Pressure-driven analysis (PDA) of water distribution networks necessitates an assessment of the supplying capacity of a network within the minimum and required pressure ranges. Pressure-deficient conditions happen due to the uncertainty of nodal demands, failure of electromechanical components, diversion of water, aging of pipes, permanent increase in the demand at certain supply nodes, fire demand, etc. As the demand-driven analysis (DDA) solves the governing equations without any bound on pressure head, it fails to replicate the real scenario, particularly when the network experiences pressure-deficient situations. Numerous researchers formulated different head–discharge relations and used them iteratively with demand-driven software, while some other approaches solve them by incorporating this relation within the analysis algorithms. Several attempts have been made by adding fictitious network elements like reservoirs, check valves (CVs), flow control valves (FCVs), emitters, dummy nodes and pipes of negligible length (i.e., negligible pressure loss) to assess the supplying capability of a network under pressure-deficient conditions using demand-driven simulation software. This paper illustrates a simple way of assessing the supplying capacity of demand nodes (DNs) under pressure-deficient conditions by assigning the respective emitter coefficient only for those nodes facing a pressure-deficit condition. The proposed method is tested with three benchmark networks, and it is able to simulate the network without addition of any fictitious network elements or changing the source code of the software like EPANET. Though the proposed approach is an iterative one, the computational burden of adding artificial elements in the other methods is avoided and is hence useful for analyzing large networks.
Analysis of water distribution systems under pressure-deficient conditions presents a challenging research area, as understanding and simulating the real scenario is complex. It is well known that demand-driven analysis (DDA) simultaneously solves the mass balance and energy balance equations to determine the flow in each pipe for a given network topology and configuration. However, such a DDA solution does not represent an exact behavior of the system when it is under pressure-deficient conditions or if a bound on service pressure is assigned (Ang and Jowitt, 2006; Siew and Tanyimboh, 2012; Suribabu, 2015). It is possible to notice the negative pressure in DDA whenever the total loss of the head occurring from the source to node exceeds the available source head. This mainly happens when the demand assigned to a node is higher than what the pipes incident to that node can actually carry based on the available source head. To compute the actual outflows from the nodes within given pressure bounds, modifications are needed, either in the source code of a demand-driven simulation engine (e.g., Cheung et al., 2005) or by adding additional fictitious components like reservoirs, check valves (CVs), flow control valves (FCVs), emitters, dummy nodes and very short pipes to the demand nodes (DNs – e.g., Ozger, 2003; Ang and Jowitt, 2006; Rossman, 2007; Suribabu and Neelakantan, 2011; Jinesh Babu and Mohan, 2012; Gorev and Kodzhespirova, 2013; Sivakumar and Prasad, 2014, 2015; Morley and Tricarico, 2014; Abdy Sayyed et al., 2014, 2015; Suribabu, 2015; Suribabu et al., 2017; Mamizadeh and Sharoonizadeh, 2016; Mahmoud et al., 2017; Pacchin et al., 2017).
Interpretation of the nodal demand vs. head curve.
Flow chart illustrating the computational steps involved in the proposed approach.
Layout of the two-loop network (example 1 and 2).
Mahmoud et al. (2017) addressed the shortcoming of each of these methods for evaluating outflow in the case of large networks and under extended-period simulation (EPS). They have developed a new way to handle PDA using EPANET in single-iterative type after an introduction of a check valve, a flow control valve and a flow emitter for both the steady state and EPS.
Various head–flow relationships for PDA.
In the beginning, the pressure-deficient condition was considered a rare phenomenon and/or a typical problem in an operational scenario. However, when concern on reliability gained importance, the failure scenarios were analyzed, and thus analysis of the pressure-deficient condition became popular. Two approaches are popular for analyzing the pressure-deficient condition. In the first approach a specific pressure–demand relationship is embedded in the source code of the simulator (requires changing of the source code). Some of the important studies by several authors using this approach are presented in tabular form below (Table 1).
Apart from the above research in the table, Liu et al. (2011) and Siew and Tanyimboh (2012) adopted different methodologies to obtain node heads in EPANET. Giustolisi et al. (2011) developed and used new Excel-based software called WDNetXL. Generally, the limitations of this approach (Mahmoud et al., 2017) are that (1) it requires a change in algorithm and program code, (2) the computer codes are not available, (3) it requires iterations, (4) it is mostly demonstrated on sample networks, and (5) it exhibits difficulty in handling extended-period simulation.
Use of artificial components in PDA.
Some of the researchers in the recent years attempted pressure-deficient analysis using EPANET (popular freeware demand-driven model) by introduction of a few artificial or imaginary components but without node head–flow relationships. This research claims a lower number of iterations, and the recent research claims single iteration (no iteration). The works using components in the demand-driven model for pressure-deficient analysis are presented in Table 2.
A literature review indicates that the approach of using a demand-driven engine to get the pressure-driven results is getting more attention. This is due to computational convenience and the promising trend of development. Hence, this research is also planned to focus on this approach. This paper proposes a simple approach to suit both the single period and EPS but without addition, deletion, opening and closing of network elements. The proposed method requires only assigning an emitter coefficient and altering nodal elevation by incorporating minimum pressure head with existing elevation. Though the method is an iterative type, it can be easily implemented, irrespective of the size of the network.
The EPANET 2 (Rossman, 2000) hydraulic simulation engine contains a special
element called the emitter that behaves as a sprinkler head at the node and
delivers an outflow proportional to the available pressure head. Rossman (2007)
discussed the possibility of building the pressure-driven network analysis
proposed by Ang and Jowitt (2006) in the EPANET hydraulic solver using
this emitter feature. Furthermore, Suribabu (2015) proposed a method to use
the emitter as a replacement to the connection of fictitious reservoirs to all
the DNs. Here, the emitter determines the possible supply at
all deficient nodes based on its available pressure head. The flow from the
emitter is expressed as follows (Rossman, 2000):
Layout of multisource pumped network (example 3).
Layout of Modena network (example 4).
In Abdy Sayyed et al. (2015), the FCV is used to fulfill the maximum flow constraint, and the CV is employed to avoid flow reversal. Single-iteration pressure-driven analysis (SIPDA) proposed by Mohmoud et al. (2017) adopted the same sequence of network elements as that of the Abdy Sayyed et al. (2015) approach. But SIPDA adds the sequence of network elements and modifies their nodal elevations only for those nodes experiencing a pressure deficit. Pacchin et al. (2017) used another new sequence of elements (general purpose valve – GPV, CV and artificial reservoir) to evaluate outflow from the node under pressure-deficient conditions. Pacchin et al. (2017) applied the proposed approach and other similar methods to two real water distribution networks and concluded that their proposed method and that of Abdy Sayyed et al. (2015) are able to correctly produce the behavior of the network under pressure-deficient conditions. However, the drawback of these methodologies is the need to include two dummy nodes per node, which further increases the number of components and the topological complexity of the network. Though the addition of elements make it a single snapshot analysis, its incorporation into each demand node makes the network too complex in topology. It consumes lot of time of the network modeler, unless a separate integrated component is created with a setting option in the existing software.
Many scientists (Bhave, 1981; Germanopoulos, 1985; Wagner et al., 1988; Reddy and Elango, 1989, 1991; Chandapillai, 1991; Fujiwara and Ganesharajah, 1993; Tucciarelli et al., 1999; Tanyimboh et al., 2001; Wu et al., 2009; Tanyimboh and Templeman, 2010) have suggested different head–flow relations for assessing the supplying capability of nodes under pressure-deficient conditions. Figure 1 presents an interpretation of the head–flow relations.
Actual outflow against design demand under no supply from reservoir ID 272 (LPS – liters per second).
Nodal pressure head under no component failure condition.
Given the variables defined in Fig. 1, there are different assumptions
that the modeler can make:
The more general case is the one in which no assumption is made for When When When Though available pressure is greater than required pressure, the outflow at
demand nodes does not exceed its design demand. This is a very basic
assumption made by municipal engineering at the project formulation stage. No outflow is possible at demand node if available pressure is less than
minimum service pressure. Pressure-dependent outflow between required and minimum pressures takes the
form shown in Fig. 1, and for the corresponding condition, the percentage
of the valve opening is defined by the curve. The water distribution network is considered a non-airtight system. Hence,
no siphonic flow is possible in the network. Emitter coefficient is considered based on either Eq. (2) or 100 times the
nodal demand to estimate the outflow at minimum residual pressure (Eq. 5).
The method proposed in this study requires no assumptions of
The present study proposes a simple approach by setting the emitter
coefficient and changing the elevation of the nodes that have been
identified as being pressure deficient through a few simulation runs of DDA. The
proposed approach completely eliminates the serial inclusion of fictitious
network elements at any node of the system. The entire procedure is
illustrated by a flow chart shown in Fig. 2.
Nodal pressure when reservoir ID 272 is disconnected (DDA).
Nodal pressure when reservoir ID 272 is disconnected (PDA).
For a given condition, the network should initially be simulated using
EPANET 2, identifying the maximum pressure-deficient node and setting its
demand as zero. This process should be implemented repeatedly until all the
nodes reach the condition
The proposed methodology was experimented with three benchmark networks. The results of example 1 and 2 were compared with SIPDA, proposed by Mahmoud et al. (2017).
Step-by-step analysis results showing nodal outflows and pressure at each level of simulation. Bracketed values denote available pressure in meters.
A single-fixed source-head two-loop network with six demand nodes and eight
links (proposed by Ang and Jowitt, 2006, for PDA) is considered for
illustrating the proposed approach (see Fig. 3). Each pipe is 1000 m long, with
a Hazen–Williams coefficient of 130. The nodal demand for each node is 25 L s
Step-by-step analysis results showing nodal outflows under two pressures.
DDA shows negative pressure at all the demand nodes except node 2, while pipe
3 was isolated from service (scenario 1). Node 4 was observed as the maximum
negative pressure node, and its nodal demand was set to zero. Again hydraulic
simulation is carried out to verify whether all nodes turned into pressure
above zero. But node 6 was still facing a higher pressure-deficit condition
from nodes 3 to 7, and its demand was set to zero. After setting the emitter
coefficient to both node 4 and 6, the hydraulic analysis shows a negative
flow at node 4 and a negative pressure at node 7. By disconnecting pipes
incident to node 4 and removing its
Nodal and pipe properties of multisource pumped network.
Design demand during different time steps for multisource pumped network.
Actual outflow against design demand when there is no supply from reservoir ID 270.
In the next case (scenario 2), a fire demand of 50 L s
Nodal outflows under pump 1 failure condition for multisource pumped network.
Total outflow from Modena-network-selected links' isolation condition.
In the third scenario, a fire demand of 50 L s
Network 1 was used as it is for further analysis by setting reservoir
elevation to 135 m instead of 100 m. The minimum and required pressures at
all the demand nodes are designated as 15 and 30 m respectively. DDA
indicates that the network can supply design demand from all the demand
nodes at the required pressure level of 30 m. SIPDA and the proposed approach
require an emitter coefficient,
PDA was carried out by the proposed approach. DDA needs to be run five
times, and results obtained are presented in Table 4. The proposed method
indicates full supply of design demand at nodes 2 and 3, while the remaining
nodes are able to supply only partial demand. For the same case study, SIPDA
makes partial supply at nodes 4, 6 and 7, while recorded pressure is in
between
Furthermore, by closing two links, 3 and 6, the network was simulated, and DDA shows pressure below minimum at nodes 4, 5, 6 and 7. By applying proposed approach, actual demands and pressures were evaluated and presented in Table 4. Under the failure condition in pipes 3 and 6, the network is able to supply full design demand at nodes 2 and 3. The remaining nodes are able to supply partial demand only.
A multisource pumped water distribution network presented by Jinesh Babu and Mohan (2012) was considered for further testing of the proposed approach. Figure 4 shows the network layout, consisting of two pumps with the capacity of 125 kW each, instead of 125 hp, considered by Jinesh Babu and Mohan (2012), and was designed to deliver two-thirds of total demand. These two pumps, P1 and P2, pump the water from two sources, S1 and S2, respectively, whose elevations are 100 m each. The remaining one-third of total demand is drawn from reservoir, S3, whose elevation is 200 m, and one flow control valve is provided between reservoir S3 and node 7 in order to control the flow to one-third of total demand. A demand pattern with four intervals is considered with demand factors (DFs) of 0.2, 1.0, 0.6 and 0.8, which represent time intervals of 0.00 to 6.00, 6.00 to 12.00, 12.00 to 18.00 and 18.00 to 24.00 h respectively. The optimal speed of pumps for the respective time interval needs to be set to 0.584, 1.0, 0.842 and 0.927. The Hazen–Williams roughness coefficient of 130 is assumed for all the pipes. As Jinesh Babu and Mohan (2012) did not specify the upper and lower service pressure limit to the network, it is assumed in the present study that the required and minimum pressures needed for each demand node as 30 and 15 m respectively. Table 5 presents the pipe and nodal properties of the network. Table 6 shows the required nodal outflows at four time steps.
The pump 1 failure case was analyzed to examine the proposed approach. The
results of EPS analysis for four time steps are presented in Table 7. This
scenario produces partial flow at several nodes in all time steps. It is to
be noted that in the first and second time steps, all nodes supply some
water, whereas in the next two time steps, node 1 is unable to deliver even partial
flow. Two nodes at time steps 1 and 2 indicates pressure greater than
To examine the applicability of proposed approach on a large size benchmark
network, a Modena network (MOD) given by the Centre for Water Systems at the
University of Exeter (Wang et al., 2014) is considered. Its layout is shown
in Fig. 5, and it consists of 317 pipes, 268 demand nodes and four reservoirs
with a fixed head in the range of 72.0 to 74.5 m. In the present work, the layout,
its diameter and a Hazen–Williams roughness coefficient of 130 are
considered, as they are given by the network. The minimum and required pressures are
assumed to be 10 and 20 m respectively. Supply from reservoir ID 272 is
stopped fully by isolation of a pipe connecting the reservoir and nearest node.
DDA indicates a pressure deficit (i.e., below
Furthermore, supply from reservoir ID 270 is closed, and the proposed approach was applied. It can be noticed that DDA showed that 232 nodes are pressure-deficient nodes. In the absence of supply from reservoir ID 270, the network is able to supply 78.46 % of total design demand. From Fig. 10, it is possible to notice the large number of supply nodes becoming affected in the absence of reservoir ID 270; 49 % of total nodes could deliver full design supply, and the remaining nodes could make only partial supply. Table 8 presents the total outflow from the network obtained by isolation of selected pipes. It is evident from the results that the proposed approach is able to find the nodal outflow under any pipe failure condition, apart from the pipe connecting the source.
Pressure-driven analysis (PDA) of the water distribution network estimates realistic outflow at all demand nodes while the network is under pressure-deficient conditions. Use of available network components like the reservoir, valves and emitter to simulate pressure-based outflow is found to be a simple approach, as it could be implemented easily for small networks without a change in the source code of commercial software. But the major bottleneck in adopting such an approach is that a large number of artificial components needs to be added to either all demand nodes or deficient nodes. This increases the complexity of the network configuration and also the burden to the computational part. The proposed approach does not utilize the artificial components other than emitter. The emitter is not a physical component to be added at the demand nodes. Instead it requires an appropriate coefficient to activate the emitter and estimate the outflow based on available pressure at the node. By changing the nodal properties to those nodes categorized as pressure deficit, the pressure-based outflow is able to evaluate by proposed iterative approach using the emitter option alone. From the analysis of the results, it is evident that the proposed approach can be easily implemented for various pressure limits.
The data for example network 4 is available at the following link
All authors made equal contributions to developing the algorithm and its application to example problems and writing the paper.
The authors declare that they have no conflict of interest.
The authors are grateful to the anonymous reviewers whose comments helped in improving the quality of the paper significantly. Edited by: Luuk Rietveld Reviewed by: two anonymous referees