Emitter based approach for estimation of nodal out ow to ...scientiairanica.sharif.edu/article_1995_d568d8ea8b515486ef00fe6429f5df2c.pdf · algorithms and models for an optimal design

Scientia Iranica A (2015) 22(5), 1765{1778

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringwww.scientiairanica.com

Research Note

Emitter based approach for estimation of nodal out owto pressure de�cient water distribution networks underpressure management

C.R. Suribabu�

Centre for Advanced Research in Environment (CARE), School of Civil Engineering, SASTRA University, Thanjavur - 613401,Tamilnadu, India.

Received 21 April 2014; received in revised form 5 September 2014; accepted 18 February 2015

KEYWORDSHydraulic simulation;Water distributionsystem;Reliability;Demand drivenanalysis;Emitter;Pressure dependentanalysis.

Abstract. The hydraulic network solver simulates the behavior of a water distributionnetwork for a given set of geometric and hydraulic parameters, such as pipe length, pipediameter, tank size, pump capacity, demand, and pipe roughness, etc. Over the years,many researchers have developed a number of hydraulic simulation models (software) forthe analysis and design of water distribution networks, most of which are based on DemandDriven Analysis (DDA). This paper reviews the existing approaches and examines theusefulness of the emitter feature that is available in the hydraulic network solver (EPANET)as a tool for the pressure driven model. The emitter based method determines the possiblesupply at all de�cient nodes, based on the availability of energy at that node by introductionof an emitter. This method, along with three existing approaches, has been applied to threebenchmark networks, and important �ndings from the study, in terms of convergence andnumerical results, are presented. The framework of the head- ow based approaches andthe proposed method is carried out using the toolkit feature available in the EPANEThydraulic solver.c 2015 Sharif University of Technology. All rights reserved.

1. Introduction

Water distribution systems connect the source of awater supply to the consumer using hydraulic com-ponents, such as tanks, reservoirs, pumps, pipes andvalves. The analysis and design of such a system iscarried out for various demands and under variousoperating conditions. The size of the pipes andother hydraulic components should be able to providehydraulic heads greater than those of the minimumrequired at all demand nodes. If the size of the pipesforming the network is inadequate, then, the analysis

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may show pressure heads below the acceptable for ser-vice. In the event of an unexpected failure, the networkmay not be able to supply some or all nodal demandsat the desired service pressure. A similar situationmay also arise when the network is analyzed for �redemand, besides the base demand. Such a condition ofthe network is called the pressure de�cient condition.Traditional methods of analysis of water distributionnetworks infer that nodal demand is always satis�ed,regardless of the nodal pressure head available in thedistribution system. This approach is called demand-driven analysis and is used by almost all hydraulicnetwork solvers. This formulation is valid only whenthe hydraulic pressure at all nodes is adequate, so thatdemand is independent of pressure [1]. The analysisof water distribution systems under pressure-de�cient

1766 C.R. Suribabu/Scientia Iranica, Transactions A: Civil Engineering 22 (2015) 1765{1778

conditions is a subject of interest and importance forwater utilities around the world [2]. Assessing thenodal supply capacity under de�cient conditions isessential for the reliability assessment of the networkand the preparation of operation strategies for valvesettings in order to provide a partial supply at de�cientnodes and evolve possible equitable distribution ofwater. Demand driven analysis solves the governingexpressions (mass balance and energy principle) for theanalysis of ow for a water distribution network. But,it does not represent the exact, or even quasi, behaviorof the system when the system is under pressure de�citconditions. This happens due to a total loss of headoccurring from the source to the node exceeding theavailable source head. In such a situation, the headloss from the source to the outlet is overestimated onaccount of unrealistic out ow expected at the demandnode. Hence, an appropriate supply should be evalu-ated by considering the available pressure head at thedelivery node to overcome the pressure de�ciency. Tosolve this problem, an additional condition is requiredto limit the out ow based on pressure availability in thedistribution system. Several researchers have suggesteddi�erent methods for evaluation of out ow at nodesunder pressure de�cient conditions. Over the pastthree decades, a signi�cant amount of research hasbeen taking place into the development of optimizationalgorithms and models for an optimal design of waterdistribution networks, due to its computational andengineering complexity [3-21]. A module based ondemand driven analysis is widely coupled with anoptimization algorithm to explore pipe diameters thatsatisfy the hydraulic-head requirements with the leastcost. The requirements of pressure driven analysisdoes not arise for new network designs, as the pipediameter and size of other components are adjusted tosatisfy the hydraulic-head requirements with the leastcost. For component failure analysis, demand drivenanalysis can yield nodal pressures that are lower thanthe required minimum, or, sometimes, even becomenegative [22]. This paper presents a review of variousexisting methods in addition to their implementationstrategies using an EPANET [23] hydraulic solver andalso endeavors to examine the possibility of employingan emitter feature, available in the EPANET hydraulicsimulation engine, for predicting the behavior of de�-cient network performance.

2. Methodologies

To compute the actual out ow of nodes under pressurede�cient conditions, a head and ow based relation iscommonly used iteratively to obtain the out ow. Al-ternatively, some researchers have used arti�cial reser-voirs to obtain the out ow under such circumstances.Many investigators have suggested di�erent ow-head

based relations for assessing the supplying capabilityof nodes under pressure de�cient circumstances. Mostpopularly, the method proposed by Wagner et al [24] iscommonly used to simulate the actual ow. Todini [25]expanded the demand driven global gradient algorithmfor pressure dependent analysis. Recently, Giustolisiet al. [26,27] used a generic function proposed byWagner et al. [24] and integrated with a global gradientalgorithm for analyzing pressure de�cient networks.

The pressure driven approach treats demand asthe random variable and recognizes the dominanceof pressure by de�ning a relationship between thesupply and the pressure at each node. In a pressure-de�cient network, a relationship exists between the ow and pressure at a demand node, termed the NodeHead-Flow Relationship (NHFR). During simulation,NHFR at di�erent nodes must be satis�ed, along withequations for the conservation of mass and energyfor the network as a whole [28]. Such an analysiscan be carried out by embedding a Nodal Head-Flow Relationship (NHFR) in the governing systemof equations [29]. Probably, Bhave [28] was the �rstto provide a systematic solution, named Node FlowAnalysis (NFA), for the analysis of de�cient networksthat determine nodal supply considering the head-discharge relationship, which is given by:

qavlj = qreqj (adequate� ow) ; if Hvalj � Hmin

j

0 < qavlj < qreqj (partial ow) ; if Havlj = Hmin

j

qavlj = 0(no ow); if; Havlj � Hmin

j

9>>>>=>>>>; (1)

where qavlj is the ow available at node j, qreqj is the ow required at node j, Hval

j is the available head atj, and Hmin

j is the minimum required head at node junder normal working conditions.

In NFA, the minimum pressure and availablenodal heads, and also the required and available nodal ows, are considered simultaneously. Later, Ger-manopoulos [30] presented an empirical relationship todetermine the nodal out ow as follows:

qavlj = qreqj

�1�10�cj[(Havlj �Hmin

j )=(Hdesj �Hminj )]

�; (2)

where Cj is the node constant.The actual out ow at the node is calculated

iteratively at which each level of iteration requiresone complete demand driven analysis. Reddy andElango [31] proposed a head dependent analysis foran uncontrolled outlet with reference to residual headsavailable at the node. The relationship is given below:

qavlj = Sj�Havlj �Hmin

j�0:5

; (3)

where Sj is the node constant.

C.R. Suribabu/Scientia Iranica, Transactions A: Civil Engineering 22 (2015) 1765{1778 1767

Use of this expression requires either a calibratedor reasonable assumed node constant. Wagner etal. [24] proposed a generic formula that relates the headand ow as given below:

qavlj = qreqj (adequate� ow) ; if Hvalj � Hmin

j

qavlj = qreqj

�Havlj �Hmin

jHdesj �Hmin

j

�1=n

(partial ow) ;

if Hminj < Havl

j < Hdesj

qavlj = 0(no ow); if; Havlj � Hmin

j

9>>>>>>>>=>>>>>>>>;(4)

where n is the exponent constant (its value often takenas either 1.85 or 2).

Wagner et al. [24] suggested the use of a parabolicrelationship between nodal ow and nodal head forpressure-de�cient situations. Accordingly, they sug-gested three separate relationships, as shown in Eq. (4),for adequate-, partial- and no- ow situations. It is,however, worth noting that even though they havesuggested a parabolic relationship between nodal owand nodal head for partial- ow situations, they usethis relationship only once to �nd out the availablenodal ow for the obtained nodal head. Thus, they donot truly use the head- ow relation at the partial- ownode. It is to be noted that Wagner et al. [24] describedNHFR using two heads, Hmin

j and Hreqj , and, recently,

Abdy Sayyed and Gupta [32] compared the results ob-tained by modeling a serial and a looped network withthese two di�erent NHFRs. Chandapillai [33] proposeda relationship between the actual nodal out ows andheads in response to a minimum head as:

Havlj = Hmin

j +Kj(qavlj )n: (5)

Fujiwara and Ganesharajah [34] proposed the relation-ship between the pressure head and discharge in thedemand nodes as expressed in Box I.

Gupta and Bhave [29] reviewed di�erent methodsused for predicting the performance of a water distri-bution system under pressure de�cient conditions. Itwas found that the NFA approach based on Wagneret al. [24] predicted the behavior of the serial networkexample better than the other two approaches, namelyBhave [28] and Germanopoulos [30].

Tanyimboh et al. [35] showed the derivation forthe Wagner head- ow relation by rearranging Eq. (5)within the limitation of qj = qavlj for Hj = Hdes

j .Furthermore, Tanyimboh et al. [35] presented a modi-�ed relation for the same expression relating the sourcehead and out ow at the demand node. Tucciarelli etal. [36] suggested a pressure dependent leakage relationas follows:

qavlj = qreqj ; if Havlj � Hmin

j

qavlj = qreqj sin2�HavljHminj

�; if 0 < Havl

j < Hminj

qavlj = 0(no ow); if Havlj � 0

9>>>>>>=>>>>>>;(7)

Tabesh et al. [37] used the head-dependent ow termof Wagner et al. [24] in the continuity equations bychoosing the nodal piezo-metric heads as unknownparameters, and the resulting set of equations, alongwith the energy equations, are solved iteratively usingthe Newton-Raphson method. Kalungi and Tanyim-boh [38] presented a new hydraulic simulation modelbased on pressure driven simulation, for assessing theredundancy of water distribution systems. The noveltyof their approach is that the proposed network analysistechnique includes the introduction of a key partial ow node and the use of a joint head ow systemof equations. They de�ned key partial ow nodesas nodes whose out ows a�ect the out ow at othernodes. Ozger [39] presented the Semi-Pressure DrivenAnalysis (SPDA) framework using EPANET toolkitsfor predicting the performance of a network underpartially failed conditions and the same is used forreliability assessment of the network. Ozger [39] wasperhaps the �rst man to use arti�cial reservoirs foranalysis of pressure de�cient networks. Subsequently,Ozger and Mays [40] used SPDA for reliability as-sessment, in association with an optimization model,for optimal location of isolation valves consideringreliability aspects. Ang and Jowitt [22] introduced anovel methodology, called PDNA (Pressure-De�cientNetwork Algorithm), which uses a repeatedly demand-driven model. The novel feature of this method isthat it does not use the head- ow relationship toadjust the demand but uses the addition or deletion

qavlj = qreqj for Havlj � Hdes

j

qavlj = qreqj

0@ RHavljHminj

(Havlj �Hminj )(Hdesj �Havlj )dHRHavlj

Hminj

(Havlj �Hminj )(Hdesj �Havlj )dH

1A (partial ow); if hminj < Havl

j < Hdesj

qavlj = 0(no ow); if Havlj � Hmin

j

9>>>>=>>>>; (6)

Box I


of arti�cial reservoirs. Rossman [41] discussed thepossibility of building the PDNA proposed by Angand Jowitt [22] in an EPANET hydraulic solver usingan emitter feature. Suribabu and Neelakantan [42]introduced a new iterative method using EPANETfor this problem through connecting a complementingreservoir at the node. The basis of the method is tosupplement the ow equivalent to the shortfall froma complementary reservoir into the pressure de�cientnodes. It is to be noted that the iterative execution ofEPANET 2 with arti�cial reservoirs introduced at anydemand nodes with insu�cient pressure to carry outpressure-de�cient network analysis proposed by Ozgerand Mays [40], Ang and Jowitt [22] and Suribabu andNeelakantan [42] employed the NHFR suggested byBhave [28]. Jinesh Babu and Mohan [43] modi�edthe algorithm that Ang and Jowitt [22] proposed inorder to carry out head dependent modeling in asingle execution of the unmodi�ed EPANET 2 algo-rithm.

Recently, Wu et al. [1] proposed a Pressure Depen-dent Demand (PDD) function as below, which is inte-grated with the global gradient algorithm. Tanyimbohand Templeman [44] presented a continuous functionbetween the out ow and pressure head to overcome theconvergence di�culties prevailing in the existing dis-crete functions. A Newton-Raphson algorithm is usedto solve the set of governing equations of the networkanalysis with the proposed continuous function. Baeket al. [45] presented a pressure driven analysis modelby integrating a hydraulic simulator with the HarmonySearch algorithm. The optimization model minimizesthe di�erence between assumed and calculated heads atthe demand nodes. Head- ow relationships suggestedby Wagner et al. [24] and Chandapillai [33] are used todetermine the proper head at each demand. Gorev andKodzhespirova [46] suggested a non-iterative algorithmfor pressure-de�cient network simulation consideringthe NHFR described by the two heads. They consid-ered modeling with arti�cial pipes, having assigned asuitable resistance to simulate partial ow conditions.Siew and Tanyimboh [47] presented the extension ofthe EPANET hydraulic simulator by incorporatingpressure dependent demands. They integrated thehead- ow function developed by Tanyimboh and Tem-pleman [44,48] with the global gradient method. Theline search and back tracking procedure are used to en-hance the algorithm's performance. Shirzad et al. [49]conducted laboratory and �eld experiments to estimatethe out ow from the faucet with respect to the availablepressure. It is highlighted that the relationship betweenthe ow at the node and the pressure at that nodeis more complicated, due to varying operations ofthe faucet, the di�erence in elevation of the faucetand node levels, and the complexity of the pipingbetween them. Further, study reveals that the pressure

discharge relation proposed by Wagner et al. [24] isfound to closely match with experimental results. Junand Gouping [50] used the EPANET toolkit iterativelyto modify the nodal out ow obtained based on PressureDependent Demand Formulation (PDDF). Recently,Sivakumar and Prasad [51] developed a head-dischargerelationship based on the working principle of M-PDNA [43] and also illustrated means of applying M-PDNA with the EPANET Toolkit function using theEPANET simulation engine.

In this paper, the generic relationships betweenhead and ow proposed by Germanopoulos [30], Wag-ner et al. [24] and Tucciarelli et al. [36] are used tosimulate the out ow for pressure de�cient networks. Itis referred to herein as the head- ow based approachfor pressure driven analysis (HFPDA-I, II and III,respectively). These three relationships are selectedbased on three di�erent criteria, namely, the empiricalexponential form, the parabolic form, and the sinefunction.

The evaluation of out ow at de�cient nodes usingthe emitter feature available in the EPANET hydraulicsolver is referred to as the Emitter based Approach forPressure Driven Analysis (EPDA). The performanceof EPDA and HFPDA is examined using three samplenetworks by creating a pressure de�ciency throughisolating a link. The �rst example is a simple singleloop network having the same nodal elevations withdi�erent nodal demands. The second example is asingle source two-loop network having di�erent nodalelevations and the same nodal demands for all nodes.The framework of HFPDA and EPDA is built usingthe Toolkit feature available in the EPANET hydraulicsolver.

3. Head- ow based approach for pressuredriven analysis (HFPDA)

The head- ow relation proposed by Germanopou-los [30], Wagner et al. [24] and Tucciarelli et al. [36]are used to simulate ow using the EPANET DemandDriven Analysis (DDA) for a pressure de�cient net-work. The following are the steps taken to evaluatethe out ow at the nodes:

1. Solve the network by isolating a link.2. Set the nodal demand to zero if the nodal pressure

is negative, otherwise assume nodal pressure value(close to Hmin).

3. Calculate qavl using any one of the expressions, asgiven in Eqs. (2), (4) and (7).

4. Simulate the network after changing nodal demand(qavl).

5. Update the value of qavl according to the new Havi,and simulate the network with updated qavl.


6. Repeat steps 4 and 5 until [Pndi=1 (Hn�1

avl;i �Hnavl;i)2]

< 1� 10�9 or Havl for the node above Hmin.

where n is the number of iterations and nd is thenumber of demand nodes.

While solving the pressure de�cient network, it isvery common for the analysis to show non-serviceablepressure or even negative pressure at a few nodes,using demand driven software, According to the head- ow functions, the demand should be set to zerofor the node/nodes with a pressure head below theminimum/serviceable value. When it is set at the very�rst iteration of pressure driven analysis to all a�ecteddemand nodes, then at the end of the �rst iteration,none of the nodes will experience a de�cit scenario.In turn, those de�cit nodes will have pressure abovethe serviceable pressure. This shows that one or moreidenti�ed de�cit nodes could probably supply part ofthe designed/required demand. Hence, it is requiredto verify the condition of the network progressivelyby setting the nodal demand to zero, starting froma node that faces maximum pressure de�cit. Whenthe pressure in the de�cient nodes reaches a positivevalue after setting its demand to zero, the head- owfunction can then be used iteratively till the speci�edconvergence is achieved. This is further illustratedthrough sample networks.

4. Emitter based approach for pressure drivenanalysis (EPDA)

Pressure management becomes imperative when pres-sure de�ciency arises in the water distribution net-work. Estimation of out ow at de�cient nodes andarriving at better operating policies under such cir-cumstances are found to be complex. This paperpresents utilization of the Emitter option availablein the EPANET hydraulic solver for �nding a solu-tion to the pressure de�cient network under pressuremanagement. Emitters are devices connected withnodes that model the ow through a nozzle or ori�ce.Generally, emitters are used to model ow throughsprinkler systems and irrigation networks. In waterdistribution system modeling, emitters are used tosimulate the leakage in a pipe connected to a nodeand to compute a �re ow at the node (the owavailable at some minimum residual pressure). Theemitter feature available in EPANET can be usedfor pressure dependent ow analysis. Rossman [41]illustrates how the emitter in EPANET can be usedequivalently as arti�cial reservoirs of PDNA, providedan appropriate emitter coe�cient is used. Sivakumarand Prasad [51] highlighted that the working of Emitterdevices in the EPANET engine follows the uncon-trolled head-discharge relationship de�ned by Reddyand Elango [31]. In the present work, the Emitter

option of the EPANET is applied only to those nodesidenti�ed through demand driven analysis. Hence, anuncontrolled out ow situation does not arise in theproposed methodology.

If the head- ow loss relation chosen for the pipeswithin the EPANET hydraulic solver is the Hazen-Williams equation, then the ow rate can be expressedas follows:

Q = Kepn; (8)

where Ke = CHWD2:63(cL)�0:54; p = H � E; andn = 0:54.

The above expression for out ow at the node isused as the emitter equation in EPANET in whichKe is the emitter co-e�cient and n is the emitterexponent. The value of the emitter co-e�cient shouldbe selected according to the property of the pipe con-sidered, namely, diameter, length, and Hazen-Williamcoe�cient that connects the node and the arti�cialreservoir. The value of c = 1:209 � 1010, if theunits for H, E, and L are in meters, Q in L/s anddiameter in mm. Ang and Jowitt [22] used a pipe ofsize 350 mm, length 0.1 m and CHW - 130 to connectthe arti�cial reservoirs with the nodes. The arti�cialreservoir can be replaced by the emitter device bysetting its co-e�cient and exponent to 7949.4 and 0.54,respectively [41].

The emitter based approach presented here aimsto �nd the out ows at all de�cient nodes. Whenthe pressure de�cient network is solved by demanddriven analysis, it may show a greater number of nodesunder pressure de�cient conditions. This is due to anoverestimation of the head loss from the source to theoutlet for the sake of satisfying the unrealistic out owexpected at the demand node. But, in reality, it maynot be so. The proposed method ensures supply of thedesigned demand to all non-de�cient nodes and partialsupply to de�cient nodes. By reducing the out ow at afew or all non-de�cient nodes, the partial demand canbe supplied to the de�cient nodes. Out ow in all nodesis based on the availability of energy at that node.The design demand at the node will be fully satis�edonly if su�cient energy is available. The availability ofenergy at a particular node depends not only on thesource, but also on how the supply is drawn in eitherthe en-routed nodes or neighboring nodes. Hence, it isessential to have an approach that satis�es the required(design) out ow at all non-de�cient nodes and that,overall, imitates reality as closely as possible. Thestepwise procedure is as follows:

1. Isolate the pipe (close the link) and run the hy-draulic analysis. Check the pressure at all nodes.If the pressure at all nodes is above Hmin, it is anon-de�cient network, with respect to isolation ofthat link. Otherwise, it is considered de�cient.


2. Identify a node that experiences maximum pressurede�ciency and set the nodal demand to zero. Per-form the hydraulic analysis.

3. Repeat step 2 until no node experiences a pressurede�cit.

4. If the last updated pressure de�cient node possessesresidual pressure in excess of Hmin, then, set itsnodal elevation as Hmin and emitter co-e�cient as7949.4 in the EPANET hydraulic solver. Again,perform the hydraulic analysis.

5. Check the pressure at all nodes. If the pressureat all demand nodes is above or equal to Hmin,then, terminate, and the solution has been ob-tained. Else, if the pressure at some node/nodesis below Hmin, then, identify elevation of the nodeat which maximum pressure de�cit occurs, and setthis elevation to the last updated pressure de�cientnode. Perform hydraulic analysis, and the resultingsolution are �nal.

The procedure is further illustrated through the ow chart shown in Figure 1.

Figure 1. Flowchart for emitter based approach forpressure driven analysis (EPDA).

Figure 2. Single source one loop network.

5. Case studies

5.1. Example 1. Single loop networkFigure 2 shows a simple, single-source, one-loop net-work. The network consists of a reservoir, four demandnodes and �ve links. The elevation of the sourcereservoir is 20 m and all demand nodes are at zeroelevation. The diameter of each link is shown inFigure 2. Each link is 1000 m long, and the Hazen-Williams coe�cient is 100 for all the links. Theminimum pressure head needed at each demand nodeis 15 m. The demands for nodes 2 to 5 are 20, 20,25 and 35 L/s, respectively, under normal operatingconditions. Under normal conditions, the demanddriven analysis shows the pressure head at all nodesequal to, or above, 15 m. Pressure-de�cient conditionscan be created in this network by isolating any oneof links 2, 3, 4, and 5. Table 1 shows the resultsobtained by the demand-driven method (by EPANET)for normal operations and pressure-de�cient conditionswith isolation of links 2, 3, 4 and 5, one at a time. Itcan be seen from Table 1 that the isolation of link 2creates the de�ciency in pressure at nodes 3, 4 and 5.According to the generic relations, nodes 3, 4 and 5should be set to zero demand. Performing hydraulicanalysis again with a new set of demands shows thepressure head above the minimum pressure of 15 mat all nodes. Since it shows the pressure at all nodesabove 15 m, the identi�ed de�cit nodes could supplya portion of the demand. Now, the actual demand fornodes 3, 4 and 5 can be calculated using the genericrelation between the head and ow, and its valuesare found to be equal to the required demand. Theabove mentioned steps are presented in Table 2. Itis clear from the results of the fourth run (Table 2)that no improvement of results are feasible, since newdemands are the same as those of the required demand.It is understood that the generic relation cannot beapplied as it is in the given format. Further, it is clearthat some portion of demand can be supplied from thede�cit nodes due to the availability of some pressurein excess of that required in the node. Assessing theavailability of such residual pressure at various de�cientnodes poses a major challenge to the pressure drivenmodel.


Table 1. Out ows and pressure head for one-loop network under single link failure.

Method Status Out ows (L/s) and pressure head (m)

Node 2 Node 3 Node 4 Node 5 Totalout ow

Demand driven

No link failure 20 (17.43) 20 (16.46) 25 (15.64) 35 (15.00) 100

Link 2 isolated 20 (17.43) 20 (0.84*) 25 (10.52*) 35 (2.13*) 100

Link 3 isolated 20 (17.43) 20 (14.17*) 25 (2.36*) 35 (4.31*) 100

Link 4 isolated 20 (17.43) 20 (17.18) 25 (13.37*) 35 (9.74*) 100

Link 5 isolated 20 (17.43) 20 (15.80) 25 (16.63) 35 (12.16*) 100

Table 2. Simulated results for link 2 isolation of single loop network.

Method Simulation status Out ows (L/s) and pressure head (m)

Node 2 Node 3 Node 4 Node 5 EPANET runcounter

Pressure driven

No link failure 20 (17.43) 20 (16.46) 25 (15.64) 35 (15.00) 1

Link 2 isolated 20 (17.43) 20 (0.84*) 25 (10.52*) 35 (2.13*) 2Set demand at nodes 3,

4 and 5 as zero20 (19.87) 0 (19.87) 0 (19.87) 0 (19.87) 3

Set demand at nodes3, 4 and 5 as 20,

25 and 35, respectively20 (17.43) 20 (0.84*) 25 (10.52*) 35 (2.13*) 4

Gupta and Bhave [29] illustrated application ofthe head- ow relation for pressure dependent analysisin which, initially, nodal head (Havl) is assumed forde�cient nodes and, subsequently, nodal-head correc-tion is applied at each state of iteration. Repeatedapplication of the generic relation with nodal correctionis needed until qavlj values obtained in the Nth and(N�1)th iterations are identical. Gupta and Bhave [29]used the Hardy-Cross Head Correction method forsolving NHFR, along with continuity equations repre-sented in terms of unknown heads. The NFA results areobtained in a single run. The SPDA, PDNA and EPDAare iterative and require assumptions in each run of theEPANET. The methodology of Gupta and Bhave [29] isfree from any assumption. In the present work, insteadof nodal correction, qreq for de�cient nodes has beencorrected.

Table 3 presents the solution based on pressuredependent analysis for isolation of links 2 to 5. Theiterations within EPANET are referred to herein asinner iterations. The default values adopted for thisstudy, for the maximum amount of trials and accuracyin EPANET, are 40 and 0.001, respectively. It can beseen from Table 3 that the number of outer iterationsare more in cases of head- ow based approaches.Further, it is to be noted from the results that thenumber of hydraulic simulations for PDNA and EPDAis minimum. The main advantage of the emitterbased approach is that no addition and deletion ofthe reservoir is required. Hence, no change in the

topology of the network is resulted. For the head- owbased approach, a reasonable assumption of the initialavailable pressure head is essential, and it requires ahigher number of hydraulic analyses to converge.

It is clear from the results that PDNA and EPDAcould maximize the out ow under pressure de�cientconditions for this example. In the case of the head- ow based approach, the relation proposed by Wagneret al. [24] could maximize the out ow within thetermination criteria speci�ed. The head- ow relationof Germanopoulos [30], with nodal constant cj as 2,took a lower number of simulation runs, but fails inmaximizing out ow within the speci�ed terminationcriteria. From Table 3, it is evident that the head- ow relation of Tucciarelli et al. [36] uses a highernumber of hydraulic simulations to satisfy the speci�edtermination criteria.

5.2. Example 2. Two-loop networkThis example is a single-source, two-loop networkpresented by Ang and Jowitt [22] for pressure drivenanalysis. The network consists of a reservoir, six de-mand nodes and eight links, as shown in Figure 3. Thenodal elevations and link diameters are presented withthe layout. The length and Hazen-Williams coe�cientfor each link is 1000 m and 130, respectively. Thenodal demand for each node is 25 L/s. Under normalconditions, the demand driven analysis shows thatnodal pressure heads are greater than the minimumrequired pressure head of zero, i.e. the out ow at the


Table 3. Simulated results for isolation of links for single loop network.

Methods Status Out ows (L/s) and pressure head (m) No. ofEPANET runs

Node 2 Node 3 Node 4 Node 5 Totalout ow

HFPDA-1

Link 2 is isolated

20 (18.83) 2.25 (15.03) 25 (16.40) 18.25 (15.05) 65.50 40HFPDA-2 20 (18.82) 0.32 (15.00) 25 (16.37) 20.36 (15.00) 65.68 230HFPDA-3 20 (18.82) 1.50 (14.99) 25 (16.37) 19.19(15.00) 65.69 2839

PDNA 20 (18.82) 0 (15.00) 25 (16.37) 20.68 (15.00) 65.68 3EPDA 20 (18.82) 0 (15.00) 25 (16.37) 20.68 (15.00) 65.68 4

HFPDA-1

Link 3 is isolated

20 (18.74) 20 (17.47) 2.75 (15.03) 25.30 (15.06) 68.05 95HFPDA-2 20 (18.73) 20 (17.45) 0.44 (15.00) 27.85 (15.00) 68.28 326HFPDA-3 20 (18.73) 20 (17.45) 1.75(14.99) 26.54(15.00) 68.29 3572

PDNA 20 (18.73) 20 (17.45) 0.00 (15.00) 28.29 (15.00) 68.29 3EPDA 20 (18.73) 20(17.45) 0.00(15.00) 28.29(15.00) 68.29 4

HFPDA-1

Link 4 is isolated

20 (17.93) 20 (16.85) 25 (17.13) 23.98 (15.05) 88.98 27HFPDA-2 20 (17.92) 20 (16.83) 25 (17.12) 24.19 (15.00) 89.19 53HFPDA-3 20 (17.92) 20 (16.83) 25 (17.12) 24.21 (15.00) 89.21 1259

PDNA 20 (17.92) 20 (16.83) 25 (17.12) 24.19 (15.00) 89.19 4EPDA 20 (17.92) 20 (16.83) 25 (17.12) 24.19 (15.00) 89.19 3

HFPDA-1

Link 5 is isolated

20 (18.20) 20 (17.95) 25 (16.05) 17.57 (15.03) 82.57 40HFPDA-2 20 (18.19) 20 (17.94) 25 (16.03) 17.71 (15.00) 82.71 70HFPDA-3 20 (18.19) 20 (17.94) 25 (16.03) 17.74 (14.99) 82.74 1452

PDNA 20 (18.19) 20 (17.94) 25 (16.03) 17.71 (15.00) 82.71 4EPDA 20 (18.19) 20 (17.94) 25 (16.03) 17.71 (15.00) 82.71 3

Figure 3. Layout of single-source two-loop network.

respective nodal elevation. The isolation of links 2 to 7makes the system as the pressure de�cient conditions.

It can be seen from Tables 4(a) to 4(f) that PDNAand EPDA provided the same results for isolation ofall the links, except for links 2 and 3. The PDNAresult for isolation of links 2 and 3 shows a negativepressure head with no out ow. But EPDA for the samecases do not show any negative pressure at any nodes,even for nodes with no out ow. This distinct resultcan be viewed from a di�erent perspective. If negative

pressure at no supply node is accepted hydraulically,then, the results of PDNA for isolation of links 2 and3 should be considered a valid solution. Practically,all withdrawal from that node should cease. This ispossible only if this node is a supply node for a minordistribution network, or any branches beginning fromthat node. If this is the case, then it is possible toisolate it from the main distribution using a controlvalve. Conventionally, the demand occurring alongthe link is lumped at the nodes for convenience ofdesign. In such a case, the node takes in the air andthe continuity of ow to the down gradient nodes iswrecked.

From an engineer's point of view, the negativepressure in the node will not be observed on site, asthe pipes are usually not air-tight. Furthermore, evenif the pipes are air-tight, any consumer opening a tapwill render the pipes not air-tight. The solution ofEPDA for the isolation of any link shows the positivepressure at all demand nodes. Speci�cally, for isolationof links 2 and 3, the total out ow is lesser than theout ow obtained using the PDNA approach. It canbe observed from Tables 4(a) to 4(f) that for link 2isolation, the EPDA solution shows lesser out ow atnode 5; its value is 9.10 L/s and the corresponding


Table 4a. Simulated results for two-loop network with link 2 isolation.

Method Status Out ow (L/s) and residual pressure head (m) atTotal

out ow(L/s)

Total no. ofEPANET

runsNode 2 Node 3 Node 4 Node 5 Node 6 Node 7

HFPDA-1 2 25.00 0.00 25.00 19.32 25.00 25.00 119.32 Not converged5.79 -2.75 2.03 -0.75 0.06 0.11

HFPDA-2 25.00 0.00 25.00 16.65 25.00 25.00 116.65 2995.97 -2.00 2.50 0.00 0.68 0.53

HFPDA-3 25.00 0.00 25.00 16.75 25.00 25.00 116.75 87895.90 -2.03 2.52 -0.03 0.65 0.51

PDNA 25.00 0.00 25.00 16.65 25.00 25.00 116.65 55.97 -2.00 2.50 0.00 0.68 0.53

EPDA 25.00 0.00 25.00 9.10 25.00 25.00 109.10 56.44 0.00 3.77 2.00 2.33 2.25

Table 4b. Simulated results for two-loop network with link 3 isolation.


out ow(L/s)

Total no. ofEPANET


HFPDA-1 3 25.00 25.00 0.00 11.89 20.78 20.78 103.45 Not converged6.77 2.67 -0.96 -0.22 -0.14 -0.12

HFPDA-2 25.00 25.00 0.73 10.25 19.40 22.53 102.90 Not converged6.80 2.76 -0.84 -0.05 -0.02 -0.02

HFPDA-3 25.00 25.00 0.00 10.49 18.56 23.74 102.79 181936.81 2.77 -0.77 -0.01 -0.01 -0.01

PDNA 25.00 25.00 0.00 10.44 19.59 22.72 102.75 56.81 2.78 -0.76 0.00 0.00 0.00

EPDA 25.00 25.00 0.00 25.00 0.12 25.00 100.12 46.96 3.18 0.62 0.83 0.00 2.39

Table 4c. Simulated results for two-loop network with link 4 isolation.


out ow(L/s)

Total no. ofEPANET


HFPDA-1 4 25.00 25.00 25.00 10.36 25.00 25.00 135.36 814.69 4.19 1.89 0.01 0.39 0.30

HFPDA-2 25.00 25.00 25.00 10.39 25.00 25.00 135.39 5434.68 4.19 1.89 0.00 0.38 0.29

HFPDA-3 25.00 25.00 25.00 10.39 25.00 25.00 135.57 114584.67 4.18 1.86 -0.05 0.34 0.25

PDNA 25.00 25.00 25.00 10.38 25.00 25.00 135.38 54.68 4.19 1.89 0.00 0.38 0.29

EPDA 25.00 25.00 25.00 10.38 25.00 25.00 135.38 34.68 4.19 1.89 0.00 0.38 0.29


Table 4d. Simulated results for two-loop network with link 5 isolation.


out ow(L/s)

Total no. ofEPANET


HFPDA-1 5 25.00 25.00 25.00 21.65 25.00 25.00 146.65 133.84 0.92 3.62 0.01 1.22 0.94

HFPDA-2 25.00 25.00 25.00 21.70 25.00 25.00 146.70 2623.83 0.91 3.61 0.00 1.21 0.93

HFPDA-3 25.00 25.00 25.00 21.81 25.00 25.00 146.81 74413.82 0.89 3.60 0.03 1.19 0.91

PDNA 25.00 25.00 25.00 21.7 25.00 25.00 146.70 53.83 0.91 3.61 0.00 1.21 0.93

EPDA 25.00 25.00 25.00 21.70 25.00 25.00 146.70 33.83 0.91 3.61 0.00 1.21 0.93

Table 4e. Simulated results for two-loop network with link 6 isolation.


out ow(L/s)

Total no. ofEPANET


HFPDA-1 6 25.00 25.00 25.00 25.00 7.69 25.00 132.69 974.88 2.84 4.84 3.28 0.04 0.04

HFPDA-2 25.00 25.00 25.00 25.00 7.75 25.00 132.75 3684.87 2.83 4.83 3.27 0.00 0.41

HFPDA-3 25.00 25.00 25.00 25.00 7.82 25.00 132.82 77984.87 2.82 4.82 3.26 -0.04 0.37

PDNA 25.00 25.00 25.00 25.00 7.75 25.00 132.75 54.87 2.83 4.83 3.27 0.00 0.41

EPDA 25.00 25.00 25.00 25.00 7.75 25.00 132.75 34.87 2.83 4.83 3.27 0.00 0.41

Table 4f. Simulated results for two-loop network with link 7 isolation.


out ow(L/s)

Total no. ofEPANET


HFPDA-1 7 25.00 25.00 25.00 25.00 25.00 9.63 134.59 794.74 3.10 4.11 4.09 0.62 0.02

HFPDA-2 25.00 25.00 25.00 25.00 25.00 9.63 134.63 2994.74 3.10 4.10 4.09 0.61 0.00

HFPDA-3 25.00 25.00 25.00 25.00 25.00 9.76 134.76 40534.73 3.09 4.09 4.07 0.54 -0.08

PDNA 25.00 25.00 25.00 25.00 25.00 9.63 134.63 44.74 3.10 4.10 4.09 0.61 0.00

EPDA 25.00 25.00 25.00 25.00 25.00 9.63 134.63 37.47 3.10 4.10 4.09 0.61 0.00


out ow by PDNA is 16.65 L/s. This shows that thereduction in out ow at that particular node improvesthe pressure at several nodes. This clearly shows thatout ow at a node is strongly interdependent on otherdemand nodes. The number of hydraulic simulationsrequired for both PDNA and EPDA is almost the same,but it is considerably lower than the HFPDA.

The merit of EPDA and PDNA is that theaccuracy based termination criteria are not required.PDNA requires repeated runs of the EPANET solverwith arti�cial reservoirs added or deleted, as required,for either disallowing reverse ow from the arti�cialreservoirs back into the network or disallowing owfrom the network into the arti�cial reservoirs to exceednominal demand [52]. Babu and Mohan [43] presenteda modi�ed form of PDNA to get the PDNA solutionin a single run using the EPANET toolkit, wherethey have used a ow control valve in addition tothe arti�cial reservoir. Sivakumar and Prasad [51]presented another modi�cation to M-PDNA, showinghow M-PDNA can be used to simulate both pressure-su�cient and pressure-de�cient conditions in a sin-gle hydraulic simulation without using the EPANETtoolkit. Though the proposed approach needs repeti-tive use of EPANET, it does not require any topologicalmodi�cation of the network.

It can be seen from Tables 4(a) to 4(f) that theHFPDA could not converge to the positive pressuresolution domain for certain cases. This is a mainproblem in head- ow based approaches. The owcorrection carried out in the process of computationbecomes ine�ective after reaching a certain value. Insuch a circumstance, any minor change in the owcorrection value may lead to a pressure drop to thenodes, which have already reached a threshold value.Hence, improvisation of the result is feasible only bychanging the initially assumed pressure head. This fur-ther invites not only iterations, but also the necessityof trials in selection of the initial value. Tanyimbohand Templeman [44] pointed out that the discontinuityproperties of the pressure-dependent demand functionsand their derivatives can cause convergence di�cultiesin the computational solution of the system of equa-tions.

Figure 4 shows the trajectory of convergence forout ow and the hydraulic gradient at node 5, in thecase of HFPDA-2 for isolation of link 2. Figure 4shows the importance of a higher degree of accuracyas a termination criteria (minimizing of error). It isclear from Figure 4 that the value of out ow is notdecreasing uniformly from beginning to end of theiteration. At the early stages of iteration, there is adrastic change in the out ow and HGL values. Fromthe experiments, similar observations were made atother nodal out ows and the pressure for isolation oflink 2, and also pressure de�ciency resulted for isolation

Figure 4. Trajectory of convergence for out ow andhydraulic gradient.

of other links. The required number of hydraulicsimulations for HFPDA 3 is found to be more thanHFPDA 1 and HFPDA 2 for all the cases consideredin the study.

6. Discussion

The following general observations have been madefrom the results of PDA described in the present study:

1. Total out ow from the system is maximum and nonode experiences negative pressure, even when out- ow, as per Pressure Dependent Analysis (PDA), isfound to be zero.

2. Total out ow from the system is maximum, anda node or few nodes experience negative pressurewhile estimated out ow from those nodes are zero.

3. Total out ow from the system is not maximum, andno demand node with zero out ow and pressure atall nodes are above or equal to minimum, even forde�cient nodes.

If the solution obtained through PDA belongs inthe �rst category, then, the network will practically befree from any air entrainment, even when the consumertap is kept open. The second category depicts thatthe total out ow from the system will be maximum,but a negative pressure node with no supply maydraw air through the consumer tap. Consequently,the consumer at the down gradient and at nearbynodes experiences air entrained out ow and sometimesinterrupted out ow. As far as these two categoriesare concerned, the out ow at de�cient nodes is deter-mined by ful�lling the demand at non-pressure de�cientnodes, corresponding to their designated demand. Inthe third category, the PDA predicts the partial out owat all de�cient nodes and also at some non-pressurede�cient nodes. Overall, no pressure de�ciency occursat the cost of compromising the out ow at non-pressurede�cient nodes. Hence, maximization of total out owcould not be achieved. Ang and Jowitt [22] describedthat the behavior of a water distribution system underpressure-de�cient conditions is highly complex andnon-instinctive. It is essential to understand the


exact behavior of the network under abnormal workingconditions. Real experimental research in the �eldcould provide an answer to evaluate the exact behaviorof the system.

7. Conclusion

Simulation of networks under low pressure scenariosshould be based on PDA in order to consider the e�ectsdue to high demand. These include �re�ghting, burstpipes, pump failure, high demand over the designedpeak demand and failure in supply from one (or more)source(s) in cases of multi-source systems. In thepresent study, some head- ow functions, includingthe emitter feature available in EPANET, and alsothe use of arti�cial reservoirs as proposed by Angand Jowitt [22] are investigated as the outer modelusing the EPANET toolkit in terms of its convergence.Further, the results of the EPDA method have beencompared and analyzed with solutions obtained, basedon the head- ow based relation, for simulating a waterdistribution network under pressure de�cient condi-tions. HFPDA takes a higher number of hydraulicsimulations to converge within the speci�ed degree ofaccuracy. A simple approach is presented for analysisof a de�cient network in which additional nodes areadded at each demand node, and the required demand,according to the various pressure levels, is taken as thebase demand for simulation. The successive solutionseeking procedure, based on repeated application ofthe hydraulic solver, is used to evaluate the out ow.Even so, the Wagner et al. [24] equation is increasinglyused for evaluation of pressure dependent out ow;quanti�cation of partial out ow under pressure de�-cient conditions will be e�ective only if the demand atvarious levels is known.

Acknowledgment

The author wishes to express his gratitude to SAS-TRA University for providing the facilities for thepresent research work. The author is also gratefulto the anonymous reviewers for their critical reviewsand constructive suggestions to further improve themanuscript.

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Biography

Conety Ravi Suribabu received his BS degreein Civil Engineering from Bharathidasan University,Tiruchirapalli, India, in 1991, his MS degree in Hy-drology and Water Resources Engineering from AnnaUniversity, Chennai, India, in 1993, and his PhDdegree on the topic \Optimal Design of Water Distribu-tion Networks" from SASTRA University, Thanjavur,India, in 2006. Currently, he is Professor of CivilEngineering at SASTRA University, India, and hasalso worked with a number of engineering �rms onvarious projects in the �eld of water resources engi-neering.

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