Abstract

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 efficient 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 defining 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 significantly when the number of valves reached a threshold. The procedure applied to other real case studies seems to confirm the efficiency 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. 2000; Dandy & Engelhardt 2001); therefore, valve positioning was considered as a secondary aspect. Gupta et al. (2014) propose an iterative procedure to increase network reliability avoiding problems caused by pipe failure. The proposed methodologies are based on the redundant use of pipes and valves.

The approaches for choosing both the position and the number of the valves for the occurrence of either planned or unplanned interruptions differ. Some authors (Creaco et al. 2010; Giustolisi & Savic 2010) have proposed an algorithm based on a topological matrix. Instead, Alvisi et al. (2011) suggest a method to identify where isolation valves for network segmentation should be located based on a pseudo-inverse matrix. Giustolisi & Ridolfi (2014) present a multi-objective strategy for optimal network segmentation using a modularity index to identify groups of nodes with strong interconnections. Perelman & Ostfeld (2011) propose a new methodology for the partition of WDN based on a clustering algorithm and on topological and hydraulic connectivity properties, whereas Gao (2014) proposes an approach based on graph theory applying it in the analysis of high dimension networks.

Other authors (Giustolisi et al. 2014) have adopted an optimization procedure to define the valve subsets in the network according to the hydraulic parameter changes corresponding with inadequate network conditions. The new approach was obtained by minimizing costs and by fixing constraints on nodal heads.

Some authors (Korkana et al. 2016a, 2016b) adopted techniques based on genetic algorithms to obtain district metered areas (DMAs) and solve the problem of water loss management.

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. 2017).

Recently, other authors have proposed methodologies to ensure that the delivered water is of an appropriate age and pressure (Chatzivasili et al. 2018, 2019). These approaches are based on the concept of dividing the WDN into smaller areas via the geometric partitioning method; subsequently, the Student's t-mixture model or Gaussian mixture modelling is applied to each area defining the position of the valves and separating DMAs.

The approach described (Fiorini Morosini et al. 2018) is based on the network analysis by calculating the value of an OF in order to obtain the optimal number and better location of isolation valves in some real cases. The improvement index for system behaviour is the decreasing of OF (Fiorini Morosini et al. 2017). Starting from an initial condition, characterized by a set of existing valves, it is possible to determine the minimum number of additional isolation valves to limit disruptions in the network when a failure occurs in one or more pipes. The proposed methodology is based on a pressure-driven analysis (PDA) model and requires the definition of the head value Hmax to satisfy the requested demand at each network node. The approach does not provide an indication to prevent the burst; however, it does allow for operation in emergency conditions.

METHODOLOGY

A failure in a WDN modifies the amount of circulating flow and, in any case, the functioning conditions differ from those in normal conditions.

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 Hmax at each node is related to the ground level (z) and to the height of each supplied building (Hb); it is defined by the relationship: 
formula
(1)
where:
  • p/γmin is the minimum pressure head necessary to serve the users; it is related to building height Hb and to the parameters listed below;

  • Pms is the minimum pressure to allow the use of all devices in the building, usually 5 m;

  • Pp are the head losses along the riser column;

  • PD are the head losses starting from the network node and ending at the base of each building.

When the head is lower than Hmax, the system works in PDA conditions and the effective delivered demand Qreal is lower than base demand QBD and depends on the real head value. There is another value of the head defined as follows: 
formula
(2)

If the head is below Hmin, the node demand is zero (Figure 1).

Figure 1

Value of Qreal from each node in the PDA condition.

Figure 1

Value of Qreal from each node in the PDA condition.

Qreal can be calculated as shown: 
formula

In an isolated zone, a subset of shut-off valves operates; therefore, the system topology changes significantly. In order to avoid a real demand Qreal 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: 
formula
(3)

where:

  • ndist is the number of districts of the network;

  • nCVi is the number of operating shut-off valves isolating the district;

  • nV is the total number of shut-off valves in the network;

  • QPDAi is the deliverable demand at each district before the closure of the valves;

  • Qi is the undeliverable demand at each district after the closure of the valves;

  • QRDi is the deliverable demand at each district after the closure of the valves;

  • wi is the weight for each district calculated as the ratio between the district base demand in DDA (demand driven analysis) conditions and the total base demand in the network.

For each failure scenario, i.e. for each pipe burst, different OF values can be calculated by varying the subset of the activated shut-off valves. The minimum value of OF defines the best subset of valves to isolate the area where the broken pipe is located.

The procedure consists of a two-step approach. The first step aims to define the location of additional shut-off valves and to analyse the number of districts generated in the network. Subsequently, it is necessary to isolate the district where the broken pipe is located, and a new topology is defined. The analysis of the network in PDA conditions provides the parameter to calculate OF for the fixed number of active valves. The solving procedure was implemented in a Matlab environment using an Epanet toolkit (Figure 2).

Figure 2

Procedure to calculate OF.

Figure 2

Procedure to calculate OF.

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. An analysis of the network with closed valves was performed for each configuration.

The network in Praia a Mare consists of 73 pipes, 53 nodes and 2 source/tanks of water with a fixed head (Fiorini Morosini et al. 2018) and is shown in Figure 3. The total base demand, in summer conditions, is 47.25 l/s. The head Hmax varies from 29 to 68 m.

Figure 3

Network of Praia a Mare (CS, Italy).

Figure 3

Network of Praia a Mare (CS, Italy).

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.

Figure 4

Initial condition: eight shut-off valves and three districts (Praia a Mare).

Figure 4

Initial condition: eight shut-off valves and three districts (Praia a Mare).

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.

Table 1

Different scenarios obtained with different numbers of shut-off valves (Praia a Mare)

ScenariosDistrictsnvScenariosDistrictsnv
16 
17 
22 
10 12 26 
12 11 14 30 
14 12 21 38 
ScenariosDistrictsnvScenariosDistrictsnv
16 
17 
22 
10 12 26 
12 11 14 30 
14 12 21 38 

For scenario n°6 (see topology in Figure 5), there are 14 valves and 6 districts.

Figure 5

Scenario n°6: 14 shut-off valves and 6 districts (Praia a Mare).

Figure 5

Scenario n°6: 14 shut-off valves and 6 districts (Praia a Mare).

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 indicated in Table 2.

Table 2

Terms to calculate OF for scenario n°6 (Praia a Mare)

Districtncv/nvQ/QPDA(QPDAQRD)/QPDAwiOFi
0.43 0.37 0.38 0.26 0.307 
0.21 0.11 0.11 0.07 0.031 
0.07 0.04 0.04 0.04 0.007 
0.36 0.27 0.27 0.27 0.248 
0.43 0.35 0.41 0.26 0.311 
0.21 0.09 0.09 0.09 0.036 
    OF 0.940 
Districtncv/nvQ/QPDA(QPDAQRD)/QPDAwiOFi
0.43 0.37 0.38 0.26 0.307 
0.21 0.11 0.11 0.07 0.031 
0.07 0.04 0.04 0.04 0.007 
0.36 0.27 0.27 0.27 0.248 
0.43 0.35 0.41 0.26 0.311 
0.21 0.09 0.09 0.09 0.036 
    OF 0.940 

In the other cases, the OF value decreases when the number of total valves nv increases as shown in Table 3 and Figure 6.

Table 3

OF values for the different scenarios (Praia a Mare)

ScenarionvOFScenarionvOF
3.000 16 0.598 
1.885 17 0.643 
1.234 22 0.528 
1.167 10 26 0.425 
12 1.025 11 30 0.342 
6 14 0.940 12 38 0.249 
ScenarionvOFScenarionvOF
3.000 16 0.598 
1.885 17 0.643 
1.234 22 0.528 
1.167 10 26 0.425 
12 1.025 11 30 0.342 
6 14 0.940 12 38 0.249 
Figure 6

OF versus the number of shut-off valves nv (Praia a Mare).

Figure 6

OF versus the number of shut-off valves nv (Praia a Mare).

The OF failed when the number of valves increased; it then levelled off when the number of valves exceeded a specific value. The solution did not improve significantly when the number of valves reached a threshold. In this way, good results can be achieved also for a limited number of valves. To confirm the results, the methodology was also tested on other WDNs, including those of Marano Marchesato and Cosenza.

The Marano Marchesato skeletonized network consists of 67 pipes, 52 nodes and 2 source/tanks of water with a fixed head and is shown in Figure 7. The total base demand is about 2.0 l/s. The head Hmax varies from 422 to 435 m.

Figure 7

Network of Marano Marchesato (CS, Italy).

Figure 7

Network of Marano Marchesato (CS, Italy).

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.

Table 4

Different scenarios obtained with different numbers of shut-off valves (Marano Marchesato)

ScenariosDistrictsnvScenariosDistrictsnv
16 
18 
10 10 21 
12 10 14 26 
13 11 15 28 
6 7 14 12 22 37 
ScenariosDistrictsnvScenariosDistrictsnv
16 
18 
10 10 21 
12 10 14 26 
13 11 15 28 
6 7 14 12 22 37 
Figure 8

Scenario n°6: 14 shut-off valves and 7 districts (Marano Marchesato).

Figure 8

Scenario n°6: 14 shut-off valves and 7 districts (Marano Marchesato).

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.

Table 5

Values of the OF for the different scenarios (Marano Marchesato)

ScenarionvOFScenarionvOF
1.194 16 0.702 
1.052 18 0.591 
10 0.974 21 0.523 
12 0.810 10 26 0.371 
13 0.863 11 28 0.294 
14 0.722 12 37 0.230 
ScenarionvOFScenarionvOF
1.194 16 0.702 
1.052 18 0.591 
10 0.974 21 0.523 
12 0.810 10 26 0.371 
13 0.863 11 28 0.294 
14 0.722 12 37 0.230 
Figure 9

OF versus the number of shut-off valves nv (Marano Marchesato).

Figure 9

OF versus the number of shut-off valves nv (Marano Marchesato).

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.

Finally, the case of the Cosenza network is shown. It is significantly bigger than the other ones; the skeletonized network consists of 48 pipes, 40 nodes and 2 source/tanks of water with a fixed head. It is shown in Figure 10. The total base demand is about 257 l/s. The minimum head Hmax varies from 261 to 339 m.

Figure 10

Network of Cosenza (CS, Italy).

Figure 10

Network of Cosenza (CS, Italy).

The scenarios are shown in Table 6.

Table 6

Different scenarios obtained with different numbers of shut-off valves (Cosenza)

ScenariosDistrictsnvScenariosDistrictsnv
11 25 
15 29 12 
20 30 38 
ScenariosDistrictsnvScenariosDistrictsnv
11 25 
15 29 12 
20 30 38 

The OF values when the number of valves changes is shown in Table 7 and Figure 11.

Table 7

Values of the OF for the different scenarios (Cosenza)

ScenarionvOF
0.375 
0.289 
0.213 
0.172 
12 0.140 
38 0.126 
ScenarionvOF
0.375 
0.289 
0.213 
0.172 
12 0.140 
38 0.126 
Figure 11

OF versus the number of shut-off valves nv (Cosenza).

Figure 11

OF versus the number of shut-off valves nv (Cosenza).

Once the minimum number of valves was defined, the subsequent step was to verify how the solution changes by modifying the position of additional valves.

The OF value for each different position of the additional valves was calculated for the networks in Praia a Mare (six additional valves) and Marano Marchesato (six additional valves).

The results are shown in Table 8 and Figure 12.

Table 8

OF values with different positions of the additional valves

Praia a Mare (six additional valves)
Marano Marchesato (six additional valves)
ID positionOFID positionOF
0.940 0.722 
0.817 0.644 
0.760 0.520 
0.733 0.626 
0.759 0.547 
0.785   
Praia a Mare (six additional valves)
Marano Marchesato (six additional valves)
ID positionOFID positionOF
0.940 0.722 
0.817 0.644 
0.760 0.520 
0.733 0.626 
0.759 0.547 
0.785   
Figure 12

OF values for different positions of additional valves in Praia a Mare (a) and Marano Marchesato (b).

Figure 12

OF values for different positions of additional valves in Praia a Mare (a) and Marano Marchesato (b).

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 obtain reliable functioning of the system. This methodology is based on the definition of an OF depending on the input and output hydraulic parameters of the network deriving from a PDA of the system. The procedure was applied to three real cases with the hypothesis of failure conditions. The networks analysed were located in Italy in Praia a Mare, Marano Marchesato and Cosenza, three Calabrian Cities with different numbers of inhabitants.

An increase in the number of valves nv led to a decrease in the OF; therefore, it was possible to determine a value of nv 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.

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