Management of water distribution systems in PDA conditions using isolation valves: case studies of real networks

The current paper reports on a case study investigating water distribution system management in emergency conditions when it is necessary to seal off a zone with isolation valves to allow repair. In these conditions, the pressure-driven analysis (PDA) is considered to be the most ef ﬁ cient approach for the analysis of a water distribution network (WDN), as it takes into account whether the head in a node is adequate to ensure service. The topics of this paper are innovative because, until now, previous approaches were based on the analysis of the network behaviour in normal conditions. In emergency conditions, it is possible to measure the reliable functioning of the system by de ﬁ ning an objective function (OF) that helps to choose the optimal number of additional valves in order to obtain adequate system control. The OF takes into account the new network topology by excluding the zone where the broken pipe is located. The results show that the solution did not improve signi ﬁ cantly when the number of valves reached a threshold. The procedure applied to other real case studies seems to con ﬁ rm the ef ﬁ ciency of the methodology even if further examination of other cases in different conditions is necessary.


INTRODUCTION
In a real network, valves along pipes allow a zone to be isolated when it is necessary to operate on the system. Correct management suggests limiting the number of valves in a network due to their cost as well as to operating problems; however, an increased number of valves and their correct use guarantee good system performance in both normal and emergency conditions.
The network area where a broken pipe is located can be isolated by using a set of shut-off valves. Since the goal of isolating a broken pipe can be achieved with different subsets of operating valves, it is essential to define their position and analyse the system in the related different topologies.
Many authors have addressed water distribution network (WDN) management problems, in order to gain a better understanding regarding the choice and planning of the location of isolation valves. The first studies considered the problem of pipe rehabilitation and their goal was to prevent pipe bursts using network management (Engelhardt et al. ; Dandy & Engelhardt ); therefore, valve positioning was considered as a secondary aspect. Gupta et al. () propose an iterative procedure to increase network Other approaches separate a WDN into districts providing an optimal placement of isolation valves to achieve a water pressure management to reduce water losses and to improve water quality preventing disinfection by product growth (Gonelas et al. ).
Recently, other authors have proposed methodologies to ensure that the delivered water is of an appropriate age and pressure (Chatzivasili et al. , ). A failure in a pipe requires isolation, not only of that pipe, but also the entire zone where the pipe is located which is delimited by a subset of shut-off valves. When the valves are active, the topology of the system changes and it can determine its inefficiency. The analysis of the new system is necessary, and the new results must be analysed.
If the head in a specific node is inadequate, it is impossible to deliver the requested nodal demand necessary to satisfy users' needs.
The head value H max at each node is related to the ground level (z) and to the height of each supplied building (H b ); it is defined by the relationship: where: • p/γ min is the minimum pressure head necessary to serve the users; it is related to building height H b and to the parameters listed below; • P ms is the minimum pressure to allow the use of all devices in the building, usually 5 m; • P p are the head losses along the riser column; • P D are the head losses starting from the network node and ending at the base of each building.
When the head is lower than H max , the system works in PDA conditions and the effective delivered demand Q real is lower than base demand Q BD and depends on the real head value. There is another value of the head defined as follows: If the head is below H min , the node demand is zero ( Figure 1).
Q real can be calculated as shown: In an isolated zone, a subset of shut-off valves operates; therefore, the system topology changes significantly. In order to avoid a real demand Q real that is too low in some nodes, some other isolation valves are necessary.
The proposed methodology allows the definition of the number and location of the additional valves. By analysing the new configurations obtained by activating one or more shut-off valves, some existing and others in addition, and excluding the zone where the burst pipe is located, it is possible to acquire the parameters required to calculate the OF: where: • n dist is the number of districts of the network; • n CV i is the number of operating shut-off valves isolating the district; • n V is the total number of shut-off valves in the network; • Q PDA i is the deliverable demand at each district before the closure of the valves; • Q i is the undeliverable demand at each district after the closure of the valves; • Q RD i is the deliverable demand at each district after the closure of the valves; • w i is the weight for each district calculated as the ratio between the district base demand in the DDA condition and the total base demand in the network.

CASE STUDIES RESULTS
The methodology was applied to three real cases, and the results are presented here. Three networks, located in Italy in the Calabrian cities of Praia a Mare, Marano Marchesato and Cosenza, were analysed. The number of users for each network was different; therefore, the methodology was tested in different conditions. Starting from initial conditions characterized by existing valves, each scenario varied because the number of districts increases by adding shut-off valves; when a shut-off valve subset is activated, the topology and the parameters in the network change. In this real network, there are eight shut-off valves. By closing these shut-off valves, it is possible to obtain three districts as shown in Figure 4. Different configurations with a defined number of shut-off valves have been considered for the network.
In particular, 12 configurations were assumed. By increasing the number of valves in the network, a higher number of districts can be obtained as indicated in Table 1.
For scenario n 6 (see topology in Figure 5), there are 14 valves and 6 districts.    The analysis in PDA conditions provides the parameters for the calculation of the terms of the OF and its value. In this case study, these terms are (Table 2): In the other cases, the OF value decreases when the number of total valves n v increases as shown in Table 3 and Figure 6.      The different scenarios were obtained by adding further six shut-off valves to the initial 8. Data and topology are shown in Table 4 and Figure 8.

The trend of OF values when the number of valves
increases was similar to the previous case. The results are shown in Table 5 and Figure 9.
In all the cases, it is evident that increasing the number of network valves beyond a defined threshold leads to an improvement that is insignificant for technical purposes. The scenarios are shown in Table 6: The OF values when the number of valves changes is shown in Table 7 and Figure 11.
Once the minimum number of valves was defined, the The results are shown in Table 8 and Figure 12.
In both cases, the different position of additional valves did not significantly change the OF values and the solution can be assumed, for these cases, to be independent from the location of additional valves.

CONCLUSIONS
The use of valves, either existing or added, which are activated whenever a failure occurs, allows the WDN to be managed in emergency conditions. When there is a pipe failure, it is necessary to isolate the area where this pipe is located and suspend service to all users. The extension of the area depends both on the position and on the number of shut-off valves that modify the network topology and influence the head value at each node. In these conditions,   the delivered demand at each node must be determined using a PDA approach and the effective nodal demand is dependent on the real heads.
This paper proposed an approach to define the minimum number of valves to be installed in a real network to     An increase in the number of valves n v led to a decrease in the OF; therefore, it was possible to determine a value of n v that represents a threshold beyond which the improvement becomes negligible for technical purposes. Moreover, for the case studies analysed, the results show that the position of additional valves does not significantly change the values of OF and the solution is, for these cases, independent from the location of additional valves. The analysis seems to confirm the results of the proposed methodology. New applications of the methodology will be conducted for the analysis of other real networks and confirm the results.