional to through . Therefore, with respect to the shutter position , the adopted algorithm shows the characteristics of an integral-type controller. Moreover, the negative sign in Equation (2) allows considering the negative proportionality between and , if gain is assumed to be intrinsically positive.
Finally, valve regulation is constrained by the limits 0 and 1 (saturation), corresponding to valve fully closed (0) and fully open (1). The control module allows also including limits (of the valve manufacturer) on the mechanical velocity of the shutter of the valve, to prevent risks of unwanted transients in the network [
12].
2.4. Model Calibration
The availability of measurements in the network allowed the calibration of the simulation model, thus, increasing the reliability of the simulation results concerning the potential benefits due to implementation of leakage control strategies in the WDN.
Calibration was carried out using the Genetic Algorithm Toolbox available in MATLAB environment. The adopted procedure is based on a recent application [
31] and consists in calibrating simultaneously (through a genetic algorithm) the optimal values of the hourly multipliers of the daily curve of consumption and the optimal values of parameters
α and
β of Equation (1) for leakage evaluation. The values of the leakage parameters were assumed the same for all the network pipes, except for the coefficient
β related to the steel north–south steel pipeline that was evaluated separately, to improve model results.
In order to correctly describe the demand dynamics in the network, hourly demand multipliers of each DMA were considered, i.e., coefficients that multiply the average daily consumption and provide the hourly demand in the nodes of the WDN.
Average hourly measured values of flow and pressure, recorded during the monitoring campaign at each DMA, were provided as model input with the aim of identifying the optimal leakage parameters and hourly demand multipliers by minimizing the following objective function:
where
PC (m) and
PM (m) are computed and measured pressure values, respectively;
ni is the total number of installed pressure sensors; and
nh is the number of hourly values considered.
Use of Equation (3) was subject to the constraint that total inflow to each DMA is always equal to the sum of household consumption and leakage in the district, at any time step of the simulation.
2.5. Scenarios of Simulation
Three main scenarios were considered for the simulations that include options of rehabilitation/active pressure control of the WDN. The first scenario (S1) concerns the rehabilitation of the described north–south steel pipeline in order to eliminate leakages identified during the field surveys. Such scenario includes improvement of water supply to users of DMA1 as determined by the re-arrangement of circulation of flows in the conduits.
The second scenario (S2) adds up to S1 the installation of two PCVs to allow local control of the pressure in the network. The two PCVs are assumed to be conventional screw-based valves and to be installed at the inlet of each DMA (PCV1 at node 2 of the DMA1 and PCV2 at node 3 of the DMA2, as shown in
Figure 1). In this scenario, each valve is set with the objective of reducing as much as possible pressure levels in the respective DMA, while ensuring the full demand satisfaction to all the users of the district. This is obtained by preliminarily identifying the critical node of each DMA, that is the node with the lowest value of pressure in the district during 24 h (node 13 for DMA1 and node 14 for DMA2). Then, the scenario considers that pressure at the critical nodes can never drop down below the minimum value of 30 m. Accordingly, the local pressure setpoint at PCV1 and PCV2 outlet was set to 7.5 and 33 m for DMA1 and DMA2, respectively.
The third scenario (S3) considers the adoption of a remote RTC for pressure control in the WDN. Two plunger valves (DN300 for DMA1 and DN80 for DMA2) are assumed to be installed at the same sites as in scenario S2. Recent laboratory experiments have shown this type of valve to provide potential for accurate RTC in WDNs [
32]. The scenario assumes the same pressure setpoint (30 m) at the two critical nodes as for scenario S2 (nodes 13 and 14). However, in comparison to scenario S2, the valves are directly controlled on the basis of the remote pressure measurements acquired in real time at the critical nodes. Simulation of scenario S3 included preliminary identification of a suitable value of the controller gain
K to perform effective pressure control in the two districts without the occurrence of permanent pressure oscillations [
33]. In agreement with previous literature results (e.g., [
20,
34], the simulations under RTC were carried out using control time
= 5 min.
Scenarios S1, S2, and S3 were compared to scenario zero (S0), the current reference scenario in which no actions are taken to reduce leakage levels in the network.