Water network partitioning in district metering areas, or sectorization, is an important process for improving water network management. It can help water utilities to implement active leakage control, conduct pressure management, and prevent network contamination. It is generally achieved by closing some network pipes, thus reducing pipe redundancy and affecting system performance. No systematic set of performance indices has been defined to evaluate a sectorization design and thus allow for a comparison of different possible sectorizations on a formal basis. In this paper, several performance indices for water network partitioning are proposed and tested using two real water supply systems: Parete in Italy and Matamoros in Mexico. Both systems' sectorizations were previously designed by a novel effective automatic technique recently developed by the authors. For both the original and sectorized networks, the proposed performance indices considered energy dissipated in the network, network resilience, pressure variation, fire-fighting capacity, water age, and mechanical redundancy. Network resilience appears to be the most representative index for the entire network, whereas pressure variation indices are more appropriate for describing individual districts. Except for fire-fighting capacity in one network, system performance did not appear to be affected significantly after sectorization.

INTRODUCTION

Water network partitioning (WNP), achieved by dividing a water distribution network into k district metering areas (DMAs), represents an important management methodology that has been applied in many countries. A variant of WNP that is applicable to multiple supply source networks divides the water system into independent districts. In this variant, each district is supplied by its own water source (or water sources), with no connections to other districts, to establish sectors with an independent water supply (Di Nardo et al. 2013b) or to improve network protection (Graymann et al. 2009; Di Nardo et al. 2013c). In this case, the WNP is referred to as water network sectorization (WNS) (Di Nardo et al. 2013d), and the districts are referred to as independent district meter areas or isolated district meter areas (i-DMAs).

i-DMAs enable actions to improve the control and management of important aspects of water distribution, such as water quality (no mixing of water from distinct sources), and the intensity and spatial and temporal distribution of leaks. These actions may include the following: (1) hydraulic efficiency and non-revenue water audits; (2) water demand curve characterization, particularly of the night flow; (3) leak detection, by analyzing the evolution of the night flow; (4) fraud and under-registration, or measurement error detection; (5) investment planning to guide the water supply to the sectors with greater volumes of non-revenue water; (6) district isolation to protect water networks from accidental or malicious contamination; and (7) district pressure management. Sectorization into i-DMAs is also frequently needed as a first step in dividing a large distribution network into many small DMAs, where each i-DMA is then divided into DMAs. Under conditions of water scarcity, sectorization is typically implemented by water utilities to achieve an intermittent distribution of water resources.

Given that WNP and WNS change the hydraulic behavior of a water network, it is generally difficult to specify the number and dimensions of the districts; in many cases, WNP and WNS may worsen the hydraulic performance and reliability of the network (Wrc/WSA/WCA 1994; Di Nardo et al. 2013d). WNP and WNS are contrary to the traditional design criteria of looped and redundant water networks which increase water systems' reliability under mechanical and hydraulic failure conditions (Mays 2000). Indeed, the insertion of gate valves, which is necessary to achieve WNP or WNS, may significantly reduce network reliability, particularly during peak demands, thereby diminishing the service level provided to users. As the number of possible WNPs or WNSs is very large (Di Nardo et al. 2013a), it is essential to find procedures to define optimal layouts of DMAs (or i-DMAs) after positioning of gate valves.

Recently, in the literature, some techniques based on graph theory have been proposed to design optimal water network partitionings and sectorizations that do not rely on hydraulic indices to compare different WNPs, but essentially on partitioning performance (Deuerlein 2008; Sempewo et al. 2008; Herrera et al. 2010; Perelman & Ostfeld 2011; Izquierdo et al. 2011; Ferrari & Becciu 2012; Perelman et al. 2014) or essentially on simple measures of flow and pressure (Swamee & Sharma 1990; Gomes et al. 2012a; Gomes et al. 2012b; Diao et al. 2013). Only in Di Nardo et al. (2013a, b, d) and Alvisi & Franchini (2014), were some hydraulic performance indices (PIs) used that essentially referred to the energy and pressure characteristics of the water network. However, these indices lacked an evaluation of water quality performance, mechanical redundancy, and fire protection effects. In this paper, a more complete battery of PIs is proposed and tested using the WNS of two cities, a city in Italy and a city in Mexico.

PERFORMANCE INDICES

The PIs tested in this study compare the performances of the original networks with those of the sectorized networks. The PIs can be computed after a hydraulic simulation conducted with the EPANET (Rossman 2000) or similar software designed for distribution network analysis, using a demand-driven analysis (DDA) (Todini & Pilati 1988) or a pressure-driven analysis (PDA) (Cheung et al. 2005; Kanakoudis & Gonelas 2014).

The proposed PIs were divided into six categories: (1) energy indices; (2) entropy indices; (3) pressure indices; (4) fire protection indices; (5) water quality indices; and (6) mechanical redundancy indices. These indices are explained in detail below.

Energy indices

The power balance of a water network (Todini 2000) can be defined as 
formula
1
where is the available power (or total power); Qk and Hk are the supplied flow and hydraulic head at each of the R water sources in the network, respectively; and γ is the specific weight of water. is the dissipated power (or internal power), where qj and ΔHj describe the flow and headloss of each of the M network pipes, respectively. Finally, is the node power (or external power), where Qi and Hi are the water demand and head at each of the N network nodes, respectively.

According to Todini (2000), decreases in the energetic redundancy of a network can be measured with a ‘resilience’ index, which does not involve a statistical analysis of the different types of uncertainty required to define the reliability constraints.

Given the above definitions, the proposed energy indices are as follows:

Resilience index (Todini 2000) 
formula
2
where is the maximum power necessary to satisfy the demand constraint Qi and node head constraint; zi is the elevation head; and is the design pressure for the ith node. Higher values of Ir indicate better WNSs with lower values of dissipated power and thus greater resilience.
Resilience deviation index (Di Nardo et al. 2013d) 
formula
3
where Ir and are, respectively, the resilience indices of the original and WNS layouts, and is the dissipated power computed after the network sectorization or partitioning.

Prasad & Park (2004) proposed the concept of ‘network resilience’, which combines the effects of surplus power and reliable loops. Specifically, the surplus power at the ith node is specified as , where ; a loop is considered reliable if, for each node of the loop, the pipes incident with a node do not vary widely in diameter, as indicated by Prasad et al. (2003).

Thus, the uniformity at the ith node is defined by 
formula
4
where Mi is the number of pipes incident with the node i and dj is the diameter of the incident pipe j. Hence, the following index is used:
Network resilience index Irn (Prasad & Park 2004) 
formula
5
Higher values of Irn indicate better WNSs due to greater amounts of available power surplus, a more uniform incident pipe distribution, and thus greater network resilience. To compare different network layouts, a new index was proposed as follows:
Network resilience deviation index Irnd 
formula
6
where Irn and are the network resilience indices of the original and WNS layouts, respectively. This index immediately indicates the network resilience percentage deviation between the WNS and original water network (OWN), with higher values of Irnd indicating a worse WNS.

Entropy indices

The entropy of a water supply network has been conceptualized based on Shannon's mathematical theory of information entropy (Shannon 1948) by considering all possible Mp flow paths of water through the network, from source nodes to delivery nodes, and by assuming that the probability Pj that water flowing through a pipe belongs to the jth path and can be expressed as the ratio between the path flow Qj and total network flow Q (Awumah et al. 1990). Accordingly, the Mp flow paths constitute a set of mutually exclusive and completely exhaustive events, for which the entropy function may be expressed as the following (Tanyimboh & Templeman 1993): 
formula
7
In this study, S, the entropy of the network, was calculated by using an equivalent recursive expression proposed by Tanyimboh & Templeman (1993)  
formula
8
In Equation (8), Si and Sl is the entropy computed respectively for the ith node and lth node, the first sum is extended to all Nd nodes where the nodal inflow splits into at least two outflows, and the second sum refers to all Ni nodes reached by the outflow of the ith node. The probability Pil is calculated using the following equation: 
formula
9
where qil is the flow between the ith and lth nodes and is the total flow that reaches the ith node.

Pressure indices

These indices are traditionally used to measure the service level that a water system provides for its users. The following indices were computed: the mean pressure at network nodes hmean, the minimum and maximum pressure at network nodes hmin and hmax, and the standard deviation hsd of the pressure at network nodes. In addition, the following indices were calculated:

Mean pressure surplus (MPS) 
formula
10
A high MPS value indicates excess pressure in the network.
Mean pressure deficit (MPD) 
formula
11
MPD measures the decrease in pressure compared with the design pressure; higher values denote worse working conditions.
Mean squared deviation from the design pressure (MSDP) 
formula
12
MSDP indicates the trend in pressures at nodes based on the design pressure. Low values represent slight alterations in pressure, whereas high values indicate that the WNS or other actions performed on the network significantly influence the OWN.

Fire protection indices

Network simulations were performed in fire conditions, assuming that the fire demand was provided at the node with a minimum level of pressure and that in all other nodes, the water demand equaled 75% of the mean water demand during the day of maximum consumption. This approach was used to compare different simulation cases: one case for the OWN by choosing the lowest pressure node for the entire network and another k cases for the WNS by choosing the worst case for each sector. To compare these cases, a specific index (known as NFP) was defined based on the number of nodes with a pressure lower than the required pressure at the hydrant node (hFP) 
formula
13

Water quality indices

To estimate the change in water quality resulting from sectorization, the changes in water age were determined. Water age refers to the time spent by a parcel of water in the network, and thus, it provides a simple and indirect measure of the overall quality of the delivered drinking water (Rossman 2000). The analysis was performed over an entire day, and the mean age AGEmean, the maximum age AGEmax, and its standard deviation AGEsd at the network nodes were then computed with the EPANET software (Rossman 2000).

Mechanical redundancy indices

The analysis of network redundancy was conducted using a deterministic approach, simulating all possible combinations corresponding to the breakage of a single pipe. The following indices were computed via a PDA (Cheung et al. 2005):

Mean flow deficit index (FDI) 
formula
14
Minimum flow deficit index 
formula
15
Maximum flow deficit index 
formula
16
Standard deviation of the flow deficit index 
formula
17
in which 
formula
18
where QNDj is the total flow that is not supplied when the jth pipe is closed; Qa,i is the effective or actual delivered flow; and Qi is the water demand at the ith node.

Apart from the mechanical redundancy indices, all other indices assume that water demand is fully satisfied before and after sectorization. Because of that, the computations were accomplished using DDA, except for the mechanical redundancy indices which required PDA.

CASE STUDIES

The proposed PIs were used to analyze the effectiveness of different WNSs. Two case studies facilitated the analysis. These were developed with a novel effective automatic technique recently proposed by Di Nardo et al. (2013b) that entails dividing the water system into sectors with an independent water supply (i-DMAs).

The technique for the i-DMA design is based on two procedures: (1) a search for the minimum dissipated power flow paths from each source; and (2) a heuristic optimization achieved by swapping nodes that belong to two independent paths. The first procedure is based on graph theory, specifically on shortest-path techniques (Dijkstra 1959), that allow the minimum path of an oriented weighted graph to be defined starting from each source node. In this algorithm, each edge (or link) is weighted with its dissipated power. The shortest path is the path that may be crossed by an infinitesimal flow dq from source s to the ith node under the worst operating conditions (i.e., peak water demand) with a minimum value of dissipated power. This path is computed and can be defined as the shortest dissipated power path (SDPP). In fact, water always naturally ‘chooses’ the path with minimum dissipation to reach each node. In particular, in an oriented graph, water leaving a water source only reaches certain nodes, not all network nodes. Therefore, a node can belong to more than one dissipated power flow path, with each path stemming from a different source. In other words, the areas supplied by different sources may share certain nodes. Therefore, each group of nodes supplied by a source becomes an i-DMA because of the peculiarity of including all nodes with minimum dissipated power paths connected to that source. Each common node must be assigned to only one i-DMA. The proposed algorithm enables the identification of a new graph structure for the network that is composed of ‘trees’ and ‘branches’ (Cormen et al. 1990) and thus the definition of the ‘independent’ and ‘common’ node sets (Di Nardo et al. 2013b). After all tree graphs from each source are found, it is possible to define independent and common node sets because some nodes belong to different SDPPs.

The second procedure is heuristic optimization. Starting from a first bisection obtained from the independent node sets, the sectors (or i-DMAs) are heuristically optimized by swapping nodes that belong to the common node sets using a special genetic algorithm developed for this purpose. Thus, for each recursive bisection, the algorithm allows for the identification of all boundary pipes (obtained by node swapping) in one step, where gate valves should be located to maximize the resilience index (Todini 2000). The details of the procedure are provided in Di Nardo et al. (2013b).

The two existing water supply systems selected as case studies are as follows:

The city of Parete, with 10,800 inhabitants, is located in a densely populated area in the south of the province of Caserta (Italy). The water consumption in Parete is exclusively residential. Many of the houses were built in the 1970s and 1980s and contain three or four floors. This network is supplied by two sources.

The city of Matamoros is located in the northeast part of the state of Tamaulipas, directly across the Rio Grande from Brownsville, Texas, and 23 miles upstream from where the Rio Grande connects to the Gulf of Mexico. There are approximately 120,000 service connections to the city water distribution network. Water is collected from the Rio Grande River at two points, and there are four water treatment plants. The service provided to the water users is supposed to be continuous (24/7) in that valves in the distribution network neither open nor close during the day. Nevertheless, the level of water pressure in an important area of the city is so low during certain hours of the day that water users in that area do not receive water during those hours, and thus, the water supply is intermittent for them. The main hydraulic characteristics of the two networks are presented in Table 1.

Table 1

Hydraulic characteristics of the two networks

Hydraulic network
Network characteristicsPareteMatamoros
Number of nodes, n 182 1,283 
Number of links, m 282 1,651 
Number of reservoirs, r 
Hydraulic head of reservoirs (m) 110.0 29.0; 31.46; 26.99; 28.14; 36.06; 36.26; 26.12; 30.64; 30.73 
Total pipe length, Ltot (km) 32.7 376.6 
Minimum ground elevation, zmin (m) 53.1 5.33 
Maximum ground elevation, zmax (m) 78.6 12.9 
Pipe materials Cast iron PVC and AC 
Pipe diameters (mm) 60; 80; 100; 110; 125; 150; 200 76; 95; 152; 190; 238; 300; 338; 380;428; 476; 508; 600; 762; 914 
Peak demand, Q (m3/s) 0.110 0.987 
Design pressure, h* (m) 25 12 
Fire flow, (l/s) 20 45.4 
hFP, (m) 10 
Hydraulic network
Network characteristicsPareteMatamoros
Number of nodes, n 182 1,283 
Number of links, m 282 1,651 
Number of reservoirs, r 
Hydraulic head of reservoirs (m) 110.0 29.0; 31.46; 26.99; 28.14; 36.06; 36.26; 26.12; 30.64; 30.73 
Total pipe length, Ltot (km) 32.7 376.6 
Minimum ground elevation, zmin (m) 53.1 5.33 
Maximum ground elevation, zmax (m) 78.6 12.9 
Pipe materials Cast iron PVC and AC 
Pipe diameters (mm) 60; 80; 100; 110; 125; 150; 200 76; 95; 152; 190; 238; 300; 338; 380;428; 476; 508; 600; 762; 914 
Peak demand, Q (m3/s) 0.110 0.987 
Design pressure, h* (m) 25 12 
Fire flow, (l/s) 20 45.4 
hFP, (m) 10 

The two WNSs, obtained using the technique proposed by Di Nardo et al. (2013b), are illustrated in Figures 1 and 2. Each i-DMA is represented by dashed lines.

Figure 1

Parete WNS obtained with techniques proposed by Di Nardo et al. (2013a).

Figure 1

Parete WNS obtained with techniques proposed by Di Nardo et al. (2013a).

Figure 2

Matamoros WNS obtained with techniques proposed by Di Nardo et al. (2013a).

Figure 2

Matamoros WNS obtained with techniques proposed by Di Nardo et al. (2013a).

Parete was sectorized into two i-DMAs, and the delivered flow of each i-DMA was 49.17 l/s for i-DMA1 (4,819 customers) and 61.03 l/s for i-DMA2 (2,669 customers). Matamoros was sectorized into nine i-DMAs, where the delivered flow of each i-DMA was 72.1 l/s for i-DMA1 (30,868 customers), 50.77 l/s for i-DMA2 (21,736 customers), 210.68 l/s for i-DMA3 (90,199 customers), 118.16 l/s for i-DMA4 (50,588 customers), 40.28 l/s for i-DMA5 (17,245 customers), 164.26 l/s for i-DMA6 (70,325 customers), 270.50 l/s for i-DMA7 (115,810 customers), 13.15 l/s for i-DMA8 (5,630 customers), and 47.93 l/s for i-DMA9 (20,306 customers).

The computed PIs are shown in Tables 210. Both networks have a low original resilience index Ir, thus indicating the ‘low availability’ of the water systems for having changes made to the original layout of the networks by inserting gate valves without decreasing the hydraulic performance (Greco et al. 2012). The proposed partitioning tool nevertheless allowed network layouts that maintained a small change in the resilience index to be constructed, as shown in Table 2 by the index Ird (8.26% for the Parete network and 2.28% for the Matamoros network) and by the index Irnd (8.81% and 1.80%, respectively).

Table 2

Energy indices and entropy of both networks

OWNWNS
IrIrnSIrIrdIrnIrndS
Parete 0.35 0.32 5.77 0.32 8.26 0.29 8.81 6.33 
Matamoros 0.44 0.39 10.13 0.43 2.28 0.38 1.80 8.57 
OWNWNS
IrIrnSIrIrdIrnIrndS
Parete 0.35 0.32 5.77 0.32 8.26 0.29 8.81 6.33 
Matamoros 0.44 0.39 10.13 0.43 2.28 0.38 1.80 8.57 
Table 3

Pressure indices of Parete network

hmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDP
OWN 31.05 21.36 50.47 5.66 8.43 0.07 8.27 
WNS 31.33 23.74 49.77 4.10 7.67 0.00 7.53 
hmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDP
OWN 31.05 21.36 50.47 5.66 8.43 0.07 8.27 
WNS 31.33 23.74 49.77 4.10 7.67 0.00 7.53 
Table 4

Pressure indices of each isolated district meter areas in Parete network

OWNWNS
Nodeshmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDPhmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDP
i-DMA1 116 27.64 21.36 32.92 2.90 3.81 0.15 4.18 29.74 23.74 34.31 2.65 5.73 0.01 4.58 
i-DMA2 66 37.04 30.60 50.47 4.14 12.16 0.00 6.21 34.11 26.99 49.77 4.69 9.24 0.00 2.65 
OWNWNS
Nodeshmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDPhmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDP
i-DMA1 116 27.64 21.36 32.92 2.90 3.81 0.15 4.18 29.74 23.74 34.31 2.65 5.73 0.01 4.58 
i-DMA2 66 37.04 30.60 50.47 4.14 12.16 0.00 6.21 34.11 26.99 49.77 4.69 9.24 0.00 2.65 
Table 5

Pressure indices of Matamoros network

hmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDP
OWN 17.46 2.93 31.34 3.62 5.18 0.60 6.56 
WNS 17.16 3.04 31.39 4.61 4.81 0.83 6.92 
hmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDP
OWN 17.46 2.93 31.34 3.62 5.18 0.60 6.56 
WNS 17.16 3.04 31.39 4.61 4.81 0.83 6.92 
Table 6

Pressure indices of each isolated district meter areas in Matamoros network

OWNWNS
Nodeshmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDPhmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDP
i-DMA1 35 16.94 13.24 28.62 3.43 4.54 0.00 5.67 18.31 14.69 28.72 3.19 5.99 0.00 7.12 
i-DMA2 84 13.77 2.93 17.79 4.18 2.08 3.62 4.63 13.79 3.04 17.85 4.11 2.06 3.57 4.62 
i-DMA3 337 19.41 17.22 31.34 2.05 7.17 0.00 8.24 19.64 17.17 31.39 2.25 7.19 0.00 8.49 
i-DMA4 117 19.51 15.93 28.73 1.46 7.31 0.00 7.55 19.86 15.39 28.85 1.57 7.64 0.00 8.07 
i-DMA5 72 17.12 11.78 19.02 1.96 4.94 0.00 6.79 16.88 15.24 18.00 0.75 4.84 0.00 5.77 
i-DMA6 154 11.90 4.96 18.26 3.94 1.25 2.47 5.11 10.52 3.11 18.08 4.39 0.83 3.56 4.45 
i-DMA7 352 17.51 13.25 23.05 1.63 5.68 0.00 4.58 15.70 9.15 20.32 3.21 3.64 0.19 5.82 
i-DMA8 55 21.95 18.83 26.80 2.08 9.61 0.00 9.99 26.55 25.58 27.61 0.54 14.52 0.00 14.49 
i-DMA9 77 18.16 11.11 21.26 2.95 5.14 0.03 5.90 18.89 13.28 21.25 2.16 6.18 0.00 5.69 
OWNWNS
Nodeshmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDPhmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDP
i-DMA1 35 16.94 13.24 28.62 3.43 4.54 0.00 5.67 18.31 14.69 28.72 3.19 5.99 0.00 7.12 
i-DMA2 84 13.77 2.93 17.79 4.18 2.08 3.62 4.63 13.79 3.04 17.85 4.11 2.06 3.57 4.62 
i-DMA3 337 19.41 17.22 31.34 2.05 7.17 0.00 8.24 19.64 17.17 31.39 2.25 7.19 0.00 8.49 
i-DMA4 117 19.51 15.93 28.73 1.46 7.31 0.00 7.55 19.86 15.39 28.85 1.57 7.64 0.00 8.07 
i-DMA5 72 17.12 11.78 19.02 1.96 4.94 0.00 6.79 16.88 15.24 18.00 0.75 4.84 0.00 5.77 
i-DMA6 154 11.90 4.96 18.26 3.94 1.25 2.47 5.11 10.52 3.11 18.08 4.39 0.83 3.56 4.45 
i-DMA7 352 17.51 13.25 23.05 1.63 5.68 0.00 4.58 15.70 9.15 20.32 3.21 3.64 0.19 5.82 
i-DMA8 55 21.95 18.83 26.80 2.08 9.61 0.00 9.99 26.55 25.58 27.61 0.54 14.52 0.00 14.49 
i-DMA9 77 18.16 11.11 21.26 2.95 5.14 0.03 5.90 18.89 13.28 21.25 2.16 6.18 0.00 5.69 
Table 7

Fire protection indices of Parete network

hmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDPNFP
OWN 42.72 −45.58 54.18 9.40 12.22 29.69 20.05 
WNS-1 42.28 −7.80 55.57 8.76 12.18 13.80 19.36 
WNS-2 42.82 19.20 52.60 5.03 11.34 2.45 18.51 
hmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDPNFP
OWN 42.72 −45.58 54.18 9.40 12.22 29.69 20.05 
WNS-1 42.28 −7.80 55.57 8.76 12.18 13.80 19.36 
WNS-2 42.82 19.20 52.60 5.03 11.34 2.45 18.51 
Table 8

Fire protection indices of Matamoros network

hmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDPNFP
OWN 17.43 −72.51 31.36 7.74 5.66 6.46 9.45 21 
WNS-1 18.12 −68.28 31.42 6.00 5.31 5.59 8.57 14 
WNS-2 17.65 −79.29 31.42 8.91 5.96 7.12 10.55 38 
WNS-3 18.36 1.50 31.40 3.52 5.64 0.81 7.26 
WNS-4 17.98 −311.45 31.42 13.72 5.83 19.54 14.96 
WNS-5 18.01 −11.97 31.42 5.29 5.78 1.90 8.00 19 
WNS-6 16.38 −37.28 31.39 6.82 4.53 4.18 8.10 76 
WNS-7 18.02 2.20 31.42 4.67 5.57 1.01 7.62 
WNS-8 18.67 8.72 31.42 3.45 6.22 0.20 7.51 
WNS-9 17.90 −56.11 31.42 7.45 5.82 4.85 9.50 18 
hmean (m)hmin (m)hmax (m)hsd (m)MPSMPDMSDPNFP
OWN 17.43 −72.51 31.36 7.74 5.66 6.46 9.45 21 
WNS-1 18.12 −68.28 31.42 6.00 5.31 5.59 8.57 14 
WNS-2 17.65 −79.29 31.42 8.91 5.96 7.12 10.55 38 
WNS-3 18.36 1.50 31.40 3.52 5.64 0.81 7.26 
WNS-4 17.98 −311.45 31.42 13.72 5.83 19.54 14.96 
WNS-5 18.01 −11.97 31.42 5.29 5.78 1.90 8.00 19 
WNS-6 16.38 −37.28 31.39 6.82 4.53 4.18 8.10 76 
WNS-7 18.02 2.20 31.42 4.67 5.57 1.01 7.62 
WNS-8 18.67 8.72 31.42 3.45 6.22 0.20 7.51 
WNS-9 17.90 −56.11 31.42 7.45 5.82 4.85 9.50 18 
Table 9

Water quality indices of both networks

Agemean (h)Agemax (h)Agesd (h)
OWN Parete 2.40 24.00 2.01 
WNS Parete 2.39 24.00 2.13 
OWN Matamoros 5.41 24.00 3.78 
WNS Matamoros 6.59 24.00 4.70 
Agemean (h)Agemax (h)Agesd (h)
OWN Parete 2.40 24.00 2.01 
WNS Parete 2.39 24.00 2.13 
OWN Matamoros 5.41 24.00 3.78 
WNS Matamoros 6.59 24.00 4.70 
Table 10

Mechanical redundancy indices of both networks in pressure-driven analysis

FDImean (%)FDImax (%)FDImin (%)FDIsd (%)
OWN Parete 0.69 28.38 0.09 3.32 
WNS Parete 1.10 55.38 0.00 5.92 
OWN Matamoros 1.69 14.20 1.45 0.90 
WNS Matamoros 2.49 29.33 2.09 1.81 
FDImean (%)FDImax (%)FDImin (%)FDIsd (%)
OWN Parete 0.69 28.38 0.09 3.32 
WNS Parete 1.10 55.38 0.00 5.92 
OWN Matamoros 1.69 14.20 1.45 0.90 
WNS Matamoros 2.49 29.33 2.09 1.81 

The entropy S decreased after sectorization for the Matamoros network (from 10.13 to 8.57) due to pipe closures but increased for the Parete network (from 5.77 to 6.33), probably due to an improved flow distribution after sectorization, although future work is required to explain this increase in entropy. Therefore, as already observed by Greco et al. (2012), although high values of resilience do indicate high network robustness, network entropy does not provide coherent information regarding the capability of the network to ensure good performances following link failures, which are equivalent to pipe closures in the sectorization, even though it represents a surrogate for topological reliability that is useful in network design procedures.

The water pressure changed slightly in both networks after sectorization, as shown by the corresponding indices in Tables 36 (i.e., from hmin = 21.36 to 23.74 m for the entire Parete network, from hmin = 21.36 to 23.74 m for i-DMA1, and from hmin = 30.60 to 26.99 m for i-DMA2). In certain instances, when the water system contains more than one reservoir, the water pressure can increase, and in such cases, it is important to use other PIs to fully understand the behavior of the network. The water pressure in three i-DMAs of the Matamoros network is lower than the design pressure (12 m of head) before and after sectorization, thus reflecting the real situation in that city, where additional actions are required to achieve the design pressure.

The fire protection indices are reported in Tables 7 and 8. They are computed using the fire flow based on the suggestions of Milano (1995) for Parete and the current Mexican fire-fighting design practices for Matamoros. These fire indices exhibit some negative pressure values. Given that DDA is used to compute these indices, water cannot reach some network nodes under the simulated fire-fighting conditions.

The Parete network is almost sufficient in fire-fighting conditions, with NFP = 1 for the OWN and NFP = 2 for one i-DMA. The Matamoros network is clearly insufficient for fire fighting, both for the OWN and WNS, thus indicating that, in Mexico, water distribution networks are typically not designed for fire-fighting conditions (they are actually not equipped with fire hydrants). It is important, in principle, that the formation of DMAs includes fire-fighting capacity, but in Mexico the added cost of maintaining such capacity all the time is considered to be much higher than the value of having it, and fire-fighting relies mostly on fire-fighting trucks (moreover, because high pressures are required in network pipes in order for fire hydrants to work, there is an increase in leaks).

The maximum water age in Table 9, computed using EPANET, always equals 24.00 h, the duration of the analysis, thereby revealing that it is irrelevant as a PI in these cases but may be useful if the simulation lasts for longer analysis periods. The other two water quality indices indicated that water age was not significantly influenced by WNS because their values were very similar, that is, from Agemax = 2.40 to 2.39 h for Parete and from Agemax = 5.41 to 6.59 h for Matamoros. In certain cases, these values were better than those for the OWN.

Finally, the mechanical redundancy indices reported in Table 10 indicated some worsening of redundancy after sectorization for both networks, as expected; however, the resulting mean flow deficit for the WNS is only slightly higher than that for the OWN (from FDImean = 0.69 to 1.10 for Parete and from FDImean = 1.69 to 2.49 for Matamoros).

All proposed PIs allow for a comparison of the behavior of water networks before and after WNS. The analysis revealed that the methodology used for network sectorization is effective because the indices indicate that the alteration of hydraulic and water quality performance is compatible with the service level provided to users.

The fire protection indices indicated that the two water networks are inadequately equipped to face this emergency condition in both the original and sectorized layouts and that a PDA is more effective for such simulations.

CONCLUSIONS

WNP is widely used, but specific PIs have not been developed for comparing different possible sectorizations on a systematic and analytical basis. In this paper, several PIs are proposed for WNP and WNS, related to the following variables: energy dissipated in the network, pressure variation, fire-fighting capacity, water age, and mechanical redundancy.

The methodology was tested using two existing water supply systems: Parete (a small network in Italy) and Matamoros (a large network in Mexico).

Among the proposed indices, the resilience index appears most effective because it best represents the energy behavior of the entire network, whereas pressure indices best express the behavior of individual districts. The entropy index yielded heterogeneous results for the two networks and requires further analysis in future studies. The mechanical indices appear useful, although other operative conditions must be investigated to better understand their usefulness. Finally, even when the choice of particular indices depends on the aim of the performance analysis, this study demonstrated that a quantitative comparison between the OWN and WNS is possible. Nevertheless, additional studies are required to more comprehensively test some of the PIs. In future studies, the proposed methodology can be extended to analyze distribution networks suffering from water scarcity conditions.

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